Finite Group Databasebeta

← C2×AGL(1,ℤ/8)×C3⋊D9 #72244708

Subgroups — C2×AGL(1,ℤ/8)×C3⋊D9 #72244708

Order 3456.

8600 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D9C211yesmaximal, characteristic, complemented
2C22×D4×C3⋊D9C211yesmaximal, characteristic, complemented
3C2×C3×C9×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C2×#11721867C211yesmaximal, characteristic, complemented
5C2×#11721833C211yesmaximal, characteristic, complemented
6AGL(1,ℤ/8)×C3⋊D9C2116yesmaximal, direct product factor
7C2×#11721796C212yesmaximal, complemented
8C2×SD16×C3⋊D9C212yesmaximal, complemented
9C2×#11721790C212yesmaximal, complemented
10C2×D8×C3⋊D9C212yesmaximal, complemented
11C2×#11721783C211yesmaximal, characteristic, complemented
12C2×M16×C3⋊D9C211yesmaximal, characteristic, complemented
13C2×C3⋊D3×AGL(1,ℤ/8)—31nomaximal
14C2×D9×AGL(1,ℤ/8)—33nomaximal
15C24×C3⋊D9—21no—
16C2×C3×C9×#41C2211yescharacteristic, complemented
17C22×C3×D4×C9C2211yescharacteristic, complemented
18C22×#6233—21no—
19#41×C3⋊D9—24no—
20#41×C3⋊D9C2218yescomplemented
21C2×#88746C2211yescharacteristic, complemented
22C2×Q8×C3⋊D9C2211yescharacteristic, complemented
23C2×#88742—21no—
24C2×#88742C2211yescharacteristic, complemented
25C2×D4×C3⋊D9—21no—
26C2×D4×C3⋊D9—21no—
27C2×D4×C3⋊D9—24no—
28C2×D4×C3⋊D9—21no—
29C2×D4×C3⋊D9C2212yes—
30C2×D4×C3⋊D9C2212yescomplemented
31C2×D4×C3⋊D9C2218yescomplemented
32C2×D4×C3⋊D9C2211yescharacteristic, complemented
33C2×#88736—21no—
34C2×#88736C2211yescharacteristic, complemented
35C22×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
36C22×C4×C3⋊D9—21no—
37C22×C4×C3⋊D9C2211yescharacteristic
38C3×C9×AGL(1,ℤ/8)C2218yescomplemented
39C2×C3×C9×SD16C2212yescomplemented
40C2×C3×C9×D8C2212yescomplemented
41C2×C3×C9×M16C2211yescharacteristic, complemented
42#11721867C2218yescomplemented
43C2×#88548C2212yescomplemented
44#11721833C2218yescomplemented
45C2×#88544C2212yescomplemented
46C2×#88544C2212yescomplemented
47C2×#88543C2212yescomplemented
48C2×#88532C2211yescharacteristic, complemented
49#11721796C22116yescomplemented
50SD16×C3⋊D9C22116yescomplemented
51#11721790C22116yescomplemented
52D8×C3⋊D9C22116yescomplemented
53#11721783C2218yescomplemented
54M16×C3⋊D9C2218yescomplemented
55C2×#88525C2212yescomplemented
56C2×#88524C2212yescomplemented
57C2×#88523C2212yescomplemented
58C2×C8×C3⋊D9C2212yescomplemented
59C2×#41×C3⋊D3—31no—
60C22×D4×C3⋊D3—31no—
61C2×C32×AGL(1,ℤ/8)D311yescharacteristic
62C2×#64158—31no—
63C2×#64141—31no—
64C3⋊D3×AGL(1,ℤ/8)—316no—
65C2×#64123—32no—
66C2×SD16×C3⋊D3—32no—
67C2×#64120—32no—
68C2×D8×C3⋊D3—32no—
69C2×#64117—31no—
70C2×M16×C3⋊D3—31no—
71C2×#41×D9—33no—
72C22×D4×D9—33no—
73C2×C9×AGL(1,ℤ/8)D313yescomplemented
74C2×#63512—33no—
75C2×#63495—33no—
76D9×AGL(1,ℤ/8)—348no—
77C2×#63476—36no—
78C2×SD16×D9—36no—
79C2×#63473—36no—
80C2×D8×D9—36no—
81C2×#63470—33no—
82C2×M16×D9—33no—
83C24×C3×C9—21no—
84C23×C3⋊D9—21no—
85C23×C3⋊D9—22no—
86C23×C3⋊D9—22no—
87C23×C3⋊D9—28no—
88C23×C3⋊D9—21no—
89C23×C3⋊D9—48no—
90C23×C3⋊D9D411yescharacteristic
91C3×C9×#41—22no—
92C3×C9×#41C2314yescomplemented
93C2×C3×Q8×C9C2311yescharacteristic, complemented
94C2×C3×D4×C9—21no—
95C2×C3×D4×C9—21no—
96C2×C3×D4×C9—22no—
97C2×C3×D4×C9C2312yes—
98C2×C3×D4×C9C2314yescomplemented
99C2×C3×D4×C9C2311yescharacteristic, complemented
100C22×C3×C4×C9—21no—
101C22×C3×C4×C9C2311yescharacteristic
102C2×#6233—21no—
103C2×#6233—21no—
104C2×#6233—21no—
105C2×#6233—22no—
106C2×#6233—22no—
107C2×#6233—28no—
108C22×C3⋊Dic9—21no—
109C22×C3⋊Dic9D411yescharacteristic
110#88746—22no—
111#88746C2314yescomplemented
112Q8×C3⋊D9—22no—
113Q8×C3⋊D9C2314yescomplemented
114#88742—28no—
115#88742—22no—
116#88742C2314yescomplemented
117D4×C3⋊D9—28no—
118D4×C3⋊D9—24no—
119D4×C3⋊D9—28no—
120D4×C3⋊D9—28no—
121D4×C3⋊D9—24no—
122D4×C3⋊D9—22no—
123D4×C3⋊D9C2318yes—
124D4×C3⋊D9C2318yescomplemented
125D4×C3⋊D9C2314yescomplemented
126#88736—22no—
127#88736—28no—
128#88736C2314yescomplemented
129C2×C4⋊(C3⋊D9)—21no—
130C2×C4⋊(C3⋊D9)—22no—
131C2×C4⋊(C3⋊D9)—21no—
132C2×C4⋊(C3⋊D9)C2312yes—
133C2×C4⋊(C3⋊D9)C2314yescomplemented
134C2×C4⋊(C3⋊D9)C2311yescharacteristic, complemented
135C2×C4×C3⋊D9—21no—
136C2×C4×C3⋊D9—21no—
137C2×C4×C3⋊D9—21no—
138C2×C4×C3⋊D9—28no—
139C2×C4×C3⋊D9D411yescharacteristic
140C2×C4×C3⋊D9D411yescharacteristic
141C2×C4×C3⋊D9D414yes—
