Finite Group Databasebeta

← D4×#3799 #11902780

Subgroups — D4×#3799 #11902780

Order 1152.

3510 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C212yesmaximal, complemented
2D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×C4×D3×D4C211yesmaximal, characteristic, complemented
4C3×D4×Dic6C211yesmaximal, characteristic, complemented
5D4×#626C212yesmaximal, complemented
6D4×#624C212yesmaximal, complemented
7#10595018C212yesmaximal, complemented
8#10595005C212yesmaximal, complemented
9#10594902C212yesmaximal, complemented
10#10594518C212yesmaximal, complemented
11#10594517C212yesmaximal, complemented
12#10594187C214yesmaximal, complemented
13#10594066C214yesmaximal, complemented
14#10593970C211yesmaximal, characteristic, complemented
15C4×#3799C211yesmaximal, characteristic, complemented
16#10593902C211yesmaximal, characteristic, complemented
17#10593869C211yesmaximal, characteristic, complemented
18D4×#239—31nomaximal
19D4×#235—31nomaximal
20C2×D4×C3⋊D3C2212yes—
21C22×C4⋊(C3⋊D3)C2212yescomplemented
22C2×C3×D3×D4C2211yescharacteristic
23C22×C3×C4×D3C2212yescomplemented
24C22×C3×Dic6C2212yescomplemented
25C22×#626C2214yescomplemented
26C22×#624C2214yescomplemented
27C2×#3799—216no—
28C2×#3799C2211yescharacteristic
29C2×#3799C2214yescomplemented
30C2×#3799C2212yescomplemented
31C2×#3799C2212yescomplemented
32C2×#3799C2214yescomplemented
33C2×#3799C2212yescomplemented
34C32×C4×D4C2211yescharacteristic
35#64139C2212yescomplemented
36#64104C2212yescomplemented
37#64091C2214yescomplemented
38#64083C2211yescharacteristic, complemented
39C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
40C3×D4×Dic3C2212yes—
41C3×D4×Dic3C2211yescharacteristic
42C3×C4×#67C2212yescomplemented
43C3×#924C2212yescomplemented
44C3×#893C2211yescharacteristic, complemented
45C3×D3×C4⋊C4C2211yescharacteristic, complemented
46C3×#888C2212yescomplemented
47C3×#67⋊C4C2212yescomplemented
48C3×D3×C22⋊C4C2212yescomplemented
49C3×#878C2214yescomplemented
50C3×C4×D12C2211yescharacteristic, complemented
51C3×C42×D3C2211yescharacteristic, complemented
52C3×#869C2211yescharacteristic, complemented
53C3×C4×Dic6C2211yescharacteristic, complemented
54#63981C2214yescomplemented
55#63978C2214yescomplemented
56#63977C2214yescomplemented
57#63974C2214yescomplemented
58#63952C2214yescomplemented
59#63952C2214yescomplemented
60#63916C2212yescomplemented
61#63911C2212yescomplemented
62#63910C2214yescomplemented
63#63910C2214yescomplemented
64#63909C2212yescomplemented
65#63909C2212yescomplemented
66#63909C2212yescomplemented
67#63907C2214yescomplemented
68#63904C2214yescomplemented
69#63904C2212yescomplemented
70C4×#626C2212yescomplemented
71#63900C2212yescomplemented
72#63897C2214yescomplemented
73#63894C2212yescomplemented
74#63894C2212yescomplemented
75#63894C2212yescomplemented
76#63894C2211yescharacteristic, complemented
77#63888C2214yescomplemented
78C4×#624C2212yescomplemented
79#63864C2212yescomplemented
80#63856C2212yescomplemented
81#63854C2214yescomplemented
82#63850C2214yescomplemented
83Dic3×Dic6C2211yescharacteristic, complemented
84#63841C2211yescharacteristic, complemented
85#63836C2212yescomplemented
86C22×#239—32no—
87C22×#235—32no—
