Finite Group Databasebeta

← C2×#11724578 #13181603

Subgroups — C2×#11724578 #13181603

Order 1728.

6284 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#3828C211yesmaximal, characteristic, complemented
3C2×C32×#235C211yesmaximal, characteristic, complemented
4C2×#89039C212yesmaximal, complemented
5C2×#89029C212yesmaximal, complemented
6#11724578C2116yesmaximal, direct product factor
7C2×#89026C211yesmaximal, characteristic, complemented
8C2×C4×D3×C3⋊D3C212yesmaximal, complemented
9C2×#89020C212yesmaximal, complemented
10C2×#89019C211yesmaximal, characteristic, complemented
11C2×#89017C211yesmaximal, characteristic, complemented
12C2×#89015C211yesmaximal, characteristic, complemented
13C2×#41×C3⋊D3—31nomaximal
14C2×#64306—34nomaximal
15C23×C3⋊(C3⋊D3)C2211yescharacteristic
16C22×D3×C3⋊D3C2212yes—
17C22×C33×C4C2211yescharacteristic, complemented
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2218yescomplemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×#638C2212yescomplemented
25C3×#3828C2218yescomplemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2212yescomplemented
28C2×C3×#634C2211yescharacteristic, complemented
29C2×C32×#67C2212yescomplemented
30C32×#235C2218yescomplemented
31C2×C32×D12C2211yescharacteristic, complemented
32C2×C32×C4×D3C2212yescomplemented
33C2×C32×Dic6C2211yescharacteristic, complemented
34#89039C22116yescomplemented
35C2×#6293C2212yescomplemented
36C2×#6292C2212yescomplemented
37C2×#6291C2212yescomplemented
38C2×#6290C2212yescomplemented
39C2×#6289C2212yes—
40C2×Dic3×C3⋊D3C2212yescomplemented
41#89029C22116yescomplemented
42C2×D3×C3⋊Dic3C2212yescomplemented
43#89026C2218yescomplemented
44C4×D3×C3⋊D3C22116yescomplemented
45#89020C22116yescomplemented
46#89019C2218yescomplemented
47#89017C2218yescomplemented
48#89015C2218yescomplemented
49C2×C32×#41—31no—
50#41×C3⋊D3—316no—
51C2×#3832—31no—
52C2×Q8×C3⋊D3—31no—
53C2×#3830—32no—
54C2×#3830—31no—
55C2×D4×C3⋊D3—32no—
56C2×D4×C3⋊D3—31no—
57C2×#3828—32no—
58C2×#3828D311yescharacteristic, complemented
59C22×C4×C3⋊D3—31no—
60C22×C4×C3⋊D3—32no—
61C22×C4×C3⋊D3—34no—
62C22×C4×C3⋊D3—64no—
63C2×C3×#235—34no—
64C2×C3×#235D314yescomplemented
65C2×#3811—38no—
66C2×#3805—38no—
67#64306—364no—
68C2×#3802—34no—
69C2×C4×D32—38no—
70C2×#3798—38no—
71C2×#3797—34no—
72C2×#3796—34no—
73C2×#3796—34no—
74C23×C33C2311yescharacteristic
75C22×C3⋊(C3⋊D3)—24no—
76C22×C3⋊(C3⋊D3)C2311yescharacteristic
77C22×C3⋊(C3⋊D3)C2314yes—
78C22×C3⋊(C3⋊D3)C2311yescharacteristic
79C22×C3×C3⋊D3C2312yes—
80C22×C32×D3C2312yes—
81C2×D3×C3⋊D3—28no—
82C2×D3×C3⋊D3C2318yes—
83C2×C33×C4C2311yescharacteristic
84C2×C33×C4C2311yescharacteristic
85C2×C33×C4C2314yescomplemented
86C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
