Finite Group Databasebeta

← #11889283

Subgroups — #11889283

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5584C211yesmaximal, characteristic, complemented
2#10594007C211yesmaximal, characteristic
3#10592725C211yesmaximal, characteristic, complemented
4C3×#5028C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591634C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11#10590521C211yesmaximal, characteristic, complemented
12#10590502C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590300C211yesmaximal, characteristic, complemented
15#10590280C211yesmaximal, characteristic, complemented
16#83665—31nomaximal
17#80617—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#898—21no—
28C3×#898—21no—
29C3×#892C2211yescharacteristic
30C3×#892C2211yescharacteristic, complemented
31C3×#875—21no—
32C3×#875C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34C3×#869C2211yescharacteristic, complemented
35C3×C4×Dic6—21no—
36#63922—21no—
37#63921—21no—
38#63912—21no—
39#63908C2211yescharacteristic
40#63856C2211yescharacteristic
41#63854—21no—
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#556—31no—
62#5676—31no—
63#5584D311yescharacteristic, complemented
64#5550—31no—
65C3×#464—31no—
66#5189—31no—
67#5187—31no—
68#5171—31no—
69#5169—31no—
70#5089—31no—
71#5084—31no—
72#5055—31no—
73#5052—31no—
74#5048—31no—
75#5047—31no—
76#5046—31no—
77#5028D311yescharacteristic, complemented
78#5026—31no—
79#5026—31no—
80#5026—61no—
81#5011—31no—
82#5003—31no—
83#5002—31no—
84#5001—31no—
85#4996—31no—
86#4842—31no—
87#4836—31no—
88#4815—31no—
89#4804—31no—
90#4779—31no—
91#4770—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3799—22no—
109#3799—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3755—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—41no—
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3311—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#126—61no—
153C3×#126—61no—
154C3×#124—31no—
155C3×#124—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—61no—
160C3×C4×Q8C2×D311yescharacteristic, complemented
161C3×C4×Q8C2×D311yescharacteristic, complemented
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—31no—
165#946—31no—
166#946C2×D311yescharacteristic
167#946C2×D311yescharacteristic, complemented
168C2×#216C2×D311yescharacteristic, complemented
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—61no—
172C2×#215C2×D311yescharacteristic
173#938—31no—
174#937—61no—
175#930—31no—
176#924—31no—
177C2×#208—31no—
178C22×C3⋊C8—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181#898—21no—
182#898—21no—
183#894—61no—
184#892C2×D311yescharacteristic
185#892C2×D311yescharacteristic, complemented
186#884—61no—
187#884—61no—
188#883—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192#875—21no—
193#875C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198#869C2×D311yescharacteristic, complemented
199C4×Dic6—21no—
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#102—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#832—31no—
209#832—31no—
210#830—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216#817—31no—
217#817—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235#803—31no—
236#803—31no—
237#803—61no—
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—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—41no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#626—42no—
272#626—42no—
273#625—81no—
274#624—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—31no—
280#546—91no—
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—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309#239—62no—
310#239—121no—
311D3×D4—62no—
312D3×D4—121no—
313#235—62no—
314#235—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—121no—
322C2×D12#6711yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3C22×D311yescharacteristic
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—121no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—61no—
366#217—61no—
367#216—41no—
368#215—41no—
369#215—62no—
370#215—62no—
371#215—64no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383(C2×D3)⋊C4#6711yescharacteristic
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3#6711yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398#208—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408ΓL(1,𝔽25)—121no—
409D3×C8—121no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
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—41no—
423D32—84no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—91no—
