Finite Group Databasebeta

← C2×D3×#942 #11918704

Subgroups — C2×D3×#942 #11918704

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
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic
3C2×#64151C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×#63948C212yesmaximal, complemented
6C2×#63946C212yesmaximal, complemented
7C2×D3×#216C212yesmaximal, complemented
8D3×#942C2116yesmaximal, direct product factor
9C2×D3×#215C212yesmaximal, complemented
10C2×#63833C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C22×#942—31nomaximal
14C2×D3×#137—31nomaximal
15C22×C32×Q8C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8—21no—
19C2×C3×D3×Q8—24no—
20C2×C3×D3×Q8C2212yes—
21C2×C3×D3×Q8C2212yescomplemented
22C2×C3×D3×Q8C2218yescomplemented
23C2×C3×#235C2211yescharacteristic
24C22×C3×C4×D3—21no—
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6—21no—
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×D3×#67—21no—
29C2×#3804—21no—
30D3×#235—24no—
31D3×#235C2218yes—
32C2×D3×D12C2211yescharacteristic
33C2×C4×D32—21no—
34C2×#3799C2211yescharacteristic
35C2×#3798—21no—
36C2×#3795C2211yescharacteristic
37C2×D3×Dic6C2211yescharacteristic
38C2×#3756C2212yescomplemented
39#64151C2218yescomplemented
40C2×#3755C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C2×C3×#216C2212yescomplemented
43C3×#942C2218yescomplemented
44C2×C3×#215C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63948C22116yescomplemented
47#63946C22116yescomplemented
48D3×#216C22116yescomplemented
49D3×#215C22116yescomplemented
50C2×#3719C2212yescomplemented
51C2×#3718C2212yescomplemented
52#63833C2218yescomplemented
53C2×#3717C2212yescomplemented
54#63827C2218yescomplemented
55C2×#3715C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yes—
59C23×C3×Q8—31no—
60C2×D3×#41—31no—
61C22×D3×Q8D311yescharacteristic, complemented
62C22×#235—31no—
63C2×C3×#137—31no—
64C2×#951—31no—
65C22×#216—32no—
66C2×#942—31no—
67C2×#942—31no—
68C2×#942—31no—
69C2×#942—32no—
70C2×#942—316no—
71C2×#942—32no—
72C2×#942—31no—
73C2×#942—61no—
74C2×#942D311yescharacteristic, direct product factor
75C22×#215—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×D3D411yescharacteristic
85C22×D32—21no—
86C2×C32×Q8—21no—
87C2×C32×Q8—22no—
88C2×C32×Q8C2312yes—
89C2×C32×Q8C2314yescomplemented
90C22×C32×C4—21no—
91C22×C32×C4C2311yescharacteristic
92C2×#638—21no—
93#3828—22no—
94#3828C2314yes—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3D411yescharacteristic
101C3×D3×Q8—24no—
102C3×D3×Q8—24no—
103C3×D3×Q8—28no—
104C3×D3×Q8—28no—
105C3×D3×Q8C2318yes—
106C3×D3×Q8C2318yescomplemented
107C3×#235—22no—
108C3×#235C2314yes—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—28no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3D414yes—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2314yes—
120C2×C3×Dic6—22no—
121C2×C3×Dic6—21no—
122C2×C3×Dic6—22no—
123C2×C3×Dic6—28no—
124C2×C3×Dic6—22no—
125C2×C3×Dic6C2311yescharacteristic
126C2×C3×Dic6C2312yes—
127C2×C3×Dic6C2314yescomplemented
128D3×#67—28no—
129C2×#627—21no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#624—21no—
