Finite Group Databasebeta

← #11909794

Subgroups — #11909794

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C3×#5580C211yesmaximal, characteristic, complemented
4#10595392C212yesmaximal, complemented
5#10595377C212yesmaximal, complemented
6#10594514C214yesmaximal, complemented
7#10594487C214yesmaximal, complemented
8#10594485C212yesmaximal, complemented
9#10594367C212yesmaximal, complemented
10#10593961C212yesmaximal, complemented
11#10593960C211yesmaximal, characteristic, complemented
12#10593906C211yesmaximal, characteristic, complemented
13#10593905C212yesmaximal, complemented
14#10593897C211yesmaximal, characteristic, complemented
15#10593895C212yesmaximal, complemented
16#10593887C212yesmaximal, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18#87055—31nomaximal
19#86128—31nomaximal
20C2×#3795C2212yes—
21C2×#3795C2214yes—
22C2×#3795C2212yes—
23C2×D3×Dic6C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25Q8×C3⋊Dic3C2212yes—
26#64097C2212yes—
27#64097C2214yes—
28#64078C2212yes—
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C4×#634C2212yes—
32C3×#947C2212yes—
33C3×#947C2211yescharacteristic
34C3×#946C2211yescharacteristic
35C3×#898C2212yes—
36C3×#895C2211yescharacteristic
37C3×#894C2212yes—
38C3×#894C2214yes—
39C3×#893C2212yes—
40C3×#890C2211yescharacteristic
41C3×#875C2212yes—
42C3×#874C2211yescharacteristic
43C3×C4×D12C2212yes—
44C3×C4×D12C2211yescharacteristic
45C3×C4×D12C2212yes—
46C3×#872C2212yes—
47C3×C42×D3C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49C4×#627C2212yes—
50#63915C2214yes—
51#63914C2212yes—
52#63913C2214yes—
53#63908C2212yes—
54#63908C2212yes—
55#63908C2212yes—
56#63902C2214yes—
57#63902C2214yes—
58#63899C2214yes—
59#63898C2212yes—
60#63896C2214yes—
61#63896C2214yes—
62Dic3×D12C2212yes—
63Dic3×D12C2212yes—
64Dic3×D12C2212yes—
65#63891C2214yes—
66#63891C2214yes—
67#63891C2214yes—
68D3×C4⋊Dic3C2211yescharacteristic
69D3×C4⋊Dic3C2212yes—
70#63885C2214yes—
71#63885C2214yes—
72#63879C2214yes—
73#63878C2214yes—
74D3×Dic3⋊C4C2212yes—
75D3×Dic3⋊C4C2214yes—
76C4×D3×Dic3C2212yes—
77#63869C2212yes—
78#63861C2214yes—
79#63860C2212yes—
80#63857C2214yes—
81#63856C2212yes—
82#63844C2211yescharacteristic
83Dic3×Dic6C2211yescharacteristic
84#63837C2212yes—
85C3×#559—31no—
86C3×#529—31no—
87#5718—31no—
88#5716—31no—
89#5710—34no—
90#5690—32no—
91#5682—32no—
92#5681—32no—
93#5681—32no—
94#5680—32no—
95#5677—32no—
96#5662—34no—
97#5655—34no—
98#5655—34no—
99#5624—32no—
100#5596—32no—
101#5585D311yescharacteristic, complemented
102#5580D311yescharacteristic, complemented
103#5579—31no—
104C4×D3×Q8—31no—
105Q8×Dic6—31no—
106Q8×Dic6—31no—
107Q8×Dic6—61no—
108#5555—32no—
109#5553—31no—
110#5552—32no—
111#5551—32no—
112#5548—32no—
113#5546—32no—
114#5543—31no—
115#5539—32no—
116#5534—32no—
117#5523—32no—
118#5477—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2314yes—
122C2×#634C2312yes—
123C2×#634C2311yescharacteristic
124C2×C3×D12C2312yes—
125C2×C3×D12C2312yes—
126C2×C3×D12C2311yescharacteristic
127C2×C3×D12C2312yes—
128C2×C3×D12C2312yes—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2312yes—
136C2×#625C2314yes—
137C2×#625C2314yes—
138C2×#625C2314yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2314yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2314yes—
144#3795—28no—
145#3795—48no—
146#3795—44no—
147D3×Dic6—24no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2314yes—
