Finite Group Databasebeta

← C2×#23772510 #35153315

Subgroups — C2×#23772510 #35153315

Order 20224.

2434 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11929625C211yesmaximal, characteristic
2#23772510C2116yesmaximal, direct product factor
3C2×Q8×C79⋊C8C211yesmaximal, characteristic, complemented
4C2×C8×D316C213yesmaximal, complemented
5C2×#19098628C213yesmaximal, complemented
6C2×#19098614C213yesmaximal, complemented
7C2×C4⋊C8×D79C213yesmaximal, complemented
8C2×C8×Q8×C79C211yesmaximal, characteristic, complemented
9C22×#11929625C411yescharacteristic
10C22×C8×D79C2216yes—
11C4×#11929625C418yes—
12C4×#11929625C2218yes—
13C2×Q8×Dic79C411yescharacteristic
14C2×C4×D316C2213yes—
15C2×#14579123C413yes—
16C2×#14579119C413yes—
17C2×C42×D79C2213yes—
18Q8×C79⋊C8C2218yescomplemented
19C8×D316C22124yescomplemented
20#19098628C22124yescomplemented
21#19098614C22124yescomplemented
22C2×C4⋊(C79⋊C8)C2213yes—
23C2×Dic79⋊C8C2213yes—
24C2×Dic79⋊C8C2211yescharacteristic
25C4⋊C8×D79C22124yescomplemented
26C2×(C2×D79)⋊C8C2213yes—
27C2×(C2×D79)⋊C8C2213yes—
28C2×C4×C79⋊C8C2213yes—
29C2×C4×Q8×C79C2211yescharacteristic
30C8×Q8×C79C2218yescomplemented
31C2×C4⋊C8×C79C2213yes—
32C2×C4×C8×C79C2213yes—
33C2×#11929625C8116yescomplemented
34C2×#11929625C2×C418yes—
35C22×D316C2×C413yes—
36C22×C4×D79C2×C413yes—
37C22×C4×D79C2×C413yes—
38C22×C4×D79C2313yes—
39C22×C79⋊C8C2311yescharacteristic
40C22×C79⋊C8C2313yes—
41C2×C8×D79—412no—
42C2×C8×D79C23124yes—
43Q8×Dic79C2×C418yes—
44C4×D316C2×C4112yes—
45C4×D316C23112yes—
46#14579123C2×C4124yes—
47#14579119C2×C4124yes—
48C2×C4⋊Dic79C2×C413yes—
49C2×(C2×D79)⋊C4C2×C416yes—
50C2×C4×Dic79C2×C413yes—
51C2×C4×Dic79C2×C413yes—
52C2×C4×Dic79C2311yescharacteristic
53C42×D79C2×C4112yes—
54C42×D79C23112yes—
55C4⋊(C79⋊C8)C23112yes—
56Dic79⋊C8C23112yes—
57Dic79⋊C8C2314yes—
58(C2×D79)⋊C8C23112yes—
59(C2×D79)⋊C8C23112yes—
60C4×C79⋊C8C23112yes—
61C22×Q8×C79C2×C411yescharacteristic
62C22×C8×C79C2313yes—
63C22×C8×C79C2311yescharacteristic
64C4×Q8×C79C2×C414yes—
65C4×Q8×C79C2314yes—
66C2×C4⋊C4×C79C2×C413yes—
67C2×C42×C79C2313yes—
68C4⋊C8×C79C23112yes—
69C4×C8×C79C23112yes—
70C23×D79C22×C413yes—
71#11929625C2×C8164yescomplemented
72C2×D316C2×C8124yescomplemented
73C2×D316C22×C4112yes—
74C22×Dic79C22×C411yescharacteristic
75C22×Dic79C22×C413yes—
76C22×Dic79C22×C411yescharacteristic
77C2×C4×D79—26no—
78C2×C4×D79—26no—
79C2×C4×D79—46no—
80C2×C4×D79C2×C8124yescomplemented
81C2×C4×D79C22×C416yes—
82C2×C4×D79C22×C4112yes—
83C2×C4×D79C22×C4112yes—
84C2×C4×D79C2416yes—
85C2×C79⋊C8—26no—
86C2×C79⋊C8—22no—
87C2×C79⋊C8C2412yes—
88C2×C79⋊C8C2416yes—
89C8×D79—424no—
90C4⋊Dic79C22×C4112yes—
91(C2×D79)⋊C4C22×C4124yes—
92C4×Dic79C22×C412yes—
93C4×Dic79C22×C4112yes—
94C4×Dic79C22×C4112yes—
95C4×Dic79C2412yes—
96C2×Q8×C79C2×C818yescomplemented
97C2×Q8×C79C22×C414yes—
98C22×C4×C79C22×C413yes—
99C22×C4×C79C22×C413yes—
100C22×C4×C79C2411yescharacteristic
101C2×C8×C79—26no—
