Finite Group Databasebeta

← #49174926

Subgroups — #49174926

Order 37504.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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×#22627683C212yesmaximal, complemented
2C2×#22627682C212yesmaximal, complemented
3#34037071C211yesmaximal, characteristic, complemented
4C4×C22⋊#11924078C211yesmaximal, characteristic, complemented
5C2×#22627597C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7C2×C22⋊#11924078C2212yes—
8C2×C22⋊#11924078C2212yes—
9C2×C4×#11924078—21no—
10#22627683—24no—
11#22627682—24no—
12(C2×#11924078)⋊C4—21no—
13(C2×#11924078)⋊C4—21no—
14C22×D1172C2211yescharacteristic
15C22×C22⋊D293C411yescharacteristic, complemented
16C22×C22⋊D293C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18#22627597—21no—
19#22627597—21no—
20#22627597—21no—
21#22627597—21no—
22C2×#17989781C411yescharacteristic, complemented
23C2×#17989779C411yescharacteristic, complemented
24C2×C22⋊C4×C293C411yescharacteristic, complemented
25C22×#11924078—22no—
26C22×#11924078—22no—
27C4⋊#11924078—42no—
28C22⋊#11924078—22no—
29C22⋊#11924078—22no—
30C22⋊#11924078—22no—
31C22⋊#11924078D414yescomplemented
32C4×#11924078—42no—
33C23×D293C2×C411yescharacteristic
34C23×D293C2311yescharacteristic
35C2×D1172—21no—
36C2×D1172—21no—
37C2×D1172—22no—
38C2×D1172—22no—
39C2×C22⋊D293—21no—
40C2×C22⋊D293—21no—
41C2×C22⋊D293—22no—
42C2×C22⋊D293—22no—
43C2×C22⋊D293—21no—
44C2×C22⋊D293—21no—
45C2×C22⋊D293—42no—
46C22×Dic293C2×C411yescharacteristic
47C22×Dic293C2×C411yescharacteristic
48C2×C4×D293—42no—
49C2×C4×D293D411yescharacteristic
50C2×C4×D293D411yescharacteristic
51C2×C4×D293D411yescharacteristic
52C2×C4×D293D411yescharacteristic
53#17989781—21no—
54#17989781—21no—
55#17989779—21no—
56#17989779—21no—
57C24×C293C2×C411yescharacteristic
58C22×C4×C293C2×C411yescharacteristic
59C22×C4×C293C2×C411yescharacteristic
60C22⋊C4×C293—21no—
61C22⋊C4×C293—21no—
62C2×#11924078—24no—
63C2×#11924078—42no—
64C2×#11924078—42no—
65C2×#11924078—42no—
66C2×#11924078—42no—
67C2×#11924078—42no—
68C22×D293—21no—
69C22×D293—22no—
70C22×D293—41no—
71C22×D293—41no—
72C22×D293—41no—
73C22×D293—41no—
74C22×D293C2×D411yescharacteristic
75C22×D293C2×D411yescharacteristic
76C22×D293C2×D412yes—
77C22×D293#4112yes—
78D1172—42no—
79D1172—41no—
80D1172—41no—
81C22⋊D293—42no—
82C22⋊D293—42no—
83C22⋊D293—41no—
84C22⋊D293—41no—
85C22⋊D293—42no—
86C2×Dic293—22no—
87C2×Dic293—21no—
88C2×Dic293—22no—
89C2×Dic293C22⋊C411yescharacteristic
90C2×Dic293C22⋊C411yescharacteristic
91C4×D293—22no—
92C4×D293—22no—
93C4×D293—41no—
94C4×D293—41no—
95C23×C293—21no—
96C23×C293—22no—
97C23×C293—41no—
98C23×C293—41no—
99C23×C293C22×C411yescharacteristic
100C2×C4×C293—21no—
101C2×C4×C293—22no—
102C2×C4×C293—41no—
103C2×C4×C293C22⋊C411yescharacteristic
104C2×C4×C293C22⋊C411yescharacteristic
105C22×C293—21no—
106C22×C293—21no—
107C22×C293—41no—
108C22×C293—41no—
109C22×C293—41no—
110C22×C293—82no—
111C22×C293C2×C22⋊C411yescharacteristic
112C22×C293C4×D412yes—
113C2×D293—21no—
114C2×D293—21no—
115C2×D293—21no—
116C2×D293—21no—
117C2×D293—42no—
118C2×D293—42no—
119C2×D293—41no—
120C2×D293—41no—
121C2×D293—41no—
122C2×D293—82no—
123C2×D293#12112yes—
124C2×D293#12411yescharacteristic
125C2×D293#12711yescharacteristic
126#11924078—44no—
127#11924078—82no—
128C4×C293—21no—
129C4×C293—21no—
130C4×C293—41no—
131Dic293—21no—
132Dic293—41no—
133Dic293#9912yescomplemented
134C2×C293—22no—
135C2×C293—81no—
136C2×C293#39011yescharacteristic
137C2×C293C2×#9911yescharacteristic
