Finite Group Databasebeta

← C2×D3×#951 #11918702

Subgroups — C2×D3×#951 #11918702

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64160C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5D3×#951C2116yesmaximal, direct product factor
6C2×#63943C212yesmaximal, complemented
7C2×D3×#216C212yesmaximal, complemented
8C2×#63929C212yesmaximal, complemented
9C2×D3×#214C212yesmaximal, complemented
10C2×#63831C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C22×#951—31nomaximal
14C2×D3×#137—31nomaximal
15C2×C32×#41C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C3×D3×#41—24no—
18C3×D3×#41C2218yes—
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×#237—21no—
22C2×C3×#237C2211yescharacteristic
23C2×C3×D3×D4—21no—
24C2×C3×D3×D4C2211yescharacteristic
25C2×C3×#235—21no—
26C2×C3×#235C2211yescharacteristic
27C22×C3×C4×D3—21no—
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2211yescharacteristic, complemented
30C22×#627—21no—
31C22×D3×Dic3—21no—
32C2×D3×Dic6—24no—
33C2×D3×Dic6—21no—
34C2×D3×Dic6—21no—
35C2×D3×Dic6C2212yes—
36C2×D3×Dic6C2218yescomplemented
37C2×D3×Dic6C2212yescomplemented
38#64160C2218yescomplemented
39C2×#3756C2212yescomplemented
40C2×#3754C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C3×#951C2218yescomplemented
43C2×C3×#216C2212yescomplemented
44C2×C3×#214C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63943C22116yescomplemented
47D3×#216C22116yescomplemented
48#63929C22116yescomplemented
49D3×#214C22116yescomplemented
50C2×#3719C2212yescomplemented
51C2×#3718C2212yescomplemented
52#63831C2218yescomplemented
53C2×#3716C2212yescomplemented
54#63827C2218yescomplemented
55C2×#3715C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yes—
59C22×C3×#41—31no—
60C2×D3×#41D311yescharacteristic
61C22×D3×Q8—31no—
62C23×Dic6—31no—
63C2×C3×#137—31no—
64C2×#951—31no—
65C2×#951—31no—
66C2×#951—31no—
67C2×#951—316no—
68C2×#951—32no—
69C2×#951—32no—
70C2×#951—31no—
71C2×#951—61no—
72C2×#951D311yescharacteristic, direct product factor
73C22×#216—32no—
74C2×#942—31no—
75C22×#214—32no—
76C22×#208—31no—
77D3×#137—316no—
78C2×#918—32no—
79C2×D3×Q16—32no—
80C2×#915—32no—
81C2×D3×SD16—32no—
82C2×#909—31no—
83C2×D3×M16—31no—
84C23×C3×D3—21no—
85C23×C3×D3D411yescharacteristic
86C32×#41—22no—
87C32×#41C2314yes—
88C2×C32×Q8C2311yescharacteristic
89C2×C32×D4—21no—
90C2×C32×D4C2311yescharacteristic
91C22×C32×C4—21no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634—22no—
95C2×#634—21no—
96C2×#634C2312yes—
97C2×#634C2314yescomplemented
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×#239—22no—
105C3×#239C2314yes—
106C3×D3×Q8—22no—
107C3×D3×Q8C2314yes—
108C3×#237—28no—
109C3×#237—22no—
110C3×#237C2314yes—
111C3×D3×D4—28no—
112C3×D3×D4—22no—
113C3×D3×D4C2314yes—
114C3×#235—22no—
115C3×#235—28no—
116C3×#235C2314yes—
117C2×C3×D12—21no—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—28no—
