Finite Group Databasebeta

← #11909818

Subgroups — #11909818

Order 1152.

2357 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4#10594965C212yesmaximal, complemented
5#10594929C212yesmaximal, complemented
6#10594918C212yesmaximal, complemented
7#10594907C212yesmaximal, complemented
8#10594888C214yesmaximal, complemented
9#10593983C212yesmaximal, complemented
10#10593981C212yesmaximal, complemented
11#10593956C211yesmaximal, characteristic, complemented
12#10593951C211yesmaximal, characteristic, complemented
13#10593944C214yesmaximal, complemented
14#10593941C212yesmaximal, complemented
15#10593906C211yesmaximal, characteristic, complemented
16#10593887C212yesmaximal, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86229—31nomaximal
19#86128—31nomaximal
20C22×#634C2211yescharacteristic
21C2×C3×#235C2212yes—
22C2×#3805C2214yes—
23C2×#3795C2212yes—
24C2×C32×C42C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2212yes—
27C2×C4×C3⋊Dic3C2212yes—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C4×#634C2212yes—
31C4×#634C2212yes—
32C4×#634C2211yescharacteristic
33C4×#634C2211yescharacteristic
34C3×#930C2212yes—
35C3×#930C2211yescharacteristic
36C3×#930C2212yes—
37C3×#929C2212yes—
38C3×C4×#67C2212yes—
39C3×#924C2211yescharacteristic
40C3×#876C2212yes—
41C3×#875C2212yes—
42C3×#875C2211yescharacteristic
43C3×#874C2211yescharacteristic
44C3×C4×D12C2212yes—
45C3×C4×D12C2211yescharacteristic
46C3×C4×D12C2212yes—
47C3×#872C2212yes—
48C3×#870C2211yescharacteristic
49C3×#869C2211yescharacteristic
50C3×C4×Dic6C2211yescharacteristic
51#63980C2214yes—
52#67⋊Dic3C2214yes—
53#63962C2214yes—
54#63919C2212yes—
55#63918C2212yes—
56#63915C2214yes—
57#63914C2212yes—
58#63913C2214yes—
59#63908C2212yes—
60#63905C2214yes—
61#63902C2214yes—
62#63898C2212yes—
63#63898C2212yes—
64#63898C2212yes—
65#63896C2214yes—
66#63893C2214yes—
67Dic3×D12C2212yes—
68#63891C2214yes—
69D3×C4⋊Dic3C2212yes—
70#63887C2214yes—
71#63885C2214yes—
72#63884C2214yes—
73#63879C2214yes—
74#63878C2214yes—
75D3×Dic3⋊C4C2214yes—
76#63872C2212yes—
77#63863C2212yes—
78#63862C2214yes—
79#63860C2212yes—
80#63857C2212yes—
81#63851C2214yes—
82#63844C2212yes—
83#63843C2212yes—
84#63839C2214yes—
85C3×#532—31no—
86C3×#529—31no—
87#5824—34no—
88#5730—31no—
89#5722—31no—
90#5718—31no—
91#5713—31no—
92#5710—34no—
93#5690—32no—
94#5681—32no—
95#5669—34no—
96#5655—34no—
97#5624—32no—
98#5611—32no—
99#5600—32no—
100#5598—32no—
101#5596—32no—
102#5596—32no—
103#5585—31no—
104Q8×Dic6—31no—
105#5561—32no—
106#5559—32no—
107#5555—32no—
108#5553—31no—
109#5552—32no—
110#5546—32no—
111#5543—31no—
112#5539—32no—
113#5534—32no—
114#5523—32no—
115#5479D311yescharacteristic, complemented
116#5477D311yescharacteristic, complemented
117C2×C4×Dic6—31no—
118C2×C4×Dic6—31no—
119C2×C4×Dic6—61no—
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C22×C3⋊Dic3C2312yes—
124C22×C3⋊Dic3C2312yes—
125C2×#634—24no—
