Finite Group Databasebeta

← C2×#11724589 #13181617

Subgroups — C2×#11724589 #13181617

Order 1728.

6332 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#237C211yesmaximal, characteristic, complemented
4C2×#89039C212yesmaximal, complemented
5C2×C3⋊D3×#67C212yesmaximal, complemented
6C22×#6292C212yesmaximal, complemented
7C2×#89031C212yesmaximal, complemented
8#11724589C2116yesmaximal, direct product factor
9C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
10C2×#89020C211yesmaximal, characteristic, complemented
11C2×#89018C211yesmaximal, characteristic, complemented
12C2×#89017C211yesmaximal, characteristic, complemented
13C2×#64366—31nomaximal
14C2×#64314—34nomaximal
15C23×C3⋊(C3⋊D3)C2212yescomplemented
16C23×C3×C3⋊D3C2212yescomplemented
17C22×D3×C3⋊D3C2212yescomplemented
18C2×C33×D4C2211yescharacteristic, complemented
19C2×#6312C2212yescomplemented
20D4×C3⋊(C3⋊D3)C2218yescomplemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2212yescomplemented
24C3×D4×C3⋊D3C2218yescomplemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×#67C2212yescomplemented
28C22×C32×Dic3C2212yescomplemented
29C32×#237C2218yescomplemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C2×C32×Dic6C2211yescharacteristic, complemented
32#89039C22116yescomplemented
33C3⋊D3×#67C22116yescomplemented
34C2×#6293C2211yescharacteristic, complemented
35C2×#6292C2212yescomplemented
36C2×#6292C2212yescomplemented
37C2×#6292C2211yescharacteristic, complemented
38C2×#6292C2212yescomplemented
39C2×#6292C22116yescomplemented
40C2×#6291C2211yescharacteristic, complemented
41C2×#6290C2211yescharacteristic, complemented
42C2×#6289C2212yescomplemented
43#89031C22116yescomplemented
44C2×Dic3×C3⋊D3C2212yescomplemented
45D3×C4⋊(C3⋊D3)C2218yescomplemented
46#89020C2218yescomplemented
47#89018C2218yescomplemented
48#89017C2218yescomplemented
49C2×C32×#41—31no—
50#64366—316no—
51C2×#3832—31no—
52C2×#3832—31no—
53C2×D4×C3⋊D3—31no—
54C2×D4×C3⋊D3—32no—
55C2×D4×C3⋊D3—34no—
56C2×D4×C3⋊D3—32no—
57C2×D4×C3⋊D3—64no—
58C2×D4×C3⋊D3D311yescharacteristic, complemented
59C2×#3828—32no—
60C2×#3828—31no—
61C22×C4⋊(C3⋊D3)—31no—
62C22×C4⋊(C3⋊D3)—32no—
63C2×C3×#237D314yescomplemented
64C2×C3×D3×D4—34no—
65C2×#3811—38no—
66C2×D3×#67—38no—
67C22×#626—38no—
68C2×#3804—38no—
69#64314—364no—
70C2×D3×D12—34no—
71C2×#3799—34no—
72C2×#3798—34no—
73C2×#3796—34no—
74C23×C33C2312yes—
75C22×C3⋊(C3⋊D3)—44no—
76C22×C3⋊(C3⋊D3)C2312yes—
77C22×C3⋊(C3⋊D3)C2311yescharacteristic
78C22×C3⋊(C3⋊D3)C2318yescomplemented
79C22×C3×C3⋊D3—44no—
80C22×C3×C3⋊D3C2312yes—
81C22×C3×C3⋊D3C2311yescharacteristic
82C22×C3×C3⋊D3C2318yescomplemented
83C22×C32×D3C2311yescharacteristic
84C2×D3×C3⋊D3—44no—
85C2×D3×C3⋊D3C2318yescomplemented
86C33×D4C2314yescomplemented
87C2×C33×C4C2311yescharacteristic
