Finite Group Databasebeta

← C2×#23757457 #34109479

Subgroups — C2×#23757457 #34109479

Order 20096.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097818C211yesmaximal, characteristic
2C2×#19097804C211yesmaximal, characteristic, complemented
3C2×#19097801C211yesmaximal, characteristic, complemented
4C2×#19097771C211yesmaximal, characteristic, complemented
5#23757457C218yesmaximal, direct product factor
6C2×#19097699C211yesmaximal, characteristic, complemented
7C2×#19097689C211yesmaximal, characteristic, complemented
8C2×#104×C157C211yesmaximal, characteristic, complemented
9#19097818—22no—
10#19097818—22no—
11#19097818—22no—
12#19097818C2214yes—
13C2×#14578954—21no—
14C2×#14578954C2211yescharacteristic
15C2×#14578953—21no—
16C2×#14578953—22no—
17C22×Dic314—21no—
18C22×Dic314C2211yescharacteristic
19C22×Dic314C2211yescharacteristic
20C2×Q8×D157—21no—
21#19097804—22no—
22#19097804C2214yescomplemented
23#19097801—22no—
24#19097801C2214yescomplemented
25C2×Dic628—21no—
26C2×#14578944—21no—
27C2×#14578943—21no—
28C2×#14578942—21no—
29C2×#14578938C2211yescharacteristic
30#19097771—22no—
31#19097771C2214yescomplemented
32C2×C4⋊Dic157—22no—
33#19097699C2214yescomplemented
34#19097689C2214yescomplemented
35C2×#41×C157C2211yescharacteristic
36C2×M16×C157C2211yescharacteristic
37C2×C42×C157C2211yescharacteristic
38#104×C157C2214yescomplemented
39#14578954—24no—
40#14578954—24no—
41#14578954—21no—
42#14578954—21no—
43#14578954D412yes—
44#14578954C2312yes—
45#14578953—28no—
46#14578953—24no—
47#14578953—28no—
48#14578953—24no—
49C2×Dic314—22no—
50C2×Dic314—24no—
51C2×Dic314—24no—
52C2×Dic314—21no—
53C2×Dic314—21no—
54C2×Dic314—21no—
55C2×Dic314—21no—
56C2×Dic314—21no—
57C2×Dic314—21no—
58C2×Dic314—21no—
59C2×Dic314—21no—
60C2×Dic314—21no—
61C2×Dic314D411yescharacteristic
62C2×Dic314D412yes—
63C2×Dic314C2312yes—
64C2×Dic314C2312yes—
65Q8×D157—24no—
66Q8×D157—24no—
67C2×D628D411yescharacteristic
68C2×C22⋊D157—22no—
69C2×C22⋊D157—21no—
70C22×Dic157—22no—
71C22×Dic157—21no—
72C22×Dic157D412yes—
73C2×C4×D157—22no—
74C2×C4×D157—21no—
75Dic628—24no—
76#14578944—24no—
77#14578943—24no—
78#14578942—24no—
79#14578938—21no—
80#14578938C2312yes—
81C2×#11929434—21no—
82C4⋊Dic157—28no—
83#41×C157—21no—
84#41×C157—21no—
85#41×C157D412yes—
86#41×C157C2312yes—
87C2×Q8×C157D411yescharacteristic
88C2×D4×C157—21no—
89C2×D4×C157D411yescharacteristic
90C22×C4×C157—21no—
91C22×C4×C157—21no—
92C22×C4×C157C2311yescharacteristic
93M16×C157—21no—
94M16×C157C2312yes—
95C2×C8×C157—21no—
96C42×C157—21no—
97C42×C157C2312yes—
98C22×D157—21no—
99Dic314—28no—
100Dic314—22no—
101Dic314—21no—
102Dic314—22no—
103Dic314—22no—
104Dic314—22no—
105Dic314—22no—
106Dic314—22no—
107Dic314—41no—