88C3×D4×Q8—31no—
89C2×C3×C4×D4—31no—
90#5817—32no—
91D4×#67—32no—
92#5791—32no—
93#5726—32no—
94#5726—31no—
95#5725—32no—
96#5725—31no—
97#5630—32no—
98#5630—34no—
99#5627—32no—
100#5627—34no—
101#5577—31no—
102C4×#239—31no—
103#5553—31no—
104#5552—32no—
105#5551—31no—
106#5550—32no—
107D4×D12—32no—
108D4×D12—31no—
109D4×D12—31no—
110D4×D12—61no—
111#5548—32no—
112#5547—34no—
113C4×D3×D4—32no—
114C4×D3×D4—32no—
115C4×D3×D4D311yescharacteristic, complemented
116D4×Dic6D311yescharacteristic, complemented
117#5507—32no—
118#5490—34no—
119#5477—31no—
120C4×#235—31no—
121C23×C3⋊D3C2314yes—
122C23×C3×D3C2312yes—
123C2×C32×D4C2311yescharacteristic
124C22×C32×C4C2312yes—
125C2×#638C2314yes—
126D4×C3⋊D3—28no—
127C2×C4⋊(C3⋊D3)—28no—
128C2×C4⋊(C3⋊D3)C2312yes—
129C2×C4⋊(C3⋊D3)C2314yes—
130C2×C4⋊(C3⋊D3)C2312yes—
131C2×C4⋊(C3⋊D3)C2312yes—
132C2×C4⋊(C3⋊D3)C2311yescharacteristic
133C2×C4×C3⋊D3C2312yes—
134C2×C3×#67C2312yes—
135C22×C3×Dic3C2314yes—
136C22×C3×Dic3C2312yes—
137C3×D3×D4—24no—
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3—28no—
140C2×C3×C4×D3C2312yes—
141C2×C3×C4×D3C2312yes—
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×C4×D3C2312yes—
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×C4×D3C2311yescharacteristic
146C2×C3×Dic6—28no—
147C2×C3×Dic6C2314yes—
148C2×C3×Dic6C2312yes—
149C2×C3×Dic6C2311yescharacteristic
150C2×#626—216no—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yes—
154C2×#626C2314yes—
155C2×#626C2312yes—
156C2×#624—216no—
157C2×#624C2314yes—
158C2×#624C2314yes—
159C2×#624C2314yes—
160C2×#624C2312yes—
161C2×#624C2312yes—
162#3799—28no—
163#3799—28no—
164#3799—28no—
165#3799—216no—
166#3799—216no—
167#3799D418yesdirect product factor
168C32×C4⋊C4C2311yescharacteristic
169C32×C22⋊C4C2312yes—
170C32×C42C2311yescharacteristic
171#3752C2312yes—
172#3752C2314yes—
173C4⋊(C3⋊Dic3)C2311yescharacteristic
174C3×#217C2314yes—
175C3×#217C2312yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×C4⋊Dic3C2312yes—
179C3×C4⋊Dic3C2312yes—
180C3×C4⋊Dic3C2311yescharacteristic
181C3×C4⋊Dic3C2311yescharacteristic
182C3×Dic3⋊C4C2312yes—
183C3×Dic3⋊C4C2314yes—
184C3×Dic3⋊C4C2312yes—
185C3×C4×Dic3C2311yescharacteristic
186C3×C4×Dic3C2312yes—
187C3×C4×Dic3C2311yescharacteristic
188C3×C4×Dic3C2311yescharacteristic
189#3724C2314yes—
190Dic3⋊Dic3C2312yes—
191#3722C2312yes—
192#3722C2314yes—
193#3722C2314yes—
194#3722C2314yes—
195(C2×D3)⋊Dic3C2312yes—
196(C2×D3)⋊Dic3C2314yes—
197Dic32C2312yes—
198Dic32C2312yes—
199D4×#41—91noSylow
200C22×C3×Q8—32no—
201C22×C3×D4—31no—
202C23×C3×C4—32no—
203C22×#67—34no—
204C2×#239—31no—
205C2×#239—34no—
206C2×#239—32no—
207C2×#239—34no—
208C2×#239—32no—
209C2×#239—32no—
210C2×#239—616no—
211C2×D3×D4—32no—
212C2×D3×D4—32no—
213C2×D3×D4—62no—
214C2×D3×D4C2×D311yescharacteristic
215C2×#235—31no—
216C2×#235—32no—
217C2×#235—34no—
218C2×#235—34no—
219C2×#235—32no—
220C2×#235—32no—
221C2×#235—616no—
222C22×D12—34no—
223C22×D12—32no—
224C22×D12—32no—
225C22×D12—62no—
226C22×C4×D3—34no—
227C22×C4×D3—34no—
228C22×C4×D3C2×D312yescomplemented
229C22×Dic6C2×D312yescomplemented
230C3×C4⋊Q8—32no—
231C3×C4⋊Q8—31no—
232C3×C22⋊Q8—32no—
233C3×C22⋊Q8—34no—
234C3×C4×Q8—31no—