142C2×C4×C3⋊D9C2311yescharacteristic
143C2×C4×C3⋊D9C2311yescharacteristic
144C2×C4×C3⋊D9C2314yes—
145C2×#6226—21no—
146C2×#6226C2311yescharacteristic, complemented
147C3×C9×SD16C2318yescomplemented
148C3×C9×D8C2318yescomplemented
149C3×C9×M16C2314yescomplemented
150C2×C3×C8×C9C2312yescomplemented
151#88548C2318yescomplemented
152#88544C2318yescomplemented
153#88544C2318yescomplemented
154#88543C2318yescomplemented
155#88532C2314yescomplemented
156C2×C3⋊(C9⋊C8)C2312yescomplemented
157#88525C2318yescomplemented
158#88524C2318yescomplemented
159#88523C2318yescomplemented
160C8×C3⋊D9C2318yescomplemented
161C2×D3×AGL(1,ℤ/8)—93no—
162C2×D3×AGL(1,ℤ/8)—91no—
163C24×C3⋊D3—61no—
164C2×C32×#41C2×D311yescharacteristic
165C22×C32×D4C2×D311yescharacteristic
166C22×#638—61no—
167#41×C3⋊D3—38no—
168#41×C3⋊D3—64no—
169C2×#3832—31no—
170C2×Q8×C3⋊D3—31no—
171C2×#3830—31no—
172C2×#3830—61no—
173C2×D4×C3⋊D3—31no—
174C2×D4×C3⋊D3—32no—
175C2×D4×C3⋊D3—32no—
176C2×D4×C3⋊D3—38no—
177C2×D4×C3⋊D3—61no—
178C2×D4×C3⋊D3—61no—
179C2×D4×C3⋊D3—61no—
180C2×D4×C3⋊D3—64no—
181C2×#3828—31no—
182C2×#3828—61no—
183C22×C4⋊(C3⋊D3)—31no—
184C22×C4×C3⋊D3—31no—
185C22×C4×C3⋊D3—61no—
186C24×D9—63no—
187C32×AGL(1,ℤ/8)C2×D318yes—
188C2×C32×SD16C2×D312yes—
189C2×C32×D8C2×D312yes—
190C2×C32×M16C2×D311yescharacteristic
191#64158—38no—
192C2×#3755—32no—
193C2×#3754—32no—
194#64141—38no—
195C2×#3753—32no—
196C2×#3753—32no—
197C2×#3748—31no—
198#64123—316no—
199SD16×C3⋊D3—316no—
200#64120—316no—
201D8×C3⋊D3—316no—
202#64117—38no—
203M16×C3⋊D3—38no—
204C2×#3745—32no—
205C2×#3744—32no—
206C2×#3743—32no—
207C2×C8×C3⋊D3—32no—
208C2×C9×#41C2×D313yescomplemented
209C22×D4×C9C2×D313yescomplemented
210C22×#611—63no—
211#41×D9—324no—
212#41×D9—612no—
213C2×#3701—33no—
214C2×Q8×D9—33no—
215C2×#3699—33no—
216C2×#3699—63no—
217C2×D4×D9—36no—
218C2×D4×D9—36no—
219C2×D4×D9—324no—
220C2×D4×D9—33no—
221C2×D4×D9—63no—
222C2×D4×D9—63no—
223C2×D4×D9—612no—
224C2×D4×D9—63no—
225C2×#3697—33no—
226C2×#3697—63no—
227C22×D36—33no—
228C22×C4×D9—33no—
229C22×C4×D9—63no—
230C9×AGL(1,ℤ/8)C2×D3124yescomplemented
231C2×C9×SD16C2×D316yescomplemented
232C2×C9×D8C2×D316yescomplemented
233C2×C9×M16C2×D313yescomplemented
234#63512—324no—
235C2×#3675—36no—
236#63495—324no—
237C2×#3673—36no—
238C2×#3673—36no—
239C2×#3672—36no—
240C2×#3667—33no—
241#63476—348no—
242SD16×D9—348no—
243#63473—348no—
244D8×D9—348no—
245#63470—324no—
246M16×D9—324no—
247C2×D72—36no—
248C2×#3664—36no—
249C2×#3663—36no—
250C2×C8×D9—36no—
251C23×C3×C9—22no—
252C23×C3×C9—24no—
253C23×C3×C9—21no—
254C23×C3×C9—44no—
255C23×C3×C9C2×D411yescharacteristic
256C22×C3⋊D9—24no—
257C22×C3⋊D9—22no—
258C22×C3⋊D9—24no—
259C22×C3⋊D9—21no—
260C22×C3⋊D9—28no—
261C22×C3⋊D9—28no—
262C22×C3⋊D9—24no—
263C22×C3⋊D9—48no—
264C22×C3⋊D9—432no—
265C22×C3⋊D9—44no—
266C22×C3⋊D9—44no—
267C22×C3⋊D9—48no—
268C22×C3⋊D9C2×D411yescharacteristic
269C22×C3⋊D9C2×D414yes—
270C22×C3⋊D9C2×D411yescharacteristic
271C3×Q8×C9—21no—
272C3×Q8×C9C2412yescomplemented
273C3×D4×C9—24no—
274C3×D4×C9—22no—
275C3×D4×C9—24no—
276C3×D4×C9—21no—
277C3×D4×C9C2414yes—
278C3×D4×C9C2412yescomplemented
279C2×C3×C4×C9—21no—
280C2×C3×C4×C9—24no—
281C2×C3×C4×C9C2×D411yescharacteristic
282C2×C3×C4×C9C2×D412yes—
283C2×C3×C4×C9C2411yescharacteristic
284C2×C3×C4×C9C2412yes—
285#6233—24no—
286#6233—24no—
287#6233—24no—
288#6233—28no—
289#6233—28no—
290C2×C3⋊Dic9—21no—
291C2×C3⋊Dic9—24no—
292C2×C3⋊Dic9C2×D411yescharacteristic
293C2×C3⋊Dic9C2×D411yescharacteristic
294C2×C3⋊Dic9C2×D414yes—
295C4⋊(C3⋊D9)—24no—
296C4⋊(C3⋊D9)—22no—
297C4⋊(C3⋊D9)—24no—
298C4⋊(C3⋊D9)—21no—
299C4⋊(C3⋊D9)C2414yes—
300C4⋊(C3⋊D9)C2412yescomplemented
301C4×C3⋊D9—24no—
302C4×C3⋊D9—24no—
303C4×C3⋊D9—24no—
304C4×C3⋊D9C2×D414yes—
305C4×C3⋊D9C2×D414yes—
306C4×C3⋊D9C2×D412yes—
307C4×C3⋊D9C2×D412yes—
308C4×C3⋊D9C2412yes—
309C4×C3⋊D9C2412yes—
310#6226—21no—
311#6226—24no—
312#6226C2412yescomplemented
313C3×C8×C9C2414yescomplemented
314C3⋊(C9⋊C8)C2414yescomplemented
315C2×D3×#41—93no—
316C2×D3×#41—91no—
317C22×D3×D4—93no—
318C22×D3×D4—91no—
319C2×C3×AGL(1,ℤ/8)D913yescomplemented
320C2×C3×AGL(1,ℤ/8)C3⋊D311yescharacteristic
321C2×#949—93no—
322C2×#949—91no—
323C2×#932—93no—
324C2×#932—91no—
325D3×AGL(1,ℤ/8)—948no—
326D3×AGL(1,ℤ/8)—916no—
327C2×#914—96no—
328C2×#914—92no—
329C2×D3×SD16—96no—
330C2×D3×SD16—92no—
