Finite Group Databasebeta

← #11903655

Subgroups — #11903655

Order 1152.

2375 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5734C211yesmaximal, characteristic, complemented
3C3×#5730C211yesmaximal, characteristic, complemented
4#10595437C214yesmaximal, complemented
5#10595377C214yesmaximal, complemented
6#10594632C212yesmaximal, complemented
7#10594630C212yesmaximal, complemented
8D3×#892C212yesmaximal, complemented
9#10594584C212yesmaximal, complemented
10#10594560C212yesmaximal, complemented
11#10594456C212yesmaximal, complemented
12#10594427C212yesmaximal, complemented
13#10594358C212yesmaximal, complemented
14C4×#3802C211yesmaximal, characteristic, complemented
15#10593895C211yesmaximal, characteristic, complemented
16C4×#3796C211yesmaximal, characteristic, complemented
17#10593879C211yesmaximal, characteristic, complemented
18#86958—31nomaximal
19#86922—31nomaximal
20C2×#3802C2211yescharacteristic
21C2×C4×D32C2212yes—
22C2×#3796C2211yescharacteristic
23C2×#3795C2212yes—
24C32×C4⋊Q8C2211yescharacteristic, complemented
25#64155C2212yes—
26Q8×C3⋊Dic3C2212yescomplemented
27#64106C2212yes—
28#64101C2212yes—
29#64099C2212yescomplemented
30#64096C2212yescomplemented
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic, complemented
33C3×#947C2214yescomplemented
34C3×#946C2214yescomplemented
35C3×#897C2212yescomplemented
36C3×#895C2212yes—
37C3×#895C2212yescomplemented
38C3×#893C2212yes—
39C3×#892C2212yescomplemented
40C3×#892C2212yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#890C2212yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic
45C3×C4×D12C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63922C2214yes—
48#63921C2212yes—
49D3×(C2×D3)⋊C4C2214yes—
50#63908C2214yes—
51#63908C2212yescomplemented
52C4×#626C2212yes—
53#63902C2212yes—
54#63902C2214yescomplemented
55C4×#625C2212yes—
56#63900C2211yescharacteristic
57#63898C2211yescharacteristic
58#63898C2211yescharacteristic
59#63898C2211yescharacteristic, complemented
60#63898C2214yescomplemented
61#63891C2214yes—
62#63891C2214yescomplemented
63D3×C4⋊Dic3C2212yescomplemented
64#63884C2214yescomplemented
65#63881C2212yes—
66#63879C2214yescomplemented
67#63878C2214yescomplemented
68#63878C2212yescomplemented
69#63877C2214yescomplemented
70C4×D3×Dic3C2214yescomplemented
71C4×D3×Dic3C2212yescomplemented
72#63869C2214yescomplemented
73#63861C2214yescomplemented
74#63861C2214yescomplemented
75#63860C2212yes—
76#63858C2214yescomplemented
77#63857C2212yescomplemented
78#63856C2212yescomplemented
79#63854C2214yes—
80#63849C2211yescharacteristic
81#63844C2212yescomplemented
82#63843C2211yescharacteristic, complemented
83#63841C2212yescomplemented
84#63836C2214yes—
85C3×#555—31no—
86C3×#554—31no—
87#5734D311yescharacteristic, complemented
88#5730D311yescharacteristic, complemented
89#5728—31no—
90#5728—31no—
91#5728—61no—
92#5694—32no—
93#5691—32no—
94#5680—34no—
95#5679—34no—
96#5642—32no—
97#5637—34no—
98#5627—32no—
99#5624—34no—
100#5614—32no—
101#5612—32no—
102#5606—32no—
103#5600—32no—
104#5584—31no—
105C4×#239—31no—
106#5555—31no—
107#5554—32no—
108#5551—31no—
109C4×D3×D4—31no—
110C4×D3×D4—31no—
111#5542—31no—
112C4×#237—32no—
113C4×#237—31no—
114#5529—32no—
