Finite Group Databasebeta

← #28363414

Subgroups — #28363414

Order 13952.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#20295792C211yesmaximal, characteristic, complemented
2#20295576C211yesmaximal, characteristic
3#20295044C211yesmaximal, characteristic, complemented
4#20295042C211yesmaximal, characteristic, complemented
5#20294999C211yesmaximal, characteristic, complemented
6#20294786C211yesmaximal, characteristic, complemented
7#339×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9C2×#13182029C2211yescharacteristic
10#16812707—22no—
11#16812705—22no—
12C2×#13182013C2211yescharacteristic
13M16×D109—22no—
14#16812699C411yescharacteristic, complemented
15#16812696C411yescharacteristic, complemented
16#16812687C411yescharacteristic, complemented
17#16812687C411yescharacteristic, complemented
18#16812673—22no—
19C4×D436—22no—
20#16812658C2211yescharacteristic
21#16812627—22no—
22#16812625—22no—
23#16812613—22no—
24C2×M16×C109C2211yescharacteristic
25#117×C109C2211yescharacteristic
26C2×C42×C109C2211yescharacteristic
27#13182029—21no—
28#13182029—21no—
29#13182029—21no—
30#13182029—21no—
31#13182029—21no—
32#13182029—21no—
33#13182029—21no—
34#13182029—21no—
35C2×Dic218C2×C411yescharacteristic
36C2×Dic218C2×C411yescharacteristic
37C2×D436—22no—
38C2×D436C2×C411yescharacteristic
39C2×D436C2×C411yescharacteristic
40C2×C22⋊D109—21no—
41C2×C22⋊D109D412yes—
42C2×C4×D109—21no—
43C2×C4×D109D412yes—
44#13182013—21no—
45#13182013D412yescomplemented
46#13182012—24no—
47C2×#11724784—21no—
48C8×D109—24no—
49C4⋊Dic109—22no—
50C4⋊Dic109—21no—
51C22⋊Dic109—21no—
52#13182006—22no—
53#13182006—22no—
54C4×Dic109—21no—
55C22×C4×C109—21no—
56C22×C4×C109C2311yescharacteristic
57M16×C109—21no—
58M16×C109D412yescomplemented
59C2×C8×C109—21no—
60C4⋊C4×C109—21no—
61C22⋊C4×C109—21no—
62C42×C109—21no—
63C42×C109—21no—
64C42×C109C2×C411yescharacteristic
65C42×C109C2×C411yescharacteristic
66C23×C109C2×D411yescharacteristic
67C22×D109—21no—
68C22×D109C22⋊C412yes—
69C2×C4×C109—21no—
70C2×C4×C109—21no—
71C2×C4×C109—42no—
72C2×C4×C109—41no—
73C2×C4×C109C22×C411yescharacteristic
74C2×C4×C109C2×D411yescharacteristic
75C2×C4×C109C2×D411yescharacteristic
76C2×C4×C109C2×D411yescharacteristic
77C2×C4×C109#4111yescharacteristic
78C2×C4×C109#4111yescharacteristic
79C22⋊D109—22no—
80C22⋊D109—22no—
81C22⋊D109—41no—
82C22⋊D109—41no—
83C2×Dic109—21no—
84C2×Dic109—41no—
85C2×Dic109C22⋊C412yes—
86D436—21no—
87D436—21no—
88D436—21no—
89D436—21no—
90D436—44no—
91C4×D109—22no—
92C4×D109—22no—
93C4×D109—41no—
94C4×D109—41no—
95Dic218—21no—
96Dic218—21no—
97Dic218—21no—
98Dic218—21no—
99C8×C109—22no—
100#11724784—22no—
101C22×C109—41no—
102C22×C109C2×C22⋊C411yescharacteristic
103C22×C109#12111yescharacteristic
104C22×C109#12111yescharacteristic
105C2×D109—22no—
106C2×D109—42no—
107C2×D109—42no—
108C2×D109—41no—
109C4×C109—22no—
110C4×C109—41no—
111C4×C109—81no—
112C4×C109C4×D411yescharacteristic
113C4×C109C4×D411yescharacteristic
114C4×C109#12011yescharacteristic
115C4×C109#12311yescharacteristic
116Dic109—22no—
117Dic109—41no—
118Dic109—81no—
119C2×C109—21no—
120C2×C109—21no—
121C2×C109—21no—
122C2×C109#38611yescharacteristic
123D109—42no—
124D109—81no—
125#1884—1091nomaximal, Sylow
