Finite Group Databasebeta

← #11863904

Subgroups — #11863904

Order 1152.

1629 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2#10594922C211yesmaximal, characteristic, complemented
3C2×#63810C211yesmaximal, characteristic, complemented
4C2×#63809C211yesmaximal, characteristic, complemented
5C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4733C211yesmaximal, characteristic, complemented
8#10591170C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic, complemented
10#10590956C211yesmaximal, characteristic, complemented
11#10590956C211yesmaximal, characteristic, complemented
12#10590950C211yesmaximal, characteristic, complemented
13#10590945C211yesmaximal, characteristic, complemented
14#10590943C211yesmaximal, characteristic, complemented
15#10590824C211yesmaximal, characteristic, complemented
16#80226—31nomaximal
17#80082—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×#3811—21no—
22C2×#3805—21no—
23#64306—24no—
24#64306—24no—
25C2×#3802C2211yescharacteristic
26C2×C4×D32—21no—
27C2×#3798—21no—
28C2×#3797C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×#3796C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33C2×C8×C3⋊D3C2211yescharacteristic, complemented
34C3×#930C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×#204C2211yescharacteristic, complemented
40#63981—21no—
41#67⋊Dic3—21no—
42#63916C2211yescharacteristic
43#63881—21no—
44#63871C2211yescharacteristic
45#63853—21no—
46#63849C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51#63810—24no—
52#63809—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63647C2211yescharacteristic
56#63647C2211yescharacteristic
57C3×#821C2211yescharacteristic, complemented
58C3×#821C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64#63562C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×#919—31no—
68C2×#916—31no—
69C2×#916—31no—
70C2×#912—31no—
71#5627—31no—
72#5606—31no—
73C3×#452—31no—
74C3×#449—31no—
75#5239—31no—
76#5238—31no—
77#5186—31no—
78#5170—31no—
79#5169—31no—
80#5156—31no—
81#5047—31no—
82#5037—31no—
83#4809—31no—
84#4806—31no—
85#4804—31no—
86#4804—31no—
87#4776—31no—
88#4773—31no—
89#4772—31no—
90#4772—31no—
91#4734D311yescharacteristic, complemented
92#4733D311yescharacteristic, complemented
93D3×C22⋊C8—31no—
94D3×C22⋊C8—31no—
95D3×C22⋊C8—61no—
96C23×C3⋊D3D411yescharacteristic
97C22×D32—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3D411yescharacteristic
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3D411yescharacteristic
103C2×C4×C3⋊D3D411yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C3×#235—22no—
110C3×#235—22no—
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121#3811—28no—
122C2×#627—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#625—21no—
128C2×#624—21no—
129#3805—28no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133#3802—22no—
134#3802—22no—
135C4×D32—28no—
136#3798—28no—
137#3797—22no—
138#3797—22no—
139#3796—22no—
140#3796—22no—
141#3796—22no—
142#3796—22no—
143#3796D414yescomplemented
144#3796D414yescomplemented
145C2×C32×C8C2311yescharacteristic
146C2×C32×C8C2311yescharacteristic
147C2×C3⋊(C3⋊C8)C2311yescharacteristic
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149C8×C3⋊D3—22no—
150C8×C3⋊D3—22no—
151C3×#217—21no—
152C3×(C2×D3)⋊C4—21no—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4—21no—
156C3×Dic12—22no—
157C3×D24—22no—
158C3×#204—22no—
159C3×#204—22no—
160Dic3⋊Dic3—21no—
161#3722—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164Dic32—21no—
165#3718—22no—
166#3715—22no—
167#3715—22no—