331C2×#911—96no—
332C2×#911—92no—
333C2×D3×D8—96no—
334C2×D3×D8—92no—
335C2×#908—93no—
336C2×#908—91no—
337C2×D3×M16—93no—
338C2×D3×M16—91no—
339C24×C32—21no—
340C23×C3⋊D3—31no—
341C23×C3⋊D3—61no—
342C23×C3⋊D3—62no—
343C23×C3⋊D3—62no—
344C23×C3⋊D3—68no—
345C23×C3⋊D3—61no—
346C23×C3⋊D3—128no—
347C32×#41—22no—
348C32×#41C22×D314yes—
349C2×C32×Q8C22×D311yescharacteristic
350C2×C32×D4—21no—
351C2×C32×D4—21no—
352C2×C32×D4—22no—
353C2×C32×D4C22×D312yes—
354C2×C32×D4C22×D314yes—
355C2×C32×D4C22×D311yescharacteristic
356C22×C32×C4—21no—
357C22×C32×C4C22×D311yescharacteristic
358C2×#638—61no—
359C2×#638—62no—
360C2×#638—62no—
361C2×#638—68no—
362C2×#638—61no—
363C2×#638—61no—
364C22×C3⋊Dic3—31no—
365C22×C3⋊Dic3—61no—
366#3832—34no—
367#3832—62no—
368Q8×C3⋊D3—34no—
369Q8×C3⋊D3—62no—
370#3830—34no—
371#3830—62no—
372#3830—68no—
373D4×C3⋊D3—38no—
374D4×C3⋊D3—38no—
375D4×C3⋊D3—34no—
376D4×C3⋊D3—68no—
377D4×C3⋊D3—68no—
378D4×C3⋊D3—64no—
379D4×C3⋊D3—64no—
380D4×C3⋊D3—62no—
381D4×C3⋊D3—68no—
382#3828—34no—
383#3828—68no—
384#3828—62no—
385C2×C4⋊(C3⋊D3)—32no—
386C2×C4⋊(C3⋊D3)—34no—
387C2×C4⋊(C3⋊D3)—31no—
388C2×C4⋊(C3⋊D3)—61no—
389C2×C4⋊(C3⋊D3)—61no—
390C2×C4⋊(C3⋊D3)—62no—
391C2×C4×C3⋊D3—31no—
392C2×C4×C3⋊D3—31no—
393C2×C4×C3⋊D3—34no—
394C2×C4×C3⋊D3—31no—
395C2×C4×C3⋊D3—31no—
396C2×C4×C3⋊D3—34no—
397C2×C4×C3⋊D3—68no—
398C2×C4×C3⋊D3—61no—
399C2×C4×C3⋊D3—61no—
400C2×C4×C3⋊D3—61no—
401C2×#634—31no—
402C2×#634—61no—
403C24×C9—23no—
404C23×D9—33no—
405C23×D9—66no—
406C23×D9—66no—
407C23×D9—624no—
408C23×D9—63no—
409C23×D9—63no—
410C23×D9—1224no—
411C32×SD16C22×D318yes—
412C32×D8C22×D318yes—
413C32×M16C22×D314yes—
414C2×C32×C8C22×D312yes—
415#3755—38no—
416#3754—38no—
417#3753—38no—
418#3753—38no—
419#3748—34no—
420C2×C3⋊(C3⋊C8)—32no—
421#3745—38no—
422#3744—38no—
423#3743—38no—
424C8×C3⋊D3—38no—
425C9×#41—26no—
426C9×#41C22×D3112yescomplemented
427C2×Q8×C9C22×D313yescomplemented
428C2×D4×C9—23no—
429C2×D4×C9—23no—
430C2×D4×C9—26no—
431C2×D4×C9C22×D316yes—
432C2×D4×C9C22×D3112yescomplemented
433C2×D4×C9C22×D313yescomplemented
434C22×C4×C9—23no—
435C22×C4×C9C22×D313yes—
436C2×#611—63no—
437C2×#611—66no—
438C2×#611—66no—
439C2×#611—624no—
440C2×#611—63no—
441C2×#611—63no—
442C22×Dic9—33no—
443C22×Dic9—63no—
444#3701—312no—
445#3701—66no—
446Q8×D9—312no—
447Q8×D9—66no—
448#3699—312no—
449#3699—66no—
450#3699—624no—
451D4×D9—324no—
452D4×D9—324no—
453D4×D9—312no—
454D4×D9—624no—
455D4×D9—624no—
456D4×D9—612no—
457D4×D9—612no—
458D4×D9—66no—
459D4×D9—624no—
460#3697—312no—
461#3697—624no—
462#3697—66no—
463C2×D36—33no—
464C2×D36—36no—
465C2×D36—312no—
466C2×D36—63no—
467C2×D36—63no—
468C2×D36—66no—
469C2×C4×D9—33no—
470C2×C4×D9—33no—
471C2×C4×D9—312no—
472C2×C4×D9—33no—
473C2×C4×D9—33no—
474C2×C4×D9—312no—
475C2×C4×D9—624no—
476C2×C4×D9—63no—
477C2×C4×D9—63no—
478C2×C4×D9—63no—
479C2×Dic18—33no—
480C2×Dic18—63no—
481C9×SD16C22×D3124yescomplemented
482C9×D8C22×D3124yescomplemented
483C9×M16C22×D3112yescomplemented
484C2×C8×C9C22×D316yescomplemented
485#3675—324no—
486#3673—324no—
487#3673—324no—
488#3672—324no—
489#3667—312no—
490C2×C9⋊C8—36no—
491D72—324no—
492#3664—324no—
493#3663—324no—
494C8×D9—324no—
495C22×AGL(1,ℤ/8)—271noSylow
496C22×C3×C9—22no—
497C22×C3×C9—22no—
498C22×C3×C9—24no—
499C22×C3×C9—48no—
500C22×C3×C9—44no—
501C22×C3×C9—42no—
502C22×C3×C9C22×D412yes—
503C22×C3×C9C22×D411yescharacteristic
504C2×C3⋊D9—22no—
505C2×C3⋊D9—28no—
506C2×C3⋊D9—22no—
507C2×C3⋊D9—24no—
508C2×C3⋊D9—416no—
509C2×C3⋊D9—48no—
510C2×C3⋊D9—42no—
511C2×C3⋊D9—44no—
512C2×C3⋊D9—48no—
513C2×C3⋊D9—416no—
514C2×C3⋊D9AGL(1,ℤ/8)14yesdirect product factor
515C2×C3⋊D9C22×D412yes—
516C2×C3⋊D9C22×D412yes—
517C3×C4×C9—22no—
518C3×C4×C9C22×D411yescharacteristic
519C3×C4×C9C22×D412yes—
520C3×C4×C9C2511yescharacteristic
521C3⋊Dic9—22no—
522C3⋊Dic9C22×D412yes—
523C3⋊Dic9C22×D412yes—
524C24×D3—183no—
525C24×D3—181no—
526C2×C3×#41C2×D913yescomplemented
527C2×C3×#41C2×C3⋊D311yescharacteristic
528C22×C3×D4C2×D913yescomplemented
529C22×C3×D4C2×C3⋊D311yescharacteristic
530C22×#67—183no—
531C22×#67—181no—
532D3×#41—924no—
533D3×#41—98no—
534D3×#41—1812no—
535D3×#41—184no—
536C2×#239—93no—
537C2×#239—91no—
538C2×D3×Q8—93no—
539C2×D3×Q8—91no—
540C2×#237—93no—
541C2×#237—91no—
542C2×#237—183no—
543C2×#237—181no—
544C2×D3×D4—96no—
545C2×D3×D4—96no—
