Finite Group Databasebeta

← #11887517

Subgroups — #11887517

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5611C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic, complemented
3#10592739C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5#10591517C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591460C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9C3⋊C8×#67C211yesmaximal, characteristic, complemented
10C2×#63567C211yesmaximal, characteristic, complemented
11#10591101C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590487C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83531—31nomaximal
17#80689—31nomaximal
18C22×#634C2211yescharacteristic
19C2×C3×#237—21no—
20C2×D3×Dic6C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×#935—21no—
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#883—21no—
35C3×#878—21no—
36#63982—21no—
37#67⋊Dic3—21no—
38#63896—21no—
39#63866C2211yescharacteristic
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic
42#63840—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50#63574C2211yescharacteristic
51#63574C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#547—31no—
62#5632—31no—
63#5611D311yescharacteristic
64D4×Dic6—31no—
65C3×#465—31no—
66#5170—31no—
67#5162—31no—
68C8×#67—31no—
69C2×#816—31no—
70#5094—31no—
71#5093—31no—
72#5043—31no—
73#5041—31no—
74#5041D311yescharacteristic, complemented
75#5040—31no—
76#5040—31no—
77#5040—31no—
78#5040—61no—
79#5019—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#4971—31no—
83#4971—31no—
84C2×#810—31no—
85C2×#810—31no—
86#4862—31no—
87#4854—31no—
88D3×#103—31no—
89#4792—31no—
90#4778—31no—
91#4758—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634—22no—
97C2×#634—21no—
98C2×#634—41no—
99C2×#634C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—44no—
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⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3754—22no—
117#3754—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—41no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
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—
147C2×D3×Q8—31no—
148C2×#237—21no—
149C22×Dic6—31no—
150C22×Dic6—31no—
151C22×Dic6—31no—
152C22×Dic6—61no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×#123—61no—
157C3×#123—61no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×#121—21no—
161C3×#121—31no—
162C3×#121C2×D311yescharacteristic
163C3×#121C2×D311yescharacteristic
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168#944—31no—
169#938C2×D311yescharacteristic
170#935—21no—
171D4×Dic3—61no—
172D4×Dic3C2×D311yescharacteristic
173C2×#214—31no—
174C2×#214—31no—
175C2×#214—31no—
176C2×#214—31no—
177C2×#214—61no—
178C2×#214—61no—
179C2×#214C2×D311yescharacteristic
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3C2×D311yescharacteristic
182#924—31no—
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×D3×C8—31no—
187#897—31no—
188#896—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#888—61no—
191#888—61no—
192#888C2×D311yescharacteristic
193#887—31no—
194#883—21no—
195#67⋊C4—61no—
196#878—21no—
197#878—61no—
198#878—61no—
199#878—61no—
200#869—31no—
201C4×Dic6—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#832C2×D311yescharacteristic
208#830—31no—
209#830—31no—
210#830—31no—
211#830—61no—
212(C2×D3)⋊C8—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—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#810—61no—
231#810C2×D311yescharacteristic
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808C2×D311yescharacteristic
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—
252C2×C3⋊Dic3—42no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—42no—
257#634#4112yescomplemented
258C3×#67—42no—
259C3×#67SD1614yescomplemented
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
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—91no—
285#483—91no—
286#475—91no—
287#465—31no—
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—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—21no—
315C2×#67#6711yescharacteristic
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322D3×Q8—62no—
323D3×Q8—121no—
324#237—44no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—21no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—122no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—121no—
347C2×Dic6—122no—
348C2×Dic6C22×D311yescharacteristic
349C3×SD16—121no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373#217—21no—
374#217—21no—
375#217—21no—
376#217—61no—
377#217#6711yescharacteristic
378#214—41no—
379#214—62no—
380#214—62no—
381#214—122no—
382#214—121no—
383#214—121no—
384#214—122no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4#6711yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4#6711yescharacteristic
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—41no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416D3×C8—121no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C2×SD1612yes—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3C2×SD1612yes—
