Finite Group Databasebeta

← #28363412

Subgroups — #28363412

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#20295572C211yesmaximal, characteristic
3#20295043C211yesmaximal, characteristic, complemented
4#20294999C211yesmaximal, characteristic, complemented
5#20294787C211yesmaximal, characteristic, complemented
6#20294785C211yesmaximal, characteristic, complemented
7#421×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9#16812707—22no—
10#16812705—22no—
11C2×#13182013C2211yescharacteristic
12M16×D109—22no—
13#16812697C411yescharacteristic, complemented
14#16812695C411yescharacteristic, complemented
15#16812688C411yescharacteristic, complemented
16#16812686C411yescharacteristic, complemented
17#16812671—22no—
18C4×C22⋊D109—22no—
19#16812658C2211yescharacteristic
20C2×C4×Dic109C2211yescharacteristic
21#16812626—22no—
22#16812613—22no—
23C2×#41×C109C2211yescharacteristic
24C2×M16×C109C2211yescharacteristic
25#117×C109C2211yescharacteristic
26#104×C109—22no—
27#13182029—21no—
28#13182029—21no—
29#13182029—21no—
30#13182029—21no—
31C2×Dic218C2×C411yescharacteristic
32C2×D436C2×C411yescharacteristic
33C2×C22⋊D109—22no—
34C2×C22⋊D109D412yes—
35C22×Dic109—21no—
36C2×C4×D109D412yes—
37#13182013—21no—
38#13182013D412yescomplemented
39#13182012—24no—
40C2×#11724784—21no—
41C8×D109—24no—
42C4⋊Dic109—21no—
43#13182008—22no—
44C22⋊Dic109—22no—
45C22⋊Dic109—21no—
46#13182006—22no—
47C4×Dic109—21no—
48C4×Dic109—21no—
49C4×Dic109C2×C411yescharacteristic
50C4×Dic109C2×C411yescharacteristic
51#41×C109—21no—
52#41×C109—21no—
53#41×C109—21no—
54#41×C109—21no—
55C2×Q8×C109C2×C411yescharacteristic
56C2×D4×C109—21no—
57C2×D4×C109C2×C411yescharacteristic
58C22×C4×C109—21no—
59C22×C4×C109C2311yescharacteristic
60M16×C109—21no—
61M16×C109D412yescomplemented
62C2×C8×C109—21no—
63C4⋊C4×C109—21no—
64C22⋊C4×C109—21no—
65C42×C109—21no—
66C23×C109—21no—
67C23×C109C2×D411yescharacteristic
68C22×D109C22⋊C412yes—
69Q8×C109—21no—
70Q8×C109—21no—
71D4×C109—21no—
72D4×C109—21no—
73D4×C109—41no—
74D4×C109—41no—
75C2×C4×C109—21no—
76C2×C4×C109—41no—
77C2×C4×C109—41no—
78C2×C4×C109—41no—
79C2×C4×C109C22×C411yescharacteristic
80C2×C4×C109C2×D411yescharacteristic
81C2×C4×C109C2×D411yescharacteristic
82C2×C4×C109C2×D411yescharacteristic
83C2×C4×C109#4111yescharacteristic
84C2×C4×C109#4111yescharacteristic
85C22⋊D109—22no—
86C22⋊D109—22no—
87C22⋊D109—44no—
88C2×Dic109—21no—
89C2×Dic109—21no—
90C2×Dic109—42no—
91C2×Dic109—41no—
92C2×Dic109C22⋊C412yes—
93D436—21no—
94D436—21no—
95C4×D109—22no—
96C4×D109—22no—
97Dic218—21no—
98Dic218—21no—
99C8×C109—22no—
100#11724784—22no—
101C22×C109—41no—
102C22×C109—42no—
103C22×C109—41no—
104C22×C109C2×C22⋊C411yescharacteristic
105C22×C109#12111yescharacteristic
106C22×C109#12111yescharacteristic
107C2×D109—22no—
108C2×D109—42no—
109C4×C109—41no—
110C4×C109—81no—
111C4×C109C4×D411yescharacteristic
112C4×C109C4×D411yescharacteristic
113C4×C109#12011yescharacteristic
114C4×C109#12311yescharacteristic
115Dic109—22no—
116Dic109—22no—
117Dic109—41no—
118Dic109—81no—
119C2×C109—21no—
120C2×C109—21no—
121C2×C109—21no—
122C2×C109—81no—
123C2×C109#38611yescharacteristic
124D109—42no—
125#1884—1091nomaximal, Sylow
126C109#188411yescharacteristic, complemented, Sylow
127#568—1091no—
128#532—1091no—
129#421—1091no—
130#421D10911yescharacteristic, complemented
131#410—1091no—
132#339—1091no—
133#339—1091no—
134C2×#41—1091no—
135C2×#41C2×D10911yescharacteristic
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×C42—1091no—
150#104—22no—
151#104—2182no—
152#99—2182no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—2181no—
158#41—2181no—
159#41—2181no—
160#41—2181no—
161C2×Q8—1091no—
162C2×Q8C4×D10911yescharacteristic
163C2×D4—21no—
164C2×D4—1092no—
165C2×D4—1091no—
166C2×D4—2182no—
167C2×D4C4×D10911yescharacteristic
168C22×C4—21no—
169C22×C4—1092no—
170C22×C4—2181no—
171C22×C4C22×D10911yescharacteristic
172M16—21no—
173M16—1092no—
174M16—2184no—
175M16—2181no—
176M16C22⋊D10912yescomplemented
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—1091no—
189C42—1091no—
190C42—2181no—
191C42—2181no—
192C23—21no—
193C23—1092no—
194C23D4×D10911yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—2181no—
198Q8—2181no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—4364no—
204D4—2182no—
205D4—2182no—
206D4—2181no—
207D4—2181no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—1092no—
213C2×C4—4361no—
214C2×C4—4362no—
215C2×C4—2181no—
216C2×C4—2181no—
217C2×C4—2182no—
218C2×C4—2182no—
219C2×C4C2×C4×D10911yescharacteristic
220C2×C4D4×D10911yescharacteristic
221C2×C4D4×D10911yescharacteristic
222C2×C4C2×C22⋊D10911yescharacteristic
223C2×C4#1318202811yescharacteristic
224C2×C4#1318202911yescharacteristic
225C8—22no—
226C8—2182no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—4362no—
231C22—2182no—
232C22C22⋊C4×D10911yescharacteristic
233C22#1681267011yescharacteristic
234C22#1681267211yescharacteristic
235C4—41no—
236C4—81no—
237C4—8721no—
238C4—4361no—
239C4—2182no—
240C4—2182no—
241C4#1681265911yescharacteristic
242C4C4×C22⋊D10911yescharacteristic
243C4#1681266711yescharacteristic
244C4#1681268111yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—81no—
249C2—4362no—
250C2#2029490211yescharacteristic
subgroupG/H
centerC4#16812667
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#421×C109C2
socleC2×C109#386
prime radical#20295572C2
cosocleC22×C4×C109C23
hypercenter#421D109
hypocenterC109#1884
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #20295792C2semidirect
3. #20295043C2semidirect
4. #20294999C2semidirect
5. #20294787C2semidirect
6. #20294785C2semidirect
7. #421×C109C2semidirect
13. #16812697C4semidirect
14. #16812695C4semidirect
15. #16812688C4semidirect
16. #16812686C4semidirect
38. #13182013D4semidirect
61. M16×C109D4semidirect
126. C109#1884semidirect
130. #421D109semidirect
176. M16C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
#202957922
#202955722
#202950432
#202949992
#202947872
#202947852
#421×C1092
#1884109