Finite Group Databasebeta

← #11909919

Subgroups — #11909919

Order 1152.

2090 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596055C211yesmaximal, characteristic, complemented
2C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595403C212yesmaximal, complemented
5#10595354C212yesmaximal, complemented
6#10594348C214yesmaximal, complemented
7#10594347C212yesmaximal, complemented
8#10594333C212yesmaximal, complemented
9#10594331C214yesmaximal, complemented
10#10593976C212yesmaximal
11#10593903C211yesmaximal, characteristic, complemented
12#10593873C212yesmaximal, complemented
13#10593870C211yesmaximal, characteristic
14#10593860C211yesmaximal, characteristic, complemented
15#10593859C211yesmaximal, characteristic, complemented
16#10593852C212yesmaximal, complemented
17#10593850C212yesmaximal, complemented
18#87025—31nomaximal
19#85804—31nomaximal
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3797C2212yes—
22C32×C4×Q8C2211yescharacteristic
23#64155C2212yes—
24#64107C2214yes—
25#64101C2212yes—
26#64084C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30C3×Q8×Dic3C2211yescharacteristic
31C3×#944C2212yes—
32C3×D3×C4⋊C4C2212yes—
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#889C2214yes—
35C3×#887C2212yes—
36C3×#887C2211yescharacteristic
37C3×#887C2212yes—
38C3×C42×D3C2211yescharacteristic
39C3×C42×D3C2212yes—
40C3×#870C2212yes—
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2212yes—
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63918C2212yes—
47C4×#627C2214yes—
48#63909C2211yescharacteristic
49#63904C2214yes—
50C4×#626C2212yes—
51#63895C2214yes—
52#63894C2212yes—
53#63888C2214yes—
54#63874C2212yes—
55#63871C2212yes—
56#63870C2214yes—
57#63869C2212yes—
58#63869C2212yes—
59#63869C2211yescharacteristic
60#63868C2214yes—
61#63868C2214yes—
62#63868C2212yes—
63#63867C2214yes—
64#63866C2212yes—
65#63864C2211yescharacteristic
66#63857C2212yes—
67#63856C2212yes—
68#63856C2211yescharacteristic
69#63855C2214yes—
70#63851C2214yes—
71#63850C2212yes—
72#63850C2214yes—
73#63848C2214yes—
74#63847C2214yes—
75#63845C2214yes—
76#63844C2212yes—
77#63844C2212yes—
78Dic3×Dic6C2212yes—
79Dic3×Dic6C2212yes—
80#63841C2212yes—
81#63839C2214yes—
82#63838C2214yes—
83#63836C2214yes—
84#63836C2214yes—
85C3×#557—31no—
86C2×C3×C4×Q8—31no—
87Q8×#67—32no—
88#5731—32no—
89#5728—31no—
90#5727—32no—
91#5727—31no—
92#5696—34no—
93#5693—34no—
94#5691—32no—
95#5685—32no—
96#5584—31no—
97#5584—31no—
98#5584—32no—
99#5584—61no—
100#5583—32no—
101#5583—34no—
102#5581—32no—
103#5580—31no—
104#5578—32no—
105Q8×D12—31no—
106#5572—32no—
107#5572—32no—
108C4×D3×Q8D311yescharacteristic, complemented
109#5570—31no—
110#5568—32no—
111#5567—32no—
112#5567—31no—
113#5567D311yescharacteristic, complemented
114#5513—34no—
115#5513—32no—
116#5479—32no—
117#5479—31no—
118#5470—31no—
119#5470—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4⋊(C3⋊D3)C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×#634C2312yes—
124C3×D3×Q8—24no—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2314yes—
135C2×#626C2312yes—
136C2×#624C2314yes—
137#3797—28no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140C32×C42C2312yes—
141C32×C42C2311yescharacteristic
142#3752C2312yes—
143#3752C2314yes—
144#3752C2314yes—