87C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
88C2×C3⋊(C3⋊Dic3)C2314yescomplemented
89C4×C3⋊(C3⋊D3)C2314yes—
90C4×C3⋊(C3⋊D3)C2314yes—
91C4×C3⋊(C3⋊D3)C2314yescomplemented
92C4×C3⋊(C3⋊D3)C2314yescomplemented
93C3×#638C2318yescomplemented
94C2×C3×C3⋊Dic3C2312yes—
95C3×C4⋊(C3⋊D3)C2314yescomplemented
96C3×C4×C3⋊D3C2318yescomplemented
97C3×#634C2314yescomplemented
98C32×#67C2318yescomplemented
99C2×C32×Dic3C2312yes—
100C32×D12C2314yescomplemented
101C32×C4×D3C2318yescomplemented
102C32×Dic6C2314yescomplemented
103#6293C2318yescomplemented
104#6292C2318yescomplemented
105#6291C2318yescomplemented
106#6290C2318yescomplemented
107#6289C2318yes—
108Dic3×C3⋊D3C2318yescomplemented
109D3×C3⋊Dic3C2318yescomplemented
110C2×D3×#41—94no—
111C2×D3×#41—91no—
112C23×C3⋊D3—31no—
113C23×C3⋊D3—34no—
114C23×C3⋊D3—32no—
115C23×C3⋊D3—64no—
116C22×D32—38no—
117C32×#41—38no—
118C2×C32×Q8—31no—
119C2×C32×D4—32no—
120C2×C32×D4—31no—
121C22×C32×C4—24no—
122C22×C32×C4—32no—
123C22×C32×C4C2×D314yescomplemented
124C22×C32×C4C2×D311yescharacteristic, complemented
125C2×#638—32no—
126C2×#638—32no—
127C2×#638C2×D312yescomplemented
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—34no—
130C22×C3⋊Dic3—32no—
131C22×C3⋊Dic3—64no—
132#3832—38no—
133Q8×C3⋊D3—38no—
134#3830—316no—
135#3830—38no—
136D4×C3⋊D3—316no—
137D4×C3⋊D3—38no—
138#3828—316no—
139#3828C2×D318yescomplemented
140C2×C4⋊(C3⋊D3)—32no—
141C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
142C2×C4×C3⋊D3—32no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—34no—
148C2×C4×C3⋊D3—34no—
149C2×C4×C3⋊D3—34no—
150C2×C4×C3⋊D3—34no—
151C2×C4×C3⋊D3—38no—
152C2×C4×C3⋊D3—332no—
153C2×C4×C3⋊D3—32no—
154C2×C4×C3⋊D3—316no—
155C2×C4×C3⋊D3—64no—
156C2×C4×C3⋊D3—64no—
157C2×C4×C3⋊D3—632no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3—64no—
160C2×C4×C3⋊D3C2×D312yescomplemented
161C2×#634—32no—
162C2×#634C2×D311yescharacteristic, complemented
163C2×C3×#67—38no—
164C2×C3×#67C2×D318yescomplemented
165C3×#235—332no—
166C3×#235C2×D3132yescomplemented
167C2×C3×D12—34no—
168C2×C3×D12C2×D314yescomplemented
169C2×C3×C4×D3—38no—
170C2×C3×C4×D3C2×D318yescomplemented
171C2×C3×Dic6—34no—
172C2×C3×Dic6C2×D314yescomplemented
173#3811—364no—
174C2×#627—38no—
175C2×#626—38no—
176C2×#626—38no—
177C2×#625—38no—
178C2×#624—38no—
179#3805—364no—
180C2×D3×Dic3—38no—
181C2×D3×Dic3—38no—
182#3802—332no—
183C4×D32—364no—
184#3798—364no—
185#3797—332no—
186#3796—332no—
187#3796—332no—
188C22×C33—22no—
189C22×C33C2412yes—
190C22×C33C2411yescharacteristic
191C2×C3⋊(C3⋊D3)—22no—
192C2×C3⋊(C3⋊D3)—28no—
193C2×C3⋊(C3⋊D3)#4114yescomplemented
194C2×C3⋊(C3⋊D3)C2412yes—
195C2×C3⋊(C3⋊D3)C2412yes—
196C2×C3×C3⋊D3—24no—
197C2×C3×C3⋊D3C2414yes—
198C2×C32×D3—24no—
199C2×C32×D3C2414yes—
200D3×C3⋊D3—216no—
201C33×C4C2412yes—
