Finite Group Databasebeta

← #11887552

Subgroups — #11887552

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595403C211yesmaximal, characteristic, complemented
2#10595136C211yesmaximal, characteristic
3#10592870C211yesmaximal, characteristic, complemented
4C3×#5170C211yesmaximal, characteristic, complemented
5C3×#5162C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591553C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591518C211yesmaximal, characteristic, complemented
10#10591499C211yesmaximal, characteristic, complemented
11Dic3×#214C211yesmaximal, characteristic, complemented
12#10590906C211yesmaximal, characteristic, complemented
13#10590803C211yesmaximal, characteristic, complemented
14#10590675C211yesmaximal, characteristic, complemented
15#10590672C211yesmaximal, characteristic, complemented
16#80450—31nomaximal
17#80049—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3804—21no—
20C2×#3797C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22#64155C2211yescharacteristic
23#64147C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30#63975—21no—
31#63969—21no—
32#63964—21no—
33#63918C2211yescharacteristic
34#63904—21no—
35C4×#626C2211yescharacteristic
36#63900C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63888—21no—
39#63856C2211yescharacteristic
40#63851—21no—
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Q8×#67—31no—
62#5727—31no—
63#5611—31no—
64#5551—31no—
65C3×#461—31no—
66C3×#448—31no—
67C2×#835—31no—
68#5171—31no—
69#5171—31no—
70#5171—31no—
71#5171—61no—
72#5170—31no—
73#5170—31no—
74#5170D311yescharacteristic, complemented
75#5162D311yescharacteristic, complemented
76Dic3×SD16—31no—
77#5079—31no—
78#5041—31no—
79C4×#214—31no—
80#4851—31no—
81#4834—31no—
82#4805—31no—
83#4805—31no—
84#4805—31no—
85D3×#103—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4792—31no—
89#4791—31no—
90#67⋊C8—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109C2×#624—21no—
110#3804—44no—
111C2×D3×Dic3—21no—
112#3797—22no—
113#3797—41no—
114C32×SD16—41no—
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C8×C3⋊D3—41no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#214—22no—
126C3×#214—41no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3D411yescharacteristic
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#237—61no—
151C2×#235—61no—
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C2×C3×SD16C2×D311yescharacteristic
156C2×C3×SD16C2×D311yescharacteristic
157C3×C4⋊Q8—31no—
158C3×#121—31no—
159C3×C4×D4—31no—
160#946—31no—
161#946—31no—
162#946—31no—
163#946—61no—
164#946—61no—
165Q8×Dic3—31no—
166#944—61no—
167#944C2×D311yescharacteristic
168#938—31no—
169#938—31no—
170#938—61no—
171#938C2×D311yescharacteristic
172#935—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214C2×D311yescharacteristic
175C2×#214C2×D311yescharacteristic
176C4×#67—31no—
177C4×#67—61no—
178C2×C4⋊Dic3—31no—
179#924—31no—
180#924—61no—
181#924—61no—
182C22×C3⋊C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186C2×D3×C8—61no—
187#896—61no—
188#896—61no—
189#893—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193#888—31no—
194#888—61no—
195#883—61no—
196#883—61no—
197#883—61no—
198#878—61no—
199C4×D12—31no—
200#869—31no—
201C4×Dic6—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#832—31no—
218#832—31no—
219#832—61no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8C2×D311yescharacteristic
223#817—31no—
224#817—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#816—31no—
229#816—31no—
230#816C2×D311yescharacteristic
231#816C2×D311yescharacteristic
232Dic3⋊C8C2×D311yescharacteristic
233C8×Dic3—31no—
234#810—31no—
235#810—31no—
236#808—31no—
237#808—31no—
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248#638—42no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#627—42no—
273#626SD1614yescomplemented
274#624—42no—
275#624—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—31no—
290#448—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—121no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318D3×Q8—22no—
319D3×Q8—41no—
320D3×Q8—62no—
321D3×Q8—62no—
322D3×Q8—121no—
323D3×Q8—121no—
324#237—124no—
325#235—124no—
326C2×D12—31no—
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—21no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—41no—
345C3×SD16—41no—
346C3×SD16—42no—
347C3×SD16—62no—
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—21no—
362#217—21no—
363#217—31no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#214—22no—