145C4⋊(C3⋊Dic3)C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148#3750C2314yes—
149C4×C3⋊Dic3C2314yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2312yes—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×C4⋊Dic3C2311yescharacteristic
154C3×C4⋊Dic3C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2312yes—
157C3×Dic3⋊C4C2312yes—
158C3×Dic3⋊C4C2312yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×C4×Dic3C2312yes—
163C3×C4×Dic3C2311yescharacteristic
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170#3724C2312yes—
171#3724C2314yes—
172#3724C2314yes—
173#3724C2312yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179#3722C2312yes—
180#3722C2312yes—
181#3722C2314yes—
182#3722C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—31no—
189C2×D3×Q8—32no—
190C2×D3×Q8—32no—
191C2×D3×Q8C2×D311yescharacteristic
192C3×C4⋊Q8—32no—
193C3×C4⋊Q8—31no—
194C3×#125—34no—
195C3×#125—32no—
196C3×C4×Q8—21no—
197C3×C4×Q8—31no—
198C3×C4×Q8—31no—
199C3×C4×Q8—32no—
200C3×C4×Q8—32no—
201C3×C4×Q8—31no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×Q8C2×D311yescharacteristic
206C3×C4×Q8C2×D311yescharacteristic
207C2×C3×C4⋊C4—32no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C42—31no—
210C2×C3×C42—32no—
211#947—31no—
212#946—32no—
213#946—32no—
214#946—32no—
215#946—31no—
216#946—32no—
217#946—34no—
218#946—62no—
219Q8×Dic3—32no—
220Q8×Dic3—32no—
221Q8×Dic3C2×D311yescharacteristic
222#944—34no—
223#944—32no—
224#944C2×D312yes—
225#930—31no—
226#929—34no—
227#929—32no—
228C4×#67—34no—
229C4×#67—32no—
230#926—32no—
231#926—34no—
232#924—31no—
233#924—32no—
234#924—32no—
235#924—34no—
236#898—34no—
237#898—34no—
238#898—34no—
239#898—34no—
240#898—34no—
241#898—32no—
242#898—34no—
243#898—64no—
244#897—32no—
245#897—32no—
246#897—34no—
247#896—34no—
248#896—34no—
249#896—34no—
250#895—31no—
251#894—34no—
252#894—32no—
253#893—34no—
254#893—32no—
255#892—32no—
256#892—32no—
257#892—32no—
258#892—34no—
259#892—34no—
260#892—62no—
261D3×C4⋊C4C2×D312yes—
262D3×C4⋊C4C2×D311yescharacteristic
263#890—34no—
264#890—31no—
265#890—32no—
266#890—32no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#889C2×D314yes—
274#888—34no—
275#888—32no—
276#887—34no—
277#887—34no—
278#887—32no—
279#887—32no—
280#887C2×D312yes—
281#887C2×D312yes—
282#887C2×D311yescharacteristic
283#876—34no—
284#876—34no—
285#876—32no—
286#875—31no—
287#875—32no—
288#875—32no—
289#875—62no—
290C4×D12—32no—
291C4×D12—31no—
292C4×D12—31no—
293C4×D12—32no—
294C4×D12—61no—
295#872—34no—
296#872—34no—
297#872—34no—
298#872—32no—
299#872—32no—
300C42×D3C2×D312yes—
301C42×D3C2×D311yescharacteristic
302#870—32no—
303#870—32no—
304#870—31no—
305#870—34no—
306#870C2×D312yes—
307#869—32no—
308#869—31no—
309#869—31no—
310#869—32no—
311#869—61no—
312#869C2×D311yescharacteristic
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—34no—
320C4×Dic6—34no—
321C4×Dic6—62no—
322C4×Dic6C2×D312yes—
323C4×Dic6C2×D312yes—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D311yescharacteristic
326C22×C3⋊D3C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×Q8—22no—
329C2×C32×C4C2412yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2414yes—
335C2×C3⋊Dic3C2412yes—
336C4⋊(C3⋊D3)—22no—
337C4×C3⋊D3—24no—
338#634—24no—
339C2×C3×Dic3C2411yescharacteristic
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C3×C4×D3—22no—
