Finite Group Databasebeta

← #11863905

Subgroups — #11863905

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2#10594892C211yesmaximal, characteristic, complemented
3C2×#63807C211yesmaximal, characteristic, complemented
4C2×#63806C211yesmaximal, characteristic, complemented
5#10592432C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10590954C211yesmaximal, characteristic, complemented
11#10590952C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590944C211yesmaximal, characteristic, complemented
14#10590822C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80082—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×#3798—21no—
29C2×#3795C2211yescharacteristic
30C2×#3795C2211yescharacteristic, complemented
31C2×D3×Dic6C2211yescharacteristic
32#64133C2211yescharacteristic, complemented
33C2×#3746C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic, complemented
40#63976—21no—
41Dic3×#67—21no—
42#63908C2211yescharacteristic
43#63905—21no—
44#63879—21no—
45#63857C2211yescharacteristic
46#63841C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51#63807—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×#916—31no—
69C2×#912—31no—
70C2×#904—31no—
71C2×#904—31no—
72#5606—31no—
73C3×#449—31no—
74C2×C3×C22⋊C8—31no—
75#5239—31no—
76#5170—31no—
77#5156—31no—
78#5113—31no—
79#5113—31no—
80#5037—31no—
81#4809—31no—
82#4804—31no—
83#4776—31no—
84#4772—31no—
85#4739—31no—
86#4738—31no—
87#4734—31no—
88#4734D311yescharacteristic, complemented
89#4733—31no—
90#4733—31no—
91#4733—31no—
92#4733—61no—
93#4732—31no—
94#4731—31no—
95D3×C22⋊C8D311yescharacteristic, complemented
96C23×C3×D3D411yescharacteristic
97C22×D32—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×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C22×C3×Dic3D411yescharacteristic
109C3×#235—22no—
110C3×#235—22no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3D411yescharacteristic
117C2×C3×C4×D3D411yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121D3×#67—28no—
122C2×#627—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×#624—21no—
129#3804—28no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3—21no—
133D3×D12—22no—
134D3×D12—22no—
135C4×D32—28no—
136#3799—22no—
137#3799D414yescomplemented
138#3798—28no—
139#3795—22no—
140#3795—22no—
141#3795—22no—
142#3795D414yescomplemented
143D3×Dic6—22no—
144D3×Dic6—22no—
145C2×C32×C8C2311yescharacteristic
146C2×C32×C8C2311yescharacteristic
147#3757—21no—
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750—21no—
150#3746—22no—
151#3744—22no—
152C3×(C2×D3)⋊C4—21no—
153C3×C4⋊Dic3C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156C3×D24—22no—
157C3×#204—22no—
158C3×D3×C8—22no—
159C3×D3×C8—22no—
160Dic3⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164Dic32—21no—
165#3719—22no—
166#3716—22no—
167#3716—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×D3×Q8—31no—
177C2×#237—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×SD16—31no—
200C2×C3×D8—31no—
201C22×C3×C8—31no—
202C22×C3×C8—31no—
203C3×#121—31no—
204#953—61no—
205C2×#216—31no—
206#938—31no—
207#937—61no—
208D4×Dic3—61no—
209C2×#214—31no—
210C2×#214—31no—
211C2×#213—31no—
212#930—31no—
213#930C2×D311yescharacteristic, complemented
214#929—61no—
215C4×#67—61no—
216C4×#67—61no—
217#926—31no—
218#924—31no—
219#924—31no—
220#924—31no—
221#924—61no—
222#916—64no—
223#912—64no—
224C2×Dic12—31no—
225C2×Dic12—31no—
226C2×Dic12—31no—
227C2×Dic12—61no—
228#904—64no—
229#904—64no—
230C2×D24—31no—
231C2×D24C2×D311yescharacteristic, complemented
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—31no—
236C2×#204—61no—
237C2×#204C2×D311yescharacteristic, complemented
238C2×D3×C8C2×D311yescharacteristic, complemented
239C2×D3×C8C2×D311yescharacteristic, complemented
240#897—31no—
241#892—31no—
