Finite Group Databasebeta

← #28365589

Subgroups — #28365589

Order 13952.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812689C211yesmaximal, characteristic
2#20294923C211yesmaximal, characteristic
3#20294921C211yesmaximal, characteristic
4#20294913C211yesmaximal, characteristic
5#20294910C211yesmaximal, characteristic
6#20294909C211yesmaximal, characteristic
7#20294890C211yesmaximal, characteristic
8C4⋊C4×Dic109C211yesmaximal, characteristic
9C4⋊C4×Dic109C211yesmaximal, characteristic
10#20294877C211yesmaximal, characteristic
11#20294877C211yesmaximal, characteristic
12#20294877C211yesmaximal, characteristic
13#20294877C211yesmaximal, characteristic
14C42×Dic109C211yesmaximal, characteristic
15#387×C109C211yesmaximal, characteristic
16#16812689C418yescomplemented
17C2×C4⋊Dic109C2211yescharacteristic
18C2×C4⋊Dic109C2211yescharacteristic
19C2×#13182008C2211yescharacteristic
20C2×#13182008C2211yescharacteristic
21C2×#13182008C2211yescharacteristic
22C2×#13182008C2211yescharacteristic
23C2×#13182008C2211yescharacteristic
24C2×#13182008C2211yescharacteristic
25C2×#13182008C2211yescharacteristic
26C2×#13182008C2211yescharacteristic
27C2×C4×Dic109C2211yescharacteristic
28C2×C4×Dic109C2211yescharacteristic
29C2×C4×Dic109C2211yescharacteristic
30C2×C4×Dic109C2211yescharacteristic
31C2×C4×Dic109C2211yescharacteristic
32C2×C4×Dic109C2211yescharacteristic
33C2×C4×Dic109C2211yescharacteristic
34C2×C4×Dic109C2211yescharacteristic
35C2×C4×Dic109C2211yescharacteristic
36C2×C4×Dic109C2211yescharacteristic
37#16812606C2211yescharacteristic
38#16812606C2211yescharacteristic
39#16812606C2211yescharacteristic
40#16812606C2211yescharacteristic
41#16812606C2211yescharacteristic
42#16812606C2211yescharacteristic
43#16812606C2211yescharacteristic
44#16812606C2211yescharacteristic
45C2×C4⋊C4×C109C2211yescharacteristic
46C2×C4⋊C4×C109C2211yescharacteristic
47C2×C42×C109C2211yescharacteristic
48#95×C109C2211yescharacteristic
49#95×C109C2211yescharacteristic
50#95×C109C2211yescharacteristic
51#95×C109C2211yescharacteristic
52C22×Dic109C2311yescharacteristic
53C22×Dic109C2311yescharacteristic
54C22×Dic109C2311yescharacteristic
55C22×Dic109C2311yescharacteristic
56C22×Dic109C2311yescharacteristic
57C22×Dic109C2311yescharacteristic
58C22×Dic109C2311yescharacteristic
59C22×Dic109C2311yescharacteristic
60C4⋊Dic109—22no—
61C4⋊Dic109C2×C414yes—
62#13182008—22no—
63#13182008—22no—
64#13182008—22no—
65#13182008—22no—
66#13182008C2×C414yes—
67#13182008C2×C414yes—
68#13182008C2×C414yes—
69#13182008C2×C414yes—
70C4×Dic109—22no—
71C4×Dic109—22no—
72C4×Dic109—22no—
73C4×Dic109—22no—
74C4×Dic109—22no—
75C4×Dic109—22no—
76C4×Dic109—22no—
77C4×Dic109—22no—
78C4×Dic109C2×C414yes—
79C4×Dic109Q814yes—
80C22×C4×C109C2311yescharacteristic
81C22×C4×C109C2311yescharacteristic