88#6312C2318yescomplemented
89C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
91C4×C3⋊(C3⋊D3)C2314yescomplemented
92C3×#638C2318yescomplemented
93C2×C3×C3⋊Dic3C2311yescharacteristic
94C3×C4⋊(C3⋊D3)C2314yescomplemented
95C3×C4×C3⋊D3C2314yescomplemented
96C32×#67C2318yescomplemented
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2318yescomplemented
100C32×C4×D3C2314yescomplemented
101C32×Dic6C2314yescomplemented
102#6293C2314yescomplemented
103#6292C2318yescomplemented
104#6292C2318yescomplemented
105#6292C2314yescomplemented
106#6292C2318yescomplemented
107#6291C2314yescomplemented
108#6290C2314yescomplemented
109#6289C2318yescomplemented
110Dic3×C3⋊D3C2318yescomplemented
111C2×#1009—94no—
112C2×#1004—91no—
113C23×C3⋊D3—32no—
114C23×C3⋊D3—38no—
115C23×C3⋊D3—32no—
116C23×C3⋊D3—68no—
117C23×C3⋊D3C2×D312yescomplemented
118C23×C3×D3—38no—
119C22×D32—38no—
120C32×#41—38no—
121C2×C32×Q8—31no—
122C2×C32×D4—24no—
123C2×C32×D4—32no—
124C2×C32×D4C2×D314yescomplemented
125C2×C32×D4C2×D311yescharacteristic, complemented
126C22×C32×C4—32no—
127C22×C32×C4—31no—
128C2×#638—32no—
129C2×#638—38no—
130C2×#638—31no—
131C2×#638—31no—
132C2×#638—68no—
133C2×#638C2×D312yescomplemented
134#3832—38no—
135#3832—38no—
136D4×C3⋊D3—316no—
137D4×C3⋊D3—38no—
138D4×C3⋊D3—332no—
139D4×C3⋊D3—316no—
140D4×C3⋊D3—632no—
141D4×C3⋊D3C2×D318yescomplemented
142#3828—316no—
143#3828—38no—
144C2×C4⋊(C3⋊D3)—32no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—32no—
147C2×C4⋊(C3⋊D3)—32no—
148C2×C4⋊(C3⋊D3)—316no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—34no—
151C2×C4⋊(C3⋊D3)—38no—
152C2×C4⋊(C3⋊D3)—64no—
153C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
154C2×C4×C3⋊D3—32no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—32no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
160C2×#634—31no—
161C2×C3×#67—38no—
162C2×C3×#67C2×D318yescomplemented
163C22×C3×Dic3C2×D318yescomplemented
164C3×#237C2×D3132yescomplemented
165C3×D3×D4—332no—
166C2×C3×D12—34no—
167C2×C3×C4×D3—34no—
168C2×C3×C4×D3C2×D314yescomplemented
169C2×C3×Dic6C2×D314yescomplemented
170#3811—364no—
171D3×#67—364no—
172C2×#627—34no—
173C2×#626—34no—
174C2×#626—38no—
175C2×#626—34no—
176C2×#626—38no—
177C2×#626—38no—
178C2×#626—364no—
179C2×#625—34no—
180C2×#624—38no—
181#3804—364no—
182C2×D3×Dic3—38no—
183D3×D12—332no—
184#3799—332no—
185#3798—332no—
186#3796—332no—
187C22×C33—24no—
188C22×C33C2414yes—
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—22no—
191C2×C3⋊(C3⋊D3)—24no—
192C2×C3⋊(C3⋊D3)—48no—
193C2×C3⋊(C3⋊D3)C2414yes—
194C2×C3⋊(C3⋊D3)C2412yes—
195C2×C3×C3⋊D3—24no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—48no—
198C2×C3×C3⋊D3C2414yes—
199C2×C3×C3⋊D3C2412yes—
200C2×C32×D3—22no—
201C2×C32×D3C2412yes—
202D3×C3⋊D3—48no—
203C33×C4C2412yes—
204C3⋊(C3⋊Dic3)C2412yes—