126C109#188411yescharacteristic, complemented, Sylow
127#568—1091no—
128#532—1091no—
129#421—1091no—
130#421—1091no—
131#410—1091no—
132#339—1091no—
133#339D10911yescharacteristic, complemented
134C2×#41—1091no—
135C2×#41—1091no—
136#131—2182no—
137#131—2182no—
138C2×M16—1091no—
139C2×M16—2182no—
140C2×M16C2×D10911yescharacteristic
141C4⋊Q8—1091no—
142#127—1091no—
143#124—1091no—
144#124—1091no—
145#121—2182no—
146C4×D4—2182no—
147#117—1091no—
148#117C2×D10911yescharacteristic
149C2×C42C2×D10911yescharacteristic
150#104—2182no—
151#104—2182no—
152#99—2182no—
153#41—2181no—
154#41—2181no—
155#41—2181no—
156#41—2181no—
157#41—2181no—
158#41—2181no—
159#41—2181no—
160#41—2181no—
161C2×Q8—1091no—
162C2×Q8—1091no—
163C2×D4—1092no—
164C2×D4—1091no—
165C2×D4—1091no—
166C2×D4—2182no—
167C2×D4—2181no—
168C22×C4—21no—
169C22×C4—1092no—
170C22×C4—2181no—
171C22×C4C22×D10911yescharacteristic
172M16—21no—
173M16—1092no—
174M16—2184no—
175M16—2181no—
176M16D43612yescomplemented
177C2×C8—21no—
178C2×C8—2184no—
179C2×C8—2181no—
180C4⋊C4—21no—
181C4⋊C4—2182no—
182C4⋊C4—2181no—
183C22⋊C4—21no—
184C22⋊C4—2182no—
185C22⋊C4—2182no—
186C22⋊C4—2181no—
187C42—21no—
188C42—21no—
189C42—2181no—
190C42C4×D10911yescharacteristic
191C42C4×D10911yescharacteristic
192C23—1092no—
193C23—2181no—
194C23D4×D10911yescharacteristic
195Q8—2181no—
196Q8—2181no—
197Q8—2181no—
198Q8—2181no—
199D4—4364no—
200D4—4361no—
201D4—4361no—
202D4—2182no—
203D4—2182no—
204D4—2181no—
205D4—2181no—
206D4—2181no—
207D4—2181no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—1092no—
213C2×C4—4361no—
214C2×C4—4361no—
215C2×C4—4361no—
216C2×C4—2181no—
217C2×C4—2182no—
218C2×C4—2182no—
219C2×C4C2×C4×D10911yescharacteristic
220C2×C4D4×D10911yescharacteristic
221C2×C4D4×D10911yescharacteristic
222C2×C4C2×D43611yescharacteristic
223C2×C4#1318202911yescharacteristic
224C2×C4#1318203011yescharacteristic
225C8—22no—
226C8—2182no—
227C22—41no—
228C22—4362no—
229C22—4362no—
230C22—4361no—
231C22—2182no—
232C22C22⋊C4×D10911yescharacteristic
233C22#1681267211yescharacteristic
234C22#1681267411yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—8721no—
239C4—4361no—
240C4—2182no—
241C4#1681266111yescharacteristic
242C4C4×D43611yescharacteristic
243C4#1681266911yescharacteristic
244C4#1681268411yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—8721no—
249C2—4362no—
250C2#2029490411yescharacteristic
subgroupG/H
centerC4#16812669
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#339×C109C2
socleC2×C109#386
prime radical#20295576C2
cosocleC22×C4×C109C23
hypercenter#339D109
hypocenterC109#1884
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #20295792C2semidirect
3. #20295044C2semidirect
4. #20295042C2semidirect
5. #20294999C2semidirect
6. #20294786C2semidirect
7. #339×C109C2semidirect
14. #16812699C4semidirect
15. #16812696C4semidirect
16. #16812687C4semidirect
17. #16812687C4semidirect
45. #13182013D4semidirect
58. M16×C109D4semidirect
126. C109#1884semidirect
133. #339D109semidirect
176. M16D436semidirect

Maximal subgroups

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

subgroupindex
#202957922
#202955762
#202950442
#202950422
#202949992
#202947862
#339×C1092
#1884109