Finite Group Databasebeta

← #37582640

Subgroups — #37582640

Order 24448.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133210C211yesmaximal, characteristic
2C4×Q8×D191C211yesmaximal, characteristic, complemented
3#27132978C211yesmaximal, characteristic, complemented
4#27132975C211yesmaximal, characteristic, complemented
5#27132957C211yesmaximal, characteristic, complemented
6#27132956C211yesmaximal, characteristic, complemented
7#27132862C211yesmaximal, characteristic, complemented
8#27132861C211yesmaximal, characteristic, complemented
9#27132803C211yesmaximal, characteristic, complemented
10#27132800C211yesmaximal, characteristic, complemented
11#27132765C211yesmaximal, characteristic, complemented
12#27132763C211yesmaximal, characteristic, complemented
13#27132761C211yesmaximal, characteristic, complemented
14#27132718C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×#15690287—21no—
17C2×Q8×D191C2211yescharacteristic
18C2×#15690276C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×#15690274C2211yescharacteristic
21#20259321C2211yescharacteristic
22#20259318C2211yescharacteristic
23#20259308—21no—
24#20259297C2211yescharacteristic
25#20259295—21no—
26#20259293C2211yescharacteristic
27Q8×Dic191C2211yescharacteristic
28C4×Dic382—21no—
29C4×Dic382C2211yescharacteristic
30#20259287—21no—
31#20259287C2211yescharacteristic
32C4×D764C2211yescharacteristic
33C4×C22⋊D191—21no—
34C4⋊C4×D191—21no—
35C4⋊C4×D191C2211yescharacteristic
36C42×D191—21no—
37C42×D191C2211yescharacteristic
38#20259256C2211yescharacteristic
39#20259255C2211yescharacteristic
40#20259255C2211yescharacteristic
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#107×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58#97×C191C2211yescharacteristic
59#15690287—44no—
60C2×Dic382—21no—
61C2×Dic382—21no—
62C2×Dic382C2311yescharacteristic
63Q8×D191—22no—
64Q8×D191—22no—
65C2×D764—21no—
66C2×D764C2311yescharacteristic
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191D411yescharacteristic
74C2×C4×D191D411yescharacteristic
75C2×C4×D191C2311yescharacteristic
76#15690276—22no—
77#15690275—22no—
78#15690274—22no—
79C2×C191⋊C8C2311yescharacteristic
80C2×C191⋊C8C2311yescharacteristic
81C4⋊Dic191—21no—
82C4⋊Dic191C2311yescharacteristic
83C4⋊Dic191C2311yescharacteristic
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—
91C4×Dic191—21no—
92C4×Dic191—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—24no—
112Dic382—21no—
113Dic382—42no—
114Dic382#4112yescomplemented
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—24no—
128C4×D191—22no—
129C4×D191—21no—
130C4×D191—21no—
131C4×D191—22no—
132C4×D191—42no—
133C4×D191—42no—
134C191⋊C8—21no—
135C191⋊C8—21no—
136C23×C191—21no—
137Q8×C191—21no—
138Q8×C191#4112yescomplemented
139D4×C191—21no—
140D4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—42no—
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2×D411yescharacteristic
147C2×C4×C191C2411yescharacteristic
148C8×C191—21no—
149C8×C191—21no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191C22×D411yescharacteristic
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C2×D191AGL(1,ℤ/8)12yes—
160C4×C191—22no—
161C4×C191—21no—
162C4×C191—21no—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191C2×#4111yescharacteristic
166C4×C191C2×#4111yescharacteristic
167Dic191—22no—
168Dic191—21no—
169Dic191—21no—
170Dic191—41no—
171Dic191—41no—
172Dic191#13712yes—
173C2×C191—81no—
174C2×C191#52511yescharacteristic
175C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C191C2×#13711yescharacteristic
177D191—22no—
178D191—81no—
179C191#311211yescharacteristic, complemented, Sylow
180#3112—1911nomaximal, Sylow
181#532—1911no—
182C2×C4×Q8—1911no—
183#480—1911no—
184#480—1911no—
185#477—1911no—
186#477—1911no—
187#460—1911no—
188#460—1911no—
189#448—1911no—
190#448—1911no—
191#440—1911no—
192#440—1911no—
