Finite Group Databasebeta

← #37581973

Subgroups — #37581973

Order 24448.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259344C211yesmaximal, characteristic, complemented
2C2×#20259342C211yesmaximal, characteristic, complemented
3#27133209C211yesmaximal, characteristic, complemented
4#27133131C211yesmaximal, characteristic, complemented
5#27132888C211yesmaximal, characteristic, complemented
6#27132884C211yesmaximal, characteristic, complemented
7#27132881C211yesmaximal, characteristic, complemented
8#27132877C211yesmaximal, characteristic, complemented
9#27132872C211yesmaximal, characteristic, complemented
10#27132867C211yesmaximal, characteristic, complemented
11#27132862C211yesmaximal, characteristic, complemented
12#27132857C211yesmaximal, characteristic, complemented
13C2×Dic191⋊C8C211yesmaximal, characteristic, complemented
14#27132657C211yesmaximal, characteristic, complemented
15#416×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18#20259344—24no—
19#20259342—24no—
20C2×Dic764C2211yescharacteristic
21C2×#15690277C2211yescharacteristic
22C2×#15690276C2211yescharacteristic
23C2×#15690276C2211yescharacteristic
24C2×#15690275C2211yescharacteristic
25C2×#15690274C2211yescharacteristic
26C2×D1528C2211yescharacteristic
27C2×#15690272C2211yescharacteristic
28C22×C191⋊C8C2211yescharacteristic
29#20259320C2211yescharacteristic
30#20259318C2211yescharacteristic
31#20259311C2211yescharacteristic
32#20259309C2211yescharacteristic
33#20259294—21no—
34#20259294—21no—
35#20259287C2211yescharacteristic
36#20259287C2211yescharacteristic
37#20259284C2211yescharacteristic
38#20259284C2211yescharacteristic
39C4×C22⋊D191—21no—
40C4×C22⋊D191—21no—
41(C22⋊D191)⋊C4—21no—
42(C22⋊D191)⋊C4—21no—
43#20259279—21no—
44C2×C4×Dic191C2211yescharacteristic
45C42×D191—21no—
46Dic191⋊C8C2211yescharacteristic
47Dic191⋊C8C2211yescharacteristic
48Dic191⋊C8C2211yescharacteristic
49Dic191⋊C8C2211yescharacteristic
50#20259245C2211yescharacteristic
51#20259245C2211yescharacteristic
52#20259242C2211yescharacteristic
53#20259242C2211yescharacteristic
54C2×#41×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic
56#117×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58#103×C191C2211yescharacteristic
59#102×C191C2211yescharacteristic
60#102×C191C2211yescharacteristic
61#15690287—22no—
62#15690287—22no—
63#15690287—22no—
64#15690287D414yescomplemented
65C2×Dic382C2311yescharacteristic
66C2×Dic382C2311yescharacteristic
67C2×D764C2311yescharacteristic
68C2×D764C2311yescharacteristic
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191—21no—
72C2×C22⋊D191—21no—
73C22×Dic191D411yescharacteristic
74C22×Dic191D411yescharacteristic
75C2×C4×D191—21no—
76C2×C4×D191—21no—
77C2×C4×D191—21no—
78C2×C4×D191—21no—
79Dic764—22no—
80#15690277—22no—
81#15690276—22no—
82#15690276—22no—
83#15690275—22no—
84#15690274—22no—
85D1528—22no—
86#15690272—22no—
87C2×C191⋊C8—22no—
88C2×C191⋊C8C2311yescharacteristic
89C2×C191⋊C8C2311yescharacteristic
90Dic191⋊C4—21no—
91Dic191⋊C4—21no—
92Dic191⋊C4—21no—
93Dic191⋊C4—21no—
94C22⋊Dic191—21no—
95C22⋊Dic191—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99(C2×D191)⋊C4—21no—
100C4×Dic191—21no—
101C4×Dic191—21no—
102C4×Dic191D411yescharacteristic
103C4×Dic191D411yescharacteristic
104C4×Dic191C2311yescharacteristic