202C33×C4C2412yes—
203C3⋊(C3⋊Dic3)C2412yes—
204C3⋊(C3⋊Dic3)C2412yes—
205C3×C3⋊Dic3C2414yes—
206C32×Dic3C2414yes—
207C2×C3×#41—34no—
208C2×C3×#41—91no—
209D3×#41—964no—
210D3×#41—916no—
211C2×#239—94no—
212C2×#239—91no—
213C2×D3×Q8—94no—
214C2×D3×Q8—91no—
215C2×#237—94no—
216C2×#237—98no—
217C2×#237—92no—
218C2×#237—91no—
219C2×D3×D4—94no—
220C2×D3×D4—98no—
221C2×D3×D4—92no—
222C2×D3×D4—91no—
223C2×#235—34no—
224C2×#235—98no—
225C2×#235—92no—
226C2×#235C3⋊D311yescharacteristic, complemented
227C22×C4×D3—98no—
228C22×C4×D3—94no—
229C22×C4×D3—91no—
230C22×C4×D3—92no—
231C22×C4×D3—184no—
232C23×C32—24no—
233C23×C32—32no—
234C23×C32C22×D314yes—
235C23×C32C22×D311yescharacteristic
236C22×C3⋊D3—31no—
237C22×C3⋊D3—31no—
238C22×C3⋊D3—34no—
239C22×C3⋊D3—38no—
240C22×C3⋊D3—34no—
241C22×C3⋊D3—34no—
242C22×C3⋊D3—316no—
243C22×C3⋊D3—64no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—616no—
246C22×C3⋊D3—68no—
247C22×C3⋊D3—64no—
248C22×C3⋊D3—616no—
249C22×C3⋊D3—632no—
250C22×C3⋊D3C22×D312yes—
251C22×C3×D3—38no—
252C22×C3×D3C22×D318yes—
253C2×D32—332no—
254C2×D32—632no—
255C32×Q8—34no—
256C32×D4—38no—
257C32×D4—34no—
258C2×C32×C4—24no—
259C2×C32×C4—24no—
260C2×C32×C4—216no—
261C2×C32×C4—32no—
262C2×C32×C4—38no—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D3116yescomplemented
268C2×C32×C4C22×D314yescomplemented
269#638—38no—
270#638—38no—
271#638C22×D318yescomplemented
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—38no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—316no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—616no—
282C2×C3⋊Dic3C22×D312yes—
283C4⋊(C3⋊D3)—38no—
284C4⋊(C3⋊D3)C22×D314yescomplemented
285C4×C3⋊D3—38no—
286C4×C3⋊D3—34no—
287C4×C3⋊D3—34no—
288C4×C3⋊D3—34no—
289C4×C3⋊D3—34no—
290C4×C3⋊D3—38no—
291C4×C3⋊D3—316no—
292C4×C3⋊D3—316no—
293C4×C3⋊D3—316no—
294C4×C3⋊D3—316no—
295C4×C3⋊D3—616no—
296C4×C3⋊D3—616no—
297C4×C3⋊D3—616no—
298C4×C3⋊D3—616no—
299C4×C3⋊D3C22×D318yescomplemented
300#634—38no—
301#634C22×D314yescomplemented
302C3×#67—332no—
303C3×#67C22×D3132yescomplemented
304C2×C3×Dic3—38no—
305C2×C3×Dic3C22×D318yes—
306C3×D12—316no—
307C3×D12C22×D3116yescomplemented
308C3×C4×D3—332no—
309C3×C4×D3C22×D3132yescomplemented
310C3×Dic6—316no—
311C3×Dic6C22×D3116yescomplemented
312#627—332no—
313#626—332no—
314#626—332no—
315#625—332no—
316#624—332no—
317D3×Dic3—332no—
318D3×Dic3—332no—
319C22×#41—271noSylow
320C2×C33—22no—
321C2×C33C2×#4112yescomplemented
322C2×C33C2511yescharacteristic
323C3⋊(C3⋊D3)—22no—
324C3⋊(C3⋊D3)C2×#4114yescomplemented
325C3×C3⋊D3—24no—
326C32×D3—24no—
327C23×D3—98no—
328C23×D3—94no—
329C23×D3—91no—
330C23×D3—92no—
331C23×D3—184no—
332C3×#41—332no—
333C3×#41—98no—
334C2×C3×Q8—34no—
335C2×C3×Q8—91no—
336C2×C3×D4—38no—
337C2×C3×D4—34no—
