Finite Group Databasebeta

← #11909785

Subgroups — #11909785

Order 1152.

2364 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic, complemented
3C3×#5543C211yesmaximal, characteristic, complemented
4#10595210C212yesmaximal, complemented
5#10595131C212yesmaximal, complemented
6#10594990C212yesmaximal, complemented
7#10594916C212yesmaximal, complemented
8#10594906C212yesmaximal, complemented
9#10594814C212yesmaximal, complemented
10#10594484C212yesmaximal, complemented
11#10594453C212yesmaximal, complemented
12#10594064C214yesmaximal, complemented
13#10594032C214yesmaximal, complemented
14#10593970C211yesmaximal, characteristic, complemented
15#10593963C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86936—31nomaximal
19#86128—31nomaximal
20C2×#3828C2212yes—
21C2×#3804C2214yes—
22C2×#3799C2212yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25#64149C2212yes—
26#64139C2212yes—
27#64102C2212yes—
28#64093C2214yes—
29#64083C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C3×#936C2211yescharacteristic
33C3×D4×Dic3C2212yes—
34C3×C4×#67C2212yes—
35C3×#926C2212yes—
36C2×C3×C4⋊Dic3C2212yes—
37C3×#924C2212yes—
38C3×#897C2211yescharacteristic
39C3×#890C2212yes—
40C3×#890C2211yescharacteristic
41C3×#883C2212yes—
42C3×#879C2212yes—
43C3×#878C2214yes—
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48#63975C2214yes—
49#63971C2214yes—
50#63966C2214yes—
51#63953C2214yes—
52#63953C2214yes—
53#63952C2214yes—
54#63952C2214yes—
55#63919C2212yes—
56#63918C2212yes—
57C4×#627C2212yes—
58#63909C2212yes—
59#63909C2212yes—
60#63900C2214yes—
61#63897C2214yes—
62#63895C2214yes—
63#63895C2214yes—
64#63894C2212yes—
65#63894C2212yes—
66#63894C2212yes—
67#63894C2212yes—
68#63890C2214yes—
69D3×C4⋊Dic3C2211yescharacteristic
70#63881C2214yes—
71D3×Dic3⋊C4C2212yes—
72C4×D3×Dic3C2212yes—
73#63865C2214yes—
74#63864C2212yes—
75#63864C2212yes—
76#63864C2212yes—
77#63849C2214yes—
78#63848C2214yes—
79#63844C2212yes—
80#63844C2211yescharacteristic
81#63843C2212yes—
82Dic3×Dic6C2211yescharacteristic
83#63839C2214yes—
84#63837C2212yes—
85C3×#554—31no—
86C3×#529—31no—
87#5725—31no—
88#5722—31no—
89#5710—34no—
90#5691—32no—
91#5690—32no—
92#5690—32no—
93#5681—32no—
94#5655—34no—
95#5643—32no—
96#5640—34no—
97#5633—32no—
98#5631—34no—
99#5624—32no—
100#5596—32no—
101#5585—31no—
102#5585—31no—
103C4×D3×Q8—31no—
104Q8×Dic6—31no—
105#5559—32no—
106#5557D311yescharacteristic, complemented
107#5555—32no—
108#5553—31no—
109#5553—31no—
110#5553—61no—
111#5552—32no—
112#5548—32no—
113#5543D311yescharacteristic, complemented
114#5534—32no—
115#5523—32no—
116#5507—32no—
117#5504—32no—
118#5477—31no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#638C2314yes—
123C2×#638C2314yes—
124#3828—28no—
125C2×C4⋊(C3⋊D3)C2312yes—
126C2×C4⋊(C3⋊D3)C2312yes—
127C2×C4⋊(C3⋊D3)C2312yes—
128C2×C4×C3⋊D3C2314yes—
129C2×#634C2311yescharacteristic
130C2×C3×#67C2312yes—
131C22×C3×Dic3C2314yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×Dic6C2311yescharacteristic
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2312yes—
138C2×#627C2312yes—
139C2×#627C2314yes—
140C2×#626C2314yes—
141C2×#624C2314yes—
142C2×#624C2314yes—
143#3804—48no—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146#3799—44no—
147D3×Dic6—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153#3750C2312yes—
154C4×C3⋊Dic3C2312yes—
155C3×#217C2314yes—
156C3×#217C2312yes—
