Finite Group Databasebeta

← #11779596

Subgroups — #11779596

Order 1152.

411 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5570C211yesmaximal, characteristic
2C3×#5021C211yesmaximal, characteristic
3#10590310C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic
6#10589092C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic
8#71936—31nomaximal
9#71158—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×Q8×Dic3—21no—
12C3×#890—21no—
13C3×#890—22no—
14C3×#869—21no—
15C3×#869C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×C4×Dic6—21no—
18C3×C4×Dic6C2211yescharacteristic
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#835—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—21no—
25#63565—21no—
26#63565—22no—
27C3×#557—31no—
28#5570D311yescharacteristic
29C3×#477—31no—
30#5093—31no—
31#5091—31no—
32#5079—31no—
33#5021—31no—
34#5021D311yescharacteristic
35#4547—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—61no—
40#4486—31no—
41#4484—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D411yescharacteristic
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C42—21no—
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—22no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D412yes—
58C3×C4⋊Dic3D411yescharacteristic
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—22no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#1636—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—61no—
68C3×#125—62no—
69C3×#125—61no—
70C3×C4×Q8—21no—
71C3×C4×Q8—31no—
72C3×C4×Q8—61no—
73C3×C4×Q8—61no—
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×Q8C2×D311yescharacteristic
76Q8×Dic3—21no—
77#890—21no—
78#890—22no—
79#869—21no—
80#869C2×D311yescharacteristic
81#869C2×D311yescharacteristic
82C4×Dic6—21no—
83C4×Dic6C2×D311yescharacteristic
84C3×#107—61no—
85C3×C4⋊C8—31no—
86C3×#103—61no—
87#835—21no—
88#835—61no—
89#835—62no—
90#810—62no—
91#810—61no—
92#807—21no—
93#807—61no—
94#807—61no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—61no—
98C4⋊(C3⋊C8)C2×D311yescharacteristic
99C4×C3⋊C8—31no—
100C4×C3⋊C8—31no—
101C4×C3⋊C8—61no—
102C32×Q8—21no—
103C32×Q8Q1612yes—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C3×Dic6—42no—
118C3⋊(C3⋊C8)—41no—
119C3⋊(C3⋊C8)—41no—
120C3×C3⋊C8—41no—
121#557—31no—
122#487—91no—
123#477—31no—
124#477—91no—
125#332—91no—
126Q8⋊C8—91no—
127Q8⋊C8—91no—
128C2×C3×Q8—21no—
129C2×C3×Q8—31no—
130C2×C3×Q8—61no—
131C2×C3×Q8—61no—
132C2×C3×Q8#6711yescharacteristic
133C2×C3×Q8#6711yescharacteristic
134C2×Dic6—21no—
135C2×Dic6—21no—
136C2×Dic6#6711yescharacteristic
137C2×C3×C8—61no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—31no—
142C3×C4⋊C4—32no—
143C3×C4⋊C4—41no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4#6711yescharacteristic
152C3×C4⋊C4#6711yescharacteristic
153C3×C42—21no—
154C3×C42—21no—
155C3×C42—21no—
156C3×C42—41no—
157C3×C42—62no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161C4⋊Dic3—22no—
162C4⋊Dic3—22no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3#6711yescharacteristic
167C4⋊Dic3#6712yes—
168Dic3⋊C4—22no—
169Dic3⋊C4—21no—
170C4×Dic3—22no—
171C4×Dic3—21no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—121no—
178C2×C3⋊C8—121no—
179C22×C32#12011yescharacteristic
180C32×C4—22no—
181C32×C4—21no—
182C32×C4—41no—
183C32×C4C2×Q1611yescharacteristic
184C32×C4#13511yescharacteristic
185C32×C4#13711yescharacteristic
186C32×C4#13711yescharacteristic
