Finite Group Databasebeta

← #11887639

Subgroups — #11887639

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#626C211yesmaximal, characteristic
2#10594536C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4790C211yesmaximal, characteristic, complemented
6#10591603C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591546C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590855C211yesmaximal, characteristic, complemented
11#10590848C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic
13#10590561C211yesmaximal, characteristic, complemented
14#10590528C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#79735—31nomaximal
17#78806—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#887C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#626—21no—
29C4×#626—21no—
30C4×#626C2211yescharacteristic
31#63871—21no—
32#63871C2211yescharacteristic
33#63871C2211yescharacteristic
34#63867—21no—
35#63866—21no—
36#63866C2211yescharacteristic
37#63865—21no—
38#63857—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63851—21no—
42C2×#3719C2211yescharacteristic
43C2×#3718C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54#63576C2211yescharacteristic
55#63575C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61Q8×#67—31no—
62#5579—31no—
63Q8×D12—31no—
64#5511—31no—
65C3×C4×Q16—31no—
66C2×C3×#103—31no—
67#5228—31no—
68#5186—31no—
69#5186—31no—
70#5116—31no—
71C8×#67—31no—
72#5031—31no—
73#5021—31no—
74#4970—31no—
75#4884—31no—
76#4884—31no—
77#4813—31no—
78#4813—31no—
79#4813—31no—
80#4811—31no—
81#4809—31no—
82D3×#103—31no—
83D3×#103—31no—
84D3×#103—61no—
85D3×#103D311yescharacteristic, complemented
86#4795—31no—
87#4793—31no—
88#4792—31no—
89#4790D311yescharacteristic, complemented
90C8×D12—31no—
91#4681—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3—41no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×#626D411yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C8×C3⋊D3—41no—
116C3×#216—22no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×D3×C8—41no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3719—41no—
143#3718—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—61no—
149C2×D3×Q8C2×D311yescharacteristic
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—61no—
159Q8×Dic3C2×D311yescharacteristic
160#944—31no—
161#944—61no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216C2×D311yescharacteristic
166C4×#67—31no—
167C4×#67—61no—
168C4×#67—61no—
169#924—31no—
170#924—31no—
171#924—61no—
172#924—61no—
173C2×Dic12—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177C2×D3×C8C2×D311yescharacteristic
178#897—31no—
179#897—31no—
180#897—31no—
181#897—61no—
182#897—61no—
183#896—61no—
184#896—61no—
185#896—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#889—61no—
191#888—31no—
192#887C2×D311yescharacteristic
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196#870—61no—
197#869—31no—
198#869—31no—
199#869—61no—
200C3×#107—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic
214#830—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218#818—31no—
219#816—31no—
220#816—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#810—31no—
231#810—61no—
232#810C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807C2×D311yescharacteristic
237C4⋊(C3⋊C8)—31no—
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
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3—42no—
251C4×C3⋊D3—81no—
252#634—21no—
253#634—21no—
254#634—42no—
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—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#627—81no—
272#626Q1614yescomplemented
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—91no—
287#451—91no—
288C4×Q16—31no—
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—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—31no—
304D3×Q8—22no—
305D3×Q8—41no—
306D3×Q8—64no—
307D3×Q8—62no—
308D3×Q8—62no—
309D3×Q8—121no—
310D3×Q8—121no—
311D3×Q8—122no—
312C2×D12—31no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—121no—
323C2×C4×D3—121no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—121no—
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C42—31no—
352C3×C42—61no—
353C3×C42—61no—
354#217—31no—
355#217—61no—
356#217—61no—
357#216—22no—
358#216—121no—
359#216—121no—
360#216—121no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—21no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406D3×C8—41no—
407D3×C8—121no—
408D3×C8—121no—
409D3×C8—122no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3C2×Q1612yes—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3C2×Q1612yes—
