Finite Group Databasebeta

← #11860598

Subgroups — #11860598

Order 1152.

1000 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595347C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic
3#10594327C211yesmaximal, characteristic
4#10592516C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6C3×#4789C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590795C211yesmaximal, characteristic, complemented
10#10590791C211yesmaximal, characteristic, complemented
11#10590693C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic
13#10590581C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#78774—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63948C418yescomplemented
29#63904—21no—
30C4×#626—21no—
31#63894C2211yescharacteristic
32#63883—21no—
33#63855—21no—
34#63855C2211yescharacteristic
35#63843—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
42#63836—21no—
43C2×#3718C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63648C2211yescharacteristic
48#63642C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63575C2211yescharacteristic
57#63574C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63553C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62#5812—31no—
63C2×#942—31no—
64C2×#918—31no—
65#5574—31no—
66#5572—31no—
67#5504—31no—
68C3×#441—31no—
69C2×C3×#103—31no—
70Dic3×Q16—31no—
71#5113—31no—
72#5101—31no—
73C4×#216—31no—
74C4×#215—31no—
75#4964—31no—
76#4861—31no—
77#4852—31no—
78#4817—31no—
79#4817—31no—
80#4817—31no—
81#4817—61no—
82#4804—31no—
83D3×#103D311yescharacteristic, complemented
84#4790—31no—
85#4790—31no—
86#4789—31no—
87#4789—31no—
88#4789D311yescharacteristic, complemented
89#4788—31no—
90#4788—31no—
91#4710—31no—
92#4708—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×D3×Q8—22no—
97C3×D3×Q8C2×C414yescomplemented
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107#3799—22no—
108#3799C2×C414yes—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3755C2×C414yescomplemented
112#3752—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216C2×C414yescomplemented
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—22no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3718C2×C414yescomplemented
144#3717C2×C414yescomplemented
145#3711C2×C414yescomplemented
146#2947—91noSylow
147C22×C3×Q8—31no—
148C2×#239—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C2×C3×C4⋊C4—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—61no—
162Q8×Dic3—61no—
163Q8×Dic3—61no—
164Q8×Dic3C2×D311yescharacteristic
165C2×#216—31no—
166C2×#216—31no—
167C2×#216C2×D311yescharacteristic
168#942—38no—
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C4×#67—61no—
174C4×#67—61no—
175#926—31no—
176#926—31no—
177#926—61no—
178#926—61no—
179C2×#208—31no—
180#918—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8C2×D311yescharacteristic
184#893—31no—
185#893—31no—
186#893—31no—
187#893—61no—
188#893—61no—
189#892—31no—
190#892—61no—
191#892—61no—
192D3×C4⋊C4—61no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4C2×D311yescharacteristic
195#887—31no—
196#887—31no—
197#887—61no—
198#887C2×D311yescharacteristic
199C4×D12—31no—
200C4×D12—61no—
201#872—31no—
202#872—61no—
203#872—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#97—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#818—31no—
222#816—31no—
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—61no—
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810C2×D311yescharacteristic
233#809—31no—
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241C4×C3⋊C8—31no—
242C22×C3⋊D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)C22×C412yes—
254C4×C3⋊D3—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—24no—
263C3×C4×D3—81no—
264C3×C4×D3C22×C412yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—24no—
269C3×Dic6C22×C412yes—
270C3×Dic6C22×C412yes—
271#626—24no—
272#624—24no—
273#624—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)C22×C412yes—
276C3×C3⋊C8—21no—
277C3×C3⋊C8C22×C412yes—
278C2×#137—91no—
279#520—91no—
280#519—91no—
281#441—31no—
282#441—91no—
283#440—91no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—31no—
292#405—91no—
293C2×C3×Q8—21no—
294C2×C3×Q8—34no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—61no—
305#239—34no—
306#239—62no—
307D3×Q8—22no—
308D3×Q8C4×D314yescomplemented
309#235—34no—
310#235—62no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×C4×D3—21no—
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—21no—
326C2×Dic6C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—34no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—62no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C42—31no—
344C3×C42—61no—
345C3×C42—61no—
346#217—31no—
347#217—31no—
348#217—61no—
349#216—34no—
350#216—34no—
351#216C4×D314yescomplemented
352#215—34no—
353#215—34no—
354#215—34no—
355#215—64no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—121no—
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—121no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
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—121no—
401C4×Dic3C22×D311yescharacteristic
402#208—34no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408#204—34no—
