Finite Group Databasebeta

← C4×D3×#239 #11899963

Subgroups — C4×D3×#239 #11899963

Order 1152.

3611 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2C4×#3832C211yesmaximal, characteristic, complemented
3C3×C4×#239C211yesmaximal, characteristic, complemented
4C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
5#10595386C211yesmaximal, characteristic, complemented
6Dic3×#239C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8D3×#893C213yesmaximal, complemented
9D3×#892C213yesmaximal, complemented
10#10594362C213yesmaximal, complemented
11#10594360C213yesmaximal, complemented
12C4×D3×D12C213yesmaximal, complemented
13C42×D32C213yesmaximal, complemented
14C4×#3799C213yesmaximal, complemented
15C4×#3796C213yesmaximal, complemented
16C4×D3×#41—31nomaximal
17C2×C4×#239—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239C4116yesdirect product factor
22C2×D3×D12C2213yes—
23C2×C4×D32C2213yes—
24C2×C4×D32C2213yes—
25C2×C4×D32C2213yes—
26C2×#3799C2213yes—
27C2×#3796C2213yes—
28C32×C4×Q8C2211yescharacteristic, complemented
29Q8×C3⋊Dic3C2211yescharacteristic, complemented
30#64102C2213yescomplemented
31#64101C2213yescomplemented
32C4×C4⋊(C3⋊D3)C2213yescomplemented
33C42×C3⋊D3C2213yescomplemented
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×Q8×Dic3C2211yescharacteristic, complemented
36C3×#893C2213yescomplemented
37C3×#892C2213yescomplemented
38C3×D3×C4⋊C4C2213yes—
39C3×#887C2213yescomplemented
40C3×C4×D12C2213yescomplemented
41C3×C42×D3C2213yes—
42C3×C42×D3C2213yescomplemented
43C3×C4×Dic6C2213yescomplemented
44D3×(C2×D3)⋊C4C2216yes—
45#63904C2216yescomplemented
46C4×#626C2216yescomplemented
47#63898C2213yescomplemented
48#63894C2213yescomplemented
49#63894C2213yescomplemented
50Dic3×D12C2213yescomplemented
51D3×C4⋊Dic3C2213yes—
52C4×#624C2213yescomplemented
53C4×#624C2213yescomplemented
54C4×#624C2213yescomplemented
55#63881C2216yescomplemented
56#63880C2216yescomplemented
57#63878C2216yescomplemented
58C4×D3×Dic3C2213yes—
59C4×D3×Dic3C2213yes—
60C4×D3×Dic3C2211yescharacteristic
61C4×D3×Dic3C2213yescomplemented
62C4×D3×Dic3C2213yescomplemented
63C4×D3×Dic3C2213yescomplemented
64#63849C2213yescomplemented
65#63843C2213yescomplemented
66Dic3×Dic6C2213yescomplemented
67#63841C2213yescomplemented
68#63836C2216yescomplemented
69C2×D3×#41—31no—
70C22×#239—31no—
71C3×C4×#41—31no—
72C2×C3×C4×Q8—31no—
73Dic3×#41—31no—
74C2×Q8×Dic3—31no—
75C4×#239—31no—
76C4×#239—31no—
77C4×#239—31no—
78C4×#239—31no—
79C4×#239—31no—
80C4×#239—33no—
81C4×#239—33no—
82C4×#239—33no—
83C4×#239—33no—
