Finite Group Databasebeta

← #37581990

Subgroups — #37581990

Order 24448.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259354C211yesmaximal, characteristic, complemented
2C2×#20259351C211yesmaximal, characteristic, complemented
3#27133212C211yesmaximal, characteristic
4C4×Q8×D191C211yesmaximal, characteristic, complemented
5#27132886C211yesmaximal, characteristic, complemented
6#27132885C211yesmaximal, characteristic, complemented
7#27132882C211yesmaximal, characteristic, complemented
8#27132872C211yesmaximal, characteristic, complemented
9#27132871C211yesmaximal, characteristic, complemented
10#27132862C211yesmaximal, characteristic, complemented
11#27132861C211yesmaximal, characteristic, complemented
12#27132685C211yesmaximal, characteristic, complemented
13#27132663C211yesmaximal, characteristic, complemented
14#27132661C211yesmaximal, characteristic, complemented
15#464×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C2×Q8×D191C2211yescharacteristic
19#20259354—24no—
20#20259351—24no—
21C2×Dic764C2211yescharacteristic
22C2×#15690277C2211yescharacteristic
23C2×#15690277C2211yescharacteristic
24C2×#15690276C2211yescharacteristic
25C2×#15690275C2211yescharacteristic
26C2×#15690274C2211yescharacteristic
27C2×#15690270C2211yescharacteristic
28C2×#15690270C2211yescharacteristic
29#20259320C2211yescharacteristic
30#20259318C2211yescharacteristic
31#20259310C2211yescharacteristic
32#20259295—21no—
33#20259295—21no—
34Q8×Dic191C2211yescharacteristic
35C4×Dic382—21no—
36C4×Dic382C2211yescharacteristic
37#20259287—21no—
38#20259287C2211yescharacteristic
39(C22⋊D191)⋊C4—21no—
40(C22⋊D191)⋊C4—21no—
41C4⋊C4×D191—21no—
42C4⋊C4×D191C2211yescharacteristic
43C42×D191—21no—
44C42×D191C2211yescharacteristic
45C4⋊(C191⋊C8)C2211yescharacteristic
46Dic191⋊C8C2211yescharacteristic
47Dic191⋊C8C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259246C2211yescharacteristic
50#20259245C2211yescharacteristic
51#20259244C2211yescharacteristic
52#20259243C2211yescharacteristic
53#20259242C2211yescharacteristic
54C2×Q16×C191C2211yescharacteristic
55C2×SD16×C191C2211yescharacteristic
56#124×C191C2211yescharacteristic
57C4×Q8×C191C2211yescharacteristic
58C4⋊C8×C191C2211yescharacteristic
59#103×C191C2211yescharacteristic
60#102×C191C2211yescharacteristic
61#15690288—22no—
62#15690288—22no—
63#15690286—22no—
64#15690286—22no—
65C2×Dic382—21no—
66C2×Dic382C2311yescharacteristic
67C2×Dic382C2311yescharacteristic
68Q8×D191—22no—
69Q8×D191D414yescomplemented
70C2×D764—21no—
71C2×D764C2311yescharacteristic
72C2×C22⋊D191—21no—
73C2×C22⋊D191—21no—
74C2×C22⋊D191—21no—
75C22×Dic191—21no—
76C2×C4×D191—21no—
77C2×C4×D191—21no—
78C2×C4×D191—21no—
79C2×C4×D191D411yescharacteristic
80C2×C4×D191D411yescharacteristic
81C2×C4×D191C2311yescharacteristic
82Dic764—22no—
83#15690277—22no—
84#15690277—22no—
85#15690276—22no—
86#15690275—22no—
87#15690274—22no—
88#15690270—22no—
89#15690270—22no—
90C2×C191⋊C8C2311yescharacteristic
91C2×C191⋊C8C2311yescharacteristic
92C4⋊Dic191—21no—
93C4⋊Dic191C2311yescharacteristic
94Dic191⋊C4—21no—
95Dic191⋊C4—21no—
96Dic191⋊C4—21no—
97Dic191⋊C4—21no—
98Dic191⋊C4—21no—
99(C2×D191)⋊C4—21no—
100(C2×D191)⋊C4—21no—
101C4×Dic191—21no—
102C4×Dic191—21no—
