Finite Group Databasebeta

← #34055911

Subgroups — #34055911

Order 19072.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C4⋊Q8×D149C211yesmaximal, characteristic, complemented
2#23750157C211yesmaximal, characteristic
3#23750032C212yesmaximal, complemented
4#23749983C212yesmaximal, complemented
5#23749957C212yesmaximal, complemented
6#23749937C212yesmaximal
7#23749921C211yesmaximal, characteristic, complemented
8#23749917C211yesmaximal, characteristic, complemented
9#23749915C211yesmaximal, characteristic, complemented
10#23749681C211yesmaximal, characteristic, complemented
11#476×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149—21no—
13#18011911C2211yescharacteristic
14#18011910—21no—
15#18011910C2212yes—
16#18011909—21no—
17#18011904—21no—
18#18011902C2211yescharacteristic
19#18011898C2211yescharacteristic
20#18011893—21no—
21#18011891C2211yescharacteristic
22#18011882C2211yescharacteristic
23C4×Dic298C2211yescharacteristic
24C4×C22⋊D149—21no—
25#18011870—21no—
26C4⋊C4×D149—21no—
27C4⋊C4×D149C2212yes—
28C42×D149C2211yescharacteristic
29#18011845C2212yes—
30#18011844C2212yes—
31#18011842C2212yes—
32C4⋊#11924746C2211yescharacteristic
33#18011836C2212yes—
34#18011834C2212yes—
35#18011832C2212yes—
36#18011823C2212yes—
37#18011821C2212yes—
38C4⋊Q8×C149C2211yescharacteristic
39C4×D4×C149C2211yescharacteristic
40#106×C149C2212yes—
41C4⋊C8×C149C2211yescharacteristic
42#102×C149C2212yes—
43C2×Dic298—22no—
44C2×Dic298—21no—
45C2×Dic298C2311yescharacteristic
46Q8×D149—44no—
47C2×C22⋊D149—21no—
48C2×C4×D149—22no—
49C2×C4×D149D411yescharacteristic
50C2×C4×D149D411yescharacteristic
51C2×C4×D149C2311yescharacteristic
52C2×#11924746C2312yes—
53C4⋊Dic149—21no—
54C4⋊Dic149—21no—
55C4⋊Dic149—21no—
56C4⋊Dic149C2312yes—
57C4⋊Dic149C2311yescharacteristic
58#14558715—21no—
59#14558715—22no—
60#14558715—22no—
61#14558715—21no—
62C22⋊Dic149—21no—
63C22⋊Dic149—21no—
64C22⋊Dic149—21no—
65#14558713—21no—
66C4×Dic149—21no—
67C4×Dic149D411yescharacteristic
68C4×Dic149D411yescharacteristic
69C4×Dic149C2311yescharacteristic
70C2×Q8×C149—21no—
71C2×D4×C149C2311yescharacteristic
72C22×C4×C149—21no—
73C2×C8×C149C2312yes—
74C4⋊C4×C149—21no—
75C4⋊C4×C149C2312yes—
76C4⋊C4×C149C2311yescharacteristic
77C22⋊C4×C149—21no—
78C42×C149C2311yescharacteristic
79C22×D149C2×D411yescharacteristic
80Dic298—21no—
81Dic298—21no—
82Dic298—44no—
83Dic298—42no—
84C22⋊D149—42no—
85C2×Dic149—22no—
86C2×Dic149—21no—
87C2×Dic149—21no—
88C2×Dic149C2×D411yescharacteristic
89C2×Dic149C2×D411yescharacteristic
90C2×Dic149C2×D411yescharacteristic
91C4×D149—22no—
92C4×D149—22no—
93C4×D149—21no—
94C4×D149—21no—
95C4×D149—44no—
96#11924746—22no—
97C23×C149—21no—
98Q8×C149—42no—
99D4×C149—21no—
100D4×C149—21no—
101C2×C4×C149—22no—
102C2×C4×C149—21no—
103C2×C4×C149—42no—
104C2×C4×C149C2×D411yescharacteristic
105C2×C4×C149C2×D411yescharacteristic
106C2×C4×C149C2411yescharacteristic
107C8×C149—22no—
108C22×C149—41no—
109C22×C149—41no—
110C22×C149—41no—
111C22×C149C22×D411yescharacteristic
112C2×D149—21no—
113C2×D149—21no—
114C2×D149AGL(1,ℤ/8)12yes—
115C4×C149—21no—
116C4×C149—42no—
117C4×C149—41no—
118C4×C149#13712yes—
119C4×C1492−1+411yescharacteristic
120C4×C1492−1+411yescharacteristic
121Dic149—21no—
122Dic149—21no—
123Dic149—21no—
124Dic149—41no—
125Dic149—42no—
126Dic149—41no—
