Finite Group Databasebeta

← C4×#15693011 #27197700

Subgroups — C4×#15693011 #27197700

Order 13184.

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×#15693011C211yesmaximal, characteristic
2#20267688C211yesmaximal, characteristic
3#20267686C211yesmaximal, characteristic
4#20267677C211yesmaximal, characteristic
5#20267676C211yesmaximal, characteristic
6#20267673C211yesmaximal, characteristic
7#20267672C211yesmaximal, characteristic
8#20267655C211yesmaximal, characteristic
9C4×Dic103⋊C4C211yesmaximal, characteristic
10C4×Dic103⋊C4C211yesmaximal, characteristic
11C4×Dic103⋊C4C211yesmaximal, characteristic
12C4×Dic103⋊C4C211yesmaximal, characteristic
13C4×C4⋊Dic103C211yesmaximal, characteristic
14C42×Dic103C211yesmaximal, characteristic
15C4×C4⋊C4×C103C211yesmaximal, characteristic
16#15693011C418yesdirect product factor
17C2×C4⋊Dic103C2211yescharacteristic
18C2×C4⋊Dic103C2211yescharacteristic
19C2×Dic103⋊C4C2211yescharacteristic
20C2×Dic103⋊C4C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×C4×Dic103C2211yescharacteristic
28C2×C4×Dic103C2211yescharacteristic
29C2×C4×Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C42×C103C2211yescharacteristic
48C2×C42×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C22×Dic103C2311yescharacteristic
53C22×Dic103C2311yescharacteristic
54C22×Dic103C2311yescharacteristic
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C4⋊Dic103—22no—
61C4⋊Dic103C2×C414yes—
62Dic103⋊C4—22no—
63Dic103⋊C4—22no—
64Dic103⋊C4—22no—
65Dic103⋊C4—22no—
66Dic103⋊C4C2×C414yes—
67Dic103⋊C4C2×C414yes—
68Dic103⋊C4C2×C414yes—
69Dic103⋊C4C2×C414yes—
70C4×Dic103—22no—
71C4×Dic103—22no—
72C4×Dic103—22no—
73C4×Dic103—22no—
74C4×Dic103—22no—
75C4×Dic103—22no—
76C4×Dic103C2×C414yes—
77C4×Dic103Q814yes—
78C22×C4×C103C2311yescharacteristic
79C22×C4×C103C2311yescharacteristic
80C22×C4×C103C2311yescharacteristic
81C22×C4×C103C2311yescharacteristic
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C4⋊C4×C103—22no—
86C4⋊C4×C103C2×C414yes—
87C42×C103—22no—
88C42×C103—22no—
89C42×C103—22no—
90C23×C103C2411yescharacteristic
91C2×C4×C103—21no—
92C2×C4×C103—21no—
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103C22×C412yes—
106C2×C4×C103C22×C412yes—
107C2×C4×C103C22×C412yes—
108C2×C4×C103C2×Q812yes—
109C2×C4×C103#4112yes—
110C2×C4×C103#4112yes—
111C2×C4×C103#4112yes—
112C2×Dic103—21no—
113C2×Dic103—21no—
114C2×Dic103—21no—
115C2×Dic103—21no—
116C2×Dic103—21no—
117C2×Dic103—21no—
118C2×Dic103—21no—
119C2×Dic103—21no—
120C2×Dic103—21no—
121C2×Dic103—21no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103C22×C412yes—
129C2×Dic103C22×C412yes—
130C2×Dic103C22×C412yes—
131C2×Dic103C22×C412yes—
132C2×Dic103C2×Q812yes—
133C2×Dic103C2×Q812yes—
134C2×Dic103#4112yes—
135C2×Dic103#4112yes—
136C22×C103C23×C411yescharacteristic
137C22×C103C22×Q811yescharacteristic
138C22×C103C2×#4111yescharacteristic
139C22×C103C2×#4111yescharacteristic
140C22×C103C2×#4111yescharacteristic
141C22×C103C2×#4111yescharacteristic
142C22×C103C2×#4111yescharacteristic
143C4×C103—22no—
144C4×C103—22no—
145C4×C103—22no—
146C4×C103—22no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103#12514yescomplemented
150Dic103—22no—
151Dic103—22no—
152Dic103—22no—
153Dic103—22no—
154Dic103—22no—
155Dic103—41no—
156Dic103—41no—
157Dic103C4×Q814yes—
158C2×C103C2×C4×Q811yescharacteristic
159C2×C103C4×#4111yescharacteristic
160C2×C103C4×#4111yescharacteristic
161C2×C103C2×#12511yescharacteristic
162C2×C103#52911yescharacteristic
163C2×C103#52911yescharacteristic
164C2×C103#53311yescharacteristic
165C4×#125—1031nomaximal, Sylow
166C103C4×#12511yescharacteristic, complemented, Sylow
167C2×#125—1031no—
168#389—1031no—
169#389—1031no—