84C4×#239—61no—
85C4×#239D311yescharacteristic, direct product factor
86C4×D3×Q8—31no—
87C4×D3×Q8D311yescharacteristic, complemented
88C4×D3×D4—33no—
89C4×D3×D4—33no—
90C4×#237—33no—
91C4×#237—33no—
92#5522—33no—
93D3×#117—33no—
94C2×#893—33no—
95C2×#892—33no—
96C4×#235—33no—
97C2×C4×D12—33no—
98C2×C42×D3—33no—
99C2×C42×D3—33no—
100C22×D32C2313yes—
101C2×C32×Q8C2311yescharacteristic
102#3832C2×C418yescomplemented
103C2×C4⋊(C3⋊D3)C2313yes—
104C2×C4×C3⋊D3C2313yes—
105C2×C4×C3⋊D3C2313yes—
106C2×C4×C3⋊D3C2313yes—
107C3×#239C2×C418yescomplemented
108C3×D3×Q8C2×C418yescomplemented
109C2×C3×D12C2313yes—
110C2×C3×C4×D3C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2313yes—
117C2×#626C2316yes—
118C2×#624C2313yes—
119C2×#624C2313yes—
120C2×#624C2313yes—
121C2×D3×Dic3C2313yes—
122C2×D3×Dic3C2313yes—
123C2×D3×Dic3C2313yes—
124C2×D3×Dic3C2311yescharacteristic
125C2×D3×Dic3C2313yes—
126C2×D3×Dic3C2311yescharacteristic
127D3×D12C2×C4124yescomplemented
128C4×D32—212no—
129C4×D32—212no—
130C4×D32C2×C4124yescomplemented
131#3799C2×C4124yescomplemented
132#3796C2×C4124yescomplemented
133C32×C4⋊C4C2313yes—
134C32×C42C2313yes—
135#3752C2316yes—
136C4⋊(C3⋊Dic3)C2313yes—
137C4×C3⋊Dic3C2311yescharacteristic
138C4×C3⋊Dic3C2313yes—
139C4×C3⋊Dic3C2313yes—
140C3×(C2×D3)⋊C4C2316yes—
141C3×C4⋊Dic3C2313yes—
142C3×C4⋊Dic3C2313yes—
143C3×Dic3⋊C4C2316yes—
144C3×C4×Dic3C2313yes—
145C3×C4×Dic3C2313yes—
146C3×C4×Dic3C2313yes—
147C3×C4×Dic3C2313yes—
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2313yes—
150Dic3⋊Dic3C2316yes—
151#3722C2316yes—
152(C2×D3)⋊Dic3C2316yes—
153Dic32C2313yes—
154Dic32C2313yes—
155Dic32C2313yes—
156Dic32C2313yes—
157Dic32C2311yescharacteristic
158Dic32C2311yescharacteristic
159C2×C4×#41—91noSylow
160C2×C3×#41—31no—
161C22×C3×Q8—31no—
162D3×#41—316no—
163C2×#239—31no—
164C2×#239—31no—
165C2×#239—316no—
166C2×#239—33no—
167C2×#239—33no—
168C2×#239—61no—
169C2×#239C2×D311yescharacteristic
170C2×D3×Q8C2×D311yescharacteristic
171C2×#237—33no—
172C2×D3×D4—33no—
173C2×#235—33no—
174C22×D12—33no—
175C22×C4×D3—33no—
176C22×C4×D3—33no—
177C22×C4×D3—33no—
178C22×C4×D3—33no—
179C22×C4×D3—33no—
180C22×C4×D3—33no—
181C3×C4×Q8—21no—
182C3×C4×Q8—31no—
183C3×C4×Q8—31no—
184C3×C4×Q8—33no—
185C3×C4×Q8—33no—
186C3×C4×Q8C2×D311yescharacteristic, complemented
187C3×C4×Q8C2×D311yescharacteristic, complemented
188C3×C4×D4—33no—
189C3×C4×D4—33no—
190C3×#117—33no—
191C2×C3×C4⋊C4—33no—
192C2×C3×C42—33no—
193C2×C3×C42—33no—
194Q8×Dic3—31no—
195Q8×Dic3—31no—
196Q8×Dic3—33no—
197Q8×Dic3—33no—
198Q8×Dic3—61no—
