Finite Group Databasebeta

← #28379117

Subgroups — #28379117

Order 13952.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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
1#20296037C211yesmaximal, characteristic
2#20296019C211yesmaximal, characteristic
3C2×#16812762C211yesmaximal, characteristic
4#20295992C211yesmaximal, characteristic
5#20295905C211yesmaximal, characteristic
6#20295901C211yesmaximal, characteristic
7#101×D109C211yesmaximal, characteristic
8D109⋊M16C2211yescharacteristic
9C2×D109⋊C8C2211yescharacteristic
10#16812778C2211yescharacteristic
11C2×C4⋊#89137C2211yescharacteristic
12#16812768—21no—
13#16812767—21no—
14#16812762—21no—
15#16812762—21no—
16#16812762—21no—
17#16812762—21no—
18#16812753—21no—
19C8×#89137—21no—
20C2×Q8×D109C2211yescharacteristic
21M16×D109C2211yescharacteristic
22M16×D109C2211yescharacteristic
23#16812618C411yescharacteristic, complemented
24#16812617C411yescharacteristic, complemented
25#16812617C411yescharacteristic, complemented
26#101×C109C411yescharacteristic, complemented
27C22×#89137—21no—
28#13182039—21no—
29#13182038—21no—
30D109⋊C8—21no—
31D109⋊C8—21no—
32D109⋊C8D411yescharacteristic
33D109⋊C8D411yescharacteristic
34C2×#11724786—21no—
35C4⋊#89137—21no—
36C4⋊#89137—21no—
37C4⋊#89137D411yescharacteristic
38C4⋊#89137D411yescharacteristic
39C22⋊#89137—21no—
40C4×#89137—21no—
41C2×Dic218—21no—
42C2×Dic218C2×C411yescharacteristic
43Q8×D109—21no—
44Q8×D109—21no—
45Q8×D109—21no—
46Q8×D109—21no—
47C2×C4×D109—21no—
48C2×C4×D109C2311yescharacteristic
49#13182013C2×C411yescharacteristic
50#13182013C2×C411yescharacteristic
51#13182012—21no—
52#13182012—21no—
53C8×D109—21no—
54C8×D109—21no—
55C2×Q8×C109C2×C411yescharacteristic
56M16×C109C2×C411yescharacteristic
57M16×C109C2×C411yescharacteristic
58C22×D109#4111yescharacteristic
59C2×#89137—21no—
60C2×#89137—21no—
61C2×#89137—41no—
62C2×#89137—81no—
63Q8×C109—21no—
64Q8×C109—21no—
65C2×C4×C109—21no—
66C2×C4×C109C22×C411yescharacteristic
67C2×Dic109—21no—
68C2×Dic109#4111yescharacteristic
69C4×D109—41no—
70C4×D109—41no—
71C4×D109C2×D411yescharacteristic
72C4×D109C2×D411yescharacteristic
73C4×D109#4111yescharacteristic
74C4×D109#4111yescharacteristic
75Dic218—21no—
76Dic218—21no—
77Dic218—41no—
78Dic218—41no—
79#11724786—21no—
80#11724786—21no—
81#11724786—41no—
82C8×C109—21no—
83C8×C109—21no—
84#11724784—21no—
85#11724784—21no—
86C22×C109#11711yescharacteristic
87C2×D109—21no—
88C2×D109—21no—
89C2×D109#12111yescharacteristic
90C2×D109#12611yescharacteristic
91#89137—41no—
92#89137—41no—
93#89137—81no—
94C4×C109—41no—
95C4×C109C4×D411yescharacteristic
96C4×C109C4×D411yescharacteristic
97Dic109—41no—
98Dic109#12311yescharacteristic
99Dic109#12411yescharacteristic
100C2×C109—21no—
101C2×C109#38811yescharacteristic
102D109—21no—
103D109#47111yescharacteristic
104D109#47311yescharacteristic
105#1930—1091nomaximal, Sylow
106C109#193011yescharacteristic, complemented, Sylow
107#428—1091no—
108#419—1091no—
109C2×#103—1091no—
110C2×#101—1091no—
111#405—1091no—
112#343—1091no—
113#341—1091no—
114C22×Q8—1091no—
115C2×M16—1091no—
116C2×M16—1091no—
117C2×M16—1091no—
118C22×C8—1091no—
119#117—1091no—
120C2×C4⋊C4—1091no—
121#107—2181no—
122#106—2181no—
123#103—2181no—
124#103—2181no—
125#103—2181no—
126#103—2181no—
127#101—1091no—
128#101—1091no—
129#101—1091no—
130#101#8913711yescharacteristic, complemented
131#97—2181no—
132C4×C8—2181no—
133C2×Q8—1091no—
134C2×Q8—2181no—
135C2×Q8—2181no—
136C2×Q8—2181no—
137C2×Q8—2181no—
138C2×Q8—2181no—
139C2×Q8C2×#8913711yescharacteristic
140C22×C4—1091no—
141C22×C4—2181no—
142C22×C4—2181no—
143M16—1091no—
144M16—1091no—
145M16—2181no—
146M16—2181no—
147M16—2181no—
148M16—2181no—
149M16C2×#8913711yescharacteristic
150M16C2×#8913711yescharacteristic
151C2×C8—1091no—
152C2×C8—1091no—
153C2×C8—2181no—
154C2×C8—2181no—
155C2×C8—2181no—
156C2×C8—2181no—
157C2×C8—2181no—
158C4⋊C4—1091no—
159C4⋊C4—1091no—
160C4⋊C4—2181no—
161C4⋊C4—2181no—
162C22⋊C4—2181no—
163C42—2181no—
164C23—1091no—
165Q8—21no—
166Q8—21no—
167Q8—4361no—
168Q8—4361no—
169Q8—2181no—
170Q8—2181no—
171C2×C4—21no—
172C2×C4—8721no—
173C2×C4—1091no—
174C2×C4—1091no—
175C2×C4—1091no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—4361no—
179C2×C4—4361no—
180C2×C4—4361no—
181C2×C4—2181no—
182C2×C4—2181no—
183C2×C4—2181no—
184C2×C4C22×#8913711yescharacteristic
185C8—21no—
186C8—21no—
187C8—4361no—
188C8—2181no—
189C8—2181no—
190C8—2181no—
191C8—2181no—
192C22—1091no—
193C22—1091no—
194C22—2181no—
195C22—2181no—
196C22#1681277811yescharacteristic
197C4—41no—
198C4—8721no—
199C4—1091no—
200C4—1091no—
201C4—4361no—
202C4—4361no—
203C4—4361no—
204C4D4×#8913711yescharacteristic
205C4D4×#8913711yescharacteristic
206C2—21no—
207C2—1091no—
208C2—1091no—
209C2—2181no—
210C2#2029597611yescharacteristic
subgroupG/H
centerC2#20295976
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#101×C109C4
socleC2×C109#388
prime radicalC22×D109#41
cosocleC2×C4×D109C23
hypercenter#101#89137
hypocenterC109#1930
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #16812618C4semidirect
24. #16812617C4semidirect
25. #16812617C4semidirect
26. #101×C109C4semidirect
106. C109#1930semidirect
130. #101#89137semidirect

Maximal subgroups

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

subgroupindex
#202960372
#202960192
C2×#168127622
#202959922
#202959052
#202959012
#101×D1092
#1930109