Finite Group Databasebeta

← C2×D3×#912 #11918608

Subgroups — C2×D3×#912 #11918608

Order 1152.

3141 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C212yesmaximal, complemented
2C2×#64121C211yesmaximal, characteristic, complemented
3C2×C3×#912C211yesmaximal, characteristic, complemented
4C2×C3×D3×D8C211yesmaximal, characteristic, complemented
5C2×#63936C212yesmaximal, complemented
6C2×#63933C212yesmaximal, complemented
7C2×D3×#214C212yesmaximal, complemented
8D3×#912C2116yesmaximal, direct product factor
9C2×#63810C211yesmaximal, characteristic, complemented
10C2×#63807C211yesmaximal, characteristic, complemented
11C2×D3×Dic12C211yesmaximal, characteristic, complemented
12C2×D32×C8C211yesmaximal, characteristic, complemented
13C2×D3×#135—31nomaximal
14C22×#912—31nomaximal
15C2×#3830C2212yescomplemented
16C2×C3×#237C2212yescomplemented
17C2×C3×D3×D4C2212yes—
18C2×D3×#67—22no—
19C2×#3805—22no—
20C2×#3804—22no—
21C22×D3×Dic3—22no—
22D3×#237—28no—
23D3×#237C22116yescomplemented
24C2×C4×D32C2211yescharacteristic
25C2×#3796C2212yescomplemented
26C2×#3795C2212yescomplemented
27C2×D3×Dic6C2212yes—
28C2×C32×D8C2211yescharacteristic, complemented
29C2×#3754C2212yescomplemented
30#64121C2218yescomplemented
31C2×#3746C2211yescharacteristic, complemented
32C2×C8×C3⋊D3C2211yescharacteristic, complemented
33C2×C3×#214C2212yescomplemented
34C2×C3×#213C2212yescomplemented
35C3×#912C2218yescomplemented
36C3×D3×D8C2218yescomplemented
37C2×C3×Dic12C2211yescharacteristic, complemented
38C2×C3×D24C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic, complemented
41#63936C22116yescomplemented
42#63933C22116yescomplemented
43D3×#214C22116yescomplemented
44C2×#3719C2212yescomplemented
45C2×#3716C2212yescomplemented
46C2×#3715C2212yescomplemented
47C2×#3710C2211yescharacteristic, complemented
48C2×D3×C3⋊C8C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50#63810C2218yescomplemented
51#63807C2218yescomplemented
52D3×Dic12C2218yescomplemented
53D32×C8C2218yescomplemented
54C2×D3×#41—32no—
55C22×#237—32no—
56C2×C3×#135—31no—
57C22×C3×D8—31no—
58C2×#950—32no—
59C22×#214—32no—
60D3×#135—316no—
61C2×#919—31no—
62C2×D3×Q16—31no—
63C2×#916—32no—
64C2×D3×SD16—32no—
65C2×#912—32no—
66C2×#912—31no—
67C2×#912—31no—
68C2×#912—32no—
69C2×#912—316no—
70C2×#912—31no—
71C2×#912—31no—
72C2×#912—61no—
73C2×#912D311yescharacteristic, direct product factor
74C2×D3×D8D311yescharacteristic, complemented
75C22×Dic12—31no—
76C2×#904—31no—
77C22×D3×C8—31no—
78C22×D3×C8—31no—
79C23×C3×D3—22no—
80C22×D32D411yescharacteristic
81C2×C32×D4C2312yes—
82C2×#638—22no—
83C22×C3⋊Dic3—22no—
84#3830—24no—
85#3830C2318yescomplemented
86C2×C4×C3⋊D3C2311yescharacteristic
87C2×#634C2312yes—
88C2×C3×#67—22no—
89C2×C3×#67—22no—
90C22×C3×Dic3—22no—
91C3×#237—24no—
92C3×#237C2318yescomplemented
93C3×D3×D4—24no—
94C3×D3×D4C2318yes—
95C2×C3×D12C2312yes—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2312yes—
99D3×#67—216no—
100C2×#627—22no—
101C2×#626—22no—
102C2×#625—22no—
103C2×#624D411yescharacteristic
104#3805—216no—
105#3804—216no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—22no—
