Finite Group Databasebeta

← #11860443

Subgroups — #11860443

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic
3C4×#3796C211yesmaximal, characteristic
4C3×#5030C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic, complemented
6#10591581C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591562C211yesmaximal, characteristic, complemented
9#10590612C211yesmaximal, characteristic
10#10590583C211yesmaximal, characteristic, complemented
11#10590482C211yesmaximal, characteristic, complemented
12#10590460C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590247C211yesmaximal, characteristic, complemented
16#79829—31nomaximal
17#79774—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22C4⋊C4×C3⋊D3—21no—
23C4⋊C4×C3⋊D3C2211yescharacteristic
24#64096—21no—
25#64096C2211yescharacteristic
26C42×C3⋊D3—21no—
27C42×C3⋊D3C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63951C418yescomplemented
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63881—21no—
38#63878—21no—
39C4×D3×Dic3—21no—
40#63849C2211yescharacteristic
41#63843C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63553C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64C4×#239—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8—31no—
67C4×D3×Q8—61no—
68C4×#237—31no—
69C3×#441—31no—
70C3×#440—31no—
71Dic3×Q16—31no—
72Dic3×SD16—31no—
73#5030—31no—
74#5030D311yescharacteristic, complemented
75#5026D311yescharacteristic, complemented
76#5018—31no—
77#4881—31no—
78#4873—31no—
79#4861—31no—
80#4852—31no—
81#4803—31no—
82#4802—31no—
83#4802—31no—
84#4790—31no—
85#4790—31no—
86#4788—31no—
87#4771—31no—
88#4758—31no—
89#4716—31no—
90#4710—31no—
91#4707—31no—
92#4707—31no—
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3C2×C414yescomplemented
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3D411yescharacteristic
99C2×C4×C3⋊D3D411yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×#634—21no—
102C2×#634C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3796—22no—
110#3796C2×C414yes—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C42—21no—
114C32×C42C2311yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3D411yescharacteristic
124C4×C3⋊Dic3D411yescharacteristic
125C4×C3⋊Dic3C2311yescharacteristic
126C3×#216C2×C414yescomplemented
127C3×#215C2×C414yescomplemented
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3716C2×C414yescomplemented
144#3712—22no—
145#3712C2×C414yescomplemented
146C4×#137—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×D4—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163C2×#216—31no—
164C2×#216C2×D311yescharacteristic
165C2×#215C2×D311yescharacteristic
166D4×Dic3—31no—
167C2×#214—31no—
168C4×#67—61no—
169C2×C4×Dic3—61no—
170#918—38no—
171#915—38no—
172C2×Dic12—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178#893—31no—
179#893—61no—
180#892—31no—
181#892—31no—
182#892—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—62no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—61no—
193#887—61no—
194#887—61no—
195#887—62no—
196#67⋊C4—61no—
197#877—61no—
198C4×D12—61no—
199C4×D12C2×D311yescharacteristic
200C42×D3—31no—
201C42×D3—31no—
202C42×D3—61no—
203C42×D3—61no—
204C42×D3—61no—
205C42×D3—61no—
206C42×D3—62no—
207C4×Dic6—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6—62no—
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×#97—31no—
222#835—31no—
223#835C2×D311yescharacteristic
224#835C2×D311yescharacteristic
225#832—31no—
226#821—31no—
227#818—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810C2×D311yescharacteristic
239#809C2×D311yescharacteristic
240#808—31no—
241#808C2×D311yescharacteristic
242#807—31no—
243#807C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245#803C2×D311yescharacteristic
246C22×C3⋊D3C2×D411yescharacteristic
247C22×C3×D3—21no—
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—24no—
261C4×C3⋊D3—22no—
262C4×C3⋊D3—41no—
263C4×C3⋊D3—42no—