82C22×C4×C109C2311yescharacteristic
83C22×C4×C109C2311yescharacteristic
84C22×C4×C109C2311yescharacteristic
85C22×C4×C109C2311yescharacteristic
86C22×C4×C109C2311yescharacteristic
87C4⋊C4×C109—22no—
88C4⋊C4×C109C2×C414yes—
89C42×C109—22no—
90C23×C109C2411yescharacteristic
91C2×C4×C109—21no—
92C2×C4×C109—21no—
93C2×C4×C109—21no—
94C2×C4×C109—21no—
95C2×C4×C109—21no—
96C2×C4×C109—21no—
97C2×C4×C109—21no—
98C2×C4×C109—21no—
99C2×C4×C109—21no—
100C2×C4×C109—21no—
101C2×C4×C109—21no—
102C2×C4×C109—21no—
103C2×C4×C109—21no—
104C2×C4×C109—21no—
105C2×C4×C109—21no—
106C2×C4×C109—21no—
107C2×C4×C109C22×C412yes—
108C2×C4×C109C22×C412yes—
109C2×C4×C109C22×C412yes—
110C2×C4×C109C2×Q812yes—
111C2×C4×C109#4112yes—
112C2×Dic109—21no—
113C2×Dic109—21no—
114C2×Dic109—21no—
115C2×Dic109—21no—
116C2×Dic109—21no—
117C2×Dic109—21no—
118C2×Dic109—21no—
119C2×Dic109—21no—
120C2×Dic109—21no—
121C2×Dic109—21no—
122C2×Dic109—21no—
123C2×Dic109—21no—
124C2×Dic109—21no—
125C2×Dic109—21no—
126C2×Dic109C22×C412yes—
127C2×Dic109C22×C412yes—
128C2×Dic109C22×C412yes—
129C2×Dic109C22×C412yes—
130C2×Dic109C2×Q812yes—
131C2×Dic109C2×Q812yes—
132C2×Dic109#4112yes—
133C2×Dic109#4112yes—
134C2×Dic109#4112yes—
135C2×Dic109#4112yes—
136C22×C109C23×C411yescharacteristic
137C22×C109C22×Q811yescharacteristic
138C22×C109C2×#4111yescharacteristic
139C22×C109C2×#4111yescharacteristic
140C22×C109C2×#4111yescharacteristic
141C22×C109C2×#4111yescharacteristic
142C22×C109C2×#4111yescharacteristic
143C4×C109—22no—
144C4×C109—22no—
145C4×C109—22no—
146C4×C109—22no—
147C4×C109—22no—
148C4×C109—41no—
149C4×C109—41no—
150Dic109—22no—
151Dic109—22no—
152Dic109—22no—
153Dic109—22no—
154Dic109—41no—
155Dic109—41no—
156Dic109C4×Q814yes—
157Dic109#12514yescomplemented
158C2×C109C2×C4×Q811yescharacteristic
159C2×C109C4×#4111yescharacteristic
160C2×C109C4×#4111yescharacteristic
161C2×C109C2×#12511yescharacteristic
162C2×C109#52911yescharacteristic
163C2×C109#52911yescharacteristic
164C2×C109#53311yescharacteristic
165C4×#125—1091nomaximal, Sylow
166C109C4×#12511yescharacteristic, complemented, Sylow
167C2×#125—1091no—
168#389—1091no—
169#389—1091no—
170#387—1091no—
171#387—1091no—
172#387—1091no—
173#387D10911yescharacteristic
174#382—1091no—
175C4×C4⋊C4—1091no—
176C4×C4⋊C4—1091no—
177C4×C4⋊C4—1091no—
178C4×C4⋊C4—1091no—
179C4×C4⋊C4—1091no—
180C4×C4⋊C4—1091no—
181C43—1091no—
182#125—1098no—
183C2×C4⋊C4—1091no—
184C2×C4⋊C4—1091no—
185C2×C4⋊C4—1091no—
186C2×C4⋊C4—1091no—
187C2×C4⋊C4—1091no—
188C2×C4⋊C4—1091no—
189C2×C4⋊C4—1091no—
190C2×C4⋊C4—1091no—
191C2×C4⋊C4—1091no—
192C2×C4⋊C4—1091no—
193C2×C4⋊C4C2×D10911yescharacteristic
194C2×C4⋊C4C2×D10911yescharacteristic
195C2×C42—1091no—
196C2×C42—1091no—
197C2×C42—1091no—
198C2×C42—1091no—
199C2×C42—1091no—
200C2×C42—1091no—
201C2×C42—1091no—
