Finite Group Databasebeta

← #11889301

Subgroups — #11889301

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic
2#10593879C211yesmaximal, characteristic, complemented
3#10592754C211yesmaximal, characteristic, complemented
4C3×#5054C211yesmaximal, characteristic, complemented
5#10591638C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591559C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10591499C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11#10591422C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14#10590330C211yesmaximal, characteristic, complemented
15#10590268C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#80617—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21#64078C2211yescharacteristic, complemented
22C3×#946C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×#884—21no—
27C3×#883—21no—
28C3×#882—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63861—21no—
34#63861—21no—
35#63860—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic, complemented
38#63844—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48#63630C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5676D311yescharacteristic
63#5584—31no—
64#5542—31no—
65C3×#464—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69#5215—31no—
70#5189—31no—
71#5187—31no—
72#5171—31no—
73#5169—31no—
74#5055—31no—
75#5055—31no—
76#5055—61no—
77#5054D311yescharacteristic, complemented
78#5052—31no—
79#5045—31no—
80#5041—31no—
81#5035—31no—
82#5026—31no—
83#5018—31no—
84#5011—31no—
85#5008—31no—
86#4842—31no—
87#4836—31no—
88#4815—31no—
89#4804—31no—
90#4779—31no—
91#4770—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#634—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#216—41no—
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3715—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×#124—21no—
152C3×#124C2×D311yescharacteristic
153C3×#124C2×D311yescharacteristic
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#946—31no—
164#946—31no—
165#946C2×D311yescharacteristic
166C2×#216C2×D311yescharacteristic, complemented
167C2×#215—31no—
168#938C2×D311yescharacteristic
169#936—61no—
170C2×#214—31no—
171C2×#214C2×D311yescharacteristic
172#926—31no—
173#926—31no—
174#924—31no—
175#924—31no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—61no—
181#898—61no—
182#892—31no—
183#892—31no—
184#887—61no—
185#884—21no—
186#883—21no—
187#882—21no—
188D3×C22⋊C4—21no—
189#879—61no—
190#879—61no—
191#875—61no—
192C4×D12C2×D311yescharacteristic
193C4×D12C2×D311yescharacteristic
194#869—31no—
195#869—31no—
196#869—61no—
197C4×Dic6—61no—
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#830—31no—
221#830—31no—
222#821—31no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#817—31no—
227#817—31no—
228#810—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235#803—31no—
236#803—31no—
237#803—61no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—42no—
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—41no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—31no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—31no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318#239—22no—
319#239—41no—
320D3×D4—22no—
321D3×D4—41no—
322C2×D12—21no—
323C2×D12#6711yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—121no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—121no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#216—41no—
363#215—62no—
364#214—41no—
365#214—62no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4#6711yescharacteristic
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3#6711yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397#208—121no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—91no—
441C22×C8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#126—181no—
445#124—181no—
446#124D3211yescharacteristic
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—31no—
455C4×Q8—181no—
456C4×D4—31no—
457C4×D4—31no—
458#117—91no—
459#117—91no—
460C2×C22⋊C4—61no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3C2×#6711yescharacteristic
492C22×D3C2×#6711yescharacteristic
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—61no—
509C3×D4—121no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
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×C4—241no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—81no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549D12—21no—
550D12—41no—
551D12—42no—
552D12#23712yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—81no—
559Dic6—21no—
560Dic6—21no—
561Dic6—122no—
562Dic6—122no—
563Dic6—242no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8—121no—
574C2×C32—81no—
575C2×C32#54611yescharacteristic
576C2×C32#57511yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—41no—
579C3×D3—41no—
580C3×D3—42no—
581C24—61no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8—181no—
586C2×Q8C2×D3211yescharacteristic
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—121no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—61no—
599Q16—121no—
600SD16—121no—
601SD16—182no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—361no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—61no—
630C42—181no—
631C42—181no—
632C42C2×D3211yescharacteristic
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—62no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—244no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—84no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23711yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695Dic3—241no—
696C32#331111yescharacteristic, complemented, Sylow
697C23—21no—
698C23—31no—
699C23—31no—
700C23—61no—
701C23—122no—
702C23—122no—
703C23—241no—
704Q8—21no—
705Q8—21no—
706Q8—61no—
707Q8—61no—
708Q8—362no—
709D4—21no—
710D4—21no—
711D4—32no—
712D4—61no—
713D4—121no—
714D4—122no—
715D4—122no—
716D4—241no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—241no—
731C2×C4D3×#6711yescharacteristic
732C2×C4D3×#6711yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—61no—
735C8—61no—
736C8—181no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—81no—
742C2×C3—81no—
743C2×C3—121no—
744C2×C3—121no—
745C2×C3—122no—
746C2×C3—161no—
747C2×C3#561211yescharacteristic
748C2×C3#577011yescharacteristic
749C2×C3#577711yescharacteristic
750C2×C3#580611yescharacteristic
751C2×C3#582211yescharacteristic
752C2×C3#583611yescharacteristic
753D3—41no—
754D3—41no—
755D3—42no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—244no—
769C22C2×D3×#6711yescharacteristic
770C4—21no—
771C4—21no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6431311yescharacteristic
782C3—21no—
783C3#8061711yescharacteristic, complemented
784C3#8349711yescharacteristic, complemented
785C2—81no—
786C2—121no—
787C2—121no—
788C2—122no—
789C2#1059522811yescharacteristic
790C2#1059546611yescharacteristic
791C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5676C2
hypercenter#124D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593879C2semidirect
3. #10592754C2semidirect
4. C3×#5054C2semidirect
5. #10591638C2semidirect
6. #10591597C2semidirect
7. #10591559C2semidirect
8. #10591556C2semidirect
9. #10591499C2semidirect
10. #10591458C2semidirect
11. #10591422C2semidirect
12. #10591421C2semidirect
13. #10590358C2semidirect
14. #10590330C2semidirect
15. #10590268C2semidirect
21. #64078C22semidirect
23. C2×C3×#216C22semidirect
32. C3×C4×Dic6C22semidirect
37. #63856C22semidirect
40. #63841C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
48. #63630C22semidirect
49. C3×#835C22semidirect
51. C3×C4⋊(C3⋊C8)C22semidirect
52. #63576C22semidirect
53. #63573C22semidirect
54. #63573C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
77. #5054D3semidirect
166. C2×#216C2×D3semidirect
198. C4×Dic6C2×D3semidirect
209. #835C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
696. C32#3311semidirect
783. C3#80617semidirect
784. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
#105938792
#105927542
C3×#50542
#105916382
#105915972
#105915592
#105915562
#105914992
#105914582
#105914222
#105914212
#105903582
#105903302
#105902682
#834973
#806173