Finite Group Databasebeta

← #11889730

Subgroups — #11889730

Order 1152.

896 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic
2#10595371C211yesmaximal, characteristic, complemented
3#10592886C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591624C211yesmaximal, characteristic, complemented
8#10591590C211yesmaximal, characteristic, complemented
9#10591554C211yesmaximal, characteristic, complemented
10#10591551C211yesmaximal, characteristic, complemented
11#10591540C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic, complemented
13#10590764C211yesmaximal, characteristic, complemented
14#10590727C211yesmaximal, characteristic, complemented
15#10590650C211yesmaximal, characteristic, complemented
16#80777—31nomaximal
17#80619—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21#64155C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63923—21no—
30#63921—21no—
31#63918C2211yescharacteristic, complemented
32#63916C2211yescharacteristic
33#63910—21no—
34C4×#626C2211yescharacteristic
35#63900C2211yescharacteristic, complemented
36#63899—21no—
37#63895—21no—
38#63894C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63880—21no—
41#63867—21no—
42#63853—21no—
43C2×#3712C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5676—31no—
62#5635—31no—
63#5630—31no—
64#5579—31no—
65C3×#467—31no—
66C3×#464—31no—
67#5188D311yescharacteristic, complemented
68#5187—31no—
69#5187—31no—
70#5187—61no—
71#5185D311yescharacteristic, complemented
72#5174—31no—
73#5169—31no—
74C2×#821—31no—
75#5111—31no—
76#5055—31no—
77#5046—31no—
78#5044—31no—
79#5026—31no—
80#4890—31no—
81#4882—31no—
82#4846—31no—
83#4836—31no—
84#4817—31no—
85#4812—31no—
86#4811—31no—
87#4803—31no—
88#4803—31no—
89#4794—31no—
90#4774—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95#3832—22no—
96#3832—41no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×#624—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12—41no—
112C32×Q16—41no—
113C2×C32×C8C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#215—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—41no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3712—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×Q16—21no—
151C2×C3×Q16C2×D311yescharacteristic, complemented
152C2×C3×Q16C2×D311yescharacteristic, complemented
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#124—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159#947C2×D311yescharacteristic
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3C2×D311yescharacteristic, complemented
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169C2×#215C2×D311yescharacteristic
170#938—31no—
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×D3×C8C2×D311yescharacteristic
176#897—61no—
177#896—61no—
178#896—61no—
179#895—31no—
180#895—61no—
181#894—61no—
182#893—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#889—61no—
187#888—31no—
188#884—61no—
189#883—61no—
190#882—61no—
191#882—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#878—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199#870—61no—
200#869—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic, complemented
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—61no—
227#818—31no—
228#818C2×D311yescharacteristic, complemented
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231#809—31no—
232#809—31no—
233#809—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#803—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)#4112yes—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270#627—81no—
271#626—22no—
272#626—42no—
273#626—81no—
274#624—81no—
275#624—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—31no—
289#464—31no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310#239—62no—
311#239—62no—
312#239—122no—
313#239—121no—
314#239—121no—
315#239—122no—
316D3×D4—62no—
317D3×D4—121no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—121no—
328C2×D12—121no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6—61no—
343C2×Dic6—61no—
344C3×Q16—41no—
345C3×Q16—41no—
346C3×Q16—42no—
347C3×SD16—121no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—31no—
367#217—61no—
368#215—41no—
369#215—62no—
370#215—62no—
371#215—122no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—31no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—21no—
406C4×Dic3C22×D311yescharacteristic
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412ΓL(1,𝔽25)—121no—
413ΓL(1,𝔽25)—121no—
414D3×C8—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3#13712yes—
428D32—84no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×Q16D3211yescharacteristic, complemented
444C2×SD16—31no—
445C2×SD16—91no—
446C2×M16—91no—
447C22×C8—31no—
448C4⋊Q8—91no—
449#125—181no—
450#124—31no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—91no—
458#121—181no—
459#120—181no—
460C4×Q8—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—181no—
467#107—31no—
468#107—91no—
469#107—91no—
470C4⋊C8—31no—
471#103—31no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483#97—91no—
