Finite Group Databasebeta

← #11903773

Subgroups — #11903773

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3830C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic, complemented
3C3×D4×Dic6C211yesmaximal, characteristic, complemented
4#10595272C212yesmaximal, complemented
5#10595190C212yesmaximal
6#10594991C212yesmaximal, complemented
7C2×#63843C212yesmaximal, complemented
8#10594810C212yesmaximal, complemented
9#10594803C212yesmaximal, complemented
10#10594448C212yesmaximal, complemented
11#10594318C212yesmaximal, complemented
12#10594141C214yesmaximal, complemented
13#10594030C214yesmaximal, complemented
14C4×#3797C211yesmaximal, characteristic, complemented
15#10593866C211yesmaximal, characteristic, complemented
16#10593864C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86923—31nomaximal
19Q8×#237—31nomaximal
20C2×#3830C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C2×#3797C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C4×#638C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27#64101C2211yescharacteristic
28#64096C2211yescharacteristic
29#64090C2212yes—
30#64086C2212yes—
31C42×C3⋊D3C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C3×D4×Dic3C2212yes—
34C3×D4×Dic3C2212yes—
35C2×C3×C4⋊Dic3C2212yes—
36C3×#924C2212yes—
37C3×#924C2212yes—
38C3×#890C2212yes—
39C3×#888C2212yes—
40C3×#878C2214yes—
41C3×#878C2214yes—
42C3×#869C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63982C2214yes—
47C2×Dic3⋊Dic3C2214yes—
48#63964C2214yes—
49#63964C2214yes—
50#63957C2214yes—
51C2×Dic32C2214yes—
52#63952C2214yes—
53#63952C2214yes—
54#63919C2212yes—
55#63918C2212yes—
56C4×#627C2212yes—
57#63900C2211yescharacteristic
58#63895C2214yes—
59#63888C2214yes—
60#63883C2212yes—
61C4×#624C2212yes—
62#63873C2212yes—
63#63872C2212yes—
64#63871C2212yes—
65#63871C2212yes—
66#63870C2214yes—
67#63869C2212yes—
68#63849C2212yes—
69#63847C2214yes—
70#63847C2214yes—
71#63844C2212yes—
72#63844C2212yes—
73#63843C2211yescharacteristic
74#63843C2214yes—
75#63843C2212yes—
76#63843C2212yes—
77#63843C2212yes—
78#63843C2214yes—
79#63843C2212yes—
80#63843C2211yescharacteristic
81#63839C2214yes—
82#63839C2214yes—
83#63838C2212yes—
84#63838C2214yes—
85C3×#554—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×Q8×Dic3—32no—
89#5728—32no—
90#5728—31no—
91#5728—31no—
92#5722—31no—
93#5721—32no—
94#5721—31no—
95#5688—32no—
96#5685—32no—
97#5636—34no—
98#5635—32no—
99#5635—34no—
100#5632—32no—
101#5622—32no—
102#5622—32no—
103#5622—34no—
104#5622—34no—
105C4×D3×Q8—31no—
106C4×D3×Q8—31no—
107#5567—31no—
108Q8×Dic6—31no—
109#5543—32no—
110#5543D311yescharacteristic, complemented
111#5539—32no—
112D4×Dic6D311yescharacteristic, complemented
113C4×#237—31no—
114C4×#237—31no—
115C4×#237—32no—
116C4×#237—32no—
117C4×#237—61no—
118#5511—32no—
119C2×#887—32no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#638C2312yes—
123C22×C3⋊Dic3C2312yes—
124C22×C3⋊Dic3C2312yes—
125#3830Q818yescomplemented
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C4×C3⋊D3C2311yescharacteristic
128C2×C4×C3⋊D3C2311yescharacteristic
129C2×#634C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C22×C3×Dic3C2314yes—
132C2×C3×Dic6—28no—
133C2×C3×Dic6C2314yes—
134C2×C3×Dic6C2311yescharacteristic
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2312yes—
139C2×#627C2314yes—
140C2×#624C2312yes—
141C2×#624C2312yes—
142#3797—24no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3757C2312yes—
147#3752C2312yes—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750C2312yes—