115#5529—32no—
116#5522—32no—
117D3×#117—32no—
118#5514—32no—
119C2×#892—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2312yes—
126C2×C3×D12C2311yescharacteristic
127C2×C3×D12C2311yescharacteristic
128C2×C3×D12C2314yes—
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×#626C2312yes—
136C2×#625C2314yes—
137C2×#625C2312yes—
138C2×#624C2312yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2312yes—
144#3802—24no—
145C4×D32—28no—
146#3796—24no—
147#3795—28no—
148C32×C4⋊C4C2312yes—
149C32×C4⋊C4C2312yes—
150C32×C42C2311yescharacteristic
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2314yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2311yescharacteristic
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2314yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2311yescharacteristic
170C3×C4⋊Dic3C2311yescharacteristic
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2314yes—
175#3724C2314yes—
176#3724C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179#3722C2312yes—
180(C2×D3)⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3475—91noSylow
190C2×#239—31no—
191C2×#237—32no—
192C2×#237—31no—
193C2×D3×D4—31no—
194C2×D3×D4—31no—
195C2×#235—32no—
196C22×C4×D3—32no—
197C22×C4×D3—32no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8C2×D311yescharacteristic, complemented
200C3×C4⋊Q8C2×D311yescharacteristic, complemented
201C3×#125—32no—
202C3×#124—34no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—32no—
205C3×#121—32no—
206C3×#121—32no—
207C3×C4×Q8—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×#117—32no—
213C3×#117—32no—
214C2×C3×C4⋊C4—32no—
215#947C2×D314yescomplemented
216#946—32no—
217#946—32no—
218#946—32no—
219#946—62no—
220#946C2×D314yescomplemented
221Q8×Dic3—32no—
222Q8×Dic3—32no—
223Q8×Dic3—31no—
224Q8×Dic3—62no—
225#938—34no—
226#938—32no—
227#937—34no—
228#936—32no—
229#935—34no—
230D4×Dic3—34no—
231D4×Dic3—31no—
232D4×Dic3—31no—
233D4×Dic3—31no—
234#930—34no—
235#930—32no—
236C4×#67—32no—
237C4×#67—32no—
238C4×#67—34no—
239C4×#67—32no—
240C2×(C2×D3)⋊C4—34no—
241#926—32no—
242C2×C4⋊Dic3—32no—
243#924—32no—
244#924—32no—
245C2×C4×Dic3—34no—
246C2×C4×Dic3—32no—
247#898—34no—
248#898—34no—
249#898—34no—
250#897—32no—
251#897—32no—
252#897—32no—
253#897—62no—
254#897C2×D312yescomplemented
255#895C2×D312yes—
256#895C2×D312yescomplemented
257#894—34no—
258#894—34no—
259#893—31no—
260#893—34no—
261#893—31no—
262#893—31no—
263#893—32no—
264#893C2×D312yes—
265#892—32no—
266#892—32no—
267#892—32no—
268#892—34no—
269#892—32no—
270#892—31no—
271#892—31no—
272#892—34no—
273#892—62no—
274#892C2×D312yescomplemented
275#892C2×D312yescomplemented
276D3×C4⋊C4—32no—
277D3×C4⋊C4—31no—
278D3×C4⋊C4—31no—
279D3×C4⋊C4C2×D312yescomplemented
280#890—32no—
281#890—32no—
282#890—34no—
283#890—62no—
284#890C2×D312yescomplemented
285#887—31no—
286#887—32no—
287#887—32no—
288#887—32no—
289#887—62no—
290#886—34no—
291#886—34no—
292#883—34no—
293#883—34no—
294#883—34no—
295#882—34no—
296#67⋊C4—34no—
297#67⋊C4—32no—
298#67⋊C4—34no—
299#67⋊C4—32no—
300#67⋊C4—34no—
301#67⋊C4—32no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4—32no—
304D3×C22⋊C4—32no—
305#879—34no—
306#879—34no—
307#879—34no—