108C2×D3×Dic3—22no—
109C2×D3×Dic3—216no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112C4×D32D414yes—
113C4×D32C2314yes—
114#3796—24no—
115#3796C2318yescomplemented
116#3795—24no—
117#3795C2318yescomplemented
118D3×Dic6—24no—
119D3×Dic6C2318yes—
120C32×D8C2314yescomplemented
121C2×C32×C8C2311yescharacteristic
122#3754C2318yescomplemented
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746C2314yescomplemented
125C8×C3⋊D3C2314yescomplemented
126C3×#214C2318yescomplemented
127C3×#213C2318yescomplemented
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×Dic12C2314yescomplemented
131C3×D24C2314yescomplemented
132C3×D3×C8C2314yes—
133C3×D3×C8C2314yescomplemented
134#3719C2318yescomplemented
135#3716C2318yescomplemented
136#3715C2318yescomplemented
137#3710C2314yescomplemented
138D3×C3⋊C8C2314yes—
139D3×C3⋊C8C2314yescomplemented
140C22×#135—91noSylow
141C2×C3×#41—32no—
142C22×C3×D4—32no—
143C22×#67—62no—
144C23×Dic3—62no—
145D3×#41—316no—
146D3×#41—68no—
147C2×#239—32no—
148C2×D3×Q8—32no—
149C2×#237—32no—
150C2×#237—32no—
151C2×#237—316no—
152C2×#237—32no—
153C2×#237—32no—
154C2×#237—62no—
155C2×#237—68no—
156C2×#237—62no—
157C2×#237—62no—
158C2×#237—62no—
159C2×#237C2×D312yescomplemented
160C2×D3×D4—62no—
161C2×D3×D4C2×D312yes—
162C2×#235—32no—
163C2×#235—62no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—62no—
167C22×Dic6—32no—
168C3×#135—38no—
169C2×C3×Q16—31no—
170C2×C3×SD16—32no—
171C2×C3×D8—21no—
172C2×C3×D8—32no—
173C2×C3×D8—38no—
174C2×C3×D8—31no—
175C2×C3×D8C2×D311yescharacteristic, complemented
176C2×C3×D8C2×D311yescharacteristic, complemented
177C22×C3×C8—31no—
178C22×C3×C8—31no—
179#950—316no—
180C2×#216—32no—
181C2×#215—32no—
182C2×#214—32no—
183C2×#214—32no—
184C2×#214—32no—
185C2×#214—316no—
186C2×#214—32no—
187C2×#214—62no—
188C2×#214C2×D312yescomplemented
189C2×#213C2×D312yescomplemented
190C22×C3⋊C8—31no—
191C22×C3⋊C8—31no—
192#919—38no—
193D3×Q16—38no—
194#916—316no—
195D3×SD16—316no—
196#912—316no—
197#912—38no—
198#912—38no—
199#912—316no—
200#912—38no—
201#912—38no—
202#912—68no—
203#912C2×D318yesdirect product factor
204D3×D8C2×D318yescomplemented
205C2×Dic12—32no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—38no—
209C2×Dic12—61no—
210C2×Dic12C2×D311yescharacteristic, complemented
211#904—38no—
212C2×D24C2×D311yescharacteristic, complemented
213C2×#204—32no—
214C2×D3×C8—31no—
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217C2×D3×C8—31no—
218C2×D3×C8—31no—
219C2×D3×C8—31no—
220C2×D3×C8—38no—
221C2×D3×C8—38no—
222C2×D3×C8—61no—
223C2×D3×C8C2×D311yescharacteristic
224C2×D3×C8C2×D311yescharacteristic, complemented
225C23×C32—22no—
226C22×C3⋊D3C2×D411yescharacteristic
227C22×C3×D3—22no—
228C22×C3×D3—28no—
229C22×C3×D3—48no—
230C22×C3×D3C2×D411yescharacteristic
231C22×C3×D3C2×D411yescharacteristic
232C2×D32—24no—
233C2×D32C2×D414yes—
234C32×D4—22no—
235C32×D4C2414yes—
236C2×C32×C4C2411yescharacteristic
237#638—28no—
238C2×C3⋊Dic3—22no—
239C2×C3⋊Dic3—28no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C4×C3⋊D3C2×D412yes—
242C4×C3⋊D3C2412yes—
