Finite Group Databasebeta

← #11889143

Subgroups — #11889143

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595380C211yesmaximal, characteristic, complemented
2#10595288C211yesmaximal, characteristic
3#10592862C211yesmaximal, characteristic, complemented
4C3×#5174C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591585C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591480C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590780C211yesmaximal, characteristic, complemented
14#10590724C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80821—31nomaximal
17#80160—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24#64149C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#938C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30#63983—21no—
31#63977—21no—
32#63971—21no—
33#63909C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63891—21no—
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63878—21no—
39#63872C2211yescharacteristic, complemented
40#63862—21no—
41#63845—21no—
42#63841C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61D4×#67—31no—
62#5642—31no—
63#5639—31no—
64#5609—31no—
65C3×#468—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174D311yescharacteristic, complemented
69#5169—31no—
70#5169D311yescharacteristic, complemented
71#5164—31no—
72#5163—31no—
73#5163—31no—
74#5163—61no—
75#5131—31no—
76#5127—31no—
77#5048—31no—
78#5046—31no—
79#5035—31no—
80#4891—31no—
81#4882—31no—
82#4817—31no—
83#4807—31no—
84#4784—31no—
85#4770—31no—
86D3×#102—31no—
87#4766—31no—
88#4764—31no—
89#4764—31no—
90#4736—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—41no—
114C32×SD16—41no—
115C2×C32×C8C2311yescharacteristic
116#3755—41no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#215—22no—
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—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×ΓL(1,𝔽25)—41no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C2×C3×SD16—21no—
153C2×C3×SD16—31no—
154C2×C3×SD16C2×D311yescharacteristic, complemented
155C2×C3×SD16C2×D311yescharacteristic, complemented
156C2×C3×M16—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160#953—61no—
161#946C2×D311yescharacteristic, complemented
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#940—31no—
171#940—31no—
172#940—61no—
173#939—61no—
174#938C2×D311yescharacteristic
175#937—61no—
176#937—61no—
177D4×Dic3—31no—
178#930—31no—
179C4×#67—31no—
180C4×#67—31no—
181#926—31no—
182C2×C4⋊Dic3—31no—
183C22×C3⋊C8—31no—
184C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
185C2×D3×C8—31no—
186#898—61no—
187#895—31no—
188#893—31no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890—31no—
193#890—31no—
194#890—61no—
195#889—61no—
196#886—61no—
197#884—61no—
198#883—61no—
199#882—61no—
200#879—61no—
201#877—61no—
202C3×#107—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832C2×D311yescharacteristic, complemented
215#832C2×D311yescharacteristic, complemented
216#830—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—61no—
223#821C2×D311yescharacteristic
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8C2×D311yescharacteristic, complemented
226#818—31no—
227#818C2×D311yescharacteristic, complemented
228#815—31no—
229#815—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—61no—
233#809—31no—
234#809—31no—
235#809—31no—
236#808—31no—
237#808—31no—
238#807—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C32×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257#638—81no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263C3×#67—42no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#626—42no—
277#626—42no—
278#625—22no—
279D3×Dic3—42no—
280D3×Dic3—42no—
281C32×C8—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—91no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—91no—
291#468—31no—
292#465—91no—
293#460—91no—
294#450—31no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C23×D3—21no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—31no—
320C2×#67—31no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—121no—
328C2×#67—121no—
329C2×#67—124no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332D3×D4—22no—
333D3×D4—41no—
334D3×D4—62no—
335D3×D4—121no—
336D3×D4—124no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—62no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—121no—
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C3×SD16—41no—
350C3×SD16—41no—
351C3×SD16—42no—
352C3×SD16—62no—
353C3×M16—121no—
354C2×C3×C8—21no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367#217—21no—
368#217—31no—
369#217—31no—
370#217—61no—
371#217—61no—
372#215—22no—
373#215—121no—
374#215—121no—
375#215—122no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—121no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—121no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—121no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417ΓL(1,𝔽25)—41no—
418D3×C8—121no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3AGL(1,ℤ/8)12yes—
436D32—84no—
437C32×C4—41no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—21no—
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×SD16D3211yescharacteristic, complemented
454C2×M16—31no—
455C22×C8—91no—
456#127—91no—
457#126—181no—
458#125—91no—
459#125—181no—
460#123—181no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463#121—31no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—91no—
470C4×D4—91no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—31no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490#97—91no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C22×D3—21no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—81no—