546C2×D3×D4—924no—
547C2×D3×D4—93no—
548C2×D3×D4—92no—
549C2×D3×D4—92no—
550C2×D3×D4—98no—
551C2×D3×D4—91no—
552C2×D3×D4—183no—
553C2×D3×D4—183no—
554C2×D3×D4—1812no—
555C2×D3×D4—181no—
556C2×D3×D4—181no—
557C2×D3×D4—184no—
558C2×D3×D4—183no—
559C2×D3×D4—181no—
560C2×#235—93no—
561C2×#235—91no—
562C2×#235—183no—
563C2×#235—181no—
564C22×D12—93no—
565C22×D12—91no—
566C22×C4×D3—93no—
567C22×C4×D3—91no—
568C22×C4×D3—183no—
569C22×C4×D3—181no—
570C3×AGL(1,ℤ/8)C2×D9124yescomplemented
571C3×AGL(1,ℤ/8)C2×C3⋊D318yes—
572C2×C3×SD16C2×D916yescomplemented
573C2×C3×SD16C2×C3⋊D312yes—
574C2×C3×D8C2×D916yescomplemented
575C2×C3×D8C2×C3⋊D312yes—
576C2×C3×M16C2×D913yescomplemented
577C2×C3×M16C2×C3⋊D311yescharacteristic
578#949—924no—
579#949—98no—
580C2×#215—96no—
581C2×#215—92no—
582C2×#214—96no—
583C2×#214—92no—
584#932—924no—
585#932—98no—
586C2×#213—96no—
587C2×#213—96no—
588C2×#213—92no—
589C2×#213—92no—
590C2×#208—93no—
591C2×#208—91no—
592#914—948no—
593#914—916no—
594D3×SD16—948no—
595D3×SD16—916no—
596#911—948no—
597#911—916no—
598D3×D8—948no—
599D3×D8—916no—
600#908—924no—
601#908—98no—
602D3×M16—924no—
603D3×M16—98no—
604C2×D24—96no—
605C2×D24—92no—
606C2×#204—96no—
607C2×#204—92no—
608C2×ΓL(1,𝔽25)—96no—
609C2×ΓL(1,𝔽25)—92no—
610C2×D3×C8—96no—
611C2×D3×C8—92no—
612C23×C32—22no—
613C23×C32—24no—
614C23×C32—21no—
615C23×C32—44no—
616C23×C32D3×D411yescharacteristic
617C22×C3⋊D3—31no—
618C22×C3⋊D3—31no—
619C22×C3⋊D3—34no—
620C22×C3⋊D3—64no—
621C22×C3⋊D3—68no—
622C22×C3⋊D3—68no—
623C22×C3⋊D3—64no—
624C22×C3⋊D3—64no—
625C22×C3⋊D3—62no—
626C22×C3⋊D3—61no—
627C22×C3⋊D3—128no—
628C22×C3⋊D3—124no—
629C22×C3⋊D3—1232no—
630C22×C3⋊D3—128no—
631C22×C3⋊D3—124no—
632C32×Q8—21no—
633C32×Q8C23×D312yes—
634C32×D4—24no—
635C32×D4—22no—
636C32×D4—24no—
637C32×D4—21no—
638C32×D4C23×D314yes—
639C32×D4C23×D312yes—
640C2×C32×C4—21no—
641C2×C32×C4—24no—
642C2×C32×C4D3×D411yescharacteristic
643C2×C32×C4D3×D412yes—
644C2×C32×C4C23×D311yescharacteristic
645C2×C32×C4C23×D312yes—
646#638—64no—
647#638—68no—
648#638—68no—
649#638—64no—
650#638—64no—
651C2×C3⋊Dic3—31no—
652C2×C3⋊Dic3—31no—
653C2×C3⋊Dic3—34no—
654C2×C3⋊Dic3—64no—
655C2×C3⋊Dic3—61no—
656C4⋊(C3⋊D3)—34no—
657C4⋊(C3⋊D3)—32no—
658C4⋊(C3⋊D3)—64no—
659C4⋊(C3⋊D3)—62no—
660C4⋊(C3⋊D3)—64no—
661C4⋊(C3⋊D3)—61no—
662C4×C3⋊D3—34no—
663C4×C3⋊D3—34no—
664C4×C3⋊D3—32no—
665C4×C3⋊D3—32no—
666C4×C3⋊D3—32no—
667C4×C3⋊D3—32no—
668C4×C3⋊D3—64no—
669C4×C3⋊D3—64no—
670C4×C3⋊D3—64no—
671#634—32no—
672#634—64no—
673#634—61no—
674C23×C9—23no—
675C23×C9—26no—
676C23×C9—212no—
677C23×C9—412no—
678C23×C9D3×D413yes—
679C22×D9—33no—
680C22×D9—33no—
681C22×D9—312no—
682C22×D9—612no—
683C22×D9—612no—
684C22×D9—624no—
685C22×D9—624no—
686C22×D9—63no—
687C22×D9—612no—
688C22×D9—66no—
689C22×D9—1212no—
690C22×D9—1224no—
691C22×D9—1296no—
692C22×D9—1224no—
693C22×D9—1212no—
694C32×C8C23×D314yes—
695C3⋊(C3⋊C8)—34no—
696Q8×C9—23no—
697Q8×C9C23×D316yescomplemented
698D4×C9—212no—
699D4×C9—26no—
700D4×C9—212no—
701D4×C9—23no—
702D4×C9C23×D3112yes—
703D4×C9C23×D316yescomplemented
704C2×C4×C9—23no—
705C2×C4×C9—212no—
706C2×C4×C9D3×D413yes—
707C2×C4×C9D3×D416yes—
708C2×C4×C9C23×D313yes—
709C2×C4×C9C23×D316yes—
710#611—612no—
711#611—624no—
712#611—624no—
713#611—612no—
714#611—612no—
715C2×Dic9—33no—
716C2×Dic9—33no—
717C2×Dic9—312no—
718C2×Dic9—612no—
719C2×Dic9—63no—
720D36—312no—
721D36—36no—
722D36—612no—
723D36—66no—
724D36—612no—
725D36—63no—
726C4×D9—312no—
727C4×D9—312no—
728C4×D9—36no—
729C4×D9—36no—
730C4×D9—36no—
731C4×D9—36no—
732C4×D9—612no—
733C4×D9—612no—
734C4×D9—612no—
735Dic18—36no—
736Dic18—612no—
737Dic18—63no—
738C8×C9C23×D3112yescomplemented
739C9⋊C8—312no—
740C22×#41—271no—
741C23×D4—271no—
742C2×AGL(1,ℤ/8)—271no—
743C2×AGL(1,ℤ/8)—271no—
744C2×AGL(1,ℤ/8)—2716no—
745C2×AGL(1,ℤ/8)—272no—
746C2×AGL(1,ℤ/8)—272no—
747C2×AGL(1,ℤ/8)—271no—
748C2×AGL(1,ℤ/8)C3⋊D911yescharacteristic, direct product factor
749C22×SD16—272no—
750C22×D8—272no—
751C22×M16—271no—
752C2×C3×C9—22no—
753C2×C3×C9—44no—
754C2×C3×C9—42no—
755C2×C3×C9C2×AGL(1,ℤ/8)12yescomplemented
756C2×C3×C9C23×D411yescharacteristic
757C3⋊D9—22no—
758C3⋊D9—42no—
759C3⋊D9—44no—
760C3⋊D9C2×AGL(1,ℤ/8)14yesdirect product factor
761C24×C3—23no—
762C24×C3—21no—
763C23×D3—93no—
764C23×D3—91no—
765C23×D3—181no—
766C23×D3—182no—
767C23×D3—182no—
