Finite Group Databasebeta

← #11910719

Subgroups — #11910719

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 1193 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#123C211yesmaximal, characteristic, complemented
2C3×#5661C212yesmaximal, complemented
3#10595308C211yesmaximal, characteristic, complemented
4#10595260C212yesmaximal, complemented
5#10595241C211yesmaximal, characteristic, complemented
6#10595087C211yesmaximal, characteristic, complemented
7#10595030C211yesmaximal, characteristic, complemented
8#10595016C212yesmaximal, complemented
9#10594638C212yesmaximal, complemented
10#10594542C212yesmaximal, complemented
11#10594515C212yesmaximal, complemented
12#10594471C212yesmaximal, complemented
13#10594310C211yesmaximal, characteristic, complemented
14#10594279C212yesmaximal, complemented
15#10594226C212yesmaximal, complemented
16#10594205C212yesmaximal, complemented
17#10594100C212yesmaximal, complemented
18#10594040C212yesmaximal, complemented
19#10594036C211yesmaximal, characteristic, complemented
20#86914—32nomaximal
21C2×D4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×#3811C2211yescharacteristic
24C2×#3798C2212yes—
25C2×#3798C2211yescharacteristic, complemented
26C32×#123C2211yescharacteristic, complemented
27#64144C2211yescharacteristic, complemented
28#64138C2211yescharacteristic
29#64103C2212yes—
30C4⋊C4×C3⋊D3C2212yescomplemented
31#64095C2211yescharacteristic
32#64092C2212yescomplemented
33C22⋊C4×C3⋊D3C2212yes—
34C22⋊C4×C3⋊D3C2211yescharacteristic, complemented
35C3×#939C2212yes—
36C3×#938C2212yescomplemented
37C3×C4×#67C2212yescomplemented
38C3×C4×#67C2212yescomplemented
39C3×#898C2212yescomplemented
40C3×#893C2212yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#889C2212yescomplemented
43C3×#884C2212yescomplemented
44C3×#884C2212yescomplemented
45C3×#883C2212yescomplemented
46C3×#67⋊C4C2212yescomplemented
47C3×#879C2212yescomplemented
48C3×#877C2212yescomplemented
49#63983C2211yescharacteristic
50#63982C2212yescomplemented
51#63981C2212yes—
52#63981C2212yes—
53#63981C2212yescomplemented
54#63980C2212yescomplemented
55#63979C2211yescharacteristic
56#63979C2211yescharacteristic, complemented
57#63978C2212yes—
58#63975C2211yescharacteristic
59#63970C2212yescomplemented
60#63969C2212yescomplemented
61#63964C2212yescomplemented
62C2×#3722C2211yescharacteristic
63#63961C2212yescomplemented
64#63959C2212yescomplemented
65#63959C2212yescomplemented
66#63953C2211yescharacteristic
67#63953C2211yescharacteristic, complemented
68#63923C2211yescharacteristic
69#63922C2212yescomplemented
70D3×(C2×D3)⋊C4C2212yescomplemented
71#63918C2212yescomplemented
72#63916C2212yes—
73#63912C2212yescomplemented
74#63909C2212yes—
75#63908C2212yescomplemented
76#63905C2212yescomplemented
77#63905C2212yescomplemented
78#63904C2212yescomplemented
79C4×#626C2212yescomplemented
80C4×#626C2212yescomplemented
81C4×#626C2212yescomplemented
82#63899C2212yescomplemented
