Finite Group Databasebeta

← #37583452

Subgroups — #37583452

Order 24448.

438 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133212C211yesmaximal, characteristic, complemented
2#27133210C211yesmaximal, characteristic, complemented
3#27133038C211yesmaximal, characteristic, complemented
4#27133034C211yesmaximal, characteristic, complemented
5#27133012C211yesmaximal, characteristic, complemented
6#27133008C211yesmaximal, characteristic, complemented
7#27132879C211yesmaximal, characteristic, complemented
8#27132878C211yesmaximal, characteristic, complemented
9#27132875C211yesmaximal, characteristic, complemented
10#27132811C211yesmaximal, characteristic, complemented
11#27132809C211yesmaximal, characteristic, complemented
12#27132807C211yesmaximal, characteristic, complemented
13#27132805C211yesmaximal, characteristic, complemented
14#27132715C211yesmaximal, characteristic, complemented
15#463×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287—21no—
18C2×#15690286C2211yescharacteristic
19C2×#15690276C2211yescharacteristic
20C2×#15690275C2211yescharacteristic
21C2×#15690274C2211yescharacteristic
22C2×D1528C2211yescharacteristic
23C2×#15690272C2211yescharacteristic
24C2×#15690272C2211yescharacteristic
25#20259321C2211yescharacteristic
26#20259320C2211yescharacteristic
27#20259318C2211yescharacteristic
28#20259318C2211yescharacteristic
29#20259310C2211yescharacteristic
30#20259308—21no—
31#20259297C2211yescharacteristic
32#20259295—21no—
33#20259295—21no—
34#20259295—21no—
35#20259293C2211yescharacteristic
36C4×D764C2211yescharacteristic
37C4×C22⋊D191—21no—
38(C22⋊D191)⋊C4—21no—
39(C22⋊D191)⋊C4—21no—
40C42×D191C2211yescharacteristic
41C4⋊(C191⋊C8)C2211yescharacteristic
42#20259247C2211yescharacteristic
43#20259246C2211yescharacteristic
44#20259245C2211yescharacteristic
45#20259244C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259242C2211yescharacteristic
48(C2×D191)⋊C8C2211yescharacteristic
49(C2×D191)⋊C8C2211yescharacteristic
50C8×Dic191C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52C2×SD16×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54#124×C191C2211yescharacteristic
55C4×D4×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59#15690288—41no—
60#15690288—41no—
61#15690287—44no—
62#15690286—41no—
63#15690286—41no—
64C2×Dic382—21no—
65C2×Dic382C2311yescharacteristic
66C2×D764—21no—
67C2×D764—21no—
68C2×D764C2311yescharacteristic
69C2×D764C2311yescharacteristic
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C2×C22⋊D191—21no—
73C2×C22⋊D191—21no—
74C2×C22⋊D191—21no—
75C2×C22⋊D191—21no—
76C22×Dic191—21no—
77C2×C4×D191—21no—
78C2×C4×D191—21no—
79C2×C4×D191D411yescharacteristic
80C2×C4×D191D411yescharacteristic
81C2×C4×D191C2311yescharacteristic
82#15690276—41no—
83#15690275—41no—
84#15690274—41no—
85D1528—41no—
86#15690272—41no—
87#15690272—41no—
88C2×C191⋊C8C2311yescharacteristic
89C2×C191⋊C8C2311yescharacteristic
90C4⋊Dic191C2311yescharacteristic
91Dic191⋊C4—21no—
92Dic191⋊C4—21no—
93Dic191⋊C4—21no—
94C22⋊Dic191—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99C4×Dic191D411yescharacteristic
100C4×Dic191D411yescharacteristic
101C4×Dic191C2311yescharacteristic
102C2×Q8×C191C2311yescharacteristic