199Q8×Dic3C2×D311yescharacteristic, complemented
200Q8×Dic3C2×D311yescharacteristic, complemented
201D4×Dic3—33no—
202D4×Dic3—33no—
203C4×#67—36no—
204C4×#67—36no—
205C2×(C2×D3)⋊C4—36no—
206#926—33no—
207C2×C4⋊Dic3—33no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—33no—
210C2×C4×Dic3—33no—
211C2×C4×Dic3—33no—
212C2×C4×Dic3—33no—
213C2×C4×Dic3—33no—
214#893—33no—
215#893—36no—
216#893—33no—
217#893—33no—
218#893—36no—
219#893—33no—
220#893—33no—
221#893—63no—
222#893C2×D313yescomplemented
223#892—33no—
224#892—33no—
225#892—33no—
226#892—36no—
227#892—33no—
228#892—33no—
229#892—36no—
230#892—63no—
231#892C2×D313yescomplemented
232D3×C4⋊C4—33no—
233D3×C4⋊C4C2×D313yes—
234#887—33no—
235#887C2×D313yescomplemented
236#67⋊C4—36no—
237#67⋊C4—36no—
238D3×C22⋊C4—36no—
239#877—36no—
240C4×D12—33no—
241C4×D12—36no—
242C4×D12—33no—
243C4×D12—33no—
244C4×D12—36no—
245C4×D12—33no—
246C4×D12—33no—
247C4×D12—63no—
248C4×D12C2×D313yescomplemented
249#872—36no—
250C42×D3—31no—
251C42×D3—33no—
252C42×D3—33no—
253C42×D3—33no—
254C42×D3—33no—
255C42×D3—33no—
256C42×D3—33no—
257C42×D3—33no—
258C42×D3—33no—
259C42×D3—33no—
260C42×D3—33no—
261C42×D3—33no—
262C42×D3—33no—
263C42×D3—33no—
264C42×D3—63no—
265C42×D3C2×D313yes—
266C42×D3C2×D313yescomplemented
267C4×Dic6—33no—
268C4×Dic6C2×D313yescomplemented
269C22×C3⋊D3C2413yes—
270C22×C3×D3C2413yes—
271C22×C3×D3C2411yescharacteristic
272C2×D32—26no—
273C2×D32—26no—
274C2×D32C22×C4112yes—
275C32×Q8C22×C414yescomplemented
276C2×C32×C4C2413yes—
277C2×C32×C4C2413yes—
278C2×C32×C4C2411yescharacteristic
279C2×C3⋊Dic3C2413yes—
280C2×C3⋊Dic3C2411yescharacteristic
281C2×C3⋊Dic3C2411yescharacteristic
282C4⋊(C3⋊D3)C22×C4112yescomplemented
283C4×C3⋊D3—26no—
284C4×C3⋊D3—26no—
285C4×C3⋊D3C22×C4112yescomplemented
286C2×C3×Dic3C2413yes—
287C2×C3×Dic3C2413yes—
288C2×C3×Dic3C2411yescharacteristic
289C2×C3×Dic3C2413yes—
290C2×C3×Dic3C2411yescharacteristic
291C2×C3×Dic3C2411yescharacteristic
292C3×D12C22×C4112yescomplemented
293C3×C4×D3—26no—
294C3×C4×D3—26no—
295C3×C4×D3—26no—
296C3×C4×D3C22×C4112yes—
297C3×C4×D3C22×C4112yescomplemented
298C3×C4×D3#4114yescomplemented
299C3×Dic6C22×C4112yescomplemented
300#626C22×C4124yescomplemented
301#624—26no—
302#624—26no—
303#624C22×C4112yescomplemented
304D3×Dic3—26no—
305D3×Dic3—26no—
306D3×Dic3—26no—
307D3×Dic3C22×C414yes—
308D3×Dic3C22×C4112yescomplemented
309D3×Dic3#4114yescomplemented
310C22×#41—91no—
311C4×#41—31no—
312C4×#41—93no—
313C4×#41—93no—
314C4×#41—93no—
315C4×#41—93no—
316C4×#41—91no—
317C4×#41—91no—
318C4×#41—91no—
319C2×C4×Q8—31no—