123C2×C3×C4×D3D411yescharacteristic
124C2×C3×C4×D3D411yescharacteristic
125C2×C3×C4×D3D414yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6—22no—
130C2×C3×Dic6—21no—
131C2×C3×Dic6—21no—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2314yescomplemented
135C2×#627—22no—
136C2×#627—28no—
137C2×#627—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—28no—
140C2×D3×Dic3—22no—
141D3×Dic6—24no—
142D3×Dic6—28no—
143D3×Dic6—28no—
144D3×Dic6—24no—
145D3×Dic6C2318yes—
146D3×Dic6C2318yescomplemented
147#3756C2318yescomplemented
148#3754C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#216C2318yescomplemented
152C3×#214C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3719C2318yescomplemented
156#3718C2318yescomplemented
157#3716C2318yescomplemented
158#3715C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yes—
161C22×#137—91noSylow
162C2×C3×#41—21no—
163C2×C3×#41—38no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C2×C3×#41—61no—
168C2×C3×#41—61no—
169C2×C3×#41—64no—
170C2×C3×#41C2×D311yescharacteristic
171C2×C3×#41C2×D311yescharacteristic
172C22×C3×Q8—31no—
173C22×C3×Q8—31no—
174C22×C3×D4—31no—
175C22×C3×D4—61no—
176C23×C3×C4—31no—
177C23×C3×C4—61no—
178C23×Dic3—61no—
179D3×#41—24no—
180D3×#41C2×D318yes—
181C2×#239C2×D311yescharacteristic
182C2×D3×Q8—32no—
183C2×D3×Q8—32no—
184C2×D3×Q8—38no—
185C2×D3×Q8—61no—
186C2×D3×Q8—61no—
187C2×D3×Q8—64no—
188C2×D3×Q8C2×D311yescharacteristic
189C2×#237—21no—
190C2×#237C2×D311yescharacteristic
191C2×D3×D4—21no—
192C2×D3×D4C2×D311yescharacteristic
193C2×#235—21no—
194C2×#235C2×D311yescharacteristic
195C22×C4×D3—21no—
196C22×C4×D3—61no—
197C22×C4×D3C2×D311yescharacteristic
198C22×Dic6—31no—
199C22×Dic6—31no—
200C22×Dic6—32no—
201C22×Dic6—32no—
202C22×Dic6—38no—
203C22×Dic6—61no—
204C22×Dic6—61no—
205C22×Dic6—64no—
206C22×Dic6—61no—
207C22×Dic6—61no—
208C22×Dic6—61no—
209C22×Dic6C2×D311yescharacteristic, complemented
210C3×#137—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×M16—31no—
214#951—38no—
215#951—38no—
216#951—38no—
217#951—316no—
218#951—316no—
219#951—38no—
220#951—68no—
221#951C2×D318yesdirect product factor
222C2×#216—32no—
223C2×#216—32no—
224C2×#216—32no—
225C2×#216—32no—
226C2×#216—316no—
227C2×#216—32no—
228C2×#216—62no—
229C2×#216C2×D312yescomplemented
230#942—38no—
231C2×#215—32no—
232C2×#214—32no—
233C2×#214—32no—
234C2×#214—32no—
235C2×#214—316no—
236C2×#214—32no—
237C2×#214—62no—
238C2×#214C2×D312yescomplemented
239C2×#208—31no—
240C2×#208—31no—
241C2×#208—38no—
242C2×#208—32no—
243C2×#208—61no—
244C2×#208C2×D311yescharacteristic, complemented
245C22×C3⋊C8—32no—
246#918—316no—
247D3×Q16—316no—
248#915—316no—
249D3×SD16—316no—
250#909—38no—
251D3×M16—38no—
252C2×Dic12—32no—
253C2×#204—32no—
254C2×ΓL(1,𝔽25)—32no—
255C2×D3×C8—32no—
256C23×C32—21no—
257C23×C32C2×D411yescharacteristic
258C22×C3×D3—24no—
259C22×C3×D3—21no—
260C22×C3×D3—24no—
261C22×C3×D3—44no—