126C2×#634C2311yescharacteristic
127C2×#634C2312yes—
128C2×#634C2311yescharacteristic
129C2×C3×#67C2312yes—
130C2×C3×#67C2314yes—
131C3×#235—44no—
132C2×C3×D12C2312yes—
133C2×C3×D12C2312yes—
134C2×C3×D12C2311yescharacteristic
135C2×C3×D12C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2314yes—
138C2×C3×Dic6C2311yescharacteristic
139C2×C3×Dic6C2312yes—
140C2×#627C2314yes—
141C2×#625C2314yes—
142C2×#625C2314yes—
143#3805—48no—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2314yes—
146C2×D3×Dic3C2314yes—
147#3795—28no—
148C32×C42C2311yescharacteristic
149C32×C42C2311yescharacteristic
150C32×C42C2311yescharacteristic
151C32×C42C2311yescharacteristic
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155#3750C2312yes—
156#3750C2312yes—
157#3750C2312yes—
158#3750C2312yes—
159C4×C3⋊Dic3C2312yes—
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2312yes—
163C3×#217C2312yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yes—
169C3×(C2×D3)⋊C4C2312yes—
170C3×C4⋊Dic3C2311yescharacteristic
171C3×C4⋊Dic3C2312yes—
172C3×C4⋊Dic3C2312yes—
173C3×C4⋊Dic3C2311yescharacteristic
174C3×Dic3⋊C4C2312yes—
175C3×Dic3⋊C4C2312yes—
176C3×Dic3⋊C4C2312yes—
177C3×Dic3⋊C4C2312yes—
178C3×C4×Dic3C2312yes—
179#3724C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2314yes—
189#3522—91noSylow
190C2×C3×#41—32no—
191C2×#237—34no—
192C2×#237—34no—
193C2×#237—32no—
194C2×#235—32no—
195C2×#235C2×D312yes—
196C22×Dic6—31no—
197C22×Dic6—31no—
198C22×Dic6—61no—
199C3×C4⋊Q8—31no—
200C3×#127—31no—
201C3×#126—32no—
202C3×#125—31no—
203C3×#124—32no—
204C3×#124—31no—
205C3×#123—32no—
206C3×C22⋊Q8—31no—
207C3×#121—31no—
208C3×#121—32no—
209C3×#121—32no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—32no—
213C3×C4×D4—31no—
214C3×C4×D4—32no—
215C3×#117—32no—
216C2×C3×C42—21no—
217C2×C3×C42C2×D311yescharacteristic
218C2×C3×C42C2×D311yescharacteristic
219#947—32no—
220#946—34no—
221Q8×Dic3—32no—
222#944—34no—
223#940—32no—
224#940—32no—
225#939—34no—
226#939—34no—
227#939—34no—
228#938—32no—
229#936—32no—
230#936—32no—
231#935—34no—
232#935—34no—
233D4×Dic3—34no—
234D4×Dic3—32no—
235D4×Dic3—32no—
236D4×Dic3—32no—
237D4×Dic3—32no—
238#930—32no—
239#930C2×D312yes—
240#930C2×D312yes—
241#930C2×D311yescharacteristic
242#929—34no—
243#929C2×D312yes—
244C4×#67—34no—
245C4×#67C2×D312yes—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—32no—
249C2×C4⋊Dic3—61no—
250#924—32no—
251#924—34no—
252#924C2×D311yescharacteristic
253C2×Dic3⋊C4—32no—
254C2×Dic3⋊C4—32no—
255C2×Dic3⋊C4—34no—
256C2×Dic3⋊C4—62no—
257C2×C4×Dic3—32no—
258C2×C4×Dic3—32no—
259C2×C4×Dic3—62no—
260#898—34no—
261#897—32no—
262#897—34no—
263#896—34no—
264#896—34no—
265#894—34no—
266#893—32no—
267#893—32no—
268#893—32no—
269#892—34no—
270D3×C4⋊C4—34no—
271D3×C4⋊C4—32no—
272#890—32no—
273#890—32no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888—32no—
278#887—32no—
279#887—32no—
280#886—34no—
