Finite Group Databasebeta

← #11863903

Subgroups — #11863903

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2#10595005C211yesmaximal, characteristic, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4C2×#63806C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
8#10591184C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#10590954C211yesmaximal, characteristic, complemented
11#10590951C211yesmaximal, characteristic, complemented
12#10590949C211yesmaximal, characteristic, complemented
13#10590947C211yesmaximal, characteristic, complemented
14#10590942C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80226—31nomaximal
17#78610—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3804—21no—
23D3×#235—24no—
24D3×#235—24no—
25C2×D3×D12C2211yescharacteristic
26C2×C4×D32—21no—
27C2×#3799C2211yescharacteristic
28C2×#3799C2211yescharacteristic, complemented
29C2×#3798—21no—
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32#64139C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C3×#924C2211yescharacteristic, complemented
36C2×C3×Dic12C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic, complemented
40#63977—21no—
41#63952—21no—
42#63909C2211yescharacteristic
43#63904—21no—
44#63856C2211yescharacteristic
45#63850—21no—
46#63841C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63808—24no—
52#63806—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic
60C3×#816C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#235—31no—
67#5791—31no—
68C2×#919—31no—
69C2×#916—31no—
70C2×#904—31no—
71C2×#904—31no—
72#5627—31no—
73C3×#452—31no—
74C2×C3×C22⋊C8—31no—
75#5238—31no—
76#5186—31no—
77#5169—31no—
78#5113—31no—
79#5113—31no—
80#5047—31no—
81#4806—31no—
82#4804—31no—
83#4773—31no—
84#4772—31no—
85#4739—31no—
86#4738—31no—
87#4734—31no—
88#4734—31no—
89#4734—31no—
90#4734—61no—
91#4733—31no—
92#4733D311yescharacteristic, complemented
93#4732—31no—
94#4731—31no—
95D3×C22⋊C8D311yescharacteristic, complemented
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101#3828—22no—
102#3828—22no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C22×C3×Dic3D411yescharacteristic
109C3×#235—22no—
110C3×#235—22no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3D411yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121D3×#67—28no—
122C2×#627—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#625—21no—
128C2×#624—21no—
129C2×#624—21no—
130#3804—28no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133D3×D12—22no—
134D3×D12—22no—
135C4×D32—28no—
136#3799—22no—
137#3799—22no—
138#3799—22no—
139#3799D414yescomplemented
140#3798—28no—
141#3795—22no—
142#3795D414yescomplemented
143D3×Dic6—22no—
144D3×Dic6—22no—
145C2×C32×C8C2311yescharacteristic
146C2×C32×C8C2311yescharacteristic
147#3752—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3745—22no—
150#3744—22no—
151C3×#217—21no—
152C3×C4⋊Dic3C2311yescharacteristic
153C3×Dic3⋊C4—21no—
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C3×Dic12—22no—
157C3×#204—22no—
158C3×D3×C8—22no—
159C3×D3×C8—22no—
160#3724—21no—
161#3722—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164Dic32—21no—
165#3719—22no—
166#3717—22no—
167#3717—22no—
168#3714—22no—
169#3002—91noSylow
170C2×C3×#41—31no—
171C23×C3×C4—31no—
172C22×#67—61no—
173D3×#41—64no—
174D3×#41—64no—
175C2×#239—31no—
176C2×#239—31no—
177C2×D3×Q8—31no—
178C2×#237—31no—
179C2×#237—61no—
180C2×D3×D4—31no—
181C2×D3×D4—61no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—61no—
188C2×#235—61no—
189C2×#235—64no—
190C2×#235—64no—
191C2×#235—61no—
192C2×#235—61no—
193C2×#235C2×D311yescharacteristic
194C22×D12—31no—
195C22×C4×D3—61no—
196C22×C4×D3—61no—
197C22×C4×D3C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C22×C3×C8—31no—
202C22×C3×C8—31no—
203C3×C22⋊Q8—31no—
204#953—61no—
205#946—31no—
206C2×#216—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#213—31no—
210#930—31no—
211#930—31no—
212#930—31no—
213#930—61no—
214#929—61no—
215C4×#67—61no—
216C4×#67—61no—
217#926—31no—
218#924—31no—
219#924C2×D311yescharacteristic, complemented
220#919—64no—
221#916—64no—
222C2×Dic12—31no—
223C2×Dic12C2×D311yescharacteristic, complemented
224#904—64no—
225#904—64no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—61no—
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—61no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×D3×C8C2×D311yescharacteristic, complemented
237C2×D3×C8C2×D311yescharacteristic, complemented
238#895—31no—
239#894—61no—
240#893—61no—
241#892—31no—