243#634—22no—
244#634C2414yes—
245C3×#67—28no—
246C3×#67—28no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—28no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—22no—
252C3×D12C2414yes—
253C3×C4×D3C2×D412yes—
254C3×C4×D3C2×D412yes—
255C3×C4×D3C2412yes—
256C3×C4×D3C2412yes—
257C3×Dic6—22no—
258C3×Dic6C2414yes—
259#627—28no—
260#626—28no—
261#625—28no—
262#624C2×D414yes—
263D3×Dic3—28no—
264D3×Dic3—28no—
265D3×Dic3—28no—
266D3×Dic3C2×D414yes—
267D3×Dic3C2×D414yes—
268C32×C8C2412yes—
269C3⋊(C3⋊C8)C2412yes—
270C3×C3⋊C8C2412yes—
271C3×C3⋊C8C2412yes—
272C22×#41—92no—
273C2×#135—31no—
274C2×#135—91no—
275C2×#135—92no—
276C2×#135—91no—
277C2×#135—916no—
278C2×#135—92no—
279C2×#135—91no—
280C22×Q16—91no—
281C22×SD16—92no—
282C22×D8—31no—
283C23×C8—91no—
284C24×C3—62no—
285C23×D3—22no—
286C23×D3—31no—
287C23×D3—31no—
288C3×#41—38no—
289C3×#41—64no—
290C2×C3×Q8—32no—
291C2×C3×D4—22no—
292C2×C3×D4—38no—
293C2×C3×D4—32no—
294C2×C3×D4—64no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4C22×D312yes—
298C2×C3×D4C22×D312yes—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—62no—
302C2×#67—22no—
303C2×#67—22no—
304C2×#67—62no—
305C2×#67—616no—
306C2×#67—62no—
307C2×#67—62no—
308C2×#67—62no—
309C2×#67—62no—
310C2×#67—122no—
311C22×Dic3—22no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—62no—
315C22×Dic3—616no—
316C22×Dic3—62no—
317C22×Dic3—62no—
318C22×Dic3—62no—
319C22×Dic3—62no—
320C22×Dic3—122no—
321#239—38no—
322#239—64no—
323D3×Q8—38no—
324D3×Q8—64no—
325#237—24no—
326#237—38no—
327#237—38no—
328#237—38no—
329#237—38no—
330#237—68no—
331#237—64no—
332#237—616no—
333#237—616no—
334#237—64no—
335#237—64no—
336#237—616no—
337#237—64no—
338#237—124no—
339#237C22×D318yescomplemented
340D3×D4—24no—
341D3×D4—616no—
342D3×D4C22×D318yes—
343#235—38no—
344#235—616no—
345#235—64no—
346C2×D12—62no—
347C2×D12C22×D312yes—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—34no—
355C2×C4×D3—34no—
356C2×C4×D3—34no—
357C2×C4×D3—34no—
358C2×C4×D3—61no—
359C2×C4×D3—616no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—32no—
366C2×Dic6—32no—
367C2×Dic6—38no—
368C2×Dic6—62no—
369C2×Dic6—64no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6C22×D312yes—
373C3×Q16—34no—
374C3×SD16—38no—
375C3×D8—24no—
376C3×D8—38no—
377C3×D8—34no—
378C3×D8C22×D314yescomplemented
379C3×D8C22×D314yescomplemented
380C2×C3×C8—21no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C2×C3×C8—34no—
384C2×C3×C8—34no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387#216—38no—
388#215—38no—
389#214—38no—
390#214—38no—
391#214—38no—
392#214—38no—
393#214—68no—
394#214C22×D318yescomplemented
395#213C22×D318yescomplemented
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—34no—
399C2×C3⋊C8—34no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—38no—
404Dic12—34no—
405Dic12—34no—
406Dic12—64no—
407Dic12C22×D314yescomplemented
408D24C22×D314yescomplemented
409#204—38no—
410D3×C8—34no—
411D3×C8—34no—
412D3×C8—34no—
413D3×C8—34no—
414D3×C8—34no—
415D3×C8—34no—
416D3×C8—64no—
417D3×C8C22×D314yes—
418D3×C8C22×D314yescomplemented
