Finite Group Databasebeta

← #11887655

Subgroups — #11887655

Order 1152.

830 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#10595407C211yesmaximal, characteristic
2#10595400C211yesmaximal, characteristic
3#10592881C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10591551C211yesmaximal, characteristic, complemented
10D3×#835C211yesmaximal, characteristic, complemented
11#10591538C211yesmaximal, characteristic, complemented
12#10590817C211yesmaximal, characteristic, complemented
13#10590717C211yesmaximal, characteristic
14#10590684C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#80193—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64153C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63919C2211yescharacteristic
30#63902—21no—
31C4×#625C2211yescharacteristic
32#63893—21no—
33#63893—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63887—21no—
37#63879—21no—
38#63870—21no—
39#63857C2211yescharacteristic
40#63851—21no—
41#63843C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63643C2211yescharacteristic
46#63641C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62#5635—31no—
63#5635—31no—
64#5632—31no—
65C3×#467—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5188D311yescharacteristic, complemented
69#5186—31no—
70#5186D311yescharacteristic, complemented
71#5182—31no—
72#5182—31no—
73#5182—61no—
74Dic3×Q16—31no—
75C8×#67—31no—
76C2×#816—31no—
77#5051—31no—
78#5050—31no—
79#5044—31no—
80#4884—31no—
81#4875—31no—
82#4813—31no—
83#4811—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4793—31no—
87#4792—31no—
88#4792—31no—
89#4790—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#627—21no—
104C2×#625D411yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112#3756—41no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#216—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6—31no—
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C2×D311yescharacteristic
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157#946—61no—
158#946C2×D311yescharacteristic
159#946C2×D311yescharacteristic
160#946C2×D311yescharacteristic
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—61no—
165#944—31no—
166#944—31no—
167#944—61no—
168#944—61no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173C4×#67—31no—
174C4×#67—31no—
175C4×#67—61no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—61no—
180C22×C3⋊C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8C2×D311yescharacteristic
183#897—31no—
184#897—61no—
185#897—61no—
186#896—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189#889—61no—
190#889—61no—
191#888—31no—
192#888—31no—
193#888—61no—
194#887—31no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#878—61no—
199#878—61no—
200#878—61no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266C3×Dic6#4112yes—
267#627—42no—
268#627—81no—
269#625Q1614yescomplemented
270D3×Dic3—42no—
271D3×Dic3—81no—
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—31no—
284#467—91no—
285#462—91no—
286#451—31no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—31no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310D3×Q8—22no—
311D3×Q8—41no—
312D3×Q8—62no—
313D3×Q8—121no—
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3C22×D311yescharacteristic
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—62no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—121no—
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—41no—
332C3×Q16—41no—
333C3×Q16—42no—
334C3×Q16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—31no—
351#217—31no—
352#217—61no—
353#216—22no—
354#216—121no—
355#216—121no—
356#216—122no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—61no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—121no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—31no—
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—121no—
392Dic3⋊C4—121no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D3×C8—41no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3C2×Q1612yes—
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⋊Dic3C2×Q1612yes—
424C3×Dic3—22no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C22×Q8—91no—
432C2×Q16—31no—
433C2×Q16—91no—
434C2×Q16D3211yescharacteristic
435C22×C8—31no—
436C22×C8—91no—
437C4⋊Q8—91no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
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—91no—
455C2×C4⋊C4—91no—
456#107—31no—
457#107—91no—
458#107—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470C22⋊C8—31no—
471C22⋊C8—91no—
472C4×C8—91no—
473C23×C3—31no—
474C23×C3—31no—
475C22×D3D3×D411yescharacteristic
476C22×D3D3×D411yescharacteristic
477C3×Q8—22no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—32no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—122no—
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—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—34no—
513#67—34no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—122no—
541C4×D3—241no—
542C4×D3—241no—
543Dic6—21no—
544Dic6—42no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23712yes—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32#54611yescharacteristic
567C2×C32C22×Q1611yescharacteristic
568C2×C32#57711yescharacteristic
569C3×D3—22no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8—91no—
575C2×Q8—121no—
576C2×Q8—181no—
577C2×Q8—181no—
578C2×Q8—182no—
579C2×Q8—361no—
580C2×Q8C2×D3211yescharacteristic
581C2×Q8C2×D3211yescharacteristic
582C2×D4—91no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—41no—
590Q16—62no—
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—31no—
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⋊C4—181no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—181no—
620C42—91no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—32no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3D3×Q1612yes—
637C2×D3D3×Q1612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—42no—
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—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23711yescharacteristic
653C3×C4#100411yescharacteristic
654C3×C4#100411yescharacteristic
655C3×C4D3×#4111yescharacteristic
656Dic3—22no—
657Dic3—21no—
658Dic3—21no—
659Dic3—32no—
660Dic3—32no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—62no—
665Dic3—61no—
666Dic3—61no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—241no—
673Dic3—241no—
674C32#329911yescharacteristic, complemented, Sylow
675C23—31no—
676C23—31no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—32no—
682Q8—61no—
683Q8—122no—
684Q8—181no—
685Q8—181no—
686Q8—362no—
687Q8—721no—
688D4—94no—
689C2×C4—21no—
690C2×C4—21no—
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—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—122no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—362no—
707C2×C4—721no—
708C2×C4—721no—
709C2×C4C22×D3211yescharacteristic
710C8—21no—
711C8—61no—
712C8—61no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—62no—
718C2×C3—62no—
719C2×C3#559111yescharacteristic
720C2×C3#561011yescharacteristic
721C2×C3C2×D3×Q1611yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3#577011yescharacteristic
724C2×C3#577811yescharacteristic
725D3—22no—
726D3—22no—
727C22—32no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22D32×D411yescharacteristic
734C4—41no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—62no—
739C4—92no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—361no—
745C4—361no—
746C4D3×#23711yescharacteristic
747C4#6433011yescharacteristic
748C3—21no—
749C3#8019311yescharacteristic, complemented
750C3#8078111yescharacteristic, complemented
751C2—62no—
752C2—62no—
753C2D32×Q1611yescharacteristic
754C2#1059477011yescharacteristic
755C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#625D4
hypercenterC2×Q16D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10592881C2semidirect
4. C3×#5188C2semidirect
5. C3×#5186C2semidirect
6. #10591653C2semidirect
7. #10591596C2semidirect
8. #10591581C2semidirect
9. #10591551C2semidirect
10. D3×#835C2semidirect
11. #10591538C2semidirect
12. #10590817C2semidirect
14. #10590684C2semidirect
15. D3×#816C2semidirect
68. #5188D3semidirect
70. #5186D3semidirect
269. #625Q16semidirect
674. C32#3299semidirect
749. C3#80193semidirect
750. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105954072
#105954002
#105928812
C3×#51882
C3×#51862
#105916532
#105915962
#105915812
#105915512
D3×#8352
#105915382
#105908172
#105907172
#105906842
D3×#8162
#807813
#801933