155C4⋊(C3⋊Dic3)C2312yes—
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C4×C3⋊Dic3C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×(C2×D3)⋊C4C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×C4⋊Dic3C2311yescharacteristic
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×Dic3⋊C4C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2311yescharacteristic
177C3×C4×Dic3C2311yescharacteristic
178#3724C2312yes—
179#3724C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3522—91noSylow
190C2×D3×Q8—31no—
191C2×#237—32no—
192C2×#237—32no—
193C2×#237—34no—
194C2×#235—32no—
195C2×#235—32no—
196C2×#235—34no—
197C22×Dic6—31no—
198C3×#127—31no—
199C3×#126—32no—
200C3×#125—31no—
201C3×#124—32no—
202C3×#124—31no—
203C3×#124—32no—
204C3×#123—34no—
205C3×#123—32no—
206C3×C22⋊Q8—31no—
207C3×#121—31no—
208C3×C4×Q8—21no—
209C3×C4×Q8—31no—
210C3×C4×Q8C2×D311yescharacteristic
211C3×C4×Q8C2×D311yescharacteristic
212C3×C4×D4—32no—
213C3×C4×D4—32no—
214C3×C4×D4—31no—
215C3×C4×D4—32no—
216C3×#117—32no—
217C2×C3×C42—31no—
218#947C2×D311yescharacteristic
219#947C2×D312yes—
220#946—32no—
221#946C2×D311yescharacteristic
222Q8×Dic3—32no—
223Q8×Dic3—32no—
224Q8×Dic3—31no—
225Q8×Dic3—62no—
226#940—32no—
227#940—32no—
228#939—34no—
229#939—34no—
230#938—32no—
231#938—32no—
232#938—32no—
233#936—32no—
234D4×Dic3—32no—
235D4×Dic3—32no—
236D4×Dic3—32no—
237D4×Dic3—32no—
238#930—32no—
239#930—32no—
240#930—32no—
241C4×#67—34no—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—32no—
244#924—32no—
245#924—34no—
246C2×Dic3⋊C4—32no—
247C2×Dic3⋊C4—34no—
248C2×C4×Dic3—32no—
249#898—34no—
250#898C2×D312yes—
251#897—34no—
252#896—34no—
253#896—34no—
254#896—34no—
255#895C2×D311yescharacteristic
256#894C2×D312yes—
257#894C2×D314yes—
258#893—32no—
259#893C2×D312yes—
260#892—34no—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—34no—
263D3×C4⋊C4—32no—
264D3×C4⋊C4—31no—
265#890—32no—
266#890C2×D311yescharacteristic
267#888—34no—
268#888—34no—
269#888—32no—
270#888—32no—
271#888—62no—
272#888—64no—
273#887—32no—
274#887—31no—
275#886—34no—
276#886—34no—
277#886—34no—
278#885—34no—
279#885—34no—
280#885—34no—
281#885—34no—
282#884—34no—
283#884—34no—
284#883—34no—
285#883—34no—
286#883—34no—
287#67⋊C4—34no—
288#67⋊C4—34no—
289#67⋊C4—34no—
290#67⋊C4—34no—
291#67⋊C4—34no—
292#879—34no—
293#878—34no—
294#878—34no—
295#878—34no—
296#877—34no—
297#875—32no—
298#875C2×D312yes—
299#874C2×D311yescharacteristic
300C4×D12—32no—
301C4×D12—32no—
302C4×D12—32no—
303C4×D12C2×D312yes—
304C4×D12C2×D311yescharacteristic
305C4×D12C2×D312yes—
306#872C2×D312yes—
307C42×D3—32no—
308C42×D3C2×D311yescharacteristic
309#870—32no—
310#869—32no—
311#869—31no—
312#869—31no—
313#869—32no—
314#869—61no—
315#869—62no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—61no—
326C4×Dic6—62no—
327C4×Dic6C2×D311yescharacteristic
328C22×C3×D3C2414yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2411yescharacteristic
331C32×Q8—22no—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2412yes—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2414yes—
339C2×C3⋊Dic3C2412yes—
340#634—44no—
341#634—42no—
342#634#4114yescomplemented
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2411yescharacteristic
349C3×D12—24no—
350C3×D12—24no—
351C3×D12—24no—
352C3×D12—22no—
353C3×D12—42no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×C4×D3—24no—
357C3×C4×D3—22no—
358C3×C4×D3—44no—
