Finite Group Databasebeta

← #37582776

Subgroups — #37582776

Order 24448.

384 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#27133143C211yesmaximal, characteristic, complemented
2#27132996C211yesmaximal, characteristic, complemented
3#27132974C211yesmaximal, characteristic, complemented
4#27132955C211yesmaximal, characteristic, complemented
5#27132940C211yesmaximal, characteristic, complemented
6#27132882C211yesmaximal, characteristic, complemented
7#27132875C211yesmaximal, characteristic, complemented
8#27132823C211yesmaximal, characteristic, complemented
9#27132806C211yesmaximal, characteristic
10#27132763C211yesmaximal, characteristic, complemented
11#27132761C211yesmaximal, characteristic, complemented
12C4×#15690277C211yesmaximal, characteristic, complemented
13C4×#15690272C211yesmaximal, characteristic, complemented
14#27132724C211yesmaximal, characteristic, complemented
15#542×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690277C2211yescharacteristic
18C2×#15690275C2211yescharacteristic
19C2×#15690274C2211yescharacteristic
20C2×#15690272C2211yescharacteristic
21C4×Dic382C2211yescharacteristic
22C4×Dic382C2211yescharacteristic
23C4×D764C2211yescharacteristic
24C4×D764C2211yescharacteristic
25(C22⋊D191)⋊C4—21no—
26(C22⋊D191)⋊C4—21no—
27#20259280—21no—
28C2×C4⋊Dic191C2211yescharacteristic
29C4⋊C4×D191—21no—
30#20259255C2211yescharacteristic
31#20259255C2211yescharacteristic
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34C4⋊(C191⋊C8)C2211yescharacteristic
35C4⋊(C191⋊C8)C2211yescharacteristic
36#20259246C2211yescharacteristic
37#20259246C2211yescharacteristic
38#20259245C2211yescharacteristic
39#20259245C2211yescharacteristic
40#20259243C2211yescharacteristic
41#20259243C2211yescharacteristic
42#20259242C2211yescharacteristic
43#20259242C2211yescharacteristic
44C22⋊(C191⋊C8)C2211yescharacteristic
45C22⋊(C191⋊C8)C2211yescharacteristic
46#20259233C2211yescharacteristic
47C4×C191⋊C8C2211yescharacteristic
48C4⋊Q8×C191C2211yescharacteristic
49#126×C191—21no—
50#124×C191—21no—
51#124×C191C2211yescharacteristic
52#123×C191—21no—
53C22⋊Q8×C191—21no—
54C22⋊Q8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56C4×Q8×C191C2211yescharacteristic
57C4×D4×C191C2211yescharacteristic
58#117×C191C2211yescharacteristic
59#15690287—22no—
60#15690287—22no—
61C2×Dic382C2311yescharacteristic
62C2×D764C2311yescharacteristic
63C2×C22⋊D191—21no—
64C22×Dic191—21no—
65C2×C4×D191—21no—
66C2×C4×D191—21no—
67C2×C4×D191—21no—
68#15690277—22no—
69#15690275—22no—
70#15690274—22no—
71#15690272—22no—
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C2×C191⋊C8C2311yescharacteristic
75C2×C191⋊C8C2311yescharacteristic
76C4⋊Dic191—21no—
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80Dic191⋊C4—21no—
81(C2×D191)⋊C4—21no—
82(C2×D191)⋊C4—21no—
83C4×Dic191—21no—
84C4×Dic191—21no—
85C2×Q8×C191—21no—
86C2×Q8×C191C2311yescharacteristic
87C2×D4×C191—21no—
88C2×D4×C191C2311yescharacteristic
89C22×C4×C191—21no—
90C22×C4×C191C2311yescharacteristic
91C4⋊C4×C191—21no—
92C4⋊C4×C191—21no—
93C4⋊C4×C191—21no—
94C4⋊C4×C191D411yescharacteristic
95C4⋊C4×C191D411yescharacteristic
96C4⋊C4×C191C2311yescharacteristic
97C4⋊C4×C191C2311yescharacteristic
98C22⋊C4×C191—21no—
99C22⋊C4×C191—21no—
100C22⋊C4×C191—21no—
101C22⋊C4×C191—21no—
102C22⋊C4×C191—21no—
103C22⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C42×C191—21no—
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109Dic382—21no—
110Dic382#4112yes—
111D764—21no—
112D764#4112yes—
113C22⋊D191—24no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—81no—
118C4×D191—24no—
119C4×D191—81no—
120C4×D191—81no—
121C191⋊C8—21no—
122C191⋊C8—21no—
123C191⋊C8—21no—
124C191⋊C8—21no—
125C23×C191—21no—
126C23×C191C2×D411yescharacteristic
127Q8×C191—21no—
128Q8×C191—21no—
129Q8×C191—81no—
130D4×C191—21no—
131D4×C191—21no—
132D4×C191—81no—
133C2×C4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—81no—
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191C2411yescharacteristic
145C22×C191—21no—
146C22×C191—21no—
147C22×C191—21no—
148C22×C191—41no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191C22×D411yescharacteristic
152C2×D191—22no—
153C2×D191—41no—
154C2×D191—41no—
155C4×C191—21no—
156C4×C191—21no—
157C4×C191—21no—
158C4×C191—21no—
159C4×C191—21no—
160C4×C191—41no—
161C4×C191—41no—
162C4×C191—41no—