409ΓL(1,𝔽25)—34no—
410D3×C8—22no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C4×D412yes—
418C32×C4—22no—
419C32×C4—41no—
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C4×D412yes—
432C2×#41—91no—
433C22×Q8—31no—
434#137—98no—
435C2×Q16—31no—
436C2×Q16—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×M16—91no—
440C22×C8—31no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—91no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—91no—
454#117—91no—
455#117—181no—
456#117—181no—
457#117—181no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—181no—
460#107—91no—
461#107—91no—
462#106—31no—
463#106—91no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103D3211yescharacteristic
470#102—91no—
471#102—91no—
472#97—31no—
473#97—91no—
474C4×C8—91no—
475C4×C8—91no—
476C23×C3—31no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3D3×D411yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8C2×C4×D312yes—
491C3×Q8C2×C4×D312yes—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—64no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—241no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—64no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529D12—32no—
530D12—32no—
531D12—62no—
532D12—64no—
533D12—61no—
534D12—61no—
535D12—121no—
536C4×D3—24no—
537C4×D3—64no—
538C4×D3—64no—
539C4×D3—81no—
540C4×D3—241no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—242no—
545C4×D3C2×C4×D312yes—
546C4×D3#23712yes—
547Dic6—21no—
548Dic6—21no—
549Dic6—24no—
550Dic6C2×C4×D312yes—
551Dic6C2×C4×D312yes—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—32no—
555C3×C8—41no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—32no—
559C3⋊C8—32no—
560C3⋊C8—62no—
561C3⋊C8C2×C4×D312yes—
562C2×C32C2×C4×D411yescharacteristic
563C2×C32#57711yescharacteristic
564C2×C32#57811yescharacteristic
565C3⋊D3—42no—
566C3×D3—22no—
567#41—94no—
568#41—182no—
569C2×Q8—34no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—91no—
576C2×D4—181no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—94no—
585SD16—94no—
586SD16—94no—
587M16—94no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—62no—
591C2×C8—91no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42—91no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C42—181no—
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—122no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—241no—
636C2×D3—241no—
637C2×D3#67⋊C412yes—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—62no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—62no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C22×C4×D311yescharacteristic
654C3×C4C22×C4×D311yescharacteristic
655C3×C4C2×#23711yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—22no—
658Dic3—21no—
659Dic3—21no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3#67⋊C412yes—
673C32#294711yescharacteristic, complemented, Sylow
674C23—31no—
675C23—181no—
676Q8—21no—
677Q8—32no—
678Q8—32no—
679Q8—64no—
680Q8—61no—
681Q8—61no—
682Q8C4×D3212yes—
683D4—92no—
684D4—184no—
685D4—181no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—64no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—184no—
701C2×C4—181no—
702C2×C4—241no—
703C2×C4—721no—
704C2×C4—721no—
705C2×C4C22×D3211yescharacteristic
706C8—21no—
707C8—32no—
708C8—61no—
709C8—92no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—62no—
714C2×C3C2×#67⋊C411yescharacteristic
715C2×C3C4×D3×D411yescharacteristic
716C2×C3#576211yescharacteristic
717C2×C3#576611yescharacteristic
718C2×C3#577811yescharacteristic
719C2×C3#577911yescharacteristic
720D3—22no—
721D3—122no—
722D3—122no—
723D3—242no—
724C22—32no—
725C22—61no—
726C22—61no—
727C22—182no—
728C22—361no—
729C22—361no—
730C22D32×D411yescharacteristic
731C4—22no—
732C4—32no—
733C4—41no—
734C4—61no—
735C4—62no—
736C4—62no—
737C4—61no—
738C4—121no—
739C4—121no—
740C4—181no—
741C4—181no—
742C4—361no—
743C4C2×C4×D3211yescharacteristic
744C4D3×#23711yescharacteristic
745C3—21no—
746C3#7877411yescharacteristic, complemented
747C3#7983011yescharacteristic, complemented
748C2—62no—
749C2—362no—
750C2D3×#67⋊C411yescharacteristic
751C2#1059475111yescharacteristic
752C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595347C2semidirect
4. #10592516C2semidirect
5. C3×D3×#103C2semidirect
6. C3×#4789C2semidirect
7. #10591581C2semidirect
8. #10591536C2semidirect
9. #10590795C2semidirect
10. #10590791C2semidirect
11. #10590693C2semidirect
13. #10590581C2semidirect
14. #10590483C2semidirect
15. #10590476C2semidirect
28. #63948C4semidirect
83. D3×#103D3semidirect
88. #4789D3semidirect
97. C3×D3×Q8C2×C4semidirect
111. #3755C2×C4semidirect
118. C3×#216C2×C4semidirect
143. #3718C2×C4semidirect
144. #3717C2×C4semidirect
145. #3711C2×C4semidirect
308. D3×Q8C4×D3semidirect
351. #216C4×D3semidirect
673. C32#2947semidirect
746. C3#78774semidirect
747. C3#79830semidirect

Maximal subgroups

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

subgroupindex
#105953472
C2×#639482
#105943272
#105925162
C3×D3×#1032
C3×#47892
#105915812
#105915362
#105907952
#105907912
#105906932
#105906902
#105905812
#105904832
#105904762
#798303
#787743