281#886—34no—
282#885—34no—
283#885—34no—
284#885—34no—
285#885—34no—
286#884—34no—
287#883—34no—
288#883—34no—
289#67⋊C4—34no—
290#67⋊C4—34no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#879—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#877—34no—
298#876C2×D312yes—
299#875—32no—
300#875C2×D312yes—
301#875C2×D311yescharacteristic
302#874C2×D311yescharacteristic
303C4×D12—32no—
304C4×D12C2×D312yes—
305C4×D12C2×D311yescharacteristic
306C4×D12C2×D312yes—
307#872C2×D312yes—
308#870C2×D311yescharacteristic
309#869—32no—
310#869C2×D311yescharacteristic
311C4×Dic6—32no—
312C4×Dic6—32no—
313C4×Dic6—32no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6—62no—
326C4×Dic6—61no—
327C4×Dic6—61no—
328C4×Dic6—62no—
329C4×Dic6—61no—
330C4×Dic6C2×D311yescharacteristic
331C23×C32C2411yescharacteristic
332C22×C3×D3C2414yes—
333C22×C3×D3C2412yes—
334C2×C32×C4—22no—
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C3⋊Dic3—24no—
344C2×C3⋊Dic3—24no—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2412yes—
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2412yes—
349#634—22no—
350#634—24no—
351#634#4114yescomplemented
352C3×#67—24no—
353C3×#67—28no—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2414yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×D12—24no—
359C3×D12—24no—
360C3×D12—22no—
361C3×D12—42no—
362C3×C4×D3—24no—
363C3×C4×D3—44no—
364C3×Dic6—22no—
365C3×Dic6—42no—
366#627—44no—
367#625—28no—
368#625—44no—
369D3×Dic3—28no—
370D3×Dic3—44no—
371D3×Dic3—44no—
372#559—92no—
373#559—91no—
374Q82—91no—
375#554—92no—
376#554—91no—
377#550—91no—
378#548—92no—
379#547—92no—
380#547—94no—
381#542—92no—
382#542—94no—
383#532—31no—
384#532—92no—
385#529—31no—
386#529—92no—
387#520—92no—
388C2×C4×Q8—91no—
389C3×#41—124no—
390C2×C3×Q8—31no—
391C2×C3×Q8—32no—
392C2×C3×D4—34no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—31no—
396C2×C3×D4—32no—
397C2×C3×D4—32no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67C22×D314yes—
414C2×#67C22×D312yes—
415C22×Dic3—32no—
416C22×Dic3—32no—
417C22×Dic3—32no—
418C22×Dic3—32no—
419C22×Dic3—34no—
420C22×Dic3—34no—
421C22×Dic3—34no—
422C22×Dic3—62no—
423C22×Dic3—62no—
424#237—68no—
425#237—128no—
426#237—128no—
427#235—44no—
428#235—68no—
429C2×D12C22×D312yes—
430C2×D12C22×D312yes—
431C2×D12C22×D311yescharacteristic
432C2×D12C22×D312yes—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D314yes—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—31no—
441C2×Dic6—32no—
442C2×Dic6—32no—
443C2×Dic6—31no—
444C2×Dic6—34no—
445C2×Dic6—34no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—64no—
450C2×Dic6—64no—
451C2×Dic6—68no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D312yes—
454C3×C4⋊C4—32no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—32no—
462C3×C22⋊C4—32no—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—32no—
466C3×C22⋊C4—32no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—32no—