242#882—61no—
243#67⋊C4—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—21no—
247C3×C22⋊C8—31no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8C2×D311yescharacteristic, complemented
251C3×C22⋊C8C2×D311yescharacteristic, complemented
252#835—31no—
253#832—31no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260#821C2×D311yescharacteristic, complemented
261(C2×D3)⋊C8C2×D311yescharacteristic
262(C2×D3)⋊C8C2×D311yescharacteristic
263#816—31no—
264#816—31no—
265#816—31no—
266#816—31no—
267#816—61no—
268#816C2×D311yescharacteristic, complemented
269#810—31no—
270#809—31no—
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3⋊D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—41no—
278C22×C3×D3C2×D411yescharacteristic
279C22×C3×D3C2×D411yescharacteristic
280C2×D32—24no—
281C2×D32—42no—
282C2×D32—42no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4C2×D411yescharacteristic
286C2×C32×C4C2411yescharacteristic
287#638—24no—
288#638—42no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)—21no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)C2×D412yes—
295C4×C3⋊D3—24no—
296#634—21no—
297#634C2×D412yes—
298C3×#67—24no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12C2×D412yes—
307C3×C4×D3—24no—
308C3×C4×D3—22no—
309C3×C4×D3—21no—
310C3×C4×D3—21no—
311C3×C4×D3—22no—
312C3×C4×D3C2×D412yes—
313C3×C4×D3C2×D412yes—
314C3×Dic6—21no—
315C3×Dic6—21no—
316C3×Dic6—21no—
317C3×Dic6C2×D412yes—
318#627—24no—
319#626—24no—
320#626—24no—
321#626—42no—
322#626—42no—
323#625—24no—
324#624—24no—
325#624—42no—
326D3×Dic3—24no—
327D3×Dic3—24no—
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—91no—
341#449—91no—
342#448—91no—
343#447—91no—
344#416—91no—
345#416—91no—
346C2×C22⋊C8—31no—
347C24×C3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3D1211yescharacteristic
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—31no—
354C2×C3×Q8—31no—
355C2×C3×D4—31no—
356C2×C3×D4—61no—
357C22×C3×C4—21no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4—61no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—21no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—68no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—121no—
381C2×#67—121no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3D1211yescharacteristic
385#239—34no—
386#239—62no—
387#239—62no—
388#239—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391#237—34no—
392#237—68no—
393#237—62no—
394D3×D4—62no—
395D3×D4—62no—
396D3×D4—68no—
397#235—22no—
398#235—22no—
399#235—34no—
400#235—34no—
401#235—62no—
402#235—62no—
403#235—62no—
404#235—62no—
405#235—62no—
406#235—68no—
407#235—68no—
408#235—62no—
409#235—62no—
410#235—62no—
411#235—68no—
412#235—122no—
413#235—122no—
414C2×D12—31no—
415C2×D12—31no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—61no—
419C2×D12—61no—
420C2×D12—62no—
421C2×D12—61no—
422C2×D12—61no—
423C2×D12—62no—
424C2×D12—61no—
425C2×D12—61no—
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—21no—
428C2×C4×D3—22no—
429C2×C4×D3—22no—
430C2×C4×D3—68no—
431C2×C4×D3—68no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—121no—
441C2×C4×D3D1211yescharacteristic
442C2×C4×D3D1211yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—31no—
446C2×Dic6—31no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—62no—
452C2×Dic6C22×D311yescharacteristic
453C2×Dic6C22×D311yescharacteristic
454C3×Q16—62no—
455C3×SD16—62no—
456C2×C3×C8—21no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8—62no—
461C2×C3×C8—62no—
462C2×C3×C8C22×D311yescharacteristic
463C2×C3×C8C22×D311yescharacteristic
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—31no—
467C3×C4⋊C4—61no—
468C3×C22⋊C4—61no—
469#217—21no—
470#217—61no—
471#217—61no—
472#216—62no—
473#215—62no—
474#215—62no—
475#213—62no—
476(C2×D3)⋊C4—61no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—121no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3C22×D311yescharacteristic
487Dic3⋊C4—21no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C2×C3⋊C8C22×D311yescharacteristic
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—22no—
495Dic12—62no—
496D24—62no—
497D24—62no—
498D24—62no—
499D24—122no—
500#204—22no—
501#204—62no—
502#204—62no—
503#204—62no—
504#204—62no—
505#204—122no—
506D3×C8—22no—
507D3×C8—22no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—22no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3⋊D3—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—22no—
523C2×C3×D3—44no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527C2×C3×D3#13512yescomplemented
