Finite Group Databasebeta

← #11909795

Subgroups — #11909795

Order 1152.

2325 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596051C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595388C212yesmaximal, complemented
5#10595382C212yesmaximal, complemented
6#10594518C212yesmaximal, complemented
7#10594460C212yesmaximal, complemented
8#10594458C214yesmaximal, complemented
9#10594372C214yesmaximal, complemented
10#10593958C211yesmaximal, characteristic, complemented
11#10593955C212yesmaximal, complemented
12#10593907C211yesmaximal, characteristic, complemented
13#10593901C212yesmaximal, complemented
14#10593900C211yesmaximal, characteristic, complemented
15C4×#3797C211yesmaximal, characteristic, complemented
16#10593889C212yesmaximal, complemented
17#10593869C212yesmaximal, complemented
18#87055—31nomaximal
19#87043—31nomaximal
20C2×#3799C2214yes—
21C2×#3797C2211yescharacteristic
22C2×#3796C2212yes—
23C2×#3796C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64156C2211yescharacteristic
26#64155C2211yescharacteristic
27#64107C2212yes—
28#64104C2211yescharacteristic
29#64103C2212yes—
30#64099C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2212yes—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33#64081C2212yes—
34C42×C3⋊D3C2211yescharacteristic
35C3×#947C2212yes—
36C3×Q8×Dic3C2212yes—
37C3×#894C2214yes—
38C3×#893C2212yes—
39C3×#888C2214yes—
40C3×#888C2212yes—
41C3×#875C2212yes—
42C3×#874C2211yescharacteristic
43C3×C4×D12C2212yes—
44C3×#869C2212yes—
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49C4×#627C2212yes—
50#63916C2212yes—
51#63916C2212yes—
52#63916C2212yes—
53#63911C2212yes—
54#63910C2214yes—
55#63907C2214yes—
56#63904C2214yes—
57#63900C2211yescharacteristic
58#63900C2212yes—
59#63898C2212yes—
60#63898C2212yes—
61#63894C2212yes—
62#63893C2214yes—
63Dic3×D12C2212yes—
64#63890C2214yes—
65#63888C2214yes—
66#63887C2214yes—
67#63886C2214yes—
68#63883C2212yes—
69C4×#624C2212yes—
70#63880C2214yes—
71#63880C2214yes—
72#63877C2214yes—
73D3×Dic3⋊C4C2214yes—
74#63871C2212yes—
75#63869C2212yes—
76#63863C2212yes—
77#63858C2214yes—
78#63856C2214yes—
79#63854C2214yes—
80#63854C2214yes—
81#63852C2214yes—
82#63843C2211yescharacteristic
83#63843C2211yescharacteristic
84#63838C2212yes—
85C3×#559—31no—
86C3×Q82—31no—
87#5733—34no—
88#5733—32no—
89#5730—32no—
90#5730—31no—
91#5726—34no—
92#5726—32no—
93#5725—32no—
94#5725—31no—
95#5718—31no—
96#5716—31no—
97#5682—32no—
98#5681—32no—
99#5680—32no—
100#5677—32no—
101#5662—34no—
102#5655—34no—
103#5585—32no—
104#5585D311yescharacteristic, complemented
105#5580—31no—
106#5580—31no—
107#5580—32no—
108#5580—61no—
109#5579—31no—
110#5577—31no—
111#5576—32no—
112#5574—32no—
113C4×D3×Q8—31no—
114C4×D3×Q8—31no—
115Q8×Dic6D311yescharacteristic, complemented
116#5551—32no—
117#5548—32no—
118#5546—32no—
119#5539—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2312yes—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C3×D12C2312yes—
128C2×C3×D12C2312yes—
129C2×C3×D12C2312yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2312yes—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#624C2312yes—
140C2×#624C2312yes—
141C2×#624C2314yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2314yes—
144#3799—48no—
145#3797—24no—
146#3796—28no—
147#3796—44no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151C32×C42C2312yes—
152#3752C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155#3752C2312yes—
156#3752C2312yes—