105C4×Dic191C2311yescharacteristic
106#41×C191—22no—
107#41×C191—22no—
108C2×Q8×C191C2311yescharacteristic
109C2×D4×C191—21no—
110C2×D4×C191C2311yescharacteristic
111C22×C4×C191—21no—
112C22×C4×C191C2311yescharacteristic
113C2×C8×C191—22no—
114C2×C8×C191C2311yescharacteristic
115C2×C8×C191C2311yescharacteristic
116C4⋊C4×C191C2311yescharacteristic
117C4⋊C4×C191C2311yescharacteristic
118C22⋊C4×C191—21no—
119C42×C191—21no—
120C22×D191—21no—
121C22×D191—21no—
122Dic382—21no—
123Dic382—21no—
124Dic382—21no—
125Dic382C2×D412yes—
126D764—21no—
127D764—21no—
128D764—21no—
129D764C2×D412yes—
130C22⋊D191—24no—
131C22⋊D191—42no—
132C22⋊D191—42no—
133C22⋊D191—42no—
134C2×Dic191—21no—
135C2×Dic191—22no—
136C2×Dic191—21no—
137C2×Dic191—41no—
138C2×Dic191C2×D411yescharacteristic
139C2×Dic191C2×D411yescharacteristic
140C2×Dic191C2×D411yescharacteristic
141C2×Dic191C2×D411yescharacteristic
142C4×D191—24no—
143C4×D191—42no—
144C4×D191—42no—
145C4×D191—42no—
146C191⋊C8—21no—
147C191⋊C8—21no—
148C23×C191—21no—
149C23×C191C2×D411yescharacteristic
150Q8×C191—21no—
151Q8×C191—21no—
152D4×C191—21no—
153D4×C191—21no—
154D4×C191—42no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—42no—
159C2×C4×C191C2×D412yes—
160C2×C4×C191C2×D411yescharacteristic
161C2×C4×C191#4112yes—
162C2×C4×C191C2411yescharacteristic
163C8×C191—21no—
164C8×C191—21no—
165C22×C191—21no—
166C22×C191—21no—
167C22×C191—41no—
168C22×C191—41no—
169C22×C191—41no—
170C22×C191#12112yes—
171C22×C191C22×D411yescharacteristic
172C2×D191—22no—
173C2×D191—41no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C2×D191—41no—
178C4×C191—41no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191#12112yes—
182C4×C191C22×D411yescharacteristic
183C4×C191C2×#4111yescharacteristic
184Dic191—22no—
185Dic191—21no—
186Dic191—21no—
187Dic191—21no—
188Dic191—41no—
189Dic191#13512yescomplemented
190C2×C191—22no—
191C2×C191—81no—
192C2×C191C2×#12111yescharacteristic
193C2×C191C2×#13511yescharacteristic
194C2×C191#57511yescharacteristic
195D191—42no—
196D191—81no—
197C191#303511yescharacteristic, complemented, Sylow
198#3035—1911nomaximal, Sylow
199C2×#135—1911no—
200C2×#135—1911no—
201#532—1911no—
202C4×#41—1911no—
203#464—1911no—
204#464—1911no—
205#463—1911no—
206#463—1911no—
207#462—1911no—
208#461—1911no—
209#460—1911no—
210#459—1911no—
211C2×C4⋊C8—1911no—
212#416—1911no—
213#416D19111yescharacteristic, complemented
214C2×#41—1911no—
215C2×#41—1911no—
216C2×#41C2×D19111yescharacteristic
217#135—3824no—
218#135—3824no—
219C2×Q16—1911no—
220C2×Q16—1911no—
221C2×SD16—1911no—
222C2×SD16—1911no—
223C2×SD16—1911no—
224C2×SD16—1911no—
225C2×D8—1911no—
226C2×D8—1911no—
227C22×C8—1911no—
228C22×C8C2×D19111yescharacteristic
229C4⋊Q8—1911no—
230#127—1911no—
231#124—1911no—
232#124—1911no—
233#121—3821no—
234#121—3821no—
235C4×Q8—1911no—
236C4×Q8—1911no—
237C4×D4—3821no—
238C4×D4—3821no—
239C4×D4—3821no—
240C4×D4—3821no—
241C4×D4—1911no—
242C4×D4—1911no—
243#117—3821no—
244#117C2×D19111yescharacteristic
245C2×C42—3821no—
246C2×C42—1911no—
247C4⋊C8—1911no—
248C4⋊C8—1911no—
249C4⋊C8—1911no—
250C4⋊C8—1911no—
251#103—1911no—
252#103—1911no—
253#103C2×D19111yescharacteristic
254#103C2×D19111yescharacteristic
255#102—1911no—
256#102—1911no—
257#102C2×D19111yescharacteristic
258#102C2×D19111yescharacteristic
259#41—22no—
