Finite Group Databasebeta

← #11887252

Subgroups — #11887252

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10591188C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590616C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590577C211yesmaximal, characteristic, complemented
11#10590537C211yesmaximal, characteristic, complemented
12#10590536C211yesmaximal, characteristic, complemented
13#10590470C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#81445—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#929—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#926—21no—
25C3×#924C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#898—21no—
28C3×#897C2211yescharacteristic, complemented
29C3×#892C2211yescharacteristic, complemented
30C3×#890C2211yescharacteristic, complemented
31C3×#889—21no—
32C3×#887C2211yescharacteristic, complemented
33#63981—21no—
34#63974—21no—
35#63910—21no—
36#63909C2211yescharacteristic
37#63897—21no—
38#63894C2211yescharacteristic
39#63864C2211yescharacteristic
40C2×#3718C2211yescharacteristic, complemented
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5630—31no—
63#5550—31no—
64#5513D311yescharacteristic, complemented
65C3×#483—31no—
66#5068—31no—
67#5066—31no—
68#5051—31no—
69#5051—31no—
70#5048—31no—
71#5047—31no—
72#5046—31no—
73#5028—31no—
74C4×#215—31no—
75D4×C3⋊C8—31no—
76#5003—31no—
77#5002—31no—
78#4971D311yescharacteristic, complemented
79C2×#809—31no—
80C2×#809—31no—
81C2×#809—61no—
82#4871—31no—
83#4866—31no—
84#4864—31no—
85#4852—31no—
86#4808—31no—
87#4804—31no—
88#4800—31no—
89#4798—31no—
90#4731—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3718—41no—
141#3717—22no—
142#3717—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160C3×#117—61no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#947—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#215—31no—
168C2×#215—31no—
169#937—61no—
170#930—31no—
171#929—21no—
172C4×#67C2×D311yescharacteristic
173#926—21no—
174#924C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×D3×C8—31no—
183#898—21no—
184#897C2×D311yescharacteristic, complemented
185#895—31no—
186#895—61no—
187#894—61no—
188#894—61no—
189#893—31no—
190#892C2×D311yescharacteristic, complemented
191#890C2×D311yescharacteristic, complemented
192#889—21no—
193#887C2×D311yescharacteristic, complemented
194#884—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#875—31no—
199C4×D12—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810—31no—
216#810C2×D311yescharacteristic, complemented
217#810C2×D311yescharacteristic, complemented
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809—61no—
230#809—61no—
231#809—61no—
232#808C2×D311yescharacteristic, complemented
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)#4112yes—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—81no—
273#624—42no—
274#624—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—91no—
281#488—91no—
282#483—31no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—41no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—61no—
308C2×#67—61no—
309C2×#67#6711yescharacteristic
310#239—62no—
311#239—121no—
312#235—62no—
313#235—121no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—62no—
321C2×D12—62no—
322C2×D12—64no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—121no—
328C2×D12—121no—
329C2×D12—121no—
330C2×D12—122no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366C3×C42—61no—
367#217—21no—
368#217—21no—
369#217#6711yescharacteristic
370#216—121no—
371#216—121no—
372#215—62no—
373#215—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3—21no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—122no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410#204—121no—
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32#13512yes—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—84no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C22×C8—91no—
444C22×C8—91no—
445#126—61no—
446#125—31no—
447#125—61no—
448#124—91no—
449#123—61no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—31no—
458C4×D4—31no—
459C4×D4—91no—
460#117—31no—
461#117—61no—
462C2×C4⋊C4D3211yescharacteristic
463C2×C22⋊C4—181no—
464#107—91no—
465#106—31no—
466#106—31no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—124no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—242no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—242no—
500C22×D3C2×#6711yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—62no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
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—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—42no—
524C2×C3×C4—42no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—82no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—22no—
537#67—122no—
538#67—241no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546D12—32no—
547D12—32no—
548D12—62no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—121no—
557D12—121no—
558D12—122no—
559D12—122no—
560D12—124no—
561D12—122no—
562D12—241no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—122no—
566C4×D3—122no—
567C4×D3—241no—
568C4×D3—241no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6—21no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—22no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—42no—
588C3⋊D3—81no—
589C3×D3—41no—
590C24—181no—
591#41—182no—
592#41—361no—
593C2×Q8—31no—
594C2×Q8—31no—
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—361no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—182no—
610SD16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8—361no—
617C4⋊C4—21no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4C2×D3211yescharacteristic
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—61no—
641C42—61no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3#91612yes—
654C22×C3#95012yes—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—122no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C2×D3—248no—
681C3×C4—22no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4D3×#4111yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4#100911yescharacteristic
702C3×C4#100911yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710C32#329611yescharacteristic, complemented, Sylow
711C23—31no—
712C23—181no—
713C23—181no—
714C23—362no—
715C23—362no—
716C23—721no—
717C23D3×#6711yescharacteristic
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—61no—
722D4—62no—
723D4—92no—
724D4—181no—
725D4—181no—
726D4—181no—
727D4—362no—
728D4—362no—
729D4—721no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—42no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—362no—
745C2×C4—721no—
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—61no—
749C8—61no—
750C8—181no—
751C8—181no—
752C2×C3—24no—
753C2×C3—22no—
754C2×C3—22no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—121no—
759C2×C3#565411yescharacteristic
760C2×C3C2×#91611yescharacteristic
761C2×C3#577811yescharacteristic
762C2×C3C2×#95011yescharacteristic
763C2×C3#582911yescharacteristic
764C2×C3#583711yescharacteristic
765D3—41no—
766D3—122no—
767D3—122no—
768D3—242no—
769D3—242no—
770D3—241no—
771D3—241no—
772C22—21no—
773C22—21no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—724no—
784C22#6393512yes—
785C22C2×D3×#6711yescharacteristic
786C4—21no—
787C4—41no—
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4#6430611yescharacteristic
797C4#6430811yescharacteristic
798C3—21no—
799C3#8144511yescharacteristic, complemented
800C3#8359811yescharacteristic, complemented
801C2—22no—
802C2—121no—
803C2—362no—
804C2—721no—
805C2#1059506811yescharacteristic
806C2C2×#6393511yescharacteristic
807C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5513C2semidirect
3. C2×#63636C2semidirect
4. C3×#4971C2semidirect
5. #10591188C2semidirect
6. #10591183C2semidirect
7. #67⋊(C3⋊C8)C2semidirect
8. #10590616C2semidirect
9. #10590610C2semidirect
10. #10590577C2semidirect
11. #10590537C2semidirect
12. #10590536C2semidirect
13. #10590470C2semidirect
14. #10590458C2semidirect
15. #10590425C2semidirect
28. C3×#897C22semidirect
29. C3×#892C22semidirect
30. C3×#890C22semidirect
32. C3×#887C22semidirect
40. C2×#3718C22semidirect
43. C2×D3×C3⋊C8C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. #63576C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5513D3semidirect
78. #4971D3semidirect
184. #897C2×D3semidirect
190. #892C2×D3semidirect
191. #890C2×D3semidirect
193. #887C2×D3semidirect
216. #810C2×D3semidirect
217. #810C2×D3semidirect
232. #808C2×D3semidirect
233. #808C2×D3semidirect
710. C32#3296semidirect
799. C3#81445semidirect
800. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
#105950182
C2×#636362
C3×#49712
#105911882
#105911832
#67⋊(C3⋊C8)2
#105906162
#105906102
#105905772
#105905372
#105905362
#105904702
#105904582
#105904252
#835983
#814453