320C2×C4×Q8—91no—
321C2×C4×D4—93no—
322C2×C4×D4—93no—
323C2×#117—93no—
324C22×C42—93no—
325C23×D3—33no—
326C23×D3—33no—
327C3×#41—38no—
328C2×C3×Q8—21no—
329C2×C3×Q8—38no—
330C2×C3×Q8—33no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—33no—
334C22×C3×C4—33no—
335C22×C3×C4—33no—
336C22×C3×C4—31no—
337C22×C3×C4—33no—
338C22×C3×C4—33no—
339C22×C3×C4—33no—
340C2×#67—36no—
341C22×Dic3—33no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—33no—
345C22×Dic3—33no—
346C22×Dic3—33no—
347#239—38no—
348#239—38no—
349#239—324no—
350#239—324no—
351#239—68no—
352#239C4×D318yesdirect product factor
353D3×Q8C4×D318yescomplemented
354#237—324no—
355D3×D4—324no—
356#235—324no—
357C2×D12—36no—
358C2×D12—33no—
359C2×D12—33no—
360C2×D12—324no—
361C2×D12—63no—
362C2×D12C22×D313yes—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—33no—
366C2×C4×D3—33no—
367C2×C4×D3—33no—
368C2×C4×D3—33no—
369C2×C4×D3—33no—
370C2×C4×D3—324no—
371C2×C4×D3—324no—
372C2×C4×D3—33no—
373C2×C4×D3—33no—
374C2×C4×D3—33no—
375C2×C4×D3—33no—
376C2×C4×D3—33no—
377C2×C4×D3—33no—
378C2×C4×D3—33no—
379C2×C4×D3—33no—
380C2×C4×D3—33no—
381C2×C4×D3—33no—
382C2×C4×D3—33no—
383C2×C4×D3—63no—
384C2×C4×D3—63no—
385C2×C4×D3—63no—
386C2×C4×D3—612no—
387C2×C4×D3—612no—
388C2×C4×D3—612no—
389C2×C4×D3—612no—
390C2×C4×D3C22×D313yes—
391C2×C4×D3C22×D313yes—
392C2×C4×D3C22×D313yes—
393C2×C4×D3C22×D313yes—
394C2×C4×D3C22×D313yes—
395C2×C4×D3C22×D311yescharacteristic
396C2×Dic6C22×D313yes—
397C3×C4⋊C4—23no—
398C3×C4⋊C4—33no—
399C3×C4⋊C4—36no—
400C3×C4⋊C4—33no—
401C3×C4⋊C4C22×D313yes—
402C3×C4⋊C4C22×D313yes—
403C3×C22⋊C4—36no—
404C3×C42—23no—
405C3×C42—33no—
406C3×C42—31no—
407C3×C42—33no—
408C3×C42—33no—
409C3×C42—33no—
410C3×C42—33no—
411C3×C42C22×D313yes—
412C3×C42C22×D313yes—
413#217—36no—
414(C2×D3)⋊C4—36no—
415(C2×D3)⋊C4—36no—
416(C2×D3)⋊C4—36no—
417(C2×D3)⋊C4—36no—
418(C2×D3)⋊C4—36no—
419(C2×D3)⋊C4—66no—
420(C2×D3)⋊C4C22×D316yes—
421C4⋊Dic3—33no—
422C4⋊Dic3—33no—
423C4⋊Dic3—36no—
424C4⋊Dic3—63no—
425C4⋊Dic3C22×D313yes—
426C4⋊Dic3C22×D313yes—
427Dic3⋊C4—36no—
428Dic3⋊C4C22×D316yes—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—33no—
432C4×Dic3—33no—
433C4×Dic3—33no—
434C4×Dic3—33no—
435C4×Dic3—33no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—33no—
441C4×Dic3—33no—
442C4×Dic3—33no—
443C4×Dic3—33no—
444C4×Dic3—33no—
445C4×Dic3—33no—
446C4×Dic3—33no—
447C4×Dic3—61no—
448C4×Dic3—63no—
449C4×Dic3—63no—
450C4×Dic3C22×D313yes—
451C4×Dic3C22×D311yescharacteristic
452C4×Dic3C22×D313yes—
453C4×Dic3C22×D313yes—
454C4×Dic3C22×D313yes—
