Finite Group Databasebeta

← #37581360

Subgroups — #37581360

Order 24448.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259351C211yesmaximal, characteristic
2#27133142C211yesmaximal, characteristic
3#27133139C211yesmaximal, characteristic, complemented
4#27132771C211yesmaximal, characteristic, complemented
5#27132767C211yesmaximal, characteristic, complemented
6#27132760C211yesmaximal, characteristic, complemented
7#27132757C211yesmaximal, characteristic, complemented
8C4×#15690277C211yesmaximal, characteristic, complemented
9SD16×Dic191C211yesmaximal, characteristic, complemented
10C4×#15690275C211yesmaximal, characteristic, complemented
11#27132704C211yesmaximal, characteristic, complemented
12#27132656C211yesmaximal, characteristic
13#103×D191C211yesmaximal, characteristic, complemented
14#27132620C211yesmaximal, characteristic, complemented
15#440×C191C211yesmaximal, characteristic, complemented
16C2×#15690286C2211yescharacteristic
17C2×Q8×D191C2211yescharacteristic
18#20259351C418yescomplemented
19C2×Dic764C2211yescharacteristic
20C2×#15690277C2211yescharacteristic
21C2×#15690275C2211yescharacteristic
22C2×#15690270C2211yescharacteristic
23C2×C8×D191C2211yescharacteristic
24Q8×Dic191C2211yescharacteristic
25C4×Dic382—21no—
26C4×Dic382C2211yescharacteristic
27C4×Dic382C2211yescharacteristic
28#20259287—21no—
29#20259287C2211yescharacteristic
30#20259287C2211yescharacteristic
31D4×Dic191C2211yescharacteristic
32C4×C22⋊D191—21no—
33(C22⋊D191)⋊C4—21no—
34#20259280—21no—
35#20259280C2211yescharacteristic
36#20259279—21no—
37#20259279C2211yescharacteristic
38#20259278—21no—
39C2×Dic191⋊C4—21no—
40C4⋊C4×D191C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259254C2211yescharacteristic
43#20259253C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259247C2211yescharacteristic
46#20259246C2211yescharacteristic
47#20259245C2211yescharacteristic
48#20259245C2211yescharacteristic
49#20259243C2211yescharacteristic
50#20259232C2211yescharacteristic
51C4×C191⋊C8C2211yescharacteristic
52C8×Dic191C2211yescharacteristic
53C2×SD16×C191C2211yescharacteristic
54C4×Q8×C191C2211yescharacteristic
55C4×D4×C191C2211yescharacteristic
56#107×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59#97×C191C2211yescharacteristic
60#15690286—22no—
61#15690286C2×C414yes—
62C2×Dic382—21no—
63C2×Dic382C2311yescharacteristic
64C2×Dic382C2311yescharacteristic
65Q8×D191—22no—
66Q8×D191C2×C414yescomplemented
67C2×C22⋊D191—21no—
68C22×Dic191—21no—
69C22×Dic191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72C2×C4×D191C2311yescharacteristic
73Dic764C2×C414yescomplemented
74#15690277C2×C414yescomplemented
75#15690275C2×C414yescomplemented
76#15690270C2×C414yescomplemented
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—22no—
80C4⋊Dic191—21no—
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4D411yescharacteristic
89Dic191⋊C4D411yescharacteristic
90C22⋊Dic191—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4D411yescharacteristic
93(C2×D191)⋊C4D411yescharacteristic
94C4×Dic191—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C4×Dic191—21no—
98C4×Dic191—21no—
99C4×Dic191—21no—
100C4×Dic191C2311yescharacteristic
101C2×Q8×C191C2311yescharacteristic
102C2×D4×C191C2311yescharacteristic
103C22×C4×C191—21no—
104SD16×C191C2×C414yescomplemented
105C2×C8×C191C2311yescharacteristic
106C2×C8×C191C2311yescharacteristic
107C4⋊C4×C191—21no—
108C4⋊C4×C191C2311yescharacteristic
109C4⋊C4×C191C2311yescharacteristic
110C22⋊C4×C191—21no—
111C42×C191—21no—
112C42×C191C2311yescharacteristic
113C22×D191C2×D411yescharacteristic
114Dic382—21no—
115Dic382—21no—
116Dic382—24no—
117Dic382C22×C412yes—
118Dic382C22×C412yes—
119C22⋊D191—24no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—24no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—81no—
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C2×Dic191C2×D411yescharacteristic
129C4×D191—24no—
130C4×D191—81no—
131C4×D191C22×C412yes—
132C4×D191#4112yes—
133C191⋊C8—21no—
134C191⋊C8C22×C412yes—
135C23×C191—21no—
136Q8×C191—21no—
137Q8×C191C22×C412yes—
138D4×C191—21no—
139D4×C191C22×C412yes—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—81no—
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191C22×C412yes—
149C22×C191—22no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191C22×D411yescharacteristic
153C2×D191—21no—
154C2×D191—21no—
155C2×D191C4×D412yes—
156C4×C191—22no—
157C4×C191—21no—
158C4×C191—21no—
159C4×C191—41no—
160C4×C191—41no—
161C4×C191C23×C411yescharacteristic
162C4×C191C2×#4111yescharacteristic
163Dic191—22no—
164Dic191—22no—
