Finite Group Databasebeta

← #10764033

Subgroups — #10764033

Order 768.

1248 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86242C211yesmaximal, characteristic
2#79340C211yesmaximal, characteristic, complemented
3#79015C211yesmaximal, characteristic, complemented
4C3×#1551C211yesmaximal, characteristic, complemented
5#71807C211yesmaximal, characteristic, complemented
6#70818C211yesmaximal, characteristic, complemented
7C2×#4485C211yesmaximal, characteristic, complemented
8#68489C211yesmaximal, characteristic, complemented
9#68485C211yesmaximal, characteristic, complemented
10#68485C211yesmaximal, characteristic, complemented
11#68482C211yesmaximal, characteristic, complemented
12#68387C211yesmaximal, characteristic, complemented
13#68383C211yesmaximal, characteristic, complemented
14#68383C211yesmaximal, characteristic, complemented
15D3×#331C211yesmaximal, characteristic, complemented
16#17770—31nomaximal, Sylow
17C2×#1009C412yes—
18C3×#532C2211yescharacteristic
19#5830C412yes—
20#5725C2211yescharacteristic
21#5725C2211yescharacteristic
22D3×#127C2211yescharacteristic
23D3×#127C2211yescharacteristic
24#5674C412yes—
25#5674C412yes—
26#5609—21no—
27#5609—21no—
28#5609—21no—
29#5609—21no—
30#5553—21no—
31#5553—21no—
32D4×D12—21no—
33D4×D12—21no—
34C2×#874C2211yescharacteristic
35C4×#235C2211yescharacteristic
36C3×#432C2211yescharacteristic, complemented
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38#5111—21no—
39C8×#67—21no—
40#4926C2211yescharacteristic, complemented
41C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
42#4837C2211yescharacteristic, complemented
43#4837C2211yescharacteristic, complemented
44#4836—21no—
45#4835C2211yescharacteristic, complemented
46#4835C2211yescharacteristic, complemented
47#4833C2211yescharacteristic, complemented
48#4833C2211yescharacteristic, complemented
49D3×C4⋊C8C2211yescharacteristic, complemented
50D3×C4⋊C8C2211yescharacteristic, complemented
51#4828—21no—
52#4730—21no—
53#67⋊C8—21no—
54#4706—21no—
55#4701—21no—
56C3×#333C2211yescharacteristic, complemented
57C3×#333C2211yescharacteristic, complemented
58C3×#331C2211yescharacteristic, complemented
59C3×#331C2211yescharacteristic, complemented
60#4546C2211yescharacteristic, complemented
61#4546C2211yescharacteristic, complemented
62#4544C2211yescharacteristic, complemented
63#4544C2211yescharacteristic, complemented
64#4485C2211yescharacteristic, complemented
65#4485C2211yescharacteristic, complemented
66#4485C2211yescharacteristic, complemented
67#4485C2211yescharacteristic, complemented
68#4485C2211yescharacteristic, complemented
69#4485C2211yescharacteristic, complemented
70#4485C2211yescharacteristic, complemented
71#4485C2211yescharacteristic, complemented
72#3498—31no—
73#2990—31no—
74#2990—31no—
75#1560—31no—
76#1555—31no—
77#1555—31no—
78#1551—31no—
79#1551—31no—
80#1551—31no—
81#1551D311yescharacteristic, complemented
82#1545—31no—
83#1545—31no—
84#1543—31no—
85C2×#331—31no—
86C2×#331—31no—
87C2×C3×#41C2×C412yes—
88#1009—48no—
89C2×#239C2×C412yes—
90C2×#239C2×C412yes—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—21no—
94C2×D3×D4—21no—
95C2×D3×D4—21no—
96C2×D3×D4—21no—
97C2×D3×D4C2×C412yes—
98C2×D3×D4C2×C412yes—
99C2×#235—22no—
100C2×#235C2×C411yescharacteristic
101C22×D12—21no—
102C22×D12—21no—
103C22×D12—22no—
104C22×D12C2×C412yes—
105C22×C3×C8—21no—
106C3×C4⋊Q8C2311yescharacteristic