187C3×Dic3—41no—
188C3×Dic3—42no—
189C3×Dic3—41no—
190C3×Dic3—81no—
191C4⋊Q8—31no—
192C4⋊Q8—31no—
193C4⋊Q8—61no—
194#125—62no—
195#125—61no—
196C4×Q8—31no—
197C4×Q8—61no—
198C4×Q8—61no—
199C4×Q8D3211yescharacteristic
200#107—61no—
201#107—181no—
202C4⋊C8—31no—
203C4⋊C8—91no—
204#103—61no—
205#103—182no—
206#103—181no—
207C4×C8—91no—
208C3×Q8—21no—
209C3×Q8—21no—
210C3×Q8—22no—
211C3×Q8—41no—
212C3×Q8—61no—
213C3×Q8—61no—
214C3×Q8—122no—
215C3×Q8—121no—
216C3×Q8—121no—
217C3×Q8#21612yes—
218C3×Q8#21612yes—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—61no—
229C2×C3×C4—62no—
230C2×C3×C4—61no—
231C2×C3×C4—121no—
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—22no—
241C2×Dic3—41no—
242Dic6—21no—
243Dic6—21no—
244Dic6—41no—
245Dic6—41no—
246Dic6—42no—
247C3×C8—121no—
248C3⋊C8—41no—
249C3⋊C8—121no—
250C3⋊C8—121no—
251C3⋊C8—122no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C3⋊C8—241no—
255C2×C32#45111yescharacteristic
256C2×C32#45211yescharacteristic
257C2×C32#45411yescharacteristic
258C2×Q8—31no—
259C2×Q8—61no—
260C2×Q8—61no—
261C2×Q8#62511yescharacteristic
262C2×C8—61no—
263C2×C8—181no—
264C2×C8—181no—
265C4⋊C4—21no—
266C4⋊C4—32no—
267C4⋊C4—31no—
268C4⋊C4—62no—
269C4⋊C4—62no—
270C4⋊C4—62no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4#62511yescharacteristic
276C42—21no—
277C42—62no—
278C42—61no—
279C42C2×D3211yescharacteristic
280C22×C3—21no—
281C22×C3#93711yescharacteristic
282C22×C3#95311yescharacteristic
283C3×C4—21no—
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—42no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—81no—
296C3×C4—121no—
297C3×C4—122no—
298C3×C4—121no—
299C3×C4—241no—
300C3×C4#91811yescharacteristic
301C3×C4#91911yescharacteristic
302C3×C4#94211yescharacteristic
303C3×C4C2×#21611yescharacteristic
304C3×C4C2×#21611yescharacteristic
305C3×C4#95011yescharacteristic
306C3×C4#95111yescharacteristic
307C3×C4#95111yescharacteristic
308Dic3—41no—
309Dic3—42no—
310Dic3—41no—
311Dic3—81no—
312C32#163611yescharacteristic, complemented, Sylow
313Q8—21no—
314Q8—61no—
315Q8—61no—
316Q8—122no—
317Q8—121no—
318Q8—121no—
319Q8#371812yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—61no—
323C2×C4—62no—
324C2×C4—61no—
325C2×C4—121no—
326C2×C4C2×#62511yescharacteristic
327C2×C4D3×#6711yescharacteristic
328C2×C4D3×#6711yescharacteristic
329C8—121no—
330C8—361no—
331C8—361no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3#505011yescharacteristic
336C2×C3#518711yescharacteristic
337C2×C3#520111yescharacteristic
338C2×C3#522811yescharacteristic
339C2×C3#523911yescharacteristic
340C2×C3#524511yescharacteristic
341C22#6397611yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—121no—
346C4—122no—
347C4—121no—
348C4—241no—
349C4#6382711yescharacteristic
350C4C2×#371811yescharacteristic
351C4#6394311yescharacteristic
352C4#6394911yescharacteristic
353C3—21no—
354C3#7115811yescharacteristic, complemented
355C3#7193611yescharacteristic, complemented
356C2#1059118511yescharacteristic
357C2#1059159711yescharacteristic
358C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#120
hypercenterC4×Q8D32
hypocenterC32#1636
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
312. C32#1636semidirect
354. C3#71158semidirect
355. C3#71936semidirect

Maximal subgroups

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

subgroupindex
C3×#55702
C3×#50212
#105903102
#105902902
#105894012
#105890922
#105890832
#719363
#711583