165Dic191—21no—
166Dic191—21no—
167Dic191—41no—
168Dic191—41no—
169Dic191C4×D412yes—
170C2×C191—42no—
171C2×C191C2×C4×D411yescharacteristic
172C2×C191#57711yescharacteristic
173C2×C191#57811yescharacteristic
174D191—22no—
175C191#294711yescharacteristic, complemented, Sylow
176#2947—1911nomaximal, Sylow
177C2×#137—1911no—
178#520—1911no—
179#519—1911no—
180#441—1911no—
181#441—1911no—
182#440—1911no—
183#440D19111yescharacteristic, complemented
184C4×Q16—1911no—
185C4×Q16—1911no—
186C4×SD16—1911no—
187C4×SD16—1911no—
188#428—1911no—
189#416—1911no—
190C2×#103—1911no—
191#405—1911no—
192C2×#41—1911no—
193C22×Q8—1911no—
194#137—1918no—
195C2×Q16—1911no—
196C2×Q16—1911no—
197C2×SD16—1911no—
198C2×SD16C2×D19111yescharacteristic
199C2×M16—1911no—
200C22×C8—1911no—
201C4×Q8—3821no—
202C4×Q8—3821no—
203C4×Q8—1911no—
204C4×Q8—1911no—
205C4×Q8—1911no—
206C4×Q8—1911no—
207C4×Q8—1911no—
208C4×Q8C2×D19111yescharacteristic
209C4×D4—3821no—
210C4×D4—3821no—
211C4×D4—1911no—
212C4×D4C2×D19111yescharacteristic
213#117—3821no—
214#117—3821no—
215#117—3821no—
216#117—1911no—
217#117—1911no—
218C2×C4⋊C4—3821no—
219C2×C4⋊C4—1911no—
220#107—1911no—
221#107C2×D19111yescharacteristic
222#106—1911no—
223#106—1911no—
224#103—1911no—
225#103—1911no—
226#103—1911no—
227#103—1911no—
228#103—1911no—
229#103C2×D19111yescharacteristic
230#102—1911no—
231#102C2×D19111yescharacteristic
232#97—1911no—
233#97C2×D19111yescharacteristic
234C4×C8—1911no—
235C4×C8—1911no—
236#41—3822no—
237#41—1914no—
238C2×Q8—3821no—
239C2×Q8—3822no—
240C2×Q8—1914no—
241C2×Q8—1911no—
242C2×Q8—1911no—
243C2×Q8C22×D19111yescharacteristic
244C2×D4—3821no—
245C2×D4C22×D19111yescharacteristic
246C22×C4—21no—
247C22×C4—3821no—
248C22×C4—3821no—
249C22×C4—3821no—
250C22×C4—3821no—
251C22×C4—1911no—
252Q16—1914no—
253Q16—1914no—
254SD16—1914no—
255SD16C4×D19114yescomplemented
256M16—1914no—
257C2×C8—3822no—
258C2×C8—1911no—
259C2×C8—1911no—
260C2×C8C22×D19111yescharacteristic
261C2×C8C22×D19111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3821no—
264C4⋊C4—3821no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—3821no—
268C4⋊C4—3821no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4—1911no—
272C4⋊C4—1911no—
273C4⋊C4C22×D19111yescharacteristic
274C4⋊C4C22×D19111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3821no—
277C22⋊C4—3821no—
278C22⋊C4—1911no—
279C22⋊C4—1911no—
280C42—21no—
281C42—3821no—
282C42—3821no—
283C42—3821no—
284C42—3821no—
285C42—3821no—
286C42—3821no—
287C42—1911no—
288C42C22×D19111yescharacteristic
289C23—21no—
290C23—1911no—
291Q8—21no—
292Q8—3824no—
293Q8—3821no—
294Q8—3821no—
295Q8—1912no—
296Q8—1912no—
297Q8C2×C4×D19112yes—
298D4—21no—
299D4—3824no—
300D4C2×C4×D19112yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—3824no—
306C2×C4—3821no—
307C2×C4—3821no—
308C2×C4—3824no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—1911no—
312C2×C4—1911no—
313C2×C4—1911no—
314C2×C4—1912no—
315C2×C4—1912no—
316C2×C4—15281no—
317C2×C4—15281no—
318C2×C4D4×D19111yescharacteristic
319C2×C4D4×D19111yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—21no—
322C8—3821no—
323C8—1912no—
324C8C2×C4×D19112yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—3821no—
329C22—3821no—
330C22—1912no—
331C22C2×D4×D19111yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—3821no—
338C4—3821no—
339C4—3822no—
340C4—3822no—
341C4—1912no—
342C4—7641no—
343C4—7641no—
344C4C22×C4×D19111yescharacteristic
345C4#41×D19111yescharacteristic
346C2—42no—
347C2—3822no—
348C2C4×D4×D19111yescharacteristic
349C2#2713347311yescharacteristic
350C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#440×C191C2
socleC22×C191C22×D4
prime radicalC2×#15690286C22
cosocleC2×C4×C191C24
hypercenter#440D191
hypocenterC191#2947
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #27133139C2semidirect
4. #27132771C2semidirect
5. #27132767C2semidirect
6. #27132760C2semidirect
7. #27132757C2semidirect
8. C4×#15690277C2semidirect
9. SD16×Dic191C2semidirect
10. C4×#15690275C2semidirect
11. #27132704C2semidirect
13. #103×D191C2semidirect
14. #27132620C2semidirect
15. #440×C191C2semidirect
18. #20259351C4semidirect
66. Q8×D191C2×C4semidirect
73. Dic764C2×C4semidirect
74. #15690277C2×C4semidirect
75. #15690275C2×C4semidirect
76. #15690270C2×C4semidirect
104. SD16×C191C2×C4semidirect
175. C191#2947semidirect
183. #440D191semidirect
255. SD16C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593512
#271331422
#271331392
#271327712
#271327672
#271327602
#271327572
C4×#156902772
SD16×Dic1912
C4×#156902752
#271327042
#271326562
#103×D1912
#271326202
#440×C1912
#2947191