107C3×#127C2311yescharacteristic
108C3×#124C2×C412yes—
109C3×#121—21no—
110C3×#121—21no—
111C3×C4×D4—21no—
112C3×C4×D4—21no—
113C2×C3×C42C2311yescharacteristic
114#947C2×C412yes—
115#947C2×C412yes—
116#940—21no—
117#940—21no—
118#940—21no—
119#940—21no—
120#940C2×C412yes—
121#940C2×C412yes—
122#937—22no—
123#937—22no—
124#930—22no—
125#930—22no—
126C4×#67D411yescharacteristic
127C4×#67D411yescharacteristic
128C4×#67D411yescharacteristic
129C4×#67D411yescharacteristic
130#926C2×C411yescharacteristic
131C22×C3⋊C8—21no—
132C2×ΓL(1,𝔽25)—21no—
133C2×ΓL(1,𝔽25)—21no—
134C2×D3×C8—21no—
135C2×D3×C8—21no—
136#895—21no—
137#895—21no—
138#895—21no—
139#895—21no—
140#893—21no—
141#893—21no—
142#893—21no—
143#893—21no—
144#884—22no—
145#884—22no—
146#884—22no—
147#884—22no—
148#882—22no—
149#882—22no—
150#882—22no—
151#882—22no—
152#874—21no—
153#874—21no—
154#874C2×C412yes—
155#874C2311yescharacteristic
156#874C2311yescharacteristic
157C4×D12D411yescharacteristic
158C4×D12D411yescharacteristic
159#872C2×C411yescharacteristic
160#872C2×C411yescharacteristic
161C42×D3C2311yescharacteristic
162C42×D3C2311yescharacteristic
163C4×Dic6D411yescharacteristic
164C4×Dic6D411yescharacteristic
165C3×C4⋊C8—21no—
166C3×C4⋊C8C2311yescharacteristic
167C3×C4⋊C8C2311yescharacteristic
168C3×C4⋊C8C2311yescharacteristic
169C3×C4⋊C8C2311yescharacteristic
170C3×C22⋊C8—21no—
171C3×#97—21no—
172#830—21no—
173(C2×D3)⋊C8—21no—
174(C2×D3)⋊C8—21no—
175(C2×D3)⋊C8—21no—
176(C2×D3)⋊C8—21no—
177#815—21no—
178#815—21no—
179Dic3⋊C8—21no—
180Dic3⋊C8—21no—
181Dic3⋊C8—21no—
182Dic3⋊C8—21no—
183C8×Dic3—21no—
184C8×Dic3—21no—
185C4⋊(C3⋊C8)—21no—
186C4⋊(C3⋊C8)C2311yescharacteristic
187C4⋊(C3⋊C8)C2311yescharacteristic
188C4⋊(C3⋊C8)C2311yescharacteristic
189C4⋊(C3⋊C8)C2311yescharacteristic
190#803—21no—
191C2×H(5,𝔽2)—32no—
192#550—61no—
193#550—61no—
194D42—61no—
195D42—61no—
196D42—61no—
197D42—61no—
198D42—61no—
199D42—61no—
200#535—32no—
201#535—32no—
202#535—32no—
203#532—31no—
204#532—31no—
205#532C2×D311yescharacteristic
206C2×#127—31no—
207C2×#127—31no—
208C2×#127—31no—
209C4×#41—31no—
210#446—61no—
211#446—61no—
212#435—61no—
213#435—61no—
214#435—61no—
215#435—61no—
216C8×D4—61no—
217C8×D4—61no—
218#432—31no—
219#432—31no—
220#432—31no—
221#432C2×D311yescharacteristic, complemented
222#431—31no—
223#431—31no—
224#423—31no—
225#423—31no—
226C2×C4⋊C8—31no—
227C2×C4⋊C8—31no—
228C2×C4⋊C8—31no—
229C2×C4⋊C8C2×D311yescharacteristic, complemented
230#333—31no—
231#333—31no—
232#333C2×D311yescharacteristic, complemented
233#333C2×D311yescharacteristic, complemented
234#331—31no—
235#331—31no—
236#331—31no—
237#331—31no—
238#331—31no—
239#331—31no—
240#331—31no—
241#331—31no—
242#331—31no—
243#331—31no—
244#331C2×D311yescharacteristic, complemented
245#331C2×D311yescharacteristic, complemented
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C3×#41—44no—
250C2×C3×Q8C22×C412yes—
251C2×C3×D4—22no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4C22×C412yes—
255C22×C3×C4—22no—
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67C22⋊C411yescharacteristic
266C2×#67C22⋊C411yescharacteristic
267#239—44no—
268#239—44no—
269D3×D4—44no—
270D3×D4—44no—
271D3×D4—48no—
272D3×D4—48no—
273D3×D4—81no—
274D3×D4—81no—
275D3×D4—81no—
276D3×D4—81no—
277D3×D4—81no—
278D3×D4—81no—
279D3×D4—81no—
280D3×D4—81no—
281#235—24no—
282#235—48no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—22no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—22no—
