Finite Group Databasebeta

← #11779222

Subgroups — #11779222

Order 1152.

564 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2#10592726C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590281C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71914—31nomaximal
9#68266—31nomaximal
10C2×C3×D3×Q8—21no—
11C32×C4×Q8C2211yescharacteristic
12C2×#3755—21no—
13#64083C2211yescharacteristic
14C3×#897—21no—
15C3×#897—22no—
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#869—21no—
19C3×#869C2211yescharacteristic
20C2×#3714—21no—
21#63636—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27C3×D4×Q8—31no—
28Q8×D12D311yescharacteristic, complemented
29#5088—31no—
30#5027—31no—
31#5027—31no—
32#5027—61no—
33#5015—31no—
34#4843—31no—
35#4694—31no—
36C3×Q8⋊C8—31no—
37#4547—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4486—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C3×D3×Q8—42no—
47C3×D3×Q8—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—22no—
52C2×C3×Dic6—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C42—21no—
56C32×C42C2311yescharacteristic
57#3755—42no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D412yes—
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3714—42no—
68#1627—91noSylow
69C22×C3×Q8—61no—
70C2×D3×Q8—21no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—61no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—61no—
75C3×C4×Q8—21no—
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×Q8C2×D311yescharacteristic
78C3×C4×D4—31no—
79C3×C4×D4—61no—
80C2×#215—62no—
81C2×#215—61no—
82C2×#215—61no—
83C2×#213—61no—
84C2×D24—61no—
85#897—21no—
86#897—22no—
87#874—31no—
88#874—31no—
89#874—61no—
90C4×D12—21no—
91C4×D12C2×D311yescharacteristic
92#869—21no—
93#869C2×D311yescharacteristic
94C3×C4⋊C8—31no—
95C3×C4×C8—31no—
96#821—62no—
97#821—61no—
98#809—61no—
99#809—62no—
100#809—62no—
101#809—61no—
102#809—61no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊D3—41no—
109C22×C3×D3—21no—
110C32×Q8—21no—
111C32×Q8D812yescomplemented
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—42no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C3×D12—21no—
125C3×D12SD1612yescomplemented
126C3×C4×D3—44no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129C3×Dic6—44no—
130C3×Dic6—41no—
131C3×Dic6—41no—
132C3⋊(C3⋊C8)—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8—41no—
135D4×Q8—31no—
136#486—91no—
137#460—91no—
138#459—91no—
139#332—91no—
140Q8⋊C8—31no—
141D4⋊C8—91no—
142C2×C3×Q8—21no—
143C2×C3×Q8—62no—
144C2×C3×Q8—61no—
145C2×C3×Q8—122no—
146C2×C3×Q8—122no—
147C2×C3×Q8D1211yescharacteristic
148C2×C3×Q8#6711yescharacteristic
149C2×C3×D4—31no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152D3×Q8—42no—
153D3×Q8—42no—
154C2×D12—62no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—121no—
162C2×D12—121no—
163C2×D12#6711yescharacteristic
164C2×C4×D3—22no—
165C2×C4×D3—21no—
166C2×Dic6—22no—
167C2×Dic6—21no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4D1211yescharacteristic
179C3×C4⋊C4#6711yescharacteristic
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42—21no—
184C3×C42—21no—
185C3×C42—41no—
186C3×C42C22×D311yescharacteristic
187C3×C42C22×D311yescharacteristic
188#215—124no—
189#215—122no—
190#215—122no—
191#213—122no—
192(C2×D3)⋊C4—22no—
193(C2×D3)⋊C4—21no—
194C4⋊Dic3—22no—
195C4⋊Dic3—21no—
196C4⋊Dic3#6711yescharacteristic
197C4⋊Dic3#6712yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203D24—122no—
204C22×C32#12011yescharacteristic
205C2×C3⋊D3—81no—
206C2×C3⋊D3—81no—
207C2×C3⋊D3—81no—
208C2×C3×D3—22no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C32×C4—22no—
212C32×C4—21no—
213C32×C4—41no—
214C32×C4C2×D811yescharacteristic
215C32×C4C2×SD1611yescharacteristic
216C32×C4AGL(1,ℤ/8)11yescharacteristic
217C32×C4#13711yescharacteristic
218C3×Dic3—41no—
219C3×Dic3—42no—
220C22×Q8—61no—
221C2×SD16—181no—
222C2×D8—181no—
223C4⋊Q8—31no—
224C4⋊Q8—61no—
225#127—91no—
226C22⋊Q8—62no—
227C22⋊Q8—61no—
228C4×Q8D3211yescharacteristic
229C4×D4—31no—
230C4×D4—61no—
231C4⋊C8—31no—
232C4⋊C8—91no—
233#102—181no—
234#102—182no—
235#102—181no—
236C4×C8—31no—
237C23×C3—61no—
238C22×D3—21no—
239C22×D3—122no—
240C22×D3—121no—
241C22×D3—121no—