138C2×C293#41011yescharacteristic
139D293—22no—
140D293—21no—
141D293—21no—
142D293—81no—
143C293#196411yescharacteristic, complemented, Sylow
144#1964—2931nomaximal, Sylow
145C2×#121—2931no—
146C2×#99—2932no—
147C2×#99—2932no—
148#380—2931no—
149C4×C22⋊C4—2931no—
150C22×D4—2931no—
151C22×D4—2931no—
152C22×D4—2931no—
153C23×C4—2931no—
154#121—5861no—
155#121—5861no—
156#121—5861no—
157#121—5861no—
158C2×C4⋊C4—2931no—
159C2×C4⋊C4—5861no—
160C2×C22⋊C4—2932no—
161C2×C22⋊C4—2931no—
162C2×C22⋊C4—2932no—
163C2×C22⋊C4#1192407811yescharacteristic, complemented
164C2×C42—5861no—
165#99—5864no—
166#99—5864no—
167#95—5861no—
168#95—5861no—
169C24—2931no—
170C24—2931no—
171C24C2×#1192407811yescharacteristic
172C2×D4—5862no—
173C2×D4—5861no—
174C2×D4—5861no—
175C2×D4—5862no—
176C2×D4—5861no—
177C2×D4—5861no—
178C2×D4—5862no—
179C2×D4—5861no—
180C2×D4—5861no—
181C2×D4—5862no—
182C2×D4—11722no—
183C22×C4—2931no—
184C22×C4—2931no—
185C22×C4—2931no—
186C22×C4—2931no—
187C22×C4—2931no—
188C22×C4—2931no—
189C22×C4—5862no—
190C22×C4—5862no—
191C22×C4—11722no—
192C22×C4C2×#1192407811yescharacteristic
193C22×C4C2×#1192407811yescharacteristic
194C4⋊C4—5861no—
195C4⋊C4—5861no—
196C4⋊C4—11722no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—2934no—
200C22⋊C4—5862no—
201C22⋊C4—5861no—
202C22⋊C4—5861no—
203C22⋊C4—5862no—
204C22⋊C4—5862no—
205C42—11722no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—2931no—
211C23—2931no—
212C23—2932no—
213C23—2932no—
214C23—5862no—
215C23—5861no—
216C23—11721no—
217C23—11721no—
218C23—11721no—
219C23—11721no—
220C23C22×#1192407811yescharacteristic
221D4—11722no—
222D4—11721no—
223D4—11721no—
224D4—11722no—
225D4—11722no—
226D4—11722no—
227D4—11721no—
228D4—11721no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—2931no—
233C2×C4—2931no—
234C2×C4—5862no—
235C2×C4—5862no—
236C2×C4—5862no—
237C2×C4—5864no—
238C2×C4—5861no—
239C2×C4—5862no—
240C2×C4—11721no—
241C2×C4—11721no—
242C2×C4—11722no—
243C2×C4—11722no—
244C2×C4—11722no—
245C2×C4—11722no—
246C2×C4—11722no—
247C2×C4C22⋊#1192407811yescharacteristic
248C2×C4C22⋊#1192407811yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—2932no—
256C22—2931no—
257C22—2931no—
258C22—23442no—
259C22—5861no—
260C22—5861no—
261C22—5861no—
262C22—5861no—
263C22—11722no—
264C22—11722no—
265C22—11721no—
266C22—11721no—
267C22—11721no—
268C22C2×C22⋊#1192407811yescharacteristic
269C22D4×#1192407812yes—
270C4—21no—
271C4—21no—
272C4—41no—
273C4—2932no—
274C4—23442no—
275C4—5861no—
276C4—11724no—
277C4—11721no—
278C2—22no—
279C2—81no—
280C2—23441no—
281C2—5861no—
282C2—5862no—
283C2—5861no—
284C2#3403708111yescharacteristic
285C2D293⋊#9911yescharacteristic
286C2#3403710811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC23×C293C22×C4
FrattiniC23C22×#11924078
FittingC2×C22⋊C4×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×#22627597C2
cosocleC23×D293C23
hypercenterC2×C22⋊C4#11924078
hypocenterC293#1964
LCSG ▷ C23×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#22627683C2semidirect
2. C2×#22627682C2semidirect
3. #34037071C2semidirect
4. C4×C22⋊#11924078C2semidirect
15. C22×C22⋊D293C4semidirect
22. C2×#17989781C4semidirect
23. C2×#17989779C4semidirect
24. C2×C22⋊C4×C293C4semidirect
31. C22⋊#11924078D4semidirect
133. Dic293#99semidirect
143. C293#1964semidirect
163. C2×C22⋊C4#11924078semidirect

Maximal subgroups

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

subgroupindex
C2×#226276832
C2×#226276822
#340370712
C4×C22⋊#119240782
C2×#226275972
#1964293