157C3×#217C2312yes—
158C3×#217C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2312yes—
176#3724C2314yes—
177#3724C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2312yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184#3722C2314yes—
185#3722C2314yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×#239—32no—
191C2×D3×Q8—31no—
192C2×#237—34no—
193C2×#235—32no—
194C2×#235—32no—
195C2×#235—34no—
196C2×#235—32no—
197C2×#235—62no—
198C22×Dic6—31no—
199C3×C4⋊Q8—31no—
200C3×#126—32no—
201C3×#125—31no—
202C3×#125—32no—
203C3×#124—31no—
204C3×#123—32no—
205C3×C22⋊Q8—32no—
206C3×C22⋊Q8—31no—
207C3×C22⋊Q8—34no—
208C3×#121—31no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—21no—
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C3×C4×D4C2×D311yescharacteristic
215C3×C4×D4C2×D311yescharacteristic
216C3×#117—32no—
217C2×C3×C4⋊C4—32no—
218C2×C3×C42—31no—
219#947—32no—
220#947—32no—
221#947—32no—
222Q8×Dic3—32no—
223Q8×Dic3—31no—
224#944—34no—
225#940—32no—
226#940—32no—
227#940—62no—
228#939—34no—
229#938C2×D311yescharacteristic
230#936C2×D311yescharacteristic
231D4×Dic3C2×D312yes—
232#930—32no—
233#930—32no—
234#930—32no—
235#930—32no—
236#930—62no—
237#929—34no—
238C4×#67—34no—
239C4×#67—34no—
240C4×#67C2×D312yes—
241#926C2×D312yes—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3C2×D312yes—
244#924C2×D312yes—
245C2×Dic3⋊C4—32no—
246C2×C4×Dic3—32no—
247#898—34no—
248#898—34no—
249#897—34no—
250#897—34no—
251#897C2×D311yescharacteristic
252#896—34no—
253#896—34no—
254#896—34no—
255#896—34no—
256#895—32no—
257#895—32no—
258#894—34no—
259#894—34no—
260#894—34no—
261#893—32no—
262#893—32no—
263#893—34no—
264#893—32no—
265#893—32no—
266#893—32no—
267#893—32no—
268#893—62no—
269#892—34no—
270#892—34no—
271D3×C4⋊C4—31no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—34no—
274D3×C4⋊C4—34no—
275#890C2×D311yescharacteristic
276#890C2×D312yes—
277#888—34no—
278#888—32no—
279#888—32no—
280#888—32no—
281#887—32no—
282#887—32no—
283#887—32no—
284#887—31no—
285#886—34no—
286#886—34no—
287#885—34no—
288#885—34no—
289#885—34no—
290#885—34no—
291#884—34no—
292#884—34no—
293#884—34no—
294#884—64no—
295#883—34no—
296#883—34no—
297#883C2×D312yes—
298#67⋊C4—34no—
299#67⋊C4—34no—
300#67⋊C4—34no—
301#879C2×D312yes—
302#878C2×D314yes—
303#875—32no—
304#875—32no—
305#875—32no—
306#874—31no—
307#874—31no—
308#874—61no—
309C4×D12—32no—
310C4×D12—32no—
311C4×D12—32no—
312C4×D12—32no—
313C42×D3—32no—
314C42×D3C2×D311yescharacteristic
315#869—32no—
316#869C2×D311yescharacteristic
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C23×C32C2412yes—
329C22×C3⋊D3C2414yes—
330C22×C3×D3C2411yescharacteristic
331C32×D4—22no—
332C2×C32×C4—24no—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337#638—28no—
338#638—44no—
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2412yes—
341C4⋊(C3⋊D3)—24no—
342C4⋊(C3⋊D3)—24no—
343C4⋊(C3⋊D3)—42no—
344C4×C3⋊D3—28no—
345#634#4114yescomplemented
346C3×#67—24no—
347C2×C3×Dic3—44no—
348C2×C3×Dic3C2411yescharacteristic
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2411yescharacteristic
356C3×C4×D3—22no—
357C3×C4×D3—22no—
358C3×C4×D3—22no—
359C3×Dic6—22no—
360C3×Dic6—22no—
361C3×Dic6—42no—
362#627—24no—
363#627—44no—
364#626—28no—
365#624—44no—
366#624—44no—
367D3×Dic3—24no—
368D3×Dic3—24no—
369#559—92no—
370#559—91no—
371Q82—91no—
372#554—31no—
373#554—92no—