348C3×C4×D3—24no—
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3—24no—
352C3×Dic6—24no—
353C3×Dic6—22no—
354C3×Dic6—24no—
355C3×Dic6#4114yes—
356#627—28no—
357#626—24no—
358#624—28no—
359#557—31no—
360#557—91no—
361#557—92no—
362#556—92no—
363#556—91no—
364#552—92no—
365#552—94no—
366D4×Q8—91no—
367D4×Q8—92no—
368#541—94no—
369#541—92no—
370#533—92no—
371#533—91no—
372#529—91no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—31no—
376C2×C3×Q8—21no—
377C2×C3×Q8—31no—
378C2×C3×Q8—32no—
379C2×C3×Q8—31no—
380C2×C3×Q8—32no—
381C2×C3×Q8—64no—
382C2×C3×Q8C22×D311yescharacteristic
383C2×C3×Q8C22×D311yescharacteristic
384C22×C3×C4—31no—
385C22×C3×C4—32no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—32no—
389C2×#67—32no—
390D3×Q8—24no—
391D3×Q8—68no—
392D3×Q8—68no—
393C2×D12—32no—
394C2×D12—31no—
395C2×D12—31no—
396C2×D12—61no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—62no—
402C2×C4×D3C22×D311yescharacteristic
403C2×C4×D3C22×D312yes—
404C2×C4×D3C22×D311yescharacteristic
405C2×C4×D3C22×D311yescharacteristic
406C2×C4×D3C22×D312yes—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—62no—
412C2×Dic6C22×D312yes—
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D312yes—
415C2×Dic6C22×D311yescharacteristic
416C3×C4⋊C4—21no—
417C3×C4⋊C4—22no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4—31no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4C22×D311yescharacteristic
431C3×C4⋊C4C22×D311yescharacteristic
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C42—22no—
435C3×C42—21no—
436C3×C42—31no—
437C3×C42—32no—
438C3×C42—31no—
439C3×C42—32no—
440C3×C42—32no—
441C3×C42—34no—
442C3×C42—31no—
443C3×C42—32no—
444C3×C42C22×D312yes—
445C3×C42C22×D312yes—
446C3×C42C22×D311yescharacteristic
447C3×C42C22×D311yescharacteristic
448#217—34no—
449#217—32no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—32no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—64no—
468(C2×D3)⋊C4—64no—
469C4⋊Dic3—31no—
470C4⋊Dic3—31no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—34no—
479C4⋊Dic3—32no—
480C4⋊Dic3—61no—
481C4⋊Dic3—62no—
482C4⋊Dic3—62no—
483C4⋊Dic3C22×D311yescharacteristic
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D312yes—
487C4⋊Dic3C22×D312yes—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—64no—
504Dic3⋊C4C22×D314yes—
505Dic3⋊C4C22×D312yes—
506Dic3⋊C4C22×D312yes—
507Dic3⋊C4C22×D312yes—
508Dic3⋊C4C22×D312yes—
509Dic3⋊C4C22×D314yes—
510Dic3⋊C4C22×D314yes—
511C4×Dic3—34no—
512C4×Dic3—34no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—64no—
518C4×Dic3C22×D312yes—
519C4×Dic3C22×D314yes—
520C4×Dic3C22×D311yescharacteristic
521C4×Dic3C22×D312yes—
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D311yescharacteristic
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D312yes—
526C22×C32C2511yescharacteristic
527C2×C3⋊D3—22no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—22no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D32−1+412yes—
533C32×C4—22no—
534C32×C4—22no—
535C32×C4—21no—
536C32×C4C2×#4112yes—
537C32×C42−1+412yes—
538C3⋊Dic3—22no—
539C3⋊Dic3—24no—
540C3×Dic3—24no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—22no—
547C3×Dic3C2×#4114yes—
548C22×Q8—31no—
549C22×Q8—92no—
550C4⋊Q8—32no—
551C4⋊Q8—31no—
552C4⋊Q8—92no—
