Finite Group Databasebeta

← #11887636

Subgroups — #11887636

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5#10591635C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591574C211yesmaximal, characteristic, complemented
9Dic3×#216C211yesmaximal, characteristic, complemented
10#10591551C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10591546C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic
15#10591103C211yesmaximal, characteristic, complemented
16#83551—31nomaximal
17#80193—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#946—21no—
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944—21no—
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67C2211yescharacteristic
31C3×#924—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63982—21no—
35#67⋊Dic3—21no—
36#63918C2211yescharacteristic
37#63893—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63856C2211yescharacteristic
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic
63#5635—31no—
64#5543—31no—
65C3×#451—31no—
66#5228—31no—
67#5228D311yescharacteristic, complemented
68C2×#835—31no—
69C2×#835—31no—
70C2×#835—31no—
71C2×#835—61no—
72#5188—31no—
73#5186—31no—
74#5182—31no—
75Dic3×Q16—31no—
76#5090—31no—
77#5079—31no—
78#5051—31no—
79#5051—31no—
80#5051—31no—
81#5044—31no—
82#5044—31no—
83C4×#216—31no—
84#5021—31no—
85D4×C3⋊C8—31no—
86#4811—31no—
87D3×#103—31no—
88#4793—31no—
89#4792—31no—
90#67⋊C8—31no—
91#4722—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
99C22×C3⋊Dic3—21no—
100C2×C3×#67D411yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109C2×D3×Dic3—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—22no—
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
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⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
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#3718—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
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C3×C4⋊Q8—31no—
153C3×C4⋊Q8—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162#946—21no—
163#946—31no—
164#946C2×D311yescharacteristic
165Q8×Dic3—31no—
166Q8×Dic3C2×D311yescharacteristic
167#944—21no—
168#944C2×D311yescharacteristic
169C2×#216—31no—
170C2×#216—31no—
171C2×#216C2×D311yescharacteristic
172C2×#216C2×D311yescharacteristic
173D4×Dic3—61no—
174C4×#67—21no—
175C4×#67C2×D311yescharacteristic
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180#924—21no—
181#924—31no—
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×D3×C8—31no—
189#897—61no—
190D3×C4⋊C4—31no—
191#890—61no—
192#889—61no—
193#888—31no—
194#67⋊C4—61no—
195#878—61no—
196#878—61no—
197#878—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—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—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835—61no—
217#835—61no—
218#835—61no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#818—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#810—31no—
231#810—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—
254C2×C3⋊Dic3—81no—
255C3×#67Q1614yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
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—31no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—91no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—24no—
295C2×C3×Q8—22no—
296C2×C3×Q8—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—41no—
302C2×C3×Q8—41no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—61no—
306C2×C3×Q8—62no—
307C2×C3×Q8—121no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×D4—31no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67#6711yescharacteristic
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—121no—
326D3×Q8—22no—
327D3×Q8—41no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—62no—
337C3×Q16—121no—
338C2×C3×C8—31no—
339C2×C3×C8—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×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—61no—
356#217—21no—
357#217—21no—
358#217—61no—
359#217#6711yescharacteristic
360#216—22no—
361#216—41no—
362#216—121no—
363#216—121no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4#6711yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—121no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4#6711yescharacteristic
393C4×Dic3—21no—
394C4×Dic3—61no—
395C4×Dic3—61no—
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
409D3×C8—121no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C2×Q1612yes—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3C2×Q1612yes—
417C32×C4—21no—
418C32×C4—22no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3C2×Q1612yes—
431C22×Q8—31no—
432C22×Q8D3211yescharacteristic
433C2×Q16—31no—
434C2×Q16—31no—
435C2×Q16—91no—
436C22×C8—91no—
437C22×C8—91no—
438C4⋊Q8—31no—
439C4⋊Q8—61no—
440C4⋊Q8—91no—
441#125—181no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C4×Q8—31no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—181no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457#107—91no—
458#107—91no—
459#107—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3C2×#6711yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—42no—
490C3×Q8—42no—
491C3×Q8—44no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×Q8#23712yes—
498C3×Q8#23712yes—
499C3×D4—34no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
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—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—44no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
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—121no—
541C2×Dic3—121no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—242no—
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—241no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557Dic6—42no—
558Dic6—241no—
559Dic6—241no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—121no—
569C3⋊C8—121no—
570C2×C32—22no—
571C2×C32#54611yescharacteristic
572C2×C32C22×Q1611yescharacteristic
573C2×C32#57711yescharacteristic
574C3×D3—22no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—31no—
578C2×Q8—31no—
579C2×Q8—41no—
580C2×Q8—61no—
581C2×Q8—62no—
582C2×Q8—121no—
583C2×Q8—181no—
584C2×Q8C2×D3211yescharacteristic
585C2×Q8C2×D3211yescharacteristic
586C2×D4—31no—
587C22×C4—21no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593Q16—62no—
594Q16—121no—
595Q16—361no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8—91no—
600C2×C8—361no—
601C2×C8—361no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C42—31no—
625C42—61no—
626C42—181no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3D3×Q1612yes—
639C22×C3C2×#21612yes—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3C2×#21612yes—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×#23711yescharacteristic
665C3×C4#100411yescharacteristic
666C3×C4#100411yescharacteristic
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679Dic3C2×#21612yes—
680C32#329911yescharacteristic, complemented, Sylow
681C23—31no—
682C23D3×#6711yescharacteristic
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—42no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—61no—
691Q8—122no—
692Q8—721no—
693Q8#380512yes—
694D4—34no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—42no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—122no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4D3×#6711yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—61no—
717C8—61no—
718C8—181no—
719C8—181no—
720C2×C3—24no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—62no—
727C2×C3#559111yescharacteristic
728C2×C3C2×D3×Q1611yescharacteristic
729C2×C3#577811yescharacteristic
730C2×C3#580611yescharacteristic
731C2×C3C22×#21611yescharacteristic
732C2×C3#583711yescharacteristic
733D3—22no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22D3×#21612yes—
740C22C2×D3×#6711yescharacteristic
741C4—21no—
742C4—22no—
743C4—32no—
744C4—41no—
745C4—61no—
746C4—61no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—361no—
752C4—361no—
753C4C2×#380511yescharacteristic
754C4#6433011yescharacteristic
755C3—21no—
756C3#8019311yescharacteristic, complemented
757C3#8355111yescharacteristic, complemented
758C2—22no—
759C2—62no—
760C2#1059531911yescharacteristic
761C2C2×D3×#21611yescharacteristic
762C2#1059549411yescharacteristic
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. C2×#63662C2semidirect
4. C3×#5228C2semidirect
5. #10591635C2semidirect
6. #10591623C2semidirect
7. #10591594C2semidirect
8. #10591574C2semidirect
9. Dic3×#216C2semidirect
10. #10591551C2semidirect
11. D3×#835C2semidirect
12. #10591546C2semidirect
13. #10591188C2semidirect
15. #10591103C2semidirect
67. #5228D3semidirect
255. C3×#67Q16semidirect
531. #67#216semidirect
680. C32#3299semidirect
756. C3#80193semidirect
757. 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
#105949932
C2×#636622
C3×#52282
#105916352
#105916232
#105915942
#105915742
Dic3×#2162
#105915512
D3×#8352
#105915462
#105911882
#67⋊(C3⋊C8)2
#105911032
#835513
#801933