Finite Group Databasebeta

← #37582073

Subgroups — #37582073

Order 24448.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259354C211yesmaximal, characteristic, complemented
2C2×#20259343C211yesmaximal, characteristic
3#27133233C211yesmaximal, characteristic, complemented
4#27133145C211yesmaximal, characteristic, complemented
5#27132883C211yesmaximal, characteristic, complemented
6#27132877C211yesmaximal, characteristic, complemented
7#27132875C211yesmaximal, characteristic, complemented
8#27132873C211yesmaximal, characteristic, complemented
9#27132871C211yesmaximal, characteristic, complemented
10#27132869C211yesmaximal, characteristic, complemented
11#27132867C211yesmaximal, characteristic, complemented
12#27132688C211yesmaximal, characteristic, complemented
13#27132661C211yesmaximal, characteristic, complemented
14#103×D191C211yesmaximal, characteristic, complemented
15#464×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C2×Q8×D191C2211yescharacteristic
19#20259354—24no—
20#20259343—24no—
21C2×#15690277C2211yescharacteristic
22C2×#15690277C2211yescharacteristic
23C2×#15690276C2211yescharacteristic
24C2×#15690276C2211yescharacteristic
25C2×#15690274C2211yescharacteristic
26C2×#15690272C2211yescharacteristic
27C2×#15690270C2211yescharacteristic
28C2×C8×D191C2211yescharacteristic
29#20259322C2211yescharacteristic
30#20259320C2211yescharacteristic
31#20259309C2211yescharacteristic
32#20259304—21no—
33#20259304—21no—
34#20259299—21no—
35#20259299—21no—
36Q8×Dic191C2211yescharacteristic
37C4×D764—21no—
38C4×D764C2211yescharacteristic
39#20259284—21no—
40#20259284C2211yescharacteristic
41#20259279—21no—
42#20259279C2211yescharacteristic
43C4⋊C4×D191—21no—
44C4⋊C4×D191C2211yescharacteristic
45C4⋊(C191⋊C8)C2211yescharacteristic
46Dic191⋊C8C2211yescharacteristic
47Dic191⋊C8C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259247C2211yescharacteristic
50#20259246C2211yescharacteristic
51#20259245C2211yescharacteristic
52#20259245C2211yescharacteristic
53#20259243C2211yescharacteristic
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#15690288D414yes—
63#15690286—22no—
64#15690286—22no—
65C2×Dic382—21no—
66C2×Dic382C2311yescharacteristic
67C2×Dic382C2311yescharacteristic
68Q8×D191—22no—
69Q8×D191—22no—
70C2×D764—21no—
71C2×D764C2311yescharacteristic
72C2×C22⋊D191—21no—
73C22×Dic191—21no—
74C2×C4×D191—21no—
75C2×C4×D191—21no—
76C2×C4×D191—21no—
77C2×C4×D191—21no—
78C2×C4×D191—21no—
79C2×C4×D191C2311yescharacteristic
80#15690277—22no—
81#15690277—22no—
82#15690276—22no—
83#15690276—22no—
84#15690274—22no—
85#15690272—22no—
86#15690270—22no—
87C2×C191⋊C8C2311yescharacteristic
88C2×C191⋊C8C2311yescharacteristic
89C8×D191—22no—
90C4⋊Dic191—21no—
91C4⋊Dic191—21no—
92C4⋊Dic191—21no—
93C4⋊Dic191C2311yescharacteristic
94Dic191⋊C4—21no—
95Dic191⋊C4—21no—
96Dic191⋊C4—21no—
97Dic191⋊C4D411yescharacteristic
98Dic191⋊C4D411yescharacteristic
99C22⋊Dic191—21no—
100C22⋊Dic191—21no—