157C4⋊(C3⋊Dic3)C2312yes—
158C4⋊(C3⋊Dic3)C2311yescharacteristic
159#3750C2312yes—
160#3750C2312yes—
161C4×C3⋊Dic3C2311yescharacteristic
162C4×C3⋊Dic3C2311yescharacteristic
163C4×C3⋊Dic3C2311yescharacteristic
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×C4⋊Dic3C2314yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×C4⋊Dic3C2311yescharacteristic
171C3×C4⋊Dic3C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×Dic3⋊C4C2314yes—
174C3×Dic3⋊C4C2312yes—
175C3×C4×Dic3C2314yes—
176C3×C4×Dic3C2312yes—
177C3×C4×Dic3C2312yes—
178#3724C2312yes—
179#3724C2314yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2312yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3522—91noSylow
190C2×#239—32no—
191C2×#239—32no—
192C2×#239—34no—
193C2×D3×Q8—31no—
194C2×D3×Q8—31no—
195C2×#237—32no—
196C2×#237—32no—
197C2×#235—34no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—34no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8—32no—
202C3×#127—31no—
203C3×#124—32no—
204C3×#124—32no—
205C3×#123—34no—
206C3×C4×Q8—21no—
207C3×C4×Q8—32no—
208C3×C4×Q8—31no—
209C3×C4×Q8—32no—
210C3×C4×Q8—31no—
211C3×C4×Q8C2×D311yescharacteristic
212C3×C4×Q8C2×D311yescharacteristic
213C3×C4×D4—32no—
214C3×C4×D4—32no—
215#947—31no—
216#947—31no—
217#947—32no—
218#947—34no—
219#947—61no—
220#947C2×D312yes—
221#946—31no—
222#946—31no—
223#946—34no—
224#946—34no—
225#946—32no—
226#946—34no—
227#946—61no—
228Q8×Dic3—31no—
229Q8×Dic3—31no—
230Q8×Dic3C2×D312yes—
231#940—32no—
232#939—34no—
233#938—32no—
234#938—32no—
235#938—32no—
236#936—32no—
237D4×Dic3—32no—
238D4×Dic3—32no—
239D4×Dic3—32no—
240C4×#67—34no—
241#924—34no—
242C2×Dic3⋊C4—34no—
243#898—32no—
244#898—32no—
245#898—34no—
246#898—62no—
247#897—32no—
248#897—34no—
249#896—34no—
250#895—32no—
251#895—32no—
252#895—34no—
253#895—32no—
254#895—31no—
255#895—31no—
256#895—34no—
257#895—61no—
258#894—32no—
259#894—32no—
260#894—34no—
261#894—34no—
262#894—34no—
263#894—62no—
264#894C2×D314yes—
265#893—32no—
266#893—32no—
267#893—34no—
268#893—32no—
269#893C2×D312yes—
270D3×C4⋊C4—34no—
271D3×C4⋊C4—31no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—31no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277#890—31no—
278#890—31no—
279#890—32no—
280#890—61no—
281#888C2×D314yes—
282#888C2×D312yes—
283#887—31no—
284#887—31no—
285#887—32no—
286#887—32no—
287#886—34no—
288#885—34no—
289#885—34no—
290#884—34no—
291#883—34no—
292#883—34no—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#879—34no—
296#878—34no—
297#878—34no—
298#877—34no—
299#875—34no—
300#875C2×D312yes—
301#874—32no—
302#874C2×D311yescharacteristic
303C4×D12—32no—
304C4×D12—32no—
305C4×D12—31no—
306C4×D12—32no—
307C4×D12—31no—
308C4×D12—34no—
309C4×D12—34no—
310C4×D12—32no—
311C4×D12—62no—
312C4×D12—61no—
313C4×D12C2×D312yes—
314#872—32no—
315#872—32no—
316#872—34no—
317#872—62no—
318C42×D3—31no—
319C42×D3—31no—
320C42×D3—32no—
321C42×D3—32no—
322C42×D3—61no—
323#870—32no—
324#869C2×D312yes—
325#869C2×D311yescharacteristic
326C4×Dic6—32no—
327C4×Dic6—32no—
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D311yescharacteristic
330C4×Dic6C2×D311yescharacteristic
331C22×C3⋊D3C2412yes—
332C22×C3⋊D3C2411yescharacteristic
333C22×C3×D3C2414yes—
334C32×Q8—22no—
335C2×C32×C4C2412yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2412yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C4⋊(C3⋊D3)—24no—
345C4⋊(C3⋊D3)—22no—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—24no—