419C22×C32—24no—
420C22×C32—44no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—22no—
423C2×C3⋊D3C22×D412yes—
424C2×C3×D3—22no—
425C2×C3×D3—24no—
426C2×C3×D3—44no—
427C2×C3×D3—416no—
428C2×C3×D3#13514yescomplemented
429C2×C3×D3C22×D412yes—
430C2×C3×D3C22×D412yes—
431D32—28no—
432C32×C4C22×D411yescharacteristic
433C32×C4C2511yescharacteristic
434C3⋊Dic3—24no—
435C3⋊Dic3C22×D412yes—
436C3×Dic3—24no—
437C3×Dic3C22×D412yes—
438C3×Dic3C22×D412yes—
439C2×#41—32no—
440C2×#41—92no—
441C2×#41—92no—
442C2×#41—916no—
443C2×#41—92no—
444C2×#41—182no—
445C2×#41—182no—
446C2×#41—188no—
447C22×Q8—92no—
448C22×D4—32no—
449C22×D4—182no—
450C23×C4—91no—
451C23×C4—182no—
452#135—38no—
453#135—98no—
454#135—916no—
455#135—98no—
456#135—916no—
457#135—98no—
458C2×Q16—31no—
459C2×Q16—98no—
460C2×Q16—92no—
461C2×Q16—91no—
462C2×SD16—32no—
463C2×SD16—92no—
464C2×SD16—916no—
465C2×SD16—92no—
466C2×SD16—92no—
467C2×D8—32no—
468C2×D8—38no—
469C2×D8—31no—
470C2×D8D3211yescharacteristic, complemented
471C22×C8—31no—
472C22×C8—31no—
473C22×C8—91no—
474C22×C8—98no—
475C22×C8—91no—
476C22×C8—91no—
477C22×C8—91no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—42no—
483C23×C3—68no—
484C23×C3—62no—
485C23×C3—128no—
486C22×D3—22no—
487C22×D3—28no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—34no—
491C22×D3—34no—
492C22×D3—48no—
493C22×D3—61no—
494C22×D3—64no—
495C22×D3—64no—
496C22×D3D3×D411yescharacteristic
497C22×D3D3×D411yescharacteristic
498C3×Q8—34no—
499C3×Q8—62no—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—24no—
503C3×D4—34no—
504C3×D4—42no—
505C3×D4—68no—
506C3×D4—68no—
507C3×D4—62no—
508C3×D4C23×D314yes—
509C3×D4C23×D314yes—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—68no—
518C2×C3×C4—62no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—28no—
522#67—28no—
523#67—68no—
524#67—68no—
525#67—68no—
526#67—68no—
527#67—68no—
528#67—128no—
529C2×Dic3—22no—
530C2×Dic3—28no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—34no—
534C2×Dic3—34no—
535C2×Dic3—61no—
536C2×Dic3—68no—
537C2×Dic3—68no—
538C2×Dic3—68no—
539C2×Dic3—68no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—68no—
543C2×Dic3—128no—
544C2×Dic3—122no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—22no—
548D12—68no—
549D12C23×D314yes—
550C4×D3—34no—
551C4×D3—34no—
552C4×D3—32no—
553C4×D3—32no—
554C4×D3—32no—
555C4×D3—32no—
556C4×D3—34no—
557C4×D3—34no—
558C4×D3—62no—
559C4×D3—62no—
560C4×D3—68no—
561C4×D3—68no—
562C4×D3—68no—
563C4×D3D3×D412yes—
564C4×D3D3×D412yes—
565C4×D3C23×D312yes—
566C4×D3C23×D312yes—
567Dic6—22no—
568Dic6—34no—
569Dic6—34no—
570Dic6—64no—
571Dic6—68no—
572Dic6—62no—
573Dic6—62no—
574Dic6—68no—
575Dic6—122no—
576Dic6C23×D314yes—
577C3×C8—22no—
578C3×C8—32no—
579C3×C8—32no—
580C3×C8C23×D312yes—
581C3×C8C23×D312yes—
582C3⋊C8—32no—
583C3⋊C8—32no—
584C3⋊C8—62no—
585C3⋊C8C23×D312yes—
586C3⋊C8C23×D312yes—
587C2×C32—44no—
588C2×C32C2×#13512yescomplemented
589C2×C32C23×D411yescharacteristic
590C3⋊D3—22no—
591C3×D3—22no—
592C3×D3—44no—
593C3×D3C2×#13514yescomplemented
594C24—62no—
595C24—91no—
596#41—38no—
