Finite Group Databasebeta

← #34108976

Subgroups — #34108976

Order 20096.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097800C211yesmaximal, characteristic
2#23757752C211yesmaximal, characteristic
3#23757749C211yesmaximal, characteristic, complemented
4#23757381C211yesmaximal, characteristic, complemented
5#23757377C211yesmaximal, characteristic, complemented
6#23757370C211yesmaximal, characteristic, complemented
7#23757367C211yesmaximal, characteristic, complemented
8C4×#14578944C211yesmaximal, characteristic, complemented
9SD16×Dic157C211yesmaximal, characteristic, complemented
10C4×#14578942C211yesmaximal, characteristic, complemented
11#23757314C211yesmaximal, characteristic, complemented
12#23757266C211yesmaximal, characteristic
13#103×D157C211yesmaximal, characteristic, complemented
14#23757230C211yesmaximal, characteristic, complemented
15#440×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×Q8×D157C2211yescharacteristic
18#19097800C418yescomplemented
19C2×Dic628C2211yescharacteristic
20C2×#14578944C2211yescharacteristic
21C2×#14578942C2211yescharacteristic
22C2×#14578937C2211yescharacteristic
23C2×C8×D157C2211yescharacteristic
24Q8×Dic157C2211yescharacteristic
25C4×Dic314—21no—
26C4×Dic314C2211yescharacteristic
27C4×Dic314C2211yescharacteristic
28#19097736—21no—
29#19097736C2211yescharacteristic
30#19097736C2211yescharacteristic
31D4×Dic157C2211yescharacteristic
32C4×C22⋊D157—21no—
33#19097731—21no—
34#19097729—21no—
35#19097729C2211yescharacteristic
36#19097728—21no—
37#19097728C2211yescharacteristic
38#19097727—21no—
39C2×#14578933—21no—
40C4⋊C4×D157C2211yescharacteristic
41#19097704C2211yescharacteristic
42#19097703C2211yescharacteristic
43#19097702C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097694C2211yescharacteristic
48#19097694C2211yescharacteristic
49#19097692C2211yescharacteristic
50#19097681C2211yescharacteristic
51C4×#11929434C2211yescharacteristic
52C8×Dic157C2211yescharacteristic
53C2×SD16×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic
55C4×D4×C157C2211yescharacteristic
56#107×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#97×C157C2211yescharacteristic
60#14578953—22no—
61#14578953C2×C414yes—
62C2×Dic314—21no—
63C2×Dic314C2311yescharacteristic
64C2×Dic314C2311yescharacteristic
65Q8×D157—22no—
66Q8×D157C2×C414yescomplemented
67C2×C22⋊D157—21no—
68C22×Dic157—21no—
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157C2311yescharacteristic
73Dic628C2×C414yescomplemented
74#14578944C2×C414yescomplemented
75#14578942C2×C414yescomplemented
76#14578937C2×C414yescomplemented
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C8×D157—22no—
80C4⋊Dic157—21no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89#14578933D411yescharacteristic
90C22⋊Dic157—21no—
91#14578931—21no—
92#14578931D411yescharacteristic
93#14578931D411yescharacteristic
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C4×Dic157—21no—
98C4×Dic157—21no—
99C4×Dic157—21no—
100C4×Dic157C2311yescharacteristic
101C2×Q8×C157C2311yescharacteristic
102C2×D4×C157C2311yescharacteristic
103C22×C4×C157—21no—
104SD16×C157C2×C414yescomplemented
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157—21no—
108C4⋊C4×C157C2311yescharacteristic
109C4⋊C4×C157C2311yescharacteristic
110C22⋊C4×C157—21no—
111C42×C157—21no—
112C42×C157C2311yescharacteristic
113C22×D157C2×D411yescharacteristic
114Dic314—21no—
115Dic314—21no—
116Dic314—24no—
117Dic314C22×C412yes—
118Dic314C22×C412yes—
119C22⋊D157—24no—
120C2×Dic157—21no—
121C2×Dic157—21no—
122C2×Dic157—24no—
123C2×Dic157—21no—
124C2×Dic157—21no—
125C2×Dic157—81no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—24no—
130C4×D157—81no—
131C4×D157C22×C412yes—
132C4×D157#4112yes—
133#11929434—21no—
134#11929434C22×C412yes—
135C23×C157—21no—
136Q8×C157—21no—
137Q8×C157C22×C412yes—
138D4×C157—21no—
139D4×C157C22×C412yes—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—81no—
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2411yescharacteristic
147C8×C157—21no—
148C8×C157C22×C412yes—
149C22×C157—22no—
150C22×C157—41no—
151C22×C157—41no—
152C22×C157C22×D411yescharacteristic
153C2×D157—21no—
154C2×D157—21no—
155C2×D157C4×D412yes—
156C4×C157—22no—
157C4×C157—21no—
158C4×C157—21no—
159C4×C157—41no—
160C4×C157—41no—
161C4×C157C23×C411yescharacteristic
162C4×C157C2×#4111yescharacteristic
163Dic157—22no—
164Dic157—22no—
165Dic157—21no—
166Dic157—21no—
167Dic157—41no—
168Dic157—41no—
169Dic157C4×D412yes—
170C2×C157—42no—
171C2×C157C2×C4×D411yescharacteristic