338C2×C3×D4—92no—
339C2×C3×D4—91no—
340C22×C3×C4—24no—
341C22×C3×C4—38no—
342C22×C3×C4—92no—
343C22×C3×C4D3214yescomplemented
344C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
345C2×#67—38no—
346C2×#67—98no—
347C2×#67—98no—
348C2×#67—92no—
349C2×#67—92no—
350C2×#67C2×C3⋊D312yescomplemented
351C22×Dic3—98no—
352C22×Dic3—94no—
353C22×Dic3—91no—
354C22×Dic3—92no—
355C22×Dic3—184no—
356#239—932no—
357#239—98no—
358D3×Q8—932no—
359D3×Q8—98no—
360#237—932no—
361#237—964no—
362#237—916no—
363#237—98no—
364D3×D4—932no—
365D3×D4—964no—
366D3×D4—916no—
367D3×D4—98no—
368#235—332no—
369#235—964no—
370#235—916no—
371#235C2×C3⋊D318yescomplemented
372C2×D12—34no—
373C2×D12—98no—
374C2×D12—92no—
375C2×D12C2×C3⋊D311yescharacteristic, complemented
376C2×C4×D3—38no—
377C2×C4×D3—964no—
378C2×C4×D3—98no—
379C2×C4×D3—98no—
380C2×C4×D3—92no—
381C2×C4×D3—94no—
382C2×C4×D3—94no—
383C2×C4×D3—94no—
384C2×C4×D3—94no—
385C2×C4×D3—932no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—98no—
391C2×C4×D3—92no—
392C2×C4×D3—916no—
393C2×C4×D3—184no—
394C2×C4×D3—184no—
395C2×C4×D3—184no—
396C2×C4×D3—184no—
397C2×C4×D3—1832no—
398C2×C4×D3C2×C3⋊D312yescomplemented
399C2×Dic6—34no—
400C2×Dic6—98no—
401C2×Dic6—92no—
402C2×Dic6C2×C3⋊D311yescharacteristic, complemented
403C22×C32—216no—
404C22×C32—28no—
405C22×C32—22no—
406C22×C32—28no—
407C22×C32—24no—
408C22×C32—34no—
409C22×C32—64no—
410C22×C32C23×D318yes—
411C22×C32C23×D314yes—
412C22×C32C23×D312yes—
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—24no—
415C2×C3⋊D3—34no—
416C2×C3⋊D3—32no—
417C2×C3⋊D3—32no—
418C2×C3⋊D3—316no—
419C2×C3⋊D3—38no—
420C2×C3⋊D3—38no—
421C2×C3⋊D3—616no—
422C2×C3⋊D3—68no—
423C2×C3⋊D3—68no—
424C2×C3⋊D3—616no—
425C2×C3⋊D3—68no—
426C2×C3⋊D3—632no—
427C2×C3⋊D3—664no—
428C2×C3⋊D3—616no—
429C2×C3⋊D3—68no—
430C2×C3⋊D3—62no—
431C2×C3⋊D3C23×D314yes—
432C2×C3×D3—216no—
433C2×C3×D3—316no—
434C2×C3×D3—616no—
435C2×C3×D3C23×D3116yes—
436D32—664no—
437C32×C4—28no—
438C32×C4—28no—
439C32×C4—34no—
440C32×C4C23×D318yes—
441C32×C4C23×D318yes—
442C32×C4C23×D312yes—
443C32×C4C23×D312yes—
444C3⋊Dic3—32no—
445C3⋊Dic3—32no—
446C3⋊Dic3—38no—
447C3⋊Dic3—38no—
448C3⋊Dic3—68no—
449C3⋊Dic3—68no—
450C3⋊Dic3C23×D314yes—
451C3×Dic3—316no—
452C3×Dic3C23×D3116yes—
453C2×#41—31no—
454C2×#41—91no—
455C2×#41—272no—
456C2×#41—272no—
457C2×#41—271no—
458C2×#41—271no—
459C2×#41—2716no—
460C22×Q8—271no—
461C22×D4—272no—
462C22×D4—271no—
463C23×C4—272no—
464C23×C4—271no—
465C33C22×#4111yescharacteristic, complemented, Sylow
466C23×C3—24no—
467C23×C3—38no—
468C23×C3—92no—
469C23×C3C2×D3214yes—
470C23×C3C22×C3⋊D311yescharacteristic
471C22×D3—38no—
472C22×D3—932no—
473C22×D3—94no—
474C22×D3—91no—
475C22×D3—94no—
476C22×D3—916no—
477C22×D3—91no—
478C22×D3—94no—
479C22×D3—98no—
