Finite Group Databasebeta

← C2×#23776067 #35167861

Subgroups — C2×#23776067 #35167861

Order 20224.

2174 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic158C211yesmaximal, characteristic, complemented
2#23776067C2116yesmaximal, direct product factor
3C2×#19098909C213yesmaximal, complemented
4C2×#19098853C213yesmaximal, complemented
5C2×#19098760C213yesmaximal, complemented
6C2×Q8×C79⋊C8C211yesmaximal, characteristic, complemented
7C2×C4×#11929612C213yesmaximal, complemented
8C2×#550×C79C211yesmaximal, characteristic
9C22×#11929612C2213yes—
10Q8×Dic158—24no—
11Q8×Dic158C2218yescomplemented
12C2×#14579161C2213yes—
13C2×#14579160—23no—
14C2×Q8×Dic79—21no—
15C2×C4×Dic158C2213yes—
16#19098909C22124yescomplemented
17#19098853C22124yescomplemented
18#19098760C22124yescomplemented
19Q8×C79⋊C8C2218yescomplemented
20C4×#11929612C22124yescomplemented
21C2×#14579092C2213yes—
22C2×C4⋊(C79⋊C8)C2213yes—
23C2×#14579084C2211yescharacteristic
24C2×#14579082C2213yes—
25C2×#14579082C2216yes—
26C2×C4×C79⋊C8C2213yes—
27C22×#41×C79—21no—
28#550×C79—24no—
29#550×C79C2218yes—
30C2×#127×C79C2213yes—
31C2×#121×C79—23no—
32C2×C4×Q8×C79C2211yescharacteristic
33C2×C4×D4×C79C2213yes—
34C22×Dic158—23no—
35C22×Dic158C2311yescharacteristic
36C2×#11929612—212no—
37C2×#11929612C23112yes—
38C22×C79⋊C8C2311yescharacteristic
39C22×C79⋊C8C2313yes—
40#14579161—26no—
41#14579161C23112yes—
42#14579160—224no—
43Q8×Dic79—28no—
44C4×Dic158—26no—
45C4×Dic158C23112yes—
46C2×C4⋊Dic79—23no—
47C2×C4⋊Dic79C2313yes—
48C2×Dic79⋊C4—23no—
49C2×C4×Dic79—23no—
50#14579092C23112yes—
51C4⋊(C79⋊C8)C23112yes—
52#14579084C2314yes—
53#14579082C23112yes—
54#14579082C23124yes—
55C4×C79⋊C8C23112yes—
56C2×#41×C79—28no—
57C2×#41×C79—48no—
58C22×Q8×C79D411yescharacteristic
59C22×D4×C79—23no—
60C22×D4×C79—23no—
61C22×D4×C79C2313yes—
62C23×C4×C79—23no—
63#127×C79—26no—
64#127×C79C23112yes—
65#121×C79—224no—
66C4×Q8×C79D414yes—
67C4×Q8×C79C2314yes—
68C4×D4×C79—26no—
69C4×D4×C79C23112yes—
70C2×C4⋊C4×C79D413yes—
71C2×C4⋊C4×C79C2311yescharacteristic
72C2×C22⋊C4×C79—23no—
73C2×C42×C79C2313yes—
74C2×Dic158—21no—
75C2×Dic158—212no—
76C2×Dic158—22no—
77C2×Dic158—86no—
78C2×Dic158#4114yescomplemented
79C2×Dic158C2412yes—
80C22×Dic79—21no—
81C22×Dic79—23no—
82#11929612—224no—
83C2×C79⋊C8—26no—
84C2×C79⋊C8—22no—
85C2×C79⋊C8C2412yes—
86C2×C79⋊C8C2416yes—
87C4⋊Dic79—212no—
88C4⋊Dic79—23no—
89C4⋊Dic79C2416yes—
90Dic79⋊C4—212no—
91C4×Dic79—212no—
92C24×C79—23no—
93#41×C79—432no—
94C2×Q8×C79SD1618yescomplemented
95C2×Q8×C79C2×D414yes—
96C2×D4×C79—23no—
97C2×D4×C79—212no—
98C2×D4×C79—212no—
99C2×D4×C79—26no—
100C2×D4×C79—26no—
101C2×D4×C79—412no—
102C2×D4×C79—86no—
103C2×D4×C79C2416yes—
104C22×C4×C79—21no—
105C22×C4×C79—212no—
106C22×C4×C79—412no—
107C22×C4×C79C2×D413yes—
108C22×C4×C79C2×D413yes—
109C22×C4×C79C2411yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79C2×D4112yes—