168#3713—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172D3×#41—64no—
173D3×#41—64no—
174D3×#41—64no—
175D3×#41—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—31no—
184C2×#237—61no—
185C2×#237—61no—
186C2×D3×D4—31no—
187C2×D3×D4—31no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—61no—
191C2×#235—61no—
192C2×#235C2×D311yescharacteristic
193C2×#235C2×D311yescharacteristic
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×C4×D3—61no—
198C22×C4×D3—61no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C2×C3×SD16—31no—
202C2×C3×D8—31no—
203C3×C22⋊Q8—31no—
204C3×#121—31no—
205#946—31no—
206C2×#216—31no—
207C2×#216—31no—
208C2×#215—31no—
209C2×#215—31no—
210#938—31no—
211#937—61no—
212D4×Dic3—61no—
213C2×#214—31no—
214C2×#214—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930C2×D311yescharacteristic, complemented
218#924C2×D311yescharacteristic, complemented
219#919—64no—
220#916—64no—
221#916—64no—
222#912—64no—
223C2×Dic12C2×D311yescharacteristic, complemented
224C2×D24C2×D311yescharacteristic, complemented
225C2×#204C2×D311yescharacteristic, complemented
226C2×#204C2×D311yescharacteristic, complemented
227C2×D3×C8—31no—
228C2×D3×C8—31no—
229C2×D3×C8—31no—
230C2×D3×C8—31no—
231C2×D3×C8—61no—
232C2×D3×C8—61no—
233#897—31no—
234#895—31no—
235#894—61no—
236#893—61no—
237#892—31no—
238#892—31no—
239#883—61no—
240#882—61no—
241#67⋊C4—61no—
242#67⋊C4—61no—
243C3×#103—31no—
244C3×#103—31no—
245C3×#102—31no—
246C3×#102—31no—
247C3×C22⋊C8—21no—
248C3×C22⋊C8C2×D311yescharacteristic, complemented
249C3×C22⋊C8C2×D311yescharacteristic, complemented
250#835—31no—
251#835—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#830—31no—
256#830—61no—
257#821C2×D311yescharacteristic, complemented
258#821C2×D311yescharacteristic, complemented
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—61no—
264(C2×D3)⋊C8—61no—
265#816C2×D311yescharacteristic, complemented
266#816C2×D311yescharacteristic, complemented
267#810—31no—
268#810—31no—
269#809—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3—41no—
275C22×C3⋊D3C2×D411yescharacteristic
276C22×C3⋊D3C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—21no—
279C22×C3×D3—21no—
280C2×D32—24no—
281C2×D32—42no—
282C2×D32—42no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4C2×D411yescharacteristic
286C2×C32×C4C2411yescharacteristic
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3C2×D411yescharacteristic
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4×C3⋊D3—22no—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—22no—
294C4×C3⋊D3C2×D412yes—
295C4×C3⋊D3C2×D412yes—
296C3×#67—24no—
297C3×#67—24no—
298C3×#67—42no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12C2×D412yes—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×Dic6—21no—
313C3×Dic6—21no—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6C2×D412yes—
317C3×Dic6C2×D412yes—
318#627—24no—
319#626—24no—
320#626—24no—
321#626—42no—
322#626—42no—
323#625—24no—
324#624—24no—
325D3×Dic3—24no—
326D3×Dic3—24no—
327D3×Dic3—42no—
328C32×C8—21no—
329C32×C8—21no—
330C3⋊(C3⋊C8)—21no—
331C3⋊(C3⋊C8)—21no—
332C22×#41—91no—
333C2×#135—91no—
334C2×#135—91no—
335#525—91no—
336#452—31no—
337#452—91no—
338#451—91no—
339#450—91no—
340#449—31no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—91no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C3×#41—62no—
356C2×C3×Q8—31no—
357C2×C3×Q8—31no—
358C2×C3×Q8—31no—
359C2×C3×D4—31no—
360C2×C3×D4—31no—
361C2×C3×D4—31no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C22×C3×C4—21no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385#239—34no—