506C22×D3—121no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3D3×D411yescharacteristic
514C22×D3D3×D411yescharacteristic
515C3×Q8—22no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—41no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—32no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—61no—
529C3×D4—122no—
530C3×D4—122no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—42no—
547#67—42no—
548#67—62no—
549#67—62no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—242no—
555#67—241no—
556#67—241no—
557#67—242no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—121no—
570C2×Dic3—122no—
571C2×Dic3—122no—
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574D12—21no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12#23712yes—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—122no—
589C4×D3—122no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—121no—
600C2×C32—81no—
601C2×C32#54611yescharacteristic
602C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
603C2×C32#57711yescharacteristic
604C3⋊D3—81no—
605C3×D3—22no—
606C3×D3—41no—
607C3×D3—42no—
608C24—61no—
609C24—181no—
610C2×Q8C2×D3211yescharacteristic
611C2×D4—31no—
612C2×D4—61no—
613C2×D4—62no—
614C2×D4—61no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—121no—
618C2×D4—181no—
619C2×D4—182no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—361no—
624C2×D4—364no—
625C2×D4C2×D3211yescharacteristic
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—181no—
629C22×C4—181no—
630SD16—41no—
631SD16—62no—
632SD16—361no—
633M16—121no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8—361no—
638C2×C8C2×D3211yescharacteristic
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—91no—
659C42—181no—
660C42—181no—
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—62no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—22no—
688C2×D3—21no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—84no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3#91412yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—42no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4—121no—
714C3×C4C2×#23711yescharacteristic
715C3×C4#100411yescharacteristic
716C3×C4#100411yescharacteristic
717C3×C4D3×#4111yescharacteristic
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—41no—
723Dic3—62no—
724Dic3—61no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732C32#331011yescharacteristic, complemented, Sylow
733C23—21no—
734C23—31no—
735C23—31no—
736C23—61no—
737C23—122no—
738C23—122no—
739C23—181no—
740C23—241no—
741C23—362no—
742C23—362no—
743C23—721no—
744Q8—21no—
745Q8—21no—
746D4—21no—
747D4—21no—
748D4—32no—
749D4—61no—
750D4—122no—
751D4—122no—
752D4—182no—
753D4—181no—
754D4—181no—
755D4—362no—
756D4—362no—
757D4—362no—
758D4—721no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—181no—
772C2×C4—362no—
773C2×C4—362no—
774C2×C4C22×D3211yescharacteristic
775C8—21no—
776C8—61no—
777C8—61no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—81no—
784C2×C3—81no—
785C2×C3—121no—
786C2×C3—122no—
787C2×C3—161no—
788C2×C3#559111yescharacteristic
789C2×C3#561011yescharacteristic
790C2×C3C2×#91411yescharacteristic
791C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
792C2×C3#577511yescharacteristic
793C2×C3#577811yescharacteristic
794D3—22no—
795D3—42no—
796D3—41no—
797D3—241no—
798D3—241no—
799D3—481no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—244no—
813C22—361no—
814C22—361no—
815C22—361no—
816C22—724no—
817C22D32×D411yescharacteristic
818C4—41no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—181no—
826C4—361no—
827C4D3×#23711yescharacteristic
828C4#6433011yescharacteristic
829C3—21no—
830C3#8016011yescharacteristic, complemented
831C3#8082111yescharacteristic, complemented
832C2—62no—
833C2—81no—
834C2—121no—
835C2—122no—
836C2—721no—
837C2D3×#91411yescharacteristic
838C2#1059475411yescharacteristic
839C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595288C2
hypercenterC2×SD16D32
hypocenterC32#3310
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. #10595380C2semidirect
3. #10592862C2semidirect
4. C3×#5174C2semidirect
5. C3×#5169C2semidirect
6. #10591651C2semidirect
7. #10591585C2semidirect
8. #10591572C2semidirect
9. #10591480C2semidirect
10. #10591423C2semidirect
11. D3×#832C2semidirect
12. #10590939C2semidirect
13. #10590780C2semidirect
14. #10590724C2semidirect
15. #10590679C2semidirect
21. C2×C32×SD16C22semidirect
22. Q8×C3⋊Dic3C22semidirect
23. C2×#3755C22semidirect
25. C3×#946C22semidirect
26. C3×#946C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
37. D3×C4⋊Dic3C22semidirect
39. #63872C22semidirect
42. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63648C22semidirect
46. #63641C22semidirect
47. C3×#835C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
68. #5174D3semidirect
70. #5169D3semidirect
154. C2×C3×SD16C2×D3semidirect
155. C2×C3×SD16C2×D3semidirect
161. #946C2×D3semidirect
162. #946C2×D3semidirect
184. C2×ΓL(1,𝔽25)C2×D3semidirect
208. #835C2×D3semidirect
214. #832C2×D3semidirect
215. #832C2×D3semidirect
225. (C2×D3)⋊C8C2×D3semidirect
227. #818C2×D3semidirect
453. C2×SD16D32semidirect
732. C32#3310semidirect
830. C3#80160semidirect
831. C3#80821semidirect

Maximal subgroups

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

subgroupindex
#105953802
#105952882
#105928622
C3×#51742
C3×#51692
#105916512
#105915852
#105915722
#105914802
#105914232
D3×#8322
#105909392
#105907802
#105907242
#105906792
#808213
#801603