Finite Group Databasebeta

← #37582975

Subgroups — #37582975

Order 24448.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#20259355C211yesmaximal, characteristic, complemented
2C2×#20259353C211yesmaximal, characteristic, complemented
3C2×#20259352C211yesmaximal, characteristic, complemented
4#27133209C211yesmaximal, characteristic
5C2×#20259320C211yesmaximal, characteristic, complemented
6#27133056C212yesmaximal, complemented
7#27133054C212yesmaximal, complemented
8#27133041C212yesmaximal, complemented
9#27133034C212yesmaximal, complemented
10M16×Dic191C211yesmaximal, characteristic, complemented
11C2×#137×C191C211yesmaximal, characteristic, complemented
12C2×#15690287C2211yescharacteristic
13C22×Dic382C2211yescharacteristic
14#20259355—24no—
15#20259353—24no—
16#20259352—24no—
17C2×Dic764C2212yes—
18C2×#15690277C2212yes—
19C2×#15690277C2212yes—
20C2×#15690276C2212yes—
21C2×#15690275C2212yes—
22C2×#15690274C2212yes—
23C2×#15690271C2211yescharacteristic
24#20259320—22no—
25#20259320C2212yes—
26#20259320C2212yes—
27#20259320C2211yescharacteristic
28#20259318C2211yescharacteristic
29#20259311C2211yescharacteristic
30#20259309C2211yescharacteristic
31#20259294—22no—
32C4×C22⋊D191—22no—
33C2×Dic191⋊C4—22no—
34C2×C4×Dic191C2211yescharacteristic
35#20259232C2212yes—
36C8×Dic191C2212yes—
37C2×#41×C191C2211yescharacteristic
38C22×Q8×C191C2211yescharacteristic
39#137×C191—24no—
40C2×Q16×C191C2212yes—
41C2×SD16×C191C2212yes—
42C2×M16×C191C2211yescharacteristic
43#15690287—22no—
44#15690287—22no—
45C2×Dic382—21no—
46C2×Dic382—22no—
47C2×Dic382—22no—
48C2×Dic382C2312yes—
49C2×Dic382C2311yescharacteristic
50C2×D764C2311yescharacteristic
51C2×C22⋊D191—22no—
52C2×C22⋊D191—21no—
53C22×Dic191—21no—
54C22×Dic191D412yes—
55C2×C4×D191—21no—
56Dic764—24no—
57#15690277—24no—
58#15690277—24no—
59#15690276—24no—
60#15690275—24no—
61#15690274—24no—
62#15690271D414yescomplemented
63C2×C191⋊C8C2312yes—
64Dic191⋊C4—24no—
65Dic191⋊C4—24no—
66Dic191⋊C4—22no—
67C22⋊Dic191—22no—
68(C2×D191)⋊C4—22no—
69C4×Dic191D412yes—
70C4×Dic191C2311yescharacteristic
71C4×Dic191C2311yescharacteristic
72#41×C191—22no—
73#41×C191—22no—
74C2×Q8×C191—21no—
75C2×Q8×C191—22no—
76C2×Q8×C191—22no—
77C2×Q8×C191C2312yes—
78C2×Q8×C191C2311yescharacteristic
79C2×D4×C191—21no—
80C2×D4×C191C2311yescharacteristic
81C22×C4×C191—21no—
82C22×C4×C191—21no—
83C22×C4×C191C2311yescharacteristic
84Q16×C191—24no—
85SD16×C191—24no—
86M16×C191D414yescomplemented
87C2×C8×C191C2312yes—
88C22×D191—21no—
89Dic382—22no—
90Dic382—22no—
91Dic382—21no—
92Dic382—21no—
93Dic382—42no—
94D764—21no—
95D764—21no—
96C22⋊D191—42no—
97C22⋊D191—44no—
98C2×Dic191—24no—
99C2×Dic191—21no—
100C2×Dic191—22no—
101C2×Dic191—42no—
102C2×Dic191C2×D412yes—
103C2×Dic191C2×D412yes—
104C4×D191—42no—
105C191⋊C8C2×D414yes—
106C23×C191—21no—
107C23×C191C2×D411yescharacteristic
108Q8×C191—22no—
109Q8×C191—21no—
110Q8×C191—22no—
111Q8×C191—21no—
112Q8×C191—42no—
113D4×C191—21no—
114D4×C191—21no—
115D4×C191—42no—
116C2×C4×C191—21no—
117C2×C4×C191—22no—
118C2×C4×C191—42no—
119C2×C4×C191—42no—
120C2×C4×C191C2×D411yescharacteristic
121C2×C4×C191C2×D412yes—
122C2×C4×C191C2×D412yes—
123C2×C4×C191C2411yescharacteristic
124C8×C191C2×D414yes—
125C22×C191—22no—
126C22×C191—41no—
127C22×C191—42no—
128C22×C191#12712yes—
129C22×C191C22×D411yescharacteristic
130C2×D191—41no—
131C2×D191—42no—
132C4×C191—41no—
133C4×C191—42no—
134C4×C191#12712yes—
135C4×C191C22×D411yescharacteristic
136C4×C191C22×D411yescharacteristic
137Dic191—22no—
138Dic191—41no—
139Dic191—42no—
140Dic191#13714yescomplemented
141C2×C191—22no—