260#41—22no—
261#41—3822no—
262#41—3822no—
263#41—3822no—
264#41—1914no—
265C2×Q8—1911no—
266C2×Q8—1911no—
267C2×Q8C22×D19111yescharacteristic
268C2×D4—21no—
269C2×D4—3821no—
270C2×D4—3821no—
271C2×D4—3821no—
272C2×D4—3821no—
273C2×D4—1911no—
274C2×D4—1911no—
275C2×D4C22×D19111yescharacteristic
276C22×C4—21no—
277C22×C4—3821no—
278C22×C4—3821no—
279C22×C4—3821no—
280C22×C4—3821no—
281C22×C4—1911no—
282C22×C4—1911no—
283C22×C4C22×D19111yescharacteristic
284Q16—3822no—
285Q16—3822no—
286SD16—3822no—
287SD16—3822no—
288SD16—3822no—
289SD16—3822no—
290D8—3822no—
291D8—3822no—
292C2×C8—22no—
293C2×C8—3822no—
294C2×C8—1911no—
295C2×C8—1911no—
296C2×C8C22×D19111yescharacteristic
297C2×C8C22×D19111yescharacteristic
298C4⋊C4—3821no—
299C4⋊C4—3821no—
300C4⋊C4—3821no—
301C4⋊C4—3821no—
302C4⋊C4C22×D19111yescharacteristic
303C4⋊C4C22×D19111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—3821no—
306C22⋊C4—3821no—
307C22⋊C4—3821no—
308C22⋊C4—3821no—
309C22⋊C4—3821no—
310C22⋊C4—3821no—
311C42—21no—
312C42—3821no—
313C42—3821no—
314C42—1911no—
315C42—1911no—
316C42—1911no—
317C42—1911no—
318C23—21no—
319C23—3821no—
320C23—3821no—
321C23D4×D19111yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—3821no—
325Q8—3821no—
326Q8—3821no—
327Q8—1912no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—3824no—
332D4—3821no—
333D4—3821no—
334D4—3821no—
335D4—1912no—
336D4—7642no—
337D4—7642no—
338D4—7642no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3821no—
344C2×C4—3822no—
345C2×C4—3824no—
346C2×C4—3821no—
347C2×C4—1911no—
348C2×C4—1911no—
349C2×C4—1911no—
350C2×C4—1911no—
351C2×C4—7642no—
352C2×C4—7642no—
353C2×C4—7641no—
354C2×C4—7642no—
355C2×C4D4×D19112yes—
356C2×C4D4×D19111yescharacteristic
357C2×C4#1569028712yes—
358C2×C4C23×D19111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3821no—
362C8—3821no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3822no—
369C22—7641no—
370C22—7641no—
371C22—7641no—
372C22—7641no—
373C22—7641no—
374C22#2025929512yes—
375C22C2×D4×D19111yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—3821no—
380C4—3821no—
381C4—3821no—
382C4—3822no—
383C4—1912no—
384C4—7641no—
385C4#2025929512yes—
386C4C2×D4×D19111yescharacteristic
387C4C2×#1569028711yescharacteristic
388C2—22no—
389C2—81no—
390C2—15281no—
391C2—7642no—
392C2C2×#2025929511yescharacteristic
393C2#135×D19111yescharacteristic
394C2#2713346011yescharacteristic
subgroupG/H
centerC2×C4D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#416×C191C2
socleC22×C191C22×D4
hypercenter#416D191
hypocenterC191#3035
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#20259344C2semidirect
2. C2×#20259342C2semidirect
3. #27133209C2semidirect
4. #27133131C2semidirect
5. #27132888C2semidirect
6. #27132884C2semidirect
7. #27132881C2semidirect
8. #27132877C2semidirect
9. #27132872C2semidirect
10. #27132867C2semidirect
11. #27132862C2semidirect
12. #27132857C2semidirect
13. C2×Dic191⋊C8C2semidirect
14. #27132657C2semidirect
15. #416×C191C2semidirect
64. #15690287D4semidirect
189. Dic191#135semidirect
197. C191#3035semidirect
213. #416D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593442
C2×#202593422
#271332092
#271331312
#271328882
#271328842
#271328812
#271328772
#271328722
#271328672
#271328622
#271328572
C2×Dic191⋊C82
#271326572
#416×C1912
#3035191