Finite Group Databasebeta

← #11887647

Subgroups — #11887647

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic
3#10592743C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591185C211yesmaximal, characteristic, complemented
10C3⋊C8×#67C211yesmaximal, characteristic
11C2×#63566C211yesmaximal, characteristic, complemented
12#10590557C211yesmaximal, characteristic, complemented
13#10590518C211yesmaximal, characteristic, complemented
14#10590476C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83551—31nomaximal
17#80781—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×#888—21no—
30C3×#887C2211yescharacteristic
31C3×#67⋊C4—21no—
32C3×#878—21no—
33#63982—21no—
34#67⋊Dic3—21no—
35#63918C2211yescharacteristic
36#63893—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63856C2211yescharacteristic
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47#63634C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#807C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62#5635—31no—
63#5632D311yescharacteristic
64#5543—31no—
65C3×#467—31no—
66#5228—31no—
67#5228—31no—
68C2×#835—31no—
69C2×#835—31no—
70#5186—31no—
71#5182—31no—
72C8×#67—31no—
73C2×#816—31no—
74#5090—31no—
75#5079—31no—
76#5051—31no—
77#5051D311yescharacteristic, complemented
78#5050—31no—
79#5044—31no—
80#5044—31no—
81#5044—31no—
82#5044—61no—
83C4×#216—31no—
84#5021—31no—
85D4×C3⋊C8—31no—
86#4884—31no—
87#4875—31no—
88#4813—31no—
89D3×#103—31no—
90#4792—31no—
91#4790—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—41no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—22no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3718—22no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163#946—31no—
164Q8×Dic3—31no—
165#944C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216C2×D311yescharacteristic
171D4×Dic3—61no—
172C4×#67C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177#924—31no—
178#924C2×D311yescharacteristic
179C22×C3⋊C8—31no—
180C22×C3⋊C8C2×D311yescharacteristic
181C2×D3×C8—31no—
182#897—61no—
183#897C2×D311yescharacteristic
184#896—21no—
185D3×C4⋊C4—31no—
186#890—61no—
187#889—61no—
188#888—21no—
189#888—31no—
190#887C2×D311yescharacteristic
191#67⋊C4—21no—
192#67⋊C4—61no—
193#878—21no—
194#878—61no—
195#878—61no—
196#878—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#107—31no—
200C3×#103—31no—
201C3×#103—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835—61no—
214#835C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219(C2×D3)⋊C8—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226#810—31no—
227#810—31no—
228#810C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807—61no—
235#807C2×D311yescharacteristic
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251C3×#67Q1614yescomplemented
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271#627—81no—
272D3×Dic3—81no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—31no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—31no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8—121no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67#6711yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—121no—
317D3×Q8—22no—
318D3×Q8—41no—
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6—41no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—121no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—121no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—61no—
357#217—21no—
358#217—61no—
359#217#6711yescharacteristic
360#216—41no—
361#216—62no—
362#216—62no—
363#216—121no—
364#216—121no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—121no—
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—41no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406D3×C8—121no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C2×Q1612yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3C2×Q1612yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—31no—
431C2×Q16—91no—
432C2×Q16—91no—
433C22×C8—31no—
434C22×C8—91no—
435C4⋊Q8—31no—
436C4⋊Q8—61no—
437C4⋊Q8—91no—
438#125—181no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—61no—
442C22⋊Q8—61no—
443C22⋊Q8—91no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8D3211yescharacteristic
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—61no—
451C4×D4—181no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454#107—31no—
455#107—91no—
456#107—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×#6711yescharacteristic
475C22×D3C2×#6711yescharacteristic
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—122no—
490C3×D4—34no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67#21614yescomplemented
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—42no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—242no—
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—42no—
542C4×D3—241no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549Dic6—42no—
550Dic6—241no—
551Dic6—241no—
552Dic6#23712yes—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—121no—
562C3⋊C8—121no—
563C2×C32—22no—
564C2×C32#54611yescharacteristic
565C2×C32C22×Q1611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—62no—
573C2×Q8—61no—
574C2×Q8—62no—
575C2×Q8—121no—
576C2×Q8—121no—
577C2×Q8—181no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4C2×D3211yescharacteristic
586Q16—121no—
587Q16—182no—
588Q16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—121no—
594C2×C8—361no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
619C42—181no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3D3×Q1612yes—
632C22×C3C2×#21612yes—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×#6711yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C2×#21612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—62no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C2×#23711yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4#100411yescharacteristic
659C3×C4D3×#4111yescharacteristic
660Dic3—22no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3C2×#21612yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23D3×#6711yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8—32no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8—122no—
686Q8—721no—
687D4—34no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—721no—
706C2×C4—721no—
707C2×C4D3×#6711yescharacteristic
708C2×C4C22×D3211yescharacteristic
709C8—61no—
710C8—61no—
711C8—181no—
712C8—181no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—42no—
719C2×C3—62no—
720C2×C3#561011yescharacteristic
721C2×C3C2×D3×Q1611yescharacteristic
722C2×C3#577011yescharacteristic
723C2×C3#580611yescharacteristic
724C2×C3C22×#21611yescharacteristic
725C2×C3#583711yescharacteristic
726D3—22no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22D3×#21612yes—
733C22C2×D3×#6711yescharacteristic
734C4—21no—
735C4—32no—
736C4—41no—
737C4—41no—
738C4—61no—
739C4—62no—
740C4—61no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—361no—
745C4—361no—
746C4D3×#23711yescharacteristic
747C4#6431311yescharacteristic
748C3—21no—
749C3#8078111yescharacteristic, complemented
750C3#8355111yescharacteristic, complemented
751C2—22no—
752C2—62no—
753C2#1059515011yescharacteristic
754C2C2×D3×#21611yescharacteristic
755C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22⋊Q8D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592743C2semidirect
4. C3×#5051C2semidirect
5. #10591623C2semidirect
6. #10591594C2semidirect
7. #10591574C2semidirect
8. D3×#835C2semidirect
9. #10591185C2semidirect
11. C2×#63566C2semidirect
12. #10590557C2semidirect
13. #10590518C2semidirect
14. #10590476C2semidirect
15. #10590440C2semidirect
77. #5051D3semidirect
251. C3×#67Q16semidirect
520. #67#216semidirect
673. C32#3299semidirect
749. C3#80781semidirect
750. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
#105949932
#105927432
C3×#50512
#105916232
#105915942
#105915742
D3×#8352
#105911852
C3⋊C8×#672
C2×#635662
#105905572
#105905182
#105904762
#105904402
#835513
#807813