Finite Group Databasebeta

← #28374786

Subgroups — #28374786

Order 13952.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16812722C211yesmaximal, characteristic, complemented
2#20295695C212yesmaximal, complemented
3#20295401C211yesmaximal, characteristic, complemented
4#20295262C211yesmaximal, characteristic, complemented
5#20295259C211yesmaximal, characteristic, complemented
6#20295224C212yesmaximal, complemented
7#20295171C212yesmaximal, complemented
8#20295170C212yesmaximal, complemented
9Q16×Dic109C211yesmaximal, characteristic, complemented
10C8×C22⋊D109C211yesmaximal, characteristic, complemented
11C2×#135×C109C211yesmaximal, characteristic, complemented
12C2×#13182030C2212yes—
13#16812722—24no—
14C2×#13182016C2212yes—
15C2×D872C2211yescharacteristic
16C2×#13182014C2212yes—
17C2×C8×D109C2211yescharacteristic
18#16812695—22no—
19#16812695C2212yes—
20#16812673—22no—
21#16812673C2212yes—
22#16812670—22no—
23#16812670C2212yes—
24Q8×Dic109C2212yes—
25C4×C22⋊D109—22no—
26C4×C22⋊D109C2211yescharacteristic
27#16812633C2211yescharacteristic
28#16812628C2211yescharacteristic
29#16812623C2212yes—
30#16812621C2212yes—
31#16812620C2212yes—
32C22⋊#11724784C2211yescharacteristic
33#16812611C2211yescharacteristic
34C8×Dic109C2211yescharacteristic
35C2×#41×C109C2212yes—
36#135×C109—24no—
37C2×Q16×C109C2211yescharacteristic
38C2×SD16×C109C2212yes—
39C2×D8×C109C2211yescharacteristic
40C22×C8×C109C2211yescharacteristic
41#13182030—24no—
42#13182030—42no—
43C2×D436—22no—
44C2×D436C2312yes—
45C2×C22⋊D109—22no—
46C2×C22⋊D109—22no—
47C2×C22⋊D109—22no—
48C2×C22⋊D109—22no—
49C2×C22⋊D109D411yescharacteristic
50C2×C4×D109—22no—
51C2×C4×D109C2311yescharacteristic
52#13182016—24no—
53D872—22no—
54#13182014—42no—
55C2×#11724784C2311yescharacteristic
56C2×#11724784C2311yescharacteristic
57C8×D109—22no—
58C4⋊Dic109—22no—
59C4⋊Dic109C2312yes—
60#13182008D411yescharacteristic
61C22⋊Dic109—22no—
62C22⋊Dic109D411yescharacteristic
63#13182006—22no—
64#13182006D411yescharacteristic
65C4×Dic109—22no—
66C4×Dic109C2311yescharacteristic
67#41×C109—24no—
68#41×C109—42no—
69C2×Q8×C109C2312yes—
70C2×D4×C109—22no—
71C2×D4×C109C2312yes—
72C22×C4×C109—22no—
73C22×C4×C109C2311yescharacteristic
74Q16×C109D414yescomplemented
75SD16×C109—24no—
76D8×C109—22no—
77C2×C8×C109—22no—
78C2×C8×C109C2311yescharacteristic
79C2×C8×C109C2311yescharacteristic
80C23×C109—22no—
81C23×C109C2×D411yescharacteristic
82C22×D109—22no—
83C22×D109C2×D411yescharacteristic
84Q8×C109—22no—
85Q8×C109C2×D414yes—
86D4×C109—22no—
87D4×C109—22no—
88D4×C109—44no—
89C2×C4×C109—22no—
90C2×C4×C109—21no—
91C2×C4×C109—21no—
92C2×C4×C109—44no—
93C2×C4×C109C2×D411yescharacteristic
94C2×C4×C109C2411yescharacteristic
95C22⋊D109—22no—
96C22⋊D109—44no—
97C22⋊D109—82no—
98C22⋊D109—82no—
99C22⋊D109—82no—
100C2×Dic109—22no—
101C2×Dic109C2×D411yescharacteristic
102C2×Dic109C2×D411yescharacteristic
103C2×Dic109C2×D411yescharacteristic
104D436—22no—
105D436—22no—
106D436—44no—
107C4×D109—21no—
108C4×D109—21no—
109C4×D109—44no—
110C8×C109—21no—
111C8×C109C2×D412yes—
112#11724784—21no—
113#11724784—21no—
114C22×C109—21no—
115C22×C109—21no—
116C22×C109—21no—
117C22×C109—42no—
118C22×C109—42no—
119C22×C109—42no—
120C22×C109C22×D411yescharacteristic
121C2×D109—21no—
122C2×D109—21no—
123C2×D109—21no—
124C2×D109—42no—
125C2×D109—42no—
126C2×D109—42no—
127C4×C109—24no—
128C4×C109—21no—
129C4×C109C22×D411yescharacteristic
130C4×C109H(5,𝔽2)11yescharacteristic
131Dic109—21no—
132Dic109—21no—
133Dic109—42no—
134Dic109#13512yescomplemented
135C2×C109—41no—
