Finite Group Databasebeta

← #37583144

Subgroups — #37583144

Order 24448.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133271C211yesmaximal, characteristic, complemented
2#27133264C211yesmaximal, characteristic
3#27133063C211yesmaximal, characteristic, complemented
4#27133034C211yesmaximal, characteristic, complemented
5#27133030C211yesmaximal, characteristic, complemented
6#27133026C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132908C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132889C211yesmaximal, characteristic, complemented
11#27132763C211yesmaximal, characteristic, complemented
12#27132761C211yesmaximal, characteristic, complemented
13C4×#15690276C211yesmaximal, characteristic, complemented
14#27132617C211yesmaximal, characteristic, complemented
15C4×SD16×C191C211yesmaximal, characteristic, complemented
16C2×#15690276C2211yescharacteristic
17C2×#15690275C2211yescharacteristic
18C2×#15690274C2211yescharacteristic
19C2×#15690270C2211yescharacteristic
20C2×C8×D191C2211yescharacteristic
21#20259320C2211yescharacteristic
22#20259318C2211yescharacteristic
23#20259317—21no—
24#20259316—21no—
25#20259314—21no—
26#20259313C2211yescharacteristic
27#20259313C2211yescharacteristic
28#20259312—21no—
29#20259305—21no—
30#20259304—21no—
31#20259302C2211yescharacteristic
32#20259298C2211yescharacteristic
33#20259297C2211yescharacteristic
34#20259296—21no—
35#20259295—21no—
36#20259293C2211yescharacteristic
37C4×Dic382C2211yescharacteristic
38C4×D764C2211yescharacteristic
39#20259279C2211yescharacteristic
40#20259255C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259254C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259242C2211yescharacteristic
49#20259233C2211yescharacteristic
50#20259232C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55#106×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C4×C8×C191C2211yescharacteristic
59C2×Dic382C2311yescharacteristic
60C2×D764—21no—
61C2×D764C2311yescharacteristic
62C2×C22⋊D191—21no—
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C4×D191—21no—
66C2×C4×D191C2311yescharacteristic
67#15690276—22no—
68#15690275—22no—
69#15690274—22no—
70#15690270—22no—
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C8×D191—22no—
74C4⋊Dic191—21no—
75C4⋊Dic191—21no—
76C4⋊Dic191—21no—
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4D411yescharacteristic
86Dic191⋊C4D411yescharacteristic
87C22⋊Dic191—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4D411yescharacteristic
93(C2×D191)⋊C4D411yescharacteristic
94C4×Dic191—21no—
95C4×Dic191C2311yescharacteristic
96C2×Q8×C191C2311yescharacteristic
97C2×D4×C191C2311yescharacteristic
98C22×C4×C191—21no—
99SD16×C191—22no—
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C22⋊C4×C191—21no—
106C42×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191C2×D411yescharacteristic
110Dic382—21no—
111Dic382—21no—
112D764—21no—
113D764—21no—
114D764—81no—
115C22⋊D191—81no—
116C22⋊D191—81no—
117C22⋊D191—81no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191C2×D411yescharacteristic
122C2×Dic191C2×D411yescharacteristic
123C2×Dic191C2×D411yescharacteristic
124C4×D191—21no—
125C4×D191—21no—
126C4×D191—81no—
127C191⋊C8—21no—
128C191⋊C8#4112yes—
129C23×C191—21no—
130Q8×C191—21no—
131Q8×C191—21no—
132D4×C191—21no—
133D4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—81no—
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2411yescharacteristic
141C8×C191—21no—
142C8×C191#4112yes—
143C22×C191—41no—
144C22×C191—41no—
145C22×C191—41no—
146C22×C191C22×D411yescharacteristic
147C2×D191—21no—
148C2×D191—21no—
149C2×D191—21no—
150C2×D191—41no—
151C2×D191—41no—
152C2×D191—41no—
153C4×C191—21no—
154C4×C191—21no—
155C4×C191—41no—
156C4×C191—41no—
157C4×C191—41no—
158C4×C191C2×#4111yescharacteristic
159C4×C191C2×#4111yescharacteristic
160Dic191—21no—
161Dic191—21no—
162Dic191—21no—
163Dic191—41no—
164Dic191—41no—
165Dic191—41no—
166C2×C191—81no—
167C2×C191#53211yescharacteristic
168C2×C191#57711yescharacteristic
169C2×C191#57711yescharacteristic
170D191—41no—