103C4×Dic191—21no—
104C4×Dic191D411yescharacteristic
105C4×Dic191D411yescharacteristic
106C4×Dic191C2311yescharacteristic
107C2×Q8×C191C2311yescharacteristic
108C2×Q8×C191C2311yescharacteristic
109C2×D4×C191C2311yescharacteristic
110Q16×C191—22no—
111SD16×C191—22no—
112C2×C8×C191C2311yescharacteristic
113C2×C8×C191C2311yescharacteristic
114C4⋊C4×C191—21no—
115C4⋊C4×C191C2311yescharacteristic
116C22⋊C4×C191—21no—
117C22⋊C4×C191—21no—
118C42×C191—21no—
119C42×C191C2311yescharacteristic
120C22×D191—21no—
121C22×D191C2×D411yescharacteristic
122Dic382—21no—
123Dic382—24no—
124Dic382—21no—
125Dic382—21no—
126Dic382C2×D412yes—
127D764—21no—
128D764—21no—
129D764—42no—
130C22⋊D191—42no—
131C22⋊D191—42no—
132C22⋊D191—42no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—42no—
137C2×Dic191C2×D411yescharacteristic
138C2×Dic191C2×D411yescharacteristic
139C2×Dic191C2×D411yescharacteristic
140C4×D191—24no—
141C4×D191—22no—
142C4×D191—41no—
143C4×D191—42no—
144C4×D191—42no—
145C4×D191C2×D412yes—
146C4×D191#4112yes—
147C191⋊C8—21no—
148C191⋊C8—21no—
149C23×C191—21no—
150Q8×C191—21no—
151Q8×C191—21no—
152Q8×C191—21no—
153Q8×C191C2×D412yes—
154D4×C191—21no—
155D4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191C2×D411yescharacteristic
160C2×C4×C191C2×D411yescharacteristic
161C2×C4×C191C2411yescharacteristic
162C8×C191—21no—
163C8×C191—21no—
164C22×C191—41no—
165C22×C191—41no—
166C22×C191—41no—
167C22×C191C22×D411yescharacteristic
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—41no—
171C2×D191—41no—
172C2×D191—41no—
173C2×D191#12112yes—
174C4×C191—22no—
175C4×C191—21no—
176C4×C191—21no—
177C4×C191—41no—
178C4×C191—41no—
179C4×C191C22×D411yescharacteristic
180C4×C191C2×#4111yescharacteristic
181Dic191—22no—
182Dic191—21no—
183Dic191—41no—
184Dic191—41no—
185Dic191#12112yes—
186Dic191#13712yescomplemented
187C2×C191—81no—
188C2×C191C2×#12111yescharacteristic
189C2×C191C2×#13711yescharacteristic
190C2×C191#57511yescharacteristic
191D191—22no—
192D191—81no—
193C191#303711yescharacteristic, complemented, Sylow
194#3037—1911nomaximal, Sylow
195C2×#137—1911no—
196C2×#137—1911no—
197#532—1911no—
198C2×C4×Q8—1911no—
199#464—1911no—
200#464—1911no—
201#464—1911no—
202#464D19111yescharacteristic, complemented
203#462—1911no—
204#462—1911no—
205#460—1911no—
206#460—1911no—
207#423—1911no—
208#417—1911no—
209#417—1911no—
210C2×#41—1911no—
211C2×#41—1911no—
212C22×Q8—1911no—
213#137—3824no—
214#137—3824no—
215C2×Q16—1911no—
216C2×Q16—1911no—
217C2×Q16—1911no—
218C2×Q16C2×D19111yescharacteristic
219C2×SD16—1911no—
220C2×SD16—1911no—
221C2×SD16—1911no—
222C2×SD16C2×D19111yescharacteristic
223C2×M16—1911no—
224C2×M16—1911no—
225C4⋊Q8—1911no—
226#127—1911no—
227#124—1911no—
228#124C2×D19111yescharacteristic
229#121—3821no—
230#121—3821no—
231C4×Q8—3821no—
232C4×Q8—3821no—
233C4×Q8—1911no—
234C4×Q8—1911no—
235C4×Q8—1911no—
236C4×Q8C2×D19111yescharacteristic
237C4×D4—3821no—
238C4×D4—3821no—
239C2×C4⋊C4—3821no—
240C2×C4⋊C4—1911no—
241C2×C42—3821no—
242C2×C42—1911no—
243C4⋊C8—1911no—
244C4⋊C8—1911no—
245C4⋊C8—1911no—
246C4⋊C8C2×D19111yescharacteristic
247#103—1911no—
248#103—1911no—
249#103—1911no—
250#103C2×D19111yescharacteristic
251#102—1911no—
252#102—1911no—
253#102—1911no—