291C2×D12—22no—
292C2×D12—48no—
293C2×D12—44no—
294C2×D12—81no—
295C2×D12—81no—
296C2×D12—81no—
297C2×D12—81no—
298C2×D12C22⋊C411yescharacteristic
299C2×D12C22×C412yes—
300C2×D12C22×C412yes—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3C22×C411yescharacteristic
304C2×C4×D3C22×C411yescharacteristic
305C2×C4×D3C2×D411yescharacteristic
306C2×C4×D3C2×D411yescharacteristic
307C2×C4×D3C2×D411yescharacteristic
308C2×C4×D3C2×D411yescharacteristic
309C2×Dic6C22⋊C411yescharacteristic
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—81no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C42C22×C411yescharacteristic
320C3×C42C2×D411yescharacteristic
321C3×C42C2×D411yescharacteristic
322C3×C42C2411yescharacteristic
323#217C22⋊C411yescharacteristic
324#217C22⋊C411yescharacteristic
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4C22⋊C411yescharacteristic
330(C2×D3)⋊C4C22⋊C411yescharacteristic
331(C2×D3)⋊C4C22⋊C411yescharacteristic
332(C2×D3)⋊C4C22⋊C411yescharacteristic
333C4⋊Dic3C22⋊C411yescharacteristic
334C4⋊Dic3C22⋊C411yescharacteristic
335Dic3⋊C4C22⋊C411yescharacteristic
336Dic3⋊C4C22⋊C411yescharacteristic
337Dic3⋊C4C22⋊C411yescharacteristic
338Dic3⋊C4C22⋊C411yescharacteristic
339C4×Dic3C22×C411yescharacteristic
340C4×Dic3C22×C411yescharacteristic
341C4×Dic3C2×D411yescharacteristic
342C4×Dic3C2×D411yescharacteristic
343C4×Dic3C2×D411yescharacteristic
344C4×Dic3C2×D411yescharacteristic
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—81no—
350ΓL(1,𝔽25)—81no—
351ΓL(1,𝔽25)—81no—
352D3×C8—81no—
353D3×C8—81no—
354H(5,𝔽2)—128no—
355C2×#41—31no—
356C2×#41—32no—
357C2×#41—32no—
358C2×#41—62no—
359C2×#41C4×D312yes—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4—32no—
363C22×D4—62no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4—61no—
367C22×D4—61no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—61no—
371C22×D4—61no—
372C2×M16—61no—
373C2×M16—61no—
374C22×C8—21no—
375C22×C8—61no—
376C22×C8—61no—
377C22×C8—61no—
378C4⋊Q8C22×D311yescharacteristic
379#127—32no—
380#127—32no—
381#127—32no—
382#127—31no—
383#127—31no—
384#127—61no—
385#127—61no—
386#127—61no—
387#127—61no—
388#127—61no—
389#127—61no—
390#127C22×D311yescharacteristic
391#124—32no—
392#124—32no—
393#124C4×D312yes—
394#121—21no—
395#121—21no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—62no—
400#121—61no—
401#121—61no—
402#121—61no—
403#121—61no—
404#121—62no—
405#121—62no—
406#120—62no—
407#120—62no—
408#120—62no—
409#120—62no—
410#120—62no—
411#120—62no—
412C4×Q8—31no—
413C4×Q8—31no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—31no—
417C4×D4—31no—
418C4×D4—31no—
419C4×D4—31no—
420C4×D4—31no—
421C4×D4—31no—
422C4×D4—61no—
423C4×D4—61no—
424C4×D4—61no—
425C4×D4—61no—
426#117—31no—
427#117—31no—
428#117—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42C22×D311yescharacteristic
432C4⋊C8—21no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8—31no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439C4⋊C8—61no—
440C4⋊C8—61no—
441C4⋊C8—61no—
442C4⋊C8C22×D311yescharacteristic
443C4⋊C8C22×D311yescharacteristic
444C4⋊C8C22×D311yescharacteristic
445C4⋊C8C22×D311yescharacteristic
446C22⋊C8—21no—
447C22⋊C8—61no—
448C22⋊C8—61no—
449C22⋊C8—61no—
450C22⋊C8—61no—
451C22⋊C8—61no—
452#97—21no—
453#97—61no—
454#97—61no—
455#97—61no—
456C4×C8—61no—
457C4×C8—61no—