374#550—91no—
375#548—92no—
376#547—92no—
377#547—94no—
378#542—92no—
379#542—94no—
380#532—91no—
381#532—92no—
382#529—31no—
383#529—92no—
384#520—92no—
385C2×C4×Q8—91no—
386C2×C3×Q8—31no—
387C2×C3×Q8—31no—
388C2×C3×Q8—32no—
389C2×C3×D4—21no—
390C2×C3×D4—32no—
391C2×C3×D4C22×D311yescharacteristic
392C2×C3×D4C22×D311yescharacteristic
393C22×C3×C4—22no—
394C22×C3×C4—34no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4C22×D312yes—
399C22×C3×C4C22×D312yes—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—64no—
406C2×#67—64no—
407C2×#67C22×D312yes—
408C22×Dic3—32no—
409C22×Dic3—32no—
410C22×Dic3C22×D314yes—
411#239—124no—
412D3×Q8—64no—
413#237—128no—
414#235—68no—
415#235—68no—
416#235—128no—
417#235—124no—
418#235—128no—
419C2×D12—34no—
420C2×D12—32no—
421C2×D12—32no—
422C2×D12—32no—
423C2×D12—32no—
424C2×D12—32no—
425C2×D12—32no—
426C2×D12—62no—
427C2×D12—62no—
428C2×D12—62no—
429C2×C4×D3—32no—
430C2×C4×D3—32no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—64no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×C4×D3C22×D311yescharacteristic
441C2×Dic6—31no—
442C2×Dic6—31no—
443C2×Dic6—32no—
444C2×Dic6—32no—
445C2×Dic6—34no—
446C2×Dic6—34no—
447C2×Dic6—61no—
448C2×Dic6—64no—
449C2×Dic6C22×D311yescharacteristic
450C2×Dic6C22×D311yescharacteristic
451C2×Dic6C22×D312yes—
452C3×C4⋊C4—21no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—32no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—34no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C4⋊C4C22×D311yescharacteristic
466C3×C22⋊C4—22no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—32no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—32no—
471C3×C22⋊C4—32no—
472C3×C22⋊C4C22×D312yes—
473C3×C22⋊C4C22×D312yes—
474C3×C42—21no—
475C3×C42—31no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—32no—
479C3×C42—32no—
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482#217C22×D314yes—
483#217C22×D312yes—
484#217C22×D312yes—
485#217C22×D312yes—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—64no—
499(C2×D3)⋊C4C22×D312yes—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—34no—
505C4⋊Dic3—61no—
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D312yes—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D314yes—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D312yes—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—34no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—62no—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D314yes—
526Dic3⋊C4C22×D312yes—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—34no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—62no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D312yes—
539C4×Dic3C22×D311yescharacteristic
540C4×Dic3C22×D311yescharacteristic
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C2511yescharacteristic
545C2×C3⋊D3—24no—
546C2×C3⋊D3—24no—
547C2×C3⋊D3—24no—
548C2×C3×D3—21no—
549C2×C3×D3—21no—
550C2×C3×D3H(5,𝔽2)12yes—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4C2×#4112yes—
554C32×C42−1+412yes—
555C3⋊Dic3—22no—
556C3⋊Dic3C2×#4114yes—
557C3×Dic3—22no—
558C3×Dic3—21no—
559C3×Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—24no—
563C3×Dic3—22no—
564C3×Dic3—21no—
565C2×#41—94no—
566C2×#41—92no—
567C2×#41—92no—
568C22×Q8—91no—
569C4⋊Q8—31no—
570C4⋊Q8—92no—
571C4⋊Q8—92no—
572C4⋊Q8—94no—
573#127—92no—
574#127—91no—