235C3×C4×D4—21no—
236C3×C4×D4—31no—
237C3×C4×D4—32no—
238C3×C4×D4—32no—
239C3×C4×D4—31no—
240C3×C4×D4—32no—
241C3×C4×D4—31no—
242C3×C4×D4C2×D311yescharacteristic
243C3×C4×D4C2×D311yescharacteristic
244C2×C3×C4⋊C4—31no—
245C2×C3×C22⋊C4—32no—
246C2×C3×C42—31no—
247#953—34no—
248#947—34no—
249#947—32no—
250#946—32no—
251#946—34no—
252Q8×Dic3—31no—
253#940—32no—
254#939—34no—
255#938—32no—
256#937—34no—
257D4×Dic3C2×D312yes—
258D4×Dic3C2×D311yescharacteristic
259#930—32no—
260#930—32no—
261#930—34no—
262#930—32no—
263#930—32no—
264#930—32no—
265#930—62no—
266#929—34no—
267C4×#67—34no—
268C4×#67—34no—
269C4×#67—32no—
270C4×#67—34no—
271C4×#67—32no—
272C4×#67C2×D312yescomplemented
273#926—31no—
274#924—32no—
275#924C2×D312yescomplemented
276#896—34no—
277#895—32no—
278#895—32no—
279#895—32no—
280#895—32no—
281#895—32no—
282#895—32no—
283#895—34no—
284#895—34no—
285#895—62no—
286#894—34no—
287#894—34no—
288#894—34no—
289#894—34no—
290#893—34no—
291#893—32no—
292#893—32no—
293#893—32no—
294#893—32no—
295#893—31no—
296#893C2×D311yescharacteristic, complemented
297#892—31no—
298#892—32no—
299D3×C4⋊C4—32no—
300D3×C4⋊C4—32no—
301D3×C4⋊C4C2×D311yescharacteristic, complemented
302#888C2×D312yescomplemented
303#885—34no—
304#884—34no—
305#884—34no—
306#883—34no—
307#882—34no—
308#882—34no—
309#882—34no—
310#882—34no—
311#882—64no—
312#67⋊C4—34no—
313#67⋊C4—34no—
314#67⋊C4C2×D312yescomplemented
315D3×C22⋊C4—34no—
316D3×C22⋊C4—34no—
317D3×C22⋊C4C2×D312yescomplemented
318#878C2×D314yescomplemented
319#875—32no—
320#874—32no—
321#874—31no—
322#874—31no—
323#874—61no—
324C4×D12—32no—
325C4×D12—31no—
326C4×D12—31no—
327C4×D12—32no—
328C4×D12—31no—
329C4×D12—32no—
330C4×D12—32no—
331C4×D12—61no—
332C4×D12C2×D311yescharacteristic, complemented
333#872—32no—
334C42×D3—32no—
335C42×D3—32no—
336C42×D3C2×D311yescharacteristic, complemented
337#869C2×D311yescharacteristic, complemented
338C4×Dic6—31no—
339C4×Dic6C2×D311yescharacteristic, complemented
340C23×C32C2412yes—
341C22×C3⋊D3—28no—
342C22×C3⋊D3—28no—
343C22×C3⋊D3—44no—
344C22×C3⋊D3C2414yes—
345C22×C3⋊D3C2412yes—
346C22×C3×D3—24no—
347C22×C3×D3—24no—
348C22×C3×D3—42no—
349C22×C3×D3C2412yes—
350C22×C3×D3C2411yescharacteristic
351C32×D4#4114yescomplemented
352C2×C32×C4—24no—
353C2×C32×C4C2411yescharacteristic
354C2×C32×C4C2412yes—
355C2×C32×C4C2411yescharacteristic
356C2×C32×C4C2411yescharacteristic
357#638—28no—
358C2×C3⋊Dic3C2412yes—
359C4⋊(C3⋊D3)—28no—
360C4⋊(C3⋊D3)—24no—
361C4⋊(C3⋊D3)—24no—
362C4⋊(C3⋊D3)—42no—
363C4⋊(C3⋊D3)C2×D414yescomplemented
364C4×C3⋊D3—24no—
365C3×#67—24no—
366C2×C3×Dic3—24no—
367C2×C3×Dic3—28no—
368C2×C3×Dic3C2411yescharacteristic
369C2×C3×Dic3C2412yes—
370C2×C3×Dic3C2414yes—
371C2×C3×Dic3C2411yescharacteristic
372C2×C3×Dic3C2412yes—
373C2×C3×Dic3C2411yescharacteristic
374C2×C3×Dic3C2412yes—
375C3×D12—22no—
376C3×C4×D3—24no—
377C3×C4×D3—24no—
378C3×C4×D3—22no—
379C3×C4×D3—24no—
380C3×C4×D3—41no—
381C3×C4×D3C2×D414yescomplemented
382C3×Dic6—24no—
383C3×Dic6—28no—
384C3×Dic6C2×D414yescomplemented
385#626—28no—
386#626—28no—
387#626—28no—
388#626—44no—
389#626C2×D418yescomplemented
390#624—28no—
391#624—28no—
392#624—28no—
393#624—42no—
394#624C2×D418yescomplemented