458C23×C3—22no—
459C23×C3C2×C22⋊C411yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—44no—
463C22×D3—44no—
464C22×D3—44no—
465C22×D3—82no—
466C22×D3—82no—
467C22×D3—82no—
468C22×D3—82no—
469C22×D3—82no—
470C22×D3—82no—
471C22×D3C2×C22⋊C411yescharacteristic
472C22×D3C2×C22⋊C411yescharacteristic
473C3×Q8—42no—
474C3×D4—42no—
475C3×D4—44no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—44no—
487C2×C3×C4C2×C22⋊C411yescharacteristic
488C2×C3×C4C2×C22⋊C411yescharacteristic
489C2×C3×C4C2×C22⋊C411yescharacteristic
490C2×C3×C4C23×C411yescharacteristic
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493#67—22no—
494#67—44no—
495#67—44no—
496#67—82no—
497#67—82no—
498#67—82no—
499#67—82no—
500#67#10014yes—
501C2×Dic3C2×C22⋊C411yescharacteristic
502C2×Dic3C2×C22⋊C411yescharacteristic
503C2×Dic3C2×C22⋊C411yescharacteristic
504C2×Dic3C2×C22⋊C411yescharacteristic
505C2×Dic3C2×C22⋊C411yescharacteristic
506C2×Dic3C2×C22⋊C411yescharacteristic
507D12—22no—
508D12—42no—
509D12—42no—
510D12—44no—
511D12—44no—
512D12—44no—
513D12—41no—
514D12—41no—
515D12—41no—
516D12—41no—
517D12—41no—
518D12—41no—
519D12—41no—
520D12—41no—
521D12—82no—
522D12—82no—
523C4×D3—22no—
524C4×D3—21no—
525C4×D3—21no—
526C4×D3—21no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—22no—
533C4×D3—44no—
534C4×D3—44no—
535Dic6—22no—
536C3×C8—41no—
537C3×C8—41no—
538C3×C8—41no—
539C3×C8—41no—
540C3⋊C8—41no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C3⋊C8—41no—
544C24—62no—
545C24—62no—
546C24—62no—
547#41—44no—
548#41—64no—
549#41—128no—
550#41—124no—
551#41—124no—
552C2×Q8—31no—
553C2×Q8C2×C4×D312yes—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—31no—
558C2×D4—31no—
559C2×D4—31no—
560C2×D4—32no—
561C2×D4—32no—
562C2×D4—62no—
563C2×D4—62no—
564C2×D4—62no—
565C2×D4—62no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—124no—
578C2×D4—128no—
579C2×D4—124no—
580C2×D4—124no—
581C2×D4—128no—
582C2×D4—128no—
583C2×D4—241no—
584C2×D4—241no—
585C2×D4—241no—
586C2×D4—241no—
587C2×D4—241no—
588C2×D4—241no—
589C2×D4—241no—
590C2×D4—241no—
591C2×D4—241no—
592C2×D4—241no—
593C2×D4—241no—
594C2×D4—241no—
595C2×D4C2×C4×D312yes—
596C22×C4—22no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4C2×C4×D311yescharacteristic
606C22×C4D3×D411yescharacteristic
607C22×C4D3×D411yescharacteristic
608M16—241no—
609M16—241no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—61no—
615C2×C8—61no—
616C2×C8—61no—
617C2×C8—61no—
618C2×C8—81no—
619C2×C8—241no—
620C2×C8—241no—
621C2×C8—241no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—62no—
639C22⋊C4—62no—
640C22⋊C4—62no—
641C22⋊C4—62no—
642C42—31no—
643C42—31no—
644C42—31no—
645C42—31no—
646C42—31no—
647C42—31no—
648C42C2×C4×D311yescharacteristic
649C42D3×D411yescharacteristic
650C42D3×D411yescharacteristic
651C42C23×D311yescharacteristic
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3C2×#10012yes—
658C22×C3C22×C22⋊C411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—164no—
671C2×D3—164no—
672C2×D3—164no—
673C2×D3C2×#10012yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—42no—
679C3×C4#57611yescharacteristic
680C3×C4#57611yescharacteristic
681C3×C4#57711yescharacteristic
682C3×C4#57711yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3C2×#10012yes—
689C23—22no—
690C23—31no—
691C23—31no—
692C23—62no—
693C23—62no—
694C23—124no—
695C23—124no—
696C23—124no—
697C23—242no—
698C23—242no—