254#102C2×D19111yescharacteristic
255#41—3822no—
256#41—3822no—
257#41—3822no—
258#41—3822no—
259C2×Q8—3821no—
260C2×Q8—3822no—
261C2×Q8—1914no—
262C2×Q8—1911no—
263C2×Q8—1911no—
264C2×Q8C22×D19111yescharacteristic
265C2×Q8C22×D19111yescharacteristic
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4—1911no—
271C2×D4C22×D19111yescharacteristic
272C22×C4—3821no—
273C22×C4—3821no—
274C22×C4—3821no—
275C22×C4—3821no—
276C22×C4—1911no—
277C22×C4—1911no—
278C22×C4—1911no—
279Q16—22no—
280Q16—3822no—
281Q16—3822no—
282Q16—3822no—
283SD16—22no—
284SD16—3822no—
285SD16—3822no—
286SD16—3822no—
287M16—3822no—
288M16—3822no—
289C2×C8—1911no—
290C2×C8—1911no—
291C2×C8C22×D19111yescharacteristic
292C2×C8C22×D19111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—3821no—
295C4⋊C4—3821no—
296C4⋊C4—3821no—
297C4⋊C4—3821no—
298C4⋊C4—3821no—
299C4⋊C4—3821no—
300C4⋊C4—1911no—
301C4⋊C4C22×D19111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—3821no—
305C22⋊C4—3821no—
306C42—21no—
307C42—3821no—
308C42—3821no—
309C42—3821no—
310C42—1911no—
311C42—1911no—
312C42—1911no—
313C42C22×D19111yescharacteristic
314C23—21no—
315C23—3821no—
316C23—1911no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—3824no—
321Q8—3821no—
322Q8—3821no—
323Q8—3821no—
324Q8—1912no—
325Q8D4×D19112yes—
326D4—21no—
327D4—21no—
328D4—3821no—
329D4—3821no—
330D4—7642no—
331D4—7642no—
332D4—7642no—
333D4—7642no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—3824no—
338C2×C4—3822no—
339C2×C4—3821no—
340C2×C4—3821no—
341C2×C4—3821no—
342C2×C4—1911no—
343C2×C4—1911no—
344C2×C4—1911no—
345C2×C4—1912no—
346C2×C4—1912no—
347C2×C4—7641no—
348C2×C4—7642no—
349C2×C4—7642no—
350C2×C4—7642no—
351C2×C4D4×D19111yescharacteristic
352C2×C4D4×D19111yescharacteristic
353C2×C4C23×D19111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3821no—
357C8—3821no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3821no—
362C22—3821no—
363C22—1912no—
364C22—7641no—
365C22—7641no—
366C22—7641no—
367C22C2×D4×D19111yescharacteristic
368C4—21no—
369C4—21no—
370C4—22no—
371C4—41no—
372C4—41no—
373C4—3821no—
374C4—3822no—
375C4—1912no—
376C4—1912no—
377C4—7641no—
378C4—7641no—
379C4C2×D4×D19111yescharacteristic
380C4#41×D19111yescharacteristic
381C2—81no—
382C2—3822no—
383C2—15281no—
384C2#121×D19111yescharacteristic
385C2#137×D19111yescharacteristic
386C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#464×C191C2
socleC22×C191C22×D4
prime radical#27133212C2
hypercenter#464D191
hypocenterC191#3037
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#20259354C2semidirect
2. C2×#20259351C2semidirect
4. C4×Q8×D191C2semidirect
5. #27132886C2semidirect
6. #27132885C2semidirect
7. #27132882C2semidirect
8. #27132872C2semidirect
9. #27132871C2semidirect
10. #27132862C2semidirect
11. #27132861C2semidirect
12. #27132685C2semidirect
13. #27132663C2semidirect
14. #27132661C2semidirect
15. #464×C191C2semidirect
69. Q8×D191D4semidirect
186. Dic191#137semidirect
193. C191#3037semidirect
202. #464D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593542
C2×#202593512
#271332122
C4×Q8×D1912
#271328862
#271328852
#271328822
#271328722
#271328712
#271328622
#271328612
#271326852
#271326632
#271326612
#464×C1912
#3037191