395C22×#41—92no—
396#550—91no—
397D4×Q8—31no—
398#548—92no—
399#547—92no—
400#547—91no—
401#546—94no—
402#546—92no—
403D42—92no—
404D42—91no—
405#532—91no—
406#532—92no—
407#525—94no—
408#525—92no—
409C4×#41—91no—
410C2×C4×D4—31no—
411C2×C4×D4—92no—
412C24×C3—32no—
413C23×D3—34no—
414C23×D3—34no—
415C23×D3—64no—
416C23×D3C22×D312yes—
417C2×C3×Q8—31no—
418C2×C3×Q8—34no—
419C2×C3×Q8—32no—
420C2×C3×Q8—68no—
421C2×C3×D4—21no—
422C2×C3×D4—32no—
423C2×C3×D4—31no—
424C2×C3×D4—64no—
425C2×C3×D4C22×D311yescharacteristic
426C2×C3×D4C22×D311yescharacteristic
427C22×C3×C4—22no—
428C22×C3×C4—31no—
429C22×C3×C4—32no—
430C22×C3×C4—34no—
431C22×C3×C4—32no—
432C22×C3×C4—31no—
433C22×C3×C4—32no—
434C22×C3×C4—32no—
435C22×C3×C4—31no—
436C22×C3×C4—68no—
437C22×C3×C4C22×D312yes—
438C22×C3×C4C22×D312yes—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—32no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—64no—
447C2×#67—616no—
448C2×#67C22×D312yes—
449C22×Dic3C22×D314yes—
450C22×Dic3C22×D312yes—
451#239—38no—
452#239—616no—
453#239—616no—
454#239—68no—
455#239—68no—
456#239—68no—
457D3×D4—24no—
458D3×D4—68no—
459D3×D4—68no—
460D3×D4—128no—
461#235—38no—
462#235—616no—
463#235—68no—
464#235—616no—
465#235—68no—
466#235—68no—
467C2×D12—32no—
468C2×D12—31no—
469C2×D12—31no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—32no—
474C2×D12—32no—
475C2×D12—32no—
476C2×D12—32no—
477C2×D12—34no—
478C2×D12—34no—
479C2×D12—34no—
480C2×D12—32no—
481C2×D12—32no—
482C2×D12—61no—
483C2×D12—62no—
484C2×D12—62no—
485C2×D12—64no—
486C2×D12—62no—
487C2×D12—68no—
488C2×D12—68no—
489C2×D12—616no—
490C2×D12—128no—
491C2×D12C22×D311yescharacteristic
492C2×C4×D3—28no—
493C2×C4×D3—32no—
494C2×C4×D3—32no—
495C2×C4×D3—32no—
496C2×C4×D3—32no—
497C2×C4×D3—34no—
498C2×C4×D3—34no—
499C2×C4×D3—34no—
500C2×C4×D3—34no—
501C2×C4×D3—34no—
502C2×C4×D3—34no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—62no—
506C2×C4×D3—616no—
507C2×C4×D3—616no—
508C2×C4×D3C22×D311yescharacteristic
509C2×C4×D3C22×D312yes—
510C2×C4×D3C22×D312yes—
511C2×C4×D3C22×D312yes—
512C2×C4×D3C22×D311yescharacteristic
513C2×C4×D3C22×D311yescharacteristic
514C2×Dic6—28no—
515C2×Dic6C22×D312yes—
516C2×Dic6C22×D314yes—
517C2×Dic6C22×D311yescharacteristic
518C3×C4⋊C4—21no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4—32no—
521C3×C4⋊C4—32no—
522C3×C4⋊C4—31no—
523C3×C4⋊C4—34no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4C22×D311yescharacteristic
527C3×C4⋊C4C22×D311yescharacteristic
528C3×C22⋊C4—22no—
529C3×C22⋊C4—32no—
530C3×C22⋊C4—34no—
531C3×C22⋊C4—32no—
532C3×C22⋊C4—32no—
533C3×C22⋊C4C22×D312yes—
534C3×C22⋊C4C22×D312yes—
535C3×C42—21no—
536C3×C42—31no—
537C3×C42—31no—
538C3×C42—32no—
539C3×C42—31no—
540C3×C42C22×D311yescharacteristic
541C3×C42C22×D311yescharacteristic
542#217—34no—
543#217—32no—
544#217C22×D314yes—
545#217C22×D312yes—
546(C2×D3)⋊C4—32no—
547(C2×D3)⋊C4—34no—
548(C2×D3)⋊C4—32no—
549(C2×D3)⋊C4—32no—
550(C2×D3)⋊C4—34no—
551(C2×D3)⋊C4—34no—
552(C2×D3)⋊C4—32no—
553(C2×D3)⋊C4—34no—
554(C2×D3)⋊C4—34no—
555(C2×D3)⋊C4—34no—
556(C2×D3)⋊C4—32no—
557(C2×D3)⋊C4—34no—
558(C2×D3)⋊C4—34no—
559(C2×D3)⋊C4—34no—
560(C2×D3)⋊C4—62no—
561(C2×D3)⋊C4—64no—