134#3804—28no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12C2314yes—
139C4×D32—28no—
140#3799—22no—
141#3799C2314yes—
142#3798—28no—
143#3795—22no—
144#3795C2314yes—
145D3×Dic6—22no—
146D3×Dic6C2314yes—
147#3756C2318yescomplemented
148#3755C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#216C2318yescomplemented
152C3×#215C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3719C2318yescomplemented
156#3718C2318yescomplemented
157#3717C2318yescomplemented
158#3715C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yes—
161C22×#137—91noSylow
162C2×C3×#41—31no—
163C22×C3×Q8—21no—
164C22×C3×Q8—32no—
165C22×C3×Q8—32no—
166C22×C3×Q8—38no—
167C22×C3×Q8—31no—
168C22×C3×Q8—61no—
169C22×C3×Q8—61no—
170C22×C3×Q8—61no—
171C22×C3×Q8—64no—
172C22×C3×Q8C2×D311yescharacteristic, complemented
173C22×C3×Q8C2×D311yescharacteristic, complemented
174C23×C3×C4—31no—
175C23×C3×C4—61no—
176C22×#67—61no—
177D3×#41—38no—
178D3×#41—64no—
179C2×#239—31no—
180C2×D3×Q8—21no—
181C2×D3×Q8—21no—
182C2×D3×Q8—24no—
183C2×D3×Q8—31no—
184C2×D3×Q8C2×D312yes—
185C2×D3×Q8C2×D312yescomplemented
186C2×D3×Q8C2×D318yescomplemented
187C2×#237—31no—
188C2×#237—61no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—38no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C2×#235—61no—
198C2×#235—64no—
199C2×#235—61no—
200C2×#235—61no—
201C2×#235C2×D311yescharacteristic
202C22×D12—31no—
203C22×C4×D3—21no—
204C22×C4×D3—61no—
205C22×C4×D3—61no—
206C22×C4×D3C2×D311yescharacteristic
207C22×Dic6—21no—
208C22×Dic6—31no—
209C22×Dic6C2×D311yescharacteristic, complemented
210C3×#137—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×M16—31no—
214#951—38no—
215C2×#216—32no—
216C2×#216—32no—
217C2×#216—32no—
218C2×#216—32no—
219C2×#216—316no—
220C2×#216—32no—
221C2×#216—62no—
222C2×#216C2×D312yescomplemented
223#942—38no—
224#942—38no—
225#942—38no—
226#942—316no—
227#942—316no—
228#942—38no—
229#942—68no—
230#942C2×D318yesdirect product factor
231C2×#215—32no—
232C2×#215—32no—
233C2×#215—32no—
234C2×#215—316no—
235C2×#215—32no—
236C2×#215—62no—
237C2×#215C2×D312yescomplemented
238C2×#214—32no—
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×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—24no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D414yes—
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—24no—
264C2×D32—44no—
265C32×Q8—22no—
266C32×Q8—24no—
267C32×Q8C2414yes—
268C2×C32×C4—22no—
269C2×C32×C4—24no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D412yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2412yes—
274#638—24no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2412yes—
278C4×C3⋊D3—24no—
279#634—21no—
280#634C2412yes—
281C3×#67—24no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—24no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D414yes—
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12C2412yes—
290C3×C4×D3—28no—
291C3×C4×D3—28no—
292C3×C4×D3—24no—
293C3×C4×D3C2×D412yes—
294C3×C4×D3C2×D412yes—
295C3×C4×D3C2×D414yes—
296C3×C4×D3C2×D414yes—
297C3×C4×D3C2412yes—
298C3×C4×D3C2412yes—
