Finite Group Databasebeta

← #11889732

Subgroups — #11889732

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic
2#10595407C211yesmaximal, characteristic, complemented
3#10592884C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5187C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591632C211yesmaximal, characteristic, complemented
8#10591589C211yesmaximal, characteristic, complemented
9#10591572C211yesmaximal, characteristic, complemented
10#10591551C211yesmaximal, characteristic, complemented
11#10591550C211yesmaximal, characteristic, complemented
12D3×#821C211yesmaximal, characteristic, complemented
13#10590778C211yesmaximal, characteristic, complemented
14#10590723C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80777—31nomaximal
17#80252—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63922—21no—
30D3×(C2×D3)⋊C4—21no—
31#63919C2211yescharacteristic, complemented
32#63909C2211yescharacteristic
33#63902—21no—
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63893—21no—
37#63893—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic, complemented
40#63886—21no—
41#63870—21no—
42#63850—21no—
43C2×#3711C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5829—31no—
62#5635—31no—
63#5635—31no—
64#5630—31no—
65C3×#467—31no—
66C3×#452—31no—
67#5232—31no—
68#5188D311yescharacteristic, complemented
69#5187D311yescharacteristic, complemented
70#5185—31no—
71#5185—31no—
72#5185—61no—
73#5169—31no—
74#5164—31no—
75C2×#821—31no—
76#5111—31no—
77#5049—31no—
78#5046—31no—
79#5044—31no—
80#4890—31no—
81#4882—31no—
82#4817—31no—
83#4812—31no—
84#4811—31no—
85#4803—31no—
86#4794—31no—
87#4794—31no—
88D3×#102—31no—
89#4759—31no—
90#4736—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110D3×D12—22no—
111D3×D12—41no—
112C32×Q16—41no—
113C2×C32×C8C2311yescharacteristic
114#3755—41no—
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—41no—
135#3724—21no—
136#3724D411yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3711—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C22×D12—31no—
149C2×C3×Q16—21no—
150C2×C3×Q16C2×D311yescharacteristic, complemented
151C2×C3×Q16C2×D311yescharacteristic, complemented
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157#947—31no—
158#947—31no—
159#947—61no—
160#946C2×D311yescharacteristic
161#946C2×D311yescharacteristic
162#946C2×D311yescharacteristic, complemented
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—61no—
169C2×#215C2×D311yescharacteristic
170#939—61no—
171#937—61no—
172D4×Dic3—31no—
173#930—31no—
174#929—61no—
175C4×#67—31no—
176C4×#67—31no—
177C2×(C2×D3)⋊C4—61no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×#208—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8C2×D311yescharacteristic
183#897—61no—
184#897—61no—
185#895—31no—
186#895—61no—
187#894—61no—
188#893—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191#889—61no—
192#889—61no—
193#888—31no—
194#888—31no—
195#882—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198D3×C22⋊C4—61no—
199#878—61no—
200#878—61no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—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)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#818C2×D311yescharacteristic, complemented
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232#809—31no—
233#809—31no—
234#809—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
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
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—42no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270#627—81no—
271#626—42no—
272#626—81no—
273#625—22no—
274D3×Dic3—81no—
275D3×Dic3—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—91no—
290#452—31no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C23×D3—61no—
297C23×D3—61no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—21no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#239—22no—
319#239—41no—
320D3×D4—62no—
321D3×D4—121no—
322C2×D12—21no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—121no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6—61no—
338C2×Dic6—61no—
339C3×Q16—41no—
340C3×Q16—41no—
341C3×Q16—42no—
342C3×SD16—62no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358#217—31no—
359#217—31no—
360#217—61no—
361#215—22no—
362#215—121no—
363#215—121no—
364#215—122no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—121no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405#208—121no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411ΓL(1,𝔽25)—121no—
412D3×C8—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yes—
426D32—84no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4—91no—
441C2×Q16D3211yescharacteristic, complemented
442C2×SD16—31no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—31no—
446C4⋊Q8—91no—
447#125—181no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3D3×D411yescharacteristic
496C22×D3D3×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×D4—32no—
510C3×D4—61no—
511C3×D4—122no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—122no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—62no—
532#67—62no—
533#67—122no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552D12—21no—
553D12—42no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—121no—
559D12—121no—
560D12—122no—
561D12—241no—
562D12#23712yes—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—42no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571Dic6—241no—
572Dic6—241no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3⋊D3—81no—
587C3×D3—22no—
588C3×D3—42no—
589C3×D3—41no—
590C24—181no—
591#41—62no—
592#41—121no—
593C2×Q8—181no—
594C2×Q8C2×D3211yescharacteristic
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—361no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—41no—
611SD16—62no—
612SD16—361no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—91no—
641C42—181no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—61no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
673C2×D3#91812yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23711yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4#100411yescharacteristic
690C3×C4D3×#4111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—31no—
708C23—61no—
709C23—181no—
710C23—362no—
711C23—362no—
712C23—721no—
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—721no—
718D4—32no—
719D4—61no—
720D4—122no—
721D4—182no—
722D4—181no—
723D4—181no—
724D4—362no—
725D4—721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—122no—
740C2×C4—181no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—61no—
747C8—61no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—122no—
754C2×C3—121no—
755C2×C3#559111yescharacteristic
756C2×C3#561011yescharacteristic
757C2×C3C2×#91811yescharacteristic
758C2×C3#576911yescharacteristic
759C2×C3#576911yescharacteristic
760C2×C3D3×#13711yescharacteristic
761D3—22no—
762D3—41no—
763D3—42no—
764D3—241no—
765D3—241no—
766D3—481no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—724no—
780C22D32×D411yescharacteristic
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—181no—
790C4—361no—
791C4D3×#23711yescharacteristic
792C4#6433011yescharacteristic
793C3—21no—
794C3#8025211yescharacteristic, complemented
795C3#8077711yescharacteristic, complemented
796C2—62no—
797C2—121no—
798C2—122no—
799C2—721no—
800C2D3×#91811yescharacteristic
801C2#1059477111yescharacteristic
802C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595427C2
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. #10595407C2semidirect
3. #10592884C2semidirect
4. C3×#5188C2semidirect
5. C3×#5187C2semidirect
6. #10591651C2semidirect
7. #10591632C2semidirect
8. #10591589C2semidirect
9. #10591572C2semidirect
10. #10591551C2semidirect
11. #10591550C2semidirect
12. D3×#821C2semidirect
13. #10590778C2semidirect
14. #10590723C2semidirect
15. #10590679C2semidirect
20. C2×C32×Q16C22semidirect
22. Q8×C3⋊Dic3C22semidirect
26. C3×#946C22semidirect
31. #63919C22semidirect
39. D3×C4⋊Dic3C22semidirect
43. C2×#3711C22semidirect
44. #63662C22semidirect
46. #63641C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
49. C3×#835C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
60. #63555C22semidirect
68. #5188D3semidirect
69. #5187D3semidirect
150. C2×C3×Q16C2×D3semidirect
151. C2×C3×Q16C2×D3semidirect
162. #946C2×D3semidirect
210. #835C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
226. #818C2×D3semidirect
441. C2×Q16D32semidirect
705. C32#3314semidirect
794. C3#80252semidirect
795. C3#80777semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105954072
#105928842
C3×#51882
C3×#51872
#105916512
#105916322
#105915892
#105915722
#105915512
#105915502
D3×#8212
#105907782
#105907232
#105906792
#807773
#802523