262C22×C3×D3C2×D411yescharacteristic
263C22×C3×D3C2×D414yes—
264C22×C3×D3C2×D411yescharacteristic
265C32×Q8—21no—
266C32×Q8C2412yes—
267C32×D4—24no—
268C32×D4—21no—
269C32×D4C2412yes—
270C2×C32×C4—21no—
271C2×C32×C4—24no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D412yes—
274C2×C32×C4C2411yescharacteristic
275C2×C32×C4C2412yes—
276C2×C3⋊Dic3—22no—
277C2×C3⋊Dic3—24no—
278#634—22no—
279#634—24no—
280#634C2414yes—
281C3×#67—24no—
282C3×#67—24no—
283C3×#67—24no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—24no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—24no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D414yes—
291C3×D12—24no—
292C3×D12—21no—
293C3×D12C2412yes—
294C3×C4×D3—24no—
295C3×C4×D3—24no—
296C3×C4×D3—24no—
297C3×C4×D3C2×D414yes—
298C3×C4×D3C2×D414yes—
299C3×C4×D3C2×D412yes—
300C3×C4×D3C2×D412yes—
301C3×C4×D3C2412yes—
302C3×C4×D3C2412yes—
303C3×Dic6—22no—
304C3×Dic6—24no—
305C3×Dic6—21no—
306C3×Dic6—24no—
307C3×Dic6C2414yes—
308C3×Dic6C2412yes—
309#627—28no—
310#627—28no—
311D3×Dic3—28no—
312D3×Dic3—28no—
313C3⋊(C3⋊C8)C2414yes—
314C3×C3⋊C8C2414yes—
315C22×#41—31no—
316C23×Q8—91no—
317C2×#137—31no—
318C2×#137—91no—
319C2×#137—92no—
320C2×#137—92no—
321C2×#137—916no—
322C2×#137—91no—
323C2×#137—91no—
324C22×Q16—92no—
325C22×SD16—92no—
326C22×M16—91no—
327C24×C3—31no—
328C24×C3—61no—
329C23×D3—21no—
330C23×D3#6711yescharacteristic
331C3×#41—22no—
332C3×#41—22no—
333C3×#41—24no—
334C3×#41—34no—
335C3×#41—34no—
336C3×#41—34no—
337C3×#41—42no—
338C3×#41—68no—
339C3×#41—68no—
340C3×#41—62no—
341C3×#41—62no—
342C3×#41—62no—
343C3×#41C22×D314yes—
344C3×#41C22×D314yes—
345C2×C3×Q8—21no—
346C2×C3×Q8—34no—
347C2×C3×Q8—32no—
348C2×C3×Q8—34no—
349C2×C3×Q8—31no—
350C2×C3×Q8—61no—
351C2×C3×Q8—62no—
352C2×C3×Q8—61no—
353C2×C3×Q8—62no—
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×D4—21no—
357C2×C3×D4—21no—
358C2×C3×D4—21no—
359C2×C3×D4—34no—
360C2×C3×D4—31no—
361C2×C3×D4—41no—
362C2×C3×D4—61no—
363C2×C3×D4—62no—
364C2×C3×D4—61no—
365C2×C3×D4—68no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—34no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
380C22×C3×C4—41no—
381C22×C3×C4—61no—
382C22×C3×C4—68no—
383C22×C3×C4—61no—
384C22×C3×C4—61no—
385C22×C3×C4—61no—
386C22×C3×C4—61no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—21no—
390C2×#67—21no—
391C2×#67—21no—
392C22×Dic3—21no—
393C22×Dic3—21no—
394C22×Dic3—62no—
395C22×Dic3—62no—
396C22×Dic3—68no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—121no—
400C22×Dic3#6711yescharacteristic
401#239—22no—
402#239C22×D314yes—
403D3×Q8—22no—
404D3×Q8—38no—
405D3×Q8—38no—
406D3×Q8—68no—
407D3×Q8—68no—
408D3×Q8—64no—
409D3×Q8—64no—
410D3×Q8C22×D314yes—
411#237—28no—
412#237—22no—
413#237C22×D314yes—
414D3×D4—28no—
415D3×D4—22no—
416D3×D4C22×D314yes—
417#235—22no—
418#235—28no—
419#235C22×D314yes—
420C2×D12—21no—
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—21no—