528D32—48no—
529C32×C4—21no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—22no—
533C3⋊Dic3—41no—
534C3×Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3#12012yes—
539C2×#41—31no—
540C2×#41—91no—
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—31no—
552C23×C4—181no—
553#135—184no—
554#135—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—91no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—31no—
565#123—181no—
566C22⋊Q8—31no—
567C22⋊Q8—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571C4×D4—181no—
572C4×D4—181no—
573#117—91no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#102—31no—
579#102—91no—
580#102—91no—
581#102—91no—
582C22⋊C8—31no—
583C22⋊C8—31no—
584C22⋊C8—31no—
585C22⋊C8D3211yescharacteristic, complemented
586C23×C3—21no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—61no—
592C23×C3—121no—
593C23×C3C2×D1211yescharacteristic
594C23×C3D3×D411yescharacteristic
595C22×D3—21no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—41no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3C2×D1211yescharacteristic
612C22×D3C2×D1211yescharacteristic
613C3×Q8—32no—
614C3×Q8—61no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×D4—32no—
618C3×D4—64no—
619C3×D4—61no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—31no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—31no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—64no—
635C2×C3×C4—62no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4C2×D1211yescharacteristic
642C2×C3×C4D3×D411yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645#67—24no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—64no—
652#67—124no—
653#67—122no—
654#67—122no—
655#67—122no—
656#67—122no—
657#67—242no—
658C2×Dic3—21no—
659C2×Dic3—22no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—64no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—64no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3C2×D1211yescharacteristic
671C2×Dic3C2×D1211yescharacteristic
672D12—21no—
673D12—32no—
674D12—32no—
675D12—62no—
676D12—64no—
677D12—64no—
678D12—61no—
679D12—61no—
680D12—61no—
681D12—61no—
682D12—61no—
683D12—61no—
684D12—121no—
685D12—121no—
686D12—121no—
687D12—122no—
688D12—122no—
689D12D3×D412yes—
690C4×D3—24no—
691C4×D3—22no—
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—22no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—64no—
698C4×D3—64no—
699C4×D3—64no—
700C4×D3—64no—
701C4×D3—124no—
702C4×D3—122no—
703C4×D3—122no—
704C4×D3D3×D412yes—
705C4×D3D3×D412yes—
706Dic6—21no—
707Dic6—21no—
708Dic6—21no—
709Dic6—32no—
710Dic6—32no—
711Dic6—62no—
712Dic6—64no—
713Dic6—64no—
714Dic6—61no—
715Dic6—61no—
716Dic6—121no—
717Dic6D3×D412yes—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—21no—
722C3×C8—41no—
723C3×C8—41no—
724C3×C8—61no—
725C3×C8—61no—
726C3⋊C8—21no—
727C3⋊C8—21no—
728C2×C32—41no—
729C2×C32C2×#12011yescharacteristic
730C2×C32C2×#13511yescharacteristic
731C2×C32#57511yescharacteristic
732C3⋊D3—42no—
733C3⋊D3—81no—
734C3×D3—22no—
735C3×D3—22no—
736C3×D3—42no—
737C24—31no—
738C24—181no—
739#41—62no—
740#41—62no—
741#41—94no—
742#41—94no—
743#41—182no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—182no—
749#41—188no—
750#41—188no—
751C2×Q8—31no—
752C2×Q8—31no—
753C2×Q8—91no—
754C2×Q8—181no—
755C2×Q8—182no—
756C2×Q8—182no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—91no—
760C2×D4—91no—
761C2×D4—181no—
762C2×D4—182no—
763C2×D4—182no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—188no—
768C2×D4—181no—
769C2×D4—181no—
770C2×D4—181no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—31no—
776C22×C4—62no—
777C22×C4—62no—
778C22×C4—61no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4—181no—
782C22×C4—188no—
783C22×C4—181no—
784C22×C4—181no—
785C22×C4C2×D3211yescharacteristic
786Q16—62no—
787Q16—182no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792D8—182no—
793D8—182no—
794C2×C8—31no—
795C2×C8—31no—
796C2×C8—62no—
797C2×C8—62no—
798C2×C8C2×D3211yescharacteristic
799C2×C8C2×D3211yescharacteristic
800C4⋊C4—31no—
801C4⋊C4—61no—
802C4⋊C4—91no—
803C4⋊C4—181no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—181no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—32no—
818C22×C3—32no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—62no—
827C22×C3—124no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3C22×D1211yescharacteristic
831C22×C3C2×D3×D411yescharacteristic
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—22no—
