Finite Group Databasebeta

← #11887657

Subgroups — #11887657

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595403C211yesmaximal, characteristic
2#10594536C211yesmaximal, characteristic
3#10592510C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4795C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591601C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10590950C211yesmaximal, characteristic, complemented
10#10590851C211yesmaximal, characteristic, complemented
11#10590804C211yesmaximal, characteristic, complemented
12#10590720C211yesmaximal, characteristic
13#10590601C211yesmaximal, characteristic, complemented
14#10590517C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#80491—31nomaximal
17#78806—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20#64155C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63918C2211yescharacteristic
29#63904—21no—
30C4×#626—21no—
31C4×#626C2211yescharacteristic
32#63888—21no—
33#63871C2211yescharacteristic
34#63867—21no—
35#63865—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63851—21no—
39#63851—21no—
40Dic3×Dic6C2211yescharacteristic
41#63839—21no—
42C2×#3718C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63647C2211yescharacteristic
47#63645C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63575C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Q8×#67—31no—
62#5727—31no—
63#5579—31no—
64#5511—31no—
65C3×#462—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5188—31no—
69#5188—31no—
70#5186—31no—
71#5186—31no—
72#5116—31no—
73C8×#67—31no—
74#5079—31no—
75C4×#216—31no—
76#4970—31no—
77#4850—31no—
78#4834—31no—
79#4813—31no—
80#4811—31no—
81#4811—31no—
82#4811—31no—
83#4811—61no—
84#4809—31no—
85D3×#103—31no—
86D3×#103—31no—
87D3×#103D311yescharacteristic, complemented
88#4795D311yescharacteristic, complemented
89#4793—31no—
90#4792—31no—
91#4790—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
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×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108#3797—22no—
109#3797—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—41no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3718—22no—
143#3710—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C4⋊Q8—31no—
153C3×C4×Q8—31no—
154C2×C3×C4⋊C4—31no—
155#946—31no—
156#946—31no—
157#946—31no—
158#946—31no—
159#946—31no—
160#946—61no—
161#946—61no—
162Q8×Dic3—31no—
163#944—61no—
164#944C2×D311yescharacteristic
165C2×#216—31no—
166C2×#216—31no—
167C2×#216C2×D311yescharacteristic
168C4×#67—31no—
169C4×#67—61no—
170C4×#67—61no—
171#924—31no—
172#924—31no—
173#924—61no—
174#924—61no—
175C2×Dic12C2×D311yescharacteristic
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8C2×D311yescharacteristic
179#897—31no—
180#896—61no—
181#896—61no—
182#896—61no—
183#896—61no—
184#896—61no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#889—61no—
191#888—31no—
192#888—61no—
193#887C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—61no—
196#870—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×C4⋊C8—31no—
200C3×#103—21no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic
206C3×#103C2×D311yescharacteristic
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#830—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818—31no—
221#818—31no—
222#818—31no—
223#818—61no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic
228Dic3⋊C8C2×D311yescharacteristic
229C8×Dic3—31no—
230#810—31no—
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
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—
250C4×C3⋊D3—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—42no—
261C3×C4×D3—81no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270#627—81no—
271#626Q1614yescomplemented
272#624—42no—
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—91no—
284#467—91no—
285#462—31no—
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—31no—
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×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—21no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—121no—
332C3×Q16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C42—31no—
348C3×C42—61no—
349#217—31no—
350#217—61no—
351#217—61no—
352#216—41no—
353#216—62no—
354#216—62no—
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—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—31no—
381Dic3⋊C4—61no—
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—
393Dic3⋊C4—121no—
394C4×Dic3—21no—
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—41no—
404D3×C8—41no—
405D3×C8—121no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—21no—
409C2×C3⋊D3—21no—
410C2×C3⋊D3C2×Q1612yes—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3C2×Q1612yes—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C22×C8—31no—
434C22×C8—91no—
435C4⋊Q8—31no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#125—181no—
439C22⋊Q8—91no—
440C22⋊Q8—91no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—91no—
454#107—91no—
455#107—91no—
456#107—91no—
457C4⋊C8—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103D3211yescharacteristic
468C22⋊C8—91no—
469C22⋊C8—91no—
470C4×C8—91no—
471C23×C3—31no—
472C22×D3—31no—
473C22×D3—31no—
474C22×D3—61no—
475C22×D3D3×D411yescharacteristic
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—122no—
506C2×C3×C4—241no—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—34no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526D12—34no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—42no—
530C4×D3—61no—
531C4×D3—61no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—81no—
535C4×D3—121no—
536C4×D3—121no—
537C4×D3—122no—
538C4×D3—122no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—242no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—42no—
548Dic6—122no—
549Dic6—122no—
550Dic6—241no—
551Dic6—241no—
552Dic6#23512yes—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32#54611yescharacteristic
564C2×C32C22×Q1611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—22no—
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—62no—
573C2×Q8—121no—
574C2×Q8—181no—
575C2×Q8—181no—
576C2×Q8—182no—
577C2×Q8—361no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—91no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—91no—
584C22×C4—181no—
585C22×C4—181no—
586Q16—121no—
587Q16—121no—
588Q16—182no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—121no—
593C2×C8—361no—
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
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—32no—
629C2×D3—32no—
630C2×D3—62no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3D3×Q1612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23511yescharacteristic
654C3×C4#100411yescharacteristic
655C3×C4#100411yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—22no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3D3×Q1612yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23—91no—
676Q8—21no—
677Q8—21no—
678Q8—32no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8—362no—
686Q8—721no—
687D4—94no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—91no—
700C2×C4—122no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—241no—
706C2×C4—362no—
707C2×C4—721no—
708C2×C4C22×D3211yescharacteristic
709C8—21no—
710C8—61no—
711C8—61no—
712C8—181no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—62no—
717C2×C3#549011yescharacteristic
718C2×C3#561211yescharacteristic
719C2×C3#576211yescharacteristic
720C2×C3C2×D3×Q1611yescharacteristic
721C2×C3C2×D3×Q1611yescharacteristic
722C2×C3#577811yescharacteristic
723D3—22no—
724D3—62no—
725D3—62no—
726D3—122no—
727C22—32no—
728C22—61no—
729C22—61no—
730C22—92no—
731C22—181no—
732C22—181no—
733C22D32×D411yescharacteristic
734C4—32no—
735C4—41no—
736C4—41no—
737C4—61no—
738C4—61no—
739C4—62no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—361no—
745C4—361no—
746C4D3×#23511yescharacteristic
747C4#6431311yescharacteristic
748C3—21no—
749C3#7880611yescharacteristic, complemented
750C3#8049111yescharacteristic, complemented
751C2—62no—
752C2—182no—
753C2#1059427811yescharacteristic
754C2#1059475111yescharacteristic
755C2D32×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. #10592510C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4795C2semidirect
6. #10591623C2semidirect
7. #10591601C2semidirect
8. #10591594C2semidirect
9. #10590950C2semidirect
10. #10590851C2semidirect
11. #10590804C2semidirect
13. #10590601C2semidirect
14. #10590517C2semidirect
15. #10590476C2semidirect
87. D3×#103D3semidirect
88. #4795D3semidirect
271. #626Q16semidirect
673. C32#3299semidirect
749. C3#78806semidirect
750. C3#80491semidirect

Maximal subgroups

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

subgroupindex
#105954032
#105945362
#105925102
C3×D3×#1032
C3×#47952
#105916232
#105916012
#105915942
#105909502
#105908512
#105908042
#105907202
#105906012
#105905172
#105904762
#804913
#788063