Finite Group Databasebeta

← #11865787

Subgroups — #11865787

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×Dic3×#41C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4#10595029C211yesmaximal, characteristic, complemented
5#10591625C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic, complemented
7#10591607C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591489C211yesmaximal, characteristic, complemented
10#10591481C211yesmaximal, characteristic, complemented
11#10591471C211yesmaximal, characteristic, complemented
12#10591468C211yesmaximal, characteristic, complemented
13C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
14#10591105C211yesmaximal, characteristic, complemented
15#10591083C211yesmaximal, characteristic, complemented
16#83900—31nomaximal
17#82525—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64159—24no—
22C2×#3756C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C22×C3⋊(C3⋊C8)C2211yescharacteristic
27C3×#950—24no—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×D4×Dic3—21no—
33C3×D4×Dic3—21no—
34C3×D4×Dic3C2211yescharacteristic
35C3×D4×Dic3C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C3×#926—21no—
39C3×#926C2211yescharacteristic
40C2×C3×C4×Dic3—21no—
41C2×C3×C4×Dic3C2211yescharacteristic
42C22×C3×C3⋊C8C2211yescharacteristic
43#63978—21no—
44#63978—21no—
45#63911C2211yescharacteristic
46C4×#626—21no—
47C4×#626—21no—
48#63866C2211yescharacteristic
49#63864C2211yescharacteristic
50#63860C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#63562C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×#135—31no—
64C3×C4×#41—31no—
65#5832—31no—
66Dic3×#41D311yescharacteristic, complemented
67C2×#950—31no—
68C2×#950—31no—
69C2×#950—61no—
70C2×#950D311yescharacteristic, complemented
71#5477—31no—
72#5233—31no—
73#5185—31no—
74#5182—31no—
75#5166—31no—
76#5165—31no—
77#5163—31no—
78#5162—31no—
79#5153—31no—
80#5150—31no—
81#5113—31no—
82C2×Dic3⋊C8—31no—
83#5031—31no—
84#5028—31no—
85#5028—31no—
86#5027—31no—
87#5019—31no—
88#5016—31no—
89#5016—31no—
90#5015—31no—
91#5002—31no—
92#5002—31no—
93C2×C4⋊(C3⋊C8)—31no—
94C32×#41—22no—
95C32×#41D414yescomplemented
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3D411yescharacteristic
111C22×C3×Dic3D411yescharacteristic
112C3×#235—22no—
113C3×#235—22no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119#3756—22no—
120#3755—22no—
121#3754—22no—
122#3753—22no—
123C2×C3⋊(C3⋊C8)—22no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—22no—
130C3×#215—22no—
131C3×#214—22no—
132C3×#213—22no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153#3035—91noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C2×D311yescharacteristic
158C2×#235—31no—
159C2×#235—31no—
160C2×#235—61no—
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×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×#117—31no—
175C3×#117—61no—
176C2×C3×C42—31no—
177C2×C3×C42—61no—
178#950—24no—
179#950—68no—
180#950—64no—
181#950—64no—
182#947—31no—
183Q8×Dic3C2×D311yescharacteristic
184Q8×Dic3C2×D311yescharacteristic
185#944—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—61no—
189C2×#216C2×D311yescharacteristic
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—61no—
193C2×#215C2×D311yescharacteristic
194#940—31no—
195#939—61no—
196#939—61no—
197#936—31no—
198D4×Dic3—21no—
199D4×Dic3—21no—
200D4×Dic3C2×D311yescharacteristic
201D4×Dic3C2×D311yescharacteristic
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#214C2×D311yescharacteristic
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213C2×D311yescharacteristic
210#930—61no—
211#930—61no—
212C4×#67—61no—
213C4×#67—61no—
214#926—21no—
215#926C2×D311yescharacteristic
216C2×C4×Dic3—21no—
217C2×C4×Dic3C2×D311yescharacteristic
218C22×C3⋊C8—31no—
219C22×C3⋊C8—31no—
220C22×C3⋊C8—61no—
221C22×C3⋊C8C2×D311yescharacteristic
222#875—31no—
223#875—31no—
224#874—31no—
225C4×D12—61no—
226C4×D12—61no—
227#869—31no—
228#835—31no—
229#835—31no—
230#832—31no—
231#832—31no—
232#821—31no—
233#821—31no—
234#816—31no—
235#816—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—31no—
243#810—31no—
244#809—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C32×Q8—21no—
257C32×Q8C2×D412yes—
258C32×D4—24no—
259C32×D4—21no—
260C32×D4C2×D412yes—
261C2×C32×C4—21no—
262C2×C32×C4—24no—
263C2×C32×C4C2×D412yes—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4#4112yes—
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4×C3⋊D3—42no—
272#634—21no—
273#634—21no—
274C3×#67—42no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—41no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291#626—42no—
292#626—42no—
293C3⋊(C3⋊C8)—21no—
294C3⋊(C3⋊C8)—21no—
295C3×C3⋊C8—21no—
296C3×C3⋊C8—21no—
297C2×#135—31no—
