Finite Group Databasebeta

← #11889739

Subgroups — #11889739

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5730C211yesmaximal, characteristic, complemented
2#10594007C211yesmaximal, characteristic
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5089C211yesmaximal, characteristic, complemented
5#10590616C211yesmaximal, characteristic, complemented
6#10590609C211yesmaximal, characteristic, complemented
7#10590596C211yesmaximal, characteristic, complemented
8D3×#809C211yesmaximal, characteristic, complemented
9#10590518C211yesmaximal, characteristic, complemented
10#10590517C211yesmaximal, characteristic, complemented
11#10590503C211yesmaximal, characteristic, complemented
12#10590498C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#81700—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#946—21no—
23C3×#946—21no—
24C3×#897C2211yescharacteristic
25C3×#897C2211yescharacteristic, complemented
26C3×#893—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29C3×#890—21no—
30C3×#875C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63922—21no—
34#63921—21no—
35#63912—21no—
36#63908C2211yescharacteristic
37#63856C2211yescharacteristic
38#63854—21no—
39C2×#3718C2211yescharacteristic, complemented
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#554—31no—
62#5730D311yescharacteristic, complemented
63#5676—31no—
64#5550—31no—
65C3×#489—31no—
66#5089D311yescharacteristic, complemented
67#5087—31no—
68#5087—31no—
69#5087—61no—
70#5054—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#4967—31no—
80#4966—31no—
81C2×#809—31no—
82#4813—31no—
83#4811—31no—
84#4808—31no—
85#4803—31no—
86#4780—31no—
87#4776—31no—
88#4774—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110#3799—22no—
111#3799—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3718—41no—
140#3717—22no—
141#3715—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C3×C4⋊Q8—21no—
150C3×C4⋊Q8C2×D311yescharacteristic, complemented
151C3×C4⋊Q8C2×D311yescharacteristic, complemented
152C3×#125—61no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163#946—21no—
164#946—21no—
165#946—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#215—31no—
169C2×#215—31no—
170#938—31no—
171#937—61no—
172C2×#214—31no—
173#930—31no—
174#924—31no—
175C2×#208—31no—
176C22×C3⋊C8—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#897C2×D311yescharacteristic
181#897C2×D311yescharacteristic, complemented
182#894—61no—
183#893—21no—
184D3×C4⋊C4C2×D311yescharacteristic
185D3×C4⋊C4C2×D311yescharacteristic, complemented
186#890—21no—
187#884—61no—
188#884—61no—
189#883—61no—
190#882—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#875C2×D311yescharacteristic
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#97—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#818—31no—
213#816—31no—
214#810—31no—
215#810C2×D311yescharacteristic, complemented
216#810C2×D311yescharacteristic, complemented
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809—61no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807—61no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic, complemented
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—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—22no—
261C3×D12—21no—
262C3×D12—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274#626—42no—
275#625—81no—
276#624—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—31no—
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—91no—
296C23×D3—61no—
297C23×D3—61no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—41no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313#239—62no—
314#239—121no—
315D3×D4—62no—
316D3×D4—121no—
317#235—62no—
318#235—121no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12#6711yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×C4×D3C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
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⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—61no—
365C3×C42C22×D311yescharacteristic
366C3×C42C22×D311yescharacteristic
367#217—61no—
368#217—61no—
369#216—121no—
370#216—121no—
371#215—62no—
372#215—121no—
373#214—121no—
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—21no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3#6711yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
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
408#204—62no—
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
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—
423C2×C3×D3#13712yes—
424D32—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8D3211yescharacteristic, complemented
445#125—61no—