242#883—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—22no—
275C22×C3×D3—22no—
276C22×C3×D3—21no—
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—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3—21no—
291C4⋊(C3⋊D3)—21no—
292C4⋊(C3⋊D3)C2×D412yes—
293C4×C3⋊D3—24no—
294#634—21no—
295#634—21no—
296#634—21no—
297#634C2×D412yes—
298C3×#67—24no—
299C3×#67—42no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12C2×D412yes—
309C3×C4×D3—24no—
310C3×C4×D3—22no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—22no—
314C3×C4×D3C2×D412yes—
315C3×C4×D3C2×D412yes—
316C3×Dic6—21no—
317C3×Dic6C2×D412yes—
318#627—24no—
319#626—24no—
320#626—24no—
321#625—24no—
322#625—42no—
323#625—42no—
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—91no—
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—31no—
347C24×C3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3D1211yescharacteristic
351C3×#41—62no—
352C3×#41—62no—
353C2×C3×Q8—31no—
354C2×C3×D4—31no—
355C2×C3×D4—31no—
356C2×C3×D4—61no—
357C2×C3×D4—61no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—62no—
365C22×C3×C4—62no—
366C22×C3×C4—61no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—21no—
370C2×#67—21no—
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—61no—
381C2×#67—61no—
382C2×#67—121no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3D1211yescharacteristic
387#239—34no—
388#239—62no—
389D3×Q8—62no—
390D3×Q8—62no—
391#237—34no—
392#237—68no—
393#237—62no—
394#237—62no—
395#237—62no—
396D3×D4—62no—
397D3×D4—62no—
398D3×D4—68no—
399#235—22no—
400#235—22no—
401#235—34no—
402#235—34no—
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—62no—
413#235—62no—
414#235—122no—
415#235—122no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—61no—
419C2×D12—62no—
420C2×D12—61no—
421C2×D12—61no—
422C2×D12—62no—
423C2×D12C22×D311yescharacteristic
424C2×D12C22×D311yescharacteristic
425C2×C4×D3—21no—
426C2×C4×D3—22no—
427C2×C4×D3—22no—
428C2×C4×D3—68no—
429C2×C4×D3—68no—
430C2×C4×D3—61no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—61no—
434C2×C4×D3—61no—
435C2×C4×D3—61no—
436C2×C4×D3—61no—
437C2×C4×D3—121no—
438C2×C4×D3D1211yescharacteristic
439C2×C4×D3D1211yescharacteristic
440C2×C4×D3C22×D311yescharacteristic
441C2×C4×D3C22×D311yescharacteristic
442C2×Dic6—31no—
443C2×Dic6—31no—
444C2×Dic6—31no—
445C2×Dic6—31no—
446C2×Dic6—61no—
447C2×Dic6—61no—
448C2×Dic6—62no—
449C2×Dic6—61no—
450C2×Dic6—61no—
451C2×Dic6—62no—
452C2×Dic6C22×D311yescharacteristic
453C3×SD16—62no—
454C3×D8—62no—
455C2×C3×C8—21no—
456C2×C3×C8—21no—
457C2×C3×C8—31no—
458C2×C3×C8—31no—
459C2×C3×C8—62no—
460C2×C3×C8—62no—
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C2×C3×C8C22×D311yescharacteristic
464C2×C3×C8C22×D311yescharacteristic
465C3×C4⋊C4—31no—
466C3×C22⋊C4—61no—
467#217—61no—
468#217—61no—
469#217—61no—
470#217—61no—
471#217—61no—
472#217—121no—
473#216—62no—
474#214—62no—
475#214—62no—
476#213—62no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481C4⋊Dic3—31no—
482C4⋊Dic3—31no—
483C4⋊Dic3—61no—
484C4⋊Dic3—61no—
485C4⋊Dic3C22×D311yescharacteristic
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—121no—
490C4×Dic3—61no—
491C4×Dic3—61no—
492C2×C3⋊C8C22×D311yescharacteristic
493C2×C3⋊C8C22×D311yescharacteristic
494Dic12—62no—
495Dic12—62no—
496Dic12—62no—
497Dic12—122no—
498D24—22no—
499D24—62no—
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—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—21no—
519C2×C3×D3—22no—
520C2×C3×D3—44no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
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—41no—
535C3×Dic3—22no—
536C3×Dic3—21no—
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—91no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×D8—31no—
562C2×D8—91no—
563C22×C8—31no—