423C2×C4×D3—21no—
424C2×C4×D3—21no—
425C2×C4×D3—28no—
426C2×C4×D3—62no—
427C2×C4×D3—68no—
428C2×C4×D3—62no—
429C2×C4×D3#6711yescharacteristic
430C2×C4×D3#6711yescharacteristic
431C2×C4×D3#6714yes—
432C2×C4×D3C22×D311yescharacteristic
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D314yes—
435C2×Dic6—22no—
436C2×Dic6—21no—
437C2×Dic6—21no—
438C2×Dic6—32no—
439C2×Dic6—34no—
440C2×Dic6—32no—
441C2×Dic6—34no—
442C2×Dic6—38no—
443C2×Dic6—38no—
444C2×Dic6—62no—
445C2×Dic6—64no—
446C2×Dic6—64no—
447C2×Dic6—64no—
448C2×Dic6—68no—
449C2×Dic6—68no—
450C2×Dic6—62no—
451C2×Dic6—62no—
452C2×Dic6—68no—
453C2×Dic6—61no—
454C2×Dic6—62no—
455C2×Dic6—61no—
456C2×Dic6—62no—
457C2×Dic6—62no—
458C2×Dic6—62no—
459C2×Dic6—68no—
460C2×Dic6—121no—
461C2×Dic6—122no—
462C2×Dic6C22×D311yescharacteristic
463C2×Dic6C22×D312yes—
464C2×Dic6C22×D314yescomplemented
465C3×Q16—38no—
466C3×SD16—38no—
467C3×M16—34no—
468C2×C3×C8—32no—
469#216—38no—
470#216—38no—
471#216—38no—
472#216—38no—
473#216—38no—
474#216—68no—
475#216C22×D318yescomplemented
476#215—38no—
477#214—38no—
478#214—38no—
479#214—38no—
480#214—38no—
481#214—68no—
482#214C22×D318yescomplemented
483#208—34no—
484#208—34no—
485#208—38no—
486#208—64no—
487#208C22×D314yescomplemented
488C2×C3⋊C8—32no—
489C2×C3⋊C8—32no—
490C2×C3⋊C8—38no—
491C2×C3⋊C8—62no—
492C2×C3⋊C8C22×D312yes—
493Dic12—38no—
494#204—38no—
495ΓL(1,𝔽25)—38no—
496D3×C8—38no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—42no—
500C22×C32C22×D412yes—
501C22×C32C22×D411yescharacteristic
502C2×C3×D3—22no—
503C2×C3×D3—28no—
504C2×C3×D3—22no—
505C2×C3×D3—42no—
506C2×C3×D3—48no—
507C2×C3×D3#13714yescomplemented
508C2×C3×D3C22×D412yes—
509C2×C3×D3C22×D412yes—
510C32×C4—22no—
511C32×C4C22×D411yescharacteristic
512C32×C4C22×D412yes—
513C32×C4C2511yescharacteristic
514C3⋊Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—22no—
517C3×Dic3C22×D412yes—
518C3×Dic3C22×D412yes—
519C2×#41—38no—
520C2×#41—31no—
521C2×#41—31no—
522C2×#41—31no—
523C2×#41—61no—
524C2×#41—61no—
525C2×#41—64no—
526C2×#41D3211yescharacteristic
527C22×Q8—31no—
528C22×Q8—31no—
529C22×Q8—92no—
530C22×Q8—92no—
531C22×Q8—98no—
532C22×Q8—91no—
533C22×Q8—181no—
534C22×Q8—181no—
535C22×Q8—184no—
536C22×Q8—181no—
537C22×D4—31no—
538C22×D4—61no—
539C23×C4—31no—
540C23×C4—61no—
541C23×C4—181no—
542#137—38no—
543#137—98no—
544#137—916no—
545#137—916no—
546#137—98no—
547#137—98no—
548C2×Q16—32no—
549C2×Q16—92no—
550C2×Q16—916no—
551C2×Q16—92no—
552C2×Q16—92no—
553C2×SD16—32no—
554C2×SD16—92no—
555C2×SD16—916no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×M16—31no—
559C2×M16—92no—
560C2×M16—98no—
561C2×M16—91no—
562C22×C8—92no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—31no—
567C23×C3—34no—
568C23×C3—31no—
569C23×C3—41no—
570C23×C3—64no—
571C23×C3—64no—
572C23×C3—61no—
573C23×C3—124no—
574C23×C3D3×D411yescharacteristic
575C23×C3C2×#6711yescharacteristic
