Finite Group Databasebeta

← #11887633

Subgroups — #11887633

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#625C211yesmaximal, characteristic
2#10594532C211yesmaximal, characteristic
3#10592492C211yesmaximal, characteristic, complemented
4C3×#4809C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590851C211yesmaximal, characteristic, complemented
10#10590798C211yesmaximal, characteristic, complemented
11#10590717C211yesmaximal, characteristic
12#10590682C211yesmaximal, characteristic, complemented
13#10590567C211yesmaximal, characteristic, complemented
14#10590518C211yesmaximal, characteristic, complemented
15#10590517C211yesmaximal, characteristic, complemented
16#80193—31nomaximal
17#78806—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64097C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C4×#625—21no—
28C4×#625C2211yescharacteristic
29#63896—21no—
30D3×C4⋊Dic3C2211yescharacteristic
31#63879—21no—
32#63873—21no—
33#63873C2211yescharacteristic
34#63857—21no—
35#63856—21no—
36#63856—21no—
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic
40#63847—21no—
41#63843C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63645C2211yescharacteristic
47#63641C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54#63575C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63#5635—31no—
64#5511—31no—
65C3×#451—31no—
66C2×C3×#103—31no—
67#5228—31no—
68C2×#835—31no—
69#5188—31no—
70#5186—31no—
71#5182—31no—
72Dic3×Q16—31no—
73#5116—31no—
74C8×#67—31no—
75#5051—31no—
76#4970—31no—
77#4813—31no—
78#4811—31no—
79#4811—31no—
80#4809D311yescharacteristic, complemented
81D3×#103—31no—
82D3×#103D311yescharacteristic, complemented
83#4795—31no—
84#4793—31no—
85#4793—31no—
86#4793—61no—
87#4792—31no—
88#4792—31no—
89#4790—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C3×D3×Q8—41no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#625D411yescharacteristic
109C2×D3×Dic3—21no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×Dic12—41no—
127C3×D3×C8—41no—
128#3724—21no—
129#3724—21no—
130#3724—21no—
131#3724—21no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×D3×Q8C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#946—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158#946—61no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163#944—31no—
164#944—31no—
165#944—61no—
166#944—61no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216C2×D311yescharacteristic
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C4×#67—61no—
174C4×#67—61no—
175C2×C4⋊Dic3—31no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180#924—61no—
181#924—61no—
182C22×C3⋊C8—31no—
183C2×Dic12C2×D311yescharacteristic
184C2×D3×C8—31no—
185C2×D3×C8C2×D311yescharacteristic
186#897—61no—
187#897C2×D311yescharacteristic
188#896—61no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191#889—61no—
192#889—61no—
193#888—31no—
194#888—31no—
195#888—61no—
196#887—31no—
197#67⋊C4—61no—
198#878—61no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103C2×D311yescharacteristic
205C3×#103C2×D311yescharacteristic
206C3×C22⋊C8—31no—
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)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818—31no—
220#818—31no—
221#818—61no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816C2×D311yescharacteristic
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—61no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810C2×D311yescharacteristic
233#810C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236#807—31no—
237#807—61no—
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249#634—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—42no—
261C3×C4×D3—42no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271#625Q1614yescomplemented
272D3×Dic3—81no—
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—91no—
286#451—31no—
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—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8—121no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—31no—
310C2×#67—31no—
311C22×Dic3—61no—
312D3×Q8—22no—
313D3×Q8—22no—
314D3×Q8—41no—
315D3×Q8—41no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—61no—
320C2×C4×D3C22×D311yescharacteristic
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—21no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—121no—
327C2×Dic6C22×D311yescharacteristic
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×Q16—62no—
331C3×Q16—121no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—61no—
345#217—31no—
346#217—31no—
347#217—61no—
348#217—61no—
349#217—61no—
350#216—22no—
351#216—121no—
352#216—121no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359C4⋊Dic3—21no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—121no—
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
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—121no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—41no—
