Finite Group Databasebeta

← #11779728

Subgroups — #11779728

Order 1152.

830 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3#10590313C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589091C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71044—31nomaximal
9#68196—31nomaximal
10C2×D4×C3⋊D3—21no—
11C22×C4⋊(C3⋊D3)—21no—
12C32×C4×D4C2211yescharacteristic
13#64139—21no—
14#64104—21no—
15#64091—22no—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic, complemented
20C3×#810—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
22C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×C4×C3⋊C8C2211yescharacteristic, complemented
24#63575—21no—
25#63564—22no—
26#63564—21no—
27D4×D12—31no—
28D4×D12—31no—
29D4×D12—61no—
30C3×#461—31no—
31#5088—31no—
32#5087—31no—
33#5019D311yescharacteristic, complemented
34#4846—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4485—31no—
39#4485—31no—
40#4483—31no—
41#4459—31no—
42C23×C3⋊D3—22no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×#638—22no—
46D4×C3⋊D3—42no—
47D4×C3⋊D3—42no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—42no—
52C2×C4⋊(C3⋊D3)—42no—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4⋊(C3⋊D3)D412yes—
55C2×C4×C3⋊D3—21no—
56C2×C3×Dic6—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42C2311yescharacteristic
60#3752—22no—
61#3752—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C3×#214—42no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1639—91noSylow
70C2×D3×D4—62no—
71C2×D3×D4—61no—
72C2×D3×D4—61no—
73C22×D12—61no—
74C22×D12—61no—
75C22×D12—62no—
76C2×C3×SD16—61no—
77C3×C4⋊Q8—31no—
78C3×C4×D4—21no—
79C3×C4×D4C2×D311yescharacteristic
80C3×C4×D4C2×D311yescharacteristic
81C2×#214—21no—
82#930—61no—
83#930—61no—
84#930—62no—
85#895—62no—
86#895—61no—
87#895—61no—
88#882—62no—
89#882—62no—
90#882—64no—
91#874—31no—
92#874—31no—
93#874—61no—
94C4×D12—31no—
95C4×D12—31no—
96C4×D12—61no—
97#869C2×D311yescharacteristic, complemented
98C3×C4⋊C8—31no—
99C3×C4⋊C8—31no—
100C3×#103—61no—
101C3×C4×C8—31no—
102#821—62no—
103#821—61no—
104#818—61no—
105#810—21no—
106#809—61no—
107#809—62no—
108#807—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
110C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
111C4×C3⋊C8C2×D311yescharacteristic, complemented
112C23×C32—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—44no—
116C22×C3⋊D3—44no—
117C22×C3⋊D3—82no—
118C32×D4—21no—
119C32×D4D812yes—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126#638—44no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—44no—
130C4⋊(C3⋊D3)—41no—
131C4⋊(C3⋊D3)—41no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C4⋊(C3⋊D3)—42no—
135C4⋊(C3⋊D3)SD1612yescomplemented
136C4×C3⋊D3—41no—
137C4×C3⋊D3—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×C3⋊C8—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144D42—91no—
145#486—91no—
146#474—91no—
147#461—31no—
148#331—91no—
149D4⋊C8—31no—
150D4⋊C8—91no—
151C23×D3—64no—
152C23×D3—62no—
153C23×D3—62no—
154C2×C3×Q8—61no—
155C2×C3×D4—21no—
156C2×C3×D4D1211yescharacteristic
157C2×C3×D4#6711yescharacteristic
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C2×#67—64no—
162C2×#67—62no—
163C2×#67—62no—
164D3×D4—124no—
165D3×D4—122no—
166D3×D4—122no—
167D3×D4—124no—
168D3×D4—122no—
169D3×D4—122no—
170C2×D12—31no—
171C2×D12—31no—
172C2×D12—32no—
173C2×D12—32no—
174C2×D12—61no—
175C2×D12—62no—
176C2×D12—62no—
177C2×D12—62no—
178C2×D12—64no—
179C2×D12—62no—
180C2×D12—62no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—122no—
186C2×D12—122no—
187C2×D12—124no—
188C2×D12—124no—
189C2×D12—122no—
190C2×D12—122no—
191C2×C4×D3—62no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×Dic6—21no—
195C3×SD16—122no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4D1211yescharacteristic
203C3×C4⋊C4#6711yescharacteristic
204C3×C22⋊C4—22no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C42—21no—
208C3×C42C22×D311yescharacteristic
209C3×C42C22×D311yescharacteristic
210#214—42no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—62no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C22×C32—22no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32#12011yescharacteristic
229C2×C3⋊D3—22no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3—42no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—88no—
236C32×C4—21no—
237C32×C4—41no—
238C32×C4C2×D811yescharacteristic
239C32×C4C2×SD1611yescharacteristic
240C32×C4AGL(1,ℤ/8)11yescharacteristic
241C32×C4AGL(1,ℤ/8)11yescharacteristic
242C3⋊Dic3—41no—
243C3×Dic3—81no—
244C22×D4—181no—
245C22×D4—181no—
246C2×SD16—61no—
247C4⋊Q8—31no—
248#127—91no—
249#121—181no—
250#121—181no—
251#120—182no—
252C4×D4—91no—
253C4×D4D3211yescharacteristic
254#107—181no—
255C4⋊C8—31no—
256C4⋊C8—31no—
257#103—61no—
258#102—181no—
259#102—182no—
260C4×C8—31no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—21no—