562(C2×D3)⋊C4C22×D312yes—
563(C2×D3)⋊C4C22×D312yes—
564C4⋊Dic3—31no—
565C4⋊Dic3—31no—
566C4⋊Dic3—32no—
567C4⋊Dic3—61no—
568C4⋊Dic3C22×D311yescharacteristic
569C4⋊Dic3C22×D312yes—
570C4⋊Dic3C22×D312yes—
571C4⋊Dic3C22×D311yescharacteristic
572Dic3⋊C4—32no—
573Dic3⋊C4—34no—
574Dic3⋊C4—34no—
575Dic3⋊C4C22×D312yes—
576Dic3⋊C4C22×D314yes—
577Dic3⋊C4C22×D312yes—
578C4×Dic3—32no—
579C4×Dic3—32no—
580C4×Dic3—32no—
581C4×Dic3—32no—
582C4×Dic3C22×D312yes—
583C4×Dic3C22×D311yescharacteristic
584C4×Dic3C22×D311yescharacteristic
585C4×Dic3C22×D311yescharacteristic
586C22×C32—22no—
587C22×C32—22no—
588C22×C32C2×#4114yescomplemented
589C22×C32C2511yescharacteristic
590C2×C3⋊D3—22no—
591C2×C3⋊D3—22no—
592C2×C3⋊D3—24no—
593C2×C3⋊D3—24no—
594C2×C3⋊D3—24no—
595C2×C3⋊D3—416no—
596C2×C3⋊D3C22×D414yes—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—22no—
600C2×C3×D3—22no—
601C2×C3×D3—22no—
602C2×C3×D3—48no—
603C2×C3×D3C22×D412yes—
604C32×C4—22no—
605C32×C4—21no—
606C32×C4C22×D412yes—
607C32×C4C2×#4112yescomplemented
608C3⋊Dic3—22no—
609C3×Dic3—22no—
610C3×Dic3—24no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—22no—
614C3×Dic3C22×D412yes—
615C3×Dic3C22×D414yes—
616C2×#41—91no—
617C2×#41—92no—
618C2×#41—94no—
619C2×#41—94no—
620C2×#41—92no—
621C2×#41—92no—
622C2×#41—1816no—
623C22×Q8—32no—
624C22×D4—31no—
625C22×D4—94no—
626C22×D4—92no—
627C22×D4—92no—
628C23×C4—32no—
629C23×C4—94no—
630C4⋊Q8—32no—
631C4⋊Q8—31no—
632#127—92no—
633#127—91no—
634#124—92no—
635#124—94no—
636#123—94no—
637#123—94no—
638#123—94no—
639C22⋊Q8—32no—
640C22⋊Q8—34no—
641C22⋊Q8—94no—
642C22⋊Q8—92no—
643#121—94no—
644#121—94no—
645#121—92no—
646#121—92no—
647#121—92no—
648#121—92no—
649#121—94no—
650#121—92no—
651#121—92no—
652#120—94no—
653#120—94no—
654#120—94no—
655C4×Q8—31no—
656C4×Q8—91no—
657C4×D4—31no—
658C4×D4—32no—
659C4×D4—32no—
660C4×D4—31no—
661C4×D4—32no—
662C4×D4—31no—
663C4×D4—92no—
664C4×D4—92no—
665C4×D4—91no—
666C4×D4—92no—
667C4×D4—92no—
668C4×D4—94no—
669C4×D4—94no—
670C4×D4—92no—
671C4×D4—94no—
672C4×D4—91no—
673C4×D4D3211yescharacteristic
674#117—92no—
675#117—91no—
676C2×C4⋊C4—31no—
677C2×C4⋊C4—92no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—94no—
680C2×C42—31no—
681C2×C42—92no—
682C23×C3—22no—
683C23×C3—31no—
684C23×C3—32no—
685C23×C3—64no—
686C23×C3—64no—
687C23×C3—122no—
688C23×C3C23×D312yes—
689C23×C3C23×D312yes—
690C22×D3—24no—
691C22×D3—24no—
692C22×D3—32no—
693C22×D3—32no—
694C22×D3—34no—
695C22×D3—34no—
696C22×D3—42no—
697C22×D3—62no—
698C22×D3—64no—
699C22×D3—68no—
700C22×D3—68no—
701C22×D3—68no—
702C22×D3—68no—
703C22×D3—128no—
704C22×D3—128no—
705C22×D3—124no—
706C22×D3—124no—
707C22×D3—244no—
708C22×D3C23×D312yes—
709C22×D3C23×D311yescharacteristic
710C3×Q8—34no—
711C3×Q8—68no—
712C3×Q8—64no—
713C3×D4—24no—
714C3×D4—64no—
715C3×D4—62no—
716C3×D4#23514yescomplemented
717C3×D4#23914yescomplemented
718C2×C3×C4—24no—
719C2×C3×C4—24no—
720C2×C3×C4—21no—
721C2×C3×C4—21no—
722C2×C3×C4—21no—
723C2×C3×C4—22no—
724C2×C3×C4—31no—
725C2×C3×C4—32no—
726C2×C3×C4—34no—
727C2×C3×C4—31no—
728C2×C3×C4—32no—
729C2×C3×C4—31no—
730C2×C3×C4—32no—
731C2×C3×C4—34no—
732C2×C3×C4—44no—
733C2×C3×C4—64no—
734C2×C3×C4—64no—