299C3×Dic6—21no—
300C3×Dic6—22no—
301C3×Dic6—24no—
302C3×Dic6—28no—
303C3×Dic6—28no—
304C3×Dic6C2414yes—
305C3×Dic6C2412yes—
306#627—24no—
307#626—24no—
308#626—24no—
309#625—24no—
310#624—24no—
311D3×Dic3—24no—
312D3×Dic3—24no—
313C3⋊(C3⋊C8)C2414yes—
314C3×C3⋊C8C2414yes—
315C22×#41—91no—
316C23×Q8—31no—
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—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3#6711yescharacteristic
331C3×#41—34no—
332C3×#41—62no—
333C2×C3×Q8—21no—
334C2×C3×Q8—22no—
335C2×C3×Q8—21no—
336C2×C3×Q8—22no—
337C2×C3×Q8—22no—
338C2×C3×Q8—24no—
339C2×C3×Q8—38no—
340C2×C3×Q8—38no—
341C2×C3×Q8—32no—
342C2×C3×Q8—34no—
343C2×C3×Q8—31no—
344C2×C3×Q8—41no—
345C2×C3×Q8—42no—
346C2×C3×Q8—62no—
347C2×C3×Q8—62no—
348C2×C3×Q8—68no—
349C2×C3×Q8—64no—
350C2×C3×Q8—68no—
351C2×C3×Q8—64no—
352C2×C3×Q8—68no—
353C2×C3×Q8—61no—
354C2×C3×Q8—62no—
355C2×C3×Q8C22×D312yes—
356C2×C3×Q8C22×D312yes—
357C2×C3×Q8C22×D314yescomplemented
358C2×C3×Q8C22×D314yescomplemented
359C2×C3×D4—31no—
360C2×C3×D4—61no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—34no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—34no—
371C22×C3×C4—41no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—68no—
375C22×C3×C4—61no—
376C22×C3×C4—61no—
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C2×#67—21no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—121no—
388C22×Dic3—21no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3#6711yescharacteristic
392#239—34no—
393#239—62no—
394D3×Q8—24no—
395D3×Q8—24no—
396D3×Q8—28no—
397D3×Q8—28no—
398D3×Q8—34no—
399D3×Q8—62no—
400D3×Q8C22×D318yes—
401D3×Q8C22×D318yescomplemented
402#237—34no—
403#237—68no—
404#237—62no—
405D3×D4—34no—
406D3×D4—68no—
407D3×D4—62no—
408#235—22no—
409#235—34no—
410#235—34no—
411#235—34no—
412#235—34no—
413#235—64no—
414#235—62no—
415#235—68no—
416#235—62no—
417#235—68no—
418#235—62no—
419#235—62no—
420#235—68no—
421#235—122no—
422#235C22×D314yes—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—34no—
426C2×D12—61no—
427C2×D12—62no—
428C2×D12—61no—
429C2×D12—61no—
430C2×D12C22×D311yescharacteristic
431C2×C4×D3—22no—
432C2×C4×D3—28no—
433C2×C4×D3—22no—
434C2×C4×D3—21no—
435C2×C4×D3—68no—
436C2×C4×D3—61no—
437C2×C4×D3—61no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—68no—
443C2×C4×D3—121no—
444C2×C4×D3#6711yescharacteristic
445C2×C4×D3#6711yescharacteristic
446C2×C4×D3#6714yes—
447C2×C4×D3C22×D311yescharacteristic
448C2×C4×D3C22×D311yescharacteristic
449C2×C4×D3C22×D314yes—
450C2×Dic6—22no—
451C2×Dic6—21no—
452C2×Dic6—22no—
453C2×Dic6—28no—
454C2×Dic6—22no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—34no—
458C2×Dic6—61no—
459C2×Dic6—62no—
460C2×Dic6—61no—
461C2×Dic6—61no—
462C2×Dic6C22×D312yes—
463C2×Dic6C22×D311yescharacteristic
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#215—38no—
478#215—38no—
479#215—38no—
480#215—68no—
481#215C22×D318yescomplemented
482#214—38no—
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×C32C22×D412yes—
499C22×C32C22×D411yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—42no—