83#63897C2211yescharacteristic
84#63895C2212yescomplemented
85#63886C2212yescomplemented
86#63881C2212yes—
87#63877C2212yescomplemented
88#63874C2212yescomplemented
89#63868C2212yescomplemented
90#63868C2212yescomplemented
91#63865C2212yescomplemented
92#63865C2212yescomplemented
93#63861C2212yescomplemented
94#63853C2212yes—
95#63853C2212yes—
96#63853C2212yescomplemented
97#63852C2212yescomplemented
98#63852C2212yescomplemented
99#63851C2212yescomplemented
100#63851C2212yescomplemented
101#63850C2212yescomplemented
102#63850C2212yescomplemented
103#63849C2211yescharacteristic, complemented
104#63848C2212yescomplemented
105#63847C2212yescomplemented
106#63845C2212yescomplemented
107#63837C2212yescomplemented
108C3×#553—32no—
109#5712—32no—
110#5708—32no—
111#5704—32no—
112#5704—32no—
113#5693—32no—
114#5692—32no—
115#5662—32no—
116#5661D312yescomplemented
117#5654—32no—
118D3×#123—32no—
119D3×#123—61no—
120#5621—32no—
121#5621—32no—
122#5620—32no—
123#5615—32no—
124#5613—32no—
125#5612—32no—
126#5607—32no—
127#5605—32no—
128#5562—32no—
129#5560—32no—
130#5559—32no—
131#5556—32no—
132#5556—32no—
133#5551—32no—
134#5547—32no—
135#5547—32no—
136#5534—32no—
137#5527—32no—
138#5515—32no—
139#5507—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C22×D32C2311yescharacteristic
143C2×C32×D4C2311yescharacteristic
144C22×C32×C4C2311yescharacteristic
145C2×#638C2311yescharacteristic
146C2×#638C2311yescharacteristic
147C22×C3⋊Dic3C2311yescharacteristic
148D4×C3⋊D3—42no—
149C2×C4⋊(C3⋊D3)C2311yescharacteristic
150C2×C4×C3⋊D3—42no—
151C2×C4×C3⋊D3C2312yes—
152C2×C4×C3⋊D3C2311yescharacteristic
153C2×C4×C3⋊D3C2312yes—
154C2×C4×C3⋊D3C2312yes—
155C2×C3×#67C2312yes—
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C22×C3×Dic3C2312yes—
160C2×C3×D12C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×C4×D3C2312yes—
163C2×C3×C4×D3C2312yes—
164C2×C3×C4×D3C2312yes—
165#3811—42no—
166C2×#627C2312yes—
167C2×#627C2311yescharacteristic
168C2×#627C2312yes—
169C2×#626C2312yes—
170C2×#626C2312yes—
171C2×#626C2312yes—
172C2×#626C2312yes—
173C2×#626C2312yes—
174C2×#625C2312yes—
175C2×#625C2311yescharacteristic
176C2×#624C2311yescharacteristic
177C2×D3×Dic3C2312yes—
178#3798—44no—
179#3798—42no—
180C32×C4⋊C4C2312yes—
181C32×C22⋊C4C2312yes—
182C32×C22⋊C4C2311yescharacteristic
183#3757C2312yes—
184#3757C2311yescharacteristic
185#3752C2312yes—
186#3752C2312yes—
187#3752C2312yes—
188C4⋊(C3⋊Dic3)C2312yes—
189#3750C2312yes—
190#3750C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×C4×Dic3C2312yes—
207C3×C4×Dic3C2312yes—
208C3×C4×Dic3C2312yes—
209#3724C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216#3722C2312yes—
217#3722C2312yes—
218#3722C2312yes—
219#3722C2311yescharacteristic
220#3722C2311yescharacteristic
221#3722C2312yes—
222#3722C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2311yescharacteristic
230Dic32C2312yes—
231Dic32C2311yescharacteristic
232#3533—91noSylow
233C2×D3×D4—32no—
234C2×D3×D4—32no—
