Finite Group Databasebeta

← #11860782

Subgroups — #11860782

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic
2C2×#63930C211yesmaximal, characteristic
3#10594347C211yesmaximal, characteristic, complemented
4#10592469C211yesmaximal, characteristic
5C3×#4758C211yesmaximal, characteristic, complemented
6C3×#4757C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#10590910C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590792C211yesmaximal, characteristic, complemented
12#10590691C211yesmaximal, characteristic, complemented
13#10590574C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#79649—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#887C2211yescharacteristic, complemented
27C3×#887C2211yescharacteristic, complemented
28#63974—21no—
29C2×#3722—21no—
30#63952—21no—
31#63952—21no—
32#63930C418yescomplemented
33C4×#627—21no—
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63874C2211yescharacteristic
37#63849C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic, complemented
39Dic3×Dic6C2211yescharacteristic, complemented
40#63838—21no—
41#63836—21no—
42#63836—21no—
43C2×#3717C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63636C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C2×D3×SD16—31no—
64#5572—31no—
65#5572—31no—
66#5545—31no—
67#5545—31no—
68C3×#440—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5026—31no—
73C4×#215—31no—
74#5018—31no—
75C4×#214—31no—
76#4889—31no—
77#4880—31no—
78#4860—31no—
79#4852—31no—
80#4817—31no—
81#4802—31no—
82#4802—31no—
83#4788—31no—
84#4770—31no—
85#4770—31no—
86#4770—61no—
87#4758D311yescharacteristic, complemented
88#4757D311yescharacteristic, complemented
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3C2×C414yes—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3797—22no—
109#3797C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3743—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214C2×C414yescomplemented
120C3×#214C2×C414yescomplemented
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724D411yescharacteristic
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139#3722D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3717C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#215—31no—
161C2×#215—31no—
162D4×Dic3C2×D311yescharacteristic
163D4×Dic3C2×D311yescharacteristic
164C2×#214C2×D311yescharacteristic
165C2×#214C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C2×(C2×D3)⋊C4—61no—
169C2×(C2×D3)⋊C4—61no—
170D3×SD16—38no—
171D3×SD16—38no—
172C2×#204—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—61no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#893—31no—
180#893—31no—
181#892—31no—
182#892—31no—
183#892—31no—
184#892—31no—
185#892—61no—
186#892—61no—
187#892—61no—
188#887—61no—
189#887—61no—
190#887C2×D311yescharacteristic, complemented
191#887C2×D311yescharacteristic, complemented
192#67⋊C4—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196C4×D12—31no—
197C4×D12—31no—
198#872—31no—
199#872—31no—
200#872—61no—
201#872—61no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#821—31no—
221#821—31no—
222#821—61no—
223#818—31no—
224#817—31no—
225#816C2×D311yescharacteristic, complemented
226#816C2×D311yescharacteristic, complemented
227#815—31no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic, complemented
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809—61no—
236#808—31no—
237#808C2×D311yescharacteristic, complemented
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240#803—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—24no—
245C22×C3⋊D3—81no—
246C22×C3⋊D3—81no—
247C22×C3⋊D3C2×D411yescharacteristic
248C32×D4—21no—
249C32×D4C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252#638—24no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×C412yes—
257C4×C3⋊D3C22×C412yes—
258C4×C3⋊D3#4112yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6C22×C412yes—
272C3×Dic6C22×C412yes—
273#627—24no—
274#624—24no—
275#624—81no—
276#624—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8C22×C412yes—
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—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—91no—
296C23×D3—61no—
297C23×D3—61no—
298C23×D3—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—21no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311D3×Q8—34no—
312D3×Q8—34no—
313D3×Q8—62no—
314D3×Q8—62no—
315D3×D4—34no—
316D3×D4—34no—
317D3×D4—64no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—122no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
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×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—34no—
338C3×SD16—34no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—31no—
355C3×C42—61no—
356C3×C42—61no—
357#217—21no—
358#217—21no—
359#215—34no—
360#215—34no—
361#214C4×D314yescomplemented
362#214C4×D314yescomplemented
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
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—121no—
402C4×Dic3C22×D311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—34no—
410#204—34no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—122no—
414D3×C8—34no—
415D3×C8—34no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—84no—
426C2×C3⋊D3C4×D412yes—
427C32×C4—41no—
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3C4×D412yes—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C22×Q8—91no—
441C22×D4—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×SD16—98no—
447C2×M16—91no—
448C22×C8—91no—
449C4×Q8—31no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×Q8—181no—