437C22×D4—91no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×M16—91no—
442C22×C8—91no—
443C4⋊Q8—31no—
444#126—61no—
445#126—61no—
446#124—31no—
447#124—61no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452#121—91no—
453#121—181no—
454#120—181no—
455C4×Q8—61no—
456C4×Q8D3211yescharacteristic, complemented
457C4×D4—31no—
458C4×D4—91no—
459#117—31no—
460#117—31no—
461C2×C22⋊C4—181no—
462#107—91no—
463#106—91no—
464#106—91no—
465C4⋊C8—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3—122no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3C2×#6711yescharacteristic
493C22×D3C2×#6711yescharacteristic
494C3×Q8—22no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—122no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—121no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—122no—
531#67—122no—
532#67—241no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—21no—
543D12—21no—
544D12—32no—
545D12—32no—
546D12—41no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—122no—
552D12—122no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—242no—
562Dic6—21no—
563Dic6—21no—
564Dic6—42no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—62no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32#54611yescharacteristic
576C2×C32#57511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—42no—
579C3×D3—41no—
580C3×D3—41no—
581C3×D3—81no—
582C24—181no—
583#41—182no—
584#41—361no—
585C2×Q8—31no—
586C2×Q8—61no—
587C2×Q8C2×D3211yescharacteristic
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—182no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—361no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—181no—
599C22×C4—181no—
600Q16—121no—
601SD16—121no—
602SD16—182no—
603M16—361no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—361no—
609C4⋊C4—21no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—21no—
631C42—61no—
632C42—61no—
633C42C2×D3211yescharacteristic
634C22×C3—21no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×#6711yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—244no—
665C2×D3—244no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#331111yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705Q8—21no—
706Q8—21no—
707Q8—61no—
708Q8—61no—
709Q8—122no—
710D4—61no—
711D4—61no—
712D4—92no—
713D4—121no—
714D4—181no—
715D4—362no—
716D4—362no—
717D4—721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—121no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#561211yescharacteristic
746C2×C3#577011yescharacteristic
747C2×C3#577711yescharacteristic
748C2×C3#582211yescharacteristic
749C2×C3#582911yescharacteristic
750C2×C3#583711yescharacteristic
751D3—41no—
752D3—41no—
753D3—81no—
754D3—122no—
755D3—122no—
756D3—242no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—182no—
767C22—361no—
768C22—361no—
769C22—724no—
770C22C2×D3×#6711yescharacteristic
771C4—21no—
772C4—21no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4#6430611yescharacteristic
782C4#6430711yescharacteristic
783C3—21no—
784C3#8061711yescharacteristic, complemented
785C3#8366511yescharacteristic, complemented
786C2—121no—
787C2—121no—
788C2—241no—
789C2—362no—
790C2#1059507011yescharacteristic
791C2#1059531711yescharacteristic
792C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4×Q8D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5584C2semidirect
3. #10592725C2semidirect
4. C3×#5028C2semidirect
5. #10591657C2semidirect
6. #10591651C2semidirect
7. #10591638C2semidirect
8. #10591634C2semidirect
9. #10590610C2semidirect
10. #10590592C2semidirect
11. #10590521C2semidirect
12. #10590502C2semidirect
13. #10590330C2semidirect
14. #10590300C2semidirect
15. #10590280C2semidirect
20. C32×C4×Q8C22semidirect
24. C3×#946C22semidirect
25. C2×C3×#216C22semidirect
30. C3×#892C22semidirect
34. C3×#869C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63662C22semidirect
46. #63634C22semidirect
47. #63630C22semidirect
48. C3×#810C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5584D3semidirect
77. #5028D3semidirect
160. C3×C4×Q8C2×D3semidirect
161. C3×C4×Q8C2×D3semidirect
167. #946C2×D3semidirect
168. C2×#216C2×D3semidirect
185. #892C2×D3semidirect
198. #869C2×D3semidirect
220. #810C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
456. C4×Q8D32semidirect
697. C32#3311semidirect
784. C3#80617semidirect
785. C3#83665semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
#105940072
#105927252
C3×#50282
#105916572
#105916512
#105916382
#105916342
#105906102
#105905922
#105905212
#105905022
#105903302
#105903002
#105902802
#836653
#806173