Finite Group Databasebeta

← #11860756

Subgroups — #11860756

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#204C211yesmaximal, characteristic
2#10593994C211yesmaximal, characteristic
3#10593885C211yesmaximal, characteristic, complemented
4#10592409C211yesmaximal, characteristic, complemented
5C3×#4710C211yesmaximal, characteristic, complemented
6C3×#4708C211yesmaximal, characteristic, complemented
7#10590948C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic
9#10590792C211yesmaximal, characteristic, complemented
10#10590773C211yesmaximal, characteristic, complemented
11#10590766C211yesmaximal, characteristic, complemented
12#10590744C211yesmaximal, characteristic, complemented
13#10590707C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15C4×#3716C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#78572—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#872C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic, complemented
29#63921—21no—
30D3×(C2×D3)⋊C4—21no—
31#63904—21no—
32#63894C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63881—21no—
35#63878—21no—
36#63877—21no—
37#63844C2211yescharacteristic, complemented
38Dic3×Dic6C2211yescharacteristic, complemented
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41#63838—21no—
42#63837—21no—
43C2×#3717C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45D3×#204C418yescomplemented
46C32×#97C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48#63645C2211yescharacteristic, complemented
49#63643C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55C3×C4×C3⋊C8C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic
62C2×D3×SD16—31no—
63C22×#204—31no—
64#5572—31no—
65#5545—31no—
66#5521—31no—
67#5516—31no—
68C3×#440—31no—
69C3×#405—31no—
70#5164—31no—
71#5131—31no—
72#5120—31no—
73#5106—31no—
74C4×#215—31no—
75C4×#214—31no—
76#4889—31no—
77#4880—31no—
78#4802—31no—
79#4788—31no—
80#4770—31no—
81#4758—31no—
82#4710—31no—
83#4710—31no—
84#4710—31no—
85#4710—31no—
86#4710—61no—
87#4710D311yescharacteristic, complemented
88#4708D311yescharacteristic, complemented
89C4×#204—31no—
90C4×#204—31no—
91C4×#204—31no—
92C4×#204—31no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12C2×C414yes—
108D3×Dic6—22no—
109D3×Dic6C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118#3744C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204C2×C414yescomplemented
132C3×ΓL(1,𝔽25)—22no—
133C3×D3×C8C2×C414yescomplemented
134#3724—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144#3717C2×C414yescomplemented
145#3716C2×C414yescomplemented
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×#117—31no—
157Q8×Dic3—31no—
158C2×#215—31no—
159D4×Dic3—31no—
160C2×#214—31no—
161C4×#67—61no—
162C2×(C2×D3)⋊C4—61no—
163#926—31no—
164#926—31no—
165D3×SD16—38no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—38no—
171C2×#204—61no—
172C2×#204C2×D311yescharacteristic
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic
174C2×D3×C8C2×D311yescharacteristic
175#893—31no—
176#893—61no—
177#893—61no—
178#892—31no—
179#892—31no—
180#892—61no—
181#887—31no—
182#887—61no—
183#887—61no—
184#887—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#877—61no—
190#877—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12C2×D311yescharacteristic
197#872—61no—
198#872C2×D311yescharacteristic
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic, complemented
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—21no—
210C3×#97—31no—
211C3×#97C2×D311yescharacteristic, complemented
212C3×#97C2×D311yescharacteristic, complemented
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223#818—31no—
224#818—31no—
225#818—61no—
226#818C2×D311yescharacteristic, complemented
227#817—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—61no—
234#816C2×D311yescharacteristic, complemented
235#815C2×D311yescharacteristic, complemented
236C8×Dic3C2×D311yescharacteristic, complemented
237#810—31no—
238#809—31no—
239#808—31no—
240#808—31no—
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C2×D32—24no—
246C2×D32—81no—
247C2×D32—81no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)C22×C412yes—
256C4×C3⋊D3—81no—
257#634—21no—
258#634C22×C412yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12C22×C412yes—
267C3×C4×D3—81no—
268C3×C4×D3C22×C412yes—
269C3×C4×D3#4112yes—
270C3×Dic6—21no—
271C3×Dic6C22×C412yes—
272#627—24no—
273#626—24no—
274#624—81no—
275D3×Dic3—24no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—91no—
283#518—91no—
284#440—31no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—31no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305D3×Q8—34no—
306D3×Q8—62no—
307D3×D4—34no—
308D3×D4—62no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—34no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12—61no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—121no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C3×M16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—34no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—61no—
358#217—61no—
359#217—61no—
360#215—34no—
361#214—34no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4D1211yescharacteristic
372(C2×D3)⋊C4D1211yescharacteristic
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389Dic3⋊C4D1211yescharacteristic
390Dic3⋊C4D1211yescharacteristic
391C4×Dic3—21no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—34no—
407#204—34no—
408#204—34no—
409#204—34no—
410#204—64no—
411#204C4×D314yescomplemented
412ΓL(1,𝔽25)—22no—
413D3×C8C4×D314yescomplemented
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424D32—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4C23×C411yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—22no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—91no—
439C22×D4—91no—
440C2×SD16—31no—
441C2×SD16—98no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—31no—