205C3×C3⋊Dic3C2412yes—
206C32×Dic3C2414yes—
207C32×Dic3C2412yes—
208C2×C3×#41—34no—
209C22×C3×D4—91no—
210C22×#67—92no—
211C22×#67—92no—
212#1009—964no—
213C2×#239—94no—
214C2×#239—94no—
215#1004—916no—
216C2×#237—92no—
217C2×#237—91no—
218C2×#237C3⋊D311yescharacteristic, complemented
219C2×D3×D4—34no—
220C2×D3×D4—98no—
221C2×D3×D4—98no—
222C2×D3×D4—94no—
223C2×D3×D4—91no—
224C2×D3×D4—92no—
225C2×D3×D4—91no—
226C2×D3×D4—184no—
227C2×#235—94no—
228C2×#235—98no—
229C2×#235—91no—
230C2×#235—91no—
231C22×D12—94no—
232C22×D12—98no—
233C23×C32—28no—
234C23×C32—31no—
235C23×C32C22×D318yes—
236C23×C32C22×D312yes—
237C22×C3⋊D3—31no—
238C22×C3⋊D3—32no—
239C22×C3⋊D3—38no—
240C22×C3⋊D3—38no—
241C22×C3⋊D3—38no—
242C22×C3⋊D3—34no—
243C22×C3⋊D3—332no—
244C22×C3⋊D3—44no—
245C22×C3⋊D3—64no—
246C22×C3⋊D3—68no—
247C22×C3⋊D3—632no—
248C22×C3⋊D3—124no—
249C22×C3⋊D3—124no—
250C22×C3⋊D3—1216no—
251C22×C3⋊D3—1232no—
252C22×C3⋊D3C22×D312yes—
253C22×C3⋊D3C22×D311yescharacteristic
254C22×C3⋊D3C22×D318yescomplemented
255C22×C3×D3—38no—
256C22×C3×D3—34no—
257C22×C3×D3—332no—
258C22×C3×D3—1216no—
259C22×C3×D3C22×D314yes—
260C2×D32—332no—
261C2×D32—1216no—
262C32×Q8—34no—
263C32×D4—216no—
264C32×D4—38no—
265C32×D4C22×D3116yescomplemented
266C32×D4C22×D314yescomplemented
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—32no—
270C2×C32×C4—38no—
271C2×C32×C4—34no—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D311yescharacteristic
274#638—38no—
275#638—34no—
276#638—34no—
277#638—332no—
278#638—632no—
279#638C22×D318yescomplemented
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—34no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C4⋊(C3⋊D3)—38no—
285C4⋊(C3⋊D3)—34no—
286C4⋊(C3⋊D3)—38no—
287C4⋊(C3⋊D3)—38no—
288C4⋊(C3⋊D3)—34no—
289C4⋊(C3⋊D3)—316no—
290C4⋊(C3⋊D3)—616no—
291C4⋊(C3⋊D3)C22×D314yescomplemented
292C4×C3⋊D3—38no—
293C4×C3⋊D3—34no—
294C4×C3⋊D3—38no—
295C4×C3⋊D3—316no—
296C4×C3⋊D3—616no—
297C4×C3⋊D3C22×D314yescomplemented
298#634—34no—
299C3×#67—332no—
300C3×#67C22×D3132yescomplemented
301C2×C3×Dic3—34no—
302C2×C3×Dic3C22×D318yes—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D3132yescomplemented
305C3×D12—316no—
306C3×C4×D3—316no—
307C3×C4×D3C22×D3116yescomplemented
308C3×Dic6C22×D3116yescomplemented
309#627—316no—
310#626—316no—
311#626—332no—
312#626—316no—
313#626—332no—
314#626—332no—
315#625—316no—
316#624—332no—
317D3×Dic3—332no—
318C2×H(5,𝔽2)—271noSylow
319C2×C33—24no—
320C2×C33H(5,𝔽2)12yescomplemented
321C2×C33C2511yescharacteristic
322C3⋊(C3⋊D3)—22no—
323C3⋊(C3⋊D3)—24no—
324C3×C3⋊D3—24no—
325C3×C3⋊D3—22no—
326C32×D3—22no—
327C24×C3—92no—
328C23×D3—38no—
329C23×D3—98no—
330C23×D3—98no—
331C23×D3—92no—
332C23×D3—92no—
333C23×D3—188no—
334C3×#41—332no—
335C2×C3×Q8—34no—
336C2×C3×D4—24no—
337C2×C3×D4—38no—