597#41—64no—
598#41—98no—
599#41—98no—
600#41—98no—
601#41—184no—
602#41—1816no—
603#41—184no—
604#41—1816no—
605#41—184no—
606C2×Q8—32no—
607C2×Q8—98no—
608C2×Q8—92no—
609C2×Q8—182no—
610C2×Q8—184no—
611C2×D4—38no—
612C2×D4—32no—
613C2×D4—64no—
614C2×D4—62no—
615C2×D4—62no—
616C2×D4—182no—
617C2×D4—1816no—
618C2×D4—182no—
619C2×D4—182no—
620C2×D4C2×D3212yes—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—62no—
624C22×C4—94no—
625C22×C4—91no—
626C22×C4—94no—
627C22×C4—91no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—182no—
631C22×C4—1816no—
632C22×C4—182no—
633C22×C4—182no—
634C22×C4—182no—
635Q16—34no—
636Q16—98no—
637Q16—94no—
638SD16—38no—
639SD16—98no—
640SD16—98no—
641SD16—98no—
642D8—38no—
643D8—34no—
644D8C2×D3214yescomplemented
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—34no—
648C2×C8—34no—
649C2×C8—94no—
650C2×C8—94no—
651C2×C8—94no—
652C2×C8—91no—
653C2×C8—94no—
654C2×C8C2×D3211yescharacteristic
655C22×C3—24no—
656C22×C3—24no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—34no—
660C22×C3—32no—
661C22×C3—44no—
662C22×C3—44no—
663C22×C3—44no—
664C22×C3—62no—
665C22×C3—64no—
666C22×C3—84no—
667C22×C3—1216no—
668C22×C3—124no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3—22no—
672C2×D3—24no—
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—44no—
676C2×D3—416no—
677C2×D3—62no—
678C2×D3—68no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—68no—
682C2×D3—122no—
683C2×D3#91214yesdirect product factor
684C2×D3C2×D3×D412yes—
685C2×D3C2×D3×D412yes—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—32no—
689C3×C4—32no—
690C3×C4—64no—
691C3×C4C2×D3×D411yescharacteristic
692C3×C4C2×D3×D411yescharacteristic
693C3×C4C24×D311yescharacteristic
694C3×C4C24×D311yescharacteristic
695Dic3—24no—
696Dic3—32no—
697Dic3—32no—
698Dic3—62no—
699Dic3—64no—
700Dic3—64no—
701Dic3—124no—
702Dic3C2×D3×D412yes—
703Dic3C2×D3×D412yes—
704C32C22×#13511yescharacteristic, complemented, Sylow
705C23—22no—
706C23—31no—
707C23—31no—
708C23—68no—
709C23—62no—
710C23—94no—
711C23—91no—
712C23—128no—
713C23—184no—
714Q8—34no—
715Q8—62no—
716Q8—94no—
717Q8—188no—
718Q8—182no—
719D4—22no—
720D4—34no—
721D4—68no—
722D4—68no—
723D4—62no—
724D4—188no—
725D4—188no—
726D4—188no—
727D4C22×D3214yes—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—68no—
735C2×C4—62no—
736C2×C4—94no—
737C2×C4—94no—
738C2×C4—94no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—188no—
743C2×C4—188no—
744C2×C4—188no—
745C2×C4—188no—
746C2×C4—182no—
747C2×C4C22×D3211yescharacteristic
748C8—32no—
749C8—32no—
750C8—92no—
751C8C22×D3212yes—
752C2×C3—21no—
753C2×C3—22no—
754C2×C3—34no—
755C2×C3—44no—
756C2×C3—44no—
757C2×C3—62no—
758C2×C3—84no—
759C2×C3—124no—
760C2×C3C2×#91212yescomplemented
761C2×C3D3×#13512yescomplemented
762C2×C3C22×D3×D411yescharacteristic
763C2×C3C22×D3×D411yescharacteristic
764D3—22no—
765D3—44no—
766D3—62no—
767D3—62no—
768D3—122no—
769D3C2×#91214yesdirect product factor
770C22—24no—
771C22—32no—
772C22—34no—
773C22—32no—
774C22—44no—
775C22—62no—
776C22—64no—
777C22—92no—
778C22—1216no—
779C22—124no—