308#877—32no—
309#877—34no—
310#877—34no—
311#875—32no—
312C4×D12—32no—
313C4×D12C2×D311yescharacteristic
314C4×D12C2×D311yescharacteristic
315C4×D12C2×D311yescharacteristic, complemented
316#872—34no—
317#872—34no—
318C42×D3—34no—
319C42×D3—32no—
320C42×D3—31no—
321C42×D3—31no—
322C42×D3—61no—
323#870—34no—
324#869—31no—
325#869—31no—
326#869—61no—
327C4×Dic6—32no—
328C4×Dic6C2×D311yescharacteristic, complemented
329C22×C3⋊D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C2×D32—24no—
334C2×D32—24no—
335C2×D32—42no—
336C32×Q8—42no—
337C2×C32×C4C2414yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2414yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2411yescharacteristic
345C4×C3⋊D3—22no—
346C4×C3⋊D3—41no—
347C4×C3⋊D3#4114yescomplemented
348#634—24no—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C3×D12—22no—
355C3×D12—22no—
356C3×D12—44no—
357C3×D12#4114yescomplemented
358C3×C4×D3—24no—
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×C4×D3—44no—
362C3×Dic6—22no—
363#626—24no—
364#625—28no—
365#625—24no—
366#624—24no—
367D3×Dic3—28no—
368D3×Dic3—24no—
369D3×Dic3—24no—
370D3×Dic3—24no—
371D3×Dic3—42no—
372#556—91no—
373#555—31no—
374#554—31no—
375#553—92no—
376#552—92no—
377#552—92no—
378#551—94no—
379#547—91no—
380#546—92no—
381#533—91no—
382#529—92no—
383#529—94no—
384#525—92no—
385C4×#41—92no—
386C4×#41—91no—
387C2×C4×D4—91no—
388C2×#117—92no—
389C23×D3—32no—
390C23×D3—32no—
391C2×C3×Q8—22no—
392C2×C3×Q8—31no—
393C2×C3×Q8C22×D312yes—
394C2×C3×Q8C22×D312yes—
395C2×C3×D4—31no—
396C2×C3×D4—31no—
397C2×C3×D4—31no—
398C2×C3×D4—34no—
399C22×C3×C4—32no—
400C22×C3×C4—32no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—32no—
408C22×Dic3—32no—
409C22×Dic3—32no—
410C22×Dic3—34no—
411C22×Dic3—32no—
412C22×Dic3—32no—
413#239—64no—
414#237—64no—
415#237—68no—
416D3×D4—64no—
417D3×D4—64no—
418#235—68no—
419C2×D12—32no—
420C2×D12C22×D311yescharacteristic
421C2×D12C22×D311yescharacteristic
422C2×D12C22×D314yes—
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—32no—
427C2×C4×D3—34no—
428C2×C4×D3—32no—
429C2×C4×D3—32no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—68no—
441C2×C4×D3—68no—
442C2×C4×D3C22×D312yes—
443C2×C4×D3C22×D312yes—
444C2×C4×D3C22×D312yes—
445C2×C4×D3C22×D314yes—
446C2×Dic6—32no—
447C2×Dic6—32no—
448C2×Dic6—62no—
449C2×Dic6C22×D311yescharacteristic
450C3×C4⋊C4—22no—
451C3×C4⋊C4—22no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—32no—
459C3×C4⋊C4C22×D312yes—
460C3×C4⋊C4C22×D312yes—
461C3×C4⋊C4C22×D312yes—
462C3×C4⋊C4C22×D312yes—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—34no—
465C3×C22⋊C4—32no—
466C3×C22⋊C4—32no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—32no—
469C3×C42—21no—
470C3×C42—32no—
471C3×C42—34no—
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474#217—32no—
475#217—32no—
476#217—34no—
477#217—32no—
478#217—34no—
479#217—34no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—32no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—64no—
491(C2×D3)⋊C4C22×D314yes—
492(C2×D3)⋊C4C22×D312yes—
493(C2×D3)⋊C4C22×D312yes—
494(C2×D3)⋊C4C22×D312yes—
495(C2×D3)⋊C4C22×D314yes—
496(C2×D3)⋊C4C22×D314yes—
497C4⋊Dic3—32no—
498C4⋊Dic3—32no—
499C4⋊Dic3—32no—
