Finite Group Databasebeta

← #37571439

Subgroups — #37571439

Order 24448.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#27133221C211yesmaximal, characteristic, complemented
2#27132799C211yesmaximal, characteristic, complemented
3#27132796C211yesmaximal, characteristic, complemented
4#27132573C211yesmaximal, characteristic, complemented
5#27132396C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic, complemented
7#327×C191C211yesmaximal, characteristic, complemented
8C22×D764—21no—
9C22×D764C2211yescharacteristic, complemented
10C2×D4×D191—21no—
11C2×D1528—21no—
12C2×#15690272—21no—
13#20259307—21no—
14#20259304—21no—
15#20259296C2211yescharacteristic
16#20259294—21no—
17#20259292—21no—
18#20259290—21no—
19C2×(C2×D191)⋊C4—21no—
20C2×(C2×D191)⋊C4C2211yescharacteristic
21#20259244—21no—
22#20259242—21no—
23C22⋊(C191⋊C8)C2211yescharacteristic, complemented
24#121×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic, complemented
26#95×C191C2211yescharacteristic, complemented
27C23×D191—21no—
28C23×D191—21no—
29C23×D191D411yescharacteristic
30C2×D764—21no—
31C2×D764—21no—
32C2×D764—21no—
33C2×D764—42no—
34C2×D764—42no—
35C2×D764—42no—
36C2×D764—42no—
37C2×D764D411yescharacteristic, complemented
38C2×C22⋊D191—21no—
39C2×C22⋊D191—21no—
40C2×C22⋊D191—21no—
41D4×D191—42no—
42D4×D191—42no—
43C22×Dic191D411yescharacteristic
44C2×C4×D191—21no—
45D1528—42no—
46#15690272—42no—
47C2×C191⋊C8—21no—
48C4⋊Dic191D411yescharacteristic, complemented
49Dic191⋊C4—21no—
50C22⋊Dic191—21no—
51(C2×D191)⋊C4—21no—
52(C2×D191)⋊C4—21no—
53(C2×D191)⋊C4—21no—
54(C2×D191)⋊C4—21no—
55(C2×D191)⋊C4—42no—
56C2×D4×C191—21no—
57C2×D4×C191D411yescharacteristic, complemented
58C22×C4×C191—21no—
59C22×C4×C191C2311yescharacteristic
60C2×C8×C191—21no—
61C4⋊C4×C191D411yescharacteristic, complemented
62C22⋊C4×C191—21no—
63C22×D191—21no—
64C22×D191—21no—
65C22×D191—22no—
66C22×D191—21no—
67C22×D191—42no—
68C22×D191—41no—
69C22×D191—41no—
70C22×D191—41no—
71C22×D191—41no—
72C22×D191—41no—
73C22×D191—41no—
74C22×D191—41no—
75C22×D191—41no—
76C22×D191—81no—
77C22×D191—81no—
78C22×D191D812yescomplemented
79D764—22no—
80D764—22no—
81D764—41no—
82D764—41no—
83D764—41no—
84D764—42no—
85D764—48no—
86C22⋊D191—42no—
87C22⋊D191—41no—
88C22⋊D191—41no—
89C22⋊D191—81no—
90C2×Dic191—21no—
91C2×Dic191—21no—
92C2×Dic191—41no—
93C4×D191—42no—
94C191⋊C8—41no—
95C23×C191—21no—
96C23×C191C2×D411yescharacteristic
97D4×C191—41no—
98D4×C191—41no—
99D4×C191—41no—
100C2×C4×C191—22no—
101C2×C4×C191—21no—
102C2×C4×C191—41no—
103C2×C4×C191—41no—
104C2×C4×C191—41no—
105C2×C4×C191C2×D411yescharacteristic
106C2×C4×C191C2×D411yescharacteristic
107C8×C191—41no—
108C22×C191—21no—
109C22×C191—21no—
110C22×C191—41no—
111C22×C191—41no—
112C22×C191—41no—
113C22×C191#12011yescharacteristic
114C22×C191C2×D811yescharacteristic
115C22×C191AGL(1,ℤ/8)11yescharacteristic
116C2×D191—22no—
117C2×D191—41no—
118C2×D191—41no—
119C2×D191—42no—
120C2×D191—42no—
121C2×D191—42no—
122C2×D191—41no—
123C2×D191—41no—
124C2×D191—42no—
125C2×D191—41no—
126C2×D191—81no—
127C2×D191—84no—
128C2×D191—81no—
129C2×D191—81no—
130C2×D191—81no—
131C2×D191—81no—
132C4×C191—21no—
133C4×C191—21no—
134C4×C191—42no—
135C4×C191—41no—
136Dic191—41no—
137Dic191—41no—
138C2×C191—21no—
139C2×C191—21no—
140C2×C191—81no—
141C2×C191#44711yescharacteristic
142C2×C191#45311yescharacteristic
143C2×C191B(4,𝔽2)11yescharacteristic
144D191—42no—
145D191—82no—
146D191—81no—
147C191#159511yescharacteristic, complemented, Sylow