338C2×C3×D4—92no—
339C2×C3×D4—98no—
340C2×C3×D4—91no—
341C2×C3×D4D3214yescomplemented
342C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
343C22×C3×C4—38no—
344C22×C3×C4—34no—
345C22×C3×C4—91no—
346C2×#67—38no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—98no—
350C2×#67—92no—
351C2×#67—91no—
352C2×#67—916no—
353C2×#67—91no—
354C2×#67—92no—
355C2×#67—92no—
356C2×#67—92no—
357C2×#67—916no—
358C2×#67—188no—
359C2×#67C2×C3⋊D312yescomplemented
360C22×Dic3—92no—
361C22×Dic3C2×C3⋊D312yescomplemented
362#239—932no—
363#239—932no—
364#237—916no—
365#237—98no—
366#237C2×C3⋊D318yescomplemented
367D3×D4—332no—
368D3×D4—964no—
369D3×D4—964no—
370D3×D4—932no—
371D3×D4—98no—
372D3×D4—916no—
373D3×D4—98no—
374D3×D4—1832no—
375#235—932no—
376#235—964no—
377#235—98no—
378#235—98no—
379C2×D12—34no—
380C2×D12—932no—
381C2×D12—94no—
382C2×D12—98no—
383C2×D12—98no—
384C2×D12—98no—
385C2×D12—964no—
386C2×D12—91no—
387C2×D12—94no—
388C2×D12—91no—
389C2×D12—184no—
390C2×C4×D3—34no—
391C2×C4×D3—98no—
392C2×C4×D3—98no—
393C2×C4×D3—94no—
394C2×C4×D3—91no—
395C2×C4×D3—92no—
396C2×C4×D3—184no—
397C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
398C2×Dic6—94no—
399C2×Dic6—91no—
400C2×Dic6C2×C3⋊D311yescharacteristic, complemented
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—216no—
404C22×C32—216no—
405C22×C32—32no—
406C22×C32—416no—
407C22×C32—62no—
408C22×C32C23×D3116yes—
409C22×C32C23×D314yes—
410C22×C32C23×D314yes—
411C22×C32C23×D311yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—24no—
414C2×C3⋊D3—34no—
415C2×C3⋊D3—32no—
416C2×C3⋊D3—316no—
417C2×C3⋊D3—38no—
418C2×C3⋊D3—48no—
419C2×C3⋊D3—68no—
420C2×C3⋊D3—616no—
421C2×C3⋊D3—616no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—68no—
425C2×C3⋊D3—616no—
426C2×C3⋊D3—1216no—
427C2×C3⋊D3—128no—
428C2×C3⋊D3—128no—
429C2×C3⋊D3—1232no—
430C2×C3⋊D3—1264no—
431C2×C3⋊D3C23×D314yes—
432C2×C3⋊D3C23×D312yes—
433C2×C3×D3—28no—
434C2×C3×D3—316no—
435C2×C3×D3—38no—
436C2×C3×D3—616no—
437C2×C3×D3—68no—
438C2×C3×D3—1232no—
439C2×C3×D3C23×D318yes—
440D32—1232no—
441C32×C4—28no—
442C32×C4—32no—
443C32×C4—34no—
444C32×C4C23×D318yes—
445C32×C4C23×D312yes—
446C3⋊Dic3—32no—
447C3⋊Dic3—38no—
448C3⋊Dic3—68no—
449C3⋊Dic3C23×D312yes—
450C3×Dic3—38no—
451C3×Dic3C23×D3116yes—
452C3×Dic3C23×D318yes—
453H(5,𝔽2)—2716no—
454C2×#41—31no—
455C2×#41—271no—
456C2×#41—272no—
457C2×#41—271no—
458C2×#41—271no—
459C22×D4—91no—
460C22×D4—271no—
461C22×D4—272no—
462C22×D4—272no—
463C22×D4—272no—
464C22×D4—271no—
465C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
466C23×C3—28no—
467C23×C3—34no—
468C23×C3—92no—
469C23×C3—91no—
470C23×C3—98no—
471C23×C3—364no—
472C23×C3C2×D3218yes—
473C23×C3C22×C3⋊D312yes—
474C22×D3—34no—
475C22×D3—38no—
476C22×D3—332no—
477C22×D3—932no—
478C22×D3—94no—
479C22×D3—98no—