564C22×C8—31no—
565#123—181no—
566C22⋊Q8—91no—
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—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—61no—
593C23×C3—121no—
594C23×C3C2×D1211yescharacteristic
595C23×C3D3×D411yescharacteristic
596C22×D3—21no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—21no—
600C22×D3—41no—
601C22×D3—64no—
602C22×D3—64no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3C2×D1211yescharacteristic
611C22×D3C2×D1211yescharacteristic
612C3×Q8—32no—
613C3×Q8—61no—
614C3×D4—32no—
615C3×D4—64no—
616C3×D4—61no—
617C3×D4—61no—
618C3×D4—61no—
619C3×D4—122no—
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×C4C2×D1211yescharacteristic
641C2×C3×C4D3×D411yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644#67—24no—
645#67—42no—
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—
657C2×Dic3—21no—
658C2×Dic3—22no—
659C2×Dic3—21no—
660C2×Dic3—64no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—64no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—122no—
672C2×Dic3C2×D1211yescharacteristic
673C2×Dic3C2×D1211yescharacteristic
674D12—21no—
675D12—21no—
676D12—21no—
677D12—32no—
678D12—32no—
679D12—62no—
680D12—64no—
681D12—64no—
682D12—61no—
683D12—61no—
684D12—121no—
685D12D3×D412yes—
686C4×D3—24no—
687C4×D3—22no—
688C4×D3—21no—
689C4×D3—21no—
690C4×D3—22no—
691C4×D3—64no—
692C4×D3—64no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—124no—
698C4×D3—122no—
699C4×D3D3×D412yes—
700C4×D3D3×D412yes—
701Dic6—21no—
702Dic6—32no—
703Dic6—32no—
704Dic6—62no—
705Dic6—64no—
706Dic6—64no—
707Dic6—61no—
708Dic6—61no—
709Dic6—61no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—121no—
714Dic6—121no—
715Dic6—121no—
716Dic6D3×D412yes—
717C3×C8—21no—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—21no—
721C3×C8—41no—
722C3×C8—41no—
723C3×C8—61no—
724C3×C8—61no—
725C3⋊C8—21no—
726C3⋊C8—21no—
727C2×C32—41no—
728C2×C32C2×#12011yescharacteristic
729C2×C32C2×#13511yescharacteristic
730C2×C32#57511yescharacteristic
731C3⋊D3—42no—
732C3×D3—22no—
733C3×D3—22no—
734C3×D3—42no—
735C3×D3—81no—
736C24—31no—
737C24—181no—
738#41—62no—
739#41—62no—
740#41—94no—
741#41—94no—
742#41—182no—
743#41—182no—
744#41—182no—
745#41—182no—
746#41—182no—
747#41—182no—
748#41—188no—
749#41—188no—
750C2×Q8—31no—
751C2×Q8—91no—
752C2×Q8—91no—
753C2×Q8—181no—
754C2×Q8—182no—
755C2×Q8—182no—
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—91no—
761C2×D4—181no—
762C2×D4—182no—
763C2×D4—182no—
764C2×D4—181no—
765C2×D4—188no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—181no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—31no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—61no—
778C22×C4—181no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4—188no—
782C22×C4—181no—
783C22×C4—181no—
784C22×C4C2×D3211yescharacteristic
785Q16—182no—
786Q16—182no—
787SD16—62no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791D8—62no—
792D8—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—62no—
796C2×C8—62no—
797C2×C8C2×D3211yescharacteristic
798C2×C8C2×D3211yescharacteristic
799C4⋊C4—31no—
800C4⋊C4—91no—
801C4⋊C4—181no—
802C4⋊C4—181no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—32no—
817C22×C3—32no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—62no—
826C22×C3—124no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3C22×D1211yescharacteristic
833C22×C3C2×D3×D411yescharacteristic
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—44no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—122no—
848C2×D3—128no—
849C2×D3—128no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3#88212yes—
857C2×D3#90412yescomplemented
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—32no—
863C3×C4—41no—
864C3×C4—62no—
865C3×C4—61no—
866C3×C4—121no—
867C3×C4C2×D3×D411yescharacteristic