172C2×C157#57711yescharacteristic
173C2×C157#57811yescharacteristic
174D157—22no—
175C157#294711yescharacteristic, complemented, Sylow
176#2947—1571nomaximal, Sylow
177C2×#137—1571no—
178#520—1571no—
179#519—1571no—
180#441—1571no—
181#441—1571no—
182#440—1571no—
183#440D15711yescharacteristic, complemented
184C4×Q16—1571no—
185C4×Q16—1571no—
186C4×SD16—1571no—
187C4×SD16—1571no—
188#428—1571no—
189#416—1571no—
190C2×#103—1571no—
191#405—1571no—
192C2×#41—1571no—
193C22×Q8—1571no—
194#137—1578no—
195C2×Q16—1571no—
196C2×Q16—1571no—
197C2×SD16—1571no—
198C2×SD16C2×D15711yescharacteristic
199C2×M16—1571no—
200C22×C8—1571no—
201C4×Q8—3141no—
202C4×Q8—3141no—
203C4×Q8—1571no—
204C4×Q8—1571no—
205C4×Q8—1571no—
206C4×Q8—1571no—
207C4×Q8—1571no—
208C4×Q8C2×D15711yescharacteristic
209C4×D4—3141no—
210C4×D4—3141no—
211C4×D4—1571no—
212C4×D4C2×D15711yescharacteristic
213#117—3141no—
214#117—3141no—
215#117—3141no—
216#117—1571no—
217#117—1571no—
218C2×C4⋊C4—3141no—
219C2×C4⋊C4—1571no—
220#107—1571no—
221#107C2×D15711yescharacteristic
222#106—1571no—
223#106—1571no—
224#103—1571no—
225#103—1571no—
226#103—1571no—
227#103—1571no—
228#103—1571no—
229#103C2×D15711yescharacteristic
230#102—1571no—
231#102C2×D15711yescharacteristic
232#97—1571no—
233#97C2×D15711yescharacteristic
234C4×C8—1571no—
235C4×C8—1571no—
236#41—3142no—
237#41—1574no—
238C2×Q8—3141no—
239C2×Q8—3142no—
240C2×Q8—1574no—
241C2×Q8—1571no—
242C2×Q8—1571no—
243C2×Q8C22×D15711yescharacteristic
244C2×D4—3141no—
245C2×D4C22×D15711yescharacteristic
246C22×C4—21no—
247C22×C4—3141no—
248C22×C4—3141no—
249C22×C4—3141no—
250C22×C4—3141no—
251C22×C4—1571no—
252Q16—1574no—
253Q16—1574no—
254SD16—1574no—
255SD16C4×D15714yescomplemented
256M16—1574no—
257C2×C8—3142no—
258C2×C8—1571no—
259C2×C8—1571no—
260C2×C8C22×D15711yescharacteristic
261C2×C8C22×D15711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3141no—
264C4⋊C4—3141no—
265C4⋊C4—3141no—
266C4⋊C4—3141no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—1571no—
270C4⋊C4—1571no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4C22×D15711yescharacteristic
274C4⋊C4C22×D15711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—3141no—
277C22⋊C4—3141no—
278C22⋊C4—1571no—
279C22⋊C4—1571no—
280C42—21no—
281C42—3141no—
282C42—3141no—
283C42—3141no—
284C42—3141no—
285C42—3141no—
286C42—3141no—
287C42—1571no—
288C42C22×D15711yescharacteristic
289C23—21no—
290C23—1571no—
291Q8—21no—
292Q8—3144no—
293Q8—3141no—
294Q8—3141no—
295Q8—1572no—
296Q8—1572no—
297Q8C2×C4×D15712yes—
298D4—21no—
299D4—3144no—
300D4C2×C4×D15712yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—3144no—
306C2×C4—3141no—
307C2×C4—3141no—
308C2×C4—3144no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—1571no—
312C2×C4—1571no—
313C2×C4—1571no—
314C2×C4—1572no—
315C2×C4—1572no—
316C2×C4—12561no—
317C2×C4—12561no—
318C2×C4D4×D15711yescharacteristic
319C2×C4D4×D15711yescharacteristic
320C2×C4C23×D15711yescharacteristic
321C8—21no—
322C8—3141no—
323C8—1572no—
324C8C2×C4×D15712yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—3141no—
329C22—3141no—
330C22—1572no—
331C22C2×D4×D15711yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—3141no—
338C4—3141no—
339C4—3142no—
340C4—3142no—
341C4—6281no—
342C4—6281no—
343C4—1572no—
344C4C22×C4×D15711yescharacteristic
345C4#41×D15711yescharacteristic
346C2—42no—
347C2—3142no—
348C2C4×D4×D15711yescharacteristic
349C2#2375808311yescharacteristic
350C2#2375808911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
Fitting#440×C157C2
socleC22×C157C22×D4
prime radicalC2×#14578953C22
cosocleC2×C4×C157C24
hypercenter#440D157
hypocenterC157#2947
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #23757749C2semidirect
4. #23757381C2semidirect
5. #23757377C2semidirect
6. #23757370C2semidirect
7. #23757367C2semidirect
8. C4×#14578944C2semidirect
9. SD16×Dic157C2semidirect
10. C4×#14578942C2semidirect
11. #23757314C2semidirect
13. #103×D157C2semidirect
14. #23757230C2semidirect
15. #440×C157C2semidirect
18. #19097800C4semidirect
66. Q8×D157C2×C4semidirect
73. Dic628C2×C4semidirect
74. #14578944C2×C4semidirect
75. #14578942C2×C4semidirect
76. #14578937C2×C4semidirect
104. SD16×C157C2×C4semidirect
175. C157#2947semidirect
183. #440D157semidirect
255. SD16C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978002
#237577522
#237577492
#237573812
#237573772
#237573702
#237573672
C4×#145789442
SD16×Dic1572
C4×#145789422
#237573142
#237572662
#103×D1572
#237572302
#440×C1572
#2947157