Finite Group Databasebeta

← #37583235

Subgroups — #37583235

Order 24448.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133217C211yesmaximal, characteristic, complemented
2#27133210C211yesmaximal, characteristic
3#27133067C211yesmaximal, characteristic, complemented
4#27133034C211yesmaximal, characteristic, complemented
5#27133012C211yesmaximal, characteristic, complemented
6#27133008C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132910C211yesmaximal, characteristic, complemented
9#27132908C211yesmaximal, characteristic, complemented
10#27132906C211yesmaximal, characteristic, complemented
11#27132765C211yesmaximal, characteristic, complemented
12#27132763C211yesmaximal, characteristic, complemented
13#27132761C211yesmaximal, characteristic, complemented
14#27132615C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×#15690287—21no—
17C2×#15690276C2211yescharacteristic
18C2×#15690275C2211yescharacteristic
19C2×#15690274C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×#15690270C2211yescharacteristic
22#20259321C2211yescharacteristic
23#20259321C2211yescharacteristic
24#20259320C2211yescharacteristic
25#20259318C2211yescharacteristic
26#20259312—21no—
27#20259308—21no—
28#20259302C2211yescharacteristic
29#20259300—21no—
30#20259298C2211yescharacteristic
31#20259297C2211yescharacteristic
32#20259295—21no—
33#20259293C2211yescharacteristic
34C4×Dic382—21no—
35C4×Dic382C2211yescharacteristic
36C4×D764C2211yescharacteristic
37C4×C22⋊D191—21no—
38#20259279—21no—
39C42×D191C2211yescharacteristic
40#20259256C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259255C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259242C2211yescharacteristic
49#20259233C2211yescharacteristic
50C8×Dic191C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58#97×C191C2211yescharacteristic
59#15690287—44no—
60C2×Dic382—21no—
61C2×Dic382—21no—
62C2×Dic382C2311yescharacteristic
63C2×D764—21no—
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191D411yescharacteristic
70C2×C4×D191D411yescharacteristic
71C2×C4×D191C2311yescharacteristic
72#15690276—22no—
73#15690275—22no—
74#15690274—22no—
75#15690270—22no—
76#15690270—22no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C4⋊Dic191—21no—
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93C4×Dic191—21no—
94C4×Dic191D411yescharacteristic
95C4×Dic191D411yescharacteristic
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191C2311yescharacteristic
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100SD16×C191—22no—
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C22⋊C4×C191—21no—
107C42×C191—21no—
108C42×C191C2311yescharacteristic
109C22×D191—21no—
110C22×D191C2×D411yescharacteristic
111Dic382—21no—
112Dic382—21no—
113Dic382—42no—
114Dic382—42no—
115D764—21no—
116D764—21no—
117D764—42no—
118C22⋊D191—42no—
119C22⋊D191—42no—
120C22⋊D191—42no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C4×D191—21no—
128C4×D191—21no—
129C4×D191—22no—
130C4×D191—22no—
131C4×D191—42no—
132C191⋊C8—21no—
133C191⋊C8#4112yescomplemented
134C23×C191—21no—
135Q8×C191—21no—
136Q8×C191—21no—
137D4×C191—21no—
138D4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—42no—
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C8×C191—21no—
147C8×C191#4112yescomplemented
148C22×C191—41no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191C22×D411yescharacteristic
152C2×D191—21no—
153C2×D191—21no—
154C2×D191—21no—
155C2×D191—41no—
156C2×D191—41no—
157C2×D191—41no—
158C4×C191—21no—
159C4×C191—21no—
160C4×C191—41no—
161C4×C191—41no—
162C4×C191—41no—
163C4×C191C2×#4111yescharacteristic
164C4×C191C2×#4111yescharacteristic
165Dic191—21no—
166Dic191—41no—
167Dic191—41no—
168Dic191—41no—
169Dic191AGL(1,ℤ/8)12yes—
170Dic191#13712yes—
171C2×C191—81no—
172C2×C191#53211yescharacteristic
173C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C191C2×#13711yescharacteristic
175D191—41no—
176D191—81no—
177C191#318211yescharacteristic, complemented, Sylow
178#3182—1911nomaximal, Sylow
179#533—1911no—
180#532—1911no—
181#500—1911no—