553C4⋊Q8—92no—
554C4⋊Q8—94no—
555C4⋊Q8—91no—
556#126—94no—
557#126—92no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—34no—
562#125—32no—
563#125—91no—
564#125—94no—
565#125—92no—
566#125—92no—
567#125—94no—
568#125—94no—
569#125—94no—
570#124—91no—
571#124—92no—
572#123—92no—
573#123—94no—
574C22⋊Q8—94no—
575C22⋊Q8—92no—
576C22⋊Q8—94no—
577C22⋊Q8—92no—
578C22⋊Q8—94no—
579C22⋊Q8—91no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582#121—91no—
583C4×Q8—31no—
584C4×Q8—31no—
585C4×Q8—32no—
586C4×Q8—32no—
587C4×Q8—31no—
588C4×Q8—32no—
589C4×Q8—31no—
590C4×Q8—32no—
591C4×Q8—94no—
592C4×Q8—92no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—94no—
597C4×Q8—92no—
598C4×Q8D3211yescharacteristic
599C4×D4—92no—
600C4×D4—92no—
601C4×D4—94no—
602C4×D4—91no—
603#117—92no—
604#117—94no—
605#117—94no—
606#117—94no—
607#117—92no—
608#117—92no—
609C2×C4⋊C4—32no—
610C2×C4⋊C4—31no—
611C2×C42—32no—
612C2×C42—31no—
613C23×C3—31no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—62no—
617C22×D3C23×D311yescharacteristic
618C3×Q8—22no—
619C3×Q8—22no—
620C3×Q8—34no—
621C3×Q8—42no—
622C3×Q8—64no—
623C3×Q8—64no—
624C3×Q8—62no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—21no—
630C2×C3×C4—32no—
631C2×C3×C4—31no—
632C2×C3×C4—32no—
633C2×C3×C4—34no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—64no—
639C2×C3×C4—64no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643C2×C3×C4C23×D312yes—
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D312yes—
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D312yes—
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653#67—64no—
654C2×Dic3—34no—
655C2×Dic3—34no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—62no—
659C2×Dic3—64no—
660C2×Dic3C23×D311yescharacteristic
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D314yes—
663C2×Dic3C23×D311yescharacteristic
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D311yescharacteristic
667C2×Dic3C23×D312yes—
668D12—64no—
669D12—62no—
670D12—62no—
671D12—122no—
672C4×D3—24no—
673C4×D3—22no—
674C4×D3—22no—
675C4×D3—22no—
676C4×D3—24no—
677C4×D3—68no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—68no—
681C4×D3—124no—
682Dic6—22no—
683Dic6—24no—
684Dic6—24no—
685Dic6—68no—
686Dic6—64no—
687Dic6—64no—
688Dic6—68no—
689Dic6—124no—
690Dic6#23514yes—
691C2×C32C22×#4111yescharacteristic
692C2×C32C2×2−1+411yescharacteristic
693C2×C32C2×2−1+411yescharacteristic
694C3⋊D3—42no—
695C3×D3—22no—
696C2×Q8—31no—
697C2×Q8—31no—
698C2×Q8—32no—
699C2×Q8—32no—
700C2×Q8—64no—
701C2×Q8—94no—
702C2×Q8—92no—
703C2×Q8—188no—
704C2×Q8C2×D3211yescharacteristic
705C2×D4—92no—
706C2×D4—91no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—31no—
712C22×C4—94no—
713C22×C4—92no—
714C4⋊C4—32no—
715C4⋊C4—32no—
716C4⋊C4—31no—
717C4⋊C4—32no—
718C4⋊C4—32no—
719C4⋊C4—34no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—34no—
723C4⋊C4—31no—
724C4⋊C4—34no—
725C4⋊C4—32no—
726C4⋊C4—94no—
727C4⋊C4—92no—
728C4⋊C4—94no—
729C4⋊C4—92no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—92no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—92no—
736C4⋊C4—92no—
737C4⋊C4—91no—
738C4⋊C4—94no—
739C4⋊C4C2×D3211yescharacteristic
740C4⋊C4C2×D3212yes—
741C22⋊C4—92no—
742C22⋊C4—92no—
743C22⋊C4—94no—
744C22⋊C4—92no—
