Finite Group Databasebeta

← #37582808

Subgroups — #37582808

Order 24448.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133264C211yesmaximal, characteristic
2#27133139C211yesmaximal, characteristic, complemented
3#27132989C211yesmaximal, characteristic, complemented
4#27132986C211yesmaximal, characteristic, complemented
5#27132973C211yesmaximal, characteristic, complemented
6#27132968C211yesmaximal, characteristic, complemented
7#27132862C211yesmaximal, characteristic, complemented
8#27132861C211yesmaximal, characteristic, complemented
9#27132803C211yesmaximal, characteristic, complemented
10#27132800C211yesmaximal, characteristic, complemented
11#27132763C211yesmaximal, characteristic, complemented
12#27132761C211yesmaximal, characteristic, complemented
13C4×#15690276C211yesmaximal, characteristic, complemented
14#27132722C211yesmaximal, characteristic, complemented
15C4×SD16×C191C211yesmaximal, characteristic, complemented
16C2×Q8×D191C2211yescharacteristic
17C2×#15690276C2211yescharacteristic
18C2×#15690275C2211yescharacteristic
19C2×#15690274C2211yescharacteristic
20#20259318C2211yescharacteristic
21#20259313C2211yescharacteristic
22#20259305—21no—
23#20259304—21no—
24#20259297C2211yescharacteristic
25#20259296—21no—
26#20259295—21no—
27#20259293C2211yescharacteristic
28Q8×Dic191C2211yescharacteristic
29C4×Dic382—21no—
30C4×Dic382C2211yescharacteristic
31#20259287—21no—
32#20259287C2211yescharacteristic
33C4×D764C2211yescharacteristic
34#20259280—21no—
35#20259280C2211yescharacteristic
36#20259279—21no—
37#20259279C2211yescharacteristic
38#20259255C2211yescharacteristic
39#20259255C2211yescharacteristic
40#20259254C2211yescharacteristic
41Dic191⋊C8C2211yescharacteristic
42Dic191⋊C8C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259242C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51#20259233C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54C4×D4×C191C2211yescharacteristic
55#106×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C4×C8×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382C2311yescharacteristic
61Q8×D191—22no—
62Q8×D191—22no—
63C2×D764—21no—
64C2×D764C2311yescharacteristic
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191C2311yescharacteristic
71#15690276—22no—
72#15690275—22no—
73#15690274—22no—
74C2×C191⋊C8C2311yescharacteristic
75C2×C191⋊C8C2311yescharacteristic
76C4⋊Dic191—21no—
77C4⋊Dic191—21no—
78C4⋊Dic191C2311yescharacteristic
79C4⋊Dic191C2311yescharacteristic
80Dic191⋊C4—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4D411yescharacteristic
84Dic191⋊C4D411yescharacteristic
85C22⋊Dic191—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4D411yescharacteristic
90(C2×D191)⋊C4D411yescharacteristic
91C4×Dic191—21no—
92C4×Dic191—21no—
93C4×Dic191—21no—
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—24no—
111Dic382—21no—
112Dic382#4112yes—
113D764—21no—
114D764—21no—
115D764—81no—
116C22⋊D191—81no—
117C22⋊D191—81no—
118C22⋊D191—81no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191C2×D411yescharacteristic
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C4×D191—24no—
126C4×D191—21no—
127C4×D191—21no—
128C4×D191—81no—
129C191⋊C8—21no—
130C191⋊C8—21no—
131C23×C191—21no—
132Q8×C191—21no—
133Q8×C191#4112yes—
134D4×C191—21no—
135D4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—81no—
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2411yescharacteristic
143C8×C191—21no—
144C8×C191—21no—
145C22×C191—41no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191C22×D411yescharacteristic
149C2×D191—21no—
150C2×D191—21no—
151C2×D191—21no—
152C2×D191—41no—
153C2×D191—41no—
154C2×D191—41no—
155C4×C191—22no—
156C4×C191—21no—
157C4×C191—21no—
158C4×C191—41no—
159C4×C191—41no—
160C4×C191C2×#4111yescharacteristic
161C4×C191C2×#4111yescharacteristic
162Dic191—22no—
163Dic191—21no—
164Dic191—21no—
165Dic191—21no—
166Dic191—41no—
167Dic191—41no—