768C23×D3—188no—
769C23×D3—183no—
770C23×D3—186no—
771C23×D3—186no—
772C23×D3—1824no—
773C23×D3—183no—
774C23×D3—181no—
775C23×D3—368no—
776C23×D3—3624no—
777C3×#41—26no—
778C3×#41—22no—
779C3×#41C22×D9112yescomplemented
780C3×#41C22×C3⋊D314yes—
781C2×C3×Q8C22×D913yescomplemented
782C2×C3×Q8C22×C3⋊D311yescharacteristic
783C2×C3×D4—23no—
784C2×C3×D4—21no—
785C2×C3×D4—23no—
786C2×C3×D4—26no—
787C2×C3×D4—21no—
788C2×C3×D4—22no—
789C2×C3×D4C22×D916yes—
790C2×C3×D4C22×D9112yescomplemented
791C2×C3×D4C22×D913yescomplemented
792C2×C3×D4C22×C3⋊D312yes—
793C2×C3×D4C22×C3⋊D311yescharacteristic
794C2×C3×D4C22×C3⋊D314yes—
795C22×C3×C4—23no—
796C22×C3×C4—21no—
797C22×C3×C4C22×D913yes—
798C22×C3×C4C22×C3⋊D311yescharacteristic
799C2×#67—181no—
800C2×#67—182no—
801C2×#67—182no—
802C2×#67—188no—
803C2×#67—183no—
804C2×#67—186no—
805C2×#67—186no—
806C2×#67—1824no—
807C2×#67—181no—
808C2×#67—183no—
809C2×#67—183no—
810C2×#67—181no—
811C22×Dic3—93no—
812C22×Dic3—91no—
813C22×Dic3—181no—
814C22×Dic3—183no—
815#239—94no—
816#239—912no—
817#239—182no—
818#239—186no—
819D3×Q8—94no—
820D3×Q8—912no—
821D3×Q8—182no—
822D3×Q8—186no—
823#237—94no—
824#237—912no—
825#237—182no—
826#237—186no—
827#237—188no—
828#237—1824no—
829D3×D4—94no—
830D3×D4—98no—
831D3×D4—98no—
832D3×D4—924no—
833D3×D4—924no—
834D3×D4—912no—
835D3×D4—188no—
836D3×D4—188no—
837D3×D4—184no—
838D3×D4—184no—
839D3×D4—182no—
840D3×D4—1824no—
841D3×D4—1824no—
842D3×D4—1812no—
843D3×D4—1812no—
844D3×D4—186no—
845D3×D4—188no—
846D3×D4—1824no—
847#235—94no—
848#235—912no—
849#235—188no—
850#235—1824no—
851#235—186no—
852#235—182no—
853C2×D12—92no—
854C2×D12—91no—
855C2×D12—94no—
856C2×D12—96no—
857C2×D12—93no—
858C2×D12—912no—
859C2×D12—181no—
860C2×D12—183no—
861C2×D12—183no—
862C2×D12—186no—
863C2×D12—181no—
864C2×D12—182no—
865C2×C4×D3—91no—
866C2×C4×D3—91no—
867C2×C4×D3—94no—
868C2×C4×D3—93no—
869C2×C4×D3—93no—
870C2×C4×D3—912no—
871C2×C4×D3—93no—
872C2×C4×D3—93no—
873C2×C4×D3—912no—
874C2×C4×D3—91no—
875C2×C4×D3—91no—
876C2×C4×D3—94no—
877C2×C4×D3—188no—
878C2×C4×D3—1824no—
879C2×C4×D3—181no—
880C2×C4×D3—183no—
881C2×C4×D3—181no—
882C2×C4×D3—183no—
883C2×C4×D3—183no—
884C2×C4×D3—181no—
885C2×Dic6—91no—
886C2×Dic6—93no—
887C2×Dic6—181no—
888C2×Dic6—183no—
889C3×SD16C22×D9124yescomplemented
890C3×SD16C22×C3⋊D318yes—
891C3×D8C22×D9124yescomplemented
892C3×D8C22×C3⋊D318yes—
893C3×M16C22×D9112yescomplemented
894C3×M16C22×C3⋊D314yes—
895C2×C3×C8C22×D916yescomplemented
896C2×C3×C8C22×C3⋊D312yes—
897#215—98no—
898#215—924no—
899#214—98no—
900#214—924no—
901#213—98no—
902#213—98no—
903#213—924no—
904#213—924no—
905#208—94no—
906#208—912no—
907C2×C3⋊C8—92no—
908C2×C3⋊C8—96no—
909D24—98no—
910D24—924no—
911#204—98no—
912#204—924no—
913ΓL(1,𝔽25)—98no—
914ΓL(1,𝔽25)—924no—
915D3×C8—98no—
916D3×C8—924no—
917C22×C32—22no—
918C22×C32—22no—
919C22×C32—24no—
920C22×C32—48no—
921C22×C32—44no—
922C22×C32—42no—
923C22×C32C2×D3×D412yes—
924C22×C32C2×D3×D411yescharacteristic
925C2×C3⋊D3—32no—
926C2×C3⋊D3—34no—
927C2×C3⋊D3—32no—
928C2×C3⋊D3—68no—
929C2×C3⋊D3—62no—
930C2×C3⋊D3—62no—
931C2×C3⋊D3—64no—
932C2×C3⋊D3—128no—
933C2×C3⋊D3—1216no—
934C2×C3⋊D3—1216no—
935C2×C3⋊D3—128no—
936C2×C3⋊D3—122no—
937C2×C3⋊D3—124no—
938C32×C4—22no—
939C32×C4C2×D3×D411yescharacteristic
940C32×C4C2×D3×D412yes—
941C32×C4C24×D311yescharacteristic
942C3⋊Dic3—32no—
943C3⋊Dic3—32no—
944C3⋊Dic3—62no—
945C22×C9—26no—
946C22×C9—26no—
947C22×C9—212no—
948C22×C9—424no—
949C22×C9—412no—
950C22×C9—46no—
951C22×C9C2×D3×D416yes—
952C22×C9C2×D3×D413yes—
953C2×D9—36no—
954C2×D9—312no—
955C2×D9—36no—
956C2×D9—624no—
957C2×D9—66no—
958C2×D9—66no—
959C2×D9—612no—
960C2×D9—1224no—
961C2×D9—1248no—
962C2×D9—1248no—
963C2×D9—1224no—
964C2×D9—126no—
965C2×D9—1212no—
966C4×C9—26no—
967C4×C9C2×D3×D413yes—
968C4×C9C2×D3×D416yes—
969C4×C9C24×D313yes—
970Dic9—36no—
971Dic9—36no—
972Dic9—66no—
973C25—541no—
974C2×#41—278no—
975C2×#41—271no—
976C2×#41—271no—
977C2×#41—271no—
978C2×#41—541no—
979C2×#41—541no—
980C2×#41—544no—
981C2×#41C2×C3⋊D911yescharacteristic, complemented
982C22×Q8—271no—
983C22×D4—272no—
984C22×D4—272no—
985C22×D4—271no—
986C22×D4—278no—
987C22×D4—271no—
988C22×D4—541no—
989C22×D4—544no—
990C22×D4—541no—
991C22×D4—541no—
992C22×D4—541no—
993C22×D4C2×C3⋊D911yescharacteristic, complemented
994C23×C4—271no—