576C22×D3—24no—
577C22×D3—21no—
578C22×D3—24no—
579C22×D3—44no—
580C22×D3C2×#6711yescharacteristic
581C22×D3C2×#6714yes—
582C22×D3C2×#6711yescharacteristic
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8—22no—
586C3×Q8—34no—
587C3×Q8—32no—
588C3×Q8—41no—
589C3×Q8—64no—
590C3×Q8—61no—
591C3×Q8—62no—
592C3×Q8—64no—
593C3×Q8C23×D312yes—
594C3×Q8C23×D312yes—
595C3×D4—24no—
596C3×D4—24no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—22no—
600C3×D4—32no—
601C3×D4—41no—
602C3×D4—44no—
603C3×D4—64no—
604C3×D4—64no—
605C3×D4—64no—
606C3×D4—64no—
607C3×D4—61no—
608C3×D4C23×D312yes—
609C3×D4C23×D312yes—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—24no—
613C2×C3×C4—24no—
614C2×C3×C4—21no—
615C2×C3×C4—22no—
616C2×C3×C4—21no—
617C2×C3×C4—22no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—34no—
621C2×C3×C4—34no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—34no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—44no—
628C2×C3×C4—41no—
629C2×C3×C4—64no—
630C2×C3×C4—64no—
631C2×C3×C4—64no—
632C2×C3×C4—61no—
633C2×C3×C4—64no—
634C2×C3×C4—62no—
635C2×C3×C4—64no—
636C2×C3×C4D3×D411yescharacteristic
637C2×C3×C4D3×D412yes—
638C2×C3×C4C2×#6711yescharacteristic
639C2×C3×C4C2×#6712yes—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D312yes—
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D312yes—
644#67—24no—
645#67—24no—
646#67—24no—
647C2×Dic3—22no—
648C2×Dic3—24no—
649C2×Dic3—21no—
650C2×Dic3—24no—
651C2×Dic3—68no—
652C2×Dic3—68no—
653C2×Dic3—64no—
654C2×Dic3—62no—
655C2×Dic3—64no—
656C2×Dic3—62no—
657C2×Dic3—124no—
658C2×Dic3—122no—
659C2×Dic3C2×#6711yescharacteristic
660C2×Dic3C2×#6711yescharacteristic
661C2×Dic3C2×#6714yes—
662D12—24no—
663D12—21no—
664D12C23×D312yes—
665C4×D3—24no—
666C4×D3—24no—
667C4×D3—24no—
668C4×D3—68no—
669C4×D3—68no—
670C4×D3C2×#6714yes—
671C4×D3C2×#6714yes—
672C4×D3C2×#6712yes—
673C4×D3C2×#6712yes—
674C4×D3C23×D312yes—
675C4×D3C23×D312yes—
676Dic6—22no—
677Dic6—24no—
678Dic6—21no—
679Dic6—24no—
680Dic6—34no—
681Dic6—34no—
682Dic6—64no—
683Dic6—68no—
684Dic6—68no—
685Dic6—64no—
686Dic6—62no—
687Dic6—62no—
688Dic6—64no—
689Dic6—68no—
690Dic6—68no—
691Dic6—124no—
692Dic6—122no—
693Dic6C23×D312yes—
694Dic6C23×D314yes—
695C3×C8—34no—
696C3⋊C8—34no—
697C3⋊C8—34no—
698C3⋊C8—64no—
699C3⋊C8C23×D314yes—
700C2×C32—22no—
701C2×C32—42no—
702C2×C32C2×#13712yescomplemented
703C2×C32C23×D411yescharacteristic
704C3×D3—22no—
705C3×D3—42no—
706C3×D3C2×#13714yescomplemented
707C24—31no—
708C24—61no—
709#41—22no—
710#41—34no—
711#41—34no—
712#41—34no—
713#41—68no—
714#41—68no—
715#41—62no—
716#41—62no—
717#41—62no—
718#41C2×D3214yes—
719C2×Q8—34no—
720C2×Q8—32no—
721C2×Q8—31no—
722C2×Q8—34no—
723C2×Q8—61no—
724C2×Q8—62no—
725C2×Q8—62no—
726C2×Q8—61no—
727C2×Q8—98no—
728C2×Q8—98no—
729C2×Q8—92no—
730C2×Q8—94no—
731C2×Q8—188no—
732C2×Q8—182no—
733C2×Q8—182no—
734C2×Q8—188no—