480C22×D3—184no—
481C22×D3—184no—
482C22×D3—1816no—
483C22×D3—188no—
484C22×D3—1832no—
485C22×D3—1816no—
486C22×D3—184no—
487C22×D3—1832no—
488C22×D3C22×C3⋊D312yes—
489C3×Q8—316no—
490C3×Q8—94no—
491C3×D4—332no—
492C3×D4—316no—
493C3×D4—98no—
494C3×D4—94no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—216no—
498C2×C3×C4—38no—
499C2×C3×C4—332no—
500C2×C3×C4—92no—
501C2×C3×C4—98no—
502C2×C3×C4C2×D3214yes—
503C2×C3×C4C2×D3214yes—
504C2×C3×C4C2×D32116yescomplemented
505C2×C3×C4C22×C3⋊D311yescharacteristic
506C2×C3×C4C22×C3⋊D311yescharacteristic
507C2×C3×C4C22×C3⋊D314yescomplemented
508#67—332no—
509#67—932no—
510#67—932no—
511#67—98no—
512#67—98no—
513#67C22×C3⋊D318yescomplemented
514C2×Dic3—38no—
515C2×Dic3—932no—
516C2×Dic3—94no—
517C2×Dic3—94no—
518C2×Dic3—916no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—94no—
522C2×Dic3—98no—
523C2×Dic3—184no—
524C2×Dic3—184no—
525C2×Dic3—1816no—
526C2×Dic3C22×C3⋊D312yes—
527D12—316no—
528D12—932no—
529D12—98no—
530D12C22×C3⋊D314yescomplemented
531C4×D3—332no—
532C4×D3—932no—
533C4×D3—932no—
534C4×D3—98no—
535C4×D3—916no—
536C4×D3—916no—
537C4×D3—916no—
538C4×D3—916no—
539C4×D3—94no—
540C4×D3—94no—
541C4×D3—94no—
542C4×D3—94no—
543C4×D3—98no—
544C4×D3—1816no—
545C4×D3—1816no—
546C4×D3—1816no—
547C4×D3—1816no—
548C4×D3C22×C3⋊D318yescomplemented
549Dic6—316no—
550Dic6—932no—
551Dic6—98no—
552Dic6C22×C3⋊D314yescomplemented
553C2×C32—216no—
554C2×C32—28no—
555C2×C32—22no—
556C2×C32—28no—
557C2×C32—24no—
558C2×C32—64no—
559C2×C32D3×#4118yescomplemented
560C2×C32D3×#4112yescomplemented
561C2×C32C24×D314yes—
562C2×C32C24×D311yescharacteristic
563C3⋊D3—24no—
564C3⋊D3—34no—
565C3⋊D3—316no—
566C3⋊D3—616no—
567C3⋊D3—616no—
568C3⋊D3—68no—
569C3⋊D3—62no—
570C3×D3—216no—
571C3×D3—616no—
572C24—272no—
573C24—271no—
574#41—38no—
575#41—98no—
576#41—2716no—
577#41—2716no—
578#41—278no—
579#41—278no—
580C2×Q8—31no—
581C2×Q8—91no—
582C2×Q8—272no—
583C2×Q8—278no—
584C2×D4—32no—
585C2×D4—31no—
586C2×D4—92no—
587C2×D4—91no—
588C2×D4—272no—
589C2×D4—272no—
590C2×D4—2716no—
591C2×D4—278no—
592C2×D4—272no—
593C22×C4—32no—
594C22×C4—92no—
595C22×C4—272no—
596C22×C4—2716no—
597C22×C4—272no—
598C22×C4—272no—
599C22×C4—271no—
600C22×C4—271no—
601C22×C4—271no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—278no—
605C22×C4D3×C3⋊D311yescharacteristic, complemented
606C22×C3—216no—
607C22×C3—28no—
608C22×C3—22no—
609C22×C3—28no—
610C22×C3—24no—
611C22×C3—316no—
612C22×C3—616no—
613C22×C3—94no—
614C22×C3—184no—
615C22×C3C22×D3218yes—
616C22×C3C22×D3214yes—
617C22×C3C23×C3⋊D312yes—
618C22×C3C23×C3⋊D311yescharacteristic
619C2×D3—24no—
620C2×D3—316no—
621C2×D3—616no—
622C2×D3—916no—
623C2×D3—94no—
624C2×D3—98no—
625C2×D3—92no—
626C2×D3—98no—
627C2×D3—92no—
628C2×D3—188no—