455C4×Dic3C22×D313yes—
456C22×C32C2511yescharacteristic
457C2×C3⋊D3—23no—
458C2×C3⋊D3—23no—
459C2×C3⋊D3C23×C416yes—
460C2×C3×D3—23no—
461C2×C3×D3—23no—
462C2×C3×D3C23×C416yes—
463C2×C3×D3C23×C412yes—
464C2×C3×D3C2×#4112yes—
465C2×C3×D3C2×#4112yes—
466D32—224no—
467C32×C4—23no—
468C32×C4C23×C416yes—
469C32×C4C2×#4112yescomplemented
470C3⋊Dic3—23no—
471C3⋊Dic3C23×C412yes—
472C3⋊Dic3C2×#4112yescomplemented
473C3×Dic3—23no—
474C3×Dic3—23no—
475C3×Dic3C23×C412yes—
476C3×Dic3C23×C416yes—
477C3×Dic3C2×#4112yescomplemented
478C3×Dic3C2×#4112yescomplemented
479C2×#41—31no—
480C2×#41—93no—
481C2×#41—93no—
482C2×#41—916no—
483C2×#41—91no—
484C22×Q8—31no—
485C22×D4—93no—
486C23×C4—93no—
487C23×C4—93no—
488C23×C4—93no—
489C4×Q8—31no—
490C4×Q8—31no—
491C4×Q8—33no—
492C4×Q8—33no—
493C4×Q8—93no—
494C4×Q8—93no—
495C4×Q8—91no—
496C4×Q8D3211yescharacteristic, complemented
497C4×D4—33no—
498C4×D4—33no—
499C4×D4—96no—
500C4×D4—93no—
501C4×D4—93no—
502C4×D4—96no—
503C4×D4—93no—
504C4×D4—96no—
505C4×D4—96no—
506C4×D4—93no—
507C4×D4—93no—
508C4×D4—93no—
509#117—33no—
510#117—96no—
511#117—96no—
512#117—93no—
513#117—93no—
514#117—93no—
515C2×C4⋊C4—33no—
516C2×C4⋊C4—93no—
517C2×C22⋊C4—96no—
518C2×C42—33no—
519C2×C42—33no—
520C2×C42—93no—
521C2×C42—93no—
522C2×C42—93no—
523C2×C42—93no—
524C2×C42—93no—
525C2×C42—93no—
526C2×C42—93no—
527C2×C42—93no—
528C2×C42—91no—
529C2×C42—93no—
530C23×C3—31no—
531C23×C3—33no—
532C22×D3—33no—
533C22×D3—33no—
534C22×D3—312no—
535C22×D3—312no—
536C22×D3—63no—
537C22×D3—66no—
538C22×D3—66no—
539C22×D3—66no—
540C22×D3—66no—
541C22×D3C23×D313yes—
542C22×D3C23×D311yescharacteristic
543C3×Q8—24no—
544C3×Q8—312no—
545C3×Q8C2×C4×D314yescomplemented
546C3×Q8C2×C4×D314yescomplemented
547C3×D4—312no—
548C2×C3×C4—23no—
549C2×C3×C4—23no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—33no—
554C2×C3×C4—31no—
555C2×C3×C4—312no—
556C2×C3×C4—312no—
557C2×C3×C4—34no—
558C2×C3×C4—33no—
559C2×C3×C4—33no—
560C2×C3×C4—66no—
561C2×C3×C4—66no—
562C2×C3×C4—66no—
563C2×C3×C4C23×D313yes—
564C2×C3×C4C23×D313yes—
565C2×C3×C4C23×D313yes—
566C2×C3×C4C23×D313yes—
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569#67—324no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—34no—
575C2×Dic3—312no—
576C2×Dic3—34no—
577C2×Dic3—33no—
578C2×Dic3—33no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—63no—
582C2×Dic3—66no—
583C2×Dic3—66no—
584C2×Dic3—66no—
585C2×Dic3C23×D313yes—
586C2×Dic3C23×D313yes—
587C2×Dic3C23×D311yescharacteristic
588C2×Dic3C23×D313yes—
589C2×Dic3C23×D311yescharacteristic