575#126—32no—
576#126—94no—
577#125—31no—
578#125—32no—
579#124—31no—
580#124—92no—
581#124—92no—
582#124—92no—
583#124—94no—
584#124—94no—
585#123—32no—
586#123—94no—
587#123—94no—
588#123—94no—
589#123—94no—
590C22⋊Q8—32no—
591C22⋊Q8—31no—
592C22⋊Q8—34no—
593C22⋊Q8—94no—
594C22⋊Q8—94no—
595C22⋊Q8—94no—
596#121—31no—
597#121—94no—
598#121—92no—
599#121—92no—
600#121—92no—
601#121—94no—
602C4×Q8—31no—
603C4×Q8—31no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×Q8—92no—
610C4×Q8—91no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—92no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4D3211yescharacteristic
622#117—32no—
623#117—94no—
624C2×C4⋊C4—32no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—91no—
628C2×C42—31no—
629C2×C42—92no—
630C23×C3—22no—
631C23×C3—31no—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C22×D3—34no—
635C22×D3—34no—
636C22×D3—64no—
637C22×D3C23×D311yescharacteristic
638C3×Q8—62no—
639C3×Q8—62no—
640C3×Q8—122no—
641C3×D4—22no—
642C3×D4—22no—
643C3×D4—42no—
644C3×D4—64no—
645C2×C3×C4—24no—
646C2×C3×C4—24no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—22no—
651C2×C3×C4—31no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—34no—
655C2×C3×C4—32no—
656C2×C3×C4—31no—
657C2×C3×C4—32no—
658C2×C3×C4—31no—
659C2×C3×C4—44no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—124no—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672#67—24no—
673#67—68no—
674#67—68no—
675#67—68no—
676#67—128no—
677#67—124no—
678#67—124no—
679#67—244no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—44no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—64no—
688C2×Dic3—64no—
689C2×Dic3C23×D311yescharacteristic
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D314yes—
694C2×Dic3C23×D311yescharacteristic
695C2×Dic3C23×D311yescharacteristic
696C2×Dic3C23×D312yes—
697D12—68no—
698D12—64no—
699D12—64no—
700D12—64no—
701D12—64no—
702D12—124no—
703D12—124no—
704D12—122no—
705D12—122no—
706D12—242no—
707C4×D3—22no—
708C4×D3—22no—
709C4×D3—22no—
710C4×D3—68no—
711C4×D3—68no—
712C4×D3—64no—
713C4×D3—64no—
714C4×D3—128no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719Dic6—22no—
720Dic6—22no—
721Dic6—34no—
722Dic6—34no—
723Dic6—42no—
724Dic6—64no—
725Dic6—64no—
726Dic6—64no—
727Dic6—124no—
728Dic6—124no—
729C2×C32—42no—
730C2×C32C22×#4111yescharacteristic
731C2×C32C2×H(5,𝔽2)11yescharacteristic
732C2×C32C2×2−1+411yescharacteristic
733C3⋊D3—44no—
734C3×D3—22no—
735#41—188no—
736#41—364no—
737#41—368no—
738C2×Q8—31no—
739C2×Q8—31no—
740C2×Q8—32no—
741C2×Q8—92no—
742C2×Q8—94no—
743C2×Q8—91no—
744C2×Q8—184no—
745C2×D4—32no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—92no—
750C2×D4—92no—
751C2×D4—92no—
752C2×D4C2×D3211yescharacteristic
753C22×C4—34no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—94no—
758C22×C4—94no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4—94no—
762C22×C4C2×D3212yes—
763C4⋊C4—31no—
764C4⋊C4—34no—
765C4⋊C4—32no—
766C4⋊C4—32no—
767C4⋊C4—32no—
768C4⋊C4—32no—
769C4⋊C4—32no—
770C4⋊C4—32no—
771C4⋊C4—31no—
772C4⋊C4—34no—
773C4⋊C4—32no—
774C4⋊C4—92no—
775C4⋊C4—94no—
776C4⋊C4—92no—
777C4⋊C4—92no—
778C4⋊C4—94no—
779C4⋊C4—92no—
780C4⋊C4—91no—
781C4⋊C4C2×D3211yescharacteristic
782C22⋊C4—32no—
783C22⋊C4—32no—
784C22⋊C4—34no—
785C22⋊C4—32no—
786C22⋊C4—32no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4C2×D3212yes—
794C42—31no—