235C2×D3×D4—61no—
236C2×#235—32no—
237C2×#235—32no—
238C2×#235—32no—
239C22×C4×D3—32no—
240C22×C4×D3—61no—
241C3×#126—32no—
242C3×#126—32no—
243C3×#125—32no—
244C3×#123—21no—
245C3×#123—32no—
246C3×#123C2×D312yescomplemented
247C3×#121—32no—
248C3×#121—32no—
249C3×#121—32no—
250C3×#121—32no—
251C3×C4×D4—32no—
252C3×C4×D4—32no—
253C3×C4×D4—32no—
254C3×C4×D4—32no—
255C3×#117—32no—
256C2×C3×C4⋊C4—32no—
257#940—32no—
258#940—32no—
259#939—32no—
260#939—32no—
261#939—32no—
262#939—32no—
263#939—32no—
264#939C2×D312yes—
265#938—32no—
266#938—32no—
267#938—32no—
268#938C2×D312yescomplemented
269#937—32no—
270#937—32no—
271#937—32no—
272#937—32no—
273#937—32no—
274#936—32no—
275#936—32no—
276#935—32no—
277#935—32no—
278#935—32no—
279#935—61no—
280#930—32no—
281#930—32no—
282#930—32no—
283#929—32no—
284#929—32no—
285#929—32no—
286#929—32no—
287#929—32no—
288#929—32no—
289#929—61no—
290C4×#67—32no—
291C4×#67—32no—
292C4×#67—32no—
293C4×#67—32no—
294C4×#67C2×D312yescomplemented
295C4×#67C2×D312yescomplemented
296C2×(C2×D3)⋊C4—32no—
297C2×(C2×D3)⋊C4—32no—
298#924—32no—
299#924—32no—
300#924—32no—
301#898—32no—
302#898—32no—
303#898—32no—
304#898—32no—
305#898—32no—
306#898C2×D312yescomplemented
307#897—32no—
308#896—32no—
309#896—32no—
310#896—32no—
311#896—32no—
312#896—32no—
313#896—32no—
314#896—32no—
315#896—32no—
316#895—32no—
317#895—32no—
318#895—32no—
319#894—32no—
320#894—32no—
321#894—32no—
322#894—32no—
323#894—32no—
324#894—32no—
325#894—32no—
326#894—32no—
327#894—62no—
328#893—32no—
329#893—32no—
330#893C2×D312yescomplemented
331#892—32no—
332D3×C4⋊C4—32no—
333D3×C4⋊C4—32no—
334D3×C4⋊C4—62no—
335D3×C4⋊C4C2×D312yescomplemented
336#890—32no—
337#889—32no—
338#889—32no—
339#889—32no—
340#889C2×D312yescomplemented
341#888—32no—
342#887—32no—
343#886—32no—
344#886—61no—
345#885—32no—
346#885—32no—
347#885—32no—
348#885—32no—
349#885—32no—
350#885—32no—
351#884—32no—
352#884—32no—
353#884C2×D312yescomplemented
354#884C2×D312yescomplemented
355#883—32no—
356#883—32no—
357#883—32no—
358#883—32no—
359#883—32no—
360#883—32no—
361#883—32no—
362#883—32no—
363#883—32no—
364#883—62no—
365#883C2×D312yescomplemented
366#882—32no—
367#882—32no—
368#882—32no—
369#882—32no—
370#882—32no—
371#67⋊C4—32no—
372#67⋊C4C2×D312yescomplemented
373D3×C22⋊C4—32no—
374D3×C22⋊C4—32no—
375D3×C22⋊C4—32no—
376D3×C22⋊C4—32no—
377D3×C22⋊C4—62no—
378D3×C22⋊C4—61no—
379#879—32no—
380#879C2×D312yescomplemented
381#878—32no—
382#878—32no—
383#878—32no—
384#878—32no—
385#877—32no—
386#877C2×D312yescomplemented
387#876—32no—
388#876—32no—
389#875—32no—
390#875—32no—
391C4×D12—32no—
392C4×D12—32no—
393C4×D12—32no—
394#872—32no—
395#872—32no—
396#872—32no—
397#869—32no—
398C4×Dic6—32no—
399C23×C32C2411yescharacteristic
400C23×C32C2411yescharacteristic
401C22×C3⋊D3—22no—
402C22×C3⋊D3—22no—
403C22×C3⋊D3—42no—
404C22×C3⋊D3—42no—
405C22×C3⋊D3C2411yescharacteristic
406C22×C3⋊D3C2411yescharacteristic
407C22×C3⋊D3C2411yescharacteristic
