Finite Group Databasebeta

← #11887523

Subgroups — #11887523

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5507C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic, complemented
3C2×#63637C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10591181C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590603C211yesmaximal, characteristic, complemented
9D3×#810C211yesmaximal, characteristic, complemented
10#10590578C211yesmaximal, characteristic, complemented
11#10590560C211yesmaximal, characteristic, complemented
12#10590559C211yesmaximal, characteristic, complemented
13#10590487C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83531—31nomaximal
17#81450—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×#235—21no—
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#929—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#896—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#888C2211yescharacteristic
33#63982—21no—
34#67⋊Dic3—21no—
35#63896—21no—
36#63866C2211yescharacteristic
37#63857C2211yescharacteristic
38#63844C2211yescharacteristic
39#63840—21no—
40C2×#3716C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#547—31no—
62#5632—31no—
63D4×Dic6—31no—
64#5507D311yescharacteristic
65C3×#483—31no—
66#5094—31no—
67#5093—31no—
68#5048—31no—
69#5041—31no—
70#5041—31no—
71#5040—31no—
72#5040—31no—
73#5019—31no—
74C4×#214—31no—
75D4×C3⋊C8—31no—
76#4971—31no—
77#4971D311yescharacteristic, complemented
78C2×#810—31no—
79C2×#810—31no—
80C2×#810—31no—
81C2×#810—61no—
82#4864—31no—
83#4862—31no—
84#4854—31no—
85#4852—31no—
86#4818—31no—
87#4806—31no—
88D3×#103—31no—
89#4792—31no—
90#4738—31no—
91#67⋊C8—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×#235—44no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
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#3716—22no—
142#3716—41no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C2×C3×#41—61no—
147C2×D3×Q8—31no—
148C2×#235—21no—
149C22×Dic6—31no—
150C22×Dic6—31no—
151C22×Dic6—31no—
152C22×Dic6—61no—
153C3×C4⋊Q8—31no—
154C3×#123—61no—
155C3×#123—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×#121—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C2×D311yescharacteristic
166#944—31no—
167C2×#215—31no—
168D4×Dic3—61no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172#930C2×D311yescharacteristic
173#929—21no—
174C4×#67C2×D311yescharacteristic
175#924—31no—
176#924C2×D311yescharacteristic
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—61no—
181C2×#204—31no—
182C2×#204—31no—
183C2×D3×C8—31no—
184#897—31no—
185#896—21no—
186#896—61no—
187#895C2×D311yescharacteristic
188#894—21no—
189#893C2×D311yescharacteristic
190D3×C4⋊C4C2×D311yescharacteristic
191#888—61no—
192#888—61no—
193#888C2×D311yescharacteristic
194#887—31no—
195#67⋊C4—61no—
196#878—61no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#832—31no—
208#830—31no—
209#830C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211#816—31no—
212#816—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810—61no—
229#810—61no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#809—31no—
233#808—31no—
234#808—31no—
235#808C2×D311yescharacteristic
236#808C2×D311yescharacteristic
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—42no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—42no—
252#634—21no—
253#634—21no—
254#634—21no—
255#634—42no—
256#634#4112yescomplemented
257C3×#67—42no—
258C3×#67SD1614yescomplemented
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—42no—
275#627—42no—
276D3×Dic3—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—31no—
283#487—91no—
284#483—31no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C3×#41—124no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—21no—
313C2×#67#6711yescharacteristic
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—121no—
318D3×Q8—62no—
319D3×Q8—121no—
320#235—44no—
321C2×D12—21no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—21no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—64no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—121no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—122no—
347C2×Dic6C22×D311yescharacteristic
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372#217—21no—
373#217—61no—
374#217#6711yescharacteristic
375#215—121no—
376#214—62no—
377#214—121no—
378#214—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—122no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413#204—62no—
414#204—121no—
415D3×C8—121no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C2×SD1612yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C2×SD1612yes—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3C2×SD1612yes—
439C2×#41—61no—
440C22×Q8—91no—
441C22×Q8—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C22×C8—91no—
446C22×C8—91no—
447C4⋊Q8—31no—
448C4⋊Q8—91no—