795C42—31no—
796C42—31no—
797C42—32no—
798C42—32no—
799C42—92no—
800C42—92no—
801C42—94no—
802C42—92no—
803C42C2×D3211yescharacteristic
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3C24×D311yescharacteristic
818C22×C3C24×D311yescharacteristic
819C2×D3—21no—
820C2×D3—21no—
821C2×D3—64no—
822C2×D3—64no—
823C2×D3—64no—
824C2×D3—64no—
825C2×D3—64no—
826C2×D3—64no—
827C2×D3—124no—
828C2×D3—124no—
829C2×D3—124no—
830C2×D3#100912yes—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—42no—
838C3×C4—41no—
839C3×C4—61no—
840C3×C4—62no—
841C3×C4—61no—
842C3×C4—62no—
843C3×C4—64no—
844C3×C4—62no—
845C3×C4—62no—
846C3×C4—61no—
847C3×C4#100712yes—
848C3×C4D3×#4112yes—
849C3×C4D3×#4112yes—
850C3×C4#101012yes—
851Dic3—22no—
852Dic3—21no—
853Dic3—22no—
854Dic3—21no—
855Dic3—22no—
856Dic3—21no—
857Dic3—24no—
858Dic3—22no—
859Dic3—34no—
860Dic3—34no—
861Dic3—64no—
862Dic3—62no—
863Dic3—62no—
864Dic3—122no—
865C32#352211yescharacteristic, complemented, Sylow
866C23—31no—
867C23—94no—
868C23C22×D3212yes—
869Q8—62no—
870Q8—62no—
871Q8—94no—
872Q8—122no—
873Q8—184no—
874Q8—364no—
875D4—22no—
876D4—64no—
877D4—188no—
878D4—188no—
879D4—184no—
880D4—184no—
881D4—362no—
882D4—364no—
883C2×C4—24no—
884C2×C4—31no—
885C2×C4—31no—
886C2×C4—31no—
887C2×C4—32no—
888C2×C4—32no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—34no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—188no—
899C2×C4—184no—
900C2×C4—184no—
901C2×C4—364no—
902C2×C4—364no—
903C2×C4C22×D3211yescharacteristic
904C2×C4C22×D3212yes—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—42no—
911C2×C3—42no—
912C2×C3—62no—
913C2×C3—82no—
914C2×C3C2×#100711yescharacteristic
915C2×C3C2×D3×#4111yescharacteristic
916C2×C3C2×D3×#4111yescharacteristic
917C2×C3C2×#100911yescharacteristic
918C2×C3C2×#101011yescharacteristic
919C2×C3D3×H(5,𝔽2)11yescharacteristic
920D3—22no—
921D3—124no—
922D3—124no—
923D3—244no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—32no—
928C22—61no—
929C22—61no—
930C22—184no—
931C22—184no—
932C22—184no—
933C22C23×D3211yescharacteristic
934C4—22no—
935C4—21no—
936C4—61no—
937C4—62no—
938C4—61no—
939C4—62no—
940C4—61no—
941C4—62no—
942C4—64no—
943C4—62no—
944C4—94no—
945C4—182no—
946C4#6429712yes—
947C4#6431212yes—
948C3—21no—
949C3#8612811yescharacteristic, complemented
950C3#8693611yescharacteristic, complemented
951C2—42no—
952C2—62no—
953C2—364no—
954C2C2×#6429711yescharacteristic
955C2C2×#6431211yescharacteristic
956C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596024C2semidirect
2. C3×#5557C2semidirect
3. C3×#5543C2semidirect
4. #10595210C2semidirect
5. #10595131C2semidirect
6. #10594990C2semidirect
7. #10594916C2semidirect
8. #10594906C2semidirect
9. #10594814C2semidirect
10. #10594484C2semidirect
11. #10594453C2semidirect
12. #10594064C2semidirect
13. #10594032C2semidirect
14. #10593970C2semidirect
15. #10593963C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593856C2semidirect
106. #5557D3semidirect
113. #5543D3semidirect
345. #634#41semidirect
865. C32#3522semidirect
949. C3#86128semidirect
950. C3#86936semidirect

Maximal subgroups

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

subgroupindex
#105960242
C3×#55572
C3×#55432
#105952102
#105951312
#105949902
#105949162
#105949062
#105948142
#105944842
#105944532
#105940642
#105940322
#105939702
#105939632
C4×D3×Dic62
#105938562
#869363
#861283