Finite Group Databasebeta

← #49174945

Subgroups — #49174945

Order 37504.

296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D293⋊#108C211yesmaximal, characteristic, complemented
2#34037122C211yesmaximal, characteristic, complemented
3#34037121C211yesmaximal, characteristic
4D293⋊#101C211yesmaximal, characteristic, complemented
5D293⋊#100C211yesmaximal, characteristic
6#34037092C211yesmaximal, characteristic, complemented
7C2×SD16×D293C211yesmaximal, characteristic
8D293⋊M16C2211yescharacteristic
9D293⋊M16C2211yescharacteristic
10D293⋊M16C2211yescharacteristic
11#22627703C2211yescharacteristic
12#22627695—21no—
13#22627694—21no—
14#22627687—22no—
15#22627686—22no—
16#22627685—22no—
17#22627684—22no—
18#22627678—21no—
19C8×#11924078—21no—
20C2×Q8×D293C2211yescharacteristic
21C2×D4×D293C2211yescharacteristic
22C2×#17989791C411yescharacteristic, complemented
23C2×#17989790C411yescharacteristic, complemented
24C2×#17989789C411yescharacteristic, complemented
25SD16×D293—21no—
26SD16×D293—21no—
27SD16×D293—21no—
28SD16×D293—21no—
29C2×C8×D293C2211yescharacteristic
30C2×SD16×C293C411yescharacteristic, complemented
31#17989812—21no—
32#17989812—21no—
33#17989812—21no—
34#17989811—21no—
35#17989811—21no—
36#17989811D412yes—
37D293⋊C8—21no—
38D293⋊C8—21no—
39D293⋊C8—21no—
40C4⋊#11924078D412yes—
41C22⋊#11924078—21no—
42C4×#11924078—21no—
43C23×D293—21no—
44C2×Dic586—21no—
45C2×Dic586C2×C411yescharacteristic
46Q8×D293—21no—
47Q8×D293—21no—
48Q8×D293—21no—
49Q8×D293—21no—
50C2×D1172C2×C411yescharacteristic
51C2×C22⋊D293—21no—
52D4×D293—21no—
53D4×D293—21no—
54D4×D293—21no—
55D4×D293—21no—
56C2×C4×D293—21no—
57C2×C4×D293C2311yescharacteristic
58#17989791—21no—
59#17989791—21no—
60#17989790—21no—
61#17989790—21no—
62#17989789—21no—
63#17989789—21no—
64C2×#14556873C2×C411yescharacteristic
65C8×D293D411yescharacteristic
66C8×D293D411yescharacteristic
67C8×D293D411yescharacteristic
68C8×D293D411yescharacteristic
69C2×Q8×C293C2×C411yescharacteristic
70C2×D4×C293C2×C411yescharacteristic
71SD16×C293—21no—
72SD16×C293—21no—
73C2×C8×C293C2×C411yescharacteristic
74C2×#11924078—22no—
75#14556880—22no—
76#14556880—41no—
77#14556880—41no—
78C22×D293—21no—
79C22×D293—41no—
80C22×D293—41no—
81C22×D293—82no—
82C22×D293#4111yescharacteristic
83Dic586—21no—
84Dic586—21no—
85Dic586—41no—
86Dic586—41no—
87D1172—21no—
88D1172—21no—
89C22⋊D293—41no—
90C22⋊D293—41no—
91C2×Dic293—21no—
92C2×Dic293C2×D411yescharacteristic
93C4×D293—41no—
94C4×D293—41no—
95C4×D293C2×D411yescharacteristic
96C4×D293C2×D411yescharacteristic
97C4×D293C2×D411yescharacteristic
98C4×D293#4111yescharacteristic
99#14556873C22⋊C411yescharacteristic
100#14556873C22⋊C411yescharacteristic
101C23×C293—21no—
102Q8×C293—21no—
103Q8×C293—21no—
104D4×C293—21no—
105D4×C293—21no—
106C2×C4×C293—21no—
107C2×C4×C293C22×C411yescharacteristic
108C8×C293C22⋊C411yescharacteristic
109C8×C293C22⋊C411yescharacteristic
110C22×C293—41no—
111C22×C293—81no—
112C22×C293C4×D411yescharacteristic
113C2×D293—22no—
114C2×D293—41no—
115C2×D293—82no—
116C2×D293—82no—
117C2×D293—81no—
118C2×D293#12111yescharacteristic
119C2×D293#12411yescharacteristic
120#11924078—42no—
121C4×C293—41no—
122C4×C293C2×C22⋊C411yescharacteristic
123C4×C293C4×D411yescharacteristic
124Dic293—41no—
125Dic293#12111yescharacteristic
126Dic293#12711yescharacteristic