469C3×C42—21no—
470C3×C42—21no—
471C3×C42—21no—
472C3×C42—21no—
473C3×C42—32no—
474C3×C42C22×D311yescharacteristic
475C3×C42C22×D311yescharacteristic
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D311yescharacteristic
478C3×C42C22×D311yescharacteristic
479C3×C42C22×D311yescharacteristic
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482#217—34no—
483#217—34no—
484#217—34no—
485#217—34no—
486#217—34no—
487#217C22×D312yes—
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)⋊C4C22×D312yes—
494(C2×D3)⋊C4C22×D312yes—
495(C2×D3)⋊C4C22×D314yes—
496(C2×D3)⋊C4C22×D314yes—
497(C2×D3)⋊C4C22×D312yes—
498(C2×D3)⋊C4C22×D312yes—
499C4⋊Dic3—31no—
500C4⋊Dic3—31no—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—34no—
508C4⋊Dic3—61no—
509C4⋊Dic3—61no—
510C4⋊Dic3—62no—
511C4⋊Dic3C22×D312yes—
512C4⋊Dic3C22×D311yescharacteristic
513C4⋊Dic3C22×D312yes—
514C4⋊Dic3C22×D311yescharacteristic
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—62no—
529Dic3⋊C4—62no—
530Dic3⋊C4—62no—
531Dic3⋊C4—62no—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D312yes—
534Dic3⋊C4C22×D312yes—
535Dic3⋊C4C22×D312yes—
536C4×Dic3—32no—
537C4×Dic3—32no—
538C4×Dic3—32no—
539C4×Dic3—32no—
540C4×Dic3—32no—
541C4×Dic3—32no—
542C4×Dic3—32no—
543C4×Dic3—32no—
544C4×Dic3—34no—
545C4×Dic3—34no—
546C4×Dic3—62no—
547C4×Dic3—62no—
548C4×Dic3—62no—
549C4×Dic3—62no—
550C4×Dic3C22×D312yes—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32H(5,𝔽2)12yes—
554C22×C32C2511yescharacteristic
555C2×C3×D3—24no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—24no—
559C2×C3×D3—24no—
560C2×C3×D3—22no—
561C32×C4—21no—
562C32×C4—21no—
563C32×C4—21no—
564C32×C4—21no—
565C32×C4C2×#4112yes—
566C32×C42−1+412yes—
567C3⋊Dic3—22no—
568C3⋊Dic3—22no—
569C3⋊Dic3—22no—
570C3⋊Dic3C2×#4114yes—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3—24no—
574C3×Dic3—22no—
575C2×#41—32no—
576C2×#41—92no—
577C2×#41—94no—
578C22×Q8—91no—
579C4⋊Q8—31no—
580C4⋊Q8—92no—
581C4⋊Q8—92no—
582C4⋊Q8—94no—
583#127—31no—
584#127—92no—
585#126—32no—
586#126—94no—
587#125—31no—
588#125—92no—
589#124—31no—
590#124—32no—
591#124—92no—
592#124—94no—
593#124—94no—
594#124—92no—
595#123—32no—
596#123—94no—
597#123—94no—
598#123—94no—
599#123—94no—
600C22⋊Q8—31no—
601C22⋊Q8—94no—
602C22⋊Q8—94no—
603C22⋊Q8—94no—
604C22⋊Q8—94no—
605C22⋊Q8—92no—
606#121—31no—
607#121—32no—
608#121—32no—
609#121—94no—
610#121—92no—
611#121—94no—
612C4×Q8—31no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×Q8—91no—
616C4×Q8—92no—
617C4×Q8—91no—
618C4×Q8—91no—
619C4×Q8—91no—
620C4×Q8—92no—
621C4×D4—32no—
622C4×D4—32no—
623C4×D4—31no—
624C4×D4—32no—
625C4×D4—92no—
626C4×D4—94no—
627C4×D4—94no—
628C4×D4—94no—
629C4×D4—92no—
630C4×D4—92no—
631C4×D4—92no—
632#117—32no—
633#117—94no—
634C2×C4⋊C4—94no—
635C2×C4⋊C4—92no—
636C2×C4⋊C4—92no—
637C2×C4⋊C4—91no—
638C2×C42—92no—
639C2×C42D3211yescharacteristic