995C23×C4—541no—
996AGL(1,ℤ/8)—278no—
997AGL(1,ℤ/8)—278no—
998AGL(1,ℤ/8)—2716no—
999AGL(1,ℤ/8)—2716no—
1000AGL(1,ℤ/8)—278no—
1001AGL(1,ℤ/8)C2×C3⋊D918yesdirect product factor
1002C2×SD16—272no—
1003C2×SD16—272no—
1004C2×SD16—2716no—
1005C2×SD16—272no—
1006C2×SD16C2×C3⋊D912yescomplemented
1007C2×D8—272no—
1008C2×D8—272no—
1009C2×D8—2716no—
1010C2×D8—272no—
1011C2×D8C2×C3⋊D912yescomplemented
1012C2×M16—271no—
1013C2×M16—278no—
1014C2×M16—272no—
1015C2×M16C2×C3⋊D911yescharacteristic, complemented
1016C22×C8—272no—
1017C3×C9C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
1018C23×C3—21no—
1019C23×C3—24no—
1020C23×C3—22no—
1021C23×C3—23no—
1022C23×C3—26no—
1023C23×C3—212no—
1024C23×C3—44no—
1025C23×C3—412no—
1026C23×C3D4×D913yes—
1027C23×C3D4×C3⋊D311yescharacteristic
1028C22×D3—91no—
1029C22×D3—93no—
1030C22×D3—91no—
1031C22×D3—94no—
1032C22×D3—93no—
1033C22×D3—912no—
1034C22×D3—184no—
1035C22×D3—1812no—
1036C22×D3—184no—
1037C22×D3—188no—
1038C22×D3—188no—
1039C22×D3—1812no—
1040C22×D3—1824no—
1041C22×D3—1824no—
1042C22×D3—181no—
1043C22×D3—184no—
1044C22×D3—182no—
1045C22×D3—183no—
1046C22×D3—1812no—
1047C22×D3—186no—
1048C22×D3—364no—
1049C22×D3—368no—
1050C22×D3—3612no—
1051C22×D3—3624no—
1052C22×D3—3632no—
1053C22×D3—368no—
1054C22×D3—3696no—
1055C22×D3—3624no—
1056C22×D3—364no—
1057C22×D3—3612no—
1058C3×Q8—21no—
1059C3×Q8—23no—
1060C3×Q8C23×D916yescomplemented
1061C3×Q8C23×C3⋊D312yes—
1062C3×D4—24no—
1063C3×D4—212no—
1064C3×D4—22no—
1065C3×D4—24no—
1066C3×D4—21no—
1067C3×D4—26no—
1068C3×D4—212no—
1069C3×D4—23no—
1070C3×D4C23×D9112yes—
1071C3×D4C23×D916yescomplemented
1072C3×D4C23×C3⋊D314yes—
1073C3×D4C23×C3⋊D312yes—
1074C2×C3×C4—21no—
1075C2×C3×C4—23no—
1076C2×C3×C4—24no—
1077C2×C3×C4—212no—
1078C2×C3×C4D4×D913yes—
1079C2×C3×C4D4×D916yes—
1080C2×C3×C4C23×D913yes—
1081C2×C3×C4C23×D916yes—
1082C2×C3×C4D4×C3⋊D311yescharacteristic
1083C2×C3×C4D4×C3⋊D312yes—
1084C2×C3×C4C23×C3⋊D311yescharacteristic
1085C2×C3×C4C23×C3⋊D312yes—
1086#67—184no—
1087#67—188no—
1088#67—188no—
1089#67—1812no—
1090#67—1824no—
1091#67—1824no—
1092#67—184no—
1093#67—1812no—
1094#67—184no—
1095#67—1812no—
1096C2×Dic3—91no—
1097C2×Dic3—91no—
1098C2×Dic3—94no—
1099C2×Dic3—93no—
1100C2×Dic3—93no—
1101C2×Dic3—912no—
1102C2×Dic3—184no—
1103C2×Dic3—1812no—
1104C2×Dic3—181no—
1105C2×Dic3—183no—
1106D12—94no—
1107D12—92no—
1108D12—912no—
1109D12—96no—
1110D12—184no—
1111D12—1812no—
1112D12—182no—
1113D12—184no—
1114D12—181no—
1115D12—186no—
1116D12—1812no—
1117D12—183no—
1118C4×D3—94no—
1119C4×D3—94no—
1120C4×D3—92no—
1121C4×D3—92no—
1122C4×D3—92no—
1123C4×D3—92no—
1124C4×D3—96no—
1125C4×D3—96no—
1126C4×D3—912no—
1127C4×D3—912no—
1128C4×D3—96no—
1129C4×D3—96no—
1130C4×D3—184no—
1131C4×D3—1812no—
1132C4×D3—184no—
1133C4×D3—1812no—
1134C4×D3—184no—
1135C4×D3—1812no—
1136Dic6—92no—
1137Dic6—96no—
1138Dic6—184no—
1139Dic6—1812no—
1140Dic6—181no—
1141Dic6—183no—
1142C3×C8C23×D9112yescomplemented
1143C3×C8C23×C3⋊D314yes—
1144C3⋊C8—94no—
1145C3⋊C8—912no—
1146C2×C32—22no—
1147C2×C32—44no—
1148C2×C32—42no—
1149C2×C32D3×AGL(1,ℤ/8)12yes—
1150C2×C32C22×D3×D411yescharacteristic
1151C3⋊D3—34no—
1152C3⋊D3—62no—
1153C3⋊D3—122no—
1154C3⋊D3—124no—
1155C2×C9—26no—
1156C2×C9—412no—
1157C2×C9—46no—
1158C2×C9D3×AGL(1,ℤ/8)16yescomplemented
1159C2×C9C22×D3×D413yes—
1160D9—312no—
1161D9—66no—
1162D9—126no—
1163D9—1212no—
1164C24—21no—
1165C24—271no—
1166C24—541no—
1167C24—548no—
1168C24—542no—
1169C24—542no—
1170C24—541no—
1171C24—1088no—
1172#41—22no—
1173#41—274no—
1174#41—274no—
1175#41—274no—
1176#41—548no—
1177#41—548no—
1178#41—542no—
1179#41—542no—
1180#41—542no—
1181#41C22×C3⋊D914yescomplemented
1182C2×Q8—274no—
1183C2×Q8—271no—
1184C2×Q8—541no—
1185C2×Q8—542no—
1186C2×Q8C22×C3⋊D911yescharacteristic, complemented
1187C2×D4—21no—
1188C2×D4—22no—
1189C2×D4—21no—
1190C2×D4—278no—
1191C2×D4—278no—
1192C2×D4—274no—
1193C2×D4—271no—
1194C2×D4—272no—
1195C2×D4—274no—
1196C2×D4—541no—
1197C2×D4—548no—
1198C2×D4—544no—
1199C2×D4—544no—
1200C2×D4—548no—
1201C2×D4—542no—
1202C2×D4—548no—
1203C2×D4—542no—
1204C2×D4—542no—
1205C2×D4—541no—
1206C2×D4—548no—
1207C2×D4—541no—
1208C2×D4—541no—
1209C2×D4—542no—
1210C2×D4—541no—
1211C2×D4C22×C3⋊D912yes—
1212C2×D4C22×C3⋊D914yescomplemented
1213C2×D4C22×C3⋊D911yescharacteristic, complemented
1214C22×C4—21no—
