Finite Group Databasebeta

← #11874306

Subgroups — #11874306

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4#10595029C211yesmaximal, characteristic, complemented
5C2×#63829C211yesmaximal, characteristic, complemented
6C2×#63822C211yesmaximal, characteristic, complemented
7#10591626C211yesmaximal, characteristic, complemented
8#10591618C211yesmaximal, characteristic, complemented
9#10591609C211yesmaximal, characteristic, complemented
10#10591606C211yesmaximal, characteristic, complemented
11#10591490C211yesmaximal, characteristic, complemented
12#10591482C211yesmaximal, characteristic, complemented
13#10591473C211yesmaximal, characteristic, complemented
14#10591470C211yesmaximal, characteristic, complemented
15C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
16#83903—31nomaximal
17#83285—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22#64159—24no—
23C2×#3756C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C3×#950—24no—
29C3×#947C2211yescharacteristic
30C3×#944C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#940C2211yescharacteristic
34C3×#939—22no—
35C3×#936C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×C4×#67—22no—
39C2×C3×C4×Dic3C2211yescharacteristic
40C22×C3×C3⋊C8C2211yescharacteristic
41#63978—22no—
42#63911C2211yescharacteristic
43C4×#626—22no—
44#63866C2211yescharacteristic
45#63864C2211yescharacteristic
46#63860C2211yescharacteristic
47C2×#3719C2211yescharacteristic
48C2×#3718C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50#63829—24no—
51C2×#3716C2211yescharacteristic
52C2×#3715C2211yescharacteristic
53C2×#3715C2211yescharacteristic
54C2×#3714C2211yescharacteristic
55#63822—24no—
56C2×#3713C2211yescharacteristic
57Dic3×C3⋊C8C2211yescharacteristic
58Dic3×C3⋊C8C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C2×C3×#135—31no—
62C3×#532—31no—
63#5832—31no—
64#5832D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—31no—
68C2×#950—31no—
69C2×#950—31no—
70C2×#950—61no—
71C2×#950D311yescharacteristic, complemented
72C2×#904—31no—
73#5477—31no—
74#5191—31no—
75#5183—31no—
76#5175—31no—
77#5175—31no—
78#5168—31no—
79#5168—31no—
80#5155—31no—
81#5151—31no—
82C2×C8×Dic3—31no—
83#5092—31no—
84#5085—31no—
85#5076—31no—
86#5073—31no—
87#5059—31no—
88#5059—31no—
89#5059—31no—
90#5059—31no—
91C2×C4×C3⋊C8—31no—
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100#3828—22no—
101#3828—22no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—22no—
108C22×C3×Dic3D412yes—
109C3×#235—22no—
110C3×#235—22no—
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—22no—
120#3756—22no—
121#3755—22no—
122#3754—22no—
123#3753—22no—
124C2×C3⋊(C3⋊C8)D414yescomplemented
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—22no—
128C3×#216—22no—
129C3×#215—22no—
130C3×#214—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×C4×Dic3D412yes—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8D414yescomplemented
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140Dic3⋊Dic3—22no—
141#3722—22no—
142(C2×D3)⋊Dic3—22no—
143#3719—22no—
144#3718—22no—
145#3717—22no—
146#3716—22no—
147#3715—22no—
148#3715—22no—
149#3714—22no—
150#3713—22no—
151#3147—91noSylow
152C2×C3×#41—21no—
153C2×C3×#41—31no—
154C2×C3×#41—31no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C2×D311yescharacteristic
157C2×#235—31no—
158C2×#235—31no—
159C2×#235—61no—
160C2×#235C2×D311yescharacteristic
161C2×#235C2×D311yescharacteristic
162C3×#135—64no—
163C2×C3×Q16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C22×C3×C8—31no—
168C3×C4⋊Q8—31no—
169C3×#127—31no—
170C3×#124—31no—
171C3×#124—31no—
172C3×#121—62no—
173C3×C4×D4—62no—
174C2×C3×C42—31no—
175#950—24no—
176#950—64no—
177#950—64no—
178#950—64no—
179#950—64no—
180#950—68no—
181#950—64no—
182#947—31no—
