Finite Group Databasebeta

← #49169240

Subgroups — #49169240

Order 37504.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22627657C211yesmaximal, characteristic, complemented
2C2×#22627655C211yesmaximal, characteristic, complemented
3C2×#22627654C211yesmaximal, characteristic, complemented
4#34036675C211yesmaximal, characteristic
5C2×#22627622C211yesmaximal, characteristic, complemented
6#34036522C212yesmaximal, complemented
7#34036520C212yesmaximal, complemented
8#34036507C212yesmaximal, complemented
9#34036500C212yesmaximal, complemented
10M16×Dic293C211yesmaximal, characteristic, complemented
11C2×#137×C293C211yesmaximal, characteristic, complemented
12C2×#17989802C2211yescharacteristic
13C22×Dic586C2211yescharacteristic
14#22627657—24no—
15#22627655—24no—
16#22627654—24no—
17C2×Dic1172C2212yes—
18C2×#17989792C2212yes—
19C2×#17989792C2212yes—
20C2×#17989791C2212yes—
21C2×#17989790C2212yes—
22C2×#17989789C2212yes—
23C2×#17989786C2211yescharacteristic
24#22627622—22no—
25#22627622C2212yes—
26#22627622C2211yescharacteristic
27#22627622C2212yes—
28#22627620C2211yescharacteristic
29#22627613C2211yescharacteristic
30#22627611C2211yescharacteristic
31#22627596—22no—
32C4×C22⋊D293—22no—
33C2×#17989781—22no—
34C2×C4×Dic293C2211yescharacteristic
35#22627534C2212yes—
36C8×Dic293C2212yes—
37C2×#41×C293C2211yescharacteristic
38C22×Q8×C293C2211yescharacteristic
39#137×C293—24no—
40C2×Q16×C293C2212yes—
41C2×SD16×C293C2212yes—
42C2×M16×C293C2211yescharacteristic
43#17989802—22no—
44#17989802—22no—
45C2×Dic586—21no—
46C2×Dic586—22no—
47C2×Dic586—22no—
48C2×Dic586C2311yescharacteristic
49C2×Dic586C2312yes—
50C2×D1172C2311yescharacteristic
51C2×C22⋊D293—22no—
52C2×C22⋊D293—21no—
53C22×Dic293—21no—
54C22×Dic293D412yes—
55C2×C4×D293—21no—
56Dic1172—24no—
57#17989792—24no—
58#17989792—24no—
59#17989791—24no—
60#17989790—24no—
61#17989789—24no—
62#17989786D414yescomplemented
63C2×#14556873C2312yes—
64#17989781—22no—
65#17989781—24no—
66#17989781—24no—
67C22⋊Dic293—22no—
68#17989779—22no—
69C4×Dic293D412yes—
70C4×Dic293C2311yescharacteristic
71C4×Dic293C2311yescharacteristic
72#41×C293—22no—
73#41×C293—22no—
74C2×Q8×C293—21no—
75C2×Q8×C293—22no—
76C2×Q8×C293—22no—
77C2×Q8×C293C2311yescharacteristic
78C2×Q8×C293C2312yes—
79C2×D4×C293—21no—
80C2×D4×C293C2311yescharacteristic
81C22×C4×C293—21no—
82C22×C4×C293—21no—
83C22×C4×C293C2311yescharacteristic
84Q16×C293—24no—
85SD16×C293—24no—
86M16×C293D414yescomplemented
87C2×C8×C293C2312yes—
88C22×D293—21no—
89Dic586—22no—
90Dic586—22no—
91Dic586—21no—
92Dic586—21no—
93Dic586—42no—
94D1172—21no—
95D1172—21no—
96C22⋊D293—42no—
97C22⋊D293—44no—
98C2×Dic293—24no—
99C2×Dic293—21no—
100C2×Dic293—22no—
101C2×Dic293—42no—
102C2×Dic293C2×D412yes—
103C2×Dic293C2×D412yes—
104C4×D293—42no—
105#14556873C2×D414yes—
106C23×C293—21no—
107C23×C293C2×D411yescharacteristic
108Q8×C293—22no—
109Q8×C293—21no—
110Q8×C293—22no—
111Q8×C293—21no—
112Q8×C293—42no—
113D4×C293—21no—
114D4×C293—21no—
115D4×C293—42no—
116C2×C4×C293—21no—
117C2×C4×C293—22no—
118C2×C4×C293—42no—
119C2×C4×C293—42no—
120C2×C4×C293C2×D411yescharacteristic
121C2×C4×C293C2×D412yes—
122C2×C4×C293C2×D412yes—
123C2×C4×C293C2411yescharacteristic
124C8×C293C2×D414yes—
125C22×C293—22no—
126C22×C293—41no—
127C22×C293—42no—
128C22×C293#12712yes—
129C22×C293C22×D411yescharacteristic
130C2×D293—41no—
131C2×D293—42no—
132C4×C293—41no—
133C4×C293—42no—
134C4×C293#12712yes—
135C4×C293C22×D411yescharacteristic
136C4×C293C22×D411yescharacteristic
137Dic293—22no—
138Dic293—41no—
139Dic293—42no—
140Dic293#13714yescomplemented
141C2×C293—22no—
142C2×C293—81no—