101(C2×D191)⋊C4—21no—
102(C2×D191)⋊C4—21no—
103(C2×D191)⋊C4D411yescharacteristic
104(C2×D191)⋊C4D411yescharacteristic
105C4×Dic191—21no—
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—21no—
124Dic382—21no—
125Dic382—21no—
126Dic382—42no—
127D764—24no—
128D764—21no—
129D764C2×D412yes—
130C22⋊D191—42no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—42no—
135C2×Dic191C2×D411yescharacteristic
136C2×Dic191C2×D411yescharacteristic
137C2×Dic191C2×D411yescharacteristic
138C4×D191—24no—
139C4×D191—42no—
140C4×D191—81no—
141C4×D191—81no—
142C4×D191—81no—
143C4×D191C2×D412yes—
144C4×D191#4112yes—
145C191⋊C8—21no—
146C191⋊C8—21no—
147C23×C191—21no—
148Q8×C191—21no—
149Q8×C191—21no—
150Q8×C191—21no—
151Q8×C191C2×D412yes—
152D4×C191—21no—
153D4×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191C2×D411yescharacteristic
158C2×C4×C191C2×D411yescharacteristic
159C2×C4×C191C2411yescharacteristic
160C8×C191—21no—
161C8×C191—21no—
162C22×C191—41no—
163C22×C191—41no—
164C22×C191—41no—
165C22×C191C22×D411yescharacteristic
166C2×D191—21no—
167C2×D191—21no—
168C2×D191—22no—
169C2×D191—41no—
170C2×D191—41no—
171C2×D191#12112yes—
172C4×C191—22no—
173C4×C191—21no—
174C4×C191—21no—
175C4×C191—41no—
176C4×C191—41no—
177C4×C191C22×D411yescharacteristic
178C4×C191C2×#4111yescharacteristic
179Dic191—21no—
180Dic191—21no—
181Dic191—41no—
182Dic191—41no—
183Dic191—41no—
184Dic191#12112yes—
185C2×C191—81no—
186C2×C191C2×#12111yescharacteristic
187C2×C191#57711yescharacteristic
188C2×C191#57811yescharacteristic
189D191—22no—
190D191—42no—
191C191#304611yescharacteristic, complemented, Sylow
192#3046—1911nomaximal, Sylow
193C2×#137—1911no—
194C2×#135—1911no—
195#536—1911no—
196#520—1911no—
197#464—1911no—
198#464D19111yescharacteristic, complemented
199#463—1911no—
200#463—1911no—
201#462—1911no—
202#462—1911no—
203#461—1911no—
204#461—1911no—
205#424—1911no—
206#417—1911no—
207C2×#103—1911no—
208C2×#41—1911no—
209C2×#41—1911no—
210C22×Q8—1911no—
211#137—3824no—
212#135—3824no—
213C2×Q16—1911no—
214C2×Q16—1911no—
215C2×Q16C2×D19111yescharacteristic
216C2×SD16—1911no—
217C2×SD16—1911no—
218C2×SD16—1911no—
219C2×SD16C2×D19111yescharacteristic
220C2×D8—1911no—
221C2×M16—1911no—
222C22×C8—1911no—
223C4⋊Q8—1911no—
224C4⋊Q8—1911no—
225#124—1911no—
226#124C2×D19111yescharacteristic
227#123—3821no—
228#123—3821no—
229C22⋊Q8—3821no—
230C22⋊Q8—3821no—
231C4×Q8—1911no—
232C4×Q8C2×D19111yescharacteristic
233C4×D4—3821no—
234C4×D4—3821no—
235C4×D4—1911no—
236C4×D4—1911no—
237#117—3821no—
238#117—1911no—
239C2×C4⋊C4—3821no—
240C2×C4⋊C4—1911no—
241C4⋊C8—1911no—
242C4⋊C8—1911no—
243C4⋊C8—1911no—
244C4⋊C8C2×D19111yescharacteristic
245#103—1911no—
246#103—1911no—
247#103—1911no—
248#103—1911no—
249#103—1911no—
250#103C2×D19111yescharacteristic
251#102—1911no—
252#102C2×D19111yescharacteristic
253#41—3822no—
254#41—3822no—
255#41—3822no—
256#41—1914no—
257C2×Q8—3821no—
258C2×Q8—3822no—
259C2×Q8—3822no—
260C2×Q8—1911no—
261C2×Q8—1911no—