171D191—81no—
172C191#317411yescharacteristic, complemented, Sylow
173#3174—1911nomaximal, Sylow
174#541—1911no—
175#540—1911no—
176#499—1911no—
177#492—1911no—
178#491—1911no—
179#490—1911no—
180#468—1911no—
181#468—1911no—
182#465—1911no—
183#465—1911no—
184#440—1911no—
185#440—1911no—
186C4×SD16—1911no—
187C4×SD16D19111yescharacteristic, complemented
188#405—1911no—
189C2×SD16—1911no—
190C2×SD16—1911no—
191C2×SD16—1911no—
192C2×SD16C2×D19111yescharacteristic
193C2×M16—1911no—
194C22×C8—1911no—
195C4⋊Q8—1911no—
196#127—1911no—
197#126—3821no—
198#126—3821no—
199#125—3821no—
200#125—3821no—
201#125—1911no—
202#125—1911no—
203#123—3821no—
204#123—3821no—
205C22⋊Q8—1911no—
206C22⋊Q8—1911no—
207#121—3821no—
208#121—3821no—
209#121—1911no—
210#121—1911no—
211C4×Q8—1911no—
212C4×Q8C2×D19111yescharacteristic
213C4×D4—1911no—
214C4×D4C2×D19111yescharacteristic
215#117—1911no—
216#107—1911no—
217#107—1911no—
218#106—1911no—
219#106C2×D19111yescharacteristic
220#103—1911no—
221#103—1911no—
222#103—1911no—
223#103C2×D19111yescharacteristic
224#102—1911no—
225#102—1911no—
226#102—1911no—
227#102C2×D19111yescharacteristic
228#97—1911no—
229#97—1911no—
230C4×C8—1911no—
231C4×C8C2×D19111yescharacteristic
232C2×Q8—1911no—
233C2×Q8C22×D19111yescharacteristic
234C2×D4—3821no—
235C2×D4—3821no—
236C2×D4—3821no—
237C2×D4—3821no—
238C2×D4—1911no—
239C2×D4C22×D19111yescharacteristic
240C22×C4—21no—
241C22×C4—3821no—
242C22×C4—1911no—
243SD16—22no—
244SD16—3822no—
245SD16—3822no—
246SD16—3822no—
247M16—3822no—
248C2×C8—3822no—
249C2×C8—1911no—
250C2×C8—1911no—
251C2×C8C22×D19111yescharacteristic
252C2×C8C22×D19111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—3821no—
255C4⋊C4—3821no—
256C4⋊C4—3821no—
257C4⋊C4—3821no—
258C4⋊C4—3821no—
259C4⋊C4—3821no—
260C4⋊C4—3821no—
261C4⋊C4—3821no—
262C4⋊C4—3821no—
263C4⋊C4—1911no—
264C4⋊C4—1911no—
265C4⋊C4—1911no—
266C4⋊C4—1911no—
267C4⋊C4C22×D19111yescharacteristic
268C4⋊C4C22×D19111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C22⋊C4—1911no—
276C22⋊C4—1911no—
277C42—21no—
278C42—3821no—
279C42—1911no—
280C42C22×D19111yescharacteristic
281C23—21no—
282C23—3821no—
283C23—1911no—
284Q8—21no—
285Q8—21no—
286Q8—3821no—
287Q8—3821no—
288D4—21no—
289D4—21no—
290D4—3821no—
291D4—3821no—
292D4—15281no—
293D4—15281no—
294D4—15281no—
295D4—15281no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—3821no—
301C2×C4—3821no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—1911no—
306C2×C4—1911no—
307C2×C4—1911no—
308C2×C4—15281no—
309C2×C4D4×D19111yescharacteristic
310C2×C4D4×D19111yescharacteristic
311C2×C4C23×D19111yescharacteristic
312C8—21no—
313C8—3821no—
314C8—1912no—
315C8#1569028712yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—3821no—
320C22—3821no—
321C22—3821no—
322C22—7641no—
323C22—7641no—
324C22—7641no—
325C22C2×D4×D19111yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3821no—
332C4—3821no—
333C4—3821no—
334C4—7641no—
335C4—7641no—
336C4—7641no—
337C4#41×D19111yescharacteristic
338C4C2×#1569028711yescharacteristic
339C2—81no—
340C2—15281no—
341C2—7641no—
342C2#2713321011yescharacteristic
343C2#2713346911yescharacteristic
344C2#2713347011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC4×SD16×C191C2
socleC22×C191C22×D4
prime radical#27133264C2
hypercenterC4×SD16D191
hypocenterC191#3174
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #27133271C2semidirect
3. #27133063C2semidirect
4. #27133034C2semidirect
5. #27133030C2semidirect
6. #27133026C2semidirect
7. #27132912C2semidirect
8. #27132908C2semidirect
9. #27132893C2semidirect
10. #27132889C2semidirect
11. #27132763C2semidirect
12. #27132761C2semidirect
13. C4×#15690276C2semidirect
14. #27132617C2semidirect
15. C4×SD16×C191C2semidirect
172. C191#3174semidirect
187. C4×SD16D191semidirect

Maximal subgroups

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

subgroupindex
#271332712
#271332642
#271330632
#271330342
#271330302
#271330262
#271329122
#271329082
#271328932
#271328892
#271327632
#271327612
C4×#156902762
#271326172
C4×SD16×C1912
#3174191