264C4×C3⋊D3C22×C412yes—
265C4×C3⋊D3#4112yes—
266#634—21no—
267#634—24no—
268#634C22×C412yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6C22×C412yes—
277#626—24no—
278D3×Dic3—24no—
279D3×Dic3—42no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8C22×C412yes—
283C3×C3⋊C8C22×C412yes—
284C2×#137—91no—
285C4×#41—91no—
286C2×C4×Q8—91no—
287#441—31no—
288#441—91no—
289#440—31no—
290#440—91no—
291C4×Q16—91no—
292C4×Q16—91no—
293C4×SD16—91no—
294C4×SD16—91no—
295#428—91no—
296#419—91no—
297#417—91no—
298C4×M16—91no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C22×C3×C4—61no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308#239—34no—
309#239—62no—
310D3×Q8—34no—
311D3×Q8—34no—
312D3×Q8—64no—
313D3×Q8—62no—
314D3×Q8—62no—
315D3×Q8—64no—
316#237—34no—
317#237—62no—
318C2×D12—61no—
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—62no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—62no—
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6—62no—
344C2×Dic6C22×D311yescharacteristic
345C3×Q16—34no—
346C3×SD16—34no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—61no—
361C3×C42—22no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—61no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368#217—61no—
369#216—34no—
370#216C4×D314yescomplemented
371#215C4×D314yescomplemented
372#214—34no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—62no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—62no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397C4×Dic3—21no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—62no—
416C4×Dic3—62no—
417C4×Dic3—62no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424Dic12—34no—
425#204—34no—
426ΓL(1,𝔽25)—34no—
427ΓL(1,𝔽25)—34no—
428ΓL(1,𝔽25)—62no—
429ΓL(1,𝔽25)—62no—
430C22×C32C22×D411yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3C4×D412yes—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C32×C4—22no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4C23×C411yescharacteristic
442C32×C4C2×#4111yescharacteristic
443C3⋊Dic3—22no—
444C3⋊Dic3—21no—
445C3⋊Dic3—41no—
446C3⋊Dic3C4×D412yes—
447C3⋊Dic3#13712yescomplemented
448C3×Dic3—22no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—91no—
452C22×Q8—91no—
453#137—98no—
454C2×Q16—31no—
455C2×Q16—91no—
456C2×SD16—31no—
457C2×SD16—91no—
458C2×M16—91no—
459C2×M16—91no—
460C4×Q8—31no—
461C4×Q8—91no—
462C4×Q8—91no—
463C4×Q8—91no—
464C4×Q8—91no—
465C4×Q8—181no—
466C4×Q8—181no—
467C4×Q8D3211yescharacteristic
468C4×D4—31no—
469C4×D4—91no—
470C4×D4—181no—
471C4×D4—181no—
472#117—91no—
473#117—181no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—181no—
476C2×C42—91no—
477C2×C42—181no—
478C2×C42—181no—
479#107—31no—
480#107—91no—
481#106—31no—
482#106—91no—
483#103—31no—
484#103—31no—
485#103—31no—
486#103—91no—
487#103—91no—
488#103—91no—
489#102—31no—
490#102—91no—
491#97—31no—
492#97—31no—
493C4×C8—91no—
494C4×C8—91no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—61no—
500C3×Q8—22no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—22no—
504C3×Q8—32no—
505C3×Q8—61no—
506C3×Q8C2×C4×D312yes—
507C3×Q8C2×C4×D312yes—
508C3×D4—32no—
509C3×D4—61no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—64no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—64no—
543C2×Dic3—62no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—62no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—122no—
550D12—21no—
551D12—64no—
552D12C2×C4×D312yes—
553C4×D3—32no—
554C4×D3—32no—
555C4×D3—32no—
556C4×D3—32no—
557C4×D3—42no—
558C4×D3—62no—
559C4×D3—62no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—64no—
563C4×D3—64no—
564C4×D3—64no—
565C4×D3—64no—
566C4×D3—68no—
567C4×D3—122no—
568C4×D3—121no—
569C4×D3—121no—
570C4×D3—122no—
571C4×D3—124no—
572C4×D3—122no—
573C4×D3—122no—
574Dic6—21no—
575Dic6—32no—
576Dic6—32no—
577Dic6—62no—
578Dic6—64no—
579Dic6—64no—
580Dic6—68no—
581Dic6—62no—
582Dic6—61no—
