Finite Group Databasebeta

← #37510066

Subgroups — #37510066

Order 22912.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#26039237C211yesmaximal, characteristic, complemented
2#26038951C211yesmaximal, characteristic, complemented
3#26038946C211yesmaximal, characteristic, complemented
4#26038455C211yesmaximal, characteristic, complemented
5#26038402C211yesmaximal, characteristic, complemented
6#26038195C211yesmaximal, characteristic, complemented
7#421×C179C211yesmaximal, characteristic, complemented
8C2×#15668259C2211yescharacteristic
9C22×C4×D179C2211yescharacteristic
10#19153144—21no—
11#19153143—21no—
12#19153139—21no—
13#19153138—21no—
14#19153133—22no—
15C2×#15668243C2211yescharacteristic
16#19153097—21no—
17#19153094—21no—
18#19153093—21no—
19#19153089—21no—
20#19153088—21no—
21#19153084—21no—
22#19153083—21no—
23#19153081—21no—
24C4×D716—22no—
25C4×C22⋊D179—22no—
26#19153072C2211yescharacteristic
27#19153039—22no—
28(C2×D179)⋊C8—22no—
29C2×#41×C179C2211yescharacteristic
30C2×M16×C179C2211yescharacteristic
31#117×C179C2211yescharacteristic
32#104×C179—22no—
33C23×D179D411yescharacteristic
34#15668259—21no—
35#15668259—21no—
36#15668259—21no—
37#15668259—21no—
38C2×Dic358D411yescharacteristic, complemented
39C2×D716—22no—
40C2×D716D411yescharacteristic, complemented
41C2×C22⋊D179—22no—
42C2×C22⋊D179—21no—
43C22×Dic179D411yescharacteristic
44C2×C4×D179—21no—
45C2×C4×D179—21no—
46C2×C4×D179—21no—
47C2×C4×D179—21no—
48C2×C4×D179—21no—
49C2×C4×D179—21no—
50C2×C4×D179—21no—
51#15668249—22no—
52#15668247—22no—
53#15668246—22no—
54#15668244—22no—
55#15668243—21no—
56#15668243—21no—
57C2×C179⋊C8D412yescomplemented
58C4⋊Dic179—22no—
59C4⋊Dic179—21no—
60Dic179⋊C4—22no—
61C22⋊Dic179—22no—
62C22⋊Dic179—21no—
63(C2×D179)⋊C4—22no—
64(C2×D179)⋊C4—22no—
65(C2×D179)⋊C4—22no—
66C4×Dic179D412yescomplemented
67#41×C179—21no—
68#41×C179—21no—
69#41×C179—21no—
70#41×C179—21no—
71C2×Q8×C179D411yescharacteristic, complemented
72C2×D4×C179—21no—
73C2×D4×C179D411yescharacteristic, complemented
74C22×C4×C179—21no—
75C22×C4×C179C2311yescharacteristic
76M16×C179—21no—
77M16×C179—21no—
78C2×C8×C179—21no—
79C4⋊C4×C179—21no—
80C22⋊C4×C179—21no—
81C42×C179D412yescomplemented
82C22×D179—21no—
83C22×D179—21no—
84C22×D179—21no—
85C22×D179—21no—
86C22×D179—42no—
87Dic358—21no—
88Dic358—21no—
89D716—21no—
90D716—21no—
91D716—44no—
92C22⋊D179—44no—
93C22⋊D179—41no—
94C22⋊D179—41no—
95C2×Dic179—22no—
96C2×Dic179—21no—
97C2×Dic179—21no—
98C2×Dic179—21no—
99C2×Dic179—21no—
100C4×D179—41no—
101C4×D179—41no—
102C4×D179—41no—
103C4×D179—41no—
104C4×D179—41no—
105C4×D179—41no—
106C179⋊C8—22no—
107C23×C179—21no—
108C23×C179C2×D411yescharacteristic
109Q8×C179—21no—
110Q8×C179—21no—
111D4×C179—21no—
112D4×C179—21no—
113D4×C179—41no—
114D4×C179—41no—
115C2×C4×C179—21no—
116C2×C4×C179—22no—
117C2×C4×C179—41no—
118C2×C4×C179—41no—
119C2×C4×C179C2×D411yescharacteristic
120C2×C4×C179C2×D411yescharacteristic
121C2×C4×C179C2×D411yescharacteristic
122C2×C4×C179C2×D411yescharacteristic
123C2×C4×C179C2×D411yescharacteristic
124C2×C4×C179#4111yescharacteristic
125C8×C179—41no—
126C22×C179—41no—
127C22×C179—42no—
128C22×C179—41no—
129C22×C179#12011yescharacteristic
130C22×C179#12011yescharacteristic
131C22×C179#12111yescharacteristic
132C2×D179—22no—
133C2×D179—22no—
134C2×D179—22no—
135C2×D179—41no—
136C2×D179—41no—
137C2×D179—41no—
138C2×D179—41no—
139C2×D179—42no—
140C2×D179—41no—
141C4×C179—42no—
142C4×C179—41no—
143C4×C179#12011yescharacteristic
144C4×C179#12111yescharacteristic
145C4×C179#12111yescharacteristic
146C4×C179#12711yescharacteristic
147Dic179—42no—
148Dic179—41no—
149Dic179—41no—
150C2×C179—21no—
151C2×C179—21no—
152C2×C179—21no—
153C2×C179—81no—
154C2×C179#39211yescharacteristic
155D179—42no—
156D179—81no—
157C179#201011yescharacteristic, complemented, Sylow