359C3×Dic6—22no—
360#627—24no—
361#625—28no—
362#625—28no—
363#625—44no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366D3×Dic3—28no—
367D3×Dic3—44no—
368D3×Dic3—44no—
369#559—31no—
370#559—92no—
371Q82—91no—
372#554—91no—
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—21no—
387C2×C3×Q8—31no—
388C2×C3×Q8C22×D311yescharacteristic
389C2×C3×Q8C22×D311yescharacteristic
390C2×C3×D4—32no—
391C2×C3×D4—31no—
392C2×C3×D4—32no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—32no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C22×Dic3—34no—
407C22×Dic3—32no—
408C22×Dic3—32no—
409C22×Dic3—34no—
410C22×Dic3—34no—
411D3×Q8—64no—
412#237—68no—
413#237—124no—
414#237—128no—
415#235—68no—
416#235—128no—
417#235—124no—
418C2×D12C22×D311yescharacteristic
419C2×D12C22×D312yes—
420C2×D12C22×D312yes—
421C2×D12C22×D312yes—
422C2×D12C22×D312yes—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3C22×D311yescharacteristic
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D311yescharacteristic
431C2×C4×D3C22×D312yes—
432C2×C4×D3C22×D314yes—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—32no—
436C2×Dic6—32no—
437C2×Dic6—32no—
438C2×Dic6—34no—
439C2×Dic6—34no—
440C2×Dic6—32no—
441C2×Dic6—61no—
442C2×Dic6—64no—
443C2×Dic6—62no—
444C2×Dic6—64no—
445C2×Dic6C22×D311yescharacteristic
446C3×C4⋊C4—21no—
447C3×C4⋊C4—22no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—32no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4C22×D311yescharacteristic
455C3×C4⋊C4C22×D311yescharacteristic
456C3×C4⋊C4C22×D312yes—
457C3×C4⋊C4C22×D312yes—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—32no—
460C3×C22⋊C4—34no—
461C3×C22⋊C4—34no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4—32no—
464C3×C22⋊C4—32no—
465C3×C22⋊C4—32no—
466C3×C42—21no—
467C3×C42—22no—
468C3×C42—31no—
469C3×C42—31no—
470C3×C42—31no—
471C3×C42—32no—
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D312yes—
475C3×C42C22×D312yes—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4C22×D312yes—
485(C2×D3)⋊C4C22×D312yes—
486(C2×D3)⋊C4C22×D312yes—
487(C2×D3)⋊C4C22×D314yes—
488(C2×D3)⋊C4C22×D312yes—
489(C2×D3)⋊C4C22×D312yes—
490(C2×D3)⋊C4C22×D314yes—
491(C2×D3)⋊C4C22×D314yes—
492C4⋊Dic3—31no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—31no—
496C4⋊Dic3—32no—
497C4⋊Dic3—32no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—34no—
503C4⋊Dic3—62no—
504C4⋊Dic3—61no—
505C4⋊Dic3—62no—
506C4⋊Dic3—64no—
507C4⋊Dic3C22×D311yescharacteristic
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D312yes—
510Dic3⋊C4—32no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—64no—
522Dic3⋊C4—62no—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D312yes—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—62no—
535C4×Dic3—64no—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D311yescharacteristic
539C4×Dic3C22×D311yescharacteristic
540C22×C32C2511yescharacteristic
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—24no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—24no—
547C2×C3×D3—24no—
548C2×C3×D3—22no—
549C2×C3×D3H(5,𝔽2)12yes—
550C32×C4—22no—
551C32×C4—21no—
552C32×C4—22no—
553C32×C4C2×#4112yes—
554C32×C42−1+412yes—
555C3⋊Dic3—22no—
556C3⋊Dic3—24no—
557C3⋊Dic3C2×#4114yes—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—21no—
564C2×#41—92no—
565C2×#41—92no—
566C2×#41—94no—
567C22×Q8—91no—
568C4⋊Q8—92no—
569C4⋊Q8—94no—
570C4⋊Q8—91no—
571C4⋊Q8—92no—