408C22×C3×D3C2412yes—
409C22×C3×D3C2412yes—
410C2×D32—42no—
411C2×D32—41no—
412C32×D4—41no—
413C2×C32×C4—41no—
414C2×C32×C4C2412yes—
415C2×C32×C4C2412yes—
416C2×C32×C4C2411yescharacteristic
417#638—41no—
418#638—41no—
419C2×C3⋊Dic3—41no—
420C2×C3⋊Dic3C2411yescharacteristic
421C2×C3⋊Dic3C2412yes—
422C2×C3⋊Dic3C2412yes—
423C4⋊(C3⋊D3)—41no—
424C4×C3⋊D3—24no—
425C4×C3⋊D3—22no—
426C4×C3⋊D3—42no—
427C4×C3⋊D3—42no—
428C3×#67—42no—
429C3×#67—42no—
430C3×#67—42no—
431C3×#67—42no—
432C2×C3×Dic3—42no—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C2×C3×Dic3C2412yes—
437C2×C3×Dic3C2412yes—
438C2×C3×Dic3C2412yes—
439C3×D12—42no—
440C3×C4×D3—42no—
441C3×C4×D3—42no—
442C3×C4×D3—42no—
443C3×C4×D3—42no—
444#627—42no—
445#627—41no—
446#627—42no—
447#626—24no—
448#626—24no—
449#626—42no—
450#626—42no—
451#626—42no—
452#625—42no—
453#625—41no—
454#624—41no—
455D3×Dic3—42no—
456#563—91no—
457#562—92no—
458#560—91no—
459#559—91no—
460#553—32no—
461#552—92no—
462#551—92no—
463#551—91no—
464#547—92no—
465#546—92no—
466#542—92no—
467#540—92no—
468#539—92no—
469#538—92no—
470#538—92no—
471#535—91no—
472#534—91no—
473#525—92no—
474C2×#123—91no—
475C23×D3—32no—
476C23×D3—32no—
477C23×D3—32no—
478C23×D3—61no—
479C23×D3—61no—
480C2×C3×D4—21no—
481C2×C3×D4—32no—
482C2×C3×D4—32no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4—32no—
486C2×C3×D4C22×D312yes—
487C22×C3×C4—21no—
488C22×C3×C4—32no—
489C22×C3×C4—32no—
490C22×C3×C4—32no—
491C22×C3×C4—32no—
492C22×C3×C4—32no—
493C22×C3×C4C22×D312yes—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—32no—
504C2×#67—61no—
505C2×#67—61no—
506C2×#67C22×D312yes—
507C2×#67C22×D312yes—
508C2×#67C22×D312yes—
509C2×#67C22×D312yes—
510C22×Dic3—32no—
511C22×Dic3—32no—
512C22×Dic3—61no—
513C22×Dic3C22×D312yes—
514D3×D4—124no—
515D3×D4—124no—
516D3×D4—124no—
517#235—124no—
518#235—124no—
519#235—124no—
520C2×D12—32no—
521C2×D12—32no—
522C2×D12—32no—
523C2×D12—32no—
524C2×D12—32no—
525C2×D12—32no—
526C2×D12—61no—
527C2×D12C22×D312yes—
528C2×C4×D3—32no—
529C2×C4×D3—32no—
530C2×C4×D3—32no—
531C2×C4×D3—32no—
532C2×C4×D3—32no—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—62no—
538C2×C4×D3—62no—
539C2×C4×D3—62no—
540C2×C4×D3—61no—
541C2×C4×D3—124no—
542C2×C4×D3—124no—
543C2×C4×D3C22×D312yes—
544C2×C4×D3C22×D312yes—
545C2×C4×D3C22×D312yes—
546C2×C4×D3C22×D312yes—
547C2×Dic6—32no—
548C2×Dic6—32no—
549C2×Dic6—32no—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C3×C4⋊C4—22no—
553C3×C4⋊C4—32no—
554C3×C4⋊C4—32no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4C22×D312yes—
562C3×C4⋊C4C22×D312yes—
563C3×C22⋊C4—22no—
564C3×C22⋊C4—21no—
565C3×C22⋊C4—32no—
566C3×C22⋊C4—32no—
567C3×C22⋊C4—32no—
568C3×C22⋊C4—32no—
569C3×C22⋊C4—32no—
570C3×C22⋊C4—32no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4C22×D312yes—
573C3×C22⋊C4C22×D312yes—
574C3×C22⋊C4C22×D312yes—
575C3×C42—32no—
576C3×C42—32no—
577C3×C42—32no—
578#217—32no—
579#217—32no—
580#217—32no—
581#217—32no—
582#217—32no—