183#947C2×D311yescharacteristic
184#944—31no—
185#944C2×D311yescharacteristic
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—61no—
192C2×#216C2×D311yescharacteristic
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—31no—
197C2×#215—31no—
198C2×#215—61no—
199C2×#215C2×D311yescharacteristic
200#940—31no—
201#940C2×D311yescharacteristic
202#939—22no—
203#939—62no—
204#936—31no—
205#936C2×D311yescharacteristic
206C2×#214—31no—
207C2×#214—31no—
208C2×#214—31no—
209C2×#214—31no—
210C2×#214—31no—
211C2×#214—61no—
212C2×#214C2×D311yescharacteristic
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—61no—
219C2×#213C2×D311yescharacteristic
220#930—62no—
221C4×#67—22no—
222C4×#67—62no—
223C2×C4×Dic3C2×D311yescharacteristic
224C22×C3⋊C8—31no—
225C22×C3⋊C8—31no—
226C22×C3⋊C8—61no—
227C22×C3⋊C8C2×D311yescharacteristic
228C2×Dic12—31no—
229#904—64no—
230C2×D24—31no—
231C2×#204—31no—
232C2×#204—31no—
233#875—31no—
234#875—31no—
235#874—31no—
236C4×D12—62no—
237#869—31no—
238C8×Dic3—31no—
239C8×Dic3—31no—
240C8×Dic3—31no—
241C8×Dic3—31no—
242C4×C3⋊C8—31no—
243C4×C3⋊C8—31no—
244C4×C3⋊C8—31no—
245C4×C3⋊C8—31no—
246C23×C32—21no—
247C23×C32C2×D411yescharacteristic
248C22×C3⋊D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C32×Q8—21no—
252C32×Q8—21no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—42no—
256C2×C32×C4—21no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2411yescharacteristic
262#638—42no—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)—21no—
266C4×C3⋊D3—42no—
267#634—21no—
268#634—21no—
269C3×#67—42no—
270C3×#67—42no—
271C3×#67—44no—
272C2×C3×Dic3—24no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D412yes—
276C2×C3×Dic3C2×D412yes—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—42no—
282C3×C4×D3—42no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287#626—44no—
288C3⋊(C3⋊C8)C2×D412yes—
289C3⋊(C3⋊C8)C2×D412yes—
290C3×C3⋊C8C2×D412yes—
291C3×C3⋊C8C2×D412yes—
292C2×#135—31no—
293C2×#135—91no—
294C2×#135—91no—
295C2×#135—91no—
296#532—31no—
297#532—91no—
298#495—91no—
299#495—91no—
300#495—91no—
301#495—91no—
302#494—91no—
303#493—91no—
304#492—91no—
305#492—91no—
306C2×C4×C8—91no—
307C3×#41—24no—
308C3×#41—22no—
309C3×#41—22no—
310C3×#41—22no—
311C3×#41—22no—
312C3×#41—42no—
313C3×#41—62no—
314C3×#41—62no—
315C3×#41—62no—
316C3×#41—62no—
317C2×C3×Q8—21no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—62no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—32no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—22no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—62no—
348C2×#67—121no—
349C22×Dic3#6712yes—
350#235—22no—
351#235—22no—
352#235—22no—
353#235—22no—
354#235—64no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—62no—
359#235—122no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—21no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—121no—
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—61no—
374C2×Dic6C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C3×Q16—62no—
377C3×SD16—62no—
378C3×SD16—62no—
379C3×D8—62no—
380C2×C3×C8—34no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C3×C4⋊C4—62no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—62no—
386C3×C42—32no—
387C3×C42—31no—
388C3×C42—31no—
389#217—22no—
390#217—62no—
391#216—22no—
392#216—62no—
393#216—62no—
394#216—62no—
395#216—62no—
396#216—64no—
397#216—62no—
398#215—22no—
399#215—62no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—64no—
404#215—62no—
405#214—22no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—64no—
411#214—62no—
412#213—22no—
413#213—62no—
414#213—62no—
415#213—62no—
416#213—62no—
417#213—64no—
418#213—62no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423C4⋊Dic3—62no—
424Dic3⋊C4—22no—
425Dic3⋊C4—62no—