1215C22×C4—271no—
1216C22×C4—271no—
1217C22×C4—274no—
1218C22×C4—271no—
1219C22×C4—271no—
1220C22×C4—274no—
1221C22×C4—271no—
1222C22×C4—541no—
1223C22×C4—548no—
1224C22×C4—541no—
1225C22×C4—541no—
1226C22×C4—541no—
1227C22×C4C22×C3⋊D911yescharacteristic
1228SD16—278no—
1229SD16—278no—
1230SD16—278no—
1231SD16C22×C3⋊D918yescomplemented
1232D8—278no—
1233D8—278no—
1234D8—278no—
1235D8C22×C3⋊D918yescomplemented
1236M16—274no—
1237M16—278no—
1238M16C22×C3⋊D914yescomplemented
1239C2×C8—272no—
1240C2×C8—278no—
1241C2×C8C22×C3⋊D912yescomplemented
1242C22×C3—22no—
1243C22×C3—26no—
1244C22×C3—26no—
1245C22×C3—212no—
1246C22×C3—22no—
1247C22×C3—24no—
1248C22×C3—48no—
1249C22×C3—424no—
1250C22×C3—44no—
1251C22×C3—42no—
1252C22×C3—412no—
1253C22×C3—46no—
1254C22×C3C2×D4×D916yes—
1255C22×C3C2×D4×D913yes—
1256C22×C3C2×D4×C3⋊D312yes—
1257C22×C3C2×D4×C3⋊D311yescharacteristic
1258C2×D3—96no—
1259C2×D3—92no—
1260C2×D3—94no—
1261C2×D3—912no—
1262C2×D3—96no—
1263C2×D3—92no—
1264C2×D3—188no—
1265C2×D3—1824no—
1266C2×D3—182no—
1267C2×D3—186no—
1268C2×D3—186no—
1269C2×D3—1812no—
1270C2×D3—182no—
1271C2×D3—184no—
1272C2×D3—3616no—
1273C2×D3—3648no—
1274C2×D3—368no—
1275C2×D3—3624no—
1276C2×D3—3616no—
1277C2×D3—3648no—
1278C2×D3—368no—
1279C2×D3—3624no—
1280C2×D3—364no—
1281C2×D3—362no—
1282C2×D3—3612no—
1283C2×D3—366no—
1284C3×C4—26no—
1285C3×C4—22no—
1286C3×C4C2×D4×D913yes—
1287C3×C4C2×D4×D916yes—
1288C3×C4C24×D913yes—
1289C3×C4C2×D4×C3⋊D311yescharacteristic
1290C3×C4C2×D4×C3⋊D312yes—
1291C3×C4C24×C3⋊D311yescharacteristic
1292Dic3—96no—
1293Dic3—96no—
1294Dic3—92no—
1295Dic3—92no—
1296Dic3—186no—
1297Dic3—182no—
1298C32C2×D3×AGL(1,ℤ/8)11yescharacteristic
1299C9C2×D3×AGL(1,ℤ/8)13yescomplemented
1300C23—24no—
1301C23—21no—
1302C23—22no—
1303C23—44no—
1304C23—271no—
1305C23—274no—
1306C23—271no—
1307C23—544no—
1308C23—544no—
1309C23—548no—
1310C23—548no—
1311C23—544no—
1312C23—541no—
1313C23—542no—
1314C23—1084no—
1315C23—1088no—
1316C23—1084no—
1317C23—10832no—
1318C23—1088no—
1319C23D4×C3⋊D911yescharacteristic
1320Q8—21no—
1321Q8—272no—
1322Q8—544no—
1323Q8—541no—
1324Q8C23×C3⋊D912yescomplemented
1325D4—24no—
1326D4—22no—
1327D4—24no—
1328D4—21no—
1329D4—272no—
1330D4—274no—
1331D4—544no—
1332D4—548no—
1333D4—548no—
1334D4—544no—
1335D4—544no—
1336D4—544no—
1337D4—544no—
1338D4—542no—
1339D4—541no—
1340D4C23×C3⋊D914yes—
1341D4C23×C3⋊D912yescomplemented
1342C2×C4—21no—
1343C2×C4—24no—
1344C2×C4—274no—
1345C2×C4—271no—
1346C2×C4—271no—
1347C2×C4—272no—
1348C2×C4—272no—
1349C2×C4—274no—
1350C2×C4—272no—
1351C2×C4—272no—
1352C2×C4—274no—
1353C2×C4—544no—
1354C2×C4—544no—
1355C2×C4—544no—
1356C2×C4—541no—
1357C2×C4—544no—
1358C2×C4D4×C3⋊D912yes—
1359C2×C4D4×C3⋊D911yescharacteristic
1360C2×C4C23×C3⋊D912yes—
1361C2×C4C23×C3⋊D911yescharacteristic
1362C8—274no—
1363C8C23×C3⋊D914yescomplemented
1364C2×C3—26no—
1365C2×C3—22no—
1366C2×C3—412no—
1367C2×C3—46no—
1368C2×C3—44no—
1369C2×C3—42no—
1370C2×C3D9×AGL(1,ℤ/8)16yescomplemented
1371C2×C3C22×D4×D913yes—
1372C2×C3C3⋊D3×AGL(1,ℤ/8)12yes—
1373C2×C3C22×D4×C3⋊D311yescharacteristic
1374D3—912no—
1375D3—94no—
1376D3—186no—
1377D3—182no—
1378D3—3612no—
1379D3—366no—
1380D3—364no—
1381D3—362no—
1382C22—22no—
1383C22—22no—
1384C22—24no—
1385C22—48no—
1386C22—44no—
1387C22—42no—
1388C22—274no—
1389C22—272no—
1390C22—272no—
1391C22—548no—
1392C22—542no—
1393C22—542no—
1394C22—544no—
1395C22—1088no—
1396C22—10816no—
1397C22—1088no—
1398C22—10816no—
1399C22—1084no—
1400C22—1082no—
1401C22C2×D4×C3⋊D912yes—
1402C22C2×D4×C3⋊D911yescharacteristic
1403C4—22no—
1404C4—272no—
1405C4—272no—
1406C4—542no—
1407C4C2×D4×C3⋊D912yes—
1408C4C2×D4×C3⋊D911yescharacteristic
1409C4C24×C3⋊D911yescharacteristic
1410C3C2×D9×AGL(1,ℤ/8)13yescomplemented
1411C3C2×C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
1412C2—22no—
1413C2—44no—
1414C2—42no—
1415C2—274no—
1416C2—542no—
1417C2—1084no—
1418C2—1082no—
1419C2AGL(1,ℤ/8)×C3⋊D912yesdirect product factor
1420C2C22×D4×C3⋊D911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D9
commutator, cosocleC3×C4×C9C25
FrattiniC3×C4C24×C3⋊D3
FittingC2×C3×C9×AGL(1,ℤ/8)C2
socleC22×C32C2×D3×D4
hypercenterC2×AGL(1,ℤ/8)C3⋊D9
hypocenterC3×C9C22×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#41×C3⋊D9C2semidirect
2. C22×D4×C3⋊D9C2semidirect
3. C2×C3×C9×AGL(1,ℤ/8)C2semidirect
