Finite Group Databasebeta

← #11860549

Subgroups — #11860549

Order 1152.

1078 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595222C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic
3#10594604C211yesmaximal, characteristic, complemented
4#10592484C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6C3×#4772C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590795C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12#10590693C211yesmaximal, characteristic, complemented
13#10590483C211yesmaximal, characteristic, complemented
14#10590475C211yesmaximal, characteristic, complemented
15#10590437C211yesmaximal, characteristic, complemented
16#79866—31nomaximal
17#78820—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic, complemented
21C2×#3753C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic, complemented
24C2×C3×#213C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30C2×Dic3⋊Dic3—21no—
31#63955—21no—
32#63925C418yescomplemented
33#63921—21no—
34D3×(C2×D3)⋊C4—21no—
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63880—21no—
40#63855C2211yescharacteristic
41#63843C2211yescharacteristic, complemented
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#102C2211yescharacteristic, complemented
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic, complemented
49#63635C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#808C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62#5827—31no—
63C2×#949—31no—
64C2×#911—31no—
65#5546—31no—
66#5545—31no—
67#5521—31no—
68C3×#442—31no—
69C3×#416—31no—
70Dic3×D8—31no—
71C2×#821—31no—
72#5101—31no—
73C4×#214—31no—
74C4×#213—31no—
75#4995—31no—
76#4861—31no—
77#4852—31no—
78#4817—31no—
79#4817—31no—
80#4788—31no—
81#4788—31no—
82#4785—31no—
83#4785—31no—
84#4785—61no—
85#4785D311yescharacteristic, complemented
86#4772D311yescharacteristic, complemented
87D3×#102—31no—
88#4757—31no—
89#4756—31no—
90#4756—31no—
91#4710—31no—
92#4708—31no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237C2×C414yescomplemented
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3753C2×C414yescomplemented
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#213C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—22no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3717C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3711C2×C414yescomplemented
146#2946—91noSylow
147C2×C3×#41—31no—
148C2×#237C2×D311yescharacteristic
149C2×D3×D4—31no—
150C22×D12—31no—
151C2×C3×D8—31no—
152C22×C3×C8—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×#117—31no—
156#949—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159C2×#215—31no—
160C2×#215—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3C2×D311yescharacteristic, complemented
168C2×#214—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173C4×#67—61no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#926—61no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×Dic3⋊C4—61no—
181C2×#208—31no—
182#911—38no—
183C2×#204—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×D3×C8C2×D311yescharacteristic
186#893—31no—
187#893—31no—
188#893—31no—
189#893—31no—
190#893—61no—
191#893C2×D311yescharacteristic
192#892C2×D311yescharacteristic
193D3×C4⋊C4—31no—
194#887—31no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197D3×C22⋊C4—61no—
198D3×C22⋊C4—61no—
199D3×C22⋊C4—61no—
200#877—61no—
201C4×D12—31no—
202C4×D12—61no—
203C4×D12—61no—
204#872—31no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic, complemented
213C3×#102C2×D311yescharacteristic, complemented
214C3×#97—31no—
215#832—31no—
216#832C2×D311yescharacteristic, complemented
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223#818—31no—
224#816C2×D311yescharacteristic, complemented
225#815—31no—
226#815—31no—
227#815—61no—
228#815C2×D311yescharacteristic, complemented
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810C2×D311yescharacteristic, complemented
233#809—31no—
234#808—31no—
235#808—31no—
236#808—61no—
237#808C2×D311yescharacteristic, complemented
238#807—31no—
239#807—31no—
240#807—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—81no—
248C2×D32—81no—