103C2×D4×C191C2311yescharacteristic
104C2×D4×C191C2311yescharacteristic
105C22×C4×C191—21no—
106SD16×C191—41no—
107D8×C191—41no—
108C2×C8×C191C2311yescharacteristic
109C2×C8×C191C2311yescharacteristic
110C4⋊C4×C191C2311yescharacteristic
111C22⋊C4×C191—21no—
112C22⋊C4×C191—21no—
113C22⋊C4×C191—21no—
114C42×C191C2311yescharacteristic
115C22×D191—21no—
116C22×D191—21no—
117C22×D191C2×D411yescharacteristic
118Dic382—21no—
119Dic382—21no—
120Dic382—42no—
121D764—21no—
122D764—21no—
123D764—21no—
124D764—21no—
125D764—42no—
126D764—42no—
127C22⋊D191—42no—
128C22⋊D191—42no—
129C22⋊D191—42no—
130C22⋊D191—42no—
131C22⋊D191—42no—
132C22⋊D191—42no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—42no—
136C2×Dic191C2×D411yescharacteristic
137C2×Dic191C2×D411yescharacteristic
138C2×Dic191C2×D411yescharacteristic
139C4×D191—21no—
140C4×D191—21no—
141C4×D191—22no—
142C4×D191—22no—
143C4×D191—42no—
144C4×D191—42no—
145C191⋊C8—21no—
146C191⋊C8—21no—
147C23×C191—21no—
148C23×C191—21no—
149Q8×C191—21no—
150Q8×C191—21no—
151D4×C191—21no—
152D4×C191—21no—
153D4×C191—21no—
154D4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—42no—
158C2×C4×C191C2×D411yescharacteristic
159C2×C4×C191C2×D411yescharacteristic
160C2×C4×C191C2411yescharacteristic
161C8×C191—21no—
162C8×C191—21no—
163C22×C191—41no—
164C22×C191—41no—
165C22×C191—41no—
166C22×C191—41no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191C22×D411yescharacteristic
170C2×D191—21no—
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—41no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191—41no—
178C2×D191—41no—
179C4×C191—21no—
180C4×C191—21no—
181C4×C191—41no—
182C4×C191—41no—
183C4×C191H(5,𝔽2)11yescharacteristic
184C4×C191H(5,𝔽2)11yescharacteristic
185Dic191—21no—
186Dic191—41no—
187Dic191—41no—
188Dic191#13512yes—
189Dic191AGL(1,ℤ/8)12yes—
190C2×C191—81no—
191C2×C191—81no—
192C2×C191#53511yescharacteristic
193C2×C191C2×#13511yescharacteristic
194C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
195D191—41no—
196D191—81no—
197D191—81no—
198C191#320711yescharacteristic, complemented, Sylow
199#3207—1911nomaximal, Sylow
200#532—1911no—
201#532—1911no—
202#493—1911no—
203#492—1911no—
204#487—1911no—
205#486—1911no—
206#463—1911no—
207#463—1911no—
208#463—1911no—
209#463D19111yescharacteristic, complemented
210#449—1911no—
211#449—1911no—
212#449—1911no—
213#449—1911no—
214#431—1911no—
215C2×#41—3821no—
216C2×#41—1911no—
217C2×#41—1911no—
218C2×SD16—1911no—
219C2×SD16—1911no—
220C2×SD16—1911no—
221C2×SD16C2×D19111yescharacteristic
222C2×D8—1911no—
223C2×D8—1911no—
224C2×D8—1911no—
225C2×D8C2×D19111yescharacteristic
226C4⋊Q8—1911no—
227C4⋊Q8—1911no—
228#127—1911no—
229#127—1911no—
230#124—3821no—
231#124—1911no—
232#124C2×D19111yescharacteristic
233#121—3821no—
234#121—3821no—
235#121—3821no—
236#121—1911no—
237#121—1911no—
238C4×D4—3821no—
239C4×D4—3821no—
240C4×D4—3821no—
241C4×D4—1911no—
242C4×D4C2×D19111yescharacteristic
243C2×C42—1911no—
244C4⋊C8—1911no—
245C4⋊C8C2×D19111yescharacteristic
246#103—1911no—
247#103—1911no—
248#103—1911no—
249#103C2×D19111yescharacteristic
250#102—1911no—
251#102—1911no—
252#102—1911no—
253#102C2×D19111yescharacteristic
254C22⋊C8—1911no—
255C22⋊C8—1911no—