158#2010—1791nomaximal, Sylow
159#575—1791no—
160#525—1791no—
161#525—1791no—
162#421—1791no—
163#421D17911yescharacteristic, complemented
164#407—1791no—
165H(3,ℤ/4)—1791no—
166C2×#41—1791no—
167C2×#41C2×D17911yescharacteristic
168C23×C4—1791no—
169#137—3581no—
170#137—3581no—
171AGL(1,ℤ/8)—3581no—
172AGL(1,ℤ/8)—3581no—
173#135—3582no—
174C2×M16—1791no—
175C2×M16C2×D17911yescharacteristic
176#123—3581no—
177#123—3581no—
178C22⋊Q8—3581no—
179C22⋊Q8—3581no—
180#121—3581no—
181#121—3581no—
182#120—3581no—
183#120—3581no—
184C4×D4—3582no—
185C4×D4—3582no—
186#117—1791no—
187#117C2×D17911yescharacteristic
188#104—22no—
189#104—3582no—
190C22⋊C8—3582no—
191C24—1791no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—3581no—
197#41—3581no—
198#41—3581no—
199#41—3581no—
200C2×Q8—1791no—
201C2×Q8D71611yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—3582no—
204C2×D4—3582no—
205C2×D4—3581no—
206C2×D4—1791no—
207C2×D4D71611yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—3581no—
210C22×C4—3581no—
211C22×C4—3581no—
212C22×C4—3581no—
213C22×C4—3581no—
214C22×C4—3581no—
215C22×C4—3581no—
216C22×C4—1791no—
217C22×C4C22×D17911yescharacteristic
218Q16—3582no—
219SD16—3582no—
220SD16—3582no—
221D8—3582no—
222M16—21no—
223M16—21no—
224M16—3581no—
225M16—3581no—
226C2×C8—21no—
227C2×C8—1792no—
228C4⋊C4—21no—
229C4⋊C4—3582no—
230C4⋊C4—3582no—
231C4⋊C4—3581no—
232C22⋊C4—21no—
233C22⋊C4—3582no—
234C22⋊C4—3582no—
235C22⋊C4—3582no—
236C22⋊C4—3582no—
237C22⋊C4—3581no—
238C42—1792no—
239C42C22⋊D17912yescomplemented
240C23—21no—
241C23—3581no—
242C23—3581no—
243C23—3581no—
244C23—3581no—
245C23—7162no—
246C23D4×D17911yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—3581no—
250Q8—3581no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—3581no—
256D4—3581no—
257D4—7164no—
258D4—7164no—
259D4—7161no—
260D4—7161no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3581no—
266C2×C4—3581no—
267C2×C4—3582no—
268C2×C4—3581no—
269C2×C4—3581no—
270C2×C4—7161no—
271C2×C4—7161no—
272C2×C4—7161no—
273C2×C4—7161no—
274C2×C4—7161no—
275C2×C4—7161no—
276C2×C4D4×D17911yescharacteristic
277C2×C4D4×D17911yescharacteristic
278C2×C4D4×D17911yescharacteristic
279C2×C4C2×C22⋊D17911yescharacteristic
280C2×C4C2×D71611yescharacteristic
281C2×C4#1566825911yescharacteristic
282C8—41no—
283C8—3582no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—3582no—
288C22—3582no—
289C22—3582no—
290C22—7162no—
291C22—7161no—
292C22—7161no—
293C22—7161no—
294C22—7161no—
295C22—7161no—
296C22#1915308111yescharacteristic
297C22#1915308311yescharacteristic
298C22#1915308611yescharacteristic
299C4—42no—
300C4—41no—
301C4—7162no—
302C4—7161no—
303C4—7161no—
304C4#1915308311yescharacteristic
305C4#1915308611yescharacteristic
306C4#1915308711yescharacteristic
307C4#1915310911yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—14321no—
313C2—7162no—
314C2#2603834811yescharacteristic
subgroupG/H
centerC4#19153109
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#421×C179C2
socleC2×C179#392
hypercenter#421D179
hypocenterC179#2010
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #26039237C2semidirect
2. #26038951C2semidirect
3. #26038946C2semidirect
4. #26038455C2semidirect
5. #26038402C2semidirect
6. #26038195C2semidirect
7. #421×C179C2semidirect
38. C2×Dic358D4semidirect
40. C2×D716D4semidirect
57. C2×C179⋊C8D4semidirect
66. C4×Dic179D4semidirect
71. C2×Q8×C179D4semidirect
73. C2×D4×C179D4semidirect
81. C42×C179D4semidirect
157. C179#2010semidirect
163. #421D179semidirect
201. C2×Q8D716semidirect
207. C2×D4D716semidirect
239. C42C22⋊D179semidirect

Maximal subgroups

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

subgroupindex
#260392372
#260389512
#260389462
#260384552
#260384022
#260381952
#421×C1792
#2010179