Finite Group Databasebeta

← #28361598

Subgroups — #28361598

Order 13952.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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#121×D109C211yesmaximal, characteristic
2C22⋊C8×D109C211yesmaximal, characteristic, complemented
3#20294885C211yesmaximal, characteristic, complemented
4#20294761C211yesmaximal, characteristic, complemented
5#20294760C211yesmaximal, characteristic, complemented
6#20294759C211yesmaximal, characteristic, complemented
7#327×C109C211yesmaximal, characteristic, complemented
8C2×D4×D109—21no—
9C2×D4×D109C411yescharacteristic, complemented
10C22×C4×D109C2211yescharacteristic
11C2×C8×D109—21no—
12#16812674C411yescharacteristic, complemented
13#16812673C2211yescharacteristic
14#16812672—21no—
15#16812671—21no—
16#16812670C411yescharacteristic, complemented
17C2×#13182008—21no—
18C4⋊C4×D109C411yescharacteristic, complemented
19C2×#13182006—21no—
20C22⋊C4×D109—21no—
21C22⋊#11724784C2211yescharacteristic, complemented
22#16812611—21no—
23#16812606C2211yescharacteristic, complemented
24#121×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic, complemented
26#95×C109C2211yescharacteristic, complemented
27C23×D109—21no—
28C23×D109D411yescharacteristic
29C2×D436—21no—
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C22⋊D109—21no—
34D4×D109—42no—
35D4×D109—42no—
36D4×D109—42no—
37C22×Dic109—21no—
38C22×Dic109D411yescharacteristic
39C2×C4×D109—21no—
40C2×C4×D109—42no—
41C2×C4×D109C2×C411yescharacteristic
42C2×C4×D109C2×C411yescharacteristic
43C2×C4×D109D411yescharacteristic
44C2×C4×D109D411yescharacteristic
45C2×#11724784—21no—
46C8×D109—42no—
47C4⋊Dic109C2×C411yescharacteristic
48#13182008—21no—
49#13182008—42no—
50C22⋊Dic109—21no—
51#13182006—21no—
52#13182006—21no—
53#13182006—42no—
54C2×D4×C109—21no—
55C2×D4×C109C2×C411yescharacteristic
56C22×C4×C109—21no—
57C22×C4×C109C2311yescharacteristic
58C2×C8×C109—21no—
59C4⋊C4×C109C2×C411yescharacteristic
60C22⋊C4×C109—21no—
61C23×C109—21no—
62C23×C109C2×D411yescharacteristic
63C22×D109—21no—
64C22×D109—41no—
65C22×D109—41no—
66C22×D109—42no—
67C22×D109—42no—
68C22×D109—42no—
69C22×D109C22⋊C411yescharacteristic
70C22×D109C22⋊C411yescharacteristic
71C22×D109D812yes—
72C22×D109SD1612yes—
73D4×C109—41no—
74D4×C109—41no—
75D4×C109—41no—
76C2×C4×C109—21no—
77C2×C4×C109—41no—
78C2×C4×C109—41no—
79C2×C4×C109—41no—
80C2×C4×C109—41no—
81C2×C4×C109C22×C411yescharacteristic
82C2×C4×C109C2×D411yescharacteristic
83C22⋊D109—41no—
84C22⋊D109—41no—
85C22⋊D109—42no—
86C22⋊D109—42no—
87C2×Dic109—22no—
88C2×Dic109—21no—
89C2×Dic109—41no—
90C2×Dic109—41no—
91C2×Dic109—41no—
92C2×Dic109C22⋊C411yescharacteristic
93C2×Dic109C22⋊C411yescharacteristic
94D436—41no—
95D436—42no—
96C4×D109—22no—
97C4×D109—22no—
98C4×D109—41no—
99C4×D109—41no—
100C4×D109—42no—
101C8×C109—41no—
102#11724784—41no—
103C22×C109—21no—
104C22×C109—21no—
105C22×C109—41no—
106C22×C109—41no—
107C22×C109—41no—
108C22×C109C2×C22⋊C411yescharacteristic
109C22×C109C2×D811yescharacteristic
110C22×C109C2×SD1611yescharacteristic
111C2×D109—21no—
112C2×D109—21no—
113C2×D109—21no—
114C2×D109—21no—
115C2×D109—42no—
116C2×D109—42no—
117C2×D109—41no—
118C2×D109—41no—
119C2×D109—41no—
120C2×D109—84no—
121C2×D109#10212yes—
122C2×D109#10212yes—
123C4×C109—21no—
124C4×C109—21no—
125C4×C109—41no—
126C4×C109—81no—
127Dic109—21no—
128Dic109—41no—
129Dic109—81no—
130Dic109#9912yes—
131C2×C109—21no—
132C2×C109—21no—
133C2×C109—81no—
134C2×C109C2×#9911yescharacteristic
135C2×C109C2×#10211yescharacteristic
