Finite Group Databasebeta

← #11860752

Subgroups — #11860752

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596043C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic
3#10593996C211yesmaximal, characteristic
4C3×#5026C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6#10591572C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591562C211yesmaximal, characteristic, complemented
9#10590594C211yesmaximal, characteristic
10#10590574C211yesmaximal, characteristic, complemented
11#10590461C211yesmaximal, characteristic, complemented
12#10590460C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#79649—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21Q8×C3⋊Dic3C2211yescharacteristic, complemented
22#64101—21no—
23#64101C2211yescharacteristic
24#64096—21no—
25#64096C2211yescharacteristic, complemented
26#64081—21no—
27#64081C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34#63940C418yescomplemented
35D3×(C2×D3)⋊C4—21no—
36D3×(C2×D3)⋊C4—21no—
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic
39#63879—21no—
40#63879—21no—
41#63849C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C2×D3×SD16—31no—
64#5572—31no—
65#5572—31no—
66#5572—61no—
67#5545—31no—
68#5545—31no—
69C3×#440—31no—
70C3×C4×SD16—31no—
71#5164—31no—
72Dic3×SD16—31no—
73#5026D311yescharacteristic, complemented
74C4×#215D311yescharacteristic, complemented
75#5018—31no—
76C4×#214—31no—
77#4889—31no—
78#4880—31no—
79#4860—31no—
80#4852—31no—
81#4817—31no—
82#4802—31no—
83#4802—31no—
84#4788—31no—
85#4770—31no—
86#4770—31no—
87#4758—31no—
88#4757—31no—
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95Q8×C3⋊D3—22no—
96Q8×C3⋊D3C2×C414yescomplemented
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802C2×C414yes—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3752—21no—
115#3752D411yescharacteristic
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3750D411yescharacteristic
122#3750D411yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#215C2×C414yescomplemented
129C3×#215C2×C414yescomplemented
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716C2×C414yescomplemented
143#3716C2×C414yescomplemented
144#3712—22no—
145#3710C2×C414yescomplemented
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—61no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—21no—
155C3×C4×Q8C2×D311yescharacteristic, complemented
156C3×C4×Q8C2×D311yescharacteristic, complemented
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—61no—
162C2×#215C2×D311yescharacteristic
163C2×#215C2×D311yescharacteristic
164D4×Dic3—31no—
165D4×Dic3—31no—
166C2×#214—31no—
167C2×#214—31no—
168C4×#67—61no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171C2×(C2×D3)⋊C4—61no—
172D3×SD16—38no—
173D3×SD16—38no—
174C2×#204—31no—
175C2×#204—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180#893—31no—
181#893—31no—
182#892—31no—
183#892—31no—
184#892—31no—
185#892—31no—
186#892—61no—
187#892—61no—
188#892—61no—
189#892—62no—
190#887—31no—
191#887—31no—
192#887—61no—
193#887—61no—
194#887—61no—
195#887—62no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200C4×D12C2×D311yescharacteristic
201C4×D12C2×D311yescharacteristic
202#872—31no—
203#872—31no—
204#872—61no—
205#872—61no—
206#872—61no—
207#872—62no—
208C4×Dic6—31no—
209C4×Dic6—31no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6—61no—
213C4×Dic6—62no—
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835C2×D311yescharacteristic, complemented
223#835C2×D311yescharacteristic, complemented
224#832—31no—
225#832—31no—
226#821—31no—
227#821—31no—
228#818—31no—
229#817—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#809C2×D311yescharacteristic
239#809C2×D311yescharacteristic
240#808—31no—
241#808C2×D311yescharacteristic, complemented
242#807—31no—
243#807C2×D311yescharacteristic, complemented
244#803C2×D311yescharacteristic, complemented
245C4×C3⋊C8C2×D311yescharacteristic, complemented
246C22×C3⋊D3C2×D411yescharacteristic
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C2×D32—24no—
250C2×D32—81no—
251C2×D32—81no—
252C32×Q8—21no—