386#239—34no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391D3×Q8—62no—
392D3×Q8—62no—
393D3×Q8—62no—
394D3×Q8—62no—
395#237—34no—
396#237—34no—
397#237—62no—
398#237—62no—
399#237—62no—
400#237—62no—
401#237—68no—
402#237—68no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—68no—
406D3×D4—68no—
407D3×D4—62no—
408D3×D4—62no—
409#235—22no—
410#235—22no—
411#235—22no—
412#235—22no—
413#235—68no—
414#235—68no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12C22×D311yescharacteristic
420C2×D12C22×D311yescharacteristic
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—21no—
423C2×C4×D3—21no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—68no—
437C2×C4×D3—68no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—61no—
443C2×C4×D3—61no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6C22×D311yescharacteristic
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×SD16—62no—
456C3×SD16—62no—
457C3×D8—62no—
458C2×C3×C8—21no—
459C2×C3×C8—21no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C2×C3×C8C22×D311yescharacteristic
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—61no—
467C3×C22⋊C4—61no—
468C3×C22⋊C4—61no—
469#217—21no—
470#217—61no—
471#216—62no—
472#216—62no—
473#215—62no—
474#215—62no—
475#214—62no—
476#214—62no—
477#213—62no—
478#213—62no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D311yescharacteristic
487C4⋊Dic3C22×D311yescharacteristic
488Dic3⋊C4—21no—
489Dic3⋊C4—61no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C2×C3⋊C8—31no—
493C2×C3⋊C8—31no—
494C2×C3⋊C8—31no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—61no—
497C2×C3⋊C8—61no—
498Dic12—22no—
499D24—22no—
500#204—22no—
501#204—22no—
502D3×C8—62no—
503D3×C8—62no—
504D3×C8—62no—
505D3×C8—62no—
506D3×C8—122no—
507D3×C8—122no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—44no—
517C2×C3⋊D3#12012yes—
518C2×C3⋊D3#13512yescomplemented
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528D32—48no—
529C32×C4—21no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—21no—
533C3⋊Dic3#12012yes—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C2×#41—31no—
540C2×#41—31no—
541C2×#41—91no—
542C2×#41—91no—
543C2×#41—91no—
544C2×#41—181no—
545C2×#41—181no—
546C2×#41—184no—
547C2×#41—184no—
548C22×Q8—91no—
549C22×D4—91no—
550C22×D4—181no—
551C23×C4—91no—
552C23×C4—181no—
553#135—184no—
554#135—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—31no—
562C2×D8—91no—
563C22×C8—91no—
564C22×C8—91no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—31no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—31no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—31no—
580#102—91no—
581#102—91no—
582C22⋊C8—91no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C22⋊C8D3211yescharacteristic, complemented
586C23×C3—21no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3D3×D411yescharacteristic
591C23×C3D3×D411yescharacteristic
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—31no—
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—64no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3—122no—
612C22×D3—122no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—122no—
616C3×Q8—32no—
617C3×Q8—32no—
618C3×Q8—61no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×D4—32no—
623C3×D4—32no—
624C3×D4—64no—
625C3×D4—64no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—61no—
630C3×D4—122no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—64no—