480C22×D3—92no—
481C22×D3—91no—
482C22×D3—932no—
483C22×D3—98no—
484C22×D3—98no—
485C22×D3—1216no—
486C22×D3—184no—
487C22×D3—188no—
488C22×D3—1832no—
489C22×D3—364no—
490C22×D3—3616no—
491C22×D3—3616no—
492C22×D3—364no—
493C22×D3—3632no—
494C22×D3C22×C3⋊D311yescharacteristic
495C3×Q8—316no—
496C3×D4—216no—
497C3×D4—332no—
498C3×D4—98no—
499C3×D4—94no—
500C3×D4C2×D32116yescomplemented
501C3×D4C22×C3⋊D314yescomplemented
502C2×C3×C4—24no—
503C2×C3×C4—34no—
504C2×C3×C4—38no—
505C2×C3×C4—332no—
506C2×C3×C4—316no—
507C2×C3×C4—91no—
508C2×C3×C4—94no—
509C2×C3×C4C2×D3214yes—
510C2×C3×C4C22×C3⋊D311yescharacteristic
511#67—332no—
512#67—916no—
513#67—916no—
514#67—932no—
515#67—98no—
516#67—94no—
517#67—94no—
518#67—98no—
519#67—98no—
520#67—98no—
521#67—1832no—
522#67C22×C3⋊D318yescomplemented
523C2×Dic3—34no—
524C2×Dic3—94no—
525C2×Dic3—91no—
526C2×Dic3—98no—
527C2×Dic3—184no—
528C2×Dic3C22×C3⋊D311yescharacteristic
529C2×Dic3C22×C3⋊D312yes—
530C2×Dic3C22×C3⋊D318yescomplemented
531D12—316no—
532D12—916no—
533D12—932no—
534D12—932no—
535D12—932no—
536D12—94no—
537D12—916no—
538D12—94no—
539D12—1816no—
540C4×D3—316no—
541C4×D3—932no—
542C4×D3—932no—
543C4×D3—916no—
544C4×D3—94no—
545C4×D3—98no—
546C4×D3—1816no—
547C4×D3C22×C3⋊D314yescomplemented
548Dic6—916no—
549Dic6—94no—
550Dic6C22×C3⋊D314yescomplemented
551C2×C32—24no—
552C2×C32—28no—
553C2×C32—24no—
554C2×C32—216no—
555C2×C32—416no—
556C2×C32—62no—
557C2×C32#100412yescomplemented
558C2×C32#100918yescomplemented
559C2×C32C24×D314yes—
560C2×C32C24×D311yescharacteristic
561C3⋊D3—22no—
562C3⋊D3—24no—
563C3⋊D3—616no—
564C3⋊D3—62no—
565C3⋊D3—64no—
566C3⋊D3—68no—
567C3⋊D3—616no—
568C3⋊D3—1216no—
569C3×D3—28no—
570C3×D3—616no—
571C3×D3—68no—
572C24—92no—
573C24—272no—
574C24—272no—
575#41—38no—
576#41—278no—
577#41—2716no—
578#41—278no—
579#41—278no—
580C2×Q8—31no—
581C2×Q8—271no—
582C2×D4—32no—
583C2×D4—92no—
584C2×D4—98no—
585C2×D4—91no—
586C2×D4—278no—
587C2×D4—271no—
588C2×D4—272no—
589C2×D4—272no—
590C2×D4—272no—
591C2×D4—2716no—
592C2×D4—271no—
593C2×D4—2716no—
594C2×D4—2716no—
595C2×D4—271no—
596C2×D4—272no—
597C2×D4—278no—
598C2×D4—271no—
599C2×D4D3×C3⋊D311yescharacteristic, complemented
600C22×C4—32no—
601C22×C4—31no—
602C22×C4—91no—
603C22×C4—272no—
604C22×C4—272no—
605C22×C4—271no—
606C22×C3—216no—
607C22×C3—24no—
608C22×C3—216no—
609C22×C3—24no—
610C22×C3—38no—
611C22×C3—416no—
612C22×C3—68no—
613C22×C3—94no—
614C22×C3—92no—
615C22×C3—184no—
616C22×C3—182no—
617C22×C3—368no—
618C22×C3C22×D32116yes—
619C22×C3C22×D3214yes—
620C22×C3C23×C3⋊D314yes—
621C22×C3C23×C3⋊D311yescharacteristic
622C2×D3—22no—
623C2×D3—38no—
624C2×D3—316no—
625C2×D3—68no—
626C2×D3—616no—
627C2×D3—98no—
628C2×D3—916no—
629C2×D3—92no—
630C2×D3—94no—
631C2×D3—1232no—
632C2×D3—188no—
633C2×D3—1816no—