500C4⋊Dic3—32no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—32no—
504C4⋊Dic3—34no—
505C4⋊Dic3—62no—
506C4⋊Dic3—62no—
507C4⋊Dic3—64no—
508C4⋊Dic3C22×D311yescharacteristic
509C4⋊Dic3C22×D311yescharacteristic
510C4⋊Dic3C22×D314yes—
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D311yescharacteristic
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—32no—
521Dic3⋊C4—64no—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D314yes—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—34no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—34no—
532C4×Dic3—34no—
533C4×Dic3—32no—
534C4×Dic3—34no—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—32no—
538C4×Dic3—61no—
539C4×Dic3—61no—
540C4×Dic3—61no—
541C4×Dic3—64no—
542C4×Dic3C22×D312yes—
543C4×Dic3C22×D314yes—
544C22×C32C2511yescharacteristic
545C2×C3⋊D3—21no—
546C2×C3⋊D3—21no—
547C2×C3⋊D3C2×#4112yes—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3C2×#4114yes—
557D32—48no—
558C32×C4—21no—
559C32×C4—24no—
560C32×C4C2×#4112yes—
561C32×C4C2×#4112yes—
562C3⋊Dic3—24no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3C2×#4112yes—
566C3×Dic3—22no—
567C3×Dic3—22no—
568C3×Dic3—22no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C2×#41—92no—
572C2×#41—91no—
573C22×D4—91no—
574C23×C4—92no—
575C4⋊Q8—91no—
576C4⋊Q8D3211yescharacteristic, complemented
577#126—94no—
578#126—94no—
579#126—94no—
580#125—32no—
581#125—94no—
582#125—92no—
583#124—34no—
584#124—92no—
585#123—94no—
586#123—94no—
587#123—94no—
588#123—94no—
589C22⋊Q8—34no—
590C22⋊Q8—32no—
591C22⋊Q8—92no—
592C22⋊Q8—92no—
593C22⋊Q8—92no—
594C22⋊Q8—92no—
595#121—32no—
596#121—32no—
597#121—92no—
598#121—94no—
599#120—94no—
600C4×Q8—31no—
601C4×Q8—92no—
602C4×Q8—91no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×D4—32no—
606C4×D4—31no—
607C4×D4—31no—
608C4×D4—31no—
609C4×D4—92no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—92no—
613C4×D4—94no—
614C4×D4—91no—
615C4×D4—91no—
616C4×D4—91no—
617C4×D4—94no—
618C4×D4—92no—
619#117—32no—
620#117—32no—
621#117—94no—
622#117—94no—
623#117—94no—
624#117—92no—
625#117—91no—
626#117—92no—
627#117—92no—
628C2×C4⋊C4—32no—
629C2×C4⋊C4—91no—
630C2×C4⋊C4—92no—
631C2×C22⋊C4—92no—
632C2×C22⋊C4—94no—
633C2×C42—94no—
634C2×C42—92no—
635C2×C42—91no—
636C23×C3—32no—
637C23×C3—32no—
638C23×C3—32no—
639C22×D3—31no—
640C22×D3—31no—
641C22×D3—61no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—122no—
647C22×D3—122no—
648C22×D3C23×D312yes—
649C22×D3C23×D312yes—
650C22×D3C23×D312yes—
651C3×Q8—42no—
652C3×Q8—42no—
653C3×Q8—44no—
654C3×Q8—62no—
655C3×D4—34no—
656C3×D4—62no—
657C3×D4—62no—
658C3×D4—124no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—24no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—64no—
669C2×C3×C4—64no—
670C2×C3×C4—64no—
671C2×C3×C4—124no—
672C2×C3×C4C23×D314yes—
673C2×C3×C4C23×D314yes—
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680#67—64no—
681#67—64no—
682#67—68no—
683#67—68no—
684#67—64no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—34no—
691C2×Dic3—31no—
692C2×Dic3—34no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—64no—
697C2×Dic3—64no—
698C2×Dic3—64no—
699C2×Dic3—64no—
700C2×Dic3—68no—