150#3750C2312yes—
151C4×C3⋊Dic3C2312yes—
152C4×C3⋊Dic3C2311yescharacteristic
153C4×C3⋊Dic3C2311yescharacteristic
154C4×C3⋊Dic3C2311yescharacteristic
155C4×C3⋊Dic3C2312yes—
156C4×C3⋊Dic3C2312yes—
157C3×#217C2314yes—
158C3×#217C2314yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×Dic3⋊C4C2312yes—
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172#3724C2312yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C22×C3×Q8—32no—
190C2×D3×Q8—31no—
191C2×D3×Q8—31no—
192C2×#237—31no—
193C2×#237—31no—
194C2×#237—61no—
195C22×Dic6C2×D312yes—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—31no—
198C3×C4⋊Q8—31no—
199C3×#125—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—34no—
203C3×C22⋊Q8—34no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×D4—21no—
207C3×C4×D4—32no—
208C3×C4×D4—32no—
209C3×C4×D4C2×D311yescharacteristic
210C3×C4×D4C2×D311yescharacteristic
211C2×C3×C4⋊C4—32no—
212#946—32no—
213#946—32no—
214#946—34no—
215Q8×Dic3—32no—
216Q8×Dic3—34no—
217Q8×Dic3—32no—
218Q8×Dic3—34no—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221Q8×Dic3—32no—
222Q8×Dic3—31no—
223#944—32no—
224#944—32no—
225#944—34no—
226#944—34no—
227D4×Dic3—31no—
228D4×Dic3—31no—
229D4×Dic3—61no—
230D4×Dic3C2×D312yes—
231D4×Dic3C2×D312yes—
232C4×#67—32no—
233C4×#67—32no—
234C4×#67—34no—
235C4×#67—34no—
236C4×#67—62no—
237C2×C4⋊Dic3—34no—
238C2×C4⋊Dic3C2×D312yes—
239#924—34no—
240#924—34no—
241#924C2×D312yes—
242#924C2×D312yes—
243C2×Dic3⋊C4—34no—
244C2×C4×Dic3—32no—
245C2×C4×Dic3—32no—
246C2×C4×Dic3—34no—
247C2×C4×Dic3—34no—
248C2×C4×Dic3—62no—
249#897—32no—
250#897—32no—
251#897—34no—
252#896—34no—
253#896—34no—
254#892—31no—
255#892—31no—
256#892—32no—
257#892—32no—
258#892—61no—
259D3×C4⋊C4—31no—
260D3×C4⋊C4—31no—
261D3×C4⋊C4—32no—
262D3×C4⋊C4—32no—
263#890—32no—
264#890—32no—
265#890—32no—
266#890C2×D312yes—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#888—34no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888C2×D312yes—
279#887—32no—
280#887—34no—
281#887—34no—
282#887—32no—
283#887—32no—
284#887—31no—
285#887—32no—
286#887—31no—
287#887—31no—
288#887—31no—
289#887—34no—
290#887—34no—
291#887—32no—
292#887—32no—
293#887—32no—
294#887—32no—
295#887—61no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298#67⋊C4—32no—
299#67⋊C4—32no—
300#67⋊C4—62no—
301#878—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878C2×D314yes—
306#878C2×D314yes—
307#877—32no—
308#877—32no—
309#877—34no—
310#877—34no—
311#877—62no—
312C42×D3—31no—
313C42×D3—31no—
314C42×D3—32no—
315C42×D3—32no—
316C42×D3—61no—
317#870—32no—
318#869—32no—
319#869C2×D311yescharacteristic
320#869C2×D311yescharacteristic
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—32no—
324C4×Dic6—32no—
325C4×Dic6—32no—
326C4×Dic6—32no—
327C4×Dic6—61no—
328C4×Dic6C2×D311yescharacteristic
329C4×Dic6C2×D311yescharacteristic
330C23×C32C2412yes—
331C22×C3⋊D3C2411yescharacteristic
332C32×D4C2×Q814yescomplemented
333C2×C32×C4—24no—
334C2×C32×C4C2412yes—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338#638C2×Q818yescomplemented
339C2×C3⋊Dic3—42no—
340C2×C3⋊Dic3C2×Q818yescomplemented
341C2×C3⋊Dic3C2411yescharacteristic
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2411yescharacteristic
345C2×C3⋊Dic3C2412yes—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—41no—
348C4×C3⋊D3C2×Q814yescomplemented
349#634C2×Q814yescomplemented
350C2×C3×Dic3—28no—
351C2×C3×Dic3—44no—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2414yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×Dic6—22no—