102C2×C8×C79—22no—
103C2×C8×C79C2412yes—
104C2×C8×C79C2416yes—
105C4⋊C4×C79C22×C4112yes—
106C42×C79C22×C416yes—
107C42×C79C2416yes—
108C23×C79C23×C411yescharacteristic
109C22×D79—26no—
110C22×D79—26no—
111C22×D79C22×C8112yes—
112C22×D79C23×C416yes—
113Q8×C79C22×C8116yescomplemented
114C2×C4×C79—26no—
115C2×C4×C79C22×C8112yes—
116C2×C4×C79C23×C416yes—
117C2×C4×C79C23×C411yescharacteristic
118C2×C4×C79C23×C416yes—
119C2×C4×C79H(5,𝔽2)12yes—
120C2×C4×C792−1+412yes—
121C2×C4×C79C2511yescharacteristic
122C2×Dic79—26no—
123C2×Dic79—22no—
124C2×Dic79C22×C814yes—
125C2×Dic79C23×C412yes—
126C2×Dic79C23×C416yes—
127C2×Dic79C23×C412yes—
128D316C22×C8148yescomplemented
129C4×D79—212no—
130C4×D79—26no—
131C4×D79—26no—
132C4×D79—412no—
133C4×D79C22×C8148yescomplemented
134C8×C79—26no—
135C8×C79—22no—
136C79⋊C8—26no—
137C79⋊C8—22no—
138C22×C79#52012yes—
139C22×C79C23×C812yes—
140C22×C79#56812yes—
141C22×C79C24×C411yescharacteristic
142C2×D79—26no—
143C2×D79—224no—
144C2×D79—26no—
145C2×D79C23×C8112yes—
146C4×C79—26no—
147C4×C79#52012yes—
148C4×C79C23×C8112yes—
149C4×C79C2×H(5,𝔽2)11yescharacteristic
150C4×C79C2×2−1+411yescharacteristic
151Dic79—26no—
152Dic79—22no—
153Dic79C23×C814yes—
154C2×#2988—791nomaximal, Sylow
155C2×C79#298814yescomplemented
156C2×C79C2×#52011yescharacteristic
157C2×C79C24×C811yescharacteristic
158C2×C79C2×#56811yescharacteristic
159D79—212no—
160C2×C4×#41—791no—
161#2988—7916no—
162C2×C8×Q8—791no—
163C2×C8×Q8D7911yescharacteristic, complemented
164C2×C8×D4—793no—
165C2×C8×D4—793no—
166C2×#431—793no—
167C22×C4⋊C8—793no—
168C79C2×#298811yescharacteristic, complemented, Sylow
169C22×#41—791no—
170C23×C8—796no—
171C4×#41—798no—
172C4×#41—798no—
173C2×C4×Q8—791no—
174C2×C4×Q8C2×D7911yescharacteristic
175C2×C4×D4—793no—
176C2×C4×D4—793no—
177C2×#117—793no—
178C22×C42—793no—
179C8×Q8—798no—
180C8×Q8C2×D7918yescomplemented
181C8×D4—7924no—
182C8×D4—7924no—
183#431—7924no—
184C2×C4⋊C8—793no—
185C2×C4⋊C8—791no—
186C2×C4⋊C8—793no—
187C2×C4⋊C8—7924no—
188C2×C4⋊C8C2×D7913yes—
189C2×C22⋊C8—793no—
190C2×C22⋊C8—793no—
191C2×C4×C8—793no—
192C2×C4×C8C2×D7913yes—
193C2×#41—7916no—
194C2×#41—798no—
195C22×Q8C4×D7911yescharacteristic
196C22×D4—793no—
197C23×C4—793no—
198C23×C4—793no—
199C23×C4—793no—
200C22×C8—31612no—
201C22×C8—7924no—
202C22×C8—793no—
203C22×C8—791no—
204C22×C8C22×D7913yes—
205C22×C8C22×D7911yescharacteristic
206C4×Q8—798no—
207C4×Q8C4×D7914yes—
208C4×Q8C22×D7914yes—
209C4×D4—7924no—
210C4×D4—7912no—
211C4×D4—7912no—
212#117—7924no—
213C2×C4⋊C4—793no—
214C2×C4⋊C4C4×D7913yes—
215C2×C22⋊C4—796no—
216C2×C42—793no—
217C2×C42—793no—
218C2×C42—791no—
219C2×C42—7912no—
220C2×C42—7912no—
221C2×C42C22×D7913yes—
222C4⋊C8—7912no—
223C4⋊C8—794no—
224C4⋊C8—7912no—
225C4⋊C8C22×D79112yes—
226C22⋊C8—7912no—
227C22⋊C8—7912no—
228C4×C8—7912no—
229C4×C8C22×D79112yes—
230C24—793no—
231#41—7964no—
232C2×Q8C8×D7918yescomplemented
233C2×Q8C2×C4×D7914yes—