583#217—32no—
584#217—32no—
585#217—32no—
586#217—32no—
587#217—62no—
588#217—61no—
589#217C22×D312yes—
590#217C22×D312yes—
591#217C22×D312yes—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—62no—
617(C2×D3)⋊C4—62no—
618(C2×D3)⋊C4—62no—
619(C2×D3)⋊C4C22×D312yes—
620(C2×D3)⋊C4C22×D312yes—
621(C2×D3)⋊C4C22×D312yes—
622(C2×D3)⋊C4C22×D312yes—
623C4⋊Dic3—32no—
624C4⋊Dic3—32no—
625C4⋊Dic3—32no—
626C4⋊Dic3—32no—
627C4⋊Dic3—32no—
628C4⋊Dic3—32no—
629C4⋊Dic3—62no—
630C4⋊Dic3C22×D312yes—
631C4⋊Dic3C22×D312yes—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4—32no—
646Dic3⋊C4—62no—
647Dic3⋊C4—62no—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3C22×D312yes—
659C4×Dic3C22×D312yes—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32C2511yescharacteristic
666C2×C3⋊D3—22no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—21no—
669C2×C3⋊D3—22no—
670C2×C3⋊D3—22no—
671C2×C3⋊D3—44no—
672C2×C3⋊D3—82no—
673C2×C3⋊D3H(5,𝔽2)12yes—
674C2×C3×D3—22no—
675C2×C3×D3—22no—
676C2×C3×D3—22no—
677C2×C3×D3—22no—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680D32—82no—
681C32×C4—22no—
682C32×C4—21no—
683C32×C4—22no—
684C3⋊Dic3—22no—
685C3⋊Dic3—21no—
686C3⋊Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C2×#41—92no—
694C2×#41—91no—
695C22×D4—91no—
696C22×D4—91no—
697C23×C4—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127—91no—
701#126—32no—
702#126—32no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—32no—
708#125—92no—
709#125—92no—
710#124—92no—
711#124—92no—
712#124—91no—
713#124—91no—
714#124—92no—
715#124—92no—
716#123—32no—
717#123—91no—
718#123—92no—
719#123—92no—
720#123—92no—
721#123—92no—
722#123—92no—
723#123—92no—
724#123—91no—
725#123—92no—
726#123—92no—
727#123—92no—
728#123—91no—
729#123—91no—
730#123—92no—
731#123—92no—
732#123—91no—
733#123D3211yescharacteristic, complemented
734C22⋊Q8—92no—
735C22⋊Q8—92no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742#121—32no—
743#121—32no—
744#121—32no—
745#121—32no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#120—91no—
755#120—92no—
756#120—92no—
757#120—92no—
758#120—92no—
759#120—91no—
760C4×Q8—92no—
761C4×D4—32no—
762C4×D4—32no—
763C4×D4—32no—
764C4×D4—32no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770#117—32no—
771#117—92no—
772#117—92no—
773#117—91no—
774C2×C4⋊C4—32no—
775C2×C4⋊C4—92no—
776C2×C22⋊C4—92no—
777C2×C22⋊C4—91no—
778C2×C22⋊C4—91no—
779C2×C22⋊C4—92no—
780C23×C3—21no—
781C23×C3—21no—
782C23×C3—32no—
783C23×C3—32no—
784C23×C3C23×D312yes—
785C23×C3C23×D312yes—
786C22×D3—32no—
787C22×D3—32no—
788C22×D3—32no—
789C22×D3—61no—
790C22×D3—61no—
791C22×D3—61no—
792C22×D3—64no—
793C22×D3—64no—
794C22×D3—64no—
795C22×D3—122no—
796C22×D3—122no—
797C22×D3—122no—
798C22×D3—122no—
799C22×D3—122no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3—124no—
804C22×D3—124no—
805C22×D3C23×D312yes—
806C22×D3C23×D312yes—
807C3×D4—42no—
808C3×D4—42no—
809C3×D4—122no—
810C3×D4—122no—
811C3×D4—122no—
