Finite Group Databasebeta

← #34109683

Subgroups — #34109683

Order 20096.

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×#19097803C211yesmaximal, characteristic, complemented
2C2×#19097794C211yesmaximal, characteristic
3#23757848C211yesmaximal, characteristic, complemented
4#23757755C211yesmaximal, characteristic, complemented
5#23757497C211yesmaximal, characteristic, complemented
6#23757495C211yesmaximal, characteristic, complemented
7#23757491C211yesmaximal, characteristic, complemented
8#23757489C211yesmaximal, characteristic, complemented
9#23757481C211yesmaximal, characteristic, complemented
10#23757477C211yesmaximal, characteristic, complemented
11#23757475C211yesmaximal, characteristic, complemented
12#23757298C211yesmaximal, characteristic, complemented
13#23757273C211yesmaximal, characteristic, complemented
14#103×D157C211yesmaximal, characteristic, complemented
15#462×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578955C2211yescharacteristic
18C2×Q8×D157C2211yescharacteristic
19#19097803—24no—
20#19097794—24no—
21C2×#14578944C2211yescharacteristic
22C2×#14578943C2211yescharacteristic
23C2×#14578941C2211yescharacteristic
24C2×#14578941C2211yescharacteristic
25C2×#14578941C2211yescharacteristic
26C2×D1256C2211yescharacteristic
27C2×#14578937C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097769C2211yescharacteristic
30#19097760C2211yescharacteristic
31#19097759C2211yescharacteristic
32#19097756—21no—
33#19097756—21no—
34#19097749—21no—
35#19097749—21no—
36Q8×Dic157C2211yescharacteristic
37C4×D628—21no—
38C4×D628C2211yescharacteristic
39#19097733—21no—
40#19097733C2211yescharacteristic
41#19097728—21no—
42#19097728C2211yescharacteristic
43C4⋊C4×D157—21no—
44C4⋊C4×D157C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic
46#19097700C2211yescharacteristic
47#19097700C2211yescharacteristic
48#19097696C2211yescharacteristic
49#19097695C2211yescharacteristic
50#19097695C2211yescharacteristic
51#19097694C2211yescharacteristic
52#19097693C2211yescharacteristic
53#19097691C2211yescharacteristic
54C2×Q16×C157C2211yescharacteristic
55C2×Q16×C157C2211yescharacteristic
56C4⋊Q8×C157C2211yescharacteristic
57C4×Q8×C157C2211yescharacteristic
58C4⋊C8×C157C2211yescharacteristic
59#103×C157C2211yescharacteristic
60#103×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—22no—
63#14578955—22no—
64#14578955D414yes—
65C2×Dic314—21no—
66C2×Dic314C2311yescharacteristic
67Q8×D157—22no—
68Q8×D157—22no—
69C2×D628—21no—
70C2×D628—21no—
71C2×D628C2311yescharacteristic
72C2×D628C2311yescharacteristic
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157C2311yescharacteristic
80#14578944—22no—
81#14578943—22no—
82#14578941—22no—
83#14578941—22no—
84#14578941—22no—
85D1256—22no—
86#14578937—22no—
87C2×#11929434C2311yescharacteristic
88C2×#11929434C2311yescharacteristic
89C8×D157—22no—
90C4⋊Dic157—21no—
91C4⋊Dic157C2311yescharacteristic
92#14578933—21no—
93#14578933—21no—
94#14578933—21no—
95#14578933D411yescharacteristic
96#14578933D411yescharacteristic
97#14578931—21no—
98#14578931—21no—
99#14578931—21no—
100#14578931—21no—
101#14578931—21no—
102#14578931—21no—