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)C22×C412yes—
259C4×C3⋊D3—81no—
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—24no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×C4×D3—81no—
272C3×C4×D3C22×C412yes—
273C3×C4×D3#4112yes—
274C3×Dic6—21no—
275C3×Dic6C22×C412yes—
276#626—24no—
277#624—81no—
278D3×Dic3—81no—
279D3×Dic3—81no—
280C32×C8—21no—
281C3⋊(C3⋊C8)C22×C412yes—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—91no—
285#520—91no—
286#518—91no—
287#442—31no—
288#442—91no—
289#440—91no—
290#440—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—91no—
296#416—31no—
297C2×#102—91no—
298#405—91no—
299C23×D3—61no—
300C23×D3—61no—
301C3×#41—34no—
302C3×#41—62no—
303C2×C3×Q8—31no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—61no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322#237—22no—
323#237C4×D314yescomplemented
324D3×D4—34no—
325D3×D4—62no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—34no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×D8—34no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—62no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
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×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—61no—
360#217—21no—
361#217—31no—
362#217—31no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#215—34no—
368#215—34no—
369#214—34no—
370#213—34no—
371#213—34no—
372#213—64no—
373#213C4×D314yescomplemented
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
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—121no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—21no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408#208—34no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—34no—
415ΓL(1,𝔽25)—34no—
416D3×C8—22no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3C4×D412yes—
430D32—84no—
431C32×C4—41no—
432C32×C4C23×C411yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—31no—
444C22×D4—91no—
445AGL(1,ℤ/8)—98no—
446C2×SD16—91no—
447C2×SD16—91no—
448C2×D8—31no—
449C2×D8—91no—
450C2×M16—91no—
451C22×C8—31no—
452C4×Q8—91no—
453C4×Q8—91no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464#117—31no—
465#117—91no—
466#117—181no—
467C2×C4⋊C4—91no—
468C2×C4⋊C4—181no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—91no—
472#107—91no—
473#106—31no—
474#106—91no—
475#103—31no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102D3211yescharacteristic, complemented
483#97—31no—
484#97—91no—
485C4×C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—61no—
492C22×D3—21no—
493C22×D3—64no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—64no—
497C22×D3—121no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3D3×D411yescharacteristic
503C3×Q8—32no—
504C3×Q8—61no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—64no—
511C3×D4—61no—
512C3×D4C2×C4×D312yes—
513C3×D4C2×C4×D312yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—64no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—241no—
528C2×C3×C4—241no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—24no—
532#67—64no—
533C2×Dic3—21no—
534C2×Dic3—24no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—81no—
546C2×Dic3—121no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—241no—
551C2×Dic3—242no—
552C2×Dic3D3×D411yescharacteristic
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555D12—21no—
556D12—32no—
557D12—32no—
558D12—62no—
559D12—64no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12C2×C4×D312yes—
564C4×D3—81no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—242no—
571C4×D3—241no—
572C4×D3C2×C4×D312yes—
573C4×D3#23712yes—
574Dic6—21no—
575Dic6C2×C4×D312yes—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—32no—
579C3×C8—41no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—32no—
583C3⋊C8—32no—
584C3⋊C8—62no—
585C3⋊C8C2×C4×D312yes—
586C2×C32—42no—
587C2×C32C2×C4×D411yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57711yescharacteristic
590C3⋊D3—42no—
591C3×D3—22no—
592C3×D3—42no—
593C24—181no—
594#41—34no—
595#41—62no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—94no—
600C2×D4—91no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613SD16—94no—