264C22×D3—62no—
265C22×D3—61no—
266C22×D3—61no—
267C22×D3—64no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—128no—
271C22×D3—124no—
272C22×D3—124no—
273C22×D3—128no—
274C22×D3—124no—
275C22×D3—124no—
276C22×D3—244no—
277C22×D3—242no—
278C22×D3—242no—
279C3×Q8—121no—
280C3×Q8—121no—
281C3×D4—22no—
282C3×D4—21no—
283C3×D4—21no—
284C3×D4—22no—
285C3×D4D2412yes—
286C3×D4#21312yes—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—121no—
300C2×C3×C4C2×D1211yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—128no—
307#67—124no—
308#67—124no—
309C2×Dic3—41no—
310C2×Dic3—62no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313D12—32no—
314D12—32no—
315D12—62no—
316D12—62no—
317D12—61no—
318D12—61no—
319D12—122no—
320D12—122no—
321D12—122no—
322D12—122no—
323D12—122no—
324D12—122no—
325D12—128no—
326D12—124no—
327D12—124no—
328D12—121no—
329D12—121no—
330D12—121no—
331D12—121no—
332D12—121no—
333D12—121no—
334D12—121no—
335D12—121no—
336D12—242no—
337C4×D3—122no—
338C4×D3—122no—
339C4×D3—121no—
340C4×D3—121no—
341C4×D3—121no—
342C4×D3—121no—
343Dic6—41no—
344Dic6—41no—
345C3×C8—121no—
346C3×C8—121no—
347C3×C8—121no—
348C3⋊C8—41no—
349C3⋊C8—41no—
350C3⋊C8—41no—
351C2×C32—42no—
352C2×C32#44711yescharacteristic
353C2×C32#45011yescharacteristic
354C2×C32#45511yescharacteristic
355C3⋊D3—42no—
356C3⋊D3—82no—
357C24—182no—
358C2×Q8—61no—
359C2×D4—91no—
360C2×D4—92no—
361C2×D4—182no—
362C2×D4—182no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—362no—
366C2×D4—362no—
367C2×D4—362no—
368C2×D4—362no—
369C2×D4#62611yescharacteristic
370C22×C4—21no—
371C22×C4—181no—
372SD16—122no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—91no—
379C4⋊C4#62611yescharacteristic
380C22⋊C4—21no—
381C22⋊C4—182no—
382C22⋊C4—181no—
383C42C2×D3211yescharacteristic
384C22×C3—24no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3#88211yescharacteristic
395C22×C3#93711yescharacteristic
396C2×D3—64no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—124no—
406C2×D3—124no—
407C2×D3—124no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—2416no—
415C2×D3—248no—
416C2×D3—248no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—42no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—241no—
428C3×C4C2×D2411yescharacteristic
429C3×C4#90811yescharacteristic
430C3×C4#91111yescharacteristic
431C3×C4D3×SD1611yescharacteristic
432C3×C4D3×SD1611yescharacteristic
433C3×C4#91411yescharacteristic
434C3×C4C2×#21311yescharacteristic
435C3×C4#94911yescharacteristic
436Dic3—81no—
437Dic3—122no—
438Dic3—121no—
439Dic3—121no—
440C32#163911yescharacteristic, complemented, Sylow
441C23—21no—
442C23—181no—
443C23—182no—
444C23—364no—
445C23—364no—
446C23—722no—
447Q8—121no—
448Q8—121no—
449D4—21no—
450D4—92no—
451D4—181no—
452D4—362no—
453D4—364no—
454D4—364no—
455D4—361no—
456D4—361no—
457D4—361no—
458D4—361no—
459D4#371412yes—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—121no—
464C2×C4—181no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4C2×#62611yescharacteristic
468C2×C4#381111yescharacteristic
469C2×C4#381111yescharacteristic
470C8—121no—
471C8—121no—
472C8—121no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—44no—
477C2×C3—42no—
478C2×C3—42no—
479C2×C3#473211yescharacteristic
480C2×C3#477611yescharacteristic
481C2×C3#482511yescharacteristic
482C2×C3#503611yescharacteristic
483C2×C3#516911yescharacteristic
484C2×C3#520211yescharacteristic
485D3—124no—
486D3—122no—
487D3—122no—
488D3—244no—
489D3—242no—
490D3—242no—
491C22—22no—
492C22—41no—
493C22—41no—
494C22—182no—
495C22—361no—
496C22—361no—
497C22—362no—
498C22—362no—
499C22—362no—
500C22—728no—
501C22#6398111yescharacteristic
502C4—21no—
503C4—41no—
504C4—241no—
505C4—361no—
506C4C2×#371411yescharacteristic
507C4#6382511yescharacteristic
508C4#6393011yescharacteristic
509C4#6393711yescharacteristic
510C3—21no—
511C3#6819611yescharacteristic, complemented
512C3#7104411yescharacteristic, complemented
513C2—42no—
514C2—362no—
515C2—722no—
516C2#1059116811yescharacteristic
517C2#1059146711yescharacteristic
518C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalD4×C4⋊(C3⋊D3)C2
hypercenterC4×D4D32
hypocenterC32#1639
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5019C2semidirect
3. #10590313C2semidirect
4. #10590281C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589091C2semidirect
7. #10589082C2semidirect
19. C3×#869C22semidirect
21. C3×C4⋊(C3⋊C8)C22semidirect
22. C3×C4⋊(C3⋊C8)C22semidirect
23. C3×C4×C3⋊C8C22semidirect
33. #5019D3semidirect
37. D4⋊(C3⋊C8)D3semidirect
97. #869C2×D3semidirect
109. C4⋊(C3⋊C8)C2×D3semidirect
110. C4⋊(C3⋊C8)C2×D3semidirect
111. C4×C3⋊C8C2×D3semidirect
135. C4⋊(C3⋊D3)SD16semidirect
440. C32#1639semidirect
511. C3#68196semidirect
512. C3#71044semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
C3×#50192
#105903132
#105902812
C3×D4⋊(C3⋊C8)2
#105890912
#105890822
#710443
#681963