701C2×Dic3—122no—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707D12—22no—
708D12—22no—
709D12—44no—
710D12—64no—
711D12#23914yescomplemented
712C4×D3—24no—
713C4×D3—24no—
714C4×D3—24no—
715C4×D3—34no—
716C4×D3—34no—
717C4×D3—44no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—68no—
725C4×D3—62no—
726C4×D3—62no—
727C4×D3—122no—
728C4×D3—121no—
729C4×D3—121no—
730C4×D3—122no—
731C4×D3—122no—
732Dic6—22no—
733Dic6—64no—
734Dic6—64no—
735Dic6—124no—
736C2×C32C22×#4111yescharacteristic
737C2×C32C22×#4111yescharacteristic
738C2×C32#58511yescharacteristic
739C3⋊D3—22no—
740C3×D3—24no—
741C3×D3—42no—
742C3×D3—42no—
743C24—92no—
744#41—188no—
745#41—184no—
746C2×Q8—31no—
747C2×Q8—92no—
748C2×Q8C2×D3212yes—
749C2×D4—31no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—34no—
753C2×D4—92no—
754C2×D4—94no—
755C2×D4—92no—
756C2×D4—184no—
757C22×C4—32no—
758C22×C4—32no—
759C22×C4—32no—
760C22×C4—34no—
761C22×C4—92no—
762C22×C4—92no—
763C22×C4—94no—
764C22×C4—92no—
765C22×C4—92no—
766C22×C4—92no—
767C22×C4—91no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—188no—
771C4⋊C4—31no—
772C4⋊C4—34no—
773C4⋊C4—31no—
774C4⋊C4—31no—
775C4⋊C4—31no—
776C4⋊C4—32no—
777C4⋊C4—34no—
778C4⋊C4—94no—
779C4⋊C4—92no—
780C4⋊C4—94no—
781C4⋊C4—92no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4C2×D3212yes—
787C4⋊C4C2×D3212yes—
788C22⋊C4—34no—
789C22⋊C4—32no—
790C22⋊C4—32no—
791C22⋊C4—34no—
792C22⋊C4—34no—
793C22⋊C4—32no—
794C22⋊C4—92no—
795C22⋊C4—92no—
796C22⋊C4—94no—
797C22⋊C4—92no—
798C22⋊C4—92no—
799C22⋊C4—94no—
800C22⋊C4—94no—
801C22⋊C4—94no—
802C42—34no—
803C42—32no—
804C42—92no—
805C42—94no—
806C42—92no—
807C42—91no—
808C42—94no—
809C42—91no—
810C42—91no—
811C42C2×D3211yescharacteristic
812C22×C3—21no—
813C22×C3—34no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3C24×D311yescharacteristic
823C22×C3C24×D311yescharacteristic
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—32no—
833C2×D3—32no—
834C2×D3—62no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—128no—
842C2×D3—128no—
843C2×D3C2×#23914yes—
844C3×C4—22no—
845C3×C4—24no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—24no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—44no—
852C3×C4—62no—
853C3×C4—62no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—62no—
857C3×C4C2×#23912yes—
858C3×C4D3×#4112yes—
859C3×C4D3×#4112yes—
860C3×C4D3×#4112yes—
861Dic3—22no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—32no—
867Dic3—32no—
868Dic3—62no—
869Dic3—64no—
870Dic3—61no—
871Dic3—64no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—124no—
876Dic3—121no—
877Dic3—121no—
878C32#347511yescharacteristic, complemented, Sylow
879C23—32no—
880C23—32no—
881C23—32no—
882C23—91no—
883C23—184no—
884C23—184no—
885C23—362no—
886Q8—42no—
887Q8—62no—
888Q8—184no—
889D4—34no—
890D4—62no—
891D4—62no—
892D4—124no—
893D4—184no—
894D4—184no—
895D4—188no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—64no—
902C2×C4—64no—
903C2×C4—64no—
904C2×C4—91no—
905C2×C4—94no—
906C2×C4—91no—
907C2×C4—94no—
908C2×C4—91no—
909C2×C4—124no—
910C2×C4—184no—
911C2×C4—184no—
912C2×C4—184no—
913C2×C4—184no—
914C2×C4—188no—
915C2×C4—182no—
916C2×C4—361no—
917C2×C4—362no—
918C2×C4C22×D3214yes—