449C4⋊Q8—181no—
450#123—61no—
451#123—61no—
452C22⋊Q8—31no—
453C22⋊Q8—61no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—31no—
458#121—31no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—181no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4D3211yescharacteristic
465#106—31no—
466#106—31no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3C2×#6711yescharacteristic
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—122no—
492C3×D4—34no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—122no—
496C3×D4—122no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
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—42no—
515C2×C3×C4—42no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—82no—
522C2×C3×C4—122no—
523C2×C3×C4—122no—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67#21414yescomplemented
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—124no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546D12—21no—
547D12—21no—
548D12—42no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—42no—
553C4×D3—122no—
554Dic6—21no—
555Dic6—21no—
556Dic6—32no—
557Dic6—32no—
558Dic6—42no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—62no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6—121no—
569Dic6—122no—
570Dic6—122no—
571Dic6—122no—
572Dic6—122no—
573Dic6—124no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32—22no—
585C2×C32#54611yescharacteristic
586C2×C32C22×SD1611yescharacteristic
587C2×C32#57811yescharacteristic
588C3×D3—22no—
589C3×D3—81no—
590#41—124no—
591C2×Q8—31no—
592C2×Q8—61no—
593C2×Q8—91no—
594C2×Q8—91no—
595C2×Q8—182no—
596C2×Q8—181no—
597C2×Q8—182no—
598C2×Q8—181no—
599C2×Q8—361no—
600C2×Q8—361no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—61no—
605C22×C4—21no—
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—182no—
613SD16—361no—
614SD16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—361no—
620C2×C8—361no—
621C4⋊C4—21no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4C2×D3211yescharacteristic
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—32no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3D3×SD1612yes—
658C22×C3C2×#21412yes—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3C2×#21412yes—
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—32no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4D3×#4111yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687C3×C4#100911yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—62no—
694Dic3—62no—
695Dic3—122no—
696Dic3—122no—
697Dic3—121no—
698Dic3—121no—
699Dic3C2×#21412yes—
700C32#329811yescharacteristic, complemented, Sylow
701C23—31no—
702C23—61no—
703C23D3×#6711yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—92no—
707Q8—122no—
708Q8—181no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712Q8—362no—
713D4—34no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—122no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—42no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4D3×#6711yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—181no—
742C8—181no—
743C2×C3—24no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—62no—
750C2×C3—241no—
751C2×C3#565411yescharacteristic
752C2×C3C2×D3×SD1611yescharacteristic
753C2×C3#577911yescharacteristic
754C2×C3C22×#21411yescharacteristic
755C2×C3#582911yescharacteristic
756C2×C3#583811yescharacteristic
757D3—22no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22D3×#21412yes—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—32no—
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—182no—
779C4—361no—
780C4#6430611yescharacteristic
781C4#6430811yescharacteristic
782C3—21no—
783C3#8145011yescharacteristic, complemented
784C3#8353111yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—241no—
788C2#1059506811yescharacteristic
789C2C2×D3×#21411yescharacteristic
790C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC3×#5507C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3298
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
2. #10594915C2semidirect
3. C2×#63637C2semidirect
4. C3×#4971C2semidirect
5. #10591181C2semidirect
6. #10591179C2semidirect
7. #67⋊(C3⋊C8)C2semidirect
8. #10590603C2semidirect
9. D3×#810C2semidirect
10. #10590578C2semidirect
11. #10590560C2semidirect
12. #10590559C2semidirect
13. #10590487C2semidirect
14. #10590479C2semidirect
15. #10590426C2semidirect
77. #4971D3semidirect
256. #634#41semidirect
258. C3×#67SD16semidirect
529. #67#214semidirect
700. C32#3298semidirect
783. C3#81450semidirect
784. C3#83531semidirect

Maximal subgroups

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

subgroupindex
C3×#55072
#105949152
C2×#636372
C3×#49712
#105911812
#105911792
#67⋊(C3⋊C8)2
#105906032
D3×#8102
#105905782
#105905602
#105905592
#105904872
#105904792
#105904262
#835313
#814503