182#492—1911no—
183#487—1911no—
184#486—1911no—
185#468—1911no—
186#468—1911no—
187#468—1911no—
188#468—1911no—
189#440—1911no—
190#440—1911no—
191#440—1911no—
192#440D19111yescharacteristic, complemented
193C4×M16—1911no—
194C2×#41—3821no—
195C2×SD16—1911no—
196C2×SD16—1911no—
197C2×SD16—1911no—
198C2×SD16C2×D19111yescharacteristic
199C2×M16—1911no—
200C2×M16—1911no—
201C4⋊Q8—1911no—
202C4⋊Q8—1911no—
203C4⋊Q8—1911no—
204#127—1911no—
205#125—3821no—
206#124—3821no—
207C22⋊Q8—3821no—
208C22⋊Q8—1911no—
209C22⋊Q8—1911no—
210#121—3821no—
211#121—1911no—
212#121—1911no—
213C4×Q8—3821no—
214C4×Q8—1911no—
215C4×Q8C2×D19111yescharacteristic
216C4×D4—3821no—
217C4×D4—1911no—
218C4×D4C2×D19111yescharacteristic
219#117—3821no—
220C2×C42—1911no—
221#107—1911no—
222#107—1911no—
223#107—1911no—
224#107C2×D19111yescharacteristic
225#103—1911no—
226#103—1911no—
227#103—1911no—
228#103C2×D19111yescharacteristic
229#102—1911no—
230#102—1911no—
231#102—1911no—
232#102C2×D19111yescharacteristic
233#97—1911no—
234#97C2×D19111yescharacteristic
235C4×C8—1911no—
236C4×C8—1911no—
237#41—7644no—
238C2×Q8—3821no—
239C2×Q8—3821no—
240C2×Q8—1911no—
241C2×Q8C22×D19111yescharacteristic
242C2×D4—3821no—
243C2×D4—3821no—
244C2×D4—3821no—
245C2×D4—3821no—
246C2×D4—1911no—
247C2×D4C22×D19111yescharacteristic
248C22×C4—21no—
249C22×C4—3821no—
250C22×C4—1911no—
251C22×C4—1911no—
252C22×C4—1911no—
253SD16—22no—
254SD16—3822no—
255SD16—3822no—
256SD16—3822no—
257M16—3822no—
258M16—3822no—
259C2×C8—1911no—
260C2×C8—1911no—
261C2×C8C22×D19111yescharacteristic
262C2×C8C22×D19111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—3821no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—3821no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—1911no—
272C4⋊C4—1911no—
273C4⋊C4C22×D19111yescharacteristic
274C4⋊C4C22×D19111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3821no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C42—21no—
282C42—3821no—
283C42—1911no—
284C42—1911no—
285C42—1911no—
286C42C22×D19111yescharacteristic
287C23—21no—
288C23—3821no—
289C23—1911no—
290Q8—21no—
291Q8—21no—
292Q8—3821no—
293Q8—3821no—
294Q8—7642no—
295Q8—7642no—
296D4—21no—
297D4—21no—
298D4—3821no—
299D4—3821no—
300D4—7642no—
301D4—7642no—
302D4—7642no—
303D4—7642no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3822no—
309C2×C4—3822no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—1911no—
316C2×C4—1911no—
317C2×C4—1911no—
318C2×C4—7642no—
319C2×C4D4×D19111yescharacteristic
320C2×C4D4×D19111yescharacteristic
321C2×C4C23×D19111yescharacteristic
322C8—21no—
323C8—3821no—
324C8—1912no—
325C8#1569028712yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—3821no—
330C22—3821no—
331C22—3821no—
332C22—7641no—
333C22—7641no—
334C22—7641no—
335C22C2×D4×D19111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3821no—
342C4—1912no—
343C4—1912no—
344C4—7641no—
345C4—7641no—
346C4—7641no—
347C4#41×D19111yescharacteristic
348C4C2×#1569028711yescharacteristic
349C2—81no—
350C2—15281no—
351C2—7641no—
352C2#2713321011yescharacteristic
353C2AGL(1,ℤ/8)×D19111yescharacteristic
354C2#137×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#440×C191C2
socleC22×C191C22×D4
prime radical#27133210C2
hypercenter#440D191
hypocenterC191#3182
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #27133217C2semidirect
3. #27133067C2semidirect
4. #27133034C2semidirect
5. #27133012C2semidirect
6. #27133008C2semidirect
7. #27132912C2semidirect
8. #27132910C2semidirect
9. #27132908C2semidirect
10. #27132906C2semidirect
11. #27132765C2semidirect
12. #27132763C2semidirect
13. #27132761C2semidirect
14. #27132615C2semidirect
15. #440×C191C2semidirect
133. C191⋊C8#41semidirect
147. C8×C191#41semidirect
177. C191#3182semidirect
192. #440D191semidirect
325. C8#15690287semidirect

Maximal subgroups

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

subgroupindex
#271332172
#271332102
#271330672
#271330342
#271330122
#271330082
#271329122
#271329102
#271329082
#271329062
#271327652
#271327632
#271327612
#271326152
#440×C1912
#3182191