Finite Group Databasebeta

← C2×#20295208 #28372373

Subgroups — C2×#20295208 #28372373

Order 13952.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812747C211yesmaximal, characteristic
2C2×#16812730C212yesmaximal, complemented
3#20295208C218yesmaximal, direct product factor
4C2×#16812627C212yesmaximal, complemented
5C2×#16812618C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C109C211yesmaximal, characteristic, complemented
7#16812747—24no—
8#16812747—22no—
9#16812747C2214yes—
10C2×#13182030—22no—
11C2×#13182029—22no—
12C2×#13182029C2212yes—
13C2×Q8×D109—22no—
14#16812730—24no—
15#16812730C2218yescomplemented
16C2×#13182019—22no—
17C2×#13182016—22no—
18C2×#13182013C2212yes—
19#16812627C2218yescomplemented
20#16812618C2214yescomplemented
21C22×Q8×C109C2211yescharacteristic
22C22×Q8×C109C2211yescharacteristic
23C4⋊Q8×C109—22no—
24C4⋊Q8×C109C2214yescomplemented
25C2×C4⋊C4×C109—22no—
26C2×C42×C109C2211yescharacteristic
27#13182030—28no—
28#13182030—28no—
29#13182029—28no—
30#13182029—28no—
31#13182029—22no—
32#13182029—22no—
33#13182029D414yes—
34#13182029C2314yes—
35C2×Dic218—22no—
36C2×Dic218D412yes—
37Q8×D109—28no—
38Q8×D109—28no—
39C2×D436—22no—
40C2×D436D412yes—
41C2×C22⋊D109—22no—
42C2×C4×D109—24no—
43C2×C4×D109—22no—
44#13182019—28no—
45#13182016—28no—
46#13182013—22no—
47#13182013C2314yes—
48C2×#11724784—22no—
49C2×Q8×C109—22no—
50C2×Q8×C109—22no—
51C2×Q8×C109—21no—
52C2×Q8×C109—22no—
53C2×Q8×C109—22no—
54C2×Q8×C109D412yes—
55C2×Q8×C109C2312yes—
56C2×Q8×C109C2312yes—
57C22×C4×C109—21no—
58C22×C4×C109—21no—
59C22×C4×C109D412yes—
60C22×C4×C109C2311yescharacteristic
61C4⋊C4×C109—28no—
62C42×C109—21no—
63C42×C109C2312yes—
64C23×C109C2×D411yescharacteristic
65C22×D109—22no—
66Q8×C109—24no—
67Q8×C109—24no—
68Q8×C109—24no—
69Q8×C109—42no—
70C2×C4×C109—24no—
71C2×C4×C109—22no—
72C2×C4×C109—22no—
73C2×C4×C109—22no—
74C2×C4×C109—22no—
75C2×C4×C109—41no—
76C2×C4×C109—41no—
77C2×C4×C109C2×D412yes—
78C2×C4×C109C2×D412yes—
79C2×C4×C109C2×D414yes—
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109C2411yescharacteristic
82C22⋊D109—24no—
83C22⋊D109—24no—
84C2×Dic109—22no—
85D436—28no—
86D436—22no—
87D436C2×D414yes—
88C4×D109—216no—
89C4×D109—24no—
90C4×D109—24no—
91Dic218—28no—
92Dic218—22no—
93Dic218C2×D414yes—
94#11724784—24no—
95C22×C109—22no—
96C22×C109#12011yescharacteristic
97C22×C109#12011yescharacteristic
98C22×C109C22×D411yescharacteristic
99C2×D109—24no—
100C2×D109—44no—
101C4×C109—24no—
102C4×C109—24no—
103C4×C109—42no—
104C4×C109#12012yes—
105C4×C109C22×D412yes—
106Dic109—24no—
107C2×C109—21no—
108C2×C109—21no—
109C2×C109#45612yescomplemented
110C2×C109C2×#12011yescharacteristic
111D109—44no—
112C2×#456—1091nomaximal, Sylow
113C109C2×#45611yescharacteristic, complemented, Sylow
114C2×2−1+4—1091no—
115C2×#137—1092no—
116C2×C4⋊Q8D10911yescharacteristic, complemented
117#456—1098no—
118C2×#104—1092no—
119C2×#101—1091no—
1202−1+4—1094no—
1212−1+4—2184no—
1222−1+4—2182no—
123C2×#41—1092no—
124C2×#41—2182no—
125C2×#41—2182no—
126C22×Q8—2182no—
127C22×Q8C2×D10911yescharacteristic
128C22×Q8C2×D10911yescharacteristic
129#137—1098no—
130#137—2184no—
131C2×Q16—2182no—
132C2×SD16—2182no—
133C2×M16—1092no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D10914yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D10911yescharacteristic
138#104—1098no—
139#101—1094no—
140#41—1094no—
141#41—1094no—
142#41—2188no—
143#41—2188no—
144#41—2188no—
145#41—2182no—
146#41—2182no—
147#41—2188no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—1092no—
154C2×Q8—2182no—
155C2×Q8—2188no—
156C2×Q8—2188no—
157C2×Q8C22⋊D10912yes—
158C2×Q8C22×D10912yes—
159C2×Q8C22×D10912yes—
160C2×D4—1092no—
161C2×D4—2182no—
162C2×D4—2182no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—2184no—
166C22×C4—2182no—
167C22×C4C22⋊D10912yes—
168C22×C4C22×D10911yescharacteristic
169Q16—2188no—
170SD16—2188no—
171M16—1094no—
172M16—2182no—
173C2×C8—2182no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D10912yes—
177C23—2182no—
178C23C2×C22⋊D10911yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—1094no—
184Q8—2188no—
185Q8—2182no—
186D4—1094no—
187D4—2188no—
188D4—2184no—
189D4—2184no—
190D4—2182no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—21816no—
199C2×C4—2182no—
200C2×C4—2184no—
201C2×C4—2184no—
202C2×C4D4×D10912yes—
203C2×C4D4×D10912yes—
204C2×C4C2×C22⋊D10914yes—
205C2×C4C2×C22⋊D10911yescharacteristic
206C2×C4C23×D10911yescharacteristic
207C8—2184no—
208C22—22no—
209C22—4364no—
210C22—2184no—
211C22#1681266711yescharacteristic
212C22#1681266711yescharacteristic
213C22C22×C22⋊D10911yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—2184no—
218C4#1681266712yes—
219C4C2×D4×D10912yes—
220C2—21no—
221C2—21no—
222C2—4364no—
223C2#2029520812yesdirect product factor
224C2C2×#1681266711yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×C4⋊Q8×C109C2
socleC22×C109#120
prime radicalC2×#16812747C2
hypercenterC2×C4⋊Q8D109
hypocenterC109C2×#456
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16812730C2semidirect
3. #20295208C2direct (N × H)
4. C2×#16812627C2semidirect
5. C2×#16812618C2semidirect
6. C2×C4⋊Q8×C109C2semidirect
15. #16812730C22semidirect
19. #16812627C22semidirect
20. #16812618C22semidirect
24. C4⋊Q8×C109C22semidirect
109. C2×C109#456semidirect
113. C109C2×#456semidirect
116. C2×C4⋊Q8D109semidirect
135. C4⋊Q8C2×D109semidirect
223. C2#20295208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168127472
C2×#168127302
#202952082
C2×#168126272
C2×#168126182
C2×C4⋊Q8×C1092
C2×#456109