Finite Group Databasebeta

← #11887660

Subgroups — #11887660

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595403C211yesmaximal, characteristic
2#10594537C211yesmaximal, characteristic
3#10592512C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4792C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591575C211yesmaximal, characteristic, complemented
8#10591555C211yesmaximal, characteristic, complemented
9#10590848C211yesmaximal, characteristic, complemented
10#10590793C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic
12#10590672C211yesmaximal, characteristic, complemented
13#10590605C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590489C211yesmaximal, characteristic, complemented
16#81613—31nomaximal
17#78806—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20#64155C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic
28#63904—21no—
29#63904—21no—
30C4×#626C2211yescharacteristic
31#63900C2211yescharacteristic
32#63888—21no—
33#63888—21no—
34#63857C2211yescharacteristic
35#63856—21no—
36#63856C2211yescharacteristic
37#63851—21no—
38#63845—21no—
39#63844C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63839—21no—
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63643C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61Q8×#67—31no—
62#5730—31no—
63#5727—31no—
64#5511—31no—
65C3×#487—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5116—31no—
69C8×#67—31no—
70#5091—31no—
71#5090—31no—
72#4970—31no—
73#4813—31no—
74#4813—31no—
75#4813—31no—
76#4813—61no—
77#4811—31no—
78#4811—31no—
79#4811—31no—
80#4809—31no—
81#4809—31no—
82#4809—31no—
83D3×#103—31no—
84D3×#103—31no—
85D3×#103D311yescharacteristic, complemented
86#4795—31no—
87#4793—31no—
88#4792D311yescharacteristic, complemented
89#4790—31no—
90C4×Dic12—31no—
91C8×D12—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626D411yescharacteristic
106C2×#624—21no—
107C2×#624—21no—
108#3797—22no—
109#3797—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3719—22no—
143#3719—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×C4⋊Q8—31no—
152C2×C3×C4⋊C4—31no—
153#946—31no—
154#946—31no—
155#946—31no—
156#946—61no—
157#946—61no—
158#946—61no—
159#946—61no—
160Q8×Dic3—31no—
161#944—61no—
162#944C2×D311yescharacteristic
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—61no—
168C4×#67—31no—
169C4×#67—61no—
170C4×#67—61no—
171#924—31no—
172#924—31no—
173#924—61no—
174#924—61no—
175C2×Dic12—31no—
176C2×Dic12—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—61no—
180C2×D3×C8C2×D311yescharacteristic
181#897—31no—
182#897—31no—
183#897—31no—
184#897—61no—
185#896—61no—
186#896—61no—
187#896—61no—
188#893—61no—
189#893—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4C2×D311yescharacteristic
193#890—61no—
194#889—61no—
195#888—61no—
196#888C2×D311yescharacteristic
197#887—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×C4×C8—31no—
211#835—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219#818—31no—
220#818—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic
225#816C2×D311yescharacteristic
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250#634—21no—
251#634—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—42no—
267C3×Dic6—81no—
268C3×Dic6#4112yes—
269#627—42no—
270#626Q1614yescomplemented
271#624—42no—
272#624—81no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—31no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—31no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—31no—
305D3×Q8—22no—
306D3×Q8—41no—
307D3×Q8—62no—
308D3×Q8—62no—
309D3×Q8—121no—
310D3×Q8—121no—
311C2×D12—31no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—121no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C42—31no—
347#217—31no—
348#217—61no—
349#217—61no—
350#216—62no—
351#216—121no—
352#216—121no—
353#216—121no—
354#216—122no—
355(C2×D3)⋊C4—31no—
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—61no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4—121no—
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—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—62no—
404Dic12—121no—
405D3×C8—41no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—122no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3C2×Q1612yes—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C2×Q1612yes—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—22no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C2×Q1612yes—
430C22×Q8—31no—
431C22×Q8—91no—
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C22×C8—31no—
436C22×C8—91no—
437C4⋊Q8—31no—
438C4⋊Q8—31no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—91no—
456#107—91no—
457#107—91no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470C22⋊C8—91no—
471C22⋊C8—91no—
472C4×C8—31no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—32no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—241no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—122no—
507C2×C3×C4—241no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—34no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527D12—34no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—42no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—81no—
536C4×D3—121no—
537C4×D3—121no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—241no—
541C4×D3—241no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—81no—
551Dic6—121no—
552Dic6—121no—
553Dic6—122no—
554Dic6—122no—
555Dic6#23512yes—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—62no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C2×C32#54611yescharacteristic
567C2×C32C22×Q1611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—22no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—91no—
577C2×Q8—121no—
578C2×Q8—181no—
579C2×Q8—182no—
580C2×Q8—361no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—91no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—182no—
590Q16—361no—
591Q16—361no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—121no—
596C2×C8—361no—
597C2×C8C2×D3211yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—32no—
632C2×D3—32no—
633C2×D3—62no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3D3×Q1612yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—32no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—62no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23511yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4#100911yescharacteristic
660Dic3—22no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—61no—
667Dic3—61no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3—241no—
675Dic3D3×Q1612yes—
676C32#329911yescharacteristic, complemented, Sylow
677C23—31no—
678C23—91no—
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—122no—
686Q8—181no—
687Q8—181no—
688Q8—241no—
689Q8—362no—
690D4—94no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—91no—
703C2×C4—122no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—241no—
709C2×C4—362no—
710C2×C4—721no—
711C2×C4C22×D3211yescharacteristic
712C8—21no—
713C8—61no—
714C8—61no—
715C8—181no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—62no—
720C2×C3#549011yescharacteristic
721C2×C3#567611yescharacteristic
722C2×C3#576211yescharacteristic
723C2×C3#576211yescharacteristic
724C2×C3C2×D3×Q1611yescharacteristic
725C2×C3C2×D3×Q1611yescharacteristic
726D3—22no—
727D3—62no—
728D3—62no—
729D3—122no—
730C22—32no—
731C22—61no—
732C22—61no—
733C22—92no—
734C22—181no—
735C22—181no—
736C22D32×D411yescharacteristic
737C4—32no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—62no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—181no—
747C4—361no—
748C4—361no—
749C4D3×#23511yescharacteristic
750C4#6431411yescharacteristic
751C3—21no—
752C3#7880611yescharacteristic, complemented
753C3#8161311yescharacteristic, complemented
754C2—62no—
755C2—182no—
756C2#1059428011yescharacteristic
757C2#1059474811yescharacteristic
758C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenter#103D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #10592512C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4792C2semidirect
6. #10591595C2semidirect
7. #10591575C2semidirect
8. #10591555C2semidirect
9. #10590848C2semidirect
10. #10590793C2semidirect
12. #10590672C2semidirect
13. #10590605C2semidirect
14. #10590517C2semidirect
15. #10590489C2semidirect
85. D3×#103D3semidirect
88. #4792D3semidirect
270. #626Q16semidirect
676. C32#3299semidirect
752. C3#78806semidirect
753. C3#81613semidirect

Maximal subgroups

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

subgroupindex
#105954032
#105945372
#105925122
C3×D3×#1032
C3×#47922
#105915952
#105915752
#105915552
#105908482
#105907932
C8×#6262
#105906722
#105906052
#105905172
#105904892
#816133
#788063