359C3×Dic6—24no—
360C3×Dic6—28no—
361C3×Dic6—42no—
362C3×Dic6#4114yescomplemented
363#627—24no—
364#627—44no—
365#624—24no—
366#624—42no—
367Q82—91no—
368#557—91no—
369#557—92no—
370#554—31no—
371#554—92no—
372#554—92no—
373#554—94no—
374D4×Q8—31no—
375D4×Q8—92no—
376#533—94no—
377#533—92no—
378#533—92no—
379#533—91no—
380C4×#41—92no—
381C4×#41—91no—
382C2×C4×Q8—92no—
383C2×C4×Q8—91no—
384C2×C3×Q8—31no—
385C2×C3×Q8—31no—
386C2×C3×Q8—34no—
387C2×C3×Q8—32no—
388C2×C3×Q8—32no—
389C2×C3×Q8—68no—
390C2×C3×D4—21no—
391C2×C3×D4C22×D311yescharacteristic
392C2×C3×D4C22×D311yescharacteristic
393C22×C3×C4—22no—
394C22×C3×C4—34no—
395C22×C3×C4—34no—
396C22×C3×C4C22×D312yes—
397C22×C3×C4C22×D312yes—
398C2×#67—32no—
399C2×#67—32no—
400C2×#67—62no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—32no—
404C22×Dic3—32no—
405C22×Dic3—62no—
406C22×Dic3—62no—
407C22×Dic3C22×D314yes—
408C22×Dic3C22×D314yes—
409D3×Q8—64no—
410D3×Q8—64no—
411#237—38no—
412#237—38no—
413#237—68no—
414C2×C4×D3—31no—
415C2×C4×D3—31no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—31no—
421C2×C4×D3—31no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3—61no—
425C2×C4×D3—61no—
426C2×C4×D3—61no—
427C2×Dic6—28no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—32no—
431C2×Dic6—32no—
432C2×Dic6—34no—
433C2×Dic6—34no—
434C2×Dic6—61no—
435C2×Dic6C22×D311yescharacteristic
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D314yes—
438C2×Dic6C22×D312yes—
439C2×Dic6C22×D311yescharacteristic
440C3×C4⋊C4—21no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4C22×D311yescharacteristic
453C3×C4⋊C4C22×D311yescharacteristic
454C3×C22⋊C4—22no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4C22×D312yes—
458C3×C22⋊C4C22×D312yes—
459C3×C42—21no—
460C3×C42—32no—
461C3×C42—32no—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D311yescharacteristic
464#217—32no—
465#217—32no—
466#217—62no—
467#217C22×D314yes—
468#217C22×D314yes—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—62no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—32no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—61no—
483C4⋊Dic3C22×D312yes—
484C4⋊Dic3C22×D312yes—
485C4⋊Dic3C22×D311yescharacteristic
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D314yes—
490Dic3⋊C4—32no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—62no—
509Dic3⋊C4—62no—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—32no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—34no—
533C4×Dic3—34no—
534C4×Dic3—34no—
535C4×Dic3—34no—
536C4×Dic3—62no—
537C4×Dic3—61no—
538C4×Dic3—61no—
539C4×Dic3—61no—
540C4×Dic3—62no—
541C4×Dic3—62no—
542C4×Dic3C22×D312yes—
543C4×Dic3C22×D312yes—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32C22×Q814yes—
547C22×C32C2511yescharacteristic
548C2×C3⋊D3—21no—
549C2×C3⋊D3—21no—
550C2×C3⋊D3C22×Q812yes—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4C22×Q812yes—
554C32×C4C2×#4112yes—
555C3⋊Dic3—21no—
556C3⋊Dic3—21no—
557C3⋊Dic3—22no—
558C3⋊Dic3C22×Q814yes—
559C3⋊Dic3C22×Q812yes—
560C3×Dic3—22no—
561C3×Dic3—24no—
562C3×Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—24no—
565C3×Dic3C2×#4114yes—
566C2×#41—91no—
567C22×Q8—32no—
568C22×Q8—91no—
569C4⋊Q8—32no—
570C4⋊Q8—31no—
571C4⋊Q8—31no—
572C4⋊Q8—92no—
573C4⋊Q8—92no—
574C4⋊Q8—94no—
575C4⋊Q8—94no—
576C4⋊Q8—92no—
577#125—32no—
578#125—92no—
579#125—94no—
580#125—94no—
581#125—94no—
582#125—92no—
583C22⋊Q8—32no—
584C22⋊Q8—32no—
585C22⋊Q8—34no—