919C2×C4C22×D3211yescharacteristic
920C2×C4C22×D3211yescharacteristic
921C2×C4C22×D3211yescharacteristic
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—64no—
926C2×C3—122no—
927C2×C3—122no—
928C2×C3C22×#23911yescharacteristic
929C2×C3C2×D3×#4111yescharacteristic
930C2×C3C2×D3×#4111yescharacteristic
931C2×C3C2×D3×#4111yescharacteristic
932C2×C3#596611yescharacteristic
933C2×C3#596611yescharacteristic
934D3—24no—
935D3—42no—
936D3—42no—
937D3—62no—
938D3—62no—
939D3—122no—
940C22—34no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—92no—
950C22—181no—
951C22—181no—
952C22—368no—
953C22C23×D3211yescharacteristic
954C4—24no—
955C4—21no—
956C4—62no—
957C4—62no—
958C4—62no—
959C4—62no—
960C4—62no—
961C4—92no—
962C4—181no—
963C4—181no—
964C4—184no—
965C4D3×#23912yes—
966C4#6431912yes—
967C3—21no—
968C3#8692211yescharacteristic, complemented
969C3#8695811yescharacteristic, complemented
970C2—64no—
971C2—122no—
972C2—122no—
973C2—182no—
974C2#1059667911yescharacteristic
975C2C2×D3×#23911yescharacteristic
976C2C2×#6431911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5734C2semidirect
3. C3×#5730C2semidirect
4. #10595437C2semidirect
5. #10595377C2semidirect
6. #10594632C2semidirect
7. #10594630C2semidirect
8. D3×#892C2semidirect
9. #10594584C2semidirect
10. #10594560C2semidirect
11. #10594456C2semidirect
12. #10594427C2semidirect
13. #10594358C2semidirect
14. C4×#3802C2semidirect
15. #10593895C2semidirect
16. C4×#3796C2semidirect
17. #10593879C2semidirect
24. C32×C4⋊Q8C22semidirect
26. Q8×C3⋊Dic3C22semidirect
29. #64099C22semidirect
30. #64096C22semidirect
32. #64078C22semidirect
33. C3×#947C22semidirect
34. C3×#946C22semidirect
35. C3×#897C22semidirect
37. C3×#895C22semidirect
39. C3×#892C22semidirect
40. C3×#892C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#890C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C4×Dic6C22semidirect
51. #63908C22semidirect
54. #63902C22semidirect
59. #63898C22semidirect
60. #63898C22semidirect
62. #63891C22semidirect
63. D3×C4⋊Dic3C22semidirect
64. #63884C22semidirect
66. #63879C22semidirect
67. #63878C22semidirect
68. #63878C22semidirect
69. #63877C22semidirect
70. C4×D3×Dic3C22semidirect
71. C4×D3×Dic3C22semidirect
72. #63869C22semidirect
73. #63861C22semidirect
74. #63861C22semidirect
76. #63858C22semidirect
77. #63857C22semidirect
78. #63856C22semidirect
81. #63844C22semidirect
82. #63843C22semidirect
83. #63841C22semidirect
87. #5734D3semidirect
88. #5730D3semidirect
199. C3×C4⋊Q8C2×D3semidirect
200. C3×C4⋊Q8C2×D3semidirect
215. #947C2×D3semidirect
220. #946C2×D3semidirect
254. #897C2×D3semidirect
256. #895C2×D3semidirect
274. #892C2×D3semidirect
275. #892C2×D3semidirect
279. D3×C4⋊C4C2×D3semidirect
284. #890C2×D3semidirect
315. C4×D12C2×D3semidirect
328. C4×Dic6C2×D3semidirect
347. C4×C3⋊D3#41semidirect
357. C3×D12#41semidirect
576. C4⋊Q8D32semidirect
711. D12#239semidirect
878. C32#3475semidirect
968. C3#86922semidirect
969. C3#86958semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57342
C3×#57302
#105954372
#105953772
#105946322
#105946302
D3×#8922
#105945842
#105945602
#105944562
#105944272
#105943582
C4×#38022
#105938952
C4×#37962
#105938792
#869583
#869223