640C23×C3—21no—
641C23×C3—34no—
642C23×C3—32no—
643C23×C3C23×D311yescharacteristic
644C23×C3C23×D311yescharacteristic
645C22×D3C23×D314yes—
646C22×D3C23×D312yes—
647C3×Q8—62no—
648C3×Q8—122no—
649C3×D4—64no—
650C3×D4—68no—
651C3×D4—64no—
652C3×D4—64no—
653C3×D4—62no—
654C3×D4—122no—
655C2×C3×C4—24no—
656C2×C3×C4—24no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—32no—
670C2×C3×C4—34no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—42no—
674C2×C3×C4—64no—
675C2×C3×C4—124no—
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688#67—28no—
689#67—24no—
690#67—68no—
691#67—68no—
692#67—124no—
693#67—124no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—32no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—68no—
707C2×Dic3—64no—
708C2×Dic3—64no—
709C2×Dic3—68no—
710C2×Dic3—64no—
711C2×Dic3—64no—
712C2×Dic3—124no—
713C2×Dic3—124no—
714C2×Dic3—124no—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D314yes—
717C2×Dic3C23×D312yes—
718C2×Dic3C23×D312yes—
719D12—24no—
720D12—22no—
721D12—24no—
722D12—42no—
723C4×D3—24no—
724C4×D3—44no—
725C4×D3—68no—
726C4×D3—124no—
727C4×D3—124no—
728Dic6—22no—
729Dic6—34no—
730Dic6—34no—
731Dic6—42no—
732Dic6—64no—
733Dic6—64no—
734Dic6—64no—
735Dic6—68no—
736Dic6—64no—
737Dic6—62no—
738Dic6—62no—
739Dic6—124no—
740Dic6—124no—
741C2×C32—22no—
742C2×C32C22×#4111yescharacteristic
743C2×C32C2×H(5,𝔽2)11yescharacteristic
744C2×C32C2×2−1+411yescharacteristic
745C3×D3—42no—
746C3×D3—44no—
747#41—124no—
748#41—188no—
749#41—368no—
750C2×Q8—31no—
751C2×Q8—32no—
752C2×Q8—94no—
753C2×Q8—91no—
754C2×Q8—92no—
755C2×Q8—91no—
756C2×Q8—184no—
757C2×D4—32no—
758C2×D4—34no—
759C2×D4—31no—
760C2×D4—32no—
761C2×D4—32no—
762C2×D4—32no—
763C2×D4—94no—
764C2×D4—94no—
765C22×C4—32no—
766C22×C4—34no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—94no—
770C22×C4—92no—
771C22×C4—92no—
772C22×C4C2×D3211yescharacteristic
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C4⋊C4—32no—
776C4⋊C4—32no—
777C4⋊C4—32no—
778C4⋊C4—31no—
779C4⋊C4—32no—
780C4⋊C4—32no—
781C4⋊C4—31no—
782C4⋊C4—32no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—92no—
788C4⋊C4—91no—
789C4⋊C4—92no—
790C4⋊C4—91no—
791C4⋊C4—92no—
792C4⋊C4—92no—
793C4⋊C4—92no—
794C22⋊C4—32no—
795C22⋊C4—32no—
796C22⋊C4—32no—
797C22⋊C4—34no—
798C22⋊C4—34no—
799C22⋊C4—32no—
800C22⋊C4—32no—
801C22⋊C4—94no—
802C22⋊C4—94no—
803C22⋊C4—94no—
804C22⋊C4—94no—
805C22⋊C4—94no—
806C42—32no—
807C42—94no—
808C42—92no—
809C42—92no—
810C42—92no—
811C42—92no—
812C42C2×D3211yescharacteristic
813C42C2×D3211yescharacteristic
814C42C2×D3211yescharacteristic
815C42C2×D3211yescharacteristic
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—62no—
825C22×C3—64no—
826C22×C3—62no—
827C22×C3—64no—
828C22×C3—64no—
829C22×C3—62no—
830C22×C3#100412yes—
831C22×C3#100912yes—
832C22×C3C24×D311yescharacteristic
833C22×C3C24×D311yescharacteristic
834C2×D3—24no—
835C2×D3—22no—