446#124—31no—
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⋊C4—31no—
462C2×C22⋊C4—181no—
463#107—91no—
464#107—91no—
465#107—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—31no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×#6711yescharacteristic
494C22×D3C2×#6711yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—81no—
500C3×Q8—81no—
501C3×Q8—82no—
502C3×D4—62no—
503C3×D4—61no—
504C3×D4—61no—
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—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—61no—
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—241no—
524C2×C3×C4—241no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—122no—
532#67—122no—
533#67—241no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543D12—22no—
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553D12—122no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—242no—
565Dic6—21no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C3⋊C8—121no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13711yescharacteristic
581C2×C32#57611yescharacteristic
582C3⋊D3—42no—
583C3×D3—22no—
584C3×D3—41no—
585C3×D3—81no—
586C24—181no—
587#41—182no—
588#41—361no—
589C2×Q8—21no—
590C2×Q8—31no—
591C2×Q8—31no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—91no—
595C2×D4—181no—
596C2×D4—182no—
597C2×D4—181no—
598C2×D4—181no—
599C2×D4—361no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606Q16—361no—
607SD16—182no—
608SD16—361no—
609M16—361no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—91no—
614C2×C8—361no—
615C4⋊C4—21no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—61no—
637C42C2×D3211yescharacteristic
638C22×C3—21no—
639C22×C3—32no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—122no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—241no—
666C2×D3—241no—
667C2×D3—244no—
668C2×D3—244no—
669C2×D3#94212yes—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4#100911yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#331411yescharacteristic, complemented, Sylow
702C23—31no—
703C23—31no—
704C23—61no—
705C23—181no—
706C23—362no—
707C23—362no—
708C23—721no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—81no—
714D4—62no—
715D4—61no—
716D4—61no—
717D4—92no—
718D4—181no—
719D4—362no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—181no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—362no—
737C2×C4—721no—
738C2×C4D3×#6711yescharacteristic
739C2×C4D3×#6711yescharacteristic
740C2×C4C22×D3211yescharacteristic
741C8—61no—
742C8—61no—
743C8—181no—
744C8—181no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—62no—
749C2×C3—121no—
750C2×C3—241no—
751C2×C3#567611yescharacteristic
752C2×C3#577411yescharacteristic
753C2×C3D3×#13711yescharacteristic
754C2×C3C2×#94211yescharacteristic
755C2×C3#582911yescharacteristic
756C2×C3#583511yescharacteristic
757D3—22no—
758D3—41no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—182no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22C2×D3×#6711yescharacteristic
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4#6431911yescharacteristic
788C4#6432011yescharacteristic
789C3—21no—
790C3#8170011yescharacteristic, complemented
791C3#8363511yescharacteristic, complemented
792C2—62no—
793C2—121no—
794C2—241no—
795C2—362no—
796C2#1059509711yescharacteristic
797C2D3×#94211yescharacteristic
798C2#1059542811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4⋊Q8D32
hypocenterC32#3314
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×#5730C2semidirect
3. #10592786C2semidirect
4. C3×#5089C2semidirect
5. #10590616C2semidirect
6. #10590609C2semidirect
7. #10590596C2semidirect
8. D3×#809C2semidirect
9. #10590518C2semidirect
10. #10590517C2semidirect
11. #10590503C2semidirect
12. #10590498C2semidirect
13. #10590362C2semidirect
14. #10590326C2semidirect
15. #10590267C2semidirect
20. C32×C4⋊Q8C22semidirect
25. C3×#897C22semidirect
28. C3×D3×C4⋊C4C22semidirect
32. C3×C4×Dic6C22semidirect
39. C2×#3718C22semidirect
42. C2×#3711C22semidirect
46. #63634C22semidirect
47. #63634C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #5730D3semidirect
66. #5089D3semidirect
150. C3×C4⋊Q8C2×D3semidirect
151. C3×C4⋊Q8C2×D3semidirect
181. #897C2×D3semidirect
185. D3×C4⋊C4C2×D3semidirect
198. C4×Dic6C2×D3semidirect
215. #810C2×D3semidirect
216. #810C2×D3semidirect
237. #803C2×D3semidirect
444. C4⋊Q8D32semidirect
701. C32#3314semidirect
790. C3#81700semidirect
791. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
#105940072
#105927862
C3×#50892
#105906162
#105906092
#105905962
D3×#8092
#105905182
#105905172
#105905032
#105904982
#105903622
#105903262
#105902672
#836353
#817003