148#1595—1911nomaximal, Sylow
149#534—1911no—
150#447—1911no—
151#447—1911no—
152#392—1911no—
153#327—1911no—
154#327D19111yescharacteristic, complemented
155#323—1911no—
156C22×D4—3821no—
157C22×D4—3821no—
158C22×D4—1911no—
159C2×D8—3821no—
160C2×D8—3821no—
161#123—3821no—
162#123—3821no—
163#121—3821no—
164#121—1911no—
165#121C2×D19111yescharacteristic
166#120—3821no—
167#120—3821no—
168C2×C22⋊C4—3821no—
169C2×C22⋊C4—1911no—
170#102—3821no—
171#102—3821no—
172C22⋊C8—1911no—
173C22⋊C8C2×D19111yescharacteristic, complemented
174#95C2×D19111yescharacteristic, complemented
175C24—3821no—
176C24—3821no—
177C24—1911no—
178C2×D4—21no—
179C2×D4—3821no—
180C2×D4—3821no—
181C2×D4—3821no—
182C2×D4—3821no—
183C2×D4—3821no—
184C2×D4—3821no—
185C2×D4—1911no—
186C2×D4—7642no—
187C2×D4—7642no—
188C2×D4—7642no—
189C2×D4—7642no—
190C2×D4—7642no—
191C2×D4—7642no—
192C2×D4D76411yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—3821no—
195C22×C4—1911no—
196C22×C4C22×D19111yescharacteristic
197D8—7642no—
198D8—7642no—
199C2×C8—21no—
200C2×C8—3821no—
201C4⋊C4—3821no—
202C4⋊C4—1911no—
203C4⋊C4D76411yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—3821no—
206C22⋊C4—3821no—
207C22⋊C4—3821no—
208C22⋊C4—3821no—
209C22⋊C4—3821no—
210C22⋊C4—7642no—
211C23—21no—
212C23—3822no—
213C23—3821no—
214C23—3821no—
215C23—3821no—
216C23—1912no—
217C23—15281no—
218C23—15281no—
219C23—7641no—
220C23—7641no—
221C23—7641no—
222C23—7641no—
223C23—7641no—
224C23—7642no—
225C23—7641no—
226C23—7641no—
227C23—7641no—
228C23D4×D19111yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—3822no—
233D4—3822no—
234D4—15281no—
235D4—7641no—
236D4—7641no—
237D4—7641no—
238D4—7642no—
239D4—7648no—
240D4—7642no—
241D4—7641no—
242D4—7641no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—3821no—
249C2×C4—3821no—
250C2×C4—7642no—
251C2×C4—7641no—
252C2×C4D4×D19111yescharacteristic
253C2×C4C2×D76411yescharacteristic
254C8—41no—
255C8—7641no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—3822no—
262C22—15281no—
263C22—15281no—
264C22—15281no—
265C22—15284no—
266C22—15281no—
267C22—15281no—
268C22—7642no—
269C22—7642no—
270C22—7642no—
271C22—7641no—
272C22—7641no—
273C22—7642no—
274C22—7641no—
275C22—7641no—
276C22—7641no—
277C22#2025929211yescharacteristic
278C22D8×D19111yescharacteristic
279C22#2025934911yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—7641no—
285C4—7641no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—15282no—
290C2—15281no—
291C2—7642no—
292C2#2713279811yescharacteristic
293C2#2713283211yescharacteristic
294C2#2713285111yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#327×C191C2
socleC22×C191#120
hypercenter#327D191
hypocenterC191#1595
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #27133221C2semidirect
2. #27132799C2semidirect
3. #27132796C2semidirect
4. #27132573C2semidirect
5. #27132396C2semidirect
6. #27132386C2semidirect
7. #327×C191C2semidirect
9. C22×D764C22semidirect
23. C22⋊(C191⋊C8)C22semidirect
25. C22⋊C8×C191C22semidirect
26. #95×C191C22semidirect
37. C2×D764D4semidirect
48. C4⋊Dic191D4semidirect
57. C2×D4×C191D4semidirect
61. C4⋊C4×C191D4semidirect
78. C22×D191D8semidirect
147. C191#1595semidirect
154. #327D191semidirect
173. C22⋊C8C2×D191semidirect
174. #95C2×D191semidirect
192. C2×D4D764semidirect
203. C4⋊C4D764semidirect

Maximal subgroups

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

subgroupindex
#271332212
#271327992
#271327962
#271325732
#271323962
#271323862
#327×C1912
#1595191