348C4×C3⋊D3—22no—
349C4×C3⋊D3—22no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2412yes—
355C3×D12—24no—
356C3×D12—24no—
357C3×D12—42no—
358C3×C4×D3—44no—
359C3×Dic6—22no—
360C3×Dic6—42no—
361C3×Dic6—44no—
362C3×Dic6#4114yescomplemented
363#627—24no—
364#626—28no—
365#626—28no—
366#626—44no—
367#624—24no—
368#624—24no—
369#624—44no—
370D3×Dic3—28no—
371D3×Dic3—44no—
372#559—31no—
373#559—92no—
374Q82—31no—
375#554—92no—
376#554—91no—
377#550—91no—
378#548—92no—
379#547—92no—
380#547—94no—
381#542—94no—
382#542—92no—
383#532—92no—
384#532—91no—
385#529—92no—
386#529—91no—
387#520—92no—
388C2×C4×Q8—91no—
389C2×C3×Q8—21no—
390C2×C3×Q8—31no—
391C2×C3×Q8—31no—
392C2×C3×Q8—34no—
393C2×C3×Q8—32no—
394C2×C3×Q8C22×D311yescharacteristic
395C2×C3×Q8C22×D311yescharacteristic
396C2×C3×D4—32no—
397C2×C3×D4—32no—
398C2×C3×D4—32no—
399C22×C3×C4—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C22×Dic3—34no—
404C22×Dic3—34no—
405#239—68no—
406#239—128no—
407#239—124no—
408D3×Q8—64no—
409D3×Q8—64no—
410#237—68no—
411#237—124no—
412#235—128no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—32no—
418C2×D12—32no—
419C2×D12—34no—
420C2×D12—62no—
421C2×D12—61no—
422C2×D12C22×D312yes—
423C2×D12C22×D312yes—
424C2×D12C22×D312yes—
425C2×C4×D3—34no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—61no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—62no—
445C2×C4×D3C22×D314yes—
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6C22×D311yescharacteristic
449C2×Dic6C22×D314yes—
450C2×Dic6C22×D312yes—
451C2×Dic6C22×D311yescharacteristic
452C3×C4⋊C4—21no—
453C3×C4⋊C4—22no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4—34no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D311yescharacteristic
465C3×C4⋊C4C22×D312yes—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C42—21no—
470C3×C42—22no—
471C3×C42—32no—
472C3×C42—32no—
473C3×C42—34no—
474C3×C42C22×D311yescharacteristic
475C3×C42C22×D312yes—
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D312yes—
478#217—34no—
479#217—34no—
480#217—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—62no—
497(C2×D3)⋊C4—62no—
498(C2×D3)⋊C4—62no—
499(C2×D3)⋊C4—62no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4C22×D314yes—
502(C2×D3)⋊C4C22×D314yes—
503(C2×D3)⋊C4C22×D314yes—
504C4⋊Dic3—31no—
505C4⋊Dic3—31no—
506C4⋊Dic3—32no—
507C4⋊Dic3—32no—
508C4⋊Dic3—32no—
509C4⋊Dic3—32no—
510C4⋊Dic3—34no—
511C4⋊Dic3—62no—
512C4⋊Dic3—61no—
513C4⋊Dic3C22×D312yes—
514C4⋊Dic3C22×D311yescharacteristic
515C4⋊Dic3C22×D311yescharacteristic
516C4⋊Dic3C22×D312yes—
517C4⋊Dic3C22×D314yes—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—32no—
524Dic3⋊C4—32no—
525Dic3⋊C4—32no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—62no—
530Dic3⋊C4—62no—
531Dic3⋊C4C22×D314yes—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D312yes—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—32no—
541C4×Dic3—32no—
542C4×Dic3—32no—
543C4×Dic3—32no—
544C4×Dic3—61no—
545C4×Dic3—61no—
546C4×Dic3—61no—
547C4×Dic3C22×D312yes—
548C4×Dic3C22×D312yes—
549C4×Dic3C22×D314yes—
550C22×C32C2511yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—22no—
556C2×C3⋊D3H(5,𝔽2)12yes—
557C2×C3×D3—24no—
558C2×C3×D3—24no—
559C2×C3×D3—24no—
560C32×C4—22no—
561C32×C4—21no—
562C32×C4—22no—
563C32×C4C2×#4112yes—
564C32×C42−1+412yes—
565C3⋊Dic3—22no—
566C3⋊Dic3—21no—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3×Dic3—22no—