629C2×D3—188no—
630C2×D3—1816no—
631C2×D3—1816no—
632C2×D3—1864no—
633C2×D3—1832no—
634C2×D3—188no—
635C2×D3—1864no—
636C2×D3—1816no—
637C2×D3—188no—
638C2×D3—182no—
639C2×D3C23×C3⋊D314yes—
640C3×C4—28no—
641C3×C4—28no—
642C3×C4—316no—
643C3×C4—94no—
644C3×C4C22×D3218yes—
645C3×C4C22×D3218yes—
646C3×C4C23×C3⋊D312yes—
647C3×C4C23×C3⋊D312yes—
648Dic3—316no—
649Dic3—98no—
650Dic3—98no—
651Dic3—92no—
652Dic3—92no—
653Dic3—188no—
654Dic3—188no—
655Dic3C23×C3⋊D314yes—
656C32—24no—
657C32C2×D3×#4114yescomplemented
658C32C2×D3×#4111yescharacteristic, complemented
659C23—32no—
660C23—92no—
661C23—278no—
662C23—271no—
663C23—274no—
664C23—271no—
665C23—544no—
666C23—548no—
667C23C2×D3×C3⋊D311yescharacteristic
668Q8—34no—
669Q8—94no—
670Q8—278no—
671D4—38no—
672D4—34no—
673D4—98no—
674D4—94no—
675D4—278no—
676D4—278no—
677D4—278no—
678C2×C4—32no—
679C2×C4—38no—
680C2×C4—92no—
681C2×C4—98no—
682C2×C4—278no—
683C2×C4—278no—
684C2×C4—278no—
685C2×C4—271no—
686C2×C4—271no—
687C2×C4—274no—
688C2×C4—274no—
689C2×C4—274no—
690C2×C4—274no—
691C2×C4—274no—
692C2×C4C2×D3×C3⋊D311yescharacteristic
693C2×C4C2×D3×C3⋊D311yescharacteristic
694C2×C4C2×D3×C3⋊D314yescomplemented
695C2×C3—216no—
696C2×C3—28no—
697C2×C3—22no—
698C2×C3—28no—
699C2×C3—24no—
700C2×C3—616no—
701C2×C3—184no—
702C2×C3#6430618yescomplemented
703C2×C3#41×C3⋊D312yescomplemented
704C2×C3C23×D3214yes—
705C2×C3C24×C3⋊D311yescharacteristic
706D3—24no—
707D3—616no—
708D3—916no—
709D3—94no—
710D3—1816no—
711D3—1816no—
712D3—188no—
713D3—182no—
714C22—22no—
715C22—34no—
716C22—64no—
717C22—94no—
718C22—184no—
719C22—274no—
720C22—272no—
721C22—272no—
722C22—548no—
723C22—5416no—
724C22—542no—
725C22C22×D3×C3⋊D312yes—
726C22C22×D3×C3⋊D311yescharacteristic
727C4—34no—
728C4—94no—
729C4—272no—
730C4—272no—
731C4C22×D3×C3⋊D312yes—
732C4C22×D3×C3⋊D312yes—
733C3—24no—
734C3C2×#6430614yescomplemented
735C3C2×#41×C3⋊D311yescharacteristic, complemented
736C2—22no—
737C2—64no—
738C2—184no—
739C2—274no—
740C2—542no—
741C2#1172457812yesdirect product factor
742C2C23×D3×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, cosocleC2×C33C25
FrattiniC2C23×D3×C3⋊D3
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊(C3⋊D3)C2semidirect
2. C2×C3×#3828C2semidirect
3. C2×C32×#235C2semidirect
4. C2×#89039C2semidirect
5. C2×#89029C2semidirect
6. #11724578C2direct (N × H)
7. C2×#89026C2semidirect
8. C2×C4×D3×C3⋊D3C2semidirect
9. C2×#89020C2semidirect
10. C2×#89019C2semidirect
11. C2×#89017C2semidirect
12. C2×#89015C2semidirect
17. C22×C33×C4C22semidirect
18. C22×C3⋊(C3⋊Dic3)C22semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×#638C22semidirect
25. C3×#3828C22semidirect
26. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×#634C22semidirect
29. C2×C32×#67C22semidirect