586C22⋊Q8—34no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—94no—
591C22⋊Q8—94no—
592C22⋊Q8—92no—
593C22⋊Q8—92no—
594C4×Q8—31no—
595C4×Q8—31no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—94no—
601C4×Q8—91no—
602C4×Q8—94no—
603C4×Q8—92no—
604C4×Q8—91no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—94no—
608C4×Q8—92no—
609C4×Q8—91no—
610C4×Q8—91no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—94no—
614C4×D4—94no—
615C4×D4—91no—
616C4×D4—92no—
617C4×D4—92no—
618C4×D4D3211yescharacteristic
619#117—94no—
620#117—92no—
621#117—91no—
622#117—92no—
623C2×C4⋊C4—32no—
624C2×C4⋊C4—91no—
625C2×C4⋊C4—92no—
626C2×C4⋊C4—94no—
627C2×C42—92no—
628C2×C42—94no—
629C2×C42—92no—
630C2×C42—91no—
631C23×C3—22no—
632C23×C3C23×D312yes—
633C23×C3C23×D312yes—
634C22×D3—31no—
635C22×D3—31no—
636C22×D3—61no—
637C3×Q8—34no—
638C3×Q8—68no—
639C3×Q8—62no—
640C3×Q8—64no—
641C3×Q8—122no—
642C3×D4—24no—
643C3×D4D3×Q814yescomplemented
644C3×D4D3×Q814yescomplemented
645C2×C3×C4—24no—
646C2×C3×C4—24no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—22no—
650C2×C3×C4—21no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—34no—
654C2×C3×C4—34no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—44no—
658C2×C3×C4—68no—
659C2×C3×C4—124no—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—38no—
669#67—38no—
670#67—68no—
671C2×Dic3—28no—
672C2×Dic3—38no—
673C2×Dic3—38no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—32no—
682C2×Dic3—31no—
683C2×Dic3—32no—
684C2×Dic3—44no—
685C2×Dic3—68no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—62no—
689C2×Dic3—61no—
690C2×Dic3—62no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—124no—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D314yes—
696C2×Dic3C23×D314yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699C2×Dic3C23×D312yes—
700C4×D3—34no—
701C4×D3—34no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—62no—
705C4×D3—62no—
706C4×D3—64no—
707C4×D3—122no—
708C4×D3—122no—
709C4×D3—122no—
710C4×D3—121no—
711C4×D3—121no—
712C4×D3—122no—
713Dic6—24no—
714Dic6—22no—
715Dic6—28no—
716Dic6—34no—
717Dic6—34no—
718Dic6—42no—
719Dic6—64no—
720Dic6—64no—
721Dic6—64no—
722Dic6—124no—
723Dic6—124no—
724Dic6#23714yescomplemented
725C2×C32—24no—
726C2×C32C23×Q811yescharacteristic
727C2×C32C22×#4111yescharacteristic
728C2×C32#58511yescharacteristic
729C3⋊D3—22no—
730#41—98no—
731C2×Q8—31no—
732C2×Q8—31no—
733C2×Q8—34no—
734C2×Q8—32no—
735C2×Q8—32no—
736C2×Q8—68no—
737C2×Q8—92no—
738C2×Q8—94no—
739C2×Q8—91no—
740C2×Q8—184no—
741C2×D4—92no—
742C2×D4C2×D3211yescharacteristic
743C22×C4—34no—
744C22×C4—34no—
745C22×C4—92no—
746C22×C4—92no—
747C22×C4—92no—
748C22×C4—91no—
749C22×C4—92no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4C2×D3212yes—
753C4⋊C4—31no—
754C4⋊C4—34no—
755C4⋊C4—32no—
756C4⋊C4—32no—
757C4⋊C4—32no—
758C4⋊C4—31no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—34no—
762C4⋊C4—34no—
763C4⋊C4—32no—
764C4⋊C4—92no—
765C4⋊C4—92no—
766C4⋊C4—94no—
767C4⋊C4—92no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—92no—
775C4⋊C4—92no—
776C4⋊C4—91no—
777C4⋊C4C2×D3211yescharacteristic
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—94no—
781C22⋊C4—92no—
782C22⋊C4—92no—
783C22⋊C4C2×D3212yes—
784C42—32no—
785C42—32no—
786C42—92no—
787C42—92no—
788C42—94no—
789C42—94no—
790C42—94no—
791C42—91no—
792C42—92no—
793C42—91no—
794C42—92no—
795C42—91no—
796C42—92no—
797C42C2×D3211yescharacteristic
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—24no—