142C2×C191—81no—
143C2×C191C2×#12711yescharacteristic
144C2×C191C2×#13712yes—
145D191—81no—
146C191#315211yescharacteristic, complemented, Sylow
147#3152—1911nomaximal, Sylow
148C2×#137—1911no—
149C2×#137—1911no—
150C2×#137—1911no—
151C2×#137D19111yescharacteristic, complemented
152#532—1911no—
153C2×C4⋊Q8—1911no—
154#497—1912no—
155#497—1912no—
156#494—1912no—
157#492—1912no—
158C4×M16—1911no—
159C2×#41—1911no—
160C2×#41C2×D19111yescharacteristic
161C22×Q8—1911no—
162C22×Q8C2×D19111yescharacteristic
163#137—24no—
164#137—3824no—
165#137—3824no—
166#137—3824no—
167C2×Q16—1912no—
168C2×Q16—1912no—
169C2×Q16—1912no—
170C2×Q16C2×D19112yes—
171C2×SD16—1912no—
172C2×SD16—1912no—
173C2×SD16—1912no—
174C2×SD16C2×D19112yes—
175C2×M16—1911no—
176C2×M16C2×D19111yescharacteristic
177C4⋊Q8—3822no—
178C4⋊Q8—1912no—
179C4⋊Q8—1912no—
180C4⋊Q8—1911no—
181#127—1911no—
182#124—1911no—
183#124—1911no—
184#121—3822no—
185C4×D4—3822no—
186C2×C4⋊C4—3822no—
187C2×C42—1911no—
188#97—1912no—
189C4×C8—1912no—
190#41—22no—
191#41—22no—
192#41—3822no—
193#41—3822no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—3821no—
198C2×Q8—3822no—
199C2×Q8—3822no—
200C2×Q8—1911no—
201C2×Q8—1912no—
202C2×Q8C22×D19111yescharacteristic
203C2×Q8C22×D19112yes—
204C2×D4—21no—
205C2×D4—3821no—
206C2×D4—3822no—
207C2×D4—1911no—
208C2×D4C22×D19111yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—3821no—
212C22×C4—3821no—
213C22×C4—1912no—
214C22×C4C22×D19111yescharacteristic
215Q16—24no—
216Q16—3824no—
217Q16—3824no—
218Q16—3824no—
219SD16—24no—
220SD16—3824no—
221SD16—3824no—
222SD16—3824no—
223M16—1914no—
224M16C22⋊D19114yescomplemented
225C2×C8—1912no—
226C2×C8C22×D19112yes—
227C4⋊C4—3824no—
228C4⋊C4—3824no—
229C4⋊C4—3822no—
230C22⋊C4—3822no—
231C22⋊C4—3822no—
232C42—1912no—
233C42—1911no—
234C42—1911no—
235C23—21no—
236C23—3821no—
237C23D4×D19111yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—3822no—
244Q8—3821no—
245Q8—3822no—
246Q8—3821no—
247Q8—7642no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—3821no—
252D4—3821no—
253D4—7644no—
254D4—7642no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—3824no—
260C2×C4—3821no—
261C2×C4—3822no—
262C2×C4—1912no—
263C2×C4—1912no—
264C2×C4—7642no—
265C2×C4—7642no—
266C2×C4D4×D19112yes—
267C2×C4D4×D19111yescharacteristic
268C2×C4C2×C22⋊D19112yes—
269C2×C4C23×D19111yescharacteristic
270C8—1914no—
271C8C2×C22⋊D19114yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—7642no—
276C22—7641no—
277C22#2025931812yes—
278C22C2×D4×D19111yescharacteristic
279C4—41no—
280C4—42no—
281C4—3822no—
282C4—1914no—
283C4—7641no—
284C4—7642no—
285C4#2025931812yes—
286C4C2×D4×D19111yescharacteristic
287C4C22×C22⋊D19111yescharacteristic
288C2—22no—
289C2—81no—
290C2—15281no—
291C2C2×#2025931811yescharacteristic
292C2#137×D19112yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#137×C191C2
socleC22×C191C22×D4
prime radical#27133209C2
hypercenterC2×#137D191
hypocenterC191#3152
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#20259355C2semidirect
2. C2×#20259353C2semidirect
3. C2×#20259352C2semidirect
5. C2×#20259320C2semidirect
6. #27133056C2semidirect
7. #27133054C2semidirect
8. #27133041C2semidirect
9. #27133034C2semidirect
10. M16×Dic191C2semidirect
11. C2×#137×C191C2semidirect
62. #15690271D4semidirect
86. M16×C191D4semidirect
140. Dic191#137semidirect
146. C191#3152semidirect
151. C2×#137D191semidirect
224. M16C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593552
C2×#202593532
C2×#202593522
#271332092
C2×#202593202
#271330562
#271330542
#271330412
#271330342
M16×Dic1912
C2×#137×C1912
#3152191