Finite Group Databasebeta

← #11777552

Subgroups — #11777552

Order 1152.

359 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 359 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C4×#3746C211yesmaximal, characteristic
2#10590296C211yesmaximal, characteristic
3#10590254C211yesmaximal, characteristic
4C3×#4458C211yesmaximal, characteristic
5C3×#4454C211yesmaximal, characteristic
6#10589085C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#68560—31nomaximal
9#68086—31nomaximal
10C2×#3746C411yescharacteristic
11C4×#634C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14#63645C411yescharacteristic
15#63643C411yescharacteristic
16#63643C411yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63572—21no—
22#63572—21no—
23#63555—21no—
24#63553—21no—
25#4831—31no—
26#4830—31no—
27C4×Dic12—31no—
28C4×Dic12—31no—
29C4×Dic12—61no—
30#4679—31no—
31C8×Dic6—31no—
32C3×#335—31no—
33C3×#322—31no—
34#4484—31no—
35#4484—31no—
36#4458D311yescharacteristic
37#4456—31no—
38#4456—31no—
39#4454D311yescharacteristic
40C2×#634C2×C411yescharacteristic
41C2×#634C2×C411yescharacteristic
42C2×C32×C8C2×C411yescharacteristic
43C2×C32×C8C2×C411yescharacteristic
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46C4⋊(C3⋊Dic3)C2×C411yescharacteristic
47#3750—21no—
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C4×C3⋊Dic3—21no—
51#3746—22no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1584—91noSylow
58C2×Dic12—31no—
59C2×Dic12—31no—
60C2×Dic12—61no—
61C4×Dic6—31no—
62C4×Dic6—31no—
63C4×Dic6—31no—
64C4×Dic6—31no—
65C4×Dic6—61no—
66C4×Dic6—61no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×C4×C8—21no—
70C3×C4×C8—31no—
71C3×C4×C8—31no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#818—31no—
75#818—31no—
76#818—61no—
77#816—31no—
78#816—31no—
79#816—31no—
80#816—31no—
81#816—61no—
82#816—61no—
83#815—61no—
84#815—61no—
85Dic3⋊C8—61no—
86Dic3⋊C8—61no—
87Dic3⋊C8—61no—
88Dic3⋊C8—61no—
89C8×Dic3—61no—
90C8×Dic3—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102#634—21no—
103#634—21no—
104#634—21no—
105#634M1612yes—
106C32×C8—21no—
107C32×C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8Q1612yescomplemented
113#446—91no—
114C8×Q8—91no—
115C4×Q16—91no—
116#335—31no—
117Q8⋊C8—91no—
118Q8⋊C8—91no—
119#322—31no—
120C2×Dic6—31no—
121C2×Dic6—31no—
122C2×Dic6—31no—
123C2×Dic6—31no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×C3×C8—21no—
127C2×C3×C8—21no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8C4×D311yescharacteristic
134C2×C3×C8C4×D311yescharacteristic
135C2×C3×C8C4×D311yescharacteristic
136C2×C3×C8C4×D311yescharacteristic
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—31no—
143C4⋊Dic3—31no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146Dic3⋊C4—61no—
147Dic3⋊C4—61no—
148Dic3⋊C4—61no—
149Dic3⋊C4—61no—
150Dic3⋊C4—121no—
151Dic3⋊C4—121no—
152C4×Dic3—61no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—121no—
157C4×Dic3—121no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8D1211yescharacteristic
162C2×C3⋊C8D1211yescharacteristic
163Dic12—62no—
164Dic12—62no—
165Dic12—64no—
166C22×C32C4×D411yescharacteristic
167C32×C4—21no—
168C32×C4C2×M1611yescharacteristic
169C32×C4#13111yescharacteristic
170C32×C4C2×Q1611yescharacteristic
171C32×C4#13511yescharacteristic
172C3⋊Dic3—22no—
173C3⋊Dic3—41no—
174C3⋊Dic3—41no—
175C3⋊Dic3—41no—
176C2×Q16—91no—
177C4×Q8—91no—
178C4×Q8—91no—