572#127—31no—
573#127—92no—
574#126—32no—
575#126—94no—
576#125—31no—
577#125—92no—
578#124—31no—
579#124—32no—
580#124—32no—
581#124—92no—
582#124—94no—
583#124—94no—
584#123—32no—
585#123—34no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—31no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—94no—
593C22⋊Q8—94no—
594C22⋊Q8—92no—
595#121—31no—
596#121—94no—
597#121—94no—
598#121—92no—
599#121—92no—
600#121—92no—
601C4×Q8—31no—
602C4×Q8—92no—
603C4×Q8—91no—
604C4×Q8—92no—
605C4×Q8—91no—
606C4×Q8—92no—
607C4×Q8—91no—
608C4×Q8—92no—
609C4×Q8D3211yescharacteristic
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—31no—
614C4×D4—92no—
615C4×D4—92no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—92no—
621#117—32no—
622#117—94no—
623C2×C4⋊C4—92no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—94no—
626C2×C4⋊C4—92no—
627C2×C42—31no—
628C2×C42—92no—
629C23×C3—31no—
630C23×C3—34no—
631C23×C3—32no—
632C22×D3C23×D314yes—
633C22×D3C23×D312yes—
634C22×D3C23×D311yescharacteristic
635C3×Q8—24no—
636C3×Q8—22no—
637C3×Q8—22no—
638C3×Q8—62no—
639C3×D4—64no—
640C3×D4—64no—
641C3×D4—64no—
642C3×D4—62no—
643C3×D4—122no—
644C2×C3×C4—22no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—22no—
649C2×C3×C4—31no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—31no—
653C2×C3×C4—32no—
654C2×C3×C4—31no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—64no—
658C2×C3×C4—62no—
659C2×C3×C4—124no—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670#67—68no—
671#67—68no—
672#67—68no—
673#67—68no—
674#67—124no—
675#67—124no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—34no—
681C2×Dic3—34no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—64no—
685C2×Dic3—64no—
686C2×Dic3—68no—
687C2×Dic3—64no—
688C2×Dic3—124no—
689C2×Dic3—124no—
690C2×Dic3C23×D311yescharacteristic
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D311yescharacteristic
694C2×Dic3C23×D311yescharacteristic
695C2×Dic3C23×D312yes—
696D12—24no—
697D12—24no—
698D12—22no—
699D12—24no—
700D12—42no—
701C4×D3—22no—
702C4×D3—24no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—44no—
706C4×D3—68no—
707C4×D3—64no—
708C4×D3—64no—
709C4×D3—124no—
710C4×D3—124no—
711Dic6—22no—
712Dic6—34no—
713Dic6—34no—
714Dic6—64no—
715Dic6—64no—
716Dic6—64no—
717Dic6—124no—
718Dic6—122no—
719Dic6—122no—
720Dic6—124no—
721Dic6—242no—
722Dic6—244no—
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C2×C32C2×2−1+411yescharacteristic
726C3×D3—22no—
727C3×D3—44no—
728C3×D3—42no—
729#41—188no—
730#41—364no—
731#41—368no—
732C2×Q8—31no—
733C2×Q8—92no—
734C2×Q8—91no—
735C2×Q8—94no—
736C2×Q8—92no—
737C2×Q8—184no—
738C2×Q8C2×D3211yescharacteristic
739C2×D4—31no—
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—32no—
743C2×D4—32no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—32no—
751C22×C4—34no—
752C22×C4—92no—
753C22×C4—92no—
754C22×C4—94no—
755C22×C4—94no—
756C22×C4—94no—
757C4⋊C4—31no—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—31no—
762C4⋊C4—32no—
763C4⋊C4—92no—
764C4⋊C4—94no—
765C4⋊C4—92no—
766C4⋊C4—92no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—92no—
770C4⋊C4—92no—
771C4⋊C4—91no—
772C4⋊C4—92no—
773C4⋊C4—94no—
774C4⋊C4C2×D3211yescharacteristic
775C4⋊C4C2×D3212yes—
776C22⋊C4—32no—
777C22⋊C4—32no—
778C22⋊C4—34no—
779C22⋊C4—32no—
780C22⋊C4—32no—
781C22⋊C4—34no—
782C22⋊C4—32no—
783C22⋊C4—34no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C42—31no—
