Finite Group Databasebeta

← #11887519

Subgroups — #11887519

Order 1152.

902 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×#5611C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic, complemented
3#10592740C211yesmaximal, characteristic, complemented
4C3×#5040C211yesmaximal, characteristic, complemented
5#10591517C211yesmaximal, characteristic, complemented
6#10591499C211yesmaximal, characteristic, complemented
7#10591489C211yesmaximal, characteristic, complemented
8Dic3×#214C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591124C211yesmaximal, characteristic, complemented
11C2×#63565C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590486C211yesmaximal, characteristic, complemented
16#83531—31nomaximal
17#80049—31nomaximal
18C2×C3×#237—21no—
19C22×C3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64133C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#883—21no—
35C3×#878—21no—
36Dic3×#67—21no—
37#63964—21no—
38#63887—21no—
39#63866C2211yescharacteristic
40#63856C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50#63573C2211yescharacteristic
51#63573C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#547—31no—
62Q8×#67—31no—
63#5611D311yescharacteristic
64D4×Dic6—31no—
65C3×#448—31no—
66C2×#835—31no—
67#5171—31no—
68#5170—31no—
69#5162—31no—
70Dic3×SD16—31no—
71#5094—31no—
72#5093—31no—
73#5041—31no—
74#5041—31no—
75#5041—31no—
76#5041—61no—
77#5040—31no—
78#5040D311yescharacteristic, complemented
79#5019—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#4971—31no—
83#4971—31no—
84C2×#810—31no—
85C2×#810—31no—
86#4805—31no—
87D3×#103—31no—
88#4792—31no—
89#4791—31no—
90#67⋊C8—31no—
91#4721—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—44no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—22no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—41no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3757—21no—
117#3754—41no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#217D411yescharacteristic
126C3×#214—22no—
127C3×#214—41no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C2×C3×#41—61no—
147C22×C3×Q8—31no—
148C2×D3×Q8—31no—
149C2×#237—21no—
150C22×Dic6—31no—
151C22×Dic6C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4⋊Q8—31no—
155C3×#123—61no—
156C3×#123—61no—
157C3×C22⋊Q8—61no—
158C3×#121—21no—
159C3×#121—31no—
160C3×#121C2×D311yescharacteristic
161C3×#121C2×D311yescharacteristic
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166#946—31no—
167#946—61no—
168Q8×Dic3—31no—
169#944—31no—
170#944—61no—
171#938C2×D311yescharacteristic
172#935—21no—
173D4×Dic3—61no—
174D4×Dic3C2×D311yescharacteristic
175C2×#214—31no—
176C2×#214—31no—
177C2×#214—61no—
178C2×#214C2×D311yescharacteristic
179C2×#214C2×D311yescharacteristic
180C4×#67—61no—
181C4×#67C2×D311yescharacteristic
182C2×C4⋊Dic3C2×D311yescharacteristic
183#924—31no—
184#924—31no—
185#924—31no—
186#924—61no—
187#924—61no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—31no—
191C22×C3⋊C8—61no—
192C2×D3×C8—31no—
193D3×C4⋊C4C2×D311yescharacteristic
194#888—61no—
195#888C2×D311yescharacteristic
196#883—21no—
197#878—21no—
198#878—61no—
199#878—61no—
200#869—31no—
201C4×Dic6—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—61no—
212#830—31no—
213#830C2×D311yescharacteristic
214(C2×D3)⋊C8—31no—
215#817—31no—
216#817—31no—
217#816—31no—
218#816—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—61no—
230#810C2×D311yescharacteristic
231#810C2×D311yescharacteristic
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—61no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252#634—21no—
253#634—21no—
254C3×#67—42no—
255C3×#67SD1614yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—42no—
273C3×Dic6—42no—
274C3×Dic6#4112yescomplemented
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—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—31no—
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—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—61no—
302C2×C3×Q8—121no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—21no—
320C2×#67#6711yescharacteristic
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—61no—
325D3×Q8—62no—
326D3×Q8—121no—
327#237—44no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—22no—
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—41no—
337C2×Dic6—61no—
338C2×Dic6—62no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—121no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—62no—
345C3×SD16—121no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365#217—21no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#217#6711yescharacteristic
372#214—22no—
373#214—41no—
374#214—121no—
375#214—121no—
376#214—122no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4#6711yescharacteristic