427C32×C4—21no—
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×Dic3—41no—
439C3×Dic3C2×SD1612yes—
440C2×#41—61no—
441C22×Q8—91no—
442C22×Q8—91no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×SD16—91no—
446C22×C8—31no—
447C22×C8—91no—
448C4⋊Q8—31no—
449C4⋊Q8—91no—
450C4⋊Q8—181no—
451#123—61no—
452#123—61no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455C22⋊Q8—91no—
456C22⋊Q8—181no—
457C22⋊Q8—181no—
458#121—31no—
459#121D3211yescharacteristic
460C4×Q8—91no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466#106—31no—
467#106—91no—
468#106—91no—
469C4⋊C8—91no—
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#103—91no—
479#102—31no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3D3×D411yescharacteristic
489C23×C3C2×#6711yescharacteristic
490C22×D3C2×#6711yescharacteristic
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—34no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—42no—
502C3×D4—42no—
503C3×D4—82no—
504C3×D4—122no—
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—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
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—122no—
527C2×C3×C4—122no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—42no—
533#67#21414yescomplemented
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—124no—
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—32no—
560Dic6—32no—
561Dic6—42no—
562Dic6—62no—
563Dic6—61no—
564Dic6—61no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—121no—
572Dic6—122no—
573Dic6—122no—
574Dic6—122no—
575Dic6—122no—
576Dic6—124no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—121no—
586C3⋊C8—121no—
587C2×C32—22no—
588C2×C32—81no—
589C2×C32#54611yescharacteristic
590C2×C32C22×SD1611yescharacteristic
591C2×C32#57811yescharacteristic
592C3×D3—22no—
593#41—124no—
594C2×Q8—31no—
595C2×Q8—61no—
596C2×Q8—91no—
597C2×Q8—91no—
598C2×Q8—182no—
599C2×Q8—181no—
600C2×Q8—182no—
601C2×Q8—181no—
602C2×Q8—361no—
603C2×Q8—361no—
604C2×D4—21no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4C2×D3211yescharacteristic
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4C2×D3211yescharacteristic
615SD16—121no—
616SD16—182no—
617SD16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—91no—
622C2×C8—121no—
623C2×C8—361no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—181no—
644C42—31no—
645C42—181no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3D3×SD1612yes—
667C22×C3C2×#21412yes—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3C2×#21412yes—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—32no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4#100411yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—62no—
700Dic3—122no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3C2×#21412yes—
705C32#329811yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23D3×#6711yescharacteristic
709Q8—61no—
710Q8—61no—
711Q8—92no—
712Q8—122no—
713Q8—181no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717Q8—362no—
718D4—21no—
719D4—21no—
720D4—34no—
721D4—42no—
722D4—122no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—122no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4D3×#6711yescharacteristic
743C2×C4C22×D3211yescharacteristic
744C8—61no—
745C8—61no—
746C8—181no—
747C8—181no—
748C2×C3—22no—
749C2×C3—22no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—42no—
754C2×C3—62no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—161no—
758C2×C3#561011yescharacteristic
759C2×C3C2×D3×SD1611yescharacteristic
760C2×C3#577111yescharacteristic
761C2×C3C22×#21411yescharacteristic
762C2×C3#582911yescharacteristic
763C2×C3#583811yescharacteristic
764D3—22no—
765C22—21no—
766C22—21no—
767C22—32no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22D3×#21412yes—
774C22C2×D3×#6711yescharacteristic
775C4—21no—
776C4—32no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—182no—
785C4—361no—
786C4#6431211yescharacteristic
787C4#6431411yescharacteristic
788C3—21no—
789C3#8068911yescharacteristic, complemented
790C3#8353111yescharacteristic, complemented
791C2—22no—
792C2—62no—
793C2—81no—
794C2C2×D3×#21411yescharacteristic
795C2#1059530511yescharacteristic
796C2#1059546711yescharacteristic
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. #10594915C2semidirect
3. #10592739C2semidirect
4. C3×#5041C2semidirect
5. #10591517C2semidirect
6. #10591489C2semidirect
7. #10591460C2semidirect
8. #10591401C2semidirect
9. C3⋊C8×#67C2semidirect
10. C2×#63567C2semidirect
11. #10591101C2semidirect
12. D3×#810C2semidirect
13. #10590560C2semidirect
14. #10590487C2semidirect
15. #10590426C2semidirect
74. #5041D3semidirect
257. #634#41semidirect
259. C3×#67SD16semidirect
533. #67#214semidirect
705. C32#3298semidirect
789. C3#80689semidirect
790. C3#83531semidirect

Maximal subgroups

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

subgroupindex
C3×#56112
#105949152
#105927392
C3×#50412
#105915172
#105914892
#105914602
#105914012
C3⋊C8×#672
C2×#635672
#105911012
D3×#8102
#105905602
#105904872
#105904262
#835313
#806893