179#107—91no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—181no—
183C4⋊C8—181no—
184#103—91no—
185#103—91no—
186#97—181no—
187C4×C8—31no—
188C4×C8—31no—
189C4×C8—181no—
190C4×C8D3211yescharacteristic
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4C2×C4×D311yescharacteristic
195C2×C3×C4C2×C4×D311yescharacteristic
196C2×C3×C4C2×D1211yescharacteristic
197C2×C3×C4#23511yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×C3×C4#23911yescharacteristic
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212Dic6—32no—
213Dic6—32no—
214Dic6—62no—
215Dic6—61no—
216Dic6—61no—
217Dic6—62no—
218Dic6—61no—
219Dic6—61no—
220Dic6—61no—
221Dic6—61no—
222Dic6—121no—
223Dic6—121no—
224C3×C8—22no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—32no—
230C3×C8—41no—
231C3×C8—61no—
232C3×C8—121no—
233C3×C8—121no—
234C3×C8—121no—
235C3⋊C8—21no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8Dic1212yescomplemented
240C2×C32#43511yescharacteristic
241C2×C32C4×Q1611yescharacteristic
242C2×C32#44411yescharacteristic
243C2×Q8—91no—
244C2×Q8—91no—
245Q16—182no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—61no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8#62411yescharacteristic
252C2×C8#62411yescharacteristic
253C4⋊C4—91no—
254C4⋊C4—91no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C42—181no—
258C42—181no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3C4×D1211yescharacteristic
262C22×C3#89311yescharacteristic
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—41no—
270C3×C4#90111yescharacteristic
271C3×C4#90411yescharacteristic
272C3×C4C2×Dic1211yescharacteristic
273C3×C4D3×M1611yescharacteristic
274C3×C4D3×M1611yescharacteristic
275C3×C4#90711yescharacteristic
276C3×C4#91211yescharacteristic
277C3×C4D3×Q1611yescharacteristic
278Dic3—62no—
279Dic3—62no—
280Dic3—122no—
281Dic3—122no—
282Dic3—121no—
283Dic3—121no—
284Dic3—121no—
285Dic3—121no—
286Dic3—121no—
287Dic3—121no—
288Dic3—241no—
289Dic3—241no—
290C32#158411yescharacteristic, complemented, Sylow
291Q8—92no—
292Q8—181no—
293Q8—181no—
294Q8—181no—
295C2×C4—181no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4—181no—
299C2×C4#379911yescharacteristic
300C2×C4D3×D1211yescharacteristic
301C2×C4C2×#62411yescharacteristic
302C8—21no—
303C8—21no—
304C8—32no—
305C8—61no—
306C8—121no—
307C8—121no—
308C8—121no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3C4×Dic1211yescharacteristic
313C2×C3#470611yescharacteristic
314C2×C3#471711yescharacteristic
315C2×C3#483611yescharacteristic
316C2×C3#487311yescharacteristic
317C2×C3#489411yescharacteristic
318C22#6389411yescharacteristic
319C4—21no—
320C4—182no—
321C4—361no—
322C4—361no—
323C4—361no—
324C4D3×Dic1211yescharacteristic
325C4#6380711yescharacteristic
326C4#6381711yescharacteristic
327C4#6381811yescharacteristic
328C3—21no—
329C3#6808611yescharacteristic, complemented
330C3#6856011yescharacteristic, complemented
331C2#1059032811yescharacteristic
332C2#1059080711yescharacteristic
333C2#1059091811yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1584
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
112. C3×C3⋊C8Q16semidirect
239. C3⋊C8Dic12semidirect
290. C32#1584semidirect
329. C3#68086semidirect
330. C3#68560semidirect

Maximal subgroups

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

subgroupindex
C4×#37462
#105902962
#105902542
C3×#44582
C3×#44542
#105890852
#685603
#680863