417C32×C4—22no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3C2×Q1612yes—
431C22×Q8—31no—
432C22×Q8—91no—
433C2×Q16—31no—
434C2×Q16—91no—
435C2×Q16—91no—
436C22×C8—31no—
437C22×C8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—91no—
440C4⋊Q8—181no—
441#125—181no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C4×Q8—31no—
451C4×Q8—31no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—91no—
457#107—31no—
458#107—91no—
459#107—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103D3211yescharacteristic
471C22⋊C8—91no—
472C22⋊C8—91no—
473C4×C8—31no—
474C23×C3—31no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—61no—
478C22×D3D3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—122no—
488C3×Q8#23512yes—
489C3×Q8#23512yes—
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—62no—
532C4×D3—62no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—81no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—124no—
541C4×D3—241no—
542C4×D3—241no—
543C4×D3—242no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549Dic6—62no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557Dic6—124no—
558Dic6—241no—
559Dic6—241no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C2×C32#54611yescharacteristic
571C2×C32C22×Q1611yescharacteristic
572C2×C32#57711yescharacteristic
573C3⋊D3—22no—
574C3×D3—22no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—61no—
578C2×Q8—62no—
579C2×Q8—91no—
580C2×Q8—121no—
581C2×Q8—181no—
582C2×Q8—181no—
583C2×Q8—182no—
584C2×Q8—361no—
585C2×Q8C2×D3211yescharacteristic
586C2×D4—91no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—91no—
591C22×C4—181no—
592C22×C4—181no—
593Q16—62no—
594Q16—361no—
595Q16—361no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—121no—
600C2×C8—361no—
601C2×C8C2×D3211yescharacteristic
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—31no—
625C42—61no—
626C42—61no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C2×D3×D411yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—32no—
636C2×D3—32no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3D3×Q1612yes—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—32no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—81no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23511yescharacteristic
661C3×C4C2×#23511yescharacteristic
662C3×C4#100411yescharacteristic
663C3×C4#100911yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
673Dic3—122no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679Dic3D3×Q1612yes—
680C32#329911yescharacteristic, complemented, Sylow
681C23—31no—
682C23—91no—
683Q8—21no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—61no—
688Q8—122no—
689Q8—181no—
690Q8—181no—
691Q8—362no—
692Q8—721no—
693Q8#379812yes—
694D4—94no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—122no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—362no—
714C2×C4—721no—
715C2×C4C22×D3211yescharacteristic
716C8—21no—
717C8—61no—
718C8—61no—
719C8—181no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—62no—
724C2×C3#549011yescharacteristic
725C2×C3#555011yescharacteristic
726C2×C3#576211yescharacteristic
727C2×C3C2×D3×Q1611yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729C2×C3#577011yescharacteristic
730D3—22no—
731D3—64no—
732D3—62no—
733D3—62no—
734C22—32no—
735C22—61no—
736C22—61no—
737C22—92no—
738C22—181no—
739C22—181no—
740C22D32×D411yescharacteristic
741C4—22no—
742C4—32no—
743C4—41no—
744C4—61no—
745C4—61no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—181no—
751C4—361no—
752C4—361no—
753C4C2×#379811yescharacteristic
754C4#6431411yescharacteristic
755C3—21no—
756C3#7880611yescharacteristic, complemented
757C3#7973511yescharacteristic, complemented
758C2—62no—
759C2—182no—
760C2#1059418611yescharacteristic
761C2#1059475311yescharacteristic
762C2D32×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. C3⋊D3×#103C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4790C2semidirect
6. #10591603C2semidirect
7. #10591594C2semidirect
8. #10591546C2semidirect
9. #10590890C2semidirect
10. #10590855C2semidirect
11. #10590848C2semidirect
13. #10590561C2semidirect
14. #10590528C2semidirect
15. #10590427C2semidirect
85. D3×#103D3semidirect
89. #4790D3semidirect
272. #626Q16semidirect
680. C32#3299semidirect
756. C3#78806semidirect
757. C3#79735semidirect

Maximal subgroups

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

subgroupindex
Q8×#6262
#105945362
C3⋊D3×#1032
C3×D3×#1032
C3×#47902
#105916032
#105915942
#105915462
#105908902
#105908552
#105908482
C8×#6262
#105905612
#105905282
#105904272
#797353
#788063