136C2×C109#42111yescharacteristic
137D109—22no—
138D109—22no—
139D109—81no—
140#1519—1091nomaximal, Sylow
141C109#151911yescharacteristic, complemented, Sylow
142C2×#121—1091no—
143C2×C22⋊C8—1091no—
144#380—1091no—
145#327—1091no—
146#327—1091no—
147#327—1091no—
148#327D10911yescharacteristic, complemented
149C22×D4—1091no—
150C22×D4—2181no—
151C23×C4—1091no—
152C22×C8—2181no—
153#121—1091no—
154#121—1091no—
155#121—1091no—
156#121—2181no—
157#121—2181no—
158#121C2×D10911yescharacteristic
159C2×C4⋊C4—1091no—
160C2×C4⋊C4—2181no—
161C2×C22⋊C4—2181no—
162C2×C22⋊C4—2181no—
163C22⋊C8—1091no—
164C22⋊C8—2181no—
165C22⋊C8C2×D10911yescharacteristic, complemented
166#95—1091no—
167#95C2×D10911yescharacteristic, complemented
168C24—1091no—
169C24—2181no—
170C2×D4—21no—
171C2×D4—1091no—
172C2×D4—4362no—
173C2×D4—4362no—
174C2×D4—4362no—
175C2×D4—2181no—
176C2×D4—2181no—
177C2×D4—2181no—
178C2×D4—2181no—
179C2×D4C4×D10911yescharacteristic
180C22×C4—21no—
181C22×C4—1091no—
182C22×C4—1091no—
183C22×C4—1091no—
184C22×C4—1091no—
185C22×C4—1091no—
186C22×C4—4362no—
187C22×C4—2181no—
188C22×C4—2181no—
189C22×C4C22×D10911yescharacteristic
190C2×C8—21no—
191C2×C8—4362no—
192C2×C8—2181no—
193C4⋊C4—1091no—
194C4⋊C4—4362no—
195C4⋊C4—2181no—
196C4⋊C4C4×D10911yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—4362no—
199C22⋊C4—2181no—
200C22⋊C4—2181no—
201C22⋊C4—2181no—
202C23—21no—
203C23—1092no—
204C23—1092no—
205C23—1091no—
206C23—1091no—
207C23—4361no—
208C23—4361no—
209C23—4362no—
210C23—4362no—
211C23—4362no—
212C23—2181no—
213C23D4×D10911yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—4361no—
218D4—4362no—
219D4—4362no—
220D4—4362no—
221D4—4361no—
222D4—4361no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—1091no—
229C2×C4—1091no—
230C2×C4—4361no—
231C2×C4—4361no—
232C2×C4—4362no—
233C2×C4—4361no—
234C2×C4—4361no—
235C2×C4—4361no—
236C2×C4—2182no—
237C2×C4—2182no—
238C2×C4—2182no—
239C2×C4—2181no—
240C2×C4C2×C4×D10911yescharacteristic
241C2×C4D4×D10911yescharacteristic
242C8—41no—
243C8—4361no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—8724no—
250C22—1092no—
251C22—1092no—
252C22—4362no—
253C22—4362no—
254C22—4361no—
255C22—4361no—
256C22—4361no—
257C22—2181no—
258C22—2181no—
259C22—2181no—
260C22—2181no—
261C22C22⋊C4×D10911yescharacteristic
262C22D8×D10911yescharacteristic
263C22SD16×D10911yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—8721no—
269C4—1092no—
270C4—4361no—
271C4—2181no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—8721no—
276C2—2182no—
277C2—2182no—
278C2#99×D10911yescharacteristic
279C2#102×D10911yescharacteristic
280C2#2029504111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC22×C4C22×D109
Fitting#327×C109C2
socleC22×C109C2×C22⋊C4
prime radical#121×D109C2
cosocleC22×C4×C109C23
hypercenter#327D109
hypocenterC109#1519
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D109C2semidirect
3. #20294885C2semidirect
4. #20294761C2semidirect
5. #20294760C2semidirect
6. #20294759C2semidirect
7. #327×C109C2semidirect
9. C2×D4×D109C4semidirect
12. #16812674C4semidirect
16. #16812670C4semidirect
18. C4⋊C4×D109C4semidirect
21. C22⋊#11724784C22semidirect
23. #16812606C22semidirect
25. C22⋊C8×C109C22semidirect
26. #95×C109C22semidirect
141. C109#1519semidirect
148. #327D109semidirect
165. C22⋊C8C2×D109semidirect
167. #95C2×D109semidirect

Maximal subgroups

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

subgroupindex
#121×D1092
C22⋊C8×D1092
#202948852
#202947612
#202947602
#202947592
#327×C1092
#1519109