405D3×C8—41no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3C2×Q1612yes—
413C2×C3×D3C2×Q1612yes—
414C32×C4—22no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3⋊Dic3C2×Q1612yes—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C22×C8—31no—
434C22×C8—91no—
435C4⋊Q8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#125—181no—
439C22⋊Q8—31no—
440C22⋊Q8—91no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—91no—
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—91no—
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—31no—
469C22⋊C8—91no—
470C4×C8—91no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3D3×D411yescharacteristic
474C22×D3D3×D411yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×Q8—122no—
487C3×Q8#23512yes—
488C3×Q8#23712yes—
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—41no—
497C2×C3×C4—41no—
498C2×C3×C4—61no—
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—61no—
506C2×C3×C4—122no—
507C2×C3×C4—122no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—34no—
512#67—34no—
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—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—42no—
537C4×D3—42no—
538C4×D3—81no—
539C4×D3—241no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—42no—
547Dic6—42no—
548Dic6—241no—
549Dic6—241no—
550Dic6—242no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C2×C32#54611yescharacteristic
562C2×C32C22×Q1611yescharacteristic
563C2×C32#57711yescharacteristic
564C3×D3—22no—
565C3×D3—22no—
566C2×Q8—31no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—61no—
570C2×Q8—61no—
571C2×Q8—62no—
572C2×Q8—62no—
573C2×Q8—121no—
574C2×Q8—121no—
575C2×Q8—181no—
576C2×Q8C2×D3211yescharacteristic
577C2×D4—91no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584Q16—62no—
585Q16—121no—
586Q16—361no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—91no—
590C2×C8—121no—
591C2×C8—361no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4C2×D3211yescharacteristic
609C22⋊C4—61no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—91no—
616C42—181no—
617C42—181no—
618C22×C3—21no—
619C22×C3—32no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3C2×D3×D411yescharacteristic
626C22×C3C2×D3×D411yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3D3×Q1612yes—
632C2×D3D3×Q1612yes—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—42no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—81no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4C2×#23511yescharacteristic
648C3×C4C2×#23711yescharacteristic
649C3×C4#100411yescharacteristic
650C3×C4#100411yescharacteristic
651Dic3—21no—
652Dic3—21no—
653Dic3—32no—
654Dic3—32no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—62no—
660Dic3—61no—
661Dic3—61no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668Dic3—241no—
669C32#329911yescharacteristic, complemented, Sylow
670C23—31no—
671C23—31no—
672Q8—21no—
673Q8—61no—
674Q8—61no—
675Q8—61no—
676Q8—61no—
677Q8—61no—
678Q8—61no—
679Q8—122no—
680Q8—122no—
681Q8—721no—
682Q8#379512yes—
683D4—94no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—241no—
703C2×C4—721no—
704C2×C4C22×D3211yescharacteristic
705C8—21no—
706C8—61no—
707C8—61no—
708C8—181no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—62no—
713C2×C3—62no—
714C2×C3#549011yescharacteristic
715C2×C3#559111yescharacteristic
716C2×C3#576211yescharacteristic
717C2×C3C2×D3×Q1611yescharacteristic
718C2×C3C2×D3×Q1611yescharacteristic
719C2×C3#577811yescharacteristic
720D3—22no—
721D3—22no—
722C22—32no—
723C22—32no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22D32×D411yescharacteristic
729C4—22no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—92no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—181no—
739C4—361no—
740C4—361no—
741C4C2×#379511yescharacteristic
742C4#6431311yescharacteristic
743C3—21no—
744C3#7880611yescharacteristic, complemented
745C3#8019311yescharacteristic, complemented
746C2—62no—
747C2—62no—
748C2#1059418411yescharacteristic
749C2#1059475111yescharacteristic
750C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#625D4
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. #10592492C2semidirect
4. C3×#4809C2semidirect
5. C3×D3×#103C2semidirect
6. #10591594C2semidirect
7. #10591581C2semidirect
8. D3×#835C2semidirect
9. #10590851C2semidirect
10. #10590798C2semidirect
12. #10590682C2semidirect
13. #10590567C2semidirect
14. #10590518C2semidirect
15. #10590517C2semidirect
80. #4809D3semidirect
82. D3×#103D3semidirect
271. #625Q16semidirect
669. C32#3299semidirect
744. C3#78806semidirect
745. C3#80193semidirect

Maximal subgroups

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

subgroupindex
Q8×#6252
#105945322
#105924922
C3×#48092
C3×D3×#1032
#105915942
#105915812
D3×#8352
#105908512
#105907982
#105907172
#105906822
#105905672
#105905182
#105905172
#801933
#788063