836C2×D3—24no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—24no—
840C3×C4—22no—
841C3×C4—22no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—64no—
857C3×C4—62no—
858C3×C4D3×#4112yes—
859C3×C4D3×#4112yes—
860C3×C4#101012yes—
861C3×C4#101012yes—
862Dic3—24no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—34no—
867Dic3—34no—
868Dic3—64no—
869Dic3—64no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—122no—
878C32#352211yescharacteristic, complemented, Sylow
879C23—32no—
880C23—34no—
881C23C22×D3211yescharacteristic
882Q8—62no—
883Q8—94no—
884Q8—122no—
885Q8—184no—
886Q8—182no—
887Q8—364no—
888D4—68no—
889D4—64no—
890D4—62no—
891D4—64no—
892D4—64no—
893D4—122no—
894D4—188no—
895D4—364no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—34no—
902C2×C4—32no—
903C2×C4—64no—
904C2×C4—92no—
905C2×C4—92no—
906C2×C4—92no—
907C2×C4—92no—
908C2×C4—124no—
909C2×C4—188no—
910C2×C4—184no—
911C2×C4—184no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3211yescharacteristic
916C2×C4C22×D3211yescharacteristic
917C2×C4C22×D3211yescharacteristic
918C2×C4C22×D3211yescharacteristic
919C2×C4C22×D3211yescharacteristic
920C2×C3—24no—
921C2×C3—22no—
922C2×C3—22no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—124no—
927C2×C3—122no—
928C2×C3C2×#100411yescharacteristic
929C2×C3C2×D3×#4111yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3C2×#100911yescharacteristic
932C2×C3C2×#101011yescharacteristic
933C2×C3C2×#101011yescharacteristic
934D3—42no—
935D3—44no—
936C22—21no—
937C22—21no—
938C22—62no—
939C22—64no—
940C22—62no—
941C22—64no—
942C22—64no—
943C22—62no—
944C22#6430712yes—
945C22C23×D3211yescharacteristic
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—62no—
951C4—62no—
952C4—64no—
953C4—62no—
954C4—94no—
955C4—182no—
956C4—182no—
957C4—182no—
958C4#6429812yes—
959C4#6430612yes—
960C3—21no—
961C3#8612811yescharacteristic, complemented
962C3#8622911yescharacteristic, complemented
963C2—22no—
964C2—122no—
965C2—124no—
966C2C2×#6429811yescharacteristic
967C2C2×#6430611yescharacteristic
968C2C2×#6430711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
2. C3×#5479C2semidirect
3. C3×#5477C2semidirect
4. #10594965C2semidirect
5. #10594929C2semidirect
6. #10594918C2semidirect
7. #10594907C2semidirect
8. #10594888C2semidirect
9. #10593983C2semidirect
10. #10593981C2semidirect
11. #10593956C2semidirect
12. #10593951C2semidirect
13. #10593944C2semidirect
14. #10593941C2semidirect
15. #10593906C2semidirect
16. #10593887C2semidirect
17. #10593856C2semidirect
115. #5479D3semidirect
116. #5477D3semidirect
351. #634#41semidirect
878. C32#3522semidirect
961. C3#86128semidirect
962. C3#86229semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#54792
C3×#54772
#105949652
#105949292
#105949182
#105949072
#105948882
#105939832
#105939812
#105939562
#105939512
#105939442
#105939412
#105939062
#105938872
#105938562
#862293
#861283