868C3×C4C2×D3×D411yescharacteristic
869C3×C4C2×D3×D411yescharacteristic
870C3×C4C2×D3×D411yescharacteristic
871Dic3—21no—
872Dic3—22no—
873Dic3—41no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—121no—
878Dic3—121no—
879Dic3—121no—
880Dic3—121no—
881Dic3—241no—
882Dic3—241no—
883Dic3#88212yes—
884C32#300211yescharacteristic, complemented, Sylow
885C23—31no—
886C23—31no—
887C23—62no—
888C23—62no—
889C23—61no—
890C23—61no—
891C23—121no—
892C23—184no—
893C23—181no—
894C23—362no—
895C23—362no—
896C23D3×D1211yescharacteristic
897Q8—32no—
898Q8—61no—
899Q8—92no—
900Q8—184no—
901Q8—181no—
902Q8—181no—
903Q8—181no—
904D4—32no—
905D4—64no—
906D4—61no—
907D4—61no—
908D4—61no—
909D4—92no—
910D4—122no—
911D4—184no—
912D4—184no—
913D4—184no—
914D4—184no—
915D4—181no—
916D4—362no—
917D4—362no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—31no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—31no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—64no—
927C2×C4—62no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—184no—
933C2×C4—184no—
934C2×C4—184no—
935C2×C4—184no—
936C2×C4—181no—
937C2×C4—181no—
938C2×C4—181no—
939C2×C4—362no—
940C2×C4D3×D1211yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C8—21no—
943C8—21no—
944C8—61no—
945C8—61no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—41no—
951C2×C3—62no—
952C2×C3—62no—
953C2×C3—81no—
954C2×C3—122no—
955C2×C3—241no—
956C2×C3C2×#88211yescharacteristic
957C2×C3D3×#12011yescharacteristic
958C2×C3C2×#90411yescharacteristic
959C2×C3#574811yescharacteristic
960C2×C3D3×#13511yescharacteristic
961C2×C3#577311yescharacteristic
962D3—22no—
963D3—22no—
964D3—42no—
965D3—81no—
966D3—122no—
967D3—122no—
968D3—242no—
969C22—21no—
970C22—21no—
971C22—21no—
972C22—32no—
973C22—32no—
974C22—61no—
975C22—61no—
976C22—61no—
977C22—61no—
978C22—62no—
979C22—124no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—182no—
986C22—368no—
987C22—361no—
988C22—361no—
989C22C2×D3×D1211yescharacteristic
990C4—21no—
991C4—32no—
992C4—61no—
993C4—62no—
994C4—121no—
995C4—182no—
996C4—361no—
997C4—361no—
998C4D32×D411yescharacteristic
999C4D32×D411yescharacteristic
1000C3—21no—
1001C3#7861011yescharacteristic, complemented
1002C3#8008211yescharacteristic, complemented
1003C2—41no—
1004C2—62no—
1005C2—62no—
1006C2—122no—
1007C2—241no—
1008C2—362no—
1009C2D3×#88211yescharacteristic
1010C2D3×#90411yescharacteristic
1011C2#1059471211yescharacteristic
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. #10594892C2semidirect
3. C2×#63807C2semidirect
4. C2×#63806C2semidirect
5. #10592432C2semidirect
6. C3×#4734C2semidirect
7. C3×D3×C22⋊C8C2semidirect
8. #10591182C2semidirect
9. #10591173C2semidirect
10. #10590954C2semidirect
11. #10590952C2semidirect
12. #10590946C2semidirect
13. #10590944C2semidirect
14. #10590822C2semidirect
15. #10590690C2semidirect
30. C2×#3795C22semidirect
32. #64133C22semidirect
33. C2×#3746C22semidirect
34. C2×#3744C22semidirect
35. C3×#930C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
38. C2×C3×D3×C8C22semidirect
39. C2×C3×D3×C8C22semidirect
46. #63841C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
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
88. #4734D3semidirect
95. D3×C22⋊C8D3semidirect
137. #3799D4semidirect
142. #3795D4semidirect
213. #930C2×D3semidirect
231. C2×D24C2×D3semidirect
237. C2×#204C2×D3semidirect
238. C2×D3×C8C2×D3semidirect
239. 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
857. C2×D3#904semidirect
884. C32#3002semidirect
1001. C3#78610semidirect
1002. C3#80082semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
#105948922
C2×#638072
C2×#638062
#105924322
C3×#47342
C3×D3×C22⋊C82
#105911822
#105911732
#105909542
#105909522
#105909462
#105909442
#105908222
#105906902
#800823
#786103