Finite Group Databasebeta

← C2×#23752403 #34078499

Subgroups — C2×#23752403 #34078499

Order 19328.

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

normal subgroups only

This group has 794 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×#18012784C211yesmaximal, characteristic
2C2×#18012723C212yesmaximal, complemented
3C2×#18012720C211yesmaximal, characteristic, complemented
4#23752403C218yesmaximal, direct product factor
5C2×#18012653C212yesmaximal, complemented
6C2×#99×C151C211yesmaximal, characteristic, complemented
7#18012784—22no—
8#18012784—24no—
9#18012784C2214yes—
10C2×#14559004—21no—
11C2×#14559003—22no—
12C22×C22⋊D151—21no—
13C22×C22⋊D151C2212yes—
14C2×D4×D151—22no—
15C23×Dic151C2211yescharacteristic, complemented
16#18012723—24no—
17#18012723C2218yescomplemented
18#18012720—22no—
19#18012720C2214yescomplemented
20C2×C4⋊Dic151—22no—
21C2×Dic151⋊C4—21no—
22C2×C22⋊Dic151—21no—
23C2×C22⋊Dic151C2211yescharacteristic, complemented
24C2×(C2×D151)⋊C4—22no—
25#18012653C2218yescomplemented
26C22×D4×C151C2211yescharacteristic
27C2×C22⋊C4×C151C2212yescomplemented
28#99×C151C2214yescomplemented
29C23×D151—21no—
30C23×D151D412yes—
31#14559004—24no—
32#14559004—24no—
33#14559003—28no—
34#14559003—28no—
35C2×Dic302—21no—
36C2×D604—21no—
37C2×C22⋊D151—22no—
38C2×C22⋊D151—24no—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—22no—
41C2×C22⋊D151—24no—
42C2×C22⋊D151—22no—
43C2×C22⋊D151—22no—
44C2×C22⋊D151D414yes—
45C2×C22⋊D151C2314yes—
46D4×D151—28no—
47D4×D151—28no—
48C22×Dic151—21no—
49C22×Dic151—22no—
50C22×Dic151—21no—
51C22×Dic151—21no—
52C22×Dic151—21no—
53C22×Dic151—22no—
54C22×Dic151D412yes—
55C22×Dic151C2312yescomplemented
56C2×C4×D151—22no—
57C4⋊Dic151—28no—
58Dic151⋊C4—24no—
59C22⋊Dic151—24no—
60C22⋊Dic151—21no—
61C22⋊Dic151C2312yescomplemented
62(C2×D151)⋊C4—28no—
63C24×C151D411yescharacteristic
64C24×C151C2311yescharacteristic
65C2×D4×C151—22no—
66C2×D4×C151—22no—
67C2×D4×C151D412yes—
68C2×D4×C151C2312yes—
69C22×C4×C151—22no—
70C22×C4×C151D411yescharacteristic
71C22⋊C4×C151—22no—
72C22⋊C4×C151C2314yescomplemented
73C22×D151—22no—
74C22×D151—24no—
75C22×D151—22no—
76C22×D151—44no—
77C22×D151—82no—
78C22×D151C2×D414yes—
79Dic302—24no—
80D604—24no—
81C22⋊D151—28no—
82C22⋊D151—24no—
83C22⋊D151—24no—
84C22⋊D151—24no—
85C22⋊D151—24no—
86C2×Dic151—24no—
87C2×Dic151—22no—
88C2×Dic151—22no—
89C2×Dic151—24no—
90C2×Dic151—22no—
91C2×Dic151—22no—
92C2×Dic151—42no—
93C2×Dic151—41no—
94C2×Dic151—42no—
95C2×Dic151—41no—
96C2×Dic151C2×D414yes—
97C4×D151—28no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—42no—
101C23×C151—42no—
102C23×C151C2×D412yes—
103C23×C151C2×D412yes—
104C23×C151C2×D411yescharacteristic
105C23×C151C2×D412yes—
106C23×C151C2×D411yescharacteristic
107C23×C151C2411yescharacteristic
108D4×C151—24no—
109D4×C151—24no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—24no—
113C2×C4×C151—44no—
114C2×C4×C151C2×D412yes—
115C22×C151—24no—
116C22×C151—22no—
117C22×C151—22no—
118C22×C151—42no—
119C22×C151—41no—
120C22×C151—41no—
121C22×C151—42no—
122C22×C151—42no—
123C22×C151—81no—
124C22×C151#12011yescharacteristic
125C22×C151#12012yes—
126C22×C151#12011yescharacteristic
127C22×C151C22×D412yes—
128C22×C151C22×D411yescharacteristic
129C2×D151—24no—
130C2×D151—44no—
131C2×D151—44no—
132C2×D151—82no—
133C2×D151—84no—
134C4×C151—22no—
135C4×C151—44no—
136Dic151—24no—
137Dic151—42no—
138Dic151—42no—
139C2×C151—21no—
140C2×C151—22no—
141C2×C151—22no—
142C2×C151—21no—
143C2×C151—42no—
144C2×C151#45812yescomplemented
145C2×C151C2×#12011yescharacteristic
146D151—44no—
147C151C2×#45811yescharacteristic, complemented, Sylow