502C2×C3×D3—22no—
503C2×C3×D3—28no—
504C2×C3×D3—22no—
505C2×C3×D3—42no—
506C2×C3×D3#13714yescomplemented
507C2×C3×D3C22×D412yes—
508C2×C3×D3C22×D412yes—
509D32—48no—
510C32×C4—24no—
511C32×C4C22×D411yescharacteristic
512C32×C4C22×D412yes—
513C32×C4C2511yescharacteristic
514C3⋊Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—24no—
517C3×Dic3C22×D412yes—
518C3×Dic3C22×D412yes—
519C2×#41—31no—
520C2×#41—91no—
521C2×#41—91no—
522C2×#41—98no—
523C2×#41—91no—
524C2×#41—181no—
525C2×#41—181no—
526C2×#41—184no—
527C22×Q8—32no—
528C22×Q8—32no—
529C22×Q8—38no—
530C22×Q8—31no—
531C22×Q8—61no—
532C22×Q8—61no—
533C22×Q8—64no—
534C22×Q8—61no—
535C22×Q8—91no—
536C22×Q8D3211yescharacteristic, complemented
537C22×D4—91no—
538C22×D4—181no—
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—31no—
565C23×C3—34no—
566C23×C3—31no—
567C23×C3—64no—
568C23×C3—61no—
569C23×C3D3×D411yescharacteristic
570C23×C3C2×#6711yescharacteristic
571C22×D3—24no—
572C22×D3—21no—
573C22×D3—64no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—64no—
577C22×D3—121no—
578C22×D3—124no—
579C22×D3—124no—
580C22×D3C2×#6711yescharacteristic
581C22×D3C2×#6714yes—
582C22×D3C2×#6711yescharacteristic
583C3×Q8—22no—
584C3×Q8—24no—
585C3×Q8—22no—
586C3×Q8—24no—
587C3×Q8—24no—
588C3×Q8—34no—
589C3×Q8—32no—
590C3×Q8—42no—
591C3×Q8—44no—
592C3×Q8—68no—
593C3×Q8—68no—
594C3×Q8—62no—
595C3×Q8—64no—
596C3×Q8—61no—
597C3×Q8C23×D314yes—
598C3×Q8C23×D314yes—
599C3×D4—32no—
600C3×D4—64no—
601C3×D4—61no—
602C2×C3×C4—22no—
603C2×C3×C4—24no—
604C2×C3×C4—22no—
605C2×C3×C4—24no—
606C2×C3×C4—21no—
607C2×C3×C4—22no—
608C2×C3×C4—21no—
609C2×C3×C4—22no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—34no—
613C2×C3×C4—32no—
614C2×C3×C4—34no—
615C2×C3×C4—34no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—44no—
620C2×C3×C4—42no—
621C2×C3×C4—68no—
622C2×C3×C4—68no—
623C2×C3×C4—64no—
624C2×C3×C4—62no—
625C2×C3×C4—61no—
626C2×C3×C4—64no—
627C2×C3×C4D3×D411yescharacteristic
628C2×C3×C4D3×D412yes—
629C2×C3×C4C2×#6711yescharacteristic
630C2×C3×C4C2×#6712yes—
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C23×D312yes—
635#67—24no—
636#67—64no—
637#67—64no—
638#67—64no—
639#67—64no—
640#67—64no—
641#67—64no—
642#67—124no—
643C2×Dic3—21no—
644C2×Dic3—22no—
645C2×Dic3—24no—
646C2×Dic3—64no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—64no—
650C2×Dic3—121no—
651C2×Dic3C2×#6711yescharacteristic
652C2×Dic3C2×#6711yescharacteristic
653C2×Dic3C2×#6714yes—
654D12—21no—
655D12—32no—
656D12—32no—
657D12—62no—
658D12—64no—
659D12—64no—
660D12—61no—
661D12—61no—
662D12—121no—
663D12C23×D312yes—
664C4×D3—28no—
665C4×D3—28no—
666C4×D3—24no—
667C4×D3—64no—
668C4×D3—64no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—124no—
674C4×D3C2×#6714yes—
675C4×D3C2×#6714yes—
676C4×D3C2×#6712yes—
677C4×D3C2×#6712yes—
678C4×D3C23×D312yes—
679C4×D3C23×D312yes—
680Dic6—21no—
681Dic6—22no—
682Dic6—24no—
683Dic6—28no—
684Dic6—28no—
685Dic6—32no—
686Dic6—32no—
687Dic6—62no—
688Dic6—64no—
689Dic6—61no—
690Dic6—61no—
691Dic6—64no—
692Dic6—121no—
693Dic6C23×D314yes—
694Dic6C23×D312yes—
695C3×C8—34no—