735C2×C3×C4—64no—
736C2×C3×C4—68no—
737C2×C3×C4—64no—
738C2×C3×C4—62no—
739C2×C3×C4—121no—
740C2×C3×C4C23×D311yescharacteristic
741C2×C3×C4C23×D311yescharacteristic
742C2×C3×C4C23×D312yes—
743C2×C3×C4C23×D312yes—
744C2×C3×C4C23×D311yescharacteristic
745C2×C3×C4C23×D311yescharacteristic
746C2×C3×C4C23×D311yescharacteristic
747C2×C3×C4C23×D311yescharacteristic
748#67—24no—
749#67—38no—
750#67—68no—
751#67—68no—
752#67—68no—
753#67—68no—
754#67—68no—
755#67—128no—
756#67—124no—
757C2×Dic3—28no—
758C2×Dic3—24no—
759C2×Dic3—32no—
760C2×Dic3—32no—
761C2×Dic3—62no—
762C2×Dic3C23×D311yescharacteristic
763C2×Dic3C23×D312yes—
764C2×Dic3C23×D311yescharacteristic
765C2×Dic3C23×D312yes—
766C2×Dic3C23×D314yes—
767C2×Dic3C23×D311yescharacteristic
768C2×Dic3C23×D312yes—
769D12—22no—
770D12—38no—
771D12—34no—
772D12—34no—
773D12—64no—
774D12—68no—
775D12—68no—
776D12—68no—
777D12—68no—
778D12—68no—
779D12—64no—
780D12—64no—
781D12—64no—
782D12—64no—
783D12—124no—
784D12—124no—
785D12—128no—
786D12—122no—
787D12—122no—
788D12—124no—
789D12—242no—
790C4×D3—24no—
791C4×D3—22no—
792C4×D3—24no—
793C4×D3—24no—
794C4×D3—38no—
795C4×D3—38no—
796C4×D3—41no—
797C4×D3—68no—
798C4×D3—68no—
799C4×D3—68no—
800C4×D3—68no—
801C4×D3—64no—
802C4×D3—64no—
803C4×D3—68no—
804C4×D3—68no—
805C4×D3—124no—
806C4×D3—122no—
807C4×D3—122no—
808C4×D3D3×D414yescomplemented
809Dic6—24no—
810Dic6—28no—
811Dic6D3×D414yescomplemented
812C2×C32—24no—
813C2×C32C23×D411yescharacteristic
814C2×C32C22×#4111yescharacteristic
815C2×C32#58511yescharacteristic
816C3⋊D3—24no—
817C3⋊D3—44no—
818C3×D3—22no—
819C3×D3—42no—
820C24—32no—
821C24—94no—
822#41—98no—
823#41—188no—
824#41—1816no—
825#41—1816no—
826#41—188no—
827#41—188no—
828C2×Q8—31no—
829C2×Q8—34no—
830C2×Q8—32no—
831C2×Q8—68no—
832C2×D4—32no—
833C2×D4—31no—
834C2×D4—64no—
835C2×D4—92no—
836C2×D4—94no—
837C2×D4—94no—
838C2×D4—94no—
839C2×D4—94no—
840C2×D4—94no—
841C2×D4—91no—
842C2×D4—92no—
843C2×D4—94no—
844C2×D4—92no—
845C2×D4—92no—
846C2×D4—188no—
847C2×D4—1816no—
848C2×D4—188no—
849C2×D4C2×D3211yescharacteristic
850C22×C4—31no—
851C22×C4—32no—
852C22×C4—34no—
853C22×C4—31no—
854C22×C4—32no—
855C22×C4—32no—
856C22×C4—32no—
857C22×C4—31no—
858C22×C4—68no—
859C22×C4—92no—
860C22×C4—94no—
861C22×C4—94no—
862C22×C4—94no—
863C22×C4—92no—
864C22×C4—92no—
865C22×C4—1816no—
866C22×C4C2×D3212yes—
867C4⋊C4—31no—
868C4⋊C4—32no—
869C4⋊C4—32no—
870C4⋊C4—32no—
871C4⋊C4—31no—
872C4⋊C4—34no—
873C4⋊C4—32no—
874C4⋊C4—94no—
875C4⋊C4—92no—
876C4⋊C4—91no—
877C4⋊C4C2×D3211yescharacteristic
878C22⋊C4—32no—
879C22⋊C4—34no—
880C22⋊C4—32no—
881C22⋊C4—32no—
882C22⋊C4—94no—
883C22⋊C4—94no—
884C22⋊C4—92no—
885C22⋊C4—94no—
886C22⋊C4—92no—
887C22⋊C4—94no—
888C22⋊C4—92no—
889C22⋊C4—94no—
890C22⋊C4C2×D3212yes—
891C42—31no—
892C42—31no—
893C42—31no—
894C42—32no—
895C42—92no—
896C42—92no—
897C42C2×D3211yescharacteristic
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—24no—
903C22×C3—21no—
904C22×C3—32no—
905C22×C3—42no—
906C22×C3—42no—
907C22×C3—61no—
908C22×C3—61no—
909C22×C3—62no—
910C22×C3—62no—
911C22×C3—62no—
912C22×C3—128no—
913C22×C3C2×#23514yescomplemented
914C22×C3C2×#23914yescomplemented
915C22×C3C24×D311yescharacteristic