256C4×C8—1911no—
257C4×C8—1911no—
258#41—7644no—
259#41—7641no—
260#41—7641no—
261#41—7641no—
262#41—7641no—
263C2×Q8—3821no—
264C2×Q8—1911no—
265C2×Q8C22×D19111yescharacteristic
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4—3821no—
271C2×D4—3821no—
272C2×D4—3821no—
273C2×D4—3821no—
274C2×D4—1911no—
275C2×D4—1911no—
276C2×D4C22×D19111yescharacteristic
277C2×D4C22×D19111yescharacteristic
278C22×C4—21no—
279C22×C4—3821no—
280C22×C4—3821no—
281C22×C4—3821no—
282C22×C4—1911no—
283C22×C4—1911no—
284C22×C4—1911no—
285SD16—41no—
286SD16—7641no—
287SD16—7641no—
288SD16—7641no—
289D8—41no—
290D8—7641no—
291D8—7641no—
292D8—7641no—
293C2×C8—1911no—
294C2×C8—1911no—
295C2×C8C22×D19111yescharacteristic
296C2×C8C22×D19111yescharacteristic
297C4⋊C4—3821no—
298C4⋊C4—3821no—
299C4⋊C4—3821no—
300C4⋊C4—1911no—
301C4⋊C4C22×D19111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—3821no—
306C22⋊C4—3821no—
307C22⋊C4—3821no—
308C22⋊C4—3821no—
309C22⋊C4—3821no—
310C42—1911no—
311C42—1911no—
312C42—1911no—
313C42C22×D19111yescharacteristic
314C23—21no—
315C23—21no—
316C23—3821no—
317C23—3821no—
318C23—1911no—
319Q8—21no—
320Q8—21no—
321Q8—3821no—
322Q8—3821no—
323Q8—7642no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—3821no—
329D4—3821no—
330D4—3821no—
331D4—3821no—
332D4—7642no—
333D4—7642no—
334D4—7642no—
335D4—7642no—
336D4—7642no—
337D4—7642no—
338D4—7642no—
339D4—7642no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3822no—
344C2×C4—3822no—
345C2×C4—3821no—
346C2×C4—3821no—
347C2×C4—3821no—
348C2×C4—3821no—
349C2×C4—1911no—
350C2×C4—1911no—
351C2×C4—1911no—
352C2×C4—7642no—
353C2×C4—7642no—
354C2×C4—7642no—
355C2×C4D4×D19111yescharacteristic
356C2×C4D4×D19111yescharacteristic
357C2×C4C23×D19111yescharacteristic
358C8—21no—
359C8—21no—
360C8—3821no—
361C8—3821no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3821no—
369C22—3821no—
370C22—3821no—
371C22—7641no—
372C22—7641no—
373C22—7641no—
374C22—7641no—
375C22—7641no—
376C22—7641no—
377C22C2×D4×D19111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—3821no—
383C4—1912no—
384C4—1912no—
385C4—7641no—
386C4—7641no—
387C4#2025936711yescharacteristic
388C4#2025936811yescharacteristic
389C2—81no—
390C2—81no—
391C2—15281no—
392C2—15281no—
393C2—7641no—
394C2#2713322911yescharacteristic
395C2#135×D19111yescharacteristic
396C2AGL(1,ℤ/8)×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#463×C191C2
socleC22×C191C22×D4
hypercenter#463D191
hypocenterC191#3207
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #27133212C2semidirect
2. #27133210C2semidirect
3. #27133038C2semidirect
4. #27133034C2semidirect
5. #27133012C2semidirect
6. #27133008C2semidirect
7. #27132879C2semidirect
8. #27132878C2semidirect
9. #27132875C2semidirect
10. #27132811C2semidirect
11. #27132809C2semidirect
12. #27132807C2semidirect
13. #27132805C2semidirect
14. #27132715C2semidirect
15. #463×C191C2semidirect
198. C191#3207semidirect
209. #463D191semidirect

Maximal subgroups

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

subgroupindex
#271332122
#271332102
#271330382
#271330342
#271330122
#271330082
#271328792
#271328782
#271328752
#271328112
#271328092
#271328072
#271328052
#271327152
#463×C1912
#3207191