696C3⋊C8—34no—
697C3⋊C8—34no—
698C3⋊C8—64no—
699C3⋊C8C23×D314yes—
700C2×C32—22no—
701C2×C32C2×#13712yescomplemented
702C2×C32C23×D411yescharacteristic
703C3⋊D3—42no—
704C3×D3—22no—
705C3×D3—42no—
706C3×D3C2×#13714yescomplemented
707C24—31no—
708C24—181no—
709#41—34no—
710#41—62no—
711#41—94no—
712#41—94no—
713#41—94no—
714#41—188no—
715#41—188no—
716#41—182no—
717#41—182no—
718#41—182no—
719C2×Q8—22no—
720C2×Q8—21no—
721C2×Q8—38no—
722C2×Q8—38no—
723C2×Q8—32no—
724C2×Q8—31no—
725C2×Q8—34no—
726C2×Q8—68no—
727C2×Q8—62no—
728C2×Q8—62no—
729C2×Q8—68no—
730C2×Q8—64no—
731C2×Q8—64no—
732C2×Q8—68no—
733C2×Q8—62no—
734C2×Q8—61no—
735C2×Q8—94no—
736C2×Q8—91no—
737C2×Q8—181no—
738C2×Q8—182no—
739C2×Q8C2×D3212yes—
740C2×Q8C2×D3214yescomplemented
741C2×D4—31no—
742C2×D4—61no—
743C2×D4—94no—
744C2×D4—91no—
745C2×D4—182no—
746C2×D4—181no—
747C2×D4—181no—
748C2×D4—188no—
749C2×D4—181no—
750C2×D4—181no—
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—68no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—181no—
765C22×C4—188no—
766C22×C4—181no—
767C22×C4—181no—
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—21no—
788C22×C3—32no—
789C22×C3—34no—
790C22×C3—32no—
791C22×C3—42no—
792C22×C3—68no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—122no—
796C22×C3C2×D3×D412yes—
797C22×C3C2×D3×D411yescharacteristic
798C22×C3C22×#6712yes—
799C22×C3C22×#6711yescharacteristic
800C2×D3—22no—
801C2×D3—28no—
802C2×D3—22no—
803C2×D3—42no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—122no—
807C2×D3—128no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—128no—
811C2×D3—242no—
812C2×D3#94214yesdirect product factor
813C2×D3C22×#6712yes—
814C2×D3C22×#6712yes—
815C3×C4—24no—
816C3×C4—24no—
817C3×C4—21no—
818C3×C4—22no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—44no—
823C3×C4—64no—
824C3×C4—62no—
825C3×C4C2×D3×D411yescharacteristic
826C3×C4C2×D3×D412yes—
827C3×C4C22×#6711yescharacteristic
828C3×C4C22×#6712yes—
829C3×C4C24×D311yescharacteristic
830C3×C4C24×D311yescharacteristic
831Dic3—22no—
832Dic3—24no—
833Dic3—62no—
834Dic3—62no—
835Dic3—122no—
836Dic3C22×#6712yes—
837Dic3C22×#6712yes—
838C32C22×#13711yescharacteristic, complemented, Sylow
839C23—31no—
840C23—34no—
841C23—31no—
842C23—64no—
843C23—61no—
844C23—184no—
845C23—181no—
846C23—364no—
847C23D3×#6711yescharacteristic
848Q8—22no—
849Q8—24no—
850Q8—34no—
851Q8—32no—
852Q8—68no—
853Q8—68no—
854Q8—64no—
855Q8—62no—
856Q8—61no—
857Q8—92no—
858Q8—184no—
859Q8—181no—
860Q8C22×D3214yes—
861D4—32no—
862D4—64no—
863D4—61no—
864D4—92no—
865D4—184no—
866D4—184no—
867D4—184no—
868D4—184no—
869D4—181no—
870C2×C4—24no—
871C2×C4—22no—
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—68no—
882C2×C4—68no—
883C2×C4—64no—
884C2×C4—62no—
885C2×C4—61no—
886C2×C4—64no—
887C2×C4—184no—
888C2×C4—184no—
889C2×C4—184no—
890C2×C4—181no—
891C2×C4—184no—
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—62no—
905C2×C3—122no—
906C2×C3D3×#13712yescomplemented
907C2×C3C2×#94212yescomplemented
908C2×C3C22×D3×D411yescharacteristic
909C2×C3C23×#6711yescharacteristic
910D3—22no—