789C42—31no—
790C42—31no—
791C42—32no—
792C42—92no—
793C42—92no—
794C42—92no—
795C42—94no—
796C42C2×D3211yescharacteristic
797C42C2×D3212yes—
798C22×C3—21no—
799C22×C3—32no—
800C22×C3—61no—
801C22×C3—61no—
802C22×C3—64no—
803C22×C3—62no—
804C22×C3—64no—
805C22×C3—62no—
806C22×C3—64no—
807C22×C3—62no—
808C22×C3C24×D311yescharacteristic
809C22×C3C24×D311yescharacteristic
810C2×D3—21no—
811C2×D3—21no—
812C2×D3—22no—
813C2×D3—24no—
814C2×D3—22no—
815C2×D3—24no—
816C2×D3—22no—
817C2×D3—24no—
818C2×D3#100912yes—
819C3×C4—24no—
820C3×C4—21no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—21no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—41no—
829C3×C4—42no—
830C3×C4—61no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4D3×#4112yes—
837C3×C4D3×#4112yes—
838C3×C4#101012yes—
839C3×C4#101012yes—
840Dic3—22no—
841Dic3—21no—
842Dic3—22no—
843Dic3—21no—
844Dic3—21no—
845Dic3—22no—
846Dic3—34no—
847Dic3—34no—
848Dic3—64no—
849Dic3—62no—
850Dic3—64no—
851Dic3—64no—
852Dic3—62no—
853Dic3—122no—
854Dic3—124no—
855C32#352211yescharacteristic, complemented, Sylow
856C23—31no—
857C23—32no—
858C23—34no—
859Q8—22no—
860Q8—62no—
861Q8—94no—
862Q8—184no—
863Q8—362no—
864Q8—364no—
865D4—64no—
866D4—62no—
867D4—64no—
868D4—64no—
869D4—122no—
870D4—188no—
871D4—188no—
872D4—364no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—64no—
883C2×C4—92no—
884C2×C4—92no—
885C2×C4—94no—
886C2×C4—124no—
887C2×C4—184no—
888C2×C4—188no—
889C2×C4—184no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4C22×D3211yescharacteristic
893C2×C4C22×D3212yes—
894C2×C4C22×D3212yes—
895C2×C4C22×D3211yescharacteristic
896C2×C4C22×D3211yescharacteristic
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—62no—
901C2×C3—122no—
902C2×C3—124no—
903C2×C3C2×D3×#4111yescharacteristic
904C2×C3C2×D3×#4111yescharacteristic
905C2×C3C2×#100911yescharacteristic
906C2×C3C2×#101011yescharacteristic
907C2×C3C2×#101011yescharacteristic
908C2×C3D3×H(5,𝔽2)11yescharacteristic
909D3—22no—
910D3—44no—
911D3—42no—
912C22—32no—
913C22—61no—
914C22—61no—
915C22—62no—
916C22—64no—
917C22—62no—
918C22—64no—
919C22—64no—
920C22—62no—
921C22C23×D3211yescharacteristic
922C4—22no—
923C4—21no—
924C4—22no—
925C4—61no—
926C4—62no—
927C4—61no—
928C4—62no—
929C4—61no—
930C4—62no—
931C4—94no—
932C4—182no—
933C4—184no—
934C4#6429812yes—
935C4#6431912yes—
936C3—21no—
937C3#8612811yescharacteristic, complemented
938C3#8705511yescharacteristic, complemented
939C2—62no—
940C2—122no—
941C2—124no—
942C2C2×#6429811yescharacteristic
943C2C2×#6431911yescharacteristic
944C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
2. C3×#5585C2semidirect
3. C3×#5580C2semidirect
4. #10595392C2semidirect
5. #10595377C2semidirect
6. #10594514C2semidirect
7. #10594487C2semidirect
8. #10594485C2semidirect
9. #10594367C2semidirect
10. #10593961C2semidirect
11. #10593960C2semidirect
12. #10593906C2semidirect
13. #10593905C2semidirect
14. #10593897C2semidirect
15. #10593895C2semidirect
16. #10593887C2semidirect
17. C4×D3×Dic6C2semidirect
101. #5585D3semidirect
102. #5580D3semidirect
342. #634#41semidirect
855. C32#3522semidirect
937. C3#86128semidirect
938. C3#87055semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55852
C3×#55802
#105953922
#105953772
#105945142
#105944872
#105944852
#105943672
#105939612
#105939602
#105939062
#105939052
#105938972
#105938952
#105938872
C4×D3×Dic62
#870553
#861283