640C2×C3×C4—64no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4D3×D411yescharacteristic
647C2×C3×C4D3×D411yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650#67—24no—
651#67—24no—
652#67—42no—
653#67—64no—
654#67—64no—
655#67—64no—
656#67—64no—
657#67—122no—
658#67—122no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—64no—
671C2×Dic3—64no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—122no—
675C2×Dic3—122no—
676D12—21no—
677D12—21no—
678D12—21no—
679D12—21no—
680D12—64no—
681D12—64no—
682D12—122no—
683D12—122no—
684D12D3×D412yes—
685D12D3×D412yes—
686C4×D3—24no—
687C4×D3—24no—
688C4×D3—32no—
689C4×D3—32no—
690C4×D3—32no—
691C4×D3—32no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—62no—
697C4×D3—62no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—62no—
701C4×D3—62no—
702C4×D3—61no—
703C4×D3—61no—
704C4×D3—61no—
705C4×D3—61no—
706C4×D3—122no—
707C4×D3—121no—
708C4×D3—121no—
709C4×D3—122no—
710C4×D3—122no—
711Dic6—21no—
712Dic6—21no—
713Dic6—21no—
714Dic6—21no—
715Dic6—64no—
716Dic6—64no—
717Dic6D3×D412yes—
718Dic6D3×D412yes—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—21no—
722C3×C8—21no—
723C3×C8—41no—
724C3×C8—41no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—61no—
728C3⋊C8—61no—
729C3⋊C8—121no—
730C3⋊C8—121no—
731C2×C32—41no—
732C2×C32C2×#12011yescharacteristic
733C2×C32C2×#13511yescharacteristic
734C2×C32#57511yescharacteristic
735C3⋊D3—22no—
736C3⋊D3—22no—
737C3×D3—42no—
738C3×D3—42no—
739C3×D3—81no—
740C24—91no—
741C24—181no—
742#41—62no—
743#41—62no—
744#41—62no—
745#41—62no—
746#41—94no—
747#41—94no—
748#41—188no—
749#41—182no—
750#41—182no—
751#41—182no—
752#41—182no—
753#41—188no—
754C2×Q8—31no—
755C2×Q8—31no—
756C2×Q8—31no—
757C2×Q8—181no—
758C2×Q8—182no—
759C2×Q8—182no—
760C2×D4—31no—
761C2×D4—31no—
762C2×D4—31no—
763C2×D4—61no—
764C2×D4—61no—
765C2×D4—61no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4—181no—
771C2×D4—182no—
772C2×D4—182no—
773C2×D4—188no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—91no—
780C22×C4—91no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—181no—
784C22×C4—188no—
785C22×C4—181no—
786C22×C4—181no—
787C22×C4—181no—
788C22×C4C2×D3211yescharacteristic
789Q16—62no—
790Q16—182no—
791SD16—62no—
792SD16—62no—
793SD16—182no—
794SD16—182no—
795D8—62no—
796D8—182no—
797C2×C8—91no—
798C2×C8—91no—
799C2×C8—182no—
800C2×C8—182no—
801C2×C8C2×D3211yescharacteristic
802C2×C8C2×D3211yescharacteristic
803C4⋊C4—31no—
804C4⋊C4—31no—
805C4⋊C4—61no—
806C4⋊C4—181no—
807C22⋊C4—61no—
808C22⋊C4—61no—
809C22⋊C4—181no—
810C22⋊C4—181no—
811C22⋊C4—181no—
812C42—181no—
813C22×C3—22no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3C2×D3×D411yescharacteristic
833C22×C3C2×D3×D411yescharacteristic
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—32no—
837C2×D3—32no—
838C2×D3—32no—
839C2×D3—32no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—128no—
862C2×D3—128no—
863C2×D3—124no—
864C2×D3—124no—
865C2×D3—128no—
866C3×C4—21no—
867C3×C4—21no—
868C3×C4—21no—
869C3×C4—21no—
870C3×C4—41no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4C2×D3×D411yescharacteristic
879C3×C4C2×D3×D411yescharacteristic
880Dic3—22no—
881Dic3—22no—
882Dic3—32no—
883Dic3—32no—
884Dic3—41no—
885Dic3—41no—
886Dic3—41no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—121no—
891C32#300211yescharacteristic, complemented, Sylow
892C23—61no—
893C23—61no—
894C23—61no—
895C23—91no—
896C23—91no—
897C23—182no—
898C23—182no—
899C23—184no—
900C23—361no—
901C23—362no—
902C23—362no—
903C23#380211yescharacteristic
904Q8—32no—
905Q8—32no—
906Q8—61no—