745C22⋊C4—92no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—92no—
749C22⋊C4—94no—
750C42—32no—
751C42—31no—
752C42—32no—
753C42—31no—
754C42—32no—
755C42—31no—
756C42—34no—
757C42—32no—
758C42—94no—
759C42—94no—
760C42—94no—
761C42C2×D3211yescharacteristic
762C42C2×D3212yes—
763C22×C3—21no—
764C22×C3—32no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3C24×D311yescharacteristic
768C22×C3C24×D311yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3#101012yes—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—34no—
790C3×C4—42no—
791C3×C4—42no—
792C3×C4—41no—
793C3×C4—64no—
794C3×C4—61no—
795C3×C4—62no—
796C3×C4—61no—
797C3×C4—62no—
798C3×C4—61no—
799C3×C4—62no—
800C3×C4C2×#23512yes—
801C3×C4#100712yes—
802C3×C4#100712yes—
803C3×C4D3×#4112yes—
804Dic3—21no—
805Dic3—22no—
806Dic3—21no—
807Dic3—24no—
808Dic3—21no—
809Dic3—22no—
810Dic3—22no—
811Dic3—62no—
812Dic3—64no—
813Dic3—64no—
814Dic3—62no—
815Dic3—124no—
816Dic3—122no—
817Dic3C2×#23514yes—
818C32#352311yescharacteristic, complemented, Sylow
819C23—31no—
820C23—92no—
821Q8—22no—
822Q8—34no—
823Q8—64no—
824Q8—64no—
825Q8—62no—
826Q8—188no—
827Q8—184no—
828D4—184no—
829D4—182no—
830C2×C4—32no—
831C2×C4—31no—
832C2×C4—32no—
833C2×C4—31no—
834C2×C4—32no—
835C2×C4—31no—
836C2×C4—32no—
837C2×C4—34no—
838C2×C4—64no—
839C2×C4—64no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—94no—
844C2×C4—92no—
845C2×C4—188no—
846C2×C4—184no—
847C2×C4C22×D3212yes—
848C2×C4C22×D3211yescharacteristic
849C2×C4C22×D3212yes—
850C2×C4C22×D3211yescharacteristic
851C2×C4C22×D3211yescharacteristic
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—62no—
856C2×C3C22×#23511yescharacteristic
857C2×C3C2×#100711yescharacteristic
858C2×C3C2×#100711yescharacteristic
859C2×C3C2×D3×#4111yescharacteristic
860C2×C3C2×#101011yescharacteristic
861C2×C3D3×2−1+411yescharacteristic
862D3—22no—
863D3—122no—
864D3—122no—
865D3—242no—
866C22—32no—
867C22—61no—
868C22—61no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22C23×D3211yescharacteristic
873C4—22no—
874C4—22no—
875C4—21no—
876C4—34no—
877C4—61no—
878C4—64no—
879C4—61no—
880C4—62no—
881C4—61no—
882C4—62no—
883C4—62no—
884C4—182no—
885C4—184no—
886C4D3×#23512yes—
887C4#6431612yes—
888C3—21no—
889C3#8580411yescharacteristic, complemented
890C3#8702511yescharacteristic, complemented
891C2—62no—
892C2—362no—
893C2C2×D3×#23511yescharacteristic
894C2C2×#6431611yescharacteristic
895C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radical#63909C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. C3×C4×D3×Q8C2semidirect
3. C3×#5567C2semidirect
4. #10595403C2semidirect
5. #10595354C2semidirect
6. #10594348C2semidirect
7. #10594347C2semidirect
8. #10594333C2semidirect
9. #10594331C2semidirect
11. #10593903C2semidirect
12. #10593873C2semidirect
14. #10593860C2semidirect
15. #10593859C2semidirect
16. #10593852C2semidirect
17. #10593850C2semidirect
108. C4×D3×Q8D3semidirect
113. #5567D3semidirect
818. C32#3523semidirect
889. C3#85804semidirect
890. C3#87025semidirect

Maximal subgroups

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

subgroupindex
#105960552
C3×C4×D3×Q82
C3×#55672
#105954032
#105953542
#105943482
#105943472
#105943332
#105943312
#105939762
#105939032
#105938732
#105938702
#105938602
#105938592
#105938522
#105938502
#870253
#858043