Finite Group Databasebeta

← #11887654

Subgroups — #11887654

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#10595371C211yesmaximal, characteristic
3#10592887C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591654C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591623C211yesmaximal, characteristic, complemented
9Dic3×#216C211yesmaximal, characteristic, complemented
10#10591555C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10590906C211yesmaximal, characteristic
13#10590804C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15#10590672C211yesmaximal, characteristic, complemented
16#80491—31nomaximal
17#80193—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21#64155C2211yescharacteristic
22#64155C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29#63918C2211yescharacteristic
30#63904—21no—
31C4×#626C2211yescharacteristic
32#63900C2211yescharacteristic
33#63899—21no—
34#63895—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63888—21no—
37#63880—21no—
38#63867—21no—
39#63856C2211yescharacteristic
40#63851—21no—
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63645C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Q8×#67—31no—
62#5727—31no—
63#5635—31no—
64#5579—31no—
65C3×#462—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5188—31no—
69#5188—31no—
70#5188—31no—
71#5188—61no—
72#5186—31no—
73#5186—31no—
74#5186D311yescharacteristic, complemented
75#5182D311yescharacteristic, complemented
76Dic3×Q16—31no—
77#5079—31no—
78#5051—31no—
79C4×#216—31no—
80#4850—31no—
81#4834—31no—
82#4811—31no—
83#4811—31no—
84#4811—31no—
85D3×#103—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4793—31no—
89#4792—31no—
90#67⋊C8—31no—
91#4722—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#627—21no—
104C2×#626D411yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3797—22no—
109#3797—41no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#216—22no—
121C3×#216—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C3×C4⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157#946—31no—
158#946—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946—61no—
164#946—61no—
165#946C2×D311yescharacteristic
166Q8×Dic3—31no—
167Q8×Dic3C2×D311yescharacteristic
168#944—61no—
169#944C2×D311yescharacteristic
170C2×#216C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C4×#67—31no—
173C4×#67—61no—
174C2×C4⋊Dic3—31no—
175#924—31no—
176#924—61no—
177C22×C3⋊C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182#897—61no—
183#896—61no—
184#896—61no—
185#896—61no—
186#896—61no—
187#893—61no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#889—61no—
192#888—31no—
193#888—61no—
194#67⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—61no—
198#870—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×C4⋊C8—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—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835—61no—
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818—31no—
224#818—31no—
225#818—31no—
226#818—61no—
227#816—31no—
228#816—31no—
229#816C2×D311yescharacteristic
230#816C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232C8×Dic3—31no—
233#810—31no—
234#810—31no—
235#807—31no—
236#807—31no—
237C4×C3⋊C8—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
250C4×C3⋊D3—21no—
251C4×C3⋊D3—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×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266C3×Dic6#4112yes—
267#627—42no—
268#627—81no—
269#626Q1614yescomplemented
270#624—42no—
271#624—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—91no—
284#467—91no—
285#462—31no—
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—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C22×Dic3—61no—
307D3×Q8—22no—
308D3×Q8—41no—
309D3×Q8—62no—
310D3×Q8—62no—
311D3×Q8—121no—
312D3×Q8—121no—
313C2×D12—31no—
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—61no—
323C2×C4×D3C22×D311yescharacteristic
324C2×Dic6—21no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—41no—
332C3×Q16—41no—
333C3×Q16—42no—
334C3×Q16—62no—
335C3×Q16—121no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—61no—
350#217—31no—
351#217—61no—
352#216—22no—
353#216—41no—
354(C2×D3)⋊C4—21no—
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—121no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
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—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D3×C8—121no—
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—31no—
433C2×Q16—31no—
434C2×Q16D3211yescharacteristic
435C22×C8—91no—
436C22×C8—91no—
437C4⋊Q8—31no—
438C4⋊Q8—91no—
439C4⋊Q8—181no—
440#125—181no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456#107—91no—
457#107—91no—
458#107—91no—
459C4⋊C8—31no—
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—
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—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—32no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—122no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—34no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—241no—
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532D12—34no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—42no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—121no—
541C4×D3—121no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550Dic6—42no—
551Dic6—122no—
552Dic6—122no—
553Dic6—241no—
554Dic6—241no—
555Dic6#23712yes—
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
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—31no—
573C2×Q8—61no—
574C2×Q8—62no—
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—61no—
585C22×C4—91no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589Q16—41no—
590Q16—62no—
591Q16—121no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8—361no—
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—91no—
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—91no—
616C22⋊C4—91no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—61no—
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—61no—
649C3×C4—62no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23711yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4#100411yescharacteristic
659C3×C4D3×#4111yescharacteristic
660Dic3—21no—
661Dic3—22no—
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—21no—
682Q8—21no—
683Q8—32no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—122no—
688Q8—362no—
689Q8—721no—
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—362no—
709C2×C4—721no—
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#559111yescharacteristic
721C2×C3#561211yescharacteristic
722C2×C3C2×D3×Q1611yescharacteristic
723C2×C3C2×D3×Q1611yescharacteristic
724C2×C3#577811yescharacteristic
725C2×C3#577811yescharacteristic
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×#23711yescharacteristic
750C4#6433011yescharacteristic
751C3—21no—
752C3#8019311yescharacteristic, complemented
753C3#8049111yescharacteristic, complemented
754C2—62no—
755C2—182no—
756C2D32×Q1611yescharacteristic
757C2#1059476711yescharacteristic
758C2#1059529411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#626D4
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. #10592887C2semidirect
4. C3×#5186C2semidirect
5. C3×#5182C2semidirect
6. #10591654C2semidirect
7. #10591635C2semidirect
8. #10591623C2semidirect
9. Dic3×#216C2semidirect
10. #10591555C2semidirect
11. D3×#835C2semidirect
13. #10590804C2semidirect
14. #10590682C2semidirect
15. #10590672C2semidirect
74. #5186D3semidirect
75. #5182D3semidirect
269. #626Q16semidirect
676. C32#3299semidirect
752. C3#80193semidirect
753. C3#80491semidirect

Maximal subgroups

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

subgroupindex
#105954032
#105953712
#105928872
C3×#51862
C3×#51822
#105916542
#105916352
#105916232
Dic3×#2162
#105915552
D3×#8352
#105909062
#105908042
#105906822
#105906722
#804913
#801933