108Dic314—41no—
109Dic314C2×D412yes—
110D628—21no—
111D628C2×D412yes—
112C22⋊D157—28no—
113C22⋊D157—22no—
114C22⋊D157—22no—
115C2×Dic157—28no—
116C2×Dic157—21no—
117C2×Dic157—22no—
118C2×Dic157—22no—
119C2×Dic157—22no—
120C2×Dic157—41no—
121C2×Dic157—41no—
122C2×Dic157C2×D414yes—
123C4×D157—28no—
124C4×D157—22no—
125C4×D157—22no—
126#11929434—22no—
127C23×C157—21no—
128C23×C157C2×D411yescharacteristic
129Q8×C157—21no—
130Q8×C157C2×D412yes—
131D4×C157—22no—
132D4×C157—22no—
133D4×C157—21no—
134D4×C157C2×D412yes—
135C2×C4×C157—24no—
136C2×C4×C157—21no—
137C2×C4×C157—22no—
138C2×C4×C157—22no—
139C2×C4×C157—22no—
140C2×C4×C157C2×D411yescharacteristic
141C2×C4×C157C2×D411yescharacteristic
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2411yescharacteristic
146C8×C157—22no—
147C22×C157—22no—
148C22×C157—22no—
149C22×C157—42no—
150C22×C157#12011yescharacteristic
151C22×C157#12011yescharacteristic
152C22×C157C22×D411yescharacteristic
153C2×D157—22no—
154C2×D157—42no—
155C4×C157—24no—
156C4×C157—22no—
157C4×C157#12011yescharacteristic
158C4×C157#12011yescharacteristic
159C4×C157C22×D411yescharacteristic
160C4×C157C22×D411yescharacteristic
161Dic157—22no—
162Dic157—24no—
163Dic157—42no—
164C2×C157—21no—
165C2×C157—21no—
166C2×C157—42no—
167C2×C157#45612yescomplemented
168C2×C157C2×#12011yescharacteristic
169D157—42no—
170C157C2×#45611yescharacteristic, complemented, Sylow
171C2×#456—1571nomaximal, Sylow
172C2×2−1+4—1571no—
173C2×#137—1571no—
174C2×#137—1571no—
175C2×C4⋊Q8—1571no—
176#456—1578no—
177C2×#104—1571no—
178C2×#104D15711yescharacteristic, complemented
179C2×#101—1571no—
1802−1+4—3142no—
1812−1+4—3142no—
1822−1+4—3142no—
1832−1+4—1574no—
184C2×#41—3141no—
185C2×#41—3141no—
186C2×#41—3142no—
187C2×#41—1571no—
188C2×#41C2×D15711yescharacteristic
189C22×Q8—3141no—
190C22×Q8—3141no—
191C22×Q8—1571no—
192C22×Q8—1571no—
193#137—3142no—
194#137—3142no—
195#137—1574no—
196#137—1574no—
197C2×Q16—3141no—
198C2×Q16—3141no—
199C2×SD16—3141no—
200C2×SD16—3141no—
201C2×M16—1571no—
202C2×M16C2×D15711yescharacteristic
203C4⋊Q8—3142no—
204C4⋊Q8—1574no—
205C2×C4⋊C4—3142no—
206C2×C42C2×D15711yescharacteristic
207#104—1574no—
208#104C2×D15714yescomplemented
209#101—1574no—
210#41—21no—
211#41—21no—
212#41—3144no—
213#41—3144no—
214#41—3148no—
215#41—3144no—
216#41—3144no—
217#41—3148no—
218#41—3141no—
219#41—3141no—
220#41—1572no—
221#41—1572no—
222#41D62812yes—
223#41C22×D15712yes—
224C2×Q8—3142no—
225C2×Q8—3144no—
226C2×Q8—3144no—
227C2×Q8—3144no—
228C2×Q8—3144no—
229C2×Q8—3141no—
230C2×Q8—3141no—
231C2×Q8—3141no—
232C2×Q8—3141no—
233C2×Q8—3141no—
234C2×Q8—3141no—
235C2×Q8—3141no—
236C2×Q8—3141no—
237C2×Q8—3141no—
238C2×Q8—1571no—
239C2×Q8—1572no—
240C2×Q8—1572no—
