Finite Group Databasebeta

← C2×#34036289 #49167992

Subgroups — C2×#34036289 #49167992

Order 37504.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#17989802C211yesmaximal, characteristic
2C22×#17989792C211yesmaximal, characteristic, complemented
3C22×#17989789C211yesmaximal, characteristic, complemented
4#34036289C218yesmaximal, direct product factor
5C2×#22627547C211yesmaximal, characteristic, complemented
6C2×#22627544C211yesmaximal, characteristic, complemented
7C2×C22⋊#14556873C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C293C211yesmaximal, characteristic, complemented
9C2×#17989802—24no—
10C2×#17989802—24no—
11C2×#17989802—22no—
12C2×#17989802C2214yes—
13C22×Dic586C2211yescharacteristic
14C22×D1172C2211yescharacteristic
15C22×C22⋊D293—21no—
16C22×C4×D293—21no—
17C2×#17989792—24no—
18C2×#17989792C2214yescomplemented
19C2×#17989789—24no—
20C2×#17989789C2214yescomplemented
21C22×#14556873C2211yescharacteristic
22C22×#14556873C2211yescharacteristic
23#22627547C2214yescomplemented
24#22627544C2214yescomplemented
25C22⋊#14556873C2214yescomplemented
26C22×Q8×C293C2211yescharacteristic
27C23×C4×C293C2211yescharacteristic
28C22⋊Q8×C293—22no—
29C22⋊Q8×C293C2214yescomplemented
30C2×C4⋊C4×C293—21no—
31C2×C4⋊C4×C293C2211yescharacteristic
32C2×C22⋊C4×C293—21no—
33C23×D293—21no—
34#17989802—216no—
35#17989802—28no—
36#17989802—28no—
37C2×Dic586—22no—
38C2×Dic586—21no—
39C2×Dic586D414yes—
40C2×Dic586C2312yes—
41C2×D1172—22no—
42C2×D1172—21no—
43C2×D1172D414yes—
44C2×D1172C2312yes—
45C2×C22⋊D293—28no—
46C2×C22⋊D293—24no—
47C22×Dic293—21no—
48C2×C4×D293—28no—
49C2×C4×D293—24no—
50#17989792—28no—
51#17989789—28no—
52C2×#14556873—22no—
53C2×#14556873—22no—
54C2×#14556873C2312yes—
55C2×#14556873C2312yes—
56C24×C293D411yescharacteristic
57C2×Q8×C293—21no—
58C2×Q8×C293—22no—
59C2×Q8×C293—22no—
60C2×Q8×C293C2312yes—
61C22×C4×C293—22no—
62C22×C4×C293—22no—
63C22×C4×C293—21no—
64C22×C4×C293—21no—
65C22×C4×C293D411yescharacteristic
66C22×C4×C293D412yes—
67C22×C4×C293C2312yes—
68C22×C4×C293C2311yescharacteristic
69C4⋊C4×C293—24no—
70C4⋊C4×C293—21no—
71C4⋊C4×C293C2312yes—
72C22⋊C4×C293—24no—
73C22×D293—24no—
74C22×D293—22no—
75C22×D293—42no—
76C22×D293—42no—
77Dic586—24no—
78Dic586—22no—
79Dic586C2×D414yes—
80D1172—24no—
81D1172—22no—
82D1172C2×D414yes—
83C22⋊D293—216no—
84C2×Dic293—24no—
85C2×Dic293—22no—
86C4×D293—216no—
87#14556873—22no—
88#14556873—22no—
89C23×C293—22no—
90C23×C293—22no—
91C23×C293—22no—
92C23×C293C2×D412yes—
93C23×C293C2×D411yescharacteristic
94Q8×C293—22no—
95Q8×C293—22no—
96Q8×C293—42no—
97C2×C4×C293—22no—
98C2×C4×C293—24no—
99C2×C4×C293—22no—
100C2×C4×C293—22no—
101C2×C4×C293—22no—
102C2×C4×C293—22no—
103C2×C4×C293—42no—
104C2×C4×C293—42no—
105C2×C4×C293C2×D412yes—
106C2×C4×C293C2×D412yes—
107C2×C4×C293C2×D412yes—
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2411yescharacteristic
110C22×C293—22no—
111C22×C293—22no—
112C22×C293—22no—
113C22×C293—44no—
114C22×C293#12012yes—
115C22×C293#13512yes—
116C22×C293#13712yes—
117C22×C293C22×D411yescharacteristic
118C2×D293—24no—
119C2×D293—42no—
120C2×D293—42no—
121C2×D293—48no—
122C4×C293—22no—
123C4×C293—42no—
124C4×C293—42no—
125C4×C293#12012yes—
126C4×C293C22×D411yescharacteristic
127C4×C293C22×D411yescharacteristic
128Dic293—24no—
129C2×C293—42no—
130C2×C293#45214yescomplemented
131C2×C293C2×#12011yescharacteristic
132C2×C293C2×#13511yescharacteristic
133C2×C293C2×#13711yescharacteristic
134D293—44no—
135C293C2×#45211yescharacteristic, complemented, Sylow