163C4×C191C2×#4111yescharacteristic
164C4×C191C2×#4111yescharacteristic
165Dic191—22no—
166Dic191—41no—
167Dic191—41no—
168C2×C191—41no—
169C2×C191—81no—
170C2×C191#52511yescharacteristic
171C2×C191#57611yescharacteristic
172C2×C191#57811yescharacteristic
173D191—42no—
174C191#312411yescharacteristic, complemented, Sylow
175#3124—1911nomaximal, Sylow
176#542D19111yescharacteristic, complemented
177#520—1911no—
178#484—1911no—
179#480—1911no—
180#477—1911no—
181#474—1911no—
182#464—1911no—
183#463—1911no—
184#452—1911no—
185#449—1911no—
186#440—1911no—
187#440—1911no—
188C4×Q16—1911no—
189C4×D8—1911no—
190#433—1911no—
191C2×#41—1911no—
192C2×Q16—1911no—
193C2×SD16—1911no—
194C2×SD16—1911no—
195C2×D8—1911no—
196C4⋊Q8C2×D19111yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D19111yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D19111yescharacteristic
203#121C2×D19111yescharacteristic
204C4×Q8—1911no—
205C4×Q8—1911no—
206C4×Q8C2×D19111yescharacteristic
207C4×D4—3821no—
208C4×D4—3821no—
209C4×D4—1911no—
210C4×D4—1911no—
211C4×D4C2×D19111yescharacteristic
212#117—3821no—
213#117C2×D19111yescharacteristic
214C2×C4⋊C4—3821no—
215C2×C4⋊C4—1911no—
216#107—1911no—
217#107—1911no—
218#107—1911no—
219#107—1911no—
220C4⋊C8—1911no—
221C4⋊C8—1911no—
222#103—1911no—
223#103—1911no—
224#103—1911no—
225#103—1911no—
226#102—1911no—
227#102—1911no—
228#102—1911no—
229#102—1911no—
230C22⋊C8—1911no—
231C22⋊C8—1911no—
232#97—1911no—
233C4×C8—1911no—
234#41—3822no—
235#41—3822no—
236C2×Q8—21no—
237C2×Q8—1911no—
238C2×Q8C22×D19111yescharacteristic
239C2×D4—21no—
240C2×D4—3821no—
241C2×D4—1911no—
242C2×D4C22×D19111yescharacteristic
243C22×C4—21no—
244C22×C4—3821no—
245C22×C4—3821no—
246C22×C4—3821no—
247C22×C4—3821no—
248C22×C4C22×D19111yescharacteristic
249Q16—3822no—
250SD16—3822no—
251SD16—3822no—
252D8—3822no—
253C2×C8—1911no—
254C2×C8—1911no—
255C2×C8—1911no—
256C2×C8—1911no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—3821no—
261C4⋊C4—3821no—
262C4⋊C4—3821no—
263C4⋊C4—1911no—
264C4⋊C4—1911no—
265C4⋊C4C22⋊D19111yescharacteristic
266C4⋊C4C22⋊D19111yescharacteristic
267C4⋊C4C22×D19111yescharacteristic
268C4⋊C4C22×D19111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—3821no—
275C22⋊C4—3821no—
276C22⋊C4C22⋊D19111yescharacteristic
277C22⋊C4C22⋊D19111yescharacteristic
278C42—21no—
279C42—3821no—
280C42—3821no—
281C42C22×D19111yescharacteristic
282C42C22×D19111yescharacteristic
283C23—21no—
284C23—3821no—
285C23C2×C22⋊D19111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—3821no—
290Q8—1912no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—3824no—
295D4—3821no—
296D4—1912no—
297C2×C4—21no—
298C2×C4—21no—
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—15281no—
308C2×C4—15281no—
309C2×C4—15281no—
310C2×C4C2×C22⋊D19111yescharacteristic
311C2×C4C2×C22⋊D19111yescharacteristic
312C2×C4C2×C22⋊D19111yescharacteristic
313C2×C4C2×C22⋊D19111yescharacteristic
314C2×C4C2×C22⋊D19111yescharacteristic
315C2×C4C23×D19111yescharacteristic
316C8—3821no—
317C8—3821no—
318C8—3821no—
319C8—3821no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3822no—
327C22—7641no—
328C22—7641no—
329C22C22×C22⋊D19111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3822no—
339C4—7641no—
340C4—7641no—
341C4#41×D19111yescharacteristic
342C4#41×D19111yescharacteristic
343C2—41no—
344C2—81no—
345C2—7642no—
346C2#2713317011yescharacteristic
347C2#2713346611yescharacteristic
348C2#2713347811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#542×C191C2
socleC22×C191C22×D4
prime radical#27132806C2
hypercenter#542D191
hypocenterC191#3124
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #27133143C2semidirect
2. #27132996C2semidirect
3. #27132974C2semidirect
4. #27132955C2semidirect
5. #27132940C2semidirect
6. #27132882C2semidirect
7. #27132875C2semidirect
8. #27132823C2semidirect
10. #27132763C2semidirect
11. #27132761C2semidirect
12. C4×#15690277C2semidirect
13. C4×#15690272C2semidirect
14. #27132724C2semidirect
15. #542×C191C2semidirect
174. C191#3124semidirect
176. #542D191semidirect

Maximal subgroups

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

subgroupindex
#271331432
#271329962
#271329742
#271329552
#271329402
#271328822
#271328752
#271328232
#271328062
#271327632
#271327612
C4×#156902772
C4×#156902722
#271327242
#542×C1912
#3124191