780C22—188no—
781C22—182no—
782C22D32×D411yescharacteristic
783C4—32no—
784C4—32no—
785C4—64no—
786C4—92no—
787C4—184no—
788C4D32×D411yescharacteristic
789C4C23×D3211yescharacteristic
790C3—21no—
791C3C22×#91211yescharacteristic, complemented
792C3C2×D3×#13511yescharacteristic, complemented
793C2—34no—
794C2—44no—
795C2—62no—
796C2—124no—
797C2—182no—
798C2D3×#91212yesdirect product factor
799C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C22×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×#64121C2semidirect
3. C2×C3×#912C2semidirect
4. C2×C3×D3×D8C2semidirect
5. C2×#63936C2semidirect
6. C2×#63933C2semidirect
7. C2×D3×#214C2semidirect
8. D3×#912C2direct (N × H)
9. C2×#63810C2semidirect
10. C2×#63807C2semidirect
11. C2×D3×Dic12C2semidirect
12. C2×D32×C8C2semidirect
15. C2×#3830C22semidirect
16. C2×C3×#237C22semidirect
23. D3×#237C22semidirect
25. C2×#3796C22semidirect
26. C2×#3795C22semidirect
28. C2×C32×D8C22semidirect
29. C2×#3754C22semidirect
30. #64121C22semidirect
31. C2×#3746C22semidirect
32. C2×C8×C3⋊D3C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#213C22semidirect
35. C3×#912C22semidirect
36. C3×D3×D8C22semidirect
37. C2×C3×Dic12C22semidirect
38. C2×C3×D24C22semidirect
40. C2×C3×D3×C8C22semidirect
41. #63936C22semidirect
42. #63933C22semidirect
43. D3×#214C22semidirect
44. C2×#3719C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C2×#3710C22semidirect
49. C2×D3×C3⋊C8C22semidirect
50. #63810C22semidirect
51. #63807C22semidirect
52. D3×Dic12C22semidirect
53. D32×C8C22semidirect
73. C2×#912D3direct (N × H)
74. C2×D3×D8D3semidirect
85. #3830C23semidirect
92. C3×#237C23semidirect
115. #3796C23semidirect
117. #3795C23semidirect
120. C32×D8C23semidirect
122. #3754C23semidirect
124. #3746C23semidirect
125. C8×C3⋊D3C23semidirect
126. C3×#214C23semidirect
127. C3×#213C23semidirect
130. C3×Dic12C23semidirect
131. C3×D24C23semidirect
133. C3×D3×C8C23semidirect
134. #3719C23semidirect
135. #3716C23semidirect
136. #3715C23semidirect
137. #3710C23semidirect
139. D3×C3⋊C8C23semidirect
159. C2×#237C2×D3semidirect
175. C2×C3×D8C2×D3semidirect
176. C2×C3×D8C2×D3semidirect
188. C2×#214C2×D3semidirect
189. C2×#213C2×D3semidirect
203. #912C2×D3direct (N × H)
204. D3×D8C2×D3semidirect
210. C2×Dic12C2×D3semidirect
212. C2×D24C2×D3semidirect
224. C2×D3×C8C2×D3semidirect
339. #237C22×D3semidirect
378. C3×D8C22×D3semidirect
379. C3×D8C22×D3semidirect
394. #214C22×D3semidirect
395. #213C22×D3semidirect
407. Dic12C22×D3semidirect
408. D24C22×D3semidirect
418. D3×C8C22×D3semidirect
428. C2×C3×D3#135semidirect
470. C2×D8D32semidirect
588. C2×C32C2×#135semidirect
593. C3×D3C2×#135semidirect
644. D8C2×D32semidirect
683. C2×D3#912direct (N × H)
704. C32C22×#135semidirect
760. C2×C3C2×#912semidirect
761. C2×C3D3×#135semidirect
769. D3C2×#912direct (N × H)
791. C3C22×#912semidirect
792. C3C2×D3×#135semidirect
798. C2D3×#912direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#641212
C2×C3×#9122
C2×C3×D3×D82
C2×#639362
C2×#639332
C2×D3×#2142
D3×#9122
C2×#638102
C2×#638072
C2×D3×Dic122
C2×D32×C82
C2×D3×#1353
C22×#9123