570C3×Dic3—24no—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3C2×#4114yes—
574C2×#41—94no—
575C2×#41—92no—
576C2×#41—92no—
577C22×Q8—91no—
578C4⋊Q8—32no—
579C4⋊Q8—34no—
580C4⋊Q8—31no—
581C4⋊Q8—32no—
582#127—31no—
583#127—92no—
584#126—94no—
585#126—92no—
586#125—92no—
587#125—91no—
588#124—32no—
589#124—32no—
590#124—94no—
591#124—94no—
592#124—92no—
593#124—91no—
594#123—34no—
595#123—94no—
596#123—94no—
597#123—94no—
598#123—92no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—94no—
604C22⋊Q8—91no—
605#121—94no—
606#121—92no—
607#121—92no—
608#121—92no—
609#121—94no—
610#121—91no—
611C4×Q8—32no—
612C4×Q8—31no—
613C4×Q8—31no—
614C4×Q8—32no—
615C4×Q8—92no—
616C4×Q8—92no—
617C4×Q8—91no—
618C4×Q8—91no—
619C4×Q8D3211yescharacteristic
620C4×D4—32no—
621C4×D4—32no—
622C4×D4—94no—
623C4×D4—94no—
624C4×D4—92no—
625C4×D4—92no—
626C4×D4—94no—
627C4×D4—92no—
628C4×D4—92no—
629C4×D4—92no—
630C4×D4—91no—
631#117—94no—
632#117—92no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—92no—
635C2×C4⋊C4—92no—
636C2×C4⋊C4—94no—
637C2×C42—92no—
638C2×C42—91no—
639C23×C3—34no—
640C22×D3—31no—
641C22×D3—31no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—61no—
645C22×D3—62no—
646C22×D3C23×D314yes—
647C3×Q8—22no—
648C3×Q8—22no—
649C3×Q8—34no—
650C3×Q8—42no—
651C3×Q8—62no—
652C3×Q8—124no—
653C3×Q8—122no—
654C3×D4—64no—
655C3×D4—64no—
656C3×D4—122no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—34no—
667C2×C3×C4—124no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678#67—68no—
679#67—68no—
680#67—124no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—62no—
693C2×Dic3—68no—
694C2×Dic3—124no—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D314yes—
699C2×Dic3C23×D312yes—
700D12—24no—
701D12—24no—
702D12—42no—
703D12—64no—
704D12—64no—
705D12—68no—
706D12—68no—
707D12—62no—
708D12—62no—
709D12—122no—
710D12—124no—
711D12—124no—
712C4×D3—44no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—62no—
717C4×D3—62no—
718C4×D3—68no—
719C4×D3—64no—
720C4×D3—62no—
721C4×D3—62no—
722C4×D3—62no—
723C4×D3—64no—
724C4×D3—62no—
725C4×D3—64no—
726C4×D3—122no—
727C4×D3—122no—
728C4×D3—124no—
729C4×D3—122no—
730C4×D3—124no—
731C4×D3—124no—
732C4×D3—124no—
733Dic6—22no—
734Dic6—44no—
735Dic6—42no—
736Dic6—64no—
737Dic6—64no—
738Dic6#23914yescomplemented
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C2×C32C2×2−1+411yescharacteristic
742C3⋊D3—22no—
743C3⋊D3—42no—
744C3×D3—44no—
745#41—188no—
746#41—368no—
747#41—364no—
748C2×Q8—31no—
749C2×Q8—31no—
750C2×Q8—34no—
751C2×Q8—32no—
752C2×Q8—92no—
753C2×Q8—184no—
754C2×Q8C2×D3211yescharacteristic
755C2×D4—32no—
756C2×D4—32no—
757C2×D4—32no—
758C2×D4—94no—
759C2×D4—94no—
760C2×D4—94no—
761C2×D4—91no—
762C2×D4—92no—
763C22×C4—34no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—94no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—92no—
773C4⋊C4—31no—
774C4⋊C4—34no—
775C4⋊C4—32no—
776C4⋊C4—32no—
777C4⋊C4—31no—
778C4⋊C4—32no—
779C4⋊C4—32no—
780C4⋊C4—34no—
781C4⋊C4—92no—
782C4⋊C4—94no—
783C4⋊C4—92no—
784C4⋊C4—92no—
785C4⋊C4—94no—
786C4⋊C4—92no—
787C4⋊C4—92no—
788C4⋊C4—91no—
789C4⋊C4—92no—
790C4⋊C4C2×D3211yescharacteristic
791C4⋊C4C2×D3212yes—
792C22⋊C4—34no—
793C22⋊C4—34no—
794C22⋊C4—34no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—92no—
803C22⋊C4—92no—
804C42—32no—
805C42—32no—
806C42—34no—
807C42—92no—
808C42—92no—
809C42—91no—
810C42—91no—
811C42—91no—
812C42C2×D3211yescharacteristic
813C42C2×D3212yes—
814C22×C3—21no—
815C22×C3—64no—