170#387—1031no—
171#387—1031no—
172#387—1031no—
173#387—1031no—
174#382—1031no—
175C4×C4⋊C4—1031no—
176C4×C4⋊C4—1031no—
177C4×C4⋊C4—1031no—
178C4×C4⋊C4—1031no—
179C4×C4⋊C4—1031no—
180C4×C4⋊C4D10311yescharacteristic
181C43—1031no—
182#125—1038no—
183C2×C4⋊C4—1031no—
184C2×C4⋊C4—1031no—
185C2×C4⋊C4—1031no—
186C2×C4⋊C4—1031no—
187C2×C4⋊C4—1031no—
188C2×C4⋊C4—1031no—
189C2×C4⋊C4—1031no—
190C2×C4⋊C4—1031no—
191C2×C4⋊C4—1031no—
192C2×C4⋊C4—1031no—
193C2×C4⋊C4C2×D10311yescharacteristic
194C2×C4⋊C4C2×D10311yescharacteristic
195C2×C42—1031no—
196C2×C42—1031no—
197C2×C42—1031no—
198C2×C42—1031no—
199C2×C42—1031no—
200C2×C42—1031no—
201C2×C42—1031no—
202C2×C42—1031no—
203C2×C42C2×D10311yescharacteristic
204C2×C42C2×D10311yescharacteristic
205C2×C42C2×D10311yescharacteristic
206#95—1031no—
207#95—1031no—
208#95—1031no—
209#95—1031no—
210#95—1031no—
211#95—1031no—
212#95—1031no—
213#95—1031no—
214#95—1031no—
215#95—1031no—
216#95C2×D10311yescharacteristic
217#95C2×D10311yescharacteristic
218C22×C4—1031no—
219C22×C4—1031no—
220C22×C4—1031no—
221C22×C4—1031no—
222C22×C4—1031no—
223C22×C4—1031no—
224C22×C4—1031no—
225C22×C4—1031no—
226C22×C4C22×D10311yescharacteristic
227C22×C4C22×D10311yescharacteristic
228C22×C4C22×D10311yescharacteristic
229C22×C4C22×D10311yescharacteristic
230C22×C4C22×D10311yescharacteristic
231C22×C4C22×D10311yescharacteristic
232C22×C4C22×D10311yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—1034no—
235C4⋊C4—1034no—
236C4⋊C4—1034no—
237C4⋊C4—1034no—
238C4⋊C4—1034no—
239C4⋊C4—2062no—
240C4⋊C4—2062no—
241C4⋊C4—2062no—
242C4⋊C4—2062no—
243C4⋊C4—2062no—
244C4⋊C4C4×D10314yes—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—1034no—
249C42—1034no—
250C42—2062no—
251C42—2062no—
252C42—2062no—
253C42—2062no—
254C42—2062no—
255C42—2062no—
256C23C23×D10311yescharacteristic
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—1032no—
272C2×C4—1032no—
273C2×C4—1032no—
274C2×C4—1032no—
275C2×C4—1032no—
276C2×C4—1032no—
277C2×C4—1032no—
278C2×C4—1032no—
279C2×C4—2061no—
280C2×C4—2061no—
281C2×C4—2061no—
282C2×C4—2061no—
283C2×C4—2061no—
284C2×C4—2061no—
285C2×C4—2061no—
286C2×C4—2061no—
287C2×C4—2061no—
288C2×C4—2061no—
289C2×C4—2061no—
290C2×C4—2061no—
291C2×C4—2061no—
292C2×C4—2061no—
293C2×C4—2061no—
294C2×C4—2061no—
295C2×C4C2×C4×D10312yes—
296C2×C4C2×C4×D10312yes—
297C2×C4C2×C4×D10312yes—
298C2×C4Q8×D10312yes—
299C2×C4#1311010412yes—
300C2×C4#1311010512yes—
301C2×C4#1311010512yes—
302C22C22×C4×D10311yescharacteristic
303C22C2×Q8×D10311yescharacteristic
304C22#41×D10311yescharacteristic
305C22#41×D10311yescharacteristic
306C22C2×#1311010411yescharacteristic
307C22C2×#1311010511yescharacteristic
308C22C2×#1311010511yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—1034no—
316C4—4121no—
317C4—4121no—
318C4—2062no—
319C4—2062no—
320C4—2062no—
321C4—2062no—
322C4—2062no—
323C4#1569301114yesdirect product factor
324C2C4×Q8×D10311yescharacteristic
325C2C4×#1311010411yescharacteristic
326C2C4×#1311010511yescharacteristic
327C2C2×#1569301111yescharacteristic
328C2#2026831911yescharacteristic
329C2#2026832111yescharacteristic
330C2#2026834511yescharacteristic
subgroupG/H
centerC22×C4C22×D103
commutatorC22×C103C23×C4
FrattiniC23C23×D103
FittingC4×C4⋊C4×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenterC4×C4⋊C4D103
hypocenterC103C4×#125
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #15693011C4direct (N × H)
149. C4×C103#125semidirect
166. C103C4×#125semidirect
323. C4#15693011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156930112
#202676882
#202676862
#202676772
#202676762
#202676732
#202676722
#202676552
C4×Dic103⋊C42
C4×C4⋊Dic1032
C42×Dic1032
C4×C4⋊C4×C1032
C4×#125103