634C2×D3—1816no—
635C2×D3—188no—
636C2×D3—1816no—
637C2×D3—182no—
638C2×D3—184no—
639C2×D3—3616no—
640C2×D3—368no—
641C2×D3—3632no—
642C2×D3—3632no—
643C2×D3—368no—
644C2×D3—3664no—
645C2×D3C23×C3⋊D312yes—
646C3×C4—28no—
647C3×C4—38no—
648C3×C4—316no—
649C3×C4—92no—
650C3×C4C22×D3218yes—
651C3×C4C23×C3⋊D312yes—
652Dic3—38no—
653Dic3—98no—
654Dic3—92no—
655Dic3—188no—
656Dic3C23×C3⋊D312yes—
657Dic3C23×C3⋊D314yes—
658C32—24no—
659C32C2×#100411yescharacteristic, complemented
660C32C2×#100914yescomplemented
661C23—31no—
662C23—91no—
663C23—92no—
664C23—98no—
665C23—278no—
666C23—271no—
667C23—272no—
668C23—278no—
669C23—364no—
670C23—1084no—
671C23—1084no—
672C23C2×D3×C3⋊D312yes—
673Q8—34no—
674Q8—274no—
675D4—38no—
676D4—98no—
677D4—94no—
678D4—274no—
679D4—278no—
680D4—278no—
681D4—278no—
682D4—274no—
683D4—274no—
684D4—278no—
685D4—274no—
686D4C2×D3×C3⋊D314yescomplemented
687C2×C4—38no—
688C2×C4—31no—
689C2×C4—32no—
690C2×C4—34no—
691C2×C4—91no—
692C2×C4—94no—
693C2×C4—278no—
694C2×C4—278no—
695C2×C4—271no—
696C2×C4—274no—
697C2×C4C2×D3×C3⋊D311yescharacteristic
698C2×C3—216no—
699C2×C3—24no—
700C2×C3—28no—
701C2×C3—24no—
702C2×C3—416no—
703C2×C3—68no—
704C2×C3—184no—
705C2×C3—182no—
706C2×C3#6431418yescomplemented
707C2×C3#6436612yescomplemented
708C2×C3C23×D3214yes—
709C2×C3C24×C3⋊D311yescharacteristic
710D3—22no—
711D3—68no—
712D3—616no—
713D3—1816no—
714D3—188no—
715D3—1816no—
716D3—182no—
717D3—184no—
718D3—3616no—
719C22—24no—
720C22—32no—
721C22—62no—
722C22—92no—
723C22—94no—
724C22—182no—
725C22—184no—
726C22—272no—
727C22—274no—
728C22—368no—
729C22—542no—
730C22—544no—
731C22—1088no—
732C22—1088no—
733C22C22×D3×C3⋊D314yes—
734C22C22×D3×C3⋊D311yescharacteristic
735C4—32no—
736C4—34no—
737C4—92no—
738C4—272no—
739C4C22×D3×C3⋊D312yes—
740C3—24no—
741C3C2×#6431414yescomplemented
742C3C2×#6436611yescharacteristic, complemented
743C2—24no—
744C2—62no—
745C2—182no—
746C2—184no—
747C2—542no—
748C2—544no—
749C2#1172458912yesdirect product factor
750C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC22C22×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C2×C32×#237C2semidirect
4. C2×#89039C2semidirect
5. C2×C3⋊D3×#67C2semidirect
6. C22×#6292C2semidirect
7. C2×#89031C2semidirect
8. #11724589C2direct (N × H)
9. C2×D3×C4⋊(C3⋊D3)C2semidirect
10. C2×#89020C2semidirect
11. C2×#89018C2semidirect
12. C2×#89017C2semidirect
15. C23×C3⋊(C3⋊D3)C22semidirect
16. C23×C3×C3⋊D3C22semidirect
17. C22×D3×C3⋊D3C22semidirect
18. C2×C33×D4C22semidirect
19. C2×#6312C22semidirect
20. D4×C3⋊(C3⋊D3)C22semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
24. C3×D4×C3⋊D3C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C32×#67C22semidirect
28. C22×C32×Dic3C22semidirect
29. C32×#237C22semidirect
30. C2×C32×C4×D3C22semidirect