148C2×#458—1511nomaximal, Sylow
149C2×H(5,𝔽2)—1511no—
150C2×#123—1511no—
151C2×#123—1512no—
152#458—1518no—
153C2×#99—1512no—
154C2×#99D15111yescharacteristic, complemented
155H(5,𝔽2)—3024no—
156H(5,𝔽2)—3022no—
157H(5,𝔽2)—1514no—
158C2×#41—3022no—
159C2×#41—3021no—
160C22×D4—3022no—
161C22×D4—3021no—
162C22×D4—1512no—
163C22×D4C2×D15111yescharacteristic
164C23×C4—1511no—
165#123—3024no—
166#123—3022no—
167#123—1514no—
168#123—1518no—
169C2×C4⋊C4—3022no—
170C2×C4⋊C4—3021no—
171C2×C22⋊C4—3022no—
172C2×C22⋊C4—3021no—
173C2×C22⋊C4—1511no—
174C2×C22⋊C4C2×D15112yescomplemented
175#99—1518no—
176#99C2×D15114yescomplemented
177C24—3021no—
178C24—1512no—
179C24D60411yescharacteristic
180C24C22×D15111yescharacteristic
181#41—3024no—
182#41—3028no—
183#41—3028no—
184#41—3024no—
185C2×Q8—3021no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—3021no—
189C2×D4—3028no—
190C2×D4—3028no—
191C2×D4—3022no—
192C2×D4—3024no—
193C2×D4—3022no—
194C2×D4—3022no—
195C2×D4—3022no—
196C2×D4—3024no—
197C2×D4—3022no—
198C2×D4—1514no—
199C2×D4—1514no—
200C2×D4D60412yes—
201C2×D4C22×D15112yes—
202C22×C4—22no—
203C22×C4—3022no—
204C22×C4—3021no—
205C22×C4—3022no—
206C22×C4—3022no—
207C22×C4—3021no—
208C22×C4—3021no—
209C22×C4—3021no—
210C22×C4—1512no—
211C22×C4—1512no—
212C22×C4D60411yescharacteristic
213C4⋊C4—3028no—
214C4⋊C4—3024no—
215C22⋊C4—22no—
216C22⋊C4—3028no—
217C22⋊C4—3024no—
218C22⋊C4—3021no—
219C22⋊C4—1512no—
220C22⋊C4C22×D15114yescomplemented
221C23—21no—
222C23—21no—
223C23—42no—
224C23—42no—
225C23—3024no—
226C23—3022no—
227C23—3022no—
228C23—6044no—
229C23—1514no—
230C23—12082no—
231C23D4×D15112yes—
232C23D4×D15112yes—
233C23C2×D60411yescharacteristic
234C23C2×D60412yes—
235C23C2×D60411yescharacteristic
236C23C23×D15111yescharacteristic
237Q8—3024no—
238D4—24no—
239D4—24no—
240D4—3024no—
241D4—3028no—
242D4—3024no—
243D4—3024no—
244D4—3024no—
245D4—3024no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—24no—
249C2×C4—44no—
250C2×C4—3028no—
251C2×C4—3024no—
252C2×C4—3022no—
253C2×C4—3022no—
254C2×C4—3024no—
255C2×C4—3022no—
256C2×C4—3022no—
257C2×C4—6042no—
258C2×C4—6041no—
259C2×C4—6042no—
260C2×C4—6041no—
261C2×C4—1514no—
262C2×C4C2×D60412yes—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—81no—
272C22—3024no—
273C22—6044no—
274C22—6044no—
275C22—12082no—
276C22—12084no—
277C22#1801270911yescharacteristic
278C22#1801270912yes—
279C22#1801270911yescharacteristic
280C22C2×D4×D15112yes—
281C22C22×D60411yescharacteristic
282C4—22no—
283C4—44no—
284C4—3024no—
285C4—6042no—
286C4—6042no—
287C2—22no—
288C2—21no—
289C2—21no—
290C2—22no—
291C2—42no—
292C2—6044no—
293C2#2375240312yesdirect product factor
294C2C2×#1801270911yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
FittingC2×#99×C151C2
socleC22×C151#120
prime radicalC2×#18012784C2
hypercenterC2×#99D151
hypocenterC151C2×#458
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#18012723C2semidirect
3. C2×#18012720C2semidirect
4. #23752403C2direct (N × H)
5. C2×#18012653C2semidirect
6. C2×#99×C151C2semidirect
15. C23×Dic151C22semidirect
17. #18012723C22semidirect
19. #18012720C22semidirect
23. C2×C22⋊Dic151C22semidirect
25. #18012653C22semidirect
27. C2×C22⋊C4×C151C22semidirect
28. #99×C151C22semidirect
55. C22×Dic151C23semidirect
61. C22⋊Dic151C23semidirect
72. C22⋊C4×C151C23semidirect
144. C2×C151#458semidirect
147. C151C2×#458semidirect
154. C2×#99D151semidirect
174. C2×C22⋊C4C2×D151semidirect
176. #99C2×D151semidirect
220. C22⋊C4C22×D151semidirect
293. C2#23752403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180127842
C2×#180127232
C2×#180127202
#237524032
C2×#180126532
C2×#99×C1512
C2×#458151