Finite Group Databasebeta

← #37583451

Subgroups — #37583451

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#27133209C211yesmaximal, characteristic, complemented
2#27133208C211yesmaximal, characteristic, complemented
3#27133038C211yesmaximal, characteristic, complemented
4#27133034C211yesmaximal, characteristic, complemented
5#27133012C211yesmaximal, characteristic, complemented
6#27133008C211yesmaximal, characteristic, complemented
7#27132881C211yesmaximal, characteristic, complemented
8#27132880C211yesmaximal, characteristic, complemented
9#27132877C211yesmaximal, characteristic, complemented
10#27132876C211yesmaximal, characteristic, complemented
11#27132810C211yesmaximal, characteristic, complemented
12#27132808C211yesmaximal, characteristic, complemented
13#27132806C211yesmaximal, characteristic, complemented
14#27132713C211yesmaximal, characteristic, complemented
15#449×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690286—21no—
18C2×#15690276C2211yescharacteristic
19C2×#15690275C2211yescharacteristic
20C2×#15690274C2211yescharacteristic
21C2×D1528C2211yescharacteristic
22C2×#15690272C2211yescharacteristic
23C2×#15690272C2211yescharacteristic
24#20259321C2211yescharacteristic
25#20259320C2211yescharacteristic
26#20259318C2211yescharacteristic
27#20259318C2211yescharacteristic
28#20259311C2211yescharacteristic
29#20259309C2211yescharacteristic
30#20259308—21no—
31#20259296C2211yescharacteristic
32#20259294—21no—
33#20259294—21no—
34#20259294—21no—
35D4×Dic191C2211yescharacteristic
36#20259284C2211yescharacteristic
37C4×C22⋊D191—21no—
38C4×C22⋊D191—21no—
39(C22⋊D191)⋊C4—21no—
40C2×C4×Dic191C2211yescharacteristic
41Dic191⋊C8C2211yescharacteristic
42Dic191⋊C8C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50C8×Dic191C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic
53C2×SD16×C191C2211yescharacteristic
54C2×D8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—41no—
60#15690287—41no—
61#15690286—44no—
62C2×Dic382—21no—
63C2×Dic382C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×D764C2311yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C22×Dic191—21no—
73C22×Dic191D411yescharacteristic
74C22×Dic191D411yescharacteristic
75C2×C4×D191—21no—
76C2×C4×D191—21no—
77#15690276—41no—
78#15690275—41no—
79#15690274—41no—
80D1528—41no—
81#15690272—41no—
82#15690272—41no—
83C2×C191⋊C8C2311yescharacteristic
84C2×C191⋊C8C2311yescharacteristic
85C4⋊Dic191C2311yescharacteristic
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4—21no—
89C22⋊Dic191—21no—
90C22⋊Dic191—21no—
91C22⋊Dic191—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96C4×Dic191D411yescharacteristic
97C4×Dic191D411yescharacteristic
98C4×Dic191C2311yescharacteristic
99C4×Dic191C2311yescharacteristic
100#41×C191—41no—
101#41×C191—41no—
102C2×Q8×C191C2311yescharacteristic
103C2×D4×C191—21no—
104C2×D4×C191—21no—
105C2×D4×C191C2311yescharacteristic
106C2×D4×C191C2311yescharacteristic
107C22×C4×C191—21no—
108C22×C4×C191C2311yescharacteristic
109SD16×C191—41no—
110D8×C191—41no—
111C2×C8×C191C2311yescharacteristic
112C2×C8×C191C2311yescharacteristic
113C4⋊C4×C191C2311yescharacteristic
114C22⋊C4×C191—21no—
115C22×D191—21no—
116C22×D191—21no—
117Dic382—21no—
118Dic382—21no—
119Dic382—42no—
120D764—21no—
121D764—21no—
122D764—21no—
123D764—21no—
124C22⋊D191—42no—
125C22⋊D191—42no—
126C22⋊D191—42no—
127C22⋊D191—42no—
128C22⋊D191—42no—
129C22⋊D191—42no—
130C2×Dic191—22no—
131C2×Dic191—22no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—42no—
135C2×Dic191C2×D411yescharacteristic
136C2×Dic191C2×D411yescharacteristic
137C2×Dic191C2×D411yescharacteristic
138C2×Dic191C2×D411yescharacteristic
139C4×D191—42no—
140C4×D191—42no—
141C191⋊C8—21no—
142C191⋊C8—21no—
143C23×C191—21no—
144C23×C191—21no—
145C23×C191C2×D411yescharacteristic
146Q8×C191—21no—
147Q8×C191—21no—
148D4×C191—21no—
149D4×C191—21no—
150D4×C191—21no—
151D4×C191—21no—
152D4×C191—42no—
153D4×C191—42no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—42no—
159C2×C4×C191C2×D411yescharacteristic