136C2×#452—2931nomaximal, Sylow
137C22×#41—2931no—
138C22×Q16—2931no—
139C22×SD16—2931no—
140C2×C22⋊Q8D29311yescharacteristic, complemented
141#452—2938no—
142C2×#103—2931no—
143C2×#102—2931no—
144C2×C22⋊C8—2931no—
145C2×#41—2934no—
146C2×#41—5864no—
147C2×#41—5864no—
148C2×#41—5862no—
149C22×Q8—2931no—
150C22×Q8C2×D29311yescharacteristic
151C22×D4—2931no—
152C22×D4—5861no—
153C23×C4—5861no—
154C23×C4C2×D29311yescharacteristic
155C2×Q16—2934no—
156C2×Q16—5864no—
157C2×SD16—2934no—
158C2×SD16—5864no—
159C22×C8—2931no—
160C22×C8—2931no—
161C22⋊Q8—22no—
162C22⋊Q8C2×D29314yescomplemented
163C2×C4⋊C4—21no—
164C2×C4⋊C4C2×D29311yescharacteristic
165C2×C22⋊C4—21no—
166#103—2934no—
167#102—2934no—
168C22⋊C8—2934no—
169C24—5861no—
170C24C22⋊D29311yescharacteristic
171#41—5868no—
172#41—5868no—
173#41—58616no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—2934no—
178C2×Q8—2932no—
179C2×Q8—5862no—
180C2×Q8—5861no—
181C2×Q8C22×D29312yes—
182C2×D4—2934no—
183C2×D4—2932no—
184C2×D4—5868no—
185C2×D4—5864no—
186C2×D4—5862no—
187C2×D4—5861no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—5868no—
193C22×C4—5861no—
194C22×C4—5864no—
195C22×C4C22⋊D29312yes—
196C22×C4C22⋊D29311yescharacteristic
197C22×C4C22×D29312yes—
198C22×C4C22×D29311yescharacteristic
199Q16—5868no—
200SD16—5868no—
201C2×C8—2932no—
202C2×C8—2932no—
203C2×C8—5862no—
204C2×C8—5862no—
205C4⋊C4—24no—
206C4⋊C4—21no—
207C4⋊C4C22×D29312yes—
208C22⋊C4—24no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—5864no—
213C23—5862no—
214C23—11722no—
215C23—11722no—
216C23C2×C22⋊D29312yes—
217C23C2×C22⋊D29311yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—42no—
221Q8—2934no—
222Q8—5864no—
223Q8—5862no—
224D4—2934no—
225D4—58616no—
226D4—5864no—
227D4—5862no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—58616no—
237C2×C4—5864no—
238C2×C4—5862no—
239C2×C4D4×D29312yes—
240C2×C4D4×D29312yes—
241C2×C4C2×C22⋊D29312yes—
242C2×C4C2×C22⋊D29311yescharacteristic
243C2×C4C23×D29311yescharacteristic
244C8—5862no—
245C8—5862no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—44no—
250C22—5864no—
251C22—11728no—
252C22—11722no—
253C22—11722no—
254C22#2262759212yes—
255C22#2262764412yes—
256C22#2262765512yes—
257C22C22×C22⋊D29311yescharacteristic
258C4—22no—
259C4—42no—
260C4—42no—
261C4—5864no—
262C4#2262759212yes—
263C4C2×D4×D29311yescharacteristic
264C4C2×D4×D29311yescharacteristic
265C2—42no—
266C2—11724no—
267C2#3403628914yesdirect product factor
268C2C2×#2262759211yescharacteristic
269C2C2×#2262764411yescharacteristic
270C2C2×#2262765511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×C22⋊Q8×C293C2
socleC23×C293C2×D4
prime radicalC22×#17989802C2
hypercenterC2×C22⋊Q8D293
hypocenterC293C2×#452
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#17989792C2semidirect
3. C22×#17989789C2semidirect
4. #34036289C2direct (N × H)
5. C2×#22627547C2semidirect
6. C2×#22627544C2semidirect
7. C2×C22⋊#14556873C2semidirect
8. C2×C22⋊Q8×C293C2semidirect
18. C2×#17989792C22semidirect
20. C2×#17989789C22semidirect
23. #22627547C22semidirect
24. #22627544C22semidirect
25. C22⋊#14556873C22semidirect
29. C22⋊Q8×C293C22semidirect
130. C2×C293#452semidirect
135. C293C2×#452semidirect
140. C2×C22⋊Q8D293semidirect
162. C22⋊Q8C2×D293semidirect
267. C2#34036289direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179898022
C22×#179897922
C22×#179897892
#340362892
C2×#226275472
C2×#226275442
C2×C22⋊#145568732
C2×C22⋊Q8×C2932
C2×#452293