614SD16—94no—
615D8—34no—
616D8—94no—
617M16—94no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—62no—
621C2×C8—91no—
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—91no—
644C42—181no—
645C42—181no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—122no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C2×D3#67⋊C412yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—32no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—62no—
689C3×C4—81no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C22×C4×D311yescharacteristic
693C3×C4C22×C4×D311yescharacteristic
694C3×C4C2×#23711yescharacteristic
695C3×C4D3×#4111yescharacteristic
696Dic3—22no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3#67⋊C412yes—
711C32#294611yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—61no—
715C23—184no—
716C23—181no—
717C23—721no—
718C23—721no—
719Q8—32no—
720Q8—61no—
721D4—21no—
722D4—32no—
723D4—64no—
724D4—61no—
725D4—92no—
726D4—184no—
727D4—181no—
728D4C4×D3212yes—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—64no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—91no—
740C2×C4—91no—
741C2×C4—181no—
742C2×C4—241no—
743C2×C4—241no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4—721no—
747C2×C4—721no—
748C2×C4—721no—
749C2×C4C22×D3211yescharacteristic
750C8—21no—
751C8—32no—
752C8—61no—
753C8—92no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—42no—
759C2×C3—62no—
760C2×C3—82no—
761C2×C3—122no—
762C2×C3C2×#67⋊C411yescharacteristic
763C2×C3C4×D3×D411yescharacteristic
764C2×C3#576911yescharacteristic
765C2×C3#577011yescharacteristic
766C2×C3#577411yescharacteristic
767C2×C3#577511yescharacteristic
768D3—22no—
769D3—42no—
770D3—122no—
771D3—122no—
772D3—242no—
773C22—22no—
774C22—32no—
775C22—41no—
776C22—41no—
777C22—61no—
778C22—61no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—182no—
783C22—361no—
784C22—361no—
785C22—724no—
786C22D32×D411yescharacteristic
787C4—32no—
788C4—41no—
789C4—61no—
790C4—61no—
791C4—62no—
792C4—121no—
793C4—121no—
794C4—181no—
795C4—181no—
796C4—361no—
797C4C2×C4×D3211yescharacteristic
798C4D3×#23711yescharacteristic
799C3—21no—
800C3#7882011yescharacteristic, complemented
801C3#7986611yescharacteristic, complemented
802C2—42no—
803C2—62no—
804C2—122no—
805C2—362no—
806C2D3×#67⋊C411yescharacteristic
807C2#1059473611yescharacteristic
808C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63925C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2946
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
1. #10595222C2semidirect
3. #10594604C2semidirect
4. #10592484C2semidirect
5. C3×#4785C2semidirect
6. C3×#4772C2semidirect
7. #10591435C2semidirect
8. #10591400C2semidirect
9. D3×#821C2semidirect
10. #10590795C2semidirect
11. #10590743C2semidirect
12. #10590693C2semidirect
13. #10590483C2semidirect
14. #10590475C2semidirect
15. #10590437C2semidirect
20. D4×C3⋊Dic3C22semidirect
23. C3×D4×Dic3C22semidirect
32. #63925C4semidirect
41. #63843C22semidirect
42. Dic3×Dic6C22semidirect
46. C32×#102C22semidirect
48. #63642C22semidirect
49. #63635C22semidirect
50. C3×#832C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×#810C22semidirect
55. C3×#808C22semidirect
56. #63576C22semidirect
57. #63575C22semidirect
60. #63553C22semidirect
61. Dic3×C3⋊C8C22semidirect
85. #4785D3semidirect
86. #4772D3semidirect
102. C3×#237C2×C4semidirect
112. D3×D12C2×C4semidirect
116. #3753C2×C4semidirect
122. C3×#213C2×C4semidirect
143. #3717C2×C4semidirect
144. #3715C2×C4semidirect
145. #3711C2×C4semidirect
167. D4×Dic3C2×D3semidirect
212. C3×#102C2×D3semidirect
213. C3×#102C2×D3semidirect
216. #832C2×D3semidirect
224. #816C2×D3semidirect
228. #815C2×D3semidirect
232. #810C2×D3semidirect
237. #808C2×D3semidirect
323. #237C4×D3semidirect
373. #213C4×D3semidirect
482. #102D32semidirect
711. C32#2946semidirect
800. C3#78820semidirect
801. C3#79866semidirect

Maximal subgroups

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

subgroupindex
#105952222
C2×#639252
#105946042
#105924842
C3×#47852
C3×#47722
#105914352
#105914002
D3×#8212
#105907952
#105907432
#105906932
#105904832
#105904752
#105904372
#798663
#788203