803C22×C3—21no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3C2×D3×Q814yes—
807C22×C3C2×D3×Q814yes—
808C22×C3C24×D311yescharacteristic
809C22×C3C24×D311yescharacteristic
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—121no—
818C2×D3—121no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—34no—
826C3×C4—41no—
827C3×C4—42no—
828C3×C4—62no—
829C3×C4—64no—
830C3×C4—62no—
831C3×C4—64no—
832C3×C4—62no—
833C3×C4C2×#23712yes—
834C3×C4C2×D3×Q812yes—
835C3×C4C2×D3×Q812yes—
836C3×C4D3×#4112yes—
837Dic3—24no—
838Dic3—22no—
839Dic3—24no—
840Dic3—22no—
841Dic3—22no—
842Dic3—34no—
843Dic3—34no—
844Dic3—32no—
845Dic3—32no—
846Dic3—64no—
847Dic3—62no—
848Dic3—62no—
849Dic3—61no—
850Dic3—61no—
851Dic3—62no—
852Dic3—61no—
853Dic3—62no—
854Dic3—61no—
855Dic3—121no—
856Dic3—122no—
857Dic3C2×#23714yes—
858C32Q8×#4111yescharacteristic, complemented, Sylow
859C23—91no—
860C23C22×D3212yes—
861Q8—34no—
862Q8—68no—
863Q8—64no—
864Q8—62no—
865Q8—94no—
866Q8—122no—
867Q8—184no—
868Q8—364no—
869D4—98no—
870D4#379714yescomplemented
871C2×C4—24no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—34no—
877C2×C4—34no—
878C2×C4—68no—
879C2×C4—98no—
880C2×C4—91no—
881C2×C4—92no—
882C2×C4—94no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—92no—
886C2×C4—124no—
887C2×C4—184no—
888C2×C4—182no—
889C2×C4—361no—
890C2×C4—362no—
891C2×C4—362no—
892C2×C4C22×D3212yes—
893C2×C4C22×D3211yescharacteristic
894C2×C4C22×D3211yescharacteristic
895C2×C4C22×D3211yescharacteristic
896C2×C3—24no—
897C2×C3—24no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—44no—
902C2×C3C22×#23711yescharacteristic
903C2×C3C22×D3×Q811yescharacteristic
904C2×C3C22×D3×Q811yescharacteristic
905C2×C3C2×D3×#4111yescharacteristic
906C2×C3#596611yescharacteristic
907C2×C3#596811yescharacteristic
908D3—62no—
909D3—62no—
910D3—122no—
911C22—22no—
912C22—22no—
913C22—92no—
914C22—181no—
915C22—181no—
916C22C2×#379714yes—
917C22C23×D3211yescharacteristic
918C4—22no—
919C4—21no—
920C4—34no—
921C4—64no—
922C4—62no—
923C4—62no—
924C4—64no—
925C4—62no—
926C4—92no—
927C4—94no—
928C4—181no—
929C4—181no—
930C4—182no—
931C4C2×#379712yes—
932C4D3×#23712yes—
933C3—21no—
934C3Q8×#23711yescharacteristic, complemented
935C3#8692311yescharacteristic, complemented
936C2—24no—
937C2—182no—
938C2C22×#379711yescharacteristic
939C2C2×D3×#23711yescharacteristic
940C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×#3830C22
hypercenterC4×D4D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5543C2semidirect
3. C3×D4×Dic6C2semidirect
4. #10595272C2semidirect
6. #10594991C2semidirect
7. C2×#63843C2semidirect
8. #10594810C2semidirect
9. #10594803C2semidirect
10. #10594448C2semidirect
11. #10594318C2semidirect
12. #10594141C2semidirect
13. #10594030C2semidirect
14. C4×#3797C2semidirect
15. #10593866C2semidirect
16. #10593864C2semidirect
17. #10593856C2semidirect
110. #5543D3semidirect
112. D4×Dic6D3semidirect
125. #3830Q8semidirect
332. C32×D4C2×Q8semidirect
338. #638C2×Q8semidirect
340. C2×C3⋊Dic3C2×Q8semidirect
348. C4×C3⋊D3C2×Q8semidirect
349. #634C2×Q8semidirect
362. C3×Dic6#41semidirect
643. C3×D4D3×Q8semidirect
644. C3×D4D3×Q8semidirect
724. Dic6#237semidirect
858. C32Q8×#41semidirect
870. D4#3797semidirect
934. C3Q8×#237semidirect
935. C3#86923semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
C3×#55432
C3×D4×Dic62
#105952722
#105951902
#105949912
C2×#638432
#105948102
#105948032
#105944482
#105943182
#105941412
#105940302
C4×#37972
#105938662
#105938642
#105938562
#869233
Q8×#2373