454C4×Q8—181no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461#117—91no—
462#117—91no—
463#117—91no—
464#117—181no—
465#117—181no—
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—91no—
470#106—31no—
471#106—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480#97—31no—
481#97—91no—
482C4×C8—31no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—41no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—64no—
491C22×D3—64no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—124no—
495C22×D3—121no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—242no—
501C22×D3—242no—
502C3×Q8—32no—
503C3×Q8—32no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—22no—
509C3×D4—41no—
510C3×D4C2×C4×D312yes—
511C3×D4C2×C4×D312yes—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—64no—
529#67—64no—
530#67—124no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—81no—
541C2×Dic3—81no—
542C2×Dic3—121no—
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—32no—
548D12—32no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—121no—
553C4×D3—32no—
554C4×D3—32no—
555C4×D3—32no—
556C4×D3—32no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—64no—
560C4×D3—64no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—21no—
567Dic6—64no—
568Dic6—64no—
569Dic6C2×C4×D312yes—
570Dic6C2×C4×D312yes—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—32no—
574C3×C8—32no—
575C3×C8—41no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8C2×C4×D312yes—
580C3⋊C8C2×C4×D312yes—
581C2×C32—42no—
582C2×C32C2×C4×D411yescharacteristic
583C2×C32#57711yescharacteristic
584C2×C32#57711yescharacteristic
585C3⋊D3—22no—
586C3⋊D3—42no—
587C24—181no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—94no—
591C2×Q8—181no—
592C2×Q8—182no—
593C2×D4—94no—
594C2×D4—91no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604SD16—34no—
605SD16—34no—
606SD16—94no—
607SD16—94no—
608M16—182no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—94no—
612C2×C8—91no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—31no—
633C42—31no—
634C42—61no—
635C42—61no—
636C42—181no—
637C42—181no—
638C42—181no—
639C42—181no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—42no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—32no—
653C2×D3—32no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—122no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—244no—
671C2×D3—244no—
672C2×D3—248no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C22×C4×D311yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4D3×#4111yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—22no—
695Dic3—22no—
696Dic3—32no—
697Dic3—32no—
698Dic3—41no—
699Dic3—41no—
700Dic3—62no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704C32#294911yescharacteristic, complemented, Sylow
705C23—21no—
706C23—91no—
707C23—184no—
708C23—181no—
709C23—721no—
710C23—721no—
711Q8—32no—
712Q8—32no—
713Q8—61no—
714Q8—61no—
715Q8—184no—
716D4—21no—
717D4—92no—
718D4—184no—
719D4—181no—
720D4C4×D3212yes—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—184no—
734C2×C4—181no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4—721no—
738C2×C4—721no—
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—32no—
742C8—32no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—42no—
749C2×C3—82no—
750C2×C3C4×D3×D411yescharacteristic
751C2×C3C4×D3×D411yescharacteristic
752C2×C3#576211yescharacteristic
753C2×C3#577011yescharacteristic
754C2×C3#577511yescharacteristic
755C2×C3#577811yescharacteristic
756D3—62no—
757D3—62no—
758D3—122no—
759D3—122no—
760D3—122no—
761D3—242no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—92no—
766C22—181no—
767C22—181no—
768C22—182no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—62no—
779C4—62no—
780C4—92no—
781C4—121no—
782C4—121no—
783C4—361no—
784C4C2×C4×D3211yescharacteristic
785C4#6431211yescharacteristic
786C3—21no—
787C3#7964911yescharacteristic, complemented
788C3#7977711yescharacteristic, complemented
789C2—42no—
790C2—182no—
791C2—362no—
792C2#1059425511yescharacteristic
793C2#1059473611yescharacteristic
794C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. #10594347C2semidirect
5. C3×#4758C2semidirect
6. C3×#4757C2semidirect
7. #10591440C2semidirect
8. Dic3×#214C2semidirect
9. #10590910C2semidirect
10. #10590795C2semidirect
11. #10590792C2semidirect
12. #10590691C2semidirect
13. #10590574C2semidirect
14. #10590458C2semidirect
15. #10590457C2semidirect
26. C3×#887C22semidirect
27. C3×#887C22semidirect
32. #63930C4semidirect
38. Dic3×Dic6C22semidirect
39. Dic3×Dic6C22semidirect
50. C3×#816C22semidirect
51. C3×#816C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63573C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
87. #4758D3semidirect
88. #4757D3semidirect
109. #3797C2×C4semidirect
119. C3×#214C2×C4semidirect
120. C3×#214C2×C4semidirect
143. #3717C2×C4semidirect
144. #3717C2×C4semidirect
145. #3710C2×C4semidirect
190. #887C2×D3semidirect
191. #887C2×D3semidirect
225. #816C2×D3semidirect
226. #816C2×D3semidirect
228. #815C2×D3semidirect
230. C8×Dic3C2×D3semidirect
237. #808C2×D3semidirect
239. #807C2×D3semidirect
361. #214C4×D3semidirect
362. #214C4×D3semidirect
704. C32#2949semidirect
787. C3#79649semidirect
788. C3#79777semidirect

Maximal subgroups

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

subgroupindex
#105952232
C2×#639302
#105943472
#105924692
C3×#47582
C3×#47572
#105914402
Dic3×#2142
#105909102
#105907952
#105907922
#105906912
#105905742
#105904582
#105904572
#797773
#796493