234C2×D4—7924no—
235C2×D4—7912no—
236C22×C4—3166no—
237C22×C4—7912no—
238C22×C4—791no—
239C22×C4—7924no—
240C22×C4—7912no—
241C22×C4—791no—
242C22×C4—793no—
243C22×C4—796no—
244C22×C4—796no—
245C22×C4—1586no—
246C22×C4—1586no—
247C22×C4C2×C4×D7913yes—
248C22×C4C2×C4×D7913yes—
249C22×C4C23×D7911yescharacteristic
250C2×C8—26no—
251C2×C8—22no—
252C2×C8—31624no—
253C2×C8—792no—
254C2×C8—796no—
255C2×C8—1586no—
256C2×C8—1582no—
257C2×C8C23×D7912yes—
258C2×C8C23×D7916yes—
259C4⋊C4—7912no—
260C4⋊C4C2×C4×D79112yes—
261C22⋊C4—7924no—
262C42—792no—
263C42—792no—
264C42—7912no—
265C42—7912no—
266C42C2×C4×D7916yes—
267C42C23×D7916yes—
268C23—7912no—
269C23—796no—
270C23—1586no—
271C23—1586no—
272C23C22×C4×D7911yescharacteristic
273Q8C2×C8×D79116yescomplemented
274D4—7948no—
275C2×C4—26no—
276C2×C4—31612no—
277C2×C4—794no—
278C2×C4—792no—
279C2×C4—7948no—
280C2×C4—792no—
281C2×C4—796no—
282C2×C4—1586no—
283C2×C4—1582no—
284C2×C4—1586no—
285C2×C4—1586no—
286C2×C4—15812no—
287C2×C4C2×C8×D79112yes—
288C2×C4C22×C4×D7916yes—
289C2×C4C22×C4×D7911yescharacteristic
290C2×C4C22×C4×D7916yes—
291C2×C4#1457920712yes—
292C2×C4#1457920912yes—
293C2×C4C24×D7911yescharacteristic
294C8—26no—
295C8—22no—
296C8—1586no—
297C8—1582no—
298C22—7912no—
299C22—1586no—
300C22—1586no—
301C22—15824no—
302C22#1909904512yes—
303C22C22×C8×D7912yes—
304C22#1909932812yes—
305C22C23×C4×D7911yescharacteristic
306C4—26no—
307C4—794no—
308C4—1582no—
309C4—1586no—
310C4#1909904512yes—
311C4C22×C8×D79112yes—
312C4C2×#1457920711yescharacteristic
313C4C2×#1457920911yescharacteristic
314C2—15812no—
315C2#2377251014yesdirect product factor
316C2C2×#1909904511yescharacteristic
317C2C23×C8×D7911yescharacteristic
318C2C2×#1909932811yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC2×C79C24×C8
FrattiniC2×C4C24×D79
FittingC2×C8×Q8×C79C2
socleC23×C79C23×C4
prime radicalC22×#11929625C4
cosocleC2×C4×C79C25
hypercenterC2×C8×Q8D79
hypocenterC79C2×#2988
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #23772510C2direct (N × H)
3. C2×Q8×C79⋊C8C2semidirect
4. C2×C8×D316C2semidirect
5. C2×#19098628C2semidirect
6. C2×#19098614C2semidirect
7. C2×C4⋊C8×D79C2semidirect
8. C2×C8×Q8×C79C2semidirect
18. Q8×C79⋊C8C22semidirect
19. C8×D316C22semidirect
20. #19098628C22semidirect
21. #19098614C22semidirect
25. C4⋊C8×D79C22semidirect
30. C8×Q8×C79C22semidirect
33. C2×#11929625C8semidirect
71. #11929625C2×C8semidirect
72. C2×D316C2×C8semidirect
80. C2×C4×D79C2×C8semidirect
96. C2×Q8×C79C2×C8semidirect
113. Q8×C79C22×C8semidirect
128. D316C22×C8semidirect
133. C4×D79C22×C8semidirect
155. C2×C79#2988semidirect
163. C2×C8×Q8D79semidirect
168. C79C2×#2988semidirect
180. C8×Q8C2×D79semidirect
232. C2×Q8C8×D79semidirect
273. Q8C2×C8×D79semidirect
315. C2#23772510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#119296252
#237725102
C2×Q8×C79⋊C82
C2×C8×D3162
C2×#190986282
C2×#190986142
C2×C4⋊C8×D792
C2×C8×Q8×C792
C2×#298879