812C3×D4—122no—
813C3×D4—122no—
814C2×C3×C4—21no—
815C2×C3×C4—22no—
816C2×C3×C4—22no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—32no—
823C2×C3×C4—42no—
824C2×C3×C4—42no—
825C2×C3×C4—122no—
826C2×C3×C4—122no—
827C2×C3×C4—122no—
828C2×C3×C4—122no—
829C2×C3×C4—122no—
830C2×C3×C4C23×D312yes—
831C2×C3×C4C23×D312yes—
832C2×C3×C4C23×D312yes—
833C2×C3×C4C23×D312yes—
834C2×C3×C4C23×D312yes—
835#67—42no—
836#67—42no—
837#67—42no—
838#67—42no—
839#67—64no—
840#67—64no—
841#67—122no—
842#67—122no—
843#67—122no—
844#67—122no—
845#67—122no—
846#67—122no—
847#67—122no—
848#67—122no—
849#67—122no—
850#67—122no—
851C2×Dic3—32no—
852C2×Dic3—32no—
853C2×Dic3—32no—
854C2×Dic3—32no—
855C2×Dic3—32no—
856C2×Dic3—42no—
857C2×Dic3—61no—
858C2×Dic3—62no—
859C2×Dic3—62no—
860C2×Dic3—122no—
861C2×Dic3—122no—
862C2×Dic3—122no—
863C2×Dic3C23×D312yes—
864C2×Dic3C23×D312yes—
865C2×Dic3C23×D312yes—
866C2×Dic3C23×D312yes—
867C2×Dic3C23×D312yes—
868C2×Dic3C23×D312yes—
869D12—42no—
870D12—64no—
871D12—64no—
872D12—122no—
873D12—122no—
874D12—122no—
875D12—122no—
876D12—122no—
877C4×D3—42no—
878C4×D3—42no—
879C4×D3—42no—
880C4×D3—42no—
881C4×D3—64no—
882C4×D3—64no—
883C4×D3—64no—
884C4×D3—124no—
885C4×D3—122no—
886C4×D3—122no—
887C4×D3—122no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891C4×D3—122no—
892C4×D3—124no—
893C4×D3—124no—
894Dic6—122no—
895Dic6—122no—
896Dic6—122no—
897Dic6—122no—
898Dic6—122no—
899C2×C32—41no—
900C2×C32—41no—
901C2×C32C2×H(5,𝔽2)11yescharacteristic
902C2×C32#58512yes—
903C3⋊D3—22no—
904C3⋊D3—41no—
905C3⋊D3—41no—
906C3×D3—42no—
907C3×D3—42no—
908C24—91no—
909C24—91no—
910C24—91no—
911#41—364no—
912#41—362no—
913C2×Q8—92no—
914C2×Q8—92no—
915C2×Q8—91no—
916C2×D4—32no—
917C2×D4—32no—
918C2×D4—32no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—92no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—91no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—91no—
931C2×D4—362no—
932C2×D4—362no—
933C2×D4C2×D3211yescharacteristic
934C22×C4—32no—
935C22×C4—32no—
936C22×C4—32no—
937C22×C4—32no—
938C22×C4—32no—
939C22×C4—91no—
940C22×C4—92no—
941C22×C4—91no—
942C22×C4—92no—
943C22×C4—91no—
944C22×C4—92no—
945C22×C4—92no—
946C22×C4—362no—
947C22×C4C2×D3211yescharacteristic
948C4⋊C4—32no—
949C4⋊C4—32no—
950C4⋊C4—32no—
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—92no—
957C4⋊C4—92no—
958C4⋊C4—92no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4—92no—
965C4⋊C4—92no—
966C4⋊C4C2×D3212yes—
967C22⋊C4—32no—
968C22⋊C4—32no—
969C22⋊C4—32no—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—92no—
975C22⋊C4—92no—
976C22⋊C4—91no—
977C22⋊C4—91no—
978C22⋊C4—92no—
979C22⋊C4—92no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—92no—
983C22⋊C4—92no—
984C22⋊C4—92no—
985C22⋊C4—92no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—91no—
989C22⋊C4—92no—
990C22⋊C4—92no—
991C22⋊C4—92no—
992C22⋊C4C2×D3212yes—
993C22⋊C4C2×D3211yescharacteristic
994C42—32no—
995C42—32no—
996C42—32no—