426C4×Dic3#6712yes—
427C4×Dic3C22×D311yescharacteristic
428C4×Dic3C22×D311yescharacteristic
429C2×C3⋊C8—34no—
430C2×C3⋊C8—34no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8—64no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8#6714yescomplemented
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441Dic12—62no—
442D24—62no—
443#204—62no—
444#204—62no—
445C22×C32—22no—
446C22×C32—41no—
447C22×C32—42no—
448C22×C32#12712yes—
449C22×C32C22×D411yescharacteristic
450C2×C3⋊D3—41no—
451C2×C3⋊D3—42no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—42no—
455C2×C3×D3—42no—
456C32×C4—41no—
457C32×C4#12712yes—
458C32×C4C22×D411yescharacteristic
459C32×C4C22×D411yescharacteristic
460C3⋊Dic3—41no—
461C3×Dic3—22no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#13514yescomplemented
465C2×#41—31no—
466C2×#41—31no—
467C2×#41—91no—
468C2×#41D3211yescharacteristic
469#135—64no—
470#135—184no—
471#135—184no—
472#135—184no—
473C2×Q16—31no—
474C2×Q16—91no—
475C2×Q16—91no—
476C2×Q16—91no—
477C2×SD16—31no—
478C2×SD16—31no—
479C2×SD16—91no—
480C2×SD16—91no—
481C2×SD16—91no—
482C2×SD16—91no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C22×C8—31no—
490C22×C8—91no—
491C4⋊Q8—31no—
492C4⋊Q8—91no—
493#127—31no—
494#127—91no—
495#124—31no—
496#124—31no—
497#124—91no—
498#124—91no—
499#121—62no—
500#121—182no—
501C4×D4—62no—
502C4×D4—182no—
503C2×C42—31no—
504C4×C8—91no—
505C4×C8—91no—
506C4×C8—91no—
507C4×C8—91no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—41no—
512C23×C3—61no—
513C23×C3—61no—
514C23×C3D3×D411yescharacteristic
515C23×C3C2×#6711yescharacteristic
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C3×Q8—22no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—41no—
527C3×Q8—61no—
528C3×Q8—61no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×D4—22no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—41no—
537C3×D4—44no—
538C3×D4—42no—
539C3×D4—42no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—124no—
545C3×D4—122no—
546C3×D4—122no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—41no—
556C2×C3×C4—44no—
557C2×C3×C4—42no—
558C2×C3×C4—42no—
559C2×C3×C4—64no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4—122no—
564C2×C3×C4D3×D412yes—
565C2×C3×C4D3×D411yescharacteristic
566C2×C3×C4D3×D412yes—
567C2×C3×C4D3×D412yes—
568C2×C3×C4C2×#6712yes—
569C2×C3×C4C2×#6711yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—42no—
573#67—42no—
574#67—44no—
575#67—124no—
576#67—122no—
577#67—122no—
578#67—124no—
579C2×Dic3—24no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3C2×#6712yes—
586C2×Dic3C2×#6712yes—
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—62no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—121no—
597D12—124no—
598C4×D3—42no—
599C4×D3—42no—
600C4×D3—124no—
601C4×D3—122no—
602C4×D3—122no—
603Dic6—21no—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—62no—
608Dic6—61no—
609Dic6—61no—
610Dic6—61no—
611Dic6—61no—
612Dic6—121no—
613C3×C8—32no—
614C3×C8—32no—
615C3⋊C8—32no—
616C3⋊C8—32no—
617C3⋊C8—32no—
618C3⋊C8—32no—
619C3⋊C8—62no—
620C3⋊C8—62no—
621C3⋊C8C2×#6712yes—
622C3⋊C8C2×#6712yes—
623C2×C32—22no—
624C2×C32—81no—
625C2×C32C2×#12711yescharacteristic
626C2×C32C2×#13512yes—
627C3⋊D3—81no—
628C3×D3—81no—
629C3×D3—81no—
630#41—22no—
631#41—22no—
632#41—62no—
633#41—62no—
634#41—62no—
635#41—62no—
636#41—182no—
637#41—182no—
638C2×Q8—31no—
639C2×Q8—31no—
640C2×Q8—91no—
641C2×Q8C2×D3211yescharacteristic
642C2×D4—21no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—62no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—91no—
649C2×D4—182no—
650C2×D4—181no—
651C2×D4C2×D3211yescharacteristic
652C22×C4—21no—
653C22×C4—32no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—181no—
657C22×C4C2×D3211yescharacteristic