590C2×Dic3C23×D311yescharacteristic
591D12—324no—
592D12—312no—
593D12—312no—
594D12—612no—
595D12C2×C4×D3112yescomplemented
596C4×D3—26no—
597C4×D3—26no—
598C4×D3—26no—
599C4×D3—34no—
600C4×D3—312no—
601C4×D3—34no—
602C4×D3—312no—
603C4×D3—312no—
604C4×D3—312no—
605C4×D3—312no—
606C4×D3—612no—
607C4×D3—66no—
608C4×D3—66no—
609C4×D3—66no—
610C4×D3—66no—
611C4×D3—66no—
612C4×D3—66no—
613C4×D3—66no—
614C4×D3—66no—
615C4×D3—66no—
616C4×D3—66no—
617C4×D3—66no—
618C4×D3—126no—
619C4×D3—126no—
620C4×D3C2×C4×D3112yes—
621C4×D3C2×C4×D3112yescomplemented
622C4×D3#23914yesdirect product factor
623Dic6C2×C4×D3112yescomplemented
624C2×C32C24×C411yescharacteristic
625C2×C32C22×#4111yescharacteristic
626C2×C32C22×#4111yescharacteristic
627C3⋊D3—26no—
628C3×D3—26no—
629C3×D3C4×#4114yescomplemented
630C24—93no—
631#41—38no—
632#41—924no—
633#41—924no—
634#41—98no—
635C2×Q8—38no—
636C2×Q8—33no—
637C2×Q8C2×D3211yescharacteristic
638C2×D4—33no—
639C2×D4—924no—
640C2×D4—96no—
641C2×D4—93no—
642C22×C4—33no—
643C22×C4—33no—
644C22×C4—31no—
645C22×C4—33no—
646C22×C4—33no—
647C22×C4—33no—
648C22×C4—93no—
649C22×C4—924no—
650C22×C4—93no—
651C22×C4—93no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—93no—
655C22×C4—93no—
656C22×C4—93no—
657C22×C4—93no—
658C22×C4—93no—
659C22×C4—93no—
660C22×C4—93no—
661C22×C4—1812no—
662C22×C4—1812no—
663C4⋊C4—36no—
664C4⋊C4—33no—
665C4⋊C4—33no—
666C4⋊C4—96no—
667C4⋊C4—93no—
668C4⋊C4C2×D3213yes—
669C22⋊C4—36no—
670C22⋊C4—96no—
671C22⋊C4—96no—
672C22⋊C4—96no—
673C42—33no—
674C42—33no—
675C42—33no—
676C42—33no—
677C42—31no—
678C42—33no—
679C42—91no—
680C42—91no—
681C42—93no—
682C42—93no—
683C42—93no—
684C42—93no—
685C42—93no—
686C42—93no—
687C42—91no—
688C42C2×D3213yes—
689C22×C3—21no—
690C22×C3—32no—
691C22×C3—32no—
692C22×C3—32no—
693C22×C3—36no—
694C22×C3—63no—
695C22×C3—63no—
696C22×C3C24×D311yescharacteristic
697C22×C3C24×D311yescharacteristic
698C2×D3—23no—
699C2×D3—23no—
700C2×D3—36no—
701C2×D3—36no—
702C2×D3—66no—
703C2×D3—624no—
704C2×D3—63no—
705C2×D3—63no—
706C2×D3—63no—
707C2×D3—63no—
708C2×D3—624no—
709C2×D3—123no—
710C2×D3—123no—
711C2×D3C22×C4×D316yes—
712C2×D3C22×C4×D312yes—
713C2×D3C2×#23912yes—
714C2×D3D3×#4112yes—
715C3×C4—23no—
716C3×C4—23no—
717C3×C4—26no—
718C3×C4—22no—
719C3×C4—32no—
720C3×C4—36no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—43no—
724C3×C4—63no—
725C3×C4—63no—
726C3×C4C22×C4×D316yes—
727C3×C4C22×C4×D316yes—
728C3×C4C2×#23912yescomplemented
729C3×C4D3×#4112yescomplemented
730Dic3—23no—
731Dic3—23no—
732Dic3—32no—
733Dic3—32no—