699C23—242no—
700C23—242no—
701C23—242no—
702C23—242no—
703C23D3×C22⋊C411yescharacteristic
704Q8—42no—
705Q8—62no—
706D4—34no—
707D4—42no—
708D4—44no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—62no—
714D4—62no—
715D4—122no—
716D4—122no—
717D4—124no—
718D4—124no—
719D4—124no—
720D4—124no—
721D4—124no—
722D4—121no—
723D4—121no—
724D4—121no—
725D4—121no—
726D4—121no—
727D4—121no—
728D4—121no—
729D4—121no—
730D4—242no—
731D4—242no—
732D4—242no—
733D4—242no—
734D4—242no—
735D4—242no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—44no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—124no—
760C2×C4—124no—
761C2×C4D3×C22⋊C411yescharacteristic
762C2×C4D3×C22⋊C411yescharacteristic
763C2×C4D3×C22⋊C411yescharacteristic
764C2×C4C22×C4×D311yescharacteristic
765C2×C4C2×D3×D411yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—121no—
772C8—121no—
773C8—121no—
774C8—121no—
775C2×C3—22no—
776C2×C3—82no—
777C2×C3C22×#10011yescharacteristic
778C2×C3#289711yescharacteristic
779C2×C3#289711yescharacteristic
780D3—22no—
781D3—41no—
782D3—82no—
783D3—82no—
784C22—21no—
785C22—21no—
786C22—32no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—61no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—484no—
802C22—484no—
803C22—484no—
804C22D3×#10012yes—
805C22C2×D3×C22⋊C411yescharacteristic
806C4—21no—
807C4—21no—
808C4—21no—
809C4—21no—
810C4—32no—
811C4—42no—
812C4—61no—
813C4—61no—
814C4—61no—
815C4—61no—
816C4—61no—
817C4#576911yescharacteristic
818C4#577011yescharacteristic
819C4#577411yescharacteristic
820C4#577811yescharacteristic
821C3#1777011yescharacteristic, complemented, Sylow
822C2—22no—
823C2—62no—
824C2—82no—
825C2—121no—
826C2—242no—
827C2—242no—
828C2C2×D3×#10011yescharacteristic
829C2#7883111yescharacteristic
830C2#7888211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1551C2
socleC22×C3C22×C22⋊C4
prime radical#86242C2
cosocleC3×C42C24
hypercenter#1551D3
hypocenterC3#17770
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #79340C2semidirect
3. #79015C2semidirect
4. C3×#1551C2semidirect
5. #71807C2semidirect
6. #70818C2semidirect
7. C2×#4485C2semidirect
8. #68489C2semidirect
9. #68485C2semidirect
10. #68485C2semidirect
11. #68482C2semidirect
12. #68387C2semidirect
13. #68383C2semidirect
14. #68383C2semidirect
15. D3×#331C2semidirect
36. C3×#432C22semidirect
37. C2×C3×C4⋊C8C22semidirect
40. #4926C22semidirect
41. C2×C4⋊(C3⋊C8)C22semidirect
42. #4837C22semidirect
43. #4837C22semidirect
45. #4835C22semidirect
46. #4835C22semidirect
47. #4833C22semidirect
48. #4833C22semidirect
49. D3×C4⋊C8C22semidirect
50. D3×C4⋊C8C22semidirect
56. C3×#333C22semidirect
57. C3×#333C22semidirect
58. C3×#331C22semidirect
59. C3×#331C22semidirect
60. #4546C22semidirect
61. #4546C22semidirect
62. #4544C22semidirect
63. #4544C22semidirect
64. #4485C22semidirect
65. #4485C22semidirect
66. #4485C22semidirect
67. #4485C22semidirect
68. #4485C22semidirect
69. #4485C22semidirect
70. #4485C22semidirect
71. #4485C22semidirect
81. #1551D3semidirect
221. #432C2×D3semidirect
229. C2×C4⋊C8C2×D3semidirect
232. #333C2×D3semidirect
233. #333C2×D3semidirect
244. #331C2×D3semidirect
245. #331C2×D3semidirect
821. C3#17770semidirect

Maximal subgroups

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

subgroupindex
#862422
#793402
#790152
C3×#15512
#718072
#708182
C2×#44852
#684892
#684852
#684822
#683872
#683832
D3×#3312
#177703