Finite Group Databasebeta

← #11887634

Subgroups — #11887634

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic
3#10592927C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591575C211yesmaximal, characteristic, complemented
9#10591551C211yesmaximal, characteristic, complemented
10D3×#835C211yesmaximal, characteristic, complemented
11#10591546C211yesmaximal, characteristic, complemented
12#10591537C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic
15#10591132C211yesmaximal, characteristic, complemented
16#83551—31nomaximal
17#78806—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#946—21no—
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944—21no—
27C3×#944C2211yescharacteristic
28C3×C4×#67—21no—
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924—21no—
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34Dic3×#67—21no—
35#63964—21no—
36#63918C2211yescharacteristic
37#63899—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63857C2211yescharacteristic
40#63846—21no—
41#63844C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic
63#5543—31no—
64#5511—31no—
65C2×C3×#103—31no—
66#5228—31no—
67#5228—31no—
68#5228—31no—
69#5228—61no—
70C2×#835—31no—
71C2×#835D311yescharacteristic, complemented
72#5116—31no—
73C8×#67—31no—
74#5090—31no—
75#5079—31no—
76#5051—31no—
77#5051—31no—
78#5044—31no—
79#5044—31no—
80C4×#216—31no—
81#5021—31no—
82D4×C3⋊C8—31no—
83#4970—31no—
84#4813—31no—
85#4811—31no—
86#4809—31no—
87D3×#103—31no—
88#4795—31no—
89#4793—31no—
90#4792—31no—
91#4790—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×D3×Dic3—21no—
110#3757—21no—
111#3756—22no—
112#3756—41no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
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×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3299—91noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C2×D311yescharacteristic
149C2×D3×Q8C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C2×C3×C4⋊C4—31no—
161#946—21no—
162#946C2×D311yescharacteristic
163Q8×Dic3C2×D311yescharacteristic
164#944—21no—
165#944C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216—61no—
173D4×Dic3—61no—
174C4×#67—21no—
175C4×#67—61no—
176C4×#67C2×D311yescharacteristic
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179#924—21no—
180#924—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184#924—61no—
185#924C2×D311yescharacteristic
186C22×C3⋊C8—31no—
187C22×C3⋊C8C2×D311yescharacteristic
188C2×Dic12—31no—
189C2×D3×C8—31no—
190#897—31no—
191#896—61no—
192D3×C4⋊C4—31no—
193#890—61no—
194#889—61no—
195#888—31no—
196#887—31no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—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#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—42no—
244C32×Q8#4112yes—
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
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67Q1614yescomplemented
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
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—91no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—31no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—22no—
295C2×C3×Q8—22no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—41no—
300C2×C3×Q8—42no—
301C2×C3×Q8—41no—
302C2×C3×Q8—41no—
303C2×C3×Q8—42no—
304C2×C3×Q8—61no—
305C2×C3×Q8—62no—
306C2×C3×Q8—121no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67#6711yescharacteristic
322C22×Dic3—21no—
323C22×Dic3—61no—
324D3×Q8—22no—
325D3×Q8—41no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—21no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#217#6711yescharacteristic
361#216—62no—
362#216—62no—
363#216—122no—
364#216—121no—
365#216—121no—
366#216—121no—
367#216—122no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4#6711yescharacteristic
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
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—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—41no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409Dic12—121no—
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C2×Q1612yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×Q1612yes—
418C32×C4—22no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C2×Q1612yes—
432C22×Q8—31no—
433C22×Q8D3211yescharacteristic
434C2×Q16—91no—
435C2×Q16—91no—
436C2×Q16—91no—
437C22×C8—31no—
438C22×C8—91no—
439C4⋊Q8—31no—
440C4⋊Q8—61no—
441C4⋊Q8—91no—
442#125—181no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449C22⋊Q8—181no—
450C22⋊Q8—181no—
451C4×Q8—31no—
452C4×Q8—91no—
453C4×D4—31no—
454C4×D4—61no—
455C4×D4—181no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—91no—
458#107—91no—
459#107—91no—
460#107—91no—
461C4⋊C8—91no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472C22⋊C8—91no—
473C22⋊C8—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3C2×#6711yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—22no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—42no—
491C3×Q8—42no—
492C3×Q8—44no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—122no—
496C3×Q8#23512yes—
497C3×Q8#23712yes—
498C3×D4—34no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—44no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67#21614yescomplemented
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—81no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—42no—
550C4×D3—241no—
551Dic6—21no—
552Dic6—21no—
553Dic6—42no—
554Dic6—61no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—121no—
559Dic6—121no—
560Dic6—241no—
561Dic6—241no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8—121no—
572C2×C32—22no—
573C2×C32#54611yescharacteristic
574C2×C32C22×Q1611yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—31no—
580C2×Q8—41no—
581C2×Q8—61no—
582C2×Q8—62no—
583C2×Q8—91no—
584C2×Q8—121no—
585C2×Q8—181no—
586C2×Q8C2×D3211yescharacteristic
587C2×Q8C2×D3211yescharacteristic
588C2×D4—31no—
589C22×C4—21no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4C2×D3211yescharacteristic
595Q16—182no—
596Q16—361no—
597Q16—361no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—91no—
601C2×C8—91no—
602C2×C8—121no—
603C2×C8—361no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—181no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3D3×Q1612yes—
641C22×C3C2×#21612yes—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C22×#6711yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3C2×#21612yes—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4#100411yescharacteristic
668C3×C4#100411yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681Dic3C2×#21612yes—
682C32#329911yescharacteristic, complemented, Sylow
683C23—31no—
684C23D3×#6711yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—42no—
689Q8—61no—
690Q8—61no—
691Q8—122no—
692Q8—181no—
693Q8—181no—
694Q8—721no—
695Q8#380412yes—
696D4—34no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—122no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—61no—
719C8—61no—
720C8—181no—
721C8—181no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—62no—
729C2×C3#549011yescharacteristic
730C2×C3#576211yescharacteristic
731C2×C3C2×D3×Q1611yescharacteristic
732C2×C3#580611yescharacteristic
733C2×C3C22×#21611yescharacteristic
734C2×C3#583711yescharacteristic
735D3—22no—
736C22—21no—
737C22—21no—
738C22—32no—
739C22—61no—
740C22—61no—
741C22D3×#21612yes—
742C22C2×D3×#6711yescharacteristic
743C4—21no—
744C4—22no—
745C4—32no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—361no—
754C4—361no—
755C4C2×#380411yescharacteristic
756C4#6433011yescharacteristic
757C3—21no—
758C3#7880611yescharacteristic, complemented
759C3#8355111yescharacteristic, complemented
760C2—22no—
761C2—62no—
762C2#1059531811yescharacteristic
763C2C2×D3×#21611yescharacteristic
764C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×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. #10592927C2semidirect
4. C2×C3×#835C2semidirect
5. #10591623C2semidirect
6. #10591596C2semidirect
7. #10591595C2semidirect
8. #10591575C2semidirect
9. #10591551C2semidirect
10. D3×#835C2semidirect
11. #10591546C2semidirect
12. #10591537C2semidirect
13. #10591187C2semidirect
15. #10591132C2semidirect
71. C2×#835D3semidirect
256. C3×#67Q16semidirect
531. #67#216semidirect
682. C32#3299semidirect
758. C3#78806semidirect
759. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
#105949882
#105929272
C2×C3×#8352
#105916232
#105915962
#105915952
#105915752
#105915512
D3×#8352
#105915462
#105915372
#105911872
C3⋊C8×#672
#105911322
#835513
#788063