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—22no—
245C3×Q8—41no—
246C3×Q8—124no—
247C3×Q8—121no—
248C3×Q8—121no—
249C3×Q8D2412yescomplemented
250C3×Q8#21312yescomplemented
251C3×D4—32no—
252C3×D4—61no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—62no—
263C2×C3×C4—61no—
264C2×C3×C4—124no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×Dic3—21no—
274C2×Dic3—22no—
275D12—21no—
276D12—122no—
277D12—122no—
278D12—122no—
279D12—122no—
280D12—121no—
281D12—121no—
282D12—121no—
283D12—121no—
284D12—121no—
285D12—121no—
286D12—121no—
287D12—121no—
288D12—241no—
289D12—241no—
290D12—242no—
291D12#21512yescomplemented
292C4×D3—44no—
293C4×D3—41no—
294C4×D3—41no—
295Dic6—44no—
296Dic6—41no—
297Dic6—41no—
298C3×C8—121no—
299C3×C8—121no—
300C3⋊C8—41no—
301C3⋊C8—41no—
302C3⋊C8—122no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C2×C32#44711yescharacteristic
306C2×C32#44811yescharacteristic
307C2×C32#45411yescharacteristic
308C3⋊D3—161no—
309C3×D3—42no—
310C2×Q8—62no—
311C2×Q8—61no—
312C2×Q8—122no—
313C2×Q8—122no—
314C2×Q8#62611yescharacteristic
315C2×D4—31no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—181no—
319C22×C4—62no—
320C22×C4—61no—
321SD16—362no—
322D8—362no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—181no—
326C4⋊C4—21no—
327C4⋊C4—31no—
328C4⋊C4—32no—
329C4⋊C4—62no—
330C4⋊C4—61no—
331C4⋊C4#62611yescharacteristic
332C22⋊C4—62no—
333C22⋊C4—61no—
334C42—21no—
335C42C2×D3211yescharacteristic
336C22×C3—21no—
337C22×C3—62no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3#88211yescharacteristic
341C22×C3#95311yescharacteristic
342C2×D3—22no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—242no—
346C2×D3—242no—
347C2×D3—242no—
348C2×D3—241no—
349C2×D3—241no—
350C2×D3—241no—
351C2×D3—241no—
352C2×D3—241no—
353C2×D3—241no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—41no—
363C3×C4—42no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—81no—
367C3×C4—122no—
368C3×C4—121no—
369C3×C4C2×D2411yescharacteristic
370C3×C4#90811yescharacteristic
371C3×C4D3×SD1611yescharacteristic
372C3×C4#91811yescharacteristic
373C3×C4C2×#21311yescharacteristic
374C3×C4#93211yescharacteristic
375C3×C4C2×#21511yescharacteristic
376C3×C4#94211yescharacteristic
377Dic3—41no—
378Dic3—42no—
379C32#162711yescharacteristic, complemented, Sylow
380C23—61no—
381C23—361no—
382Q8—21no—
383Q8—124no—
384Q8—121no—
385Q8—121no—
386Q8#371412yescomplemented
387D4—32no—
388D4—61no—
389D4—362no—
390D4—361no—
391D4—361no—
392D4—361no—
393D4—361no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—124no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4C2×#62611yescharacteristic
402C2×C4D3×#6711yescharacteristic
403C2×C4D3×#6711yescharacteristic
404C8—121no—
405C8—121no—
406C8—361no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—122no—
411C2×C3#473211yescharacteristic
412C2×C3#480611yescharacteristic
413C2×C3#482711yescharacteristic
414C2×C3#521711yescharacteristic
415C2×C3#522711yescharacteristic
416C2×C3#524511yescharacteristic
417D3—42no—
418D3—482no—
419D3—481no—
420D3—481no—
421C22—62no—
422C22—121no—
423C22—121no—
424C22—721no—
425C22—721no—
426C22—721no—
427C22#6397711yescharacteristic
428C4—22no—
429C4—21no—
430C4—41no—
431C4—122no—
432C4—121no—
433C4C2×#371411yescharacteristic
434C4#6383011yescharacteristic
435C4D3×#21511yescharacteristic
436C4#6394811yescharacteristic
437C3—21no—
438C3#6826611yescharacteristic, complemented
439C3#7191411yescharacteristic, complemented
440C2—122no—
441C2—1441no—
442C2#1059116211yescharacteristic
443C2#1059158411yescharacteristic
444C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590349C2
hypercenterC4×Q8D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
2. #10592726C2semidirect
4. #10590281C2semidirect
5. C3×#4535C2semidirect
6. #10589092C2semidirect
7. #10589081C2semidirect
28. Q8×D12D3semidirect
38. #4535D3semidirect
111. C32×Q8D8semidirect
125. C3×D12SD16semidirect
249. C3×Q8D24semidirect
250. C3×Q8#213semidirect
291. D12#215semidirect
379. C32#1627semidirect
386. Q8#3714semidirect
438. C3#68266semidirect
439. C3#71914semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
#105927262
#105903492
#105902812
C3×#45352
#105890922
#105890812
#719143
#682663