127C2×C293—21no—
128C2×C293—81no—
129C2×C293#39011yescharacteristic
130D293—21no—
131D293—81no—
132D293#47112yes—
133C293#197711yescharacteristic, complemented, Sylow
134#1977—2931nomaximal, Sylow
135C22×SD16—2931no—
136C2×#108—2931no—
137#419—2931no—
138#418—2931no—
139C2×#101—2931no—
140C2×#100—2931no—
141#405—2931no—
142C22×Q8—2931no—
143C22×D4—2931no—
144C2×SD16—2931no—
145C2×SD16—2931no—
146C2×SD16—2931no—
147C2×SD16—5861no—
148C2×SD16—5861no—
149C2×SD16—5861no—
150C2×SD16—5861no—
151C2×SD16#1192407811yescharacteristic, complemented
152C2×M16—2931no—
153C2×M16—2931no—
154C2×M16—2931no—
155C22×C8—2931no—
156#117—2931no—
157#108—5861no—
158#108—5861no—
159#103—5862no—
160#102—5862no—
161#101—5862no—
162#100—5862no—
163#97—5861no—
164C4×C8—5861no—
165C24—5861no—
166C2×Q8—2931no—
167C2×Q8—5861no—
168C2×Q8—5861no—
169C2×Q8—5861no—
170C2×Q8—5861no—
171C2×Q8—5861no—
172C2×Q8C2×#1192407811yescharacteristic
173C2×D4—2931no—
174C2×D4—5861no—
175C2×D4—5861no—
176C2×D4—5861no—
177C2×D4—5861no—
178C2×D4—5861no—
179C2×D4C2×#1192407811yescharacteristic
180C22×C4—2931no—
181C22×C4—5861no—
182SD16—21no—
183SD16—21no—
184SD16—5861no—
185SD16—5861no—
186SD16—5861no—
187SD16—5861no—
188SD16—5861no—
189SD16—5861no—
190M16—2932no—
191M16—5861no—
192M16—5861no—
193M16—5861no—
194M16—5861no—
195M16—5861no—
196C2×C8—2931no—
197C2×C8—2931no—
198C2×C8—2931no—
199C2×C8—2931no—
200C2×C8—2931no—
201C2×C8—5861no—
202C2×C8—5861no—
203C2×C8—5861no—
204C2×C8C2×#1192407811yescharacteristic
205C4⋊C4—2932no—
206C22⋊C4—5861no—
207C42—5861no—
208C23—21no—
209C23—2931no—
210C23—23442no—
211C23—5861no—
212C23—11721no—
213C23—11721no—
214Q8—21no—
215Q8—21no—
216Q8—5861no—
217Q8—5861no—
218Q8—11721no—
219Q8—11721no—
220D4—21no—
221D4—21no—
222D4—5861no—
223D4—5861no—
224D4—11721no—
225D4—11721no—
226C2×C4—21no—
227C2×C4—2931no—
228C2×C4—2931no—
229C2×C4—2931no—
230C2×C4—2931no—
231C2×C4—2931no—
232C2×C4—5862no—
233C2×C4—5861no—
234C2×C4—11721no—
235C2×C4—11721no—
236C2×C4C22×#1192407811yescharacteristic
237C8—2931no—
238C8—2931no—
239C8—5862no—
240C8—11721no—
241C8—11721no—
242C8C22⋊#1192407811yescharacteristic
243C8C22⋊#1192407811yescharacteristic
244C22—41no—
245C22—81no—
246C22—2931no—
247C22—2931no—
248C22—23441no—
249C22—23442no—
250C22—23442no—
251C22—5862no—
252C22—11721no—
253C22D4×#1192407811yescharacteristic
254C4—41no—
255C4—2931no—
256C4—2931no—
257C4—11722no—
258C4—11721no—
259C4C2×C22⋊#1192407811yescharacteristic
260C4D4×#1192407811yescharacteristic
261C2—21no—
262C2—81no—
263C2—2932no—
264C2—23441no—
265C2—5861no—
266C2#3403708111yescharacteristic
subgroupG/H
centerC2#34037081
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×SD16×C293C4
socleC2×C293#390
prime radicalC2×D4×D293C22
cosocleC2×C4×D293C23
hypercenterC2×SD16#11924078
hypocenterC293#1977
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. D293⋊#108C2semidirect
2. #34037122C2semidirect
4. D293⋊#101C2semidirect
6. #34037092C2semidirect
22. C2×#17989791C4semidirect
23. C2×#17989790C4semidirect
24. C2×#17989789C4semidirect
30. C2×SD16×C293C4semidirect
133. C293#1977semidirect
151. C2×SD16#11924078semidirect

Maximal subgroups

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

subgroupindex
D293⋊#1082
#340371222
#340371212
D293⋊#1012
D293⋊#1002
#340370922
C2×SD16×D2932
#1977293