168C2×C191—81no—
169C2×C191#52511yescharacteristic
170C2×C191#57711yescharacteristic
171C2×C191#57711yescharacteristic
172D191—41no—
173D191—81no—
174C191#312611yescharacteristic, complemented, Sylow
175#3126—1911nomaximal, Sylow
176#540—1911no—
177#519—1911no—
178#482—1911no—
179#482—1911no—
180#479—1911no—
181#479—1911no—
182#460—1911no—
183#460—1911no—
184#448—1911no—
185#448—1911no—
186#440—1911no—
187#440—1911no—
188C4×SD16—1911no—
189C4×SD16D19111yescharacteristic, complemented
190#433—1911no—
191C22×Q8—1911no—
192C2×SD16—1911no—
193C2×SD16—1911no—
194C2×SD16—1911no—
195C2×SD16C2×D19111yescharacteristic
196#127—1911no—
197#125—1911no—
198#123—3821no—
199#123—3821no—
200#121—3821no—
201#121—3821no—
202#121—1911no—
203#121—1911no—
204C4×Q8—3821no—
205C4×Q8—3821no—
206C4×Q8—1911no—
207C4×Q8—1911no—
208C4×Q8—1911no—
209C4×Q8C2×D19111yescharacteristic
210C4×D4—1911no—
211C4×D4C2×D19111yescharacteristic
212#117—3821no—
213#117—3821no—
214#117—1911no—
215#117—1911no—
216#107—1911no—
217#107—1911no—
218#106—1911no—
219#106C2×D19111yescharacteristic
220C4⋊C8—1911no—
221C4⋊C8—1911no—
222#103—1911no—
223#103—1911no—
224#103—1911no—
225#103C2×D19111yescharacteristic
226#102—1911no—
227#102—1911no—
228#102—1911no—
229#102C2×D19111yescharacteristic
230C22⋊C8—1911no—
231C22⋊C8—1911no—
232#97—1911no—
233C4×C8C2×D19111yescharacteristic
234C2×Q8—3821no—
235C2×Q8—3822no—
236C2×Q8—3822no—
237C2×Q8—1911no—
238C2×Q8C22×D19111yescharacteristic
239C2×D4—3821no—
240C2×D4—3821no—
241C2×D4—3821no—
242C2×D4—3821no—
243C2×D4—1911no—
244C2×D4C22×D19111yescharacteristic
245C22×C4—21no—
246C22×C4—3821no—
247C22×C4—3821no—
248C22×C4—1911no—
249SD16—22no—
250SD16—3822no—
251SD16—3822no—
252SD16—3822no—
253C2×C8—1911no—
254C2×C8—1911no—
255C2×C8C22×D19111yescharacteristic
256C2×C8C22×D19111yescharacteristic
257C4⋊C4—21no—
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—1911no—
275C22⋊C4—1911no—
276C42—21no—
277C42—3821no—
278C42—3821no—
279C42—3821no—
280C42—3821no—
281C42—1911no—
282C42C22×D19111yescharacteristic
283C23—21no—
284C23—3821no—
285C23—1911no—
286Q8—21no—
287Q8—3824no—
288Q8—3821no—
289Q8—1912no—
290Q8#1569028712yes—
291D4—21no—
292D4—21no—
293D4—3821no—
294D4—3821no—
295D4—15281no—
296D4—15281no—
297D4—15281no—
298D4—15281no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3824no—
304C2×C4—3821no—
305C2×C4—3821no—
306C2×C4—3821no—
307C2×C4—3821no—
308C2×C4—3821no—
309C2×C4—1911no—
310C2×C4—1911no—
311C2×C4—1911no—
312C2×C4—15281no—
313C2×C4D4×D19111yescharacteristic
314C2×C4D4×D19111yescharacteristic
315C2×C4C23×D19111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3821no—
319C8—3821no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—3821no—
324C22—3821no—
325C22—3821no—
326C22—7641no—
327C22—7641no—
328C22—7641no—
329C22C2×D4×D19111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—3821no—
336C4—3821no—
337C4—3822no—
338C4—3821no—
339C4—7641no—
340C4—7641no—
341C4#41×D19111yescharacteristic
342C4C2×#1569028711yescharacteristic
343C2—81no—
344C2—15281no—
345C2—7641no—
346C2#2713317211yescharacteristic
347C2#2713346911yescharacteristic
348C2#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#3126
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
2. #27133139C2semidirect
3. #27132989C2semidirect
4. #27132986C2semidirect
5. #27132973C2semidirect
6. #27132968C2semidirect
7. #27132862C2semidirect
8. #27132861C2semidirect
9. #27132803C2semidirect
10. #27132800C2semidirect
11. #27132763C2semidirect
12. #27132761C2semidirect
13. C4×#15690276C2semidirect
14. #27132722C2semidirect
15. C4×SD16×C191C2semidirect
174. C191#3126semidirect
189. C4×SD16D191semidirect

Maximal subgroups

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

subgroupindex
#271332642
#271331392
#271329892
#271329862
#271329732
#271329682
#271328622
#271328612
#271328032
#271328002
#271327632
#271327612
C4×#156902762
#271327222
C4×SD16×C1912
#3126191