298C2×#135—91no—
299#532—91no—
300C4×#41—31no—
301#464—91no—
302#464—91no—
303#463—91no—
304#463—91no—
305#462—91no—
306#461—91no—
307#460—91no—
308#459—91no—
309C2×C4⋊C8—91no—
310#416—91no—
311#416—91no—
312C3×#41—22no—
313C3×#41—22no—
314C3×#41—24no—
315C3×#41—42no—
316C3×#41—62no—
317C3×#41—62no—
318C3×#41D1214yescomplemented
319C3×#41#6714yescomplemented
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—41no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—121no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3#6711yescharacteristic
352C22×Dic3#6711yescharacteristic
353#235—22no—
354#235—22no—
355#235—64no—
356#235—62no—
357#235—62no—
358#235—62no—
359#235—62no—
360#235—122no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
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
375C3×Q16—62no—
376C3×SD16—62no—
377C3×SD16—62no—
378C3×D8—62no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8—62no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—31no—
390C3×C42—31no—
391C3×C42—31no—
392C3×C42—31no—
393C3×C42—61no—
394C3×C42—61no—
395C3×C42—61no—
396#217—21no—
397#217—21no—
398#217—21no—
399#217—61no—
400#217—61no—
401#216—22no—
402#216—64no—
403#216—62no—
404#216—62no—
405#215—22no—
406#215—64no—
407#215—62no—
408#215—62no—
409#214—22no—
410#214—64no—
411#214—62no—
412#214—62no—
413#213—22no—
414#213—64no—
415#213—62no—
416#213—62no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423C4⋊Dic3—21no—
424C4⋊Dic3—21no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3C22×D311yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431C4×Dic3—21no—
432C4×Dic3—21no—
433C4×Dic3—21no—
434C4×Dic3#6711yescharacteristic
435C4×Dic3#6711yescharacteristic
436C4×Dic3C22×D311yescharacteristic
437C4×Dic3C22×D311yescharacteristic
438C2×C3⋊C8—22no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—64no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—22no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32#12112yes—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C32×C4—22no—
464C32×C4#12112yes—
465C32×C4C22×D411yescharacteristic
466C32×C4C2×#4111yescharacteristic
467C3⋊Dic3—41no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3—41no—
474C3×Dic3#13512yescomplemented
475C2×#41—31no—
476C2×#41—91no—
477C2×#41D3211yescharacteristic
478#135—64no—
479#135—184no—
480C2×Q16—31no—
481C2×Q16—91no—
482C2×SD16—31no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×SD16—91no—
486C2×D8—31no—
487C2×D8—91no—
488C22×C8—31no—
489C22×C8—91no—
490C4⋊Q8—91no—
491#127—91no—
492#124—91no—
493#124—91no—
494#121—181no—
495#121—181no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×D4—31no—
499C4×D4—31no—
500C4×D4—61no—
501C4×D4—61no—
502C4×D4—181no—
503C4×D4—181no—
504#117—31no—
505#117—61no—
506C2×C42—31no—
507C2×C42—61no—
508C4⋊C8—91no—
509C4⋊C8—91no—
510C4⋊C8—91no—
511C4⋊C8—91no—
512#103—91no—
513#103—91no—
514#103—91no—
515#103—91no—
516#102—91no—
517#102—91no—
518#102—91no—
519#102—91no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—41no—
524C23×C3—61no—
525C23×C3D3×D411yescharacteristic
526C23×C3C2×#6711yescharacteristic
527C22×D3—21no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—121no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—22no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8C2×D1212yes—
538C3×Q8C2×#6712yes—
539C3×D4—24no—
540C3×D4—24no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—22no—
544C3×D4—41no—
545C3×D4—44no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—122no—
549C3×D4C2×D1212yes—
550C3×D4C2×#6712yes—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—24no—
554C2×C3×C4—24no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—44no—
564C2×C3×C4—41no—
565C2×C3×C4—62no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—122no—
570C2×C3×C4—121no—
571C2×C3×C4—122no—
572C2×C3×C4—122no—
573C2×C3×C4C2×D1212yes—
574C2×C3×C4#23512yes—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4#23712yes—
577C2×C3×C4C2×#6712yes—
578C2×C3×C4C2×#6711yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—122no—
583#67—124no—
584#67—122no—
585#67—122no—
586#67—122no—
587C2×Dic3—22no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—41no—
592C2×Dic3—42no—
593C2×Dic3—42no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3C2×#6711yescharacteristic
598C2×Dic3C2×#6711yescharacteristic
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601D12—21no—
602D12—21no—
603D12—62no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—121no—
609D12—122no—
610D12—122no—
611C4×D3—42no—
612C4×D3—124no—
613C4×D3—122no—
614C4×D3—122no—
615Dic6—21no—
616Dic6—21no—
617Dic6—62no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—121no—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—62no—