136C2×C109—82no—
137C2×C109D4211yescharacteristic
138C2×C109C2×#13511yescharacteristic
139C2×C109#57611yescharacteristic
140D109—41no—
141D109—82no—
142#3287—1091nomaximal, Sylow
143C109#328711yescharacteristic, complemented, Sylow
144C2×#135—1091no—
145C2×#135D10911yescharacteristic, complemented
146#550—1092no—
147#493—1091no—
148#466—1091no—
149#466—1091no—
150#460—1092no—
151#449—1092no—
152#449—1092no—
153C4×Q16—1091no—
154C8×D4—1091no—
155C2×#41—1092no—
156C2×#41C2×D10912yes—
157#135—24no—
158#135—2184no—
159C2×Q16C2×D10911yescharacteristic
160C2×SD16—1092no—
161C2×SD16C2×D10912yes—
162C2×D8—1092no—
163C2×D8—1091no—
164C2×D8C2×D10911yescharacteristic
165C22×C8—1091no—
166C22×C8C2×D10911yescharacteristic
167#127—1092no—
168#127—2182no—
169#121—1092no—
170#121—1092no—
171#121—2182no—
172#121—2182no—
173C4×Q8—1092no—
174C4×D4—1091no—
175C4×D4—2182no—
176#107—1091no—
177C4⋊C8—1091no—
178#103—1092no—
179#102—1092no—
180#102—1092no—
181C22⋊C8—1091no—
182C22⋊C8—1091no—
183C4×C8—1091no—
184#41—24no—
185#41—42no—
186#41—4362no—
187#41—2184no—
188C2×Q8C22×D10912yes—
189C2×D4—22no—
190C2×D4—1091no—
191C2×D4—1092no—
192C2×D4—2182no—
193C2×D4—2182no—
194C2×D4—2182no—
195C2×D4—2182no—
196C2×D4—2182no—
197C2×D4C22×D10912yes—
198C22×C4—22no—
199C22×C4—1091no—
200C22×C4—2182no—
201C22×C4C22×D10911yescharacteristic
202Q16C22⋊D10914yescomplemented
203SD16—24no—
204SD16—2184no—
205D8—22no—
206D8—4362no—
207D8—2182no—
208C2×C8—22no—
209C2×C8—1091no—
210C2×C8—1091no—
211C2×C8—2182no—
212C2×C8C22×D10911yescharacteristic
213C2×C8C22×D10911yescharacteristic
214C4⋊C4—1091no—
215C4⋊C4—1092no—
216C4⋊C4—2182no—
217C22⋊C4—1091no—
218C22⋊C4—1091no—
219C22⋊C4—2182no—
220C22⋊C4—2182no—
221C42—1091no—
222C42—2182no—
223C23—22no—
224C23—1091no—
225C23—2182no—
226C23D4×D10911yescharacteristic
227Q8—22no—
228Q8C2×C22⋊D10914yes—
229D4—22no—
230D4—22no—
231D4—44no—
232D4—8722no—
233D4—8722no—
234D4—8722no—
235D4—4364no—
236D4—4364no—
237D4—2182no—
238D4—2182no—
239D4—2182no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—44no—
244C2×C4—1091no—
245C2×C4—1091no—
246C2×C4—1091no—
247C2×C4—4364no—
248C2×C4—2182no—
249C2×C4—2181no—
250C2×C4—2181no—
251C2×C4D4×D10911yescharacteristic
252C2×C4C23×D10911yescharacteristic
253C8—21no—
254C8—2181no—
255C8—2181no—
256C8C2×C22⋊D10912yes—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—4362no—
264C22—4362no—
265C22—4362no—
266C22—2181no—
267C22—2181no—
268C22—2181no—
269C22C2×D4×D10911yescharacteristic
270C4—21no—
271C4—24no—
272C4—1092no—
273C4—4362no—
274C4—2181no—
275C4—2181no—
276C4C22×C22⋊D10911yescharacteristic
277C4#1681274411yescharacteristic
278C2—41no—
279C2—82no—
280C2—8722no—
281C2—4361no—
282C2D4×C22⋊D10911yescharacteristic
283C2#135×D10911yescharacteristic
284C2#2029582811yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#135×C109C2
socleC22×C109C22×D4
hypercenterC2×#135D109
hypocenterC109#3287
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16812722C2semidirect
2. #20295695C2semidirect
3. #20295401C2semidirect
4. #20295262C2semidirect
5. #20295259C2semidirect
6. #20295224C2semidirect
7. #20295171C2semidirect
8. #20295170C2semidirect
9. Q16×Dic109C2semidirect
10. C8×C22⋊D109C2semidirect
11. C2×#135×C109C2semidirect
74. Q16×C109D4semidirect
134. Dic109#135semidirect
143. C109#3287semidirect
145. C2×#135D109semidirect
202. Q16C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168127222
#202956952
#202954012
#202952622
#202952592
#202952242
#202951712
#202951702
Q16×Dic1092
C8×C22⋊D1092
C2×#135×C1092
#3287109