262C2×Q8C22×D19111yescharacteristic
263C2×Q8C22×D19111yescharacteristic
264C2×D4—3821no—
265C2×D4—3821no—
266C2×D4—1911no—
267C2×D4C22×D19111yescharacteristic
268C22×C4—3821no—
269C22×C4—3821no—
270C22×C4—3821no—
271C22×C4—3821no—
272C22×C4—3821no—
273C22×C4—3821no—
274C22×C4—1911no—
275Q16—22no—
276Q16—3822no—
277Q16—3822no—
278SD16—22no—
279SD16—3822no—
280SD16—3822no—
281SD16—3822no—
282D8—3822no—
283M16—3822no—
284C2×C8—3822no—
285C2×C8—1911no—
286C2×C8—1911no—
287C2×C8C22×D19111yescharacteristic
288C2×C8C22×D19111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—3821no—
291C4⋊C4—3821no—
292C4⋊C4—3821no—
293C4⋊C4—3821no—
294C4⋊C4—3821no—
295C4⋊C4—3821no—
296C4⋊C4—1911no—
297C4⋊C4—1911no—
298C4⋊C4—1911no—
299C4⋊C4C22×D19111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—3821no—
303C22⋊C4—3821no—
304C22⋊C4—3821no—
305C22⋊C4—3821no—
306C22⋊C4—1911no—
307C22⋊C4—1911no—
308C42—21no—
309C42—3821no—
310C42—1911no—
311C42C22×D19111yescharacteristic
312C23—21no—
313C23—3821no—
314C23—1911no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—3821no—
319Q8—3821no—
320Q8—3821no—
321Q8—3821no—
322Q8—7642no—
323Q8D4×D19112yes—
324D4—21no—
325D4—21no—
326D4—3824no—
327D4—3821no—
328D4—1912no—
329D4—7642no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3824no—
334C2×C4—3821no—
335C2×C4—3821no—
336C2×C4—3821no—
337C2×C4—1911no—
338C2×C4—1911no—
339C2×C4—1911no—
340C2×C4—1912no—
341C2×C4—1912no—
342C2×C4—15281no—
343C2×C4—15281no—
344C2×C4—15281no—
345C2×C4—7642no—
346C2×C4—7642no—
347C2×C4D4×D19111yescharacteristic
348C2×C4D4×D19111yescharacteristic
349C2×C4C23×D19111yescharacteristic
350C8—21no—
351C8—21no—
352C8—3821no—
353C8—3821no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3821no—
358C22—3821no—
359C22—3822no—
360C22—1912no—
361C22—7641no—
362C22—7641no—
363C22C2×D4×D19111yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—3821no—
370C4—3821no—
371C4—1912no—
372C4—7641no—
373C4—7641no—
374C4—7641no—
375C4C2×D4×D19111yescharacteristic
376C4#41×D19111yescharacteristic
377C2—81no—
378C2—3822no—
379C2—7642no—
380C2#121×D19111yescharacteristic
381C2#2713347011yescharacteristic
382C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#464×C191C2
socleC22×C191C22×D4
prime radicalC2×#20259343C2
hypercenter#464D191
hypocenterC191#3046
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
3. #27133233C2semidirect
4. #27133145C2semidirect
5. #27132883C2semidirect
6. #27132877C2semidirect
7. #27132875C2semidirect
8. #27132873C2semidirect
9. #27132871C2semidirect
10. #27132869C2semidirect
11. #27132867C2semidirect
12. #27132688C2semidirect
13. #27132661C2semidirect
14. #103×D191C2semidirect
15. #464×C191C2semidirect
191. C191#3046semidirect
198. #464D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593542
C2×#202593432
#271332332
#271331452
#271328832
#271328772
#271328752
#271328732
#271328712
#271328692
#271328672
#271326882
#271326612
#103×D1912
#464×C1912
#3046191