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—122no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C2×SD1612yes—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3C2×SD1612yes—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C2×SD1612yes—
438C2×#41—61no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C2×SD16—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—61no—
450#123—61no—
451C22⋊Q8—61no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
457#121D3211yescharacteristic
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464#106—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×#6711yescharacteristic
488C22×D3C2×#6711yescharacteristic
489C3×Q8—32no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×Q8—122no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—34no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—42no—
503C3×D4—42no—
504C3×D4—82no—
505C3×D4—122no—
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—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
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×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—42no—
535#67#21414yescomplemented
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—122no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—42no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—21no—
559Dic6—21no—
560Dic6—42no—
561Dic6—42no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567Dic6—121no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23712yescomplemented
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—22no—
582C2×C32—81no—
583C2×C32#54611yescharacteristic
584C2×C32C22×SD1611yescharacteristic
585C2×C32#57811yescharacteristic
586C3×D3—22no—
587#41—124no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—61no—
591C2×Q8—62no—
592C2×Q8—61no—
593C2×Q8—91no—
594C2×Q8—121no—
595C2×Q8—181no—
596C2×Q8—182no—
597C2×Q8—361no—
598C2×D4—21no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609SD16—62no—
610SD16—121no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—91no—
616C2×C8—361no—
617C2×C8—361no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—32no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3D3×SD1612yes—
661C22×C3C2×#21412yes—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C22×#6711yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3C2×#21412yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—32no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—62no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23711yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4D3×#4111yescharacteristic
685C3×C4#100911yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—22no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698Dic3C2×#21412yes—
699C32#329811yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23D3×#6711yescharacteristic
703Q8—32no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—122no—
708Q8—122no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712D4—21no—
713D4—21no—
714D4—34no—
715D4—42no—
716D4—122no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—362no—
736C2×C4D3×#6711yescharacteristic
737C2×C4C22×D3211yescharacteristic
738C8—61no—
739C8—61no—
740C8—181no—
741C8—181no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—62no—
749C2×C3—81no—
750C2×C3—81no—
751C2×C3—161no—
752C2×C3#559111yescharacteristic
753C2×C3C2×D3×SD1611yescharacteristic
754C2×C3#577911yescharacteristic
755C2×C3C22×#21411yescharacteristic
756C2×C3#582911yescharacteristic
757C2×C3#583811yescharacteristic
758D3—22no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—61no—
766C22—61no—
767C22D3×#21412yes—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—32no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—62no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8004911yescharacteristic, complemented
784C3#8353111yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—81no—
788C2C2×D3×#21411yescharacteristic
789C2#1059530411yescharacteristic
790C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5611C2
hypercenter#121D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. Dic6×#67C2semidirect
3. #10592740C2semidirect
4. C3×#5040C2semidirect
5. #10591517C2semidirect
6. #10591499C2semidirect
7. #10591489C2semidirect
8. Dic3×#214C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591124C2semidirect
11. C2×#63565C2semidirect
12. D3×#810C2semidirect
13. #10590560C2semidirect
14. #10590516C2semidirect
15. #10590486C2semidirect
78. #5040D3semidirect
255. C3×#67SD16semidirect
274. C3×Dic6#41semidirect
535. #67#214semidirect
570. Dic6#237semidirect
699. C32#3298semidirect
783. C3#80049semidirect
784. C3#83531semidirect

Maximal subgroups

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

subgroupindex
C3×#56112
Dic6×#672
#105927402
C3×#50402
#105915172
#105914992
#105914892
Dic3×#2142
#67⋊(C3⋊C8)2
#105911242
C2×#635652
D3×#8102
#105905602
#105905162
#105904862
#835313
#800493