Finite Group Databasebeta

← #34108958

Subgroups — #34108958

Order 20096.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097800C211yesmaximal, characteristic
2C4×#14578953C211yesmaximal, characteristic
3C4×Q8×D157C211yesmaximal, characteristic, complemented
4#23757381C211yesmaximal, characteristic, complemented
5#23757378C211yesmaximal, characteristic, complemented
6#23757373C211yesmaximal, characteristic, complemented
7#23757367C211yesmaximal, characteristic, complemented
8#23757365C211yesmaximal, characteristic, complemented
9#23757364C211yesmaximal, characteristic, complemented
10SD16×Dic157C211yesmaximal, characteristic, complemented
11#23757314C211yesmaximal, characteristic, complemented
12#23757280C211yesmaximal, characteristic, complemented
13#23757271C211yesmaximal, characteristic
14#23757225C211yesmaximal, characteristic, complemented
15#440×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×Q8×D157C2211yescharacteristic
18#19097800C418yescomplemented
19C2×Dic628C2211yescharacteristic
20C2×#14578944C2211yescharacteristic
21C2×#14578942C2211yescharacteristic
22C2×#14578937C2211yescharacteristic
23C2×#14578937C2211yescharacteristic
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#19097729C2211yescharacteristic
35#19097727—21no—
36C4⋊C4×D157—21no—
37C4⋊C4×D157C2211yescharacteristic
38C2×C4×Dic157—21no—
39C42×D157—21no—
40C42×D157C2211yescharacteristic
41#19097704C2211yescharacteristic
42#19097703C2211yescharacteristic
43#19097702C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097694C2211yescharacteristic
48#19097694C2211yescharacteristic
49#19097692C2211yescharacteristic
50#19097682C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
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×D157D411yescharacteristic
73C2×C4×D157D411yescharacteristic
74C2×C4×D157C2311yescharacteristic
75Dic628C2×C414yescomplemented
76#14578944C2×C414yescomplemented
77#14578942C2×C414yescomplemented
78#14578937—22no—
79#14578937C2×C414yescomplemented
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C4⋊Dic157—21no—
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933—21no—
89#14578933—21no—
90C22⋊Dic157—21no—
91#14578931—21no—
92C4×Dic157—21no—
93C4×Dic157—21no—
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C4×Dic157—21no—
98C4×Dic157D411yescharacteristic
99C4×Dic157D411yescharacteristic
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—42no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—24no—
130C4×D157—22no—
131C4×D157—41no—
132C4×D157—42no—
133C4×D157C22×C412yes—
134C4×D157#4112yes—
135#11929434—21no—
136#11929434C22×C412yes—
137C23×C157—21no—
138Q8×C157—21no—
139Q8×C157C22×C412yes—
140D4×C157—21no—
141D4×C157C22×C412yes—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—42no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157C22×C412yes—
151C22×C157—22no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157C22×D411yescharacteristic
155C2×D157—21no—
156C2×D157—21no—
157C2×D157C4×D412yes—
158C4×C157—22no—
159C4×C157—21no—
160C4×C157—21no—
161C4×C157—41no—
162C4×C157—41no—
163C4×C157C23×C411yescharacteristic
164C4×C157C2×#4111yescharacteristic
165Dic157—22no—
166Dic157—22no—
167Dic157—21no—
168Dic157—41no—
169Dic157—41no—
170Dic157C4×D412yes—
171Dic157#13712yescomplemented
172C2×C157—42no—
173C2×C157C2×C4×D411yescharacteristic
174C2×C157C2×#13711yescharacteristic
175C2×C157#57511yescharacteristic
176D157—22no—
177C157C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—1571nomaximal, Sylow
179C2×#137—1571no—
180C4×#41—1571no—
181C2×C4×Q8—1571no—
182#441—1571no—
183#441—1571no—
184#440—1571no—
185#440D15711yescharacteristic, complemented
186C4×Q16—1571no—
187C4×Q16—1571no—
188C4×SD16—1571no—
189C4×SD16—1571no—
190#428—1571no—
191#419—1571no—
192#417—1571no—
193C4×M16—1571no—
194C2×#41—1571no—