112C4⋊C4×C79C2412yes—
113C22⋊C4×C79—212no—
114C42×C79C2×D416yes—
115C42×C79C2416yes—
116C23×C79—26no—
117C23×C79—46no—
118C23×C79—46no—
119C23×C79—46no—
120C23×C79C22×D411yescharacteristic
121Q8×C79C2×SD16116yescomplemented
122D4×C79—26no—
123D4×C79—26no—
124D4×C79—46no—
125D4×C79—424no—
126D4×C79—812no—
127C2×C4×C79—26no—
128C2×C4×C79—22no—
129C2×C4×C79—42no—
130C2×C4×C79—424no—
131C2×C4×C79C2×SD16112yes—
132C2×C4×C79C22×D416yes—
133C2×C4×C79C22×D411yescharacteristic
134C2×C4×C79C22×D416yes—
135C2×C4×C79C2×#4112yes—
136C2×C4×C792−1+412yes—
137C2×C4×C79C2511yescharacteristic
138C2×Dic79—24no—
139C2×Dic79—22no—
140C2×Dic79—26no—
141C2×Dic79—46no—
142Dic158—24no—
143Dic158—22no—
144Dic158—812no—
145Dic158C2×#4114yescomplemented
146C79⋊C8—26no—
147C79⋊C8—22no—
148C22×C79—46no—
149C22×C79—46no—
150C22×C79—46no—
151C22×C79—812no—
152C22×C79#54812yes—
153C22×C79C22×SD1612yes—
154C22×C79#57612yes—
155C22×C79C23×D411yescharacteristic
156C4×C79—26no—
157C4×C79—42no—
158C4×C79#54812yes—
159C4×C79C22×SD16112yes—
160C4×C79C22×#4111yescharacteristic
161C4×C79C2×2−1+411yescharacteristic
162Dic79—24no—
163Dic79—46no—
164C2×#3362—791nomaximal, Sylow
165C2×C79—86no—
166C2×C79#336214yescomplemented
167C2×C79C2×#54811yescharacteristic
168C2×C79C23×SD1611yescharacteristic
169C2×C79C2×#57611yescharacteristic
170C2×Q82—791no—
171C2×#550D7911yescharacteristic
172#3362—7916no—
173C2×#486—793no—
174C2×#476—793no—
175C2×#460—793no—
176C2×C8×Q8—791no—
177C2×C4×SD16—793no—
178C79C2×#336211yescharacteristic, complemented, Sylow
179C22×#41—21no—
180C22×SD16—793no—
181Q82—798no—
182Q82—1584no—
183#550—24no—
184#550C2×D7918yes—
185C2×C4⋊Q8—793no—
186C2×C4⋊Q8—1583no—
187C2×#127C2×D7913yes—
188C2×#121—23no—
189C2×C4×Q8—793no—
190C2×C4×Q8—1581no—
191C2×C4×Q8C2×D7911yescharacteristic
192C2×C4×D4C2×D7913yes—
193#486—7924no—
194#476—7924no—
195#460—7924no—
196C8×Q8—798no—
197C4×SD16—7924no—
198C2×#106—793no—
199C2×C4⋊C8—793no—
200C2×#103—791no—
201C2×#102—793no—
202C2×#102—796no—
203C2×C4×C8—793no—
204C2×#41—28no—
205C2×#41—48no—
206C22×Q8—791no—
207C22×Q8—1583no—
208C22×Q8C22⋊D7911yescharacteristic
209C22×D4—23no—
210C22×D4—23no—
211C22×D4C22×D7913yes—
212C23×C4—23no—
213C2×SD16—7912no—
214C2×SD16—15812no—
215C22×C8—793no—
216C22×C8—791no—
217C4⋊Q8—7912no—
218C4⋊Q8—15824no—
219C4⋊Q8—1586no—
220#127—26no—
221#127C22×D79112yes—
222#121—224no—
223C4×Q8—7912no—
224C4×Q8—1588no—
225C4×Q8—1586no—
226C4×Q8C22⋊D7914yes—
227C4×Q8C22×D7914yes—
228C4×D4—26no—
229C4×D4C22×D79112yes—
230C2×C4⋊C4—793no—
231C2×C4⋊C4—1583no—
232C2×C4⋊C4—1583no—
233C2×C4⋊C4C22⋊D7913yes—
234C2×C4⋊C4C22×D7911yescharacteristic
235C2×C22⋊C4—23no—
236C2×C42—1583no—
237C2×C42C22×D7913yes—
238#106—7912no—
239C4⋊C8—7912no—
240#103—794no—
241#102—7912no—
242#102—7924no—
243C4×C8—7912no—
244C24—23no—
245#41—432no—