916C22×C3C24×D311yescharacteristic
917C2×D3—21no—
918C2×D3—21no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—34no—
923C2×D3—34no—
924C2×D3—48no—
925C2×D3—64no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—64no—
931C2×D3—64no—
932C2×D3—64no—
933C2×D3—64no—
934C2×D3—64no—
935C2×D3—64no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—124no—
939C2×D3—124no—
940C2×D3—124no—
941C2×D3—1216no—
942C2×D3—1216no—
943C2×D3—2416no—
944C2×D3C2×D3×D412yes—
945C3×C4—22no—
946C3×C4—22no—
947C3×C4—21no—
948C3×C4—21no—
949C3×C4—22no—
950C3×C4—22no—
951C3×C4—32no—
952C3×C4—34no—
953C3×C4—42no—
954C3×C4—41no—
955C3×C4—62no—
956C3×C4—64no—
957C3×C4—61no—
958C3×C4—62no—
959C3×C4—61no—
960C3×C4C2×#23512yescomplemented
961C3×C4C2×D3×D412yes—
962C3×C4C2×D3×D412yes—
963C3×C4C2×#23912yescomplemented
964Dic3—21no—
965Dic3—24no—
966Dic3—22no—
967Dic3—21no—
968Dic3—22no—
969Dic3—62no—
970Dic3—62no—
971Dic3—122no—
972Dic3C2×D3×D414yes—
973Dic3C2×D3×D412yes—
974C32D4×#4111yescharacteristic, complemented, Sylow
975C23—31no—
976C23—32no—
977C23—64no—
978C23—64no—
979C23—92no—
980C23—94no—
981C23—122no—
982C23—188no—
983C23—188no—
984C23—364no—
985C23C22×D3212yes—
986Q8—34no—
987Q8—68no—
988Q8—64no—
989D4—64no—
990D4—62no—
991D4—98no—
992D4—94no—
993D4—188no—
994D4—188no—
995D4—188no—
996D4—188no—
997D4—188no—
998D4—184no—
999D4—184no—
1000D4—362no—
1001D4—364no—
1002D4#379914yesdirect product factor
1003C2×C4—24no—
1004C2×C4—31no—
1005C2×C4—32no—
1006C2×C4—34no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—34no—
1012C2×C4—64no—
1013C2×C4—64no—
1014C2×C4—64no—
1015C2×C4—68no—
1016C2×C4—62no—
1017C2×C4—64no—
1018C2×C4—98no—
1019C2×C4—92no—
1020C2×C4—121no—
1021C2×C4—188no—
1022C2×C4—188no—
1023C2×C4—188no—
1024C2×C4—184no—
1025C2×C4—362no—
1026C2×C4C22×D3211yescharacteristic
1027C2×C4C22×D3212yes—
1028C2×C4C22×D3211yescharacteristic
1029C2×C4C22×D3211yescharacteristic
1030C2×C3—24no—
1031C2×C3—24no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—44no—
1036C2×C3—62no—
1037C2×C3—122no—
1038C2×C3C22×#23511yescharacteristic
1039C2×C3C22×D3×D411yescharacteristic
1040C2×C3C22×D3×D411yescharacteristic
1041C2×C3C22×#23911yescharacteristic
1042C2×C3#596411yescharacteristic
1043C2×C3#596811yescharacteristic
1044D3—22no—
1045D3—42no—
1046D3—64no—
1047D3—64no—
1048D3—124no—
1049D3—124no—
1050D3—124no—
1051D3—244no—
1052C22—22no—
1053C22—22no—
1054C22—32no—
1055C22—61no—
1056C22—61no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—94no—
1061C22—128no—
1062C22—182no—
1063C22—182no—
1064C22—184no—
1065C22—184no—
1066C22—184no—
1067C22—3616no—
1068C22C2×#379914yescomplemented
1069C22C23×D3211yescharacteristic
1070C4—22no—
1071C4—21no—
1072C4—32no—
1073C4—34no—
1074C4—61no—
1075C4—62no—
1076C4—64no—
1077C4—61no—
1078C4—62no—
1079C4—182no—
1080C4C2×#379912yescomplemented
1081C4D32×D412yes—
1082C3—21no—
1083C3D4×#23511yescharacteristic, complemented
1084C3D4×#23911yescharacteristic, complemented
1085C2—24no—
1086C2—62no—
1087C2—122no—
1088C2—184no—
1089C2—364no—
1090C2C22×#379911yescharacteristic
1091C2C2×D32×D411yescharacteristic
1092C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. D4×C4⋊(C3⋊D3)C2semidirect