446C22×C8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458C4×D4—181no—
459#117—31no—
460#117—91no—
461#117—91no—
462#117—181no—
463#117—181no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—91no—
469#106—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—31no—
479#97D3211yescharacteristic, complemented
480C4×C8—31no—
481C4×C8—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—64no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—64no—
489C22×D3—121no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3—241no—
494C22×D3C2×D1211yescharacteristic
495C3×Q8—32no—
496C3×Q8—61no—
497C3×D4—32no—
498C3×D4—61no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—241no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—64no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—241no—
532C2×Dic3C2×D1211yescharacteristic
533C2×Dic3C2×D1211yescharacteristic
534C2×Dic3C2×D1211yescharacteristic
535D12—21no—
536D12—32no—
537D12—32no—
538D12—62no—
539D12—64no—
540D12—61no—
541D12—61no—
542D12—121no—
543D12C2×C4×D312yes—
544C4×D3—64no—
545C4×D3—81no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—242no—
552C4×D3C2×C4×D312yes—
553C4×D3#23512yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×C4×D312yes—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—22no—
567C3×C8—32no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8C2×C4×D312yes—
571C3×C8C2×C4×D312yes—
572C3⋊C8—21no—
573C3⋊C8C2×C4×D312yes—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3⋊D3—42no—
578C3×D3—22no—
579C3×D3—42no—
580C24—181no—
581C2×Q8—31no—
582C2×Q8—94no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×D4—31no—
587C2×D4—94no—
588C2×D4—91no—
589C2×D4—182no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—34no—
598SD16—94no—
599SD16—94no—
600SD16—94no—
601M16—62no—
602C2×C8—31no—
603C2×C8—34no—
604C2×C8—31no—
605C2×C8C2×D3211yescharacteristic
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—181no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C42C2×D3211yescharacteristic
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C22×D1211yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—62no—
648C2×D3—62no—
649C2×D3—122no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—244no—
657C2×D3—244no—
658C2×D3C4×D1212yes—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—32no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—62no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4C22×C4×D311yescharacteristic
674C3×C4C22×C4×D311yescharacteristic
675C3×C4C2×#23511yescharacteristic
676C3×C4D3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—22no—
680Dic3—41no—
681Dic3—41no—
682Dic3—62no—
683Dic3—62no—
684Dic3—122no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3—241no—
691Dic3C4×D1212yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—31no—
694C23—61no—
695C23—184no—
696C23—181no—
697C23—721no—
698C23—721no—
699Q8—32no—
700Q8—61no—
701Q8—92no—
702Q8—184no—
703Q8—181no—
704D4—32no—
705D4—61no—
706D4—92no—
707D4—184no—
708D4—181no—
709C2×C4—31no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—184no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—241no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4—721no—
725C2×C4D3×D1211yescharacteristic
726C2×C4D3×D1211yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—32no—
730C8—61no—
731C8C4×D3212yes—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—62no—
736C2×C3—122no—
737C2×C3C2×C4×D1211yescharacteristic
738C2×C3C4×D3×D411yescharacteristic
739C2×C3#575111yescharacteristic
740C2×C3#575111yescharacteristic
741C2×C3#577511yescharacteristic
742C2×C3#577811yescharacteristic
743D3—22no—
744D3—42no—
745D3—122no—
746D3—122no—
747D3—242no—
748C22—32no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—182no—
755C22—361no—
756C22—361no—
757C22—724no—
758C22C2×D3×D1211yescharacteristic
759C4—21no—
760C4—21no—
761C4—32no—
762C4—61no—
763C4—61no—
764C4—62no—
765C4—121no—
766C4—121no—
767C4—182no—
768C4—361no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23511yescharacteristic
772C3—21no—
773C3#7857211yescharacteristic, complemented
774C3#7977711yescharacteristic, complemented
775C2—62no—
776C2—122no—
777C2—362no—
778C2C4×D3×D1211yescharacteristic
779C2#1059471311yescharacteristic
780C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10593885C2semidirect
4. #10592409C2semidirect
5. C3×#4710C2semidirect
6. C3×#4708C2semidirect
7. #10590948C2semidirect
9. #10590792C2semidirect
10. #10590773C2semidirect
11. #10590766C2semidirect
12. #10590744C2semidirect
13. #10590707C2semidirect
14. C4×#3717C2semidirect
15. C4×#3716C2semidirect
22. C4×#634C22semidirect
28. C3×C4×Dic6C22semidirect
37. #63844C22semidirect
38. Dic3×Dic6C22semidirect
45. D3×#204C4semidirect
46. C32×#97C22semidirect
48. #63645C22semidirect
49. #63643C22semidirect
51. C3×#818C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×C8×Dic3C22semidirect
55. C3×C4×C3⋊C8C22semidirect
56. #63573C22semidirect
57. #63573C22semidirect
58. #63567C22semidirect
59. #63566C22semidirect
87. #4710D3semidirect
88. #4708D3semidirect
109. D3×Dic6C2×C4semidirect
118. #3744C2×C4semidirect
131. C3×#204C2×C4semidirect
133. C3×D3×C8C2×C4semidirect
144. #3717C2×C4semidirect
145. #3716C2×C4semidirect
205. C4×Dic6C2×D3semidirect
211. C3×#97C2×D3semidirect
212. C3×#97C2×D3semidirect
226. #818C2×D3semidirect
234. #816C2×D3semidirect
235. #815C2×D3semidirect
236. C8×Dic3C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
411. #204C4×D3semidirect
413. D3×C8C4×D3semidirect
479. #97D32semidirect
692. C32#2949semidirect
773. C3#78572semidirect
774. C3#79777semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2042
#105939942
#105938852
#105924092
C3×#47102
C3×#47082
#105909482
#105909392
#105907922
#105907732
#105907662
#105907442
#105907072
C4×#37172
C4×#37162
#797773
#785723