997C42—91no—
998C42—91no—
999C42—92no—
1000C22×C3—22no—
1001C22×C3—22no—
1002C22×C3—22no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—21no—
1008C22×C3—42no—
1009C22×C3—41no—
1010C22×C3—42no—
1011C22×C3—62no—
1012C22×C3—62no—
1013C22×C3—62no—
1014C22×C3—62no—
1015C22×C3—62no—
1016C22×C3—62no—
1017C22×C3C24×D312yes—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—34no—
1025C2×D3—62no—
1026C2×D3—64no—
1027C2×D3—62no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—122no—
1037C2×D3—121no—
1038C2×D3—122no—
1039C2×D3—128no—
1040C2×D3—128no—
1041C2×D3—244no—
1042C2×D3—244no—
1043C2×D3—244no—
1044C3×C4—22no—
1045C3×C4—22no—
1046C3×C4—22no—
1047C3×C4—22no—
1048C3×C4—22no—
1049C3×C4—42no—
1050C3×C4—41no—
1051C3×C4—42no—
1052C3×C4—62no—
1053C3×C4—62no—
1054C3×C4—62no—
1055C3×C4—62no—
1056C3×C4—62no—
1057C3×C4—62no—
1058Dic3—22no—
1059Dic3—22no—
1060Dic3—22no—
1061Dic3—22no—
1062Dic3—22no—
1063Dic3—22no—
1064Dic3—62no—
1065Dic3—62no—
1066Dic3—62no—
1067Dic3—62no—
1068Dic3—62no—
1069Dic3—122no—
1070Dic3—121no—
1071Dic3—122no—
1072C32#353311yescharacteristic, complemented, Sylow
1073C23—32no—
1074C23—32no—
1075C23—91no—
1076C23—91no—
1077C23—91no—
1078C23—182no—
1079C23—182no—
1080C23—362no—
1081C23—362no—
1082C23—361no—
1083C23—362no—
1084C23C22×D3211yescharacteristic
1085C23C22×D3211yescharacteristic
1086Q8—361no—
1087Q8—362no—
1088Q8—362no—
1089D4—41no—
1090D4—122no—
1091D4—122no—
1092D4—122no—
1093D4—122no—
1094D4—122no—
1095D4—184no—
1096D4—184no—
1097D4—361no—
1098D4—362no—
1099D4—362no—
1100D4—362no—
1101D4—361no—
1102D4—361no—
1103D4—362no—
1104D4—361no—
1105C2×C4—32no—
1106C2×C4—32no—
1107C2×C4—32no—
1108C2×C4—32no—
1109C2×C4—32no—
1110C2×C4—32no—
1111C2×C4—41no—
1112C2×C4—91no—
1113C2×C4—92no—
1114C2×C4—92no—
1115C2×C4—122no—
1116C2×C4—122no—
1117C2×C4—122no—
1118C2×C4—122no—
1119C2×C4—122no—
1120C2×C4—184no—
1121C2×C4—182no—
1122C2×C4—362no—
1123C2×C4—362no—
1124C2×C4—361no—
1125C2×C4—362no—
1126C2×C4—361no—
1127C2×C4C22×D3212yes—
1128C2×C4C22×D3212yes—
1129C2×C4C22×D3211yescharacteristic
1130C2×C3—21no—
1131C2×C3—22no—
1132C2×C3—42no—
1133C2×C3—42no—
1134C2×C3—42no—
1135C2×C3—81no—
1136C2×C3—122no—
1137C2×C3—122no—
1138C2×C3#596412yes—
1139C2×C3#596412yes—
1140C2×C3D3×H(5,𝔽2)12yes—
1141D3—42no—
1142D3—42no—
1143D3—64no—
1144D3—64no—
1145D3—122no—
1146D3—122no—
1147D3—122no—
1148D3—241no—
1149C22—21no—
1150C22—21no—
1151C22—22no—
1152C22—22no—
1153C22—62no—
1154C22—62no—
1155C22—62no—
1156C22—62no—
1157C22—62no—
1158C22—62no—
1159C22—92no—
1160C22—182no—
1161C22—181no—
1162C22—181no—
1163C22—182no—
1164C22—182no—
1165C22—364no—
1166C22—722no—
1167C22—722no—
1168C22C23×D3211yescharacteristic
1169C4—22no—
1170C4—21no—
1171C4—22no—
1172C4—62no—
1173C4—62no—
1174C4—62no—
1175C4—62no—
1176C4—62no—
1177C4—62no—
1178C4—182no—
1179C4—181no—
1180C4—182no—
1181C3—21no—
1182C3#8691412yescomplemented
1183C2—41no—
1184C2—41no—
1185C2—122no—
1186C2—122no—
1187C2—182no—
1188C2—361no—