253C32×Q8C22×C412yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3—24no—
265C4×C3⋊D3C22×C412yes—
266C4×C3⋊D3#4112yes—
267#634—21no—
268#634—24no—
269#634C22×C412yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12C22×C412yes—
275C3×D12C22×C412yes—
276C3×C4×D3—81no—
277C3×C4×D3—81no—
278#625—24no—
279D3×Dic3—81no—
280D3×Dic3—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C3×C3⋊C8C22×C412yes—
285C22×SD16—91no—
286#519—91no—
287#518—91no—
288#440—31no—
289#440—91no—
290#440—91no—
291#440—91no—
292C4×SD16—31no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296#427—91no—
297#419—91no—
298#418—91no—
299#405—91no—
300C23×D3—61no—
301C23×D3—61no—
302C2×C3×Q8—21no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313D3×Q8—34no—
314D3×Q8—34no—
315D3×Q8—64no—
316D3×Q8—62no—
317D3×Q8—62no—
318D3×Q8—64no—
319D3×D4—34no—
320D3×D4—34no—
321D3×D4—62no—
322D3×D4—62no—
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—62no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—62no—
341C3×SD16—34no—
342C3×SD16—34no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—22no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—21no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#217—61no—
365#215C4×D314yescomplemented
366#215C4×D314yescomplemented
367#214—34no—
368#214—34no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—62no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—62no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404C4×Dic3—31no—
405C4×Dic3—31no—
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—62no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425#204—34no—
426#204—34no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429D3×C8—34no—
430D3×C8—34no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3C4×D412yes—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441D32—84no—
442C32×C4—22no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4C23×C411yescharacteristic
447C32×C4C2×#4111yescharacteristic
448C3⋊Dic3—22no—
449C3⋊Dic3—21no—
450C3⋊Dic3—21no—
451C3⋊Dic3—41no—
452C3⋊Dic3C4×D412yes—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C22×Q8—91no—
456C22×D4—91no—
457C2×SD16—31no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×SD16—91no—
461C2×SD16—98no—
462C2×M16—91no—
463C22×C8—91no—
464C4×Q8—91no—
465C4×Q8—91no—
466C4×Q8—91no—
467C4×Q8—181no—
468C4×Q8—181no—
469C4×Q8D3211yescharacteristic, complemented
470C4×D4—31no—
471C4×D4—31no—
472C4×D4—91no—
473C4×D4—91no—
474C4×D4—181no—
475C4×D4—181no—
476#117—91no—
477#117—91no—
478#117—91no—
479#117—181no—
480#117—181no—
481C2×C22⋊C4—181no—
482C2×C22⋊C4—181no—
483#107—31no—
484#107—91no—
485#106—31no—
486#106—91no—
487#103—31no—
488#103—31no—
489#103—91no—
490#103—91no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#97—31no—
496#97—91no—
497C4×C8—31no—
498C4×C8—91no—
499C23×C3—61no—
500C23×C3—61no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—241no—
509C22×D3—241no—
510C22×D3—241no—
511C22×D3—241no—
512C3×Q8—22no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—22no—
516C3×Q8C2×C4×D312yes—
517C3×Q8C2×C4×D312yes—
518C3×D4—32no—
519C3×D4—32no—
520C3×D4—61no—
521C3×D4—61no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—241no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—64no—
542#67—64no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—241no—
561C2×Dic3—241no—
562D12—21no—
563D12—21no—
564D12C2×C4×D312yes—
565D12C2×C4×D312yes—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—64no—
573C4×D3—64no—
574C4×D3—68no—
575C4×D3—81no—
576C4×D3—81no—
577C4×D3—241no—
578C4×D3—241no—
579Dic6—32no—
580Dic6—32no—
581Dic6—62no—
582Dic6—64no—
583Dic6—64no—
584Dic6—68no—
585Dic6—62no—
586Dic6—61no—
587Dic6—61no—
588C3×C8—32no—
589C3×C8—32no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8C2×C4×D312yes—
595C3⋊C8C2×C4×D312yes—
596C2×C32C2×C4×D411yescharacteristic
597C2×C32#57711yescharacteristic
598C2×C32#57711yescharacteristic
599C3⋊D3—22no—
600C3×D3—42no—
601C3×D3—42no—
602C24—181no—
603C2×Q8—94no—
604C2×Q8—91no—
605C2×Q8—181no—
606C2×Q8—182no—
607C2×Q8C2×D3211yescharacteristic