734Dic3—32no—
735Dic3—32no—
736Dic3—62no—
737Dic3—62no—
738Dic3—63no—
739Dic3—63no—
740Dic3—123no—
741Dic3C22×C4×D316yes—
742Dic3C22×C4×D312yes—
743Dic3C2×#23912yescomplemented
744Dic3D3×#4112yescomplemented
745C32C2×C4×#4111yescharacteristic, complemented, Sylow
746C23—31no—
747C23—33no—
748C23—912no—
749C23—93no—
750C23—186no—
751C23—186no—
752Q8—312no—
753Q8C4×D3214yescomplemented
754D4—312no—
755D4—924no—
756D4—912no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—33no—
761C2×C4—312no—
762C2×C4—312no—
763C2×C4—34no—
764C2×C4—33no—
765C2×C4—33no—
766C2×C4—66no—
767C2×C4—66no—
768C2×C4—66no—
769C2×C4—912no—
770C2×C4—94no—
771C2×C4—912no—
772C2×C4—94no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—912no—
776C2×C4—93no—
777C2×C4—186no—
778C2×C4—186no—
779C2×C4—186no—
780C2×C4—186no—
781C2×C4—186no—
782C2×C4—186no—
783C2×C4—186no—
784C2×C4C22×D3213yes—
785C2×C4C22×D3213yes—
786C2×C4C22×D3211yescharacteristic
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—34no—
791C2×C3—66no—
792C2×C3C23×C4×D311yescharacteristic
793C2×C3C23×C4×D311yescharacteristic
794C2×C3C22×#23911yescharacteristic
795C2×C3C2×D3×#4111yescharacteristic
796C2×C3C2×D3×#4111yescharacteristic
797C2×C3C2×D3×#4111yescharacteristic
798D3—26no—
799D3—66no—
800D3—66no—
801D3—126no—
802D3C4×#23914yesdirect product factor
803C22—32no—
804C22—32no—
805C22—32no—
806C22—36no—
807C22—63no—
808C22—63no—
809C22—96no—
810C22—1824no—
811C22—183no—
812C22—183no—
813C22C23×D3211yescharacteristic
814C4—23no—
815C4—32no—
816C4—36no—
817C4—32no—
818C4—32no—
819C4—63no—
820C4—63no—
821C4—92no—
822C4—92no—
823C4—183no—
824C4C2×C4×D3216yes—
825C4D3×#23912yesdirect product factor
826C3—21no—
827C3C2×C4×#23911yescharacteristic, complemented
828C3C4×D3×#4111yescharacteristic, complemented
829C2—34no—
830C2—66no—
831C2—186no—
832C2C22×C4×D3211yescharacteristic
833C2C2×D3×#23911yescharacteristic
834C2D32×#4111yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC32×C4×Q8C22
socle, cosocleC22×C32C25
prime radicalC2×D3×#239C2
hypercenterC4×Q8D32
hypocenterC32C2×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#3832C2semidirect
3. C3×C4×#239C2semidirect
4. C3×C4×D3×Q8C2semidirect
5. #10595386C2semidirect
6. Dic3×#239C2semidirect
7. D3×Q8×Dic3C2semidirect
8. D3×#893C2semidirect
9. D3×#892C2semidirect
10. #10594362C2semidirect
11. #10594360C2semidirect
12. C4×D3×D12C2semidirect
13. C42×D32C2semidirect
14. C4×#3799C2semidirect
15. C4×#3796C2semidirect
21. D3×#239C4direct (N × H)
28. C32×C4×Q8C22semidirect
29. Q8×C3⋊Dic3C22semidirect