160C2×C4×C191C2411yescharacteristic
161C8×C191—21no—
162C8×C191—21no—
163C22×C191—21no—
164C22×C191—21no—
165C22×C191—21no—
166C22×C191—41no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191—41no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191C22×D411yescharacteristic
173C2×D191—41no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191—41no—
178C2×D191—41no—
179C4×C191—21no—
180C4×C191—41no—
181C4×C191—41no—
182C4×C191H(5,𝔽2)11yescharacteristic
183C4×C191H(5,𝔽2)11yescharacteristic
184Dic191—21no—
185Dic191—21no—
186Dic191—41no—
187Dic191—41no—
188Dic191#13512yes—
189Dic191AGL(1,ℤ/8)12yes—
190C2×C191—41no—
191C2×C191—81no—
192C2×C191—81no—
193C2×C191#53511yescharacteristic
194C2×C191C2×#13511yescharacteristic
195C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
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#463—1911no—
210#449—1911no—
211#449—1911no—
212#449—1911no—
213#449D19111yescharacteristic, complemented
214#431—1911no—
215C2×#41—3821no—
216C2×#41—1911no—
217C2×#41C2×D19111yescharacteristic
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#124—1911no—
233#121—3821no—
234#121—3821no—
235#121—3821no—
236#121—1911no—
237#121C2×D19111yescharacteristic
238C4×D4—3821no—
239C4×D4—3821no—
240C4×D4—3821no—
241C4×D4—1911no—
242C4×D4—1911no—
243C2×C42—1911no—
244C4⋊C8—1911no—
245C4⋊C8—1911no—
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⋊C8C2×D19111yescharacteristic
256C4×C8—1911no—
257C4×C8—1911no—
258#41—41no—
259#41—41no—
260#41—7641no—
261#41—7641no—
262#41—7644no—
263C2×Q8—3821no—
264C2×Q8—1911no—
265C2×Q8C22×D19111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
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×C4C22×D19111yescharacteristic
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—3821no—
304C22⋊C4—3821no—
305C22⋊C4—3821no—
306C22⋊C4—3821no—
307C22⋊C4—3821no—
308C22⋊C4—3821no—
309C22⋊C4—3821no—
310C42—1911no—
311C42—1911no—
312C42—1911no—
313C42—1911no—
314C23—21no—
315C23—21no—
316C23—3821no—
317C23—3821no—
318C23D4×D19111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—3821no—
322Q8—3821no—
323Q8—7642no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—3821no—
331D4—3821no—
332D4—3821no—
333D4—3821no—
334D4—7642no—
335D4—7642no—
336D4—7642no—
337D4—7642no—
338D4—7642no—
339D4—7642no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—3822no—
346C2×C4—3822no—
347C2×C4—3821no—
348C2×C4—3821no—
349C2×C4—1911no—
350C2×C4—1911no—
351C2×C4—1911no—
352C2×C4—1911no—
353C2×C4—7642no—
354C2×C4—7642no—
355C2×C4—7642no—
356C2×C4D4×D19111yescharacteristic
357C2×C4C23×D19111yescharacteristic
358C8—21no—
359C8—21no—
360C8—3821no—
361C8—3821no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—7641no—
372C22—7641no—
373C22—7641no—
374C22—7641no—
375C22—7641no—
376C22—7641no—
377C22C2×D4×D19111yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—3821no—
382C4—3821no—
383C4—1912no—
384C4—1912no—
385C4—7641no—
386C4—7641no—
387C4#2025936711yescharacteristic
388C4#2025936711yescharacteristic
389C2—41no—
390C2—81no—
391C2—81no—
392C2—15281no—
393C2—15281no—
394C2#2713322811yescharacteristic
395C2#135×D19111yescharacteristic
396C2AGL(1,ℤ/8)×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#449×C191C2
socleC22×C191C22×D4
hypercenter#449D191
hypocenterC191#3207
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #27133209C2semidirect
2. #27133208C2semidirect
3. #27133038C2semidirect
4. #27133034C2semidirect
5. #27133012C2semidirect
6. #27133008C2semidirect
7. #27132881C2semidirect
8. #27132880C2semidirect
9. #27132877C2semidirect
10. #27132876C2semidirect
11. #27132810C2semidirect
12. #27132808C2semidirect
13. #27132806C2semidirect
14. #27132713C2semidirect
15. #449×C191C2semidirect
198. C191#3207semidirect
213. #449D191semidirect

Maximal subgroups

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

subgroupindex
#271332092
#271332082
#271330382
#271330342
#271330122
#271330082
#271328812
#271328802
#271328772
#271328762
#271328102
#271328082
#271328062
#271327132
#449×C1912
#3207191