1189C2—361no—
1190C2#1059667511yescharacteristic
1191C2#1059669512yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#123C2semidirect
2. C3×#5661C2semidirect
3. #10595308C2semidirect
4. #10595260C2semidirect
5. #10595241C2semidirect
6. #10595087C2semidirect
7. #10595030C2semidirect
8. #10595016C2semidirect
9. #10594638C2semidirect
10. #10594542C2semidirect
11. #10594515C2semidirect
12. #10594471C2semidirect
13. #10594310C2semidirect
14. #10594279C2semidirect
15. #10594226C2semidirect
16. #10594205C2semidirect
17. #10594100C2semidirect
18. #10594040C2semidirect
19. #10594036C2semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C2×#3798C22semidirect
26. C32×#123C22semidirect
27. #64144C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
32. #64092C22semidirect
34. C22⋊C4×C3⋊D3C22semidirect
36. C3×#938C22semidirect
37. C3×C4×#67C22semidirect
38. C3×C4×#67C22semidirect
39. C3×#898C22semidirect
40. C3×#893C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#889C22semidirect
43. C3×#884C22semidirect
44. C3×#884C22semidirect
45. C3×#883C22semidirect
46. C3×#67⋊C4C22semidirect
47. C3×#879C22semidirect
48. C3×#877C22semidirect
50. #63982C22semidirect
53. #63981C22semidirect
54. #63980C22semidirect
56. #63979C22semidirect
59. #63970C22semidirect
60. #63969C22semidirect
61. #63964C22semidirect
63. #63961C22semidirect
64. #63959C22semidirect
65. #63959C22semidirect
67. #63953C22semidirect
69. #63922C22semidirect
70. D3×(C2×D3)⋊C4C22semidirect
71. #63918C22semidirect
73. #63912C22semidirect
75. #63908C22semidirect
76. #63905C22semidirect
77. #63905C22semidirect
78. #63904C22semidirect
79. C4×#626C22semidirect
80. C4×#626C22semidirect
81. C4×#626C22semidirect
82. #63899C22semidirect
84. #63895C22semidirect
85. #63886C22semidirect
87. #63877C22semidirect
88. #63874C22semidirect
89. #63868C22semidirect
90. #63868C22semidirect
91. #63865C22semidirect
92. #63865C22semidirect
93. #63861C22semidirect
96. #63853C22semidirect
97. #63852C22semidirect
98. #63852C22semidirect
99. #63851C22semidirect
100. #63851C22semidirect
101. #63850C22semidirect
102. #63850C22semidirect
103. #63849C22semidirect
104. #63848C22semidirect
105. #63847C22semidirect
106. #63845C22semidirect
107. #63837C22semidirect
116. #5661D3semidirect
246. C3×#123C2×D3semidirect
268. #938C2×D3semidirect
294. C4×#67C2×D3semidirect
295. C4×#67C2×D3semidirect
306. #898C2×D3semidirect
330. #893C2×D3semidirect
335. D3×C4⋊C4C2×D3semidirect
340. #889C2×D3semidirect
353. #884C2×D3semidirect
354. #884C2×D3semidirect
365. #883C2×D3semidirect
372. #67⋊C4C2×D3semidirect
380. #879C2×D3semidirect
386. #877C2×D3semidirect
733. #123D32semidirect
1072. C32#3533semidirect
1182. C3#86914semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1232
C3×#56612
#105953082
#105952602
#105952412
#105950872
#105950302
#105950162
#105946382
#105945422
#105945152
#105944712
#105943102
#105942792
#105942262
#105942052
#105941002
#105940402
#105940362
#869143