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—94no—
611C2×D4—182no—
612C2×D4—181no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619SD16—34no—
620SD16—34no—
621SD16—94no—
622SD16—94no—
623M16—182no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—94no—
629C4⋊C4—21no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—21no—
648C42—91no—
649C42—181no—
650C42—181no—
651C42—181no—
652C42—181no—
653C42—181no—
654C42C2×D3211yescharacteristic
655C22×C3—21no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—32no—
667C2×D3—32no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—244no—
680C2×D3—244no—
681C3×C4—24no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—42no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C22×C4×D311yescharacteristic
698C3×C4C22×C4×D311yescharacteristic
699C3×C4D3×#4111yescharacteristic
700C3×C4D3×#4111yescharacteristic
701Dic3—32no—
702Dic3—32no—
703Dic3—41no—
704Dic3—41no—
705Dic3—62no—
706Dic3—64no—
707Dic3—61no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—62no—
712Dic3—62no—
713Dic3—121no—
714Dic3—121no—
715Dic3—122no—
716Dic3—121no—
717Dic3—121no—
718C32#294911yescharacteristic, complemented, Sylow
719C23—61no—
720C23—61no—
721C23—91no—
722C23—184no—
723C23—721no—
724C23—721no—
725Q8—21no—
726Q8—92no—
727Q8—184no—
728Q8—181no—
729Q8C4×D3212yes—
730D4—32no—
731D4—32no—
732D4—61no—
733D4—61no—
734D4—184no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—184no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—241no—
748C2×C4—241no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4#381111yescharacteristic
752C2×C4#381111yescharacteristic
753C2×C4C22×D3211yescharacteristic
754C8—32no—
755C8—32no—
756C8—61no—
757C8—61no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—122no—
762C2×C3—122no—
763C2×C3C4×D3×D411yescharacteristic
764C2×C3C4×D3×D411yescharacteristic
765C2×C3#576211yescharacteristic
766C2×C3#577011yescharacteristic
767C2×C3#577511yescharacteristic
768C2×C3#577811yescharacteristic
769D3—42no—
770D3—42no—
771D3—62no—
772D3—62no—
773D3—122no—
774C22—62no—
775C22—62no—
776C22—92no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—181no—
782C22—181no—
783C22—724no—
784C22C2×#381111yescharacteristic
785C4—21no—
786C4—22no—
787C4—21no—
788C4—41no—
789C4—92no—
790C4—121no—
791C4—121no—
792C4—181no—
793C4—182no—
794C4—181no—
795C4—361no—
796C4C2×C4×D3211yescharacteristic
797C4#6430611yescharacteristic
798C3—21no—
799C3#7964911yescharacteristic, complemented
800C3#7977711yescharacteristic, complemented
801C2—122no—
802C2—122no—
803C2—182no—
804C2C4×#381111yescharacteristic
805C2#1059532411yescharacteristic
806C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2949
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. #10596043C2semidirect
4. C3×#5026C2semidirect
5. C3×C4×#215C2semidirect
6. #10591572C2semidirect
7. #10591571C2semidirect
8. #10591562C2semidirect
10. #10590574C2semidirect
11. #10590461C2semidirect
12. #10590460C2semidirect
13. #10590360C2semidirect
14. C4×#3716C2semidirect
15. #10590321C2semidirect
20. C32×C4×Q8C22semidirect
21. Q8×C3⋊Dic3C22semidirect
25. #64096C22semidirect
29. C4×#634C22semidirect
34. #63940C4semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
60. #63555C22semidirect
61. #63553C22semidirect
73. #5026D3semidirect
74. C4×#215D3semidirect
96. Q8×C3⋊D3C2×C4semidirect
128. C3×#215C2×C4semidirect
129. C3×#215C2×C4semidirect
142. #3716C2×C4semidirect
143. #3716C2×C4semidirect
145. #3710C2×C4semidirect
155. C3×C4×Q8C2×D3semidirect
156. C3×C4×Q8C2×D3semidirect
222. #835C2×D3semidirect
223. #835C2×D3semidirect
241. #808C2×D3semidirect
243. #807C2×D3semidirect
244. #803C2×D3semidirect
245. C4×C3⋊C8C2×D3semidirect
365. #215C4×D3semidirect
366. #215C4×D3semidirect
469. C4×Q8D32semidirect
718. C32#2949semidirect
799. C3#79649semidirect
800. C3#79777semidirect

Maximal subgroups

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

subgroupindex
#105960432
C2×#639402
#105939962
C3×#50262
C3×C4×#2152
#105915722
#105915712
#105915622
#105905942
#105905742
#105904612
#105904602
#105903602
C4×#37162
#105903212
#797773
#796493