143C2×C293C2×#12711yescharacteristic
144C2×C293C2×#13712yes—
145D293—81no—
146C293#315211yescharacteristic, complemented, Sylow
147#3152—2931nomaximal, Sylow
148C2×#137—2931no—
149C2×#137—2931no—
150C2×#137—2931no—
151C2×#137D29311yescharacteristic, complemented
152#532—2931no—
153C2×C4⋊Q8—2931no—
154#497—2932no—
155#497—2932no—
156#494—2932no—
157#492—2932no—
158C4×M16—2931no—
159C2×#41—2931no—
160C2×#41C2×D29311yescharacteristic
161C22×Q8—2931no—
162C22×Q8C2×D29311yescharacteristic
163#137—24no—
164#137—5864no—
165#137—5864no—
166#137—5864no—
167C2×Q16—2932no—
168C2×Q16—2932no—
169C2×Q16—2932no—
170C2×Q16C2×D29312yes—
171C2×SD16—2932no—
172C2×SD16—2932no—
173C2×SD16—2932no—
174C2×SD16C2×D29312yes—
175C2×M16—2931no—
176C2×M16C2×D29311yescharacteristic
177C4⋊Q8—2932no—
178C4⋊Q8—2932no—
179C4⋊Q8—2931no—
180C4⋊Q8—5862no—
181#127—2931no—
182#124—2931no—
183#124—2931no—
184#121—5862no—
185C4×D4—5862no—
186C2×C4⋊C4—5862no—
187C2×C42—2931no—
188#97—2932no—
189C4×C8—2932no—
190#41—22no—
191#41—22no—
192#41—5862no—
193#41—5862no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—2931no—
198C2×Q8—2932no—
199C2×Q8—5861no—
200C2×Q8—5862no—
201C2×Q8—5862no—
202C2×Q8C22×D29311yescharacteristic
203C2×Q8C22×D29312yes—
204C2×D4—21no—
205C2×D4—2931no—
206C2×D4—5862no—
207C2×D4—5861no—
208C2×D4C22×D29311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—2932no—
212C22×C4—5861no—
213C22×C4—5861no—
214C22×C4C22×D29311yescharacteristic
215Q16—24no—
216Q16—5864no—
217Q16—5864no—
218Q16—5864no—
219SD16—24no—
220SD16—5864no—
221SD16—5864no—
222SD16—5864no—
223M16—2934no—
224M16C22⋊D29314yescomplemented
225C2×C8—2932no—
226C2×C8C22×D29312yes—
227C4⋊C4—5864no—
228C4⋊C4—5864no—
229C4⋊C4—5862no—
230C22⋊C4—5862no—
231C22⋊C4—5862no—
232C42—2932no—
233C42—2931no—
234C42—2931no—
235C23—21no—
236C23—5861no—
237C23D4×D29311yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—5862no—
244Q8—5861no—
245Q8—5862no—
246Q8—5861no—
247Q8—11722no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—5861no—
252D4—5861no—
253D4—11724no—
254D4—11722no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—2932no—
260C2×C4—2932no—
261C2×C4—5864no—
262C2×C4—5861no—
263C2×C4—5862no—
264C2×C4—11722no—
265C2×C4—11722no—
266C2×C4D4×D29311yescharacteristic
267C2×C4D4×D29312yes—
268C2×C4C2×C22⋊D29312yes—
269C2×C4C23×D29311yescharacteristic
270C8—2934no—
271C8C2×C22⋊D29314yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—11722no—
276C22—11721no—
277C22#2262762012yes—
278C22C2×D4×D29311yescharacteristic
279C4—41no—
280C4—42no—
281C4—2934no—
282C4—5862no—
283C4—11721no—
284C4—11722no—
285C4#2262762012yes—
286C4C2×D4×D29311yescharacteristic
287C4C22×C22⋊D29311yescharacteristic
288C2—22no—
289C2—81no—
290C2—23441no—
291C2C2×#2262762011yescharacteristic
292C2#137×D29312yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#137×C293C2
socleC22×C293C22×D4
prime radical#34036675C2
hypercenterC2×#137D293
hypocenterC293#3152
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#22627657C2semidirect
2. C2×#22627655C2semidirect
3. C2×#22627654C2semidirect
5. C2×#22627622C2semidirect
6. #34036522C2semidirect
7. #34036520C2semidirect
8. #34036507C2semidirect
9. #34036500C2semidirect
10. M16×Dic293C2semidirect
11. C2×#137×C293C2semidirect
62. #17989786D4semidirect
86. M16×C293D4semidirect
140. Dic293#137semidirect
146. C293#3152semidirect
151. C2×#137D293semidirect
224. M16C22⋊D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276572
C2×#226276552
C2×#226276542
#340366752
C2×#226276222
#340365222
#340365202
#340365072
#340365002
M16×Dic2932
C2×#137×C2932
#3152293