Finite Group Databasebeta

← #11777685

Subgroups — #11777685

Order 1152.

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

normal subgroups only

This group has 355 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
1C8×#634C211yesmaximal, characteristic
2C3×#4679C211yesmaximal, characteristic
3C4×#3719C211yesmaximal, characteristic
4C3×#4454C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#70957—31nomaximal
9#68087—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×Dic6C2211yescharacteristic
12C2×#3719C411yescharacteristic
13C32×C4×C8C2211yescharacteristic
14#63641—21no—
15C8×C3⋊Dic3—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#815—21no—
18C3×Dic3⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63575C411yescharacteristic
23#63567C411yescharacteristic
24#63566C411yescharacteristic
25C3×#446—31no—
26C4×#216—31no—
27C4×Dic12—31no—
28#4679D311yescharacteristic
29C8×Dic6—31no—
30C8×Dic6—31no—
31C8×Dic6—61no—
32C3×#322—31no—
33#4535—31no—
34#4484—31no—
35#4480—31no—
36#4457—31no—
37#4456—31no—
38#4456—31no—
39#4454D311yescharacteristic
40C2×#634C2×C411yescharacteristic
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C32×C8D411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×C4⋊Dic3C2×C411yescharacteristic
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56#3719—22no—
57#1587—91noSylow
58C3×C4×Q8—31no—
59C2×#216—31no—
60C2×Dic12—31no—
61C4×Dic6—31no—
62C4×Dic6—31no—
63C4×Dic6—61no—
64C4×Dic6C2×D311yescharacteristic
65C3×C4⋊C8—31no—
66C3×C4⋊C8—61no—
67C3×#97—61no—
68C3×C4×C8—21no—
69C3×C4×C8—31no—
70C3×C4×C8—31no—
71C3×C4×C8C2×D311yescharacteristic
72C3×C4×C8C2×D311yescharacteristic
73#835—31no—
74#818—31no—
75#816—31no—
76#816—31no—
77#815—21no—
78Dic3⋊C8—21no—
79Dic3⋊C8—62no—
80Dic3⋊C8—61no—
81Dic3⋊C8—61no—
82C8×Dic3—62no—
83C8×Dic3—61no—
84C8×Dic3—61no—
85#810—31no—
86#807—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98#634—21no—
99#634M1612yes—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—21no—
102C3×Dic6—21no—
103C3×Dic6—21no—
104C32×C8—21no—
105C32×C8—21no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111#446—31no—
112C8×Q8—91no—
113C4×Q16—91no—
114#334—91no—
115Q8⋊C8—91no—
116Q8⋊C8—91no—
117#322—31no—
118C2×C3×Q8—31no—
119C2×Dic6—31no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×Dic6C4×D311yescharacteristic
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C2×C3×C8—31no—
126C2×C3×C8—31no—
127C2×C3×C8—61no—
128C2×C3×C8—61no—
129C2×C3×C8D1211yescharacteristic
130C2×C3×C8D1211yescharacteristic
131C2×C3×C8#6711yescharacteristic
132C2×C3×C8#6711yescharacteristic
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42—61no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139#216—62no—
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—61no—
143C4⋊Dic3C4×D311yescharacteristic
144Dic3⋊C4—21no—
145Dic3⋊C4—62no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148C4×Dic3—21no—
149C4×Dic3—62no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—62no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8C4×D311yescharacteristic
158C2×C3⋊C8C4×D311yescharacteristic
159Dic12—62no—
160C22×C32C4×D411yescharacteristic
161C32×C4—21no—
162C32×C4C2×M1611yescharacteristic
163C32×C4#13111yescharacteristic
164C32×C4#13711yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—41no—