628C3⋊C8—62no—
629C3⋊C8—61no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C2×C32—22no—
634C2×C32—42no—
635C2×C32C2×#12111yescharacteristic
636C2×C32C2×#13511yescharacteristic
637C2×C32#57511yescharacteristic
638C3⋊D3—81no—
639C3×D3—81no—
640#41—22no—
641#41—62no—
642#41—62no—
643#41—182no—
644#41—182no—
645#41#62614yescomplemented
646C2×Q8—31no—
647C2×Q8—91no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—21no—
650C2×D4—31no—
651C2×D4—61no—
652C2×D4—91no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4C2×D3211yescharacteristic
657C22×C4—21no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—181no—
664C22×C4C2×D3211yescharacteristic
665Q16—62no—
666Q16—182no—
667SD16—62no—
668SD16—62no—
669SD16—182no—
670SD16—182no—
671D8—62no—
672D8—182no—
673C2×C8—31no—
674C2×C8—31no—
675C2×C8—62no—
676C2×C8—91no—
677C2×C8—91no—
678C2×C8—182no—
679C4⋊C4—31no—
680C4⋊C4—31no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—181no—
689C22⋊C4—181no—
690C22⋊C4—181no—
691C22⋊C4—181no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—61no—
697C42—61no—
698C42—61no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—22no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—42no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3#93012yes—
720C22×C3#93912yes—
721C22×C3C2×D3×D411yescharacteristic
722C22×C3C22×#6711yescharacteristic
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—122no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—241no—
734C2×D3—241no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—22no—
740C3×C4—32no—
741C3×C4—42no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—121no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4#93012yes—
749C3×C4#93912yes—
750C3×C4C22×D1211yescharacteristic
751C3×C4C2×#23511yescharacteristic
752C3×C4C2×#23711yescharacteristic
753C3×C4C22×#6711yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—21no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—122no—
761Dic3—121no—
762Dic3—121no—
763Dic3#95012yescomplemented
764C32#303511yescharacteristic, complemented, Sylow
765C23—21no—
766C23—61no—
767C23—181no—
768C23D3×#6711yescharacteristic
769Q8—21no—
770Q8—61no—
771Q8—61no—
772Q8—181no—
773Q8—181no—
774Q8C2×#62612yes—
775D4—24no—
776D4—21no—
777D4—61no—
778D4—61no—
779D4—122no—
780D4—181no—
781D4—181no—
782D4—362no—
783D4—362no—
784D4—362no—
785D4C2×#62612yes—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—62no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—122no—
797C2×C4—121no—
798C2×C4—122no—
799C2×C4—122no—
800C2×C4—181no—
801C2×C4—362no—
802C2×C4#380412yes—
803C2×C4C2×#62612yes—
804C2×C4D3×#6711yescharacteristic
805C2×C4C22×D3211yescharacteristic
806C8—61no—
807C8—61no—
808C8—181no—
809C8—181no—
810C2×C3—22no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—42no—
816C2×C3—42no—
817C2×C3—42no—
818C2×C3—82no—
819C2×C3—241no—
820C2×C3D3×#13511yescharacteristic
821C2×C3#576811yescharacteristic
822C2×C3C2×#93011yescharacteristic
823C2×C3C2×#93911yescharacteristic
824C2×C3C2×#95011yescharacteristic
825C2×C3#582211yescharacteristic
826D3—81no—
827D3—242no—
828D3—241no—
829D3—241no—
830C22—21no—
831C22—21no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—361no—
839C22—361no—
840C22—361no—
841C22#6397812yes—
842C22C2×D3×#6711yescharacteristic
843C4—22no—
844C4—32no—
845C4—61no—
846C4—61no—
847C4—61no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—361no—
852C4#6397812yes—
853C4C2×#380411yescharacteristic
854C4C22×#62611yescharacteristic
855C3—21no—
856C3#8252511yescharacteristic, complemented
857C3#8390011yescharacteristic, complemented
858C2—22no—
859C2—42no—
860C2—241no—
861C2—721no—
862C2D3×#95011yescharacteristic
863C2#1059545311yescharacteristic
864C2C2×#6397811yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3035
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×Dic3×#41C2semidirect
3. C2×C3×#950C2semidirect
4. #10595029C2semidirect
5. #10591625C2semidirect
6. #10591617C2semidirect
7. #10591607C2semidirect
8. #10591604C2semidirect
9. #10591489C2semidirect
10. #10591481C2semidirect
11. #10591471C2semidirect
12. #10591468C2semidirect
13. C2×Dic3⋊(C3⋊C8)C2semidirect
14. #10591105C2semidirect
15. #10591083C2semidirect
66. Dic3×#41D3semidirect
70. C2×#950D3semidirect
95. C32×#41D4semidirect
318. C3×#41D12semidirect
319. C3×#41#67semidirect
474. C3×Dic3#135semidirect
645. #41#626semidirect
763. Dic3#950semidirect
764. C32#3035semidirect
856. C3#82525semidirect
857. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×Dic3×#412
C2×C3×#9502
#105950292
#105916252
#105916172
#105916072
#105916042
#105914892
#105914812
#105914712
#105914682
C2×Dic3⋊(C3⋊C8)2
#105911052
#105910832
#839003
#825253