816C22×C3—64no—
817C22×C3—64no—
818C22×C3C24×D311yescharacteristic
819C22×C3C24×D311yescharacteristic
820C2×D3—24no—
821C2×D3—24no—
822C2×D3—24no—
823C2×D3—32no—
824C2×D3—32no—
825C2×D3—62no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—21no—
844C3×C4—22no—
845C3×C4—22no—
846C3×C4—21no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—34no—
850C3×C4—41no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—62no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—64no—
857C3×C4C2×#23912yes—
858C3×C4#100712yes—
859C3×C4D3×#4112yes—
860C3×C4#101012yes—
861Dic3—22no—
862Dic3—22no—
863Dic3—24no—
864Dic3—22no—
865Dic3—61no—
866Dic3—62no—
867Dic3—61no—
868Dic3—61no—
869Dic3—62no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—121no—
874Dic3—122no—
875Dic3—121no—
876Dic3—121no—
877Dic3C2×#23914yes—
878C32#352211yescharacteristic, complemented, Sylow
879C23—34no—
880C23—91no—
881C23—92no—
882Q8—22no—
883Q8—34no—
884Q8—62no—
885Q8—124no—
886Q8—122no—
887Q8—184no—
888D4—64no—
889D4—64no—
890D4—122no—
891D4—184no—
892D4—188no—
893D4—188no—
894D4—182no—
895D4—364no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—34no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—92no—
905C2×C4—124no—
906C2×C4—182no—
907C2×C4—184no—
908C2×C4—188no—
909C2×C4—184no—
910C2×C4—182no—
911C2×C4—182no—
912C2×C4—184no—
913C2×C4—364no—
914C2×C4—364no—
915C2×C4C22×D3212yes—
916C2×C4C22×D3211yescharacteristic
917C2×C4C22×D3212yes—
918C2×C4C22×D3211yescharacteristic
919C2×C4C22×D3211yescharacteristic
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—124no—
924C2×C3C22×#23911yescharacteristic
925C2×C3C2×#100711yescharacteristic
926C2×C3C2×D3×#4111yescharacteristic
927C2×C3C2×#101011yescharacteristic
928C2×C3D3×H(5,𝔽2)11yescharacteristic
929C2×C3D3×H(5,𝔽2)11yescharacteristic
930D3—44no—
931D3—62no—
932D3—62no—
933D3—122no—
934D3—122no—
935D3—122no—
936D3—242no—
937C22—64no—
938C22—64no—
939C22—64no—
940C22—92no—
941C22—181no—
942C22—181no—
943C22—182no—
944C22—182no—
945C22—182no—
946C22C23×D3211yescharacteristic
947C4—22no—
948C4—22no—
949C4—21no—
950C4—34no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—64no—
955C4—181no—
956C4—182no—
957C4—181no—
958C4—181no—
959C4#6429712yes—
960C4D3×#23912yes—
961C3—21no—
962C3#8704311yescharacteristic, complemented
963C3#8705511yescharacteristic, complemented
964C2—124no—
965C2—182no—
966C2—362no—
967C2C2×#6429711yescharacteristic
968C2C2×D3×#23911yescharacteristic
969C2#1059669211yescharacteristic
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. #10596051C2semidirect
2. C3×#5585C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595388C2semidirect
5. #10595382C2semidirect
6. #10594518C2semidirect
7. #10594460C2semidirect
8. #10594458C2semidirect
9. #10594372C2semidirect
10. #10593958C2semidirect
11. #10593955C2semidirect
12. #10593907C2semidirect
13. #10593901C2semidirect
14. #10593900C2semidirect
15. C4×#3797C2semidirect
16. #10593889C2semidirect
17. #10593869C2semidirect
104. #5585D3semidirect
115. Q8×Dic6D3semidirect
362. C3×Dic6#41semidirect
738. Dic6#239semidirect
878. C32#3522semidirect
962. C3#87043semidirect
963. C3#87055semidirect

Maximal subgroups

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

subgroupindex
#105960512
C3×#55852
C3×Q8×Dic62
#105953882
#105953822
#105945182
#105944602
#105944582
#105943722
#105939582
#105939552
#105939072
#105939012
#105939002
C4×#37972
#105938892
#105938692
#870553
#870433