168C3×Dic3—41no—
169C3×Dic3—41no—
170C2×Q16—91no—
171C4×Q8—31no—
172C4×Q8—91no—
173#107—91no—
174C4⋊C8—31no—
175C4⋊C8—61no—
176C4⋊C8—91no—
177C4⋊C8—181no—
178#103—91no—
179#103—91no—
180#97—61no—
181C4×C8—31no—
182C4×C8—31no—
183C4×C8—181no—
184C4×C8D3211yescharacteristic
185C3×Q8—61no—
186C3×Q8—61no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4C2×C4×D311yescharacteristic
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4#23511yescharacteristic
196C2×C3×C4#23511yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—62no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—62no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206Dic6—21no—
207Dic6—21no—
208Dic6—32no—
209Dic6—32no—
210Dic6—62no—
211Dic6—62no—
212Dic6—61no—
213Dic6—61no—
214C3×C8—22no—
215C3×C8—21no—
216C3×C8—21no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—41no—
220C3×C8—62no—
221C3×C8—61no—
222C3×C8—61no—
223C3×C8—121no—
224C3⋊C8—22no—
225C3⋊C8—21no—
226C3⋊C8—21no—
227C3⋊C8—41no—
228C3⋊C8—122no—
229C3⋊C8—121no—
230C3⋊C8—121no—
231C2×C32#43511yescharacteristic
232C2×C32#44111yescharacteristic
233C2×C32#44311yescharacteristic
234C2×Q8—31no—
235C2×Q8—91no—
236Q16—182no—
237C2×C8—31no—
238C2×C8—31no—
239C2×C8—61no—
240C2×C8—61no—
241C2×C8—181no—
242C2×C8#62611yescharacteristic
243C2×C8#62611yescharacteristic
244C4⋊C4—31no—
245C4⋊C4—61no—
246C4⋊C4—91no—
247C4⋊C4—181no—
248C42—61no—
249C42—181no—
250C42C2×D3211yescharacteristic
251C22×C3—21no—
252C22×C3C4×D1211yescharacteristic
253C22×C3C4×#6711yescharacteristic
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—121no—
262C3×C4—121no—
263C3×C4D3×M1611yescharacteristic
264C3×C4D3×M1611yescharacteristic
265C3×C4#90711yescharacteristic
266C3×C4#90711yescharacteristic
267C3×C4#90911yescharacteristic
268C3×C4#90911yescharacteristic
269C3×C4#94211yescharacteristic
270C3×C4#95111yescharacteristic
271Dic3—41no—
272Dic3—41no—
273Dic3—64no—
274Dic3—62no—
275Dic3—62no—
276Dic3—122no—
277Dic3—121no—
278Dic3—121no—
279C32#158711yescharacteristic, complemented, Sylow
280Q8—61no—
281Q8—61no—
282Q8—92no—
283Q8—181no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4#379811yescharacteristic
289C2×C4C4×D3211yescharacteristic
290C2×C4C2×#62611yescharacteristic
291C8—21no—
292C8—21no—
293C8—62no—
294C8—61no—
295C8—61no—
296C8—121no—
297C8—361no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3#470011yescharacteristic
302C2×C3#470611yescharacteristic
303C2×C3#471611yescharacteristic
304C2×C3#503011yescharacteristic
305C2×C3#512711yescharacteristic
306C2×C3#514411yescharacteristic
307C22C4×#62611yescharacteristic
308C4—21no—
309C4—121no—
310C4—121no—
311C4—182no—
312C4—361no—
313C4#6379111yescharacteristic
314C4#6380511yescharacteristic
315C4#6383111yescharacteristic
316C4#6383311yescharacteristic
317C3—21no—
318C3#6808711yescharacteristic, complemented
319C3#7095711yescharacteristic, complemented
320C2#1059038311yescharacteristic
321C2#1059073611yescharacteristic
322C2#1059092311yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1587
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
279. C32#1587semidirect
318. C3#68087semidirect
319. C3#70957semidirect

Maximal subgroups

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

subgroupindex
C8×#6342
C3×#46792
C4×#37192
C3×#44542
#105890972
#105890852
#105890842
#709573
#680873