31. C2×C32×Dic6C22semidirect
32. #89039C22semidirect
33. C3⋊D3×#67C22semidirect
34. C2×#6293C22semidirect
35. C2×#6292C22semidirect
36. C2×#6292C22semidirect
37. C2×#6292C22semidirect
38. C2×#6292C22semidirect
39. C2×#6292C22semidirect
40. C2×#6291C22semidirect
41. C2×#6290C22semidirect
42. C2×#6289C22semidirect
43. #89031C22semidirect
44. C2×Dic3×C3⋊D3C22semidirect
45. D3×C4⋊(C3⋊D3)C22semidirect
46. #89020C22semidirect
47. #89018C22semidirect
48. #89017C22semidirect
58. C2×D4×C3⋊D3D3semidirect
63. C2×C3×#237D3semidirect
78. C22×C3⋊(C3⋊D3)C23semidirect
82. C22×C3×C3⋊D3C23semidirect
85. C2×D3×C3⋊D3C23semidirect
86. C33×D4C23semidirect
88. #6312C23semidirect
90. C4⋊(C3⋊(C3⋊D3))C23semidirect
91. C4×C3⋊(C3⋊D3)C23semidirect
92. C3×#638C23semidirect
94. C3×C4⋊(C3⋊D3)C23semidirect
95. C3×C4×C3⋊D3C23semidirect
96. C32×#67C23semidirect
99. C2×C32×Dic3C23semidirect
100. C32×C4×D3C23semidirect
101. C32×Dic6C23semidirect
102. #6293C23semidirect
103. #6292C23semidirect
104. #6292C23semidirect
105. #6292C23semidirect
106. #6292C23semidirect
107. #6291C23semidirect
108. #6290C23semidirect
109. #6289C23semidirect
110. Dic3×C3⋊D3C23semidirect
117. C23×C3⋊D3C2×D3semidirect
124. C2×C32×D4C2×D3semidirect
125. C2×C32×D4C2×D3semidirect
133. C2×#638C2×D3semidirect
141. D4×C3⋊D3C2×D3semidirect
153. C2×C4⋊(C3⋊D3)C2×D3semidirect
159. C2×C4×C3⋊D3C2×D3semidirect
162. C2×C3×#67C2×D3semidirect
163. C22×C3×Dic3C2×D3semidirect
164. C3×#237C2×D3semidirect
168. C2×C3×C4×D3C2×D3semidirect
169. C2×C3×Dic6C2×D3semidirect
218. C2×#237C3⋊D3semidirect
254. C22×C3⋊D3C22×D3semidirect
265. C32×D4C22×D3semidirect
266. C32×D4C22×D3semidirect
279. #638C22×D3semidirect
291. C4⋊(C3⋊D3)C22×D3semidirect
297. C4×C3⋊D3C22×D3semidirect
300. C3×#67C22×D3semidirect
304. C2×C3×Dic3C22×D3semidirect
307. C3×C4×D3C22×D3semidirect
308. C3×Dic6C22×D3semidirect
320. C2×C33H(5,𝔽2)semidirect
341. C2×C3×D4D32semidirect
342. C2×C3×D4C2×C3⋊D3semidirect
359. C2×#67C2×C3⋊D3semidirect
361. C22×Dic3C2×C3⋊D3semidirect
366. #237C2×C3⋊D3semidirect
397. C2×C4×D3C2×C3⋊D3semidirect
400. C2×Dic6C2×C3⋊D3semidirect
465. C33C2×H(5,𝔽2)semidirect
500. C3×D4C2×D32semidirect
501. C3×D4C22×C3⋊D3semidirect
522. #67C22×C3⋊D3semidirect
530. C2×Dic3C22×C3⋊D3semidirect
547. C4×D3C22×C3⋊D3semidirect
550. Dic6C22×C3⋊D3semidirect
557. C2×C32#1004semidirect
558. C2×C32#1009semidirect
599. C2×D4D3×C3⋊D3semidirect
659. C32C2×#1004semidirect
660. C32C2×#1009semidirect
686. D4C2×D3×C3⋊D3semidirect
706. C2×C3#64314semidirect
707. C2×C3#64366semidirect
741. C3C2×#64314semidirect
742. C3C2×#64366semidirect
749. C2#11724589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×C3×D4×C3⋊D32
C2×C32×#2372
C2×#890392
C2×C3⋊D3×#672
C22×#62922
C2×#890312
#117245892
C2×D3×C4⋊(C3⋊D3)2
C2×#890202
C2×#890182
C2×#890172
C2×#643663
C2×#643143