241C2×Q8—1572no—
242C2×Q8D62811yescharacteristic
243C2×D4—21no—
244C2×D4—3142no—
245C2×D4—3141no—
246C2×D4—1571no—
247C2×D4D62811yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3142no—
251C22×C4—3142no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—1572no—
255C22×C4C22×D15711yescharacteristic
256Q16—3144no—
257Q16—3144no—
258SD16—3144no—
259SD16—3144no—
260M16—21no—
261M16—3141no—
262M16—1572no—
263M16C22×D15712yes—
264C2×C8—21no—
265C2×C8—3141no—
266C4⋊C4—3148no—
267C42—21no—
268C42C22×D15712yes—
269C23—21no—
270C23—3141no—
271C23D4×D15711yescharacteristic
272Q8—21no—
273Q8—3148no—
274Q8—3141no—
275Q8—3142no—
276Q8—3142no—
277Q8—3142no—
278Q8—3142no—
279Q8—3142no—
280Q8—3142no—
281Q8—6281no—
282Q8—6281no—
283Q8—1572no—
284Q8C2×D62812yes—
285D4—22no—
286D4—22no—
287D4—21no—
288D4—3148no—
289D4—3142no—
290D4—3142no—
291D4—3141no—
292D4—1572no—
293D4C2×D62812yes—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—3148no—
300C2×C4—3148no—
301C2×C4—3142no—
302C2×C4—3141no—
303C2×C4—3142no—
304C2×C4—3142no—
305C2×C4—3142no—
306C2×C4—3142no—
307C2×C4—6281no—
308C2×C4—6281no—
309C2×C4—1574no—
310C2×C4D4×D15711yescharacteristic
311C2×C4D4×D15711yescharacteristic
312C2×C4D4×D15711yescharacteristic
313C2×C4C2×D62811yescharacteristic
314C2×C4C2×D62811yescharacteristic
315C2×C4C23×D15711yescharacteristic
316C8—22no—
317C8—3142no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—3142no—
322C22—6282no—
323C22#1909774111yescharacteristic
324C22#1909774111yescharacteristic
325C22C2×D4×D15711yescharacteristic
326C4—24no—
327C4—22no—
328C4—3142no—
329C4—3144no—
330C4—6282no—
331C4#1909774111yescharacteristic
332C4#1909774111yescharacteristic
333C4C2×D4×D15711yescharacteristic
334C4C22×D62811yescharacteristic
335C2—21no—
336C2—21no—
337C2—42no—
338C2—6282no—
339C2#2375745712yesdirect product factor
340C2C2×#1909774111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#104×C157C2
socleC22×C157#120
prime radicalC2×#19097818C2
hypercenterC2×#104D157
hypocenterC157C2×#456
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#19097804C2semidirect
3. C2×#19097801C2semidirect
4. C2×#19097771C2semidirect
5. #23757457C2direct (N × H)
6. C2×#19097699C2semidirect
7. C2×#19097689C2semidirect
8. C2×#104×C157C2semidirect
22. #19097804C22semidirect
24. #19097801C22semidirect
31. #19097771C22semidirect
33. #19097699C22semidirect
34. #19097689C22semidirect
38. #104×C157C22semidirect
167. C2×C157#456semidirect
170. C157C2×#456semidirect
178. C2×#104D157semidirect
208. #104C2×D157semidirect
339. C2#23757457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978182
C2×#190978042
C2×#190978012
C2×#190977712
#237574572
C2×#190976992
C2×#190976892
C2×#104×C1572
C2×#456157