195C22×Q8—1571no—
196#137—1578no—
197C2×Q16—1571no—
198C2×Q16—1571no—
199C2×SD16—1571no—
200C2×SD16C2×D15711yescharacteristic
201C2×M16—1571no—
202C2×M16—1571no—
203C4×Q8—3141no—
204C4×Q8—3141no—
205C4×Q8—1571no—
206C4×Q8—1571no—
207C4×Q8—1571no—
208C4×Q8—1571no—
209C4×Q8—1571no—
210C4×Q8C2×D15711yescharacteristic
211C4×D4—3141no—
212C4×D4—3141no—
213C4×D4—1571no—
214C4×D4C2×D15711yescharacteristic
215#117—3141no—
216#117—1571no—
217C2×C4⋊C4—3141no—
218C2×C4⋊C4—1571no—
219C2×C42—3141no—
220C2×C42—3141no—
221C2×C42—1571no—
222#107—1571no—
223#107C2×D15711yescharacteristic
224#106—1571no—
225#106—1571no—
226#103—1571no—
227#103—1571no—
228#103—1571no—
229#103—1571no—
230#103—1571no—
231#103C2×D15711yescharacteristic
232#102—1571no—
233#102C2×D15711yescharacteristic
234#97—1571no—
235#97C2×D15711yescharacteristic
236C4×C8—1571no—
237C4×C8—1571no—
238#41—3142no—
239#41—1574no—
240C2×Q8—3141no—
241C2×Q8—3142no—
242C2×Q8—1574no—
243C2×Q8—1571no—
244C2×Q8—1571no—
245C2×Q8C22×D15711yescharacteristic
246C2×D4—3141no—
247C2×D4C22×D15711yescharacteristic
248C22×C4—21no—
249C22×C4—3141no—
250C22×C4—3141no—
251C22×C4—3141no—
252C22×C4—3141no—
253C22×C4—1571no—
254C22×C4—1571no—
255C22×C4—1571no—
256Q16—1574no—
257Q16—1574no—
258SD16—1574no—
259SD16C4×D15714yescomplemented
260M16—3142no—
261M16—1574no—
262C2×C8—1571no—
263C2×C8—1571no—
264C2×C8C22×D15711yescharacteristic
265C2×C8C22×D15711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—3141no—
272C4⋊C4—3141no—
273C4⋊C4—1571no—
274C4⋊C4—1571no—
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C42—21no—
281C42—3141no—
282C42—3141no—
283C42—3141no—
284C42—3141no—
285C42—3141no—
286C42—3141no—
287C42—1571no—
288C42—1571no—
289C42—1571no—
290C42C22×D15711yescharacteristic
291C23—21no—
292C23—1571no—
293Q8—21no—
294Q8—3144no—
295Q8—3141no—
296Q8—3141no—
297Q8—1572no—
298Q8—1572no—
299Q8C2×C4×D15712yes—
300D4—21no—
301D4—3144no—
302D4C2×C4×D15712yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—3144no—
308C2×C4—3142no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—3144no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—6281no—
315C2×C4—6282no—
316C2×C4—6282no—
317C2×C4—1571no—
318C2×C4—1571no—
319C2×C4—1571no—
320C2×C4—1572no—
321C2×C4—1572no—
322C2×C4D4×D15711yescharacteristic
323C2×C4D4×D15711yescharacteristic
324C2×C4C23×D15711yescharacteristic
325C8—21no—
326C8—3141no—
327C8—1572no—
328C8C2×C4×D15712yes—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—3141no—
333C22—3141no—
334C22—1572no—
335C22C2×D4×D15711yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—3142no—
342C4—3142no—
343C4—3141no—
344C4—6281no—
345C4—6281no—
346C4—1572no—
347C4—1572no—
348C4C22×C4×D15711yescharacteristic
349C4#41×D15711yescharacteristic
350C2—42no—
351C2—3142no—
352C2C4×D4×D15711yescharacteristic
353C2#137×D15711yescharacteristic
354C2#2375806911yescharacteristic
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
hypocenterC157C4×#137
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. C4×Q8×D157C2semidirect
4. #23757381C2semidirect
5. #23757378C2semidirect
6. #23757373C2semidirect
7. #23757367C2semidirect
8. #23757365C2semidirect
9. #23757364C2semidirect
10. SD16×Dic157C2semidirect
11. #23757314C2semidirect
12. #23757280C2semidirect
14. #23757225C2semidirect
15. #440×C157C2semidirect
18. #19097800C4semidirect
66. Q8×D157C2×C4semidirect
75. Dic628C2×C4semidirect
76. #14578944C2×C4semidirect
77. #14578942C2×C4semidirect
79. #14578937C2×C4semidirect
104. SD16×C157C2×C4semidirect
171. Dic157#137semidirect
177. C157C4×#137semidirect
185. #440D157semidirect
259. SD16C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978002
C4×#145789532
C4×Q8×D1572
#237573812
#237573782
#237573732
#237573672
#237573652
#237573642
SD16×Dic1572
#237573142
#237572802
#237572712
#237572252
#440×C1572
C4×#137157