30. #64102C22semidirect
31. #64101C22semidirect
32. C4×C4⋊(C3⋊D3)C22semidirect
33. C42×C3⋊D3C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×Q8×Dic3C22semidirect
36. C3×#893C22semidirect
37. C3×#892C22semidirect
39. C3×#887C22semidirect
40. C3×C4×D12C22semidirect
42. C3×C42×D3C22semidirect
43. C3×C4×Dic6C22semidirect
45. #63904C22semidirect
46. C4×#626C22semidirect
47. #63898C22semidirect
48. #63894C22semidirect
49. #63894C22semidirect
50. Dic3×D12C22semidirect
52. C4×#624C22semidirect
53. C4×#624C22semidirect
54. C4×#624C22semidirect
55. #63881C22semidirect
56. #63880C22semidirect
57. #63878C22semidirect
61. C4×D3×Dic3C22semidirect
62. C4×D3×Dic3C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63849C22semidirect
65. #63843C22semidirect
66. Dic3×Dic6C22semidirect
67. #63841C22semidirect
68. #63836C22semidirect
85. C4×#239D3direct (N × H)
87. C4×D3×Q8D3semidirect
102. #3832C2×C4semidirect
107. C3×#239C2×C4semidirect
108. C3×D3×Q8C2×C4semidirect
127. D3×D12C2×C4semidirect
130. C4×D32C2×C4semidirect
131. #3799C2×C4semidirect
132. #3796C2×C4semidirect
186. C3×C4×Q8C2×D3semidirect
187. C3×C4×Q8C2×D3semidirect
199. Q8×Dic3C2×D3semidirect
200. Q8×Dic3C2×D3semidirect
222. #893C2×D3semidirect
231. #892C2×D3semidirect
235. #887C2×D3semidirect
248. C4×D12C2×D3semidirect
266. C42×D3C2×D3semidirect
268. C4×Dic6C2×D3semidirect
275. C32×Q8C22×C4semidirect
282. C4⋊(C3⋊D3)C22×C4semidirect
285. C4×C3⋊D3C22×C4semidirect
292. C3×D12C22×C4semidirect
297. C3×C4×D3C22×C4semidirect
298. C3×C4×D3#41semidirect
299. C3×Dic6C22×C4semidirect
300. #626C22×C4semidirect
303. #624C22×C4semidirect
308. D3×Dic3C22×C4semidirect
309. D3×Dic3#41semidirect
352. #239C4×D3direct (N × H)
353. D3×Q8C4×D3semidirect
469. C32×C4C2×#41semidirect
472. C3⋊Dic3C2×#41semidirect
477. C3×Dic3C2×#41semidirect
478. C3×Dic3C2×#41semidirect
496. C4×Q8D32semidirect
545. C3×Q8C2×C4×D3semidirect
546. C3×Q8C2×C4×D3semidirect
595. D12C2×C4×D3semidirect
621. C4×D3C2×C4×D3semidirect
622. C4×D3#239direct (N × H)
623. Dic6C2×C4×D3semidirect
629. C3×D3C4×#41semidirect
728. C3×C4C2×#239semidirect
729. C3×C4D3×#41semidirect
743. Dic3C2×#239semidirect
744. Dic3D3×#41semidirect
745. C32C2×C4×#41semidirect
753. Q8C4×D32semidirect
802. D3C4×#239direct (N × H)
825. C4D3×#239direct (N × H)
827. C3C2×C4×#239semidirect
828. C3C4×D3×#41semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C4×#38322
C3×C4×#2392
C3×C4×D3×Q82
#105953862
Dic3×#2392
D3×Q8×Dic32
D3×#8932
D3×#8922
#105943622
#105943602
C4×D3×D122
C42×D322
C4×#37992
C4×#37962
C4×D3×#413
C2×C4×#2393