735C2×Q8—184no—
736C2×Q8—184no—
737C2×Q8—188no—
738C2×Q8—182no—
739C2×Q8—181no—
740C2×Q8C2×D3211yescharacteristic
741C2×D4—21no—
742C2×D4—34no—
743C2×D4—31no—
744C2×D4—61no—
745C2×D4—62no—
746C2×D4—61no—
747C2×D4—68no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4C2×D3211yescharacteristic
751C22×C4—21no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—34no—
758C22×C4—31no—
759C22×C4—61no—
760C22×C4—68no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—188no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—181no—
769C22×C4C2×D3211yescharacteristic
770Q16—38no—
771Q16—98no—
772Q16—98no—
773Q16—98no—
774SD16—38no—
775SD16—98no—
776SD16—98no—
777SD16—98no—
778M16—34no—
779M16—98no—
780M16—94no—
781C2×C8—32no—
782C2×C8—98no—
783C2×C8—92no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—21no—
790C22×C3—32no—
791C22×C3—34no—
792C22×C3—32no—
793C22×C3—42no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—42no—
797C22×C3—68no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—82no—
801C22×C3—128no—
802C22×C3—122no—
803C22×C3C2×D3×D412yes—
804C22×C3C2×D3×D411yescharacteristic
805C22×C3C22×#6712yes—
806C22×C3C22×#6711yescharacteristic
807C2×D3—22no—
808C2×D3—28no—
809C2×D3—22no—
810C2×D3—42no—
811C2×D3—48no—
812C2×D3#95114yesdirect product factor
813C2×D3C22×#6712yes—
814C2×D3C22×#6712yes—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—42no—
823C3×C4—62no—
824C3×C4—64no—
825C3×C4C2×D3×D412yes—
826C3×C4C2×D3×D411yescharacteristic
827C3×C4C22×#6711yescharacteristic
828C3×C4C22×#6712yes—
829C3×C4C24×D311yescharacteristic
830C3×C4C24×D311yescharacteristic
831Dic3—24no—
832Dic3—22no—
833Dic3—64no—
834Dic3—64no—
835Dic3—124no—
836Dic3C22×#6712yes—
837Dic3C22×#6712yes—
838C32C22×#13711yescharacteristic, complemented, Sylow
839C23—21no—
840C23—31no—
841C23—34no—
842C23—31no—
843C23—64no—
844C23—64no—
845C23—61no—
846C23—124no—
847C23D3×#6711yescharacteristic
848Q8—21no—
849Q8—34no—
850Q8—32no—
851Q8—64no—
852Q8—64no—
853Q8—62no—
854Q8—61no—
855Q8—94no—
856Q8—188no—
857Q8—188no—
858Q8—184no—
859Q8—182no—
860Q8C22×D3212yes—
861D4—24no—
862D4—21no—
863D4—32no—
864D4—64no—
865D4—64no—
866D4—64no—
867D4—64no—
868D4—61no—
869D4C22×D3212yes—
870C2×C4—21no—
871C2×C4—24no—
872C2×C4—34no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—34no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—34no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—64no—
882C2×C4—64no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—61no—
886C2×C4—62no—
887C2×C4—64no—
888C2×C4—188no—
889C2×C4—188no—
890C2×C4—184no—
891C2×C4—182no—
892C2×C4D3×#6712yes—
893C2×C4D3×#6711yescharacteristic
894C2×C4C22×D3212yes—
895C2×C4C22×D3211yescharacteristic
896C8—34no—
897C8—94no—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—21no—
901C2×C3—22no—
902C2×C3—34no—
903C2×C3—42no—
904C2×C3—42no—
905C2×C3—42no—
906C2×C3—62no—
907C2×C3—82no—
908C2×C3—122no—