583Dic6—61no—
584Dic6C2×C4×D312yes—
585C3×C8—32no—
586C3×C8—32no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C3⋊C8C2×C4×D312yes—
592C3⋊C8C2×C4×D312yes—
593C2×C32C2×C4×D411yescharacteristic
594C2×C32C2×#13711yescharacteristic
595C2×C32#57511yescharacteristic
596C3⋊D3—22no—
597C3×D3—42no—
598#41—94no—
599#41—182no—
600C2×Q8—31no—
601C2×Q8—94no—
602C2×Q8—91no—
603C2×Q8—181no—
604C2×Q8—182no—
605C2×Q8C2×D3211yescharacteristic
606C2×D4—31no—
607C2×D4—181no—
608C22×C4—61no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616Q16—34no—
617Q16—94no—
618SD16—34no—
619SD16—94no—
620M16—94no—
621M16—182no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—31no—
626C4⋊C4—21no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—21no—
641C42—61no—
642C42—91no—
643C42—91no—
644C42—91no—
645C42—181no—
646C42—181no—
647C42—181no—
648C42—181no—
649C42—181no—
650C42C2×D3211yescharacteristic
651C22×C3—21no—
652C22×C3—62no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—22no—
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C3×C4—24no—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—62no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C22×C4×D311yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4D3×#4111yescharacteristic
690Dic3—22no—
691Dic3—32no—
692Dic3—32no—
693Dic3—32no—
694Dic3—32no—
695Dic3—41no—
696Dic3—41no—
697Dic3—62no—
698Dic3—62no—
699Dic3—64no—
700Dic3—61no—
701Dic3—61no—
702Dic3—62no—
703Dic3—62no—
704Dic3—121no—
705Dic3—122no—
706Dic3—121no—
707Dic3—121no—
708C32C4×#13711yescharacteristic, complemented, Sylow
709C23—61no—
710C23—91no—
711Q8—21no—
712Q8—32no—
713Q8—61no—
714Q8—92no—
715Q8—184no—
716Q8—181no—
717Q8C4×D3212yes—
718D4—32no—
719D4—61no—
720D4—184no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—92no—
729C2×C4—92no—
730C2×C4—91no—
731C2×C4—122no—
732C2×C4—182no—
733C2×C4—184no—
734C2×C4—184no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—361no—
738C2×C4—362no—
739C2×C4—362no—
740C2×C4#381111yescharacteristic
741C2×C4#381111yescharacteristic
742C2×C4C22×D3211yescharacteristic
743C8—32no—
744C8—32no—
745C8—61no—
746C8—61no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—122no—
751C2×C3C4×D3×D411yescharacteristic
752C2×C3C4×D3×D411yescharacteristic
753C2×C3#577311yescharacteristic
754C2×C3D3×#13711yescharacteristic
755C2×C3D3×#13711yescharacteristic
756C2×C3#577711yescharacteristic
757D3—42no—
758D3—64no—
759D3—62no—
760D3—62no—
761C22—62no—
762C22—92no—
763C22—121no—
764C22—121no—
765C22—181no—
766C22—181no—
767C22C2×#381111yescharacteristic
768C4—21no—
769C4—22no—
770C4—21no—
771C4—41no—
772C4—62no—
773C4—92no—
774C4—92no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—182no—
779C4—361no—
780C4C2×C4×D3211yescharacteristic
781C4#6430611yescharacteristic
782C3—21no—
783C3#7977411yescharacteristic, complemented
784C3#7982911yescharacteristic, complemented
785C2—122no—
786C2—182no—
787C2C4×#381111yescharacteristic
788C2#1059532211yescharacteristic
789C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
4. C3×#5030C2semidirect
5. C3×#5026C2semidirect
6. #10591581C2semidirect
7. #10591571C2semidirect
8. #10591562C2semidirect
10. #10590583C2semidirect
11. #10590482C2semidirect
12. #10590460C2semidirect
13. #10590383C2semidirect
14. #10590360C2semidirect
15. #10590247C2semidirect
34. #63951C4semidirect
74. #5030D3semidirect
75. #5026D3semidirect
95. Q8×C3⋊D3C2×C4semidirect
126. C3×#216C2×C4semidirect
127. C3×#215C2×C4semidirect
142. #3719C2×C4semidirect
143. #3716C2×C4semidirect
145. #3712C2×C4semidirect
370. #216C4×D3semidirect
371. #215C4×D3semidirect
447. C3⋊Dic3#137semidirect
708. C32C4×#137semidirect
783. C3#79774semidirect
784. C3#79829semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C2×#639512
C4×#37962
C3×#50302
C3×#50262
#105915812
#105915712
#105915622
#105906122
#105905832
#105904822
#105904602
#105903832
#105903602
#105902472
#798293
#797743