193#440—1911no—
194#440D19111yescharacteristic, complemented
195#432—1911no—
196C2×#41—3821no—
197C22×Q8—1911no—
198C2×SD16—1911no—
199C2×SD16—1911no—
200C2×SD16—1911no—
201C2×SD16C2×D19111yescharacteristic
202C4⋊Q8—1911no—
203#127—1911no—
204#124—3821no—
205#121—3821no—
206#121—1911no—
207#121—1911no—
208C4×Q8—3821no—
209C4×Q8—3821no—
210C4×Q8—1911no—
211C4×Q8—1911no—
212C4×Q8—1911no—
213C4×Q8C2×D19111yescharacteristic
214C4×D4—3821no—
215C4×D4—1911no—
216C4×D4C2×D19111yescharacteristic
217C2×C4⋊C4—3821no—
218C2×C4⋊C4—1911no—
219C2×C42—3821no—
220C2×C42—1911no—
221#107—1911no—
222#107—1911no—
223#107—1911no—
224#107C2×D19111yescharacteristic
225C4⋊C8—1911no—
226C4⋊C8—1911no—
227#103—1911no—
228#103—1911no—
229#103—1911no—
230#103C2×D19111yescharacteristic
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#102C2×D19111yescharacteristic
235C22⋊C8—1911no—
236C22⋊C8—1911no—
237#97—1911no—
238#97C2×D19111yescharacteristic
239#41—7644no—
240C2×Q8—3821no—
241C2×Q8—3821no—
242C2×Q8—3822no—
243C2×Q8—3822no—
244C2×Q8—1911no—
245C2×Q8C22×D19111yescharacteristic
246C2×D4—3821no—
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4—3821no—
250C2×D4—1911no—
251C2×D4C22×D19111yescharacteristic
252C22×C4—21no—
253C22×C4—3821no—
254C22×C4—3821no—
255C22×C4—3821no—
256C22×C4—1911no—
257C22×C4—1911no—
258C22×C4—1911no—
259SD16—22no—
260SD16—3822no—
261SD16—3822no—
262SD16—3822no—
263C2×C8—1911no—
264C2×C8—1911no—
265C2×C8C22×D19111yescharacteristic
266C2×C8C22×D19111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—3821no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—1911no—
274C4⋊C4—1911no—
275C4⋊C4C22×D19111yescharacteristic
276C4⋊C4C22×D19111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C42—21no—
282C42—3821no—
283C42—3821no—
284C42—3821no—
285C42—1911no—
286C42—1911no—
287C42—1911no—
288C42C22×D19111yescharacteristic
289C23—21no—
290C23—3821no—
291C23—1911no—
292Q8—21no—
293Q8—3824no—
294Q8—3821no—
295Q8—1912no—
296Q8—7642no—
297Q8#1569028712yescomplemented
298D4—21no—
299D4—21no—
300D4—3821no—
301D4—3821no—
302D4—7642no—
303D4—7642no—
304D4—7642no—
305D4—7642no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3824no—
311C2×C4—3822no—
312C2×C4—3822no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—3821no—
318C2×C4—1911no—
319C2×C4—1911no—
320C2×C4—1911no—
321C2×C4—7642no—
322C2×C4—7642no—
323C2×C4D4×D19111yescharacteristic
324C2×C4D4×D19111yescharacteristic
325C2×C4C23×D19111yescharacteristic
326C8—21no—
327C8—21no—
328C8—3821no—
329C8—3821no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3821no—
334C22—3821no—
335C22—1912no—
336C22—7641no—
337C22—7641no—
338C22—7641no—
339C22C2×D4×D19111yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—3821no—
346C4—3822no—
347C4—3821no—
348C4—1912no—
349C4—7641no—
350C4—7641no—
351C4#41×D19111yescharacteristic
352C4C2×#1569028711yescharacteristic
353C2—81no—
354C2—3822no—
355C2—15281no—
356C2#2713317211yescharacteristic
357C2AGL(1,ℤ/8)×D19111yescharacteristic
358C2#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#3112
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
2. C4×Q8×D191C2semidirect
3. #27132978C2semidirect
4. #27132975C2semidirect
5. #27132957C2semidirect
6. #27132956C2semidirect
7. #27132862C2semidirect
8. #27132861C2semidirect
9. #27132803C2semidirect
10. #27132800C2semidirect
11. #27132765C2semidirect
12. #27132763C2semidirect
13. #27132761C2semidirect
14. #27132718C2semidirect
15. #440×C191C2semidirect
114. Dic382#41semidirect
138. Q8×C191#41semidirect
179. C191#3112semidirect
194. #440D191semidirect
297. Q8#15690287semidirect

Maximal subgroups

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

subgroupindex
#271332102
C4×Q8×D1912
#271329782
#271329752
#271329572
#271329562
#271328622
#271328612
#271328032
#271328002
#271327652
#271327632
#271327612
#271327182
#440×C1912
#3112191