30. C32×#235C22semidirect
31. C2×C32×D12C22semidirect
32. C2×C32×C4×D3C22semidirect
33. C2×C32×Dic6C22semidirect
34. #89039C22semidirect
35. C2×#6293C22semidirect
36. C2×#6292C22semidirect
37. C2×#6291C22semidirect
38. C2×#6290C22semidirect
40. C2×Dic3×C3⋊D3C22semidirect
41. #89029C22semidirect
42. C2×D3×C3⋊Dic3C22semidirect
43. #89026C22semidirect
44. C4×D3×C3⋊D3C22semidirect
45. #89020C22semidirect
46. #89019C22semidirect
47. #89017C22semidirect
48. #89015C22semidirect
58. C2×#3828D3semidirect
64. C2×C3×#235D3semidirect
85. C2×C33×C4C23semidirect
88. C2×C3⋊(C3⋊Dic3)C23semidirect
91. C4×C3⋊(C3⋊D3)C23semidirect
92. C4×C3⋊(C3⋊D3)C23semidirect
93. C3×#638C23semidirect
95. C3×C4⋊(C3⋊D3)C23semidirect
96. C3×C4×C3⋊D3C23semidirect
97. C3×#634C23semidirect
98. C32×#67C23semidirect
100. C32×D12C23semidirect
101. C32×C4×D3C23semidirect
102. C32×Dic6C23semidirect
103. #6293C23semidirect
104. #6292C23semidirect
105. #6291C23semidirect
106. #6290C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. D3×C3⋊Dic3C23semidirect
123. C22×C32×C4C2×D3semidirect
124. C22×C32×C4C2×D3semidirect
127. C2×#638C2×D3semidirect
139. #3828C2×D3semidirect
141. C2×C4⋊(C3⋊D3)C2×D3semidirect
160. C2×C4×C3⋊D3C2×D3semidirect
162. C2×#634C2×D3semidirect
164. C2×C3×#67C2×D3semidirect
166. C3×#235C2×D3semidirect
168. C2×C3×D12C2×D3semidirect
170. C2×C3×C4×D3C2×D3semidirect
172. C2×C3×Dic6C2×D3semidirect
193. C2×C3⋊(C3⋊D3)#41semidirect
226. C2×#235C3⋊D3semidirect
267. C2×C32×C4C22×D3semidirect
268. C2×C32×C4C22×D3semidirect
271. #638C22×D3semidirect
284. C4⋊(C3⋊D3)C22×D3semidirect
299. C4×C3⋊D3C22×D3semidirect
301. #634C22×D3semidirect
303. C3×#67C22×D3semidirect
307. C3×D12C22×D3semidirect
309. C3×C4×D3C22×D3semidirect
311. C3×Dic6C22×D3semidirect
321. C2×C33C2×#41semidirect
324. C3⋊(C3⋊D3)C2×#41semidirect
343. C22×C3×C4D32semidirect
344. C22×C3×C4C2×C3⋊D3semidirect
350. C2×#67C2×C3⋊D3semidirect
371. #235C2×C3⋊D3semidirect
375. C2×D12C2×C3⋊D3semidirect
398. C2×C4×D3C2×C3⋊D3semidirect
402. C2×Dic6C2×C3⋊D3semidirect
465. C33C22×#41semidirect
504. C2×C3×C4C2×D32semidirect
507. C2×C3×C4C22×C3⋊D3semidirect
513. #67C22×C3⋊D3semidirect
530. D12C22×C3⋊D3semidirect
548. C4×D3C22×C3⋊D3semidirect
552. Dic6C22×C3⋊D3semidirect
559. C2×C32D3×#41semidirect
560. C2×C32D3×#41semidirect
605. C22×C4D3×C3⋊D3semidirect
657. C32C2×D3×#41semidirect
658. C32C2×D3×#41semidirect
694. C2×C4C2×D3×C3⋊D3semidirect
702. C2×C3#64306semidirect
703. C2×C3#41×C3⋊D3semidirect
734. C3C2×#64306semidirect
735. C3C2×#41×C3⋊D3semidirect
741. C2#11724578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊(C3⋊D3)2
C2×C3×#38282
C2×C32×#2352
C2×#890392
C2×#890292
#117245782
C2×#890262
C2×C4×D3×C3⋊D32
C2×#890202
C2×#890192
C2×#890172
C2×#890152
C2×#41×C3⋊D33
C2×#643063