369#214—41no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—121no—
414D3×C8—122no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3C2×SD1612yes—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3C2×SD1612yes—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C2×SD1612yes—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C2×SD16D3211yescharacteristic
444C22×C8—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
457#121—91no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464#106—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3D3×D411yescharacteristic
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—32no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—122no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—34no—
525#67—42no—
526#67—122no—
527#67—122no—
528#67—242no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—42no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—122no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—34no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—42no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—42no—
566Dic6—122no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23712yescomplemented
571C3×C8—22no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—81no—
582C2×C32#54611yescharacteristic
583C2×C32C22×SD1611yescharacteristic
584C2×C32#57811yescharacteristic
585C3⋊D3—22no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—61no—
591C2×Q8—62no—
592C2×Q8—121no—
593C2×Q8—181no—
594C2×Q8—181no—
595C2×Q8—182no—
596C2×Q8—361no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—91no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609SD16—41no—
610SD16—62no—
611SD16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8—361no—
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—32no—
658C2×D3—32no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3D3×SD1612yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—32no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—62no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—22no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—61no—
690Dic3—61no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698Dic3D3×SD1612yes—
699C32#329811yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—91no—
703Q8—21no—
704Q8—21no—
705Q8—32no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—122no—
710Q8—362no—
711Q8—362no—
712D4—21no—
713D4—21no—
714D4—94no—
715D4—122no—
716D4—362no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4C22×D3211yescharacteristic
738C8—21no—
739C8—61no—
740C8—61no—
741C8—181no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—62no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—161no—
749C2×C3#559111yescharacteristic
750C2×C3#561211yescharacteristic
751C2×C3C2×D3×SD1611yescharacteristic
752C2×C3C2×D3×SD1611yescharacteristic
753C2×C3#577911yescharacteristic
754C2×C3#577911yescharacteristic
755D3—22no—
756D3—62no—
757D3—62no—
758D3—122no—
759C22—32no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—61no—
764C22—61no—
765C22—92no—
766C22—181no—
767C22—181no—
768C22D32×D411yescharacteristic
769C4—32no—
770C4—41no—
771C4—61no—
772C4—61no—
773C4—62no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—361no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6433011yescharacteristic
782C3—21no—
783C3#8004911yescharacteristic, complemented
784C3#8045011yescharacteristic, complemented
785C2—62no—
786C2—81no—
787C2—182no—
788C2D32×SD1611yescharacteristic
789C2#1059475211yescharacteristic
790C2#1059529411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595136C2
hypercenterC2×SD16D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595403C2semidirect
3. #10592870C2semidirect
4. C3×#5170C2semidirect
5. C3×#5162C2semidirect
6. #10591623C2semidirect
7. #10591553C2semidirect
8. D3×#835C2semidirect
9. #10591518C2semidirect
10. #10591499C2semidirect
11. Dic3×#214C2semidirect
12. #10590906C2semidirect
13. #10590803C2semidirect
14. #10590675C2semidirect
15. #10590672C2semidirect
74. #5170D3semidirect
75. #5162D3semidirect
270. C3×Dic6#41semidirect
273. #626SD16semidirect
570. Dic6#237semidirect
699. C32#3298semidirect
783. C3#80049semidirect
784. C3#80450semidirect

Maximal subgroups

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

subgroupindex
#105954032
#105951362
#105928702
C3×#51702
C3×#51622
#105916232
#105915532
D3×#8352
#105915182
#105914992
Dic3×#2142
#105909062
#105908032
#105906752
#105906722
#804503
#800493