3. C3×C4×D3×D4C2semidirect
4. C3×D4×Dic6C2semidirect
5. D4×#626C2semidirect
6. D4×#624C2semidirect
7. #10595018C2semidirect
8. #10595005C2semidirect
9. #10594902C2semidirect
10. #10594518C2semidirect
11. #10594517C2semidirect
12. #10594187C2semidirect
13. #10594066C2semidirect
14. #10593970C2semidirect
15. C4×#3799C2semidirect
16. #10593902C2semidirect
17. #10593869C2semidirect
21. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×C3×Dic6C22semidirect
25. C22×#626C22semidirect
26. C22×#624C22semidirect
29. C2×#3799C22semidirect
30. C2×#3799C22semidirect
31. C2×#3799C22semidirect
32. C2×#3799C22semidirect
33. C2×#3799C22semidirect
35. #64139C22semidirect
36. #64104C22semidirect
37. #64091C22semidirect
38. #64083C22semidirect
39. C4×C4⋊(C3⋊D3)C22semidirect
42. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. C3×#893C22semidirect
45. C3×D3×C4⋊C4C22semidirect
46. C3×#888C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×D3×C22⋊C4C22semidirect
49. C3×#878C22semidirect
50. C3×C4×D12C22semidirect
51. C3×C42×D3C22semidirect
52. C3×#869C22semidirect
53. C3×C4×Dic6C22semidirect
54. #63981C22semidirect
55. #63978C22semidirect
56. #63977C22semidirect
57. #63974C22semidirect
58. #63952C22semidirect
59. #63952C22semidirect
60. #63916C22semidirect
61. #63911C22semidirect
62. #63910C22semidirect
63. #63910C22semidirect
64. #63909C22semidirect
65. #63909C22semidirect
66. #63909C22semidirect
67. #63907C22semidirect
68. #63904C22semidirect
69. #63904C22semidirect
70. C4×#626C22semidirect
71. #63900C22semidirect
72. #63897C22semidirect
73. #63894C22semidirect
74. #63894C22semidirect
75. #63894C22semidirect
76. #63894C22semidirect
77. #63888C22semidirect
78. C4×#624C22semidirect
79. #63864C22semidirect
80. #63856C22semidirect
81. #63854C22semidirect
82. #63850C22semidirect
83. Dic3×Dic6C22semidirect
84. #63841C22semidirect
85. #63836C22semidirect
115. C4×D3×D4D3semidirect
116. D4×Dic6D3semidirect
167. #3799D4direct (N × H)
228. C22×C4×D3C2×D3semidirect
229. C22×Dic6C2×D3semidirect
272. C4×#67C2×D3semidirect
275. #924C2×D3semidirect
296. #893C2×D3semidirect
301. D3×C4⋊C4C2×D3semidirect
302. #888C2×D3semidirect
314. #67⋊C4C2×D3semidirect
317. D3×C22⋊C4C2×D3semidirect
318. #878C2×D3semidirect
332. C4×D12C2×D3semidirect
336. C42×D3C2×D3semidirect
337. #869C2×D3semidirect
339. C4×Dic6C2×D3semidirect
351. C32×D4#41semidirect
363. C4⋊(C3⋊D3)C2×D4semidirect
381. C3×C4×D3C2×D4semidirect
384. C3×Dic6C2×D4semidirect
389. #626C2×D4semidirect
394. #624C2×D4semidirect
588. C22×C32C2×#41semidirect
607. C32×C4C2×#41semidirect
716. C3×D4#235semidirect
717. C3×D4#239semidirect
808. C4×D3D3×D4semidirect
811. Dic6D3×D4semidirect
913. C22×C3C2×#235semidirect
914. C22×C3C2×#239semidirect
960. C3×C4C2×#235semidirect
963. C3×C4C2×#239semidirect
974. C32D4×#41semidirect
1002. D4#3799direct (N × H)
1068. C22C2×#3799semidirect
1080. C4C2×#3799semidirect
1083. C3D4×#235semidirect
1084. C3D4×#239semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
D4×C4⋊(C3⋊D3)2
C3×C4×D3×D42
C3×D4×Dic62
D4×#6262
D4×#6242
#105950182
#105950052
#105949022
#105945182
#105945172
#105941872
#105940662
#105939702
C4×#37992
#105939022
#105938692
D4×#2393
D4×#2353