909C2×C3D3×#13712yescomplemented
910C2×C3C2×#95112yescomplemented
911C2×C3C22×D3×D411yescharacteristic
912C2×C3C23×#6711yescharacteristic
913D3—22no—
914D3—42no—
915D3C2×#95114yesdirect product factor
916C22—22no—
917C22—22no—
918C22—32no—
919C22—34no—
920C22—32no—
921C22—42no—
922C22—68no—
923C22—62no—
924C22—62no—
925C22—128no—
926C22—122no—
927C22C2×D3×#6712yes—
928C22C2×D3×#6711yescharacteristic
929C4—22no—
930C4—32no—
931C4—32no—
932C4—62no—
933C4—64no—
934C4—184no—
935C4C2×D3×#6712yes—
936C4C2×D3×#6711yescharacteristic
937C4C23×D3211yescharacteristic
938C3—21no—
939C3C2×D3×#13711yescharacteristic, complemented
940C3C22×#95111yescharacteristic, complemented
941C2—22no—
942C2—34no—
943C2—42no—
944C2—62no—
945C2—122no—
946C2D3×#95112yesdirect product factor
947C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC2×#41D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64160C2semidirect
4. C2×C3×#951C2semidirect
5. D3×#951C2direct (N × H)
6. C2×#63943C2semidirect
7. C2×D3×#216C2semidirect
8. C2×#63929C2semidirect
9. C2×D3×#214C2semidirect
10. C2×#63831C2semidirect
11. C2×#63827C2semidirect
12. C2×D3×#208C2semidirect
16. C22×#634C22semidirect
29. C22×C3×Dic6C22semidirect
36. C2×D3×Dic6C22semidirect
37. C2×D3×Dic6C22semidirect
38. #64160C22semidirect
39. C2×#3756C22semidirect
40. C2×#3754C22semidirect
41. C2×#3748C22semidirect
42. C3×#951C22semidirect
43. C2×C3×#216C22semidirect
44. C2×C3×#214C22semidirect
45. C2×C3×#208C22semidirect
46. #63943C22semidirect
47. D3×#216C22semidirect
48. #63929C22semidirect
49. D3×#214C22semidirect
50. C2×#3719C22semidirect
51. C2×#3718C22semidirect
52. #63831C22semidirect
53. C2×#3716C22semidirect
54. #63827C22semidirect
55. C2×#3715C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
72. C2×#951D3direct (N × H)
97. C2×#634C23semidirect
134. C2×C3×Dic6C23semidirect
146. D3×Dic6C23semidirect
147. #3756C23semidirect
148. #3754C23semidirect
149. #3748C23semidirect
151. C3×#216C23semidirect
152. C3×#214C23semidirect
153. C3×#208C23semidirect
155. #3719C23semidirect
156. #3718C23semidirect
157. #3716C23semidirect
158. #3715C23semidirect
159. #3711C23semidirect
209. C22×Dic6C2×D3semidirect
221. #951C2×D3direct (N × H)
229. C2×#216C2×D3semidirect
238. C2×#214C2×D3semidirect
244. C2×#208C2×D3semidirect
464. C2×Dic6C22×D3semidirect
475. #216C22×D3semidirect
482. #214C22×D3semidirect
487. #208C22×D3semidirect
507. C2×C3×D3#137semidirect
702. C2×C32C2×#137semidirect
706. C3×D3C2×#137semidirect
812. C2×D3#951direct (N × H)
838. C32C22×#137semidirect
909. C2×C3D3×#137semidirect
910. C2×C3C2×#951semidirect
915. D3C2×#951direct (N × H)
939. C3C2×D3×#137semidirect
940. C3C22×#951semidirect
946. C2D3×#951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C22×D3×Dic62
C2×#641602
C2×C3×#9512
D3×#9512
C2×#639432
C2×D3×#2162
C2×#639292
C2×D3×#2142
C2×#638312
C2×#638272
C2×D3×#2082
C22×#9513
C2×D3×#1373