Finite Group Databasebeta

← #11889708

Subgroups — #11889708

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5511C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592669C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic, complemented
8#10590614C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10#10590532C211yesmaximal, characteristic, complemented
11#10590531C211yesmaximal, characteristic, complemented
12#10590503C211yesmaximal, characteristic, complemented
13#10590498C211yesmaximal, characteristic, complemented
14#10590463C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#78763—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×C4×#67—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#924—21no—
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#897C2211yescharacteristic, complemented
28C3×#896—21no—
29C3×D3×C4⋊C4C2211yescharacteristic, complemented
30C3×#889—21no—
31C3×#888C2211yescharacteristic, complemented
32C3×#887C2211yescharacteristic, complemented
33#63976—21no—
34D3×#217—21no—
35#63908C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63885—21no—
38#63884—21no—
39#63860C2211yescharacteristic
40C2×#3719C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#554—31no—
62#5806—31no—
63#5550—31no—
64#5511D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5218—31no—
67#5116—31no—
68#5111—31no—
69#5089—31no—
70#5087—31no—
71#5051—31no—
72#5049—31no—
73#5047—31no—
74#5046—31no—
75#5028—31no—
76#5026—31no—
77#5011—31no—
78#4970—31no—
79#4970—31no—
80#4970—61no—
81#4967—31no—
82#4966—31no—
83C2×#809D311yescharacteristic, complemented
84#4783—31no—
85#4780—31no—
86#4774—31no—
87#4771—31no—
88#4767—31no—
89#4765—31no—
90#4759—31no—
91#4757—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
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×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3719—41no—
141#3715—22no—
142#3715—41no—
143#3711—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×#125—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#953—61no—
164C2×#217—61no—
165C2×#216—31no—
166C2×#215—31no—
167C2×#215—31no—
168#939—61no—
169#938—31no—
170#937—61no—
171#936—31no—
172#935—61no—
173D4×Dic3—31no—
174C2×#214—31no—
175C2×#214—31no—
176#930—31no—
177C4×#67—21no—
178C4×#67C2×D311yescharacteristic
179#924—21no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×Dic12—31no—
187C2×ΓL(1,𝔽25)—31no—
188#897C2×D311yescharacteristic, complemented
189#896—21no—
190#894—61no—
191D3×C4⋊C4C2×D311yescharacteristic, complemented
192#889—21no—
193#888C2×D311yescharacteristic, complemented
194#887C2×D311yescharacteristic, complemented
195#884—61no—
196D3×C22⋊C4—61no—
197#875—31no—
198C4×D12—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213#816—31no—
214#815—31no—
215Dic3⋊C8—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810—61no—
223#809—31no—
224#809—31no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—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—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—81no—
273#625—42no—
274#625—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—31no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—121no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67#6711yescharacteristic
319C22×Dic3—61no—
320C22×Dic3—61no—
321#237—62no—
322#237—121no—
323#235—62no—
324#235—121no—
325C2×D12—22no—
326C2×D12—21no—
327C2×D12—41no—
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—21no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—41no—
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×C42—31no—
363C3×C42—61no—
364#217—21no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—121no—
372#217#6711yescharacteristic
373#216—121no—
374#215—62no—
375#215—121no—
376#214—62no—
377#214—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—21no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—41no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409Dic12—121no—
410ΓL(1,𝔽25)—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13712yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—31no—
445#125—61no—
446#124—91no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—61no—
451C22⋊Q8—61no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—61no—
459C4×D4—91no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4D3211yescharacteristic
462C2×C22⋊C4—181no—
463#107—91no—
464#107—91no—
465#107—91no—
466C4⋊C8—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×#6711yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—241no—
498C3×D4—32no—
499C3×D4—62no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—122no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
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—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—81no—
526C2×C3×C4—81no—
527C2×C3×C4—82no—
528C2×C3×C4—241no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—22no—
534#67—122no—
535#67—122no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—241no—
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551D12—21no—
552D12—21no—
553D12—21no—
554D12—42no—
555D12#23512yes—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—81no—
559C4×D3—122no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—81no—
568Dic6—121no—
569Dic6—121no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8—121no—
580C2×C32—22no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3×D3—41no—
585C3×D3—42no—
586C3×D3—81no—
587C24—61no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—61no—
592C2×Q8—91no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—181no—
600C2×D4—181no—
601C22×C4—21no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607Q16—361no—
608SD16—182no—
609SD16—361no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—121no—
616C4⋊C4—21no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—61no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—244no—
657C22×C3#91512yes—
658C22×C3#94212yes—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—22no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23511yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4#100911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#331411yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—61no—
706C23—122no—
707C23—122no—
708C23—241no—
709C23D3×#6711yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714Q8—241no—
715D4—32no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—122no—
721D4—362no—
722D4—721no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—81no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4D3×#6711yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—61no—
743C8—61no—
744C8—181no—
745C8—181no—
746C2×C3—22no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—42no—
752C2×C3—121no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#549011yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3C2×#91511yescharacteristic
758C2×C3C2×#94211yescharacteristic
759C2×C3#582911yescharacteristic
760C2×C3#583511yescharacteristic
761D3—42no—
762D3—41no—
763D3—81no—
764C22—21no—
765C22—21no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22#6394612yes—
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4—361no—
788C4D3×#23511yescharacteristic
789C4#6430711yescharacteristic
790C3—21no—
791C3#7876311yescharacteristic, complemented
792C3#8363511yescharacteristic, complemented
793C2—22no—
794C2—121no—
795C2—122no—
796C2—241no—
797C2#1059506511yescharacteristic
798C2#1059509611yescharacteristic
799C2C2×#6394611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3314
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×#5511C2semidirect
3. #10592669C2semidirect
4. C2×C3×#809C2semidirect
5. #10591187C2semidirect
6. #10591169C2semidirect
7. #10591155C2semidirect
8. #10590614C2semidirect
9. #10590607C2semidirect
10. #10590532C2semidirect
11. #10590531C2semidirect
12. #10590503C2semidirect
13. #10590498C2semidirect
14. #10590463C2semidirect
15. #10590454C2semidirect
27. C3×#897C22semidirect
29. C3×D3×C4⋊C4C22semidirect
31. C3×#888C22semidirect
32. C3×#887C22semidirect
40. C2×#3719C22semidirect
43. C2×#3711C22semidirect
45. #63637C22semidirect
46. #63637C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
64. #5511D3semidirect
83. C2×#809D3semidirect
188. #897C2×D3semidirect
191. D3×C4⋊C4C2×D3semidirect
193. #888C2×D3semidirect
194. #887C2×D3semidirect
702. C32#3314semidirect
791. C3#78763semidirect
792. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#55112
#105948862
#105926692
C2×C3×#8092
#105911872
#105911692
#105911552
#105906142
#105906072
#105905322
#105905312
#105905032
#105904982
#105904632
#105904542
#836353
#787633