907Q8—61no—
908Q8—61no—
909Q8—61no—
910Q8—184no—
911D4—32no—
912D4—32no—
913D4—64no—
914D4—64no—
915D4—61no—
916D4—61no—
917D4—61no—
918D4—61no—
919D4—122no—
920D4—184no—
921D4—184no—
922D4—184no—
923D4—362no—
924D4—362no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—64no—
928C2×C4—64no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—91no—
935C2×C4—92no—
936C2×C4—92no—
937C2×C4—91no—
938C2×C4—182no—
939C2×C4—182no—
940C2×C4—184no—
941C2×C4—184no—
942C2×C4—184no—
943C2×C4—182no—
944C2×C4—181no—
945C2×C4—181no—
946C2×C4—362no—
947C2×C4#380211yescharacteristic
948C2×C4C22×D3211yescharacteristic
949C8—21no—
950C8—21no—
951C8—181no—
952C8—181no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—42no—
957C2×C3—41no—
958C2×C3—41no—
959C2×C3—122no—
960C2×C3—122no—
961C2×C3—241no—
962C2×C3D3×#12011yescharacteristic
963C2×C3D3×#12011yescharacteristic
964C2×C3D3×#13511yescharacteristic
965C2×C3D3×#13511yescharacteristic
966C2×C3#577311yescharacteristic
967C2×C3#577711yescharacteristic
968D3—42no—
969D3—42no—
970D3—64no—
971D3—62no—
972D3—62no—
973D3—62no—
974D3—62no—
975D3—81no—
976D3—122no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—62no—
981C22—62no—
982C22—92no—
983C22—92no—
984C22—121no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—121no—
991C22—181no—
992C22—181no—
993C22—181no—
994C22—181no—
995C22—364no—
996C22—368no—
997C22C2×#380211yescharacteristic
998C4—21no—
999C4—62no—
1000C4—62no—
1001C4—92no—
1002C4—121no—
1003C4—121no—
1004C4—121no—
1005C4—181no—
1006C4D32×D411yescharacteristic
1007C4D32×D411yescharacteristic
1008C3—21no—
1009C3#8008211yescharacteristic, complemented
1010C3#8022611yescharacteristic, complemented
1011C2—41no—
1012C2—122no—
1013C2—122no—
1014C2—182no—
1015C2—182no—
1016C2—241no—
1017C2#1059425811yescharacteristic
1018C2#1059468411yescharacteristic
1019C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3002
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. #10594922C2semidirect
3. C2×#63810C2semidirect
4. C2×#63809C2semidirect
5. C3⋊D3×C22⋊C8C2semidirect
6. C3×#4734C2semidirect
7. C3×#4733C2semidirect
8. #10591170C2semidirect
9. #10591161C2semidirect
10. #10590956C2semidirect
11. #10590956C2semidirect
12. #10590950C2semidirect
13. #10590945C2semidirect
14. #10590943C2semidirect
15. #10590824C2semidirect
31. C2×#3796C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. C2×C8×C3⋊D3C22semidirect
34. C3×#930C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
39. C2×C3×#204C22semidirect
46. #63849C22semidirect
47. C2×#3718C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63657C22semidirect
57. C3×#821C22semidirect
58. C3×#821C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
61. #63565C22semidirect
62. #63565C22semidirect
63. #63562C22semidirect
64. #63562C22semidirect
91. #4734D3semidirect
92. #4733D3semidirect
143. #3796D4semidirect
144. #3796D4semidirect
217. #930C2×D3semidirect
218. #924C2×D3semidirect
223. C2×Dic12C2×D3semidirect
224. C2×D24C2×D3semidirect
225. C2×#204C2×D3semidirect
226. C2×#204C2×D3semidirect
248. C3×C22⋊C8C2×D3semidirect
249. C3×C22⋊C8C2×D3semidirect
257. #821C2×D3semidirect
258. #821C2×D3semidirect
265. #816C2×D3semidirect
266. #816C2×D3semidirect
518. C2×C3⋊D3#135semidirect
585. C22⋊C8D32semidirect
891. C32#3002semidirect
1009. C3#80082semidirect
1010. C3#80226semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
#105949222
C2×#638102
C2×#638092
C3⋊D3×C22⋊C82
C3×#47342
C3×#47332
#105911702
#105911612
#105909562
#105909502
#105909452
#105909432
#105908242
#802263
#800823