658Q16—62no—
659Q16—182no—
660Q16—182no—
661Q16—182no—
662SD16—62no—
663SD16—62no—
664SD16—182no—
665SD16—182no—
666SD16—182no—
667SD16—182no—
668SD16—182no—
669SD16—182no—
670D8—62no—
671D8—182no—
672D8—182no—
673D8—182no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—34no—
677C2×C8—91no—
678C2×C8—91no—
679C2×C8—94no—
680C4⋊C4—62no—
681C4⋊C4—182no—
682C22⋊C4—62no—
683C22⋊C4—62no—
684C22⋊C4—182no—
685C22⋊C4—182no—
686C42—31no—
687C42—31no—
688C42—32no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—42no—
699C22×C3—82no—
700C22×C3—122no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—122no—
704C22×C3#94012yes—
705C22×C3#94012yes—
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C22×#6711yescharacteristic
708C2×D3—42no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—42no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—122no—
717C2×D3—242no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—22no—
721C3×C4—34no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—62no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4#94012yes—
729C3×C4#94012yes—
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C22×#6711yescharacteristic
734Dic3—22no—
735Dic3—41no—
736Dic3—41no—
737Dic3—122no—
738Dic3—121no—
739Dic3—121no—
740Dic3#95014yescomplemented
741C32#314711yescharacteristic, complemented, Sylow
742C23—21no—
743C23—61no—
744C23—61no—
745C23—181no—
746C23D3×#6711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—61no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—61no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—124no—
763D4—122no—
764D4—122no—
765D4—181no—
766D4—181no—
767D4—364no—
768D4—362no—
769C2×C4—21no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—42no—
773C2×C4—64no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—181no—
779C2×C4—362no—
780C2×C4D3×#6712yes—
781C2×C4D3×#6711yescharacteristic
782C2×C4#381112yes—
783C2×C4C22×D3211yescharacteristic
784C8—32no—
785C8—32no—
786C8—92no—
787C8—92no—
788C2×C3—22no—
789C2×C3—22no—
790C2×C3—22no—
791C2×C3—21no—
792C2×C3—42no—
793C2×C3—82no—
794C2×C3—81no—
795C2×C3—81no—
796C2×C3—241no—
797C2×C3—241no—
798C2×C3D3×#13512yes—
799C2×C3C2×#94011yescharacteristic
800C2×C3C2×#94011yescharacteristic
801C2×C3C2×#95012yes—
802D3—81no—
803D3—81no—
804D3—242no—
805D3—241no—
806D3—241no—
807C22—22no—
808C22—42no—
809C22—41no—
810C22—122no—
811C22—122no—
812C22—121no—
813C22—121no—
814C22—362no—
815C22—361no—
816C22#6397912yes—
817C22C2×D3×#6711yescharacteristic
818C4—34no—
819C4—41no—
820C4—62no—
821C4—121no—
822C4—121no—
823C4—361no—
824C4#6397912yes—
825C4C2×D3×#6711yescharacteristic
826C4C2×#381111yescharacteristic
827C3—21no—
828C3#8328511yescharacteristic, complemented
829C3#8390311yescharacteristic, complemented
830C2—22no—
831C2—81no—
832C2—241no—
833C2—241no—
834C2—721no—
835C2D3×#95012yes—
836C2C2×#6397911yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64159C2semidirect
2. C3×#5832C2semidirect
3. C2×C3×#950C2semidirect
4. #10595029C2semidirect
5. C2×#63829C2semidirect
6. C2×#63822C2semidirect
7. #10591626C2semidirect
8. #10591618C2semidirect
9. #10591609C2semidirect
10. #10591606C2semidirect
11. #10591490C2semidirect
12. #10591482C2semidirect
13. #10591473C2semidirect
14. #10591470C2semidirect
15. C2×Dic3×C3⋊C8C2semidirect
64. #5832D3semidirect
71. C2×#950D3semidirect
124. C2×C3⋊(C3⋊C8)D4semidirect
137. C2×C3×C3⋊C8D4semidirect
438. C2×C3⋊C8#67semidirect
464. C3×Dic3#135semidirect
740. Dic3#950semidirect
741. C32#3147semidirect
828. C3#83285semidirect
829. C3#83903semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58322
C2×C3×#9502
#105950292
C2×#638292
C2×#638222
#105916262
#105916182
#105916092
#105916062
#105914902
#105914822
#105914732
#105914702
C2×Dic3×C3⋊C82
#839033
#832853