103#14578931D411yescharacteristic
104#14578931D411yescharacteristic
105C4×Dic157—21no—
106C4×Dic157C2311yescharacteristic
107C2×Q8×C157C2311yescharacteristic
108C2×Q8×C157C2311yescharacteristic
109C2×Q8×C157C2311yescharacteristic
110Q16×C157—22no—
111Q16×C157—22no—
112C2×C8×C157C2311yescharacteristic
113C2×C8×C157C2311yescharacteristic
114C4⋊C4×C157—21no—
115C4⋊C4×C157—21no—
116C4⋊C4×C157—21no—
117C4⋊C4×C157C2311yescharacteristic
118C42×C157—21no—
119C42×C157C2311yescharacteristic
120C22×D157—21no—
121C22×D157—21no—
122C22×D157C2×D411yescharacteristic
123Dic314—21no—
124Dic314—21no—
125Dic314—42no—
126D628—24no—
127D628—21no—
128D628—21no—
129D628—21no—
130D628—42no—
131D628C2×D412yes—
132C2×Dic157—21no—
133C2×Dic157—21no—
134C2×Dic157C2×D411yescharacteristic
135C2×Dic157C2×D411yescharacteristic
136C2×Dic157C2×D411yescharacteristic
137C4×D157—24no—
138C4×D157—42no—
139C4×D157—42no—
140C4×D157—81no—
141C4×D157—81no—
142C4×D157—81no—
143C4×D157C2×D412yes—
144C4×D157#4112yes—
145#11929434—21no—
146#11929434—21no—
147Q8×C157—21no—
148Q8×C157—21no—
149Q8×C157—21no—
150Q8×C157—21no—
151Q8×C157—21no—
152Q8×C157C2×D412yes—
153C2×C4×C157—21no—
154C2×C4×C157—21no—
155C2×C4×C157—21no—
156C2×C4×C157—21no—
157C2×C4×C157C2×D411yescharacteristic
158C2×C4×C157C2×D411yescharacteristic
159C2×C4×C157C2411yescharacteristic
160C8×C157—21no—
161C8×C157—21no—
162C22×C157C22×D411yescharacteristic
163C2×D157—21no—
164C2×D157—21no—
165C2×D157—22no—
166C2×D157—41no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C2×D157#12112yes—
172C4×C157—22no—
173C4×C157—21no—
174C4×C157—21no—
175C4×C157—41no—
176C4×C157—41no—
177C4×C157—41no—
178C4×C157C22×D411yescharacteristic
179C4×C157C2×#4111yescharacteristic
180Dic157—21no—
181Dic157—21no—
182Dic157—41no—
183Dic157—41no—
184Dic157#12112yes—
185C2×C157C2×#12111yescharacteristic
186C2×C157#57711yescharacteristic
187C2×C157#57811yescharacteristic
188D157—22no—
189D157—42no—
190D157—81no—
191C157#304611yescharacteristic, complemented, Sylow
192#3046—1571nomaximal, Sylow
193C2×#137—1571no—
194C2×#135—1571no—
195#536—1571no—
196#520—1571no—
197#464—1571no—
198#464—1571no—
199#463—1571no—
200#463—1571no—
201#462—1571no—
202#462D15711yescharacteristic, complemented
203#461—1571no—
204#461—1571no—
205#424—1571no—
206#417—1571no—
207C2×#103—1571no—
208C2×#41—1571no—
209C2×#41—1571no—
210C22×Q8—1571no—
211#137—3144no—
212#135—3144no—
213C2×Q16—1571no—
214C2×Q16C2×D15711yescharacteristic
215C2×Q16C2×D15711yescharacteristic
216C2×SD16—1571no—
217C2×SD16—1571no—
218C2×SD16—1571no—
219C2×SD16—1571no—
220C2×D8—1571no—
221C2×M16—1571no—
222C22×C8—1571no—
223C4⋊Q8—1571no—
224C4⋊Q8C2×D15711yescharacteristic
225#124—1571no—
226#124—1571no—
227#123—3141no—
228#123—3141no—
229C22⋊Q8—3141no—
230C22⋊Q8—3141no—
231C4×Q8—1571no—
232C4×Q8C2×D15711yescharacteristic
233C4×D4—3141no—
234C4×D4—3141no—
235C4×D4—1571no—
236C4×D4—1571no—
237#117—3141no—
238#117—1571no—
239C2×C4⋊C4—3141no—
240C2×C4⋊C4—1571no—
241C4⋊C8—1571no—
242C4⋊C8—1571no—
243C4⋊C8—1571no—
244C4⋊C8C2×D15711yescharacteristic
245#103—1571no—
246#103—1571no—
247#103—1571no—
248#103—1571no—
249#103C2×D15711yescharacteristic