202C2×C42—1091no—
203C2×C42—1091no—
204C2×C42—1091no—
205C2×C42C2×D10911yescharacteristic
206#95—1091no—
207#95—1091no—
208#95—1091no—
209#95—1091no—
210#95—1091no—
211#95—1091no—
212#95—1091no—
213#95—1091no—
214#95C2×D10911yescharacteristic
215#95C2×D10911yescharacteristic
216#95C2×D10911yescharacteristic
217#95C2×D10911yescharacteristic
218C22×C4—1091no—
219C22×C4—1091no—
220C22×C4—1091no—
221C22×C4—1091no—
222C22×C4—1091no—
223C22×C4—1091no—
224C22×C4—1091no—
225C22×C4—1091no—
226C22×C4C22×D10911yescharacteristic
227C22×C4C22×D10911yescharacteristic
228C22×C4C22×D10911yescharacteristic
229C22×C4C22×D10911yescharacteristic
230C22×C4C22×D10911yescharacteristic
231C22×C4C22×D10911yescharacteristic
232C22×C4C22×D10911yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—1094no—
235C4⋊C4—1094no—
236C4⋊C4—1094no—
237C4⋊C4—1094no—
238C4⋊C4—1094no—
239C4⋊C4—2182no—
240C4⋊C4—2182no—
241C4⋊C4—2182no—
242C4⋊C4—2182no—
243C4⋊C4—2182no—
244C4⋊C4C4×D10914yes—
245C42—22no—
246C42—1094no—
247C42—1094no—
248C42—2182no—
249C42—2182no—
250C42—2182no—
251C42—2182no—
252C42—2182no—
253C42—2182no—
254C42—2182no—
255C42—2182no—
256C23C23×D10911yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—1092no—
274C2×C4—1092no—
275C2×C4—1092no—
276C2×C4—1092no—
277C2×C4—1092no—
278C2×C4—1092no—
279C2×C4—1092no—
280C2×C4—1092no—
281C2×C4—1092no—
282C2×C4—1092no—
283C2×C4—2181no—
284C2×C4—2181no—
285C2×C4—2181no—
286C2×C4—2181no—
287C2×C4—2181no—
288C2×C4—2181no—
289C2×C4—2181no—
290C2×C4—2181no—
291C2×C4—2181no—
292C2×C4—2181no—
293C2×C4—2181no—
294C2×C4—2181no—
295C2×C4—2181no—
296C2×C4—2181no—
297C2×C4C2×C4×D10912yes—
298C2×C4C2×C4×D10912yes—
299C2×C4C2×C4×D10912yes—
300C2×C4Q8×D10912yes—
301C2×C4#1318202812yes—
302C22C22×C4×D10911yescharacteristic
303C22C2×Q8×D10911yescharacteristic
304C22#41×D10911yescharacteristic
305C22#41×D10911yescharacteristic
306C22#41×D10911yescharacteristic
307C22#41×D10911yescharacteristic
308C22C2×#1318202811yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—1094no—
317C4—1094no—
318C4—4361no—
319C4—4361no—
320C4—2182no—
321C4—2182no—
322C4—2182no—
323C4—2182no—
324C2C4×Q8×D10911yescharacteristic
325C2C4×#1318202811yescharacteristic
326C2#2029549411yescharacteristic
327C2#125×D10911yescharacteristic
328C2#2029555311yescharacteristic
329C2#2029555911yescharacteristic
330C2#2029557811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#387×C109C2
socle, prime radical, cosocleC23×C109C24
hypercenter#387D109
hypocenterC109C4×#125
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #16812689C4semidirect
157. Dic109#125semidirect
166. C109C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×#168126892
#202949232
#202949212
#202949132
#202949102
#202949092
#202948902
C4⋊C4×Dic1092
#202948772
C42×Dic1092
#387×C1092
C4×#125109