246C2×Q8—794no—
247C2×Q8—792no—
248C2×Q8—6326no—
249C2×Q8—1582no—
250C2×Q8—15812no—
251C2×Q8—1581no—
252C2×Q8#1192961218yescomplemented
253C2×Q8C2×C22⋊D7914yes—
254C2×D4—26no—
255C2×D4—26no—
256C2×D4—23no—
257C2×D4—212no—
258C2×D4—212no—
259C2×D4—412no—
260C2×D4—86no—
261C2×D4C23×D7916yes—
262C22×C4—21no—
263C22×C4—212no—
264C22×C4—412no—
265C22×C4—1583no—
266C22×C4—1581no—
267C22×C4C2×C22⋊D7913yes—
268C22×C4C2×C22⋊D7913yes—
269C22×C4C23×D7911yescharacteristic
270SD16—15824no—
271C2×C8—792no—
272C2×C8—796no—
273C2×C8—1586no—
274C2×C8—1582no—
275C4⋊C4—21no—
276C4⋊C4—796no—
277C4⋊C4—15812no—
278C4⋊C4—1583no—
279C4⋊C4—15812no—
280C4⋊C4C2×C22⋊D79112yes—
281C4⋊C4C23×D7912yes—
282C22⋊C4—212no—
283C42—15812no—
284C42C2×C22⋊D7916yes—
285C42C23×D7916yes—
286C23—26no—
287C23—46no—
288C23—46no—
289C23—46no—
290C23C22×C22⋊D7911yescharacteristic
291Q8—794no—
292Q8—63212no—
293Q8—1582no—
294Q8—1584no—
295Q8C2×#11929612116yescomplemented
296D4—26no—
297D4—26no—
298D4—46no—
299D4—424no—
300D4—812no—
301C2×C4—26no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—424no—
305C2×C4—3166no—
306C2×C4—1586no—
307C2×C4—1584no—
308C2×C4—1582no—
309C2×C4C2×#11929612112yes—
310C2×C4C22×C22⋊D7916yes—
311C2×C4C22×C22⋊D7911yescharacteristic
312C2×C4C22×C22⋊D7916yes—
313C2×C4#41×D7912yes—
314C2×C4#1457920812yes—
315C2×C4C24×D7911yescharacteristic
316C8—1582no—
317C8—1586no—
318C22—46no—
319C22—46no—
320C22—46no—
321C22—812no—
322C22#1909922012yes—
323C22C22×#1192961212yes—
324C22#1909936612yes—
325C22C23×C22⋊D7911yescharacteristic
326C4—26no—
327C4—42no—
328C4—3166no—
329C4—1584no—
330C4#1909922012yes—
331C4C22×#11929612112yes—
332C4C2×#41×D7911yescharacteristic
333C4C2×#1457920811yescharacteristic
334C2—86no—
335C2#2377606714yesdirect product factor
336C2C2×#1909922011yescharacteristic
337C2C23×#1192961211yescharacteristic
338C2C2×#1909936611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
Fitting, prime radicalC2×#550×C79C2
socleC23×C79C22×D4
hypercenterC2×#550D79
hypocenterC79C2×#3362
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic158C2semidirect
2. #23776067C2direct (N × H)
3. C2×#19098909C2semidirect
4. C2×#19098853C2semidirect
5. C2×#19098760C2semidirect
6. C2×Q8×C79⋊C8C2semidirect
7. C2×C4×#11929612C2semidirect
11. Q8×Dic158C22semidirect
16. #19098909C22semidirect
17. #19098853C22semidirect
18. #19098760C22semidirect
19. Q8×C79⋊C8C22semidirect
20. C4×#11929612C22semidirect
78. C2×Dic158#41semidirect
94. C2×Q8×C79SD16semidirect
121. Q8×C79C2×SD16semidirect
145. Dic158C2×#41semidirect
166. C2×C79#3362semidirect
178. C79C2×#3362semidirect
252. C2×Q8#11929612semidirect
295. Q8C2×#11929612semidirect
335. C2#23776067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1582
#237760672
C2×#190989092
C2×#190988532
C2×#190987602
C2×Q8×C79⋊C82
C2×C4×#119296122
C2×#550×C792
C2×#336279