4. C2×#11721867C2semidirect
5. C2×#11721833C2semidirect
6. AGL(1,ℤ/8)×C3⋊D9C2direct (N × H)
7. C2×#11721796C2semidirect
8. C2×SD16×C3⋊D9C2semidirect
9. C2×#11721790C2semidirect
10. C2×D8×C3⋊D9C2semidirect
11. C2×#11721783C2semidirect
12. C2×M16×C3⋊D9C2semidirect
16. C2×C3×C9×#41C22semidirect
17. C22×C3×D4×C9C22semidirect
20. #41×C3⋊D9C22semidirect
21. C2×#88746C22semidirect
22. C2×Q8×C3⋊D9C22semidirect
24. C2×#88742C22semidirect
30. C2×D4×C3⋊D9C22semidirect
31. C2×D4×C3⋊D9C22semidirect
32. C2×D4×C3⋊D9C22semidirect
34. C2×#88736C22semidirect
35. C22×C4⋊(C3⋊D9)C22semidirect
38. C3×C9×AGL(1,ℤ/8)C22semidirect
39. C2×C3×C9×SD16C22semidirect
40. C2×C3×C9×D8C22semidirect
41. C2×C3×C9×M16C22semidirect
42. #11721867C22semidirect
43. C2×#88548C22semidirect
44. #11721833C22semidirect
45. C2×#88544C22semidirect
46. C2×#88544C22semidirect
47. C2×#88543C22semidirect
48. C2×#88532C22semidirect
49. #11721796C22semidirect
50. SD16×C3⋊D9C22semidirect
51. #11721790C22semidirect
52. D8×C3⋊D9C22semidirect
53. #11721783C22semidirect
54. M16×C3⋊D9C22semidirect
55. C2×#88525C22semidirect
56. C2×#88524C22semidirect
57. C2×#88523C22semidirect
58. C2×C8×C3⋊D9C22semidirect
73. C2×C9×AGL(1,ℤ/8)D3semidirect
92. C3×C9×#41C23semidirect
93. C2×C3×Q8×C9C23semidirect
98. C2×C3×D4×C9C23semidirect
99. C2×C3×D4×C9C23semidirect
111. #88746C23semidirect
113. Q8×C3⋊D9C23semidirect
116. #88742C23semidirect
124. D4×C3⋊D9C23semidirect
125. D4×C3⋊D9C23semidirect
128. #88736C23semidirect
133. C2×C4⋊(C3⋊D9)C23semidirect
134. C2×C4⋊(C3⋊D9)C23semidirect
146. C2×#6226C23semidirect
147. C3×C9×SD16C23semidirect
148. C3×C9×D8C23semidirect
149. C3×C9×M16C23semidirect
150. C2×C3×C8×C9C23semidirect
151. #88548C23semidirect
152. #88544C23semidirect
153. #88544C23semidirect
154. #88543C23semidirect
155. #88532C23semidirect
156. C2×C3⋊(C9⋊C8)C23semidirect
157. #88525C23semidirect
158. #88524C23semidirect
159. #88523C23semidirect
160. C8×C3⋊D9C23semidirect
208. C2×C9×#41C2×D3semidirect
209. C22×D4×C9C2×D3semidirect
230. C9×AGL(1,ℤ/8)C2×D3semidirect
231. C2×C9×SD16C2×D3semidirect
232. C2×C9×D8C2×D3semidirect
233. C2×C9×M16C2×D3semidirect
272. C3×Q8×C9C24semidirect
278. C3×D4×C9C24semidirect
300. C4⋊(C3⋊D9)C24semidirect
312. #6226C24semidirect
313. C3×C8×C9C24semidirect
314. C3⋊(C9⋊C8)C24semidirect
319. C2×C3×AGL(1,ℤ/8)D9semidirect
426. C9×#41C22×D3semidirect
427. C2×Q8×C9C22×D3semidirect
432. C2×D4×C9C22×D3semidirect
433. C2×D4×C9C22×D3semidirect
481. C9×SD16C22×D3semidirect
482. C9×D8C22×D3semidirect
483. C9×M16C22×D3semidirect
484. C2×C8×C9C22×D3semidirect
514. C2×C3⋊D9AGL(1,ℤ/8)direct (N × H)
526. C2×C3×#41C2×D9semidirect
528. C22×C3×D4C2×D9semidirect
570. C3×AGL(1,ℤ/8)C2×D9semidirect
572. C2×C3×SD16C2×D9semidirect
574. C2×C3×D8C2×D9semidirect
576. C2×C3×M16C2×D9semidirect
697. Q8×C9C23×D3semidirect
703. D4×C9C23×D3semidirect
738. C8×C9C23×D3semidirect
748. C2×AGL(1,ℤ/8)C3⋊D9direct (N × H)
755. C2×C3×C9C2×AGL(1,ℤ/8)semidirect
760. C3⋊D9C2×AGL(1,ℤ/8)direct (N × H)
779. C3×#41C22×D9semidirect
781. C2×C3×Q8C22×D9semidirect
790. C2×C3×D4C22×D9semidirect
791. C2×C3×D4C22×D9semidirect
889. C3×SD16C22×D9semidirect
891. C3×D8C22×D9semidirect
893. C3×M16C22×D9semidirect
895. C2×C3×C8C22×D9semidirect
981. C2×#41C2×C3⋊D9semidirect
993. C22×D4C2×C3⋊D9semidirect
1001. AGL(1,ℤ/8)C2×C3⋊D9direct (N × H)
1006. C2×SD16C2×C3⋊D9semidirect
1011. C2×D8C2×C3⋊D9semidirect
1015. C2×M16C2×C3⋊D9semidirect
1017. C3×C9C22×AGL(1,ℤ/8)semidirect
1060. C3×Q8C23×D9semidirect
1071. C3×D4C23×D9semidirect
1142. C3×C8C23×D9semidirect
1158. C2×C9D3×AGL(1,ℤ/8)semidirect
1181. #41C22×C3⋊D9semidirect
1186. C2×Q8C22×C3⋊D9semidirect
1212. C2×D4C22×C3⋊D9semidirect
1213. C2×D4C22×C3⋊D9semidirect
1231. SD16C22×C3⋊D9semidirect
1235. D8C22×C3⋊D9semidirect
1238. M16C22×C3⋊D9semidirect
1241. C2×C8C22×C3⋊D9semidirect
1299. C9C2×D3×AGL(1,ℤ/8)semidirect
1324. Q8C23×C3⋊D9semidirect
1341. D4C23×C3⋊D9semidirect
1363. C8C23×C3⋊D9semidirect
1370. C2×C3D9×AGL(1,ℤ/8)semidirect
1410. C3C2×D9×AGL(1,ℤ/8)semidirect
1419. C2AGL(1,ℤ/8)×C3⋊D9direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#41×C3⋊D92
C22×D4×C3⋊D92
C2×C3×C9×AGL(1,ℤ/8)2
C2×#117218672
C2×#117218332
AGL(1,ℤ/8)×C3⋊D92
C2×#117217962
C2×SD16×C3⋊D92
C2×#117217902
C2×D8×C3⋊D92
C2×#117217832
C2×M16×C3⋊D92
C2×C3⋊D3×AGL(1,ℤ/8)3
C2×D9×AGL(1,ℤ/8)3