911D3—42no—
912D3—122no—
913D3—122no—
914D3—242no—
915D3C2×#94214yesdirect product factor
916C22—22no—
917C22—32no—
918C22—34no—
919C22—32no—
920C22—68no—
921C22—62no—
922C22—62no—
923C22—122no—
924C22—182no—
925C22—368no—
926C22—362no—
927C22C2×D3×#6712yes—
928C22C2×D3×#6711yescharacteristic
929C4—24no—
930C4—32no—
931C4—32no—
932C4—64no—
933C4—62no—
934C4—182no—
935C4C2×D3×#6712yes—
936C4C2×D3×#6711yescharacteristic
937C4C23×D3211yescharacteristic
938C3—21no—
939C3C2×D3×#13711yescharacteristic, complemented
940C3C22×#94211yescharacteristic, complemented
941C2—22no—
942C2—34no—
943C2—62no—
944C2—122no—
945C2—362no—
946C2D3×#94212yesdirect product factor
947C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC22×Q8D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
3. C2×#64151C2semidirect
4. C2×C3×#942C2semidirect
5. C2×#63948C2semidirect
6. C2×#63946C2semidirect
7. C2×D3×#216C2semidirect
8. D3×#942C2direct (N × H)
9. C2×D3×#215C2semidirect
10. C2×#63833C2semidirect
11. C2×#63827C2semidirect
12. C2×D3×#208C2semidirect
15. C22×C32×Q8C22semidirect
21. C2×C3×D3×Q8C22semidirect
22. C2×C3×D3×Q8C22semidirect
27. C22×C3×Dic6C22semidirect
38. C2×#3756C22semidirect
39. #64151C22semidirect
40. C2×#3755C22semidirect
41. C2×#3748C22semidirect
42. C2×C3×#216C22semidirect
43. C3×#942C22semidirect
44. C2×C3×#215C22semidirect
45. C2×C3×#208C22semidirect
46. #63948C22semidirect
47. #63946C22semidirect
48. D3×#216C22semidirect
49. D3×#215C22semidirect
50. C2×#3719C22semidirect
51. C2×#3718C22semidirect
52. #63833C22semidirect
53. C2×#3717C22semidirect
54. #63827C22semidirect
55. C2×#3715C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
61. C22×D3×Q8D3semidirect
74. C2×#942D3direct (N × H)
89. C2×C32×Q8C23semidirect
106. C3×D3×Q8C23semidirect
127. C2×C3×Dic6C23semidirect
147. #3756C23semidirect
148. #3755C23semidirect
149. #3748C23semidirect
151. C3×#216C23semidirect
152. C3×#215C23semidirect
153. C3×#208C23semidirect
155. #3719C23semidirect
156. #3718C23semidirect
157. #3717C23semidirect
158. #3715C23semidirect
159. #3711C23semidirect
172. C22×C3×Q8C2×D3semidirect
173. C22×C3×Q8C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
186. C2×D3×Q8C2×D3semidirect
209. C22×Dic6C2×D3semidirect
222. C2×#216C2×D3semidirect
230. #942C2×D3direct (N × H)
237. C2×#215C2×D3semidirect
244. C2×#208C2×D3semidirect
357. C2×C3×Q8C22×D3semidirect
358. C2×C3×Q8C22×D3semidirect
401. D3×Q8C22×D3semidirect
464. C2×Dic6C22×D3semidirect
475. #216C22×D3semidirect
481. #215C22×D3semidirect
487. #208C22×D3semidirect
506. C2×C3×D3#137semidirect
536. C22×Q8D32semidirect
701. C2×C32C2×#137semidirect
706. C3×D3C2×#137semidirect
740. C2×Q8C2×D32semidirect
812. C2×D3#942direct (N × H)
838. C32C22×#137semidirect
906. C2×C3D3×#137semidirect
907. C2×C3C2×#942semidirect
915. D3C2×#942direct (N × H)
939. C3C2×D3×#137semidirect
940. C3C22×#942semidirect
946. C2D3×#942direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×D3×#2352
C2×#641512
C2×C3×#9422
C2×#639482
C2×#639462
C2×D3×#2162
D3×#9422
C2×D3×#2152
C2×#638332
C2×#638272
C2×D3×#2082
C22×#9423
C2×D3×#1373