484C23×C3—31no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3—31no—
488C22×D3—31no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3D3×D411yescharacteristic
500C3×Q8—22no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×D4—61no—
513C3×D4—61no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—62no—
532#67—122no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—21no—
548D12—21no—
549D12—32no—
550D12—32no—
551D12—62no—
552D12—62no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12—122no—
557D12—122no—
558D12—124no—
559D12—122no—
560D12—241no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—121no—
568C4×D3—121no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—124no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577Dic6—241no—
578Dic6—241no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—61no—
583C3×C8—61no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—121no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13711yescharacteristic
591C2×C32#57611yescharacteristic
592C3⋊D3—42no—
593C3⋊D3—41no—
594C3×D3—22no—
595C3×D3—81no—
596C24—181no—
597#41—182no—
598#41—361no—
599C2×Q8—181no—
600C2×Q8C2×D3211yescharacteristic
601C2×Q8C2×D3211yescharacteristic
602C2×D4—31no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—182no—
608C2×D4—181no—
609C2×D4—361no—
610C22×C4—31no—
611C22×C4—91no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616Q16—41no—
617SD16—121no—
618SD16—182no—
619M16—361no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—91no—
623C2×C8—121no—
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C42—31no—
647C42—61no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—62no—
668C2×D3—61no—
669C2×D3—62no—
670C2×D3—122no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3#91812yes—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4#100411yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4D3×#4111yescharacteristic
700C3×C4D3×#4111yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—61no—
708Dic3—61no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—241no—
713C32#331411yescharacteristic, complemented, Sylow
714C23—31no—
715C23—61no—
716C23—91no—
717C23—181no—
718C23—362no—
719C23—362no—
720C23—721no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—721no—
726D4—61no—
727D4—61no—
728D4—92no—
729D4—182no—
730D4—181no—
731D4—362no—
732D4—362no—
733D4—721no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—91no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—362no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4C22×D3211yescharacteristic
753C8—21no—
754C8—61no—
755C8—61no—
756C8—181no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—62no—
761C2×C3—241no—
762C2×C3#561011yescharacteristic
763C2×C3#561211yescharacteristic
764C2×C3C2×#91811yescharacteristic
765C2×C3#576911yescharacteristic
766C2×C3#576911yescharacteristic
767C2×C3D3×#13711yescharacteristic
768D3—22no—
769D3—81no—
770D3—121no—
771D3—122no—
772D3—121no—
773D3—122no—
774D3—241no—
775D3—242no—
776C22—32no—
777C22—61no—
778C22—61no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—182no—
786C22—361no—
787C22—361no—
788C22—724no—
789C22D32×D411yescharacteristic
790C4—41no—
791C4—41no—
792C4—61no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—181no—
799C4—361no—
800C4#6431211yescharacteristic
801C4#6433011yescharacteristic
802C3—21no—
803C3#8061911yescharacteristic, complemented
804C3#8077711yescharacteristic, complemented
805C2—62no—
806C2—241no—
807C2—361no—
808C2—362no—
809C2D3×#91811yescharacteristic
810C2#1059477111yescharacteristic
811C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595431C2
hypercenterC2×Q16D32
hypocenterC32#3314
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
2. #10595371C2semidirect
3. #10592886C2semidirect
4. C3×#5188C2semidirect
5. C3×#5185C2semidirect
6. #10591651C2semidirect
7. #10591624C2semidirect
8. #10591590C2semidirect
9. #10591554C2semidirect
10. #10591551C2semidirect
11. #10591540C2semidirect
12. D3×#821C2semidirect
13. #10590764C2semidirect
14. #10590727C2semidirect
15. #10590650C2semidirect
20. C2×C32×Q16C22semidirect
21. #64155C22semidirect
26. C3×Q8×Dic3C22semidirect
31. #63918C22semidirect
35. #63900C22semidirect
43. C2×#3712C22semidirect
44. #63662C22semidirect
46. #63647C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
49. C3×#835C22semidirect
51. C3×#818C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
60. #63554C22semidirect
67. #5188D3semidirect
71. #5185D3semidirect
151. C2×C3×Q16C2×D3semidirect
152. C2×C3×Q16C2×D3semidirect
165. Q8×Dic3C2×D3semidirect
210. #835C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
228. #818C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
443. C2×Q16D32semidirect
713. C32#3314semidirect
803. C3#80619semidirect
804. C3#80777semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105953712
#105928862
C3×#51882
C3×#51852
#105916512
#105916242
#105915902
#105915542
#105915512
#105915402
D3×#8212
#105907642
#105907272
#105906502
#807773
#806193