837C2×D3—44no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—122no—
843C2×D3—128no—
844C2×D3—128no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3#88212yes—
861C2×D3#90412yescomplemented
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—32no—
867C3×C4—41no—
868C3×C4—62no—
869C3×C4—61no—
870C3×C4—121no—
871C3×C4—121no—
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C2×D3×D411yescharacteristic
876Dic3—21no—
877Dic3—22no—
878Dic3—41no—
879Dic3—41no—
880Dic3—62no—
881Dic3—62no—
882Dic3—122no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886Dic3#88212yes—
887C32#300211yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—62no—
891C23—62no—
892C23—61no—
893C23—121no—
894C23—184no—
895C23—181no—
896C23—181no—
897C23—362no—
898C23—362no—
899C23D3×D1211yescharacteristic
900Q8—32no—
901Q8—61no—
902Q8—61no—
903Q8—61no—
904Q8—92no—
905Q8—184no—
906Q8—181no—
907D4—32no—
908D4—64no—
909D4—61no—
910D4—92no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—181no—
917D4—181no—
918D4—362no—
919D4—362no—
920D4—362no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—31no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—31no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—64no—
930C2×C4—62no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—184no—
937C2×C4—184no—
938C2×C4—184no—
939C2×C4—184no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—362no—
943C2×C4D3×D1211yescharacteristic
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—21no—
947C8—61no—
948C8—61no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—62no—
955C2×C3—62no—
956C2×C3—81no—
957C2×C3—122no—
958C2×C3C2×#88211yescharacteristic
959C2×C3D3×#12011yescharacteristic
960C2×C3C2×#90411yescharacteristic
961C2×C3#574811yescharacteristic
962C2×C3D3×#13511yescharacteristic
963C2×C3#577711yescharacteristic
964D3—22no—
965D3—22no—
966D3—42no—
967D3—122no—
968D3—122no—
969D3—242no—
970D3—241no—
971D3—241no—
972D3—481no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—32no—
977C22—32no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—61no—
982C22—62no—
983C22—124no—
984C22—121no—
985C22—121no—
986C22—182no—
987C22—368no—
988C22—361no—
989C22—361no—
990C22—361no—
991C22—361no—
992C22—361no—
993C22C2×D3×D1211yescharacteristic
994C4—21no—
995C4—32no—
996C4—61no—
997C4—62no—
998C4—121no—
999C4—121no—
1000C4—182no—
1001C4—361no—
1002C4D32×D411yescharacteristic
1003C4D32×D411yescharacteristic
1004C3—21no—
1005C3#7861011yescharacteristic, complemented
1006C3#8022611yescharacteristic, complemented
1007C2—41no—
1008C2—62no—
1009C2—62no—
1010C2—122no—
1011C2—362no—
1012C2—721no—
1013C2D3×#88211yescharacteristic
1014C2D3×#90411yescharacteristic
1015C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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×D3×#235C2semidirect
2. #10595005C2semidirect
3. C2×#63808C2semidirect
4. C2×#63806C2semidirect
5. #10592433C2semidirect
6. C3×#4733C2semidirect
7. C3×D3×C22⋊C8C2semidirect
8. #10591184C2semidirect
9. #10591163C2semidirect
10. #10590954C2semidirect
11. #10590951C2semidirect
12. #10590949C2semidirect
13. #10590947C2semidirect
14. #10590942C2semidirect
15. #10590690C2semidirect
28. C2×#3799C22semidirect
32. #64139C22semidirect
33. C2×#3745C22semidirect
34. C2×#3744C22semidirect
35. C3×#924C22semidirect
36. C2×C3×Dic12C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×D3×C8C22semidirect
39. C2×C3×D3×C8C22semidirect
46. #63841C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3717C22semidirect
50. C2×#3714C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63643C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
60. C3×#816C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
63. #63564C22semidirect
64. #63563C22semidirect
92. #4733D3semidirect
95. D3×C22⋊C8D3semidirect
139. #3799D4semidirect
142. #3795D4semidirect
219. #924C2×D3semidirect
223. C2×Dic12C2×D3semidirect
235. C2×#204C2×D3semidirect
236. C2×D3×C8C2×D3semidirect
237. C2×D3×C8C2×D3semidirect
250. C3×C22⋊C8C2×D3semidirect
251. C3×C22⋊C8C2×D3semidirect
254. #830C2×D3semidirect
260. #821C2×D3semidirect
268. #816C2×D3semidirect
527. C2×C3×D3#135semidirect
585. C22⋊C8D32semidirect
861. C2×D3#904semidirect
887. C32#3002semidirect
1005. C3#78610semidirect
1006. C3#80226semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
#105950052
C2×#638082
C2×#638062
#105924332
C3×#47332
C3×D3×C22⋊C82
#105911842
#105911632
#105909542
#105909512
#105909492
#105909472
#105909422
#105906902
#802263
#786103