127C2×C149—81no—
128C2×C149#53611yescharacteristic
129C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C149C2×#13711yescharacteristic
131D149—22no—
132C149#323811yescharacteristic, complemented, Sylow
133#3238—1491nomaximal, Sylow
134C2×C4⋊Q8—1491no—
135#529—1491no—
136#501—1492no—
137#489—1492no—
138#483—1492no—
139#480—1492no—
140#477—1491no—
141#477—1491no—
142#476—1491no—
143#476D14911yescharacteristic, complemented
144#432—1491no—
145C22×Q8—2981no—
146C4⋊Q8—2981no—
147C4⋊Q8—2981no—
148C4⋊Q8—1492no—
149C4⋊Q8—1491no—
150C4⋊Q8C2×D14911yescharacteristic
151#126—2981no—
152#125—1491no—
153#124—1491no—
154#123—2981no—
155C22⋊Q8—1491no—
156#121—1491no—
157C4×Q8—1491no—
158C4×D4—2981no—
159C4×D4C2×D14911yescharacteristic
160#117—2981no—
161C2×C4⋊C4—2981no—
162C2×C4⋊C4—1492no—
163C2×C42—1491no—
164#107—1492no—
165#107—1492no—
166#106—1492no—
167#106C2×D14912yes—
168C4⋊C8—1491no—
169C4⋊C8C2×D14911yescharacteristic
170#103—1492no—
171#103—1492no—
172#102—1492no—
173#102C2×D14912yes—
174C22⋊C8—1492no—
175#97—1492no—
176C2×Q8—21no—
177C2×Q8—2982no—
178C2×Q8—2981no—
179C2×Q8—5964no—
180C2×Q8—1491no—
181C2×D4—2981no—
182C2×D4C22×D14911yescharacteristic
183C22×C4—21no—
184C22×C4—2982no—
185C22×C4—1491no—
186C22×C4—1491no—
187C22×C4—1491no—
188C2×C8—1492no—
189C2×C8C22×D14912yes—
190C4⋊C4—21no—
191C4⋊C4—2982no—
192C4⋊C4—2982no—
193C4⋊C4—2981no—
194C4⋊C4—2981no—
195C4⋊C4—2981no—
196C4⋊C4—2981no—
197C4⋊C4—2981no—
198C4⋊C4—1492no—
199C4⋊C4—1491no—
200C4⋊C4C22×D14912yes—
201C4⋊C4C22×D14911yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—2981no—
204C22⋊C4—2981no—
205C22⋊C4—2981no—
206C22⋊C4—2981no—
207C42—2981no—
208C42—1491no—
209C42—1491no—
210C42—1491no—
211C42C22×D14911yescharacteristic
212C23—21no—
213C23—1491no—
214Q8—42no—
215Q8—2981no—
216Q8—2981no—
217Q8—5962no—
218Q8—5964no—
219D4—21no—
220D4—21no—
221D4—5962no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—2982no—
226C2×C4—2982no—
227C2×C4—2981no—
228C2×C4—2981no—
229C2×C4—2981no—
230C2×C4—2981no—
231C2×C4—2982no—
232C2×C4—5964no—
233C2×C4—1491no—
234C2×C4—1491no—
235C2×C4—1491no—
236C2×C4D4×D14911yescharacteristic
237C2×C4D4×D14911yescharacteristic
238C2×C4C23×D14911yescharacteristic
239C8—22no—
240C8—2982no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—2981no—
245C22—2981no—
246C22—1492no—
247C22C2×D4×D14911yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—2981no—
252C4—2981no—
253C4—2981no—
254C4—5962no—
255C4—5961no—
256C4—5961no—
257C4#1801194012yes—
258C4#1801195811yescharacteristic
259C4#1801195911yescharacteristic
260C2—81no—
261C2—2982no—
262C2#2375019811yescharacteristic
263C2AGL(1,ℤ/8)×D14911yescharacteristic
264C2C2×#1801194011yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#476×C149C2
socleC22×C149C22×D4
prime radical#18011882C22
hypercenter#476D149
hypocenterC149#3238
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D149C2semidirect
3. #23750032C2semidirect
4. #23749983C2semidirect
5. #23749957C2semidirect
7. #23749921C2semidirect
8. #23749917C2semidirect
9. #23749915C2semidirect
10. #23749681C2semidirect
11. #476×C149C2semidirect
132. C149#3238semidirect
143. #476D149semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1492
#237501572
#237500322
#237499832
#237499572
#237499372
#237499212
#237499172
#237499152
#237496812
#476×C1492
#3238149