250#103C2×D15711yescharacteristic
251#102—1571no—
252#102—1571no—
253#41—3142no—
254#41—3142no—
255#41—3142no—
256#41—1574no—
257C2×Q8—3141no—
258C2×Q8—3142no—
259C2×Q8—3142no—
260C2×Q8—1571no—
261C2×Q8C22×D15711yescharacteristic
262C2×Q8C22×D15711yescharacteristic
263C2×Q8C22×D15711yescharacteristic
264C2×D4—3141no—
265C2×D4—3141no—
266C2×D4—1571no—
267C2×D4—1571no—
268C22×C4—3141no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4—3141no—
272C22×C4—3141no—
273C22×C4—3141no—
274C22×C4—1571no—
275Q16—22no—
276Q16—22no—
277Q16—3142no—
278SD16—3142no—
279SD16—3142no—
280SD16—3142no—
281SD16—3142no—
282D8—3142no—
283M16—3142no—
284C2×C8—3142no—
285C2×C8—1571no—
286C2×C8—1571no—
287C2×C8C22×D15711yescharacteristic
288C2×C8C22×D15711yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—3141no—
293C4⋊C4—3141no—
294C4⋊C4—3141no—
295C4⋊C4—3141no—
296C4⋊C4—1571no—
297C4⋊C4—1571no—
298C4⋊C4—1571no—
299C4⋊C4C22×D15711yescharacteristic
300C22⋊C4—3141no—
301C22⋊C4—3141no—
302C22⋊C4—3141no—
303C22⋊C4—3141no—
304C22⋊C4—3141no—
305C22⋊C4—3141no—
306C22⋊C4—1571no—
307C22⋊C4—1571no—
308C42—21no—
309C42—3141no—
310C42—1571no—
311C42C22×D15711yescharacteristic
312C23—3141no—
313C23—3141no—
314C23—1571no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—3141no—
321Q8—3141no—
322Q8—6282no—
323Q8D4×D15712yes—
324D4—3144no—
325D4—3141no—
326D4—3141no—
327D4—3141no—
328D4—6282no—
329D4—1572no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3144no—
335C2×C4—3141no—
336C2×C4—3141no—
337C2×C4—6282no—
338C2×C4—6282no—
339C2×C4—1571no—
340C2×C4—1571no—
341C2×C4—1571no—
342C2×C4—1572no—
343C2×C4—1572no—
344C2×C4—12561no—
345C2×C4—12561no—
346C2×C4—12561no—
347C2×C4D4×D15711yescharacteristic
348C2×C4D4×D15711yescharacteristic
349C2×C4C23×D15711yescharacteristic
350C8—21no—
351C8—21no—
352C8—3141no—
353C8—3141no—
354C22—3141no—
355C22—3141no—
356C22—3142no—
357C22—6281no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22—6281no—
362C22—1572no—
363C22C2×D4×D15711yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—3141no—
371C4—3141no—
372C4—6281no—
373C4—6281no—
374C4—1572no—
375C4C2×D4×D15711yescharacteristic
376C4#41×D15711yescharacteristic
377C2—3142no—
378C2—6282no—
379C2—12561no—
380C2#121×D15711yescharacteristic
381C2#2375808211yescharacteristic
382C2#2375808611yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#462×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097794C2
hypercenter#462D157
hypocenterC157#3046
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#19097803C2semidirect
3. #23757848C2semidirect
4. #23757755C2semidirect
5. #23757497C2semidirect
6. #23757495C2semidirect
7. #23757491C2semidirect
8. #23757489C2semidirect
9. #23757481C2semidirect
10. #23757477C2semidirect
11. #23757475C2semidirect
12. #23757298C2semidirect
13. #23757273C2semidirect
14. #103×D157C2semidirect
15. #462×C157C2semidirect
191. C157#3046semidirect
202. #462D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978032
C2×#190977942
#237578482
#237577552
#237574972
#237574952
#237574912
#237574892
#237574812
#237574772
#237574752
#237572982
#237572732
#103×D1572
#462×C1572
#3046157