Finite Group Databasebeta

← C4×#16812099 #28339017

Subgroups — C4×#16812099 #28339017

Order 13696.

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×#16812099C211yesmaximal, characteristic
2#20292524C211yesmaximal, characteristic
3#20292522C211yesmaximal, characteristic
4#20292513C211yesmaximal, characteristic
5#20292512C211yesmaximal, characteristic
6#20292509C211yesmaximal, characteristic
7#20292508C211yesmaximal, characteristic
8#20292491C211yesmaximal, characteristic
9C4×Dic107⋊C4C211yesmaximal, characteristic
10C4×Dic107⋊C4C211yesmaximal, characteristic
11C4×Dic107⋊C4C211yesmaximal, characteristic
12C4×Dic107⋊C4C211yesmaximal, characteristic
13C4×C4⋊Dic107C211yesmaximal, characteristic
14C42×Dic107C211yesmaximal, characteristic
15C4×C4⋊C4×C107C211yesmaximal, characteristic
16#16812099C418yesdirect product factor
17C2×C4⋊Dic107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×C4×Dic107C2211yescharacteristic
28C2×C4×Dic107C2211yescharacteristic
29C2×C4×Dic107C2211yescharacteristic
30C2×C4×Dic107C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C42×C107C2211yescharacteristic
48C2×C42×C107C2211yescharacteristic
49C2×C42×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52C22×Dic107C2311yescharacteristic
53C22×Dic107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C4⋊Dic107—22no—
61C4⋊Dic107C2×C414yes—
62Dic107⋊C4—22no—
63Dic107⋊C4—22no—
64Dic107⋊C4—22no—
65Dic107⋊C4—22no—
66Dic107⋊C4C2×C414yes—
67Dic107⋊C4C2×C414yes—
68Dic107⋊C4C2×C414yes—
69Dic107⋊C4C2×C414yes—
70C4×Dic107—22no—
71C4×Dic107—22no—
72C4×Dic107—22no—
73C4×Dic107—22no—
74C4×Dic107—22no—
75C4×Dic107—22no—
76C4×Dic107C2×C414yes—
77C4×Dic107Q814yes—
78C22×C4×C107C2311yescharacteristic
79C22×C4×C107C2311yescharacteristic
80C22×C4×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C4⋊C4×C107—22no—
86C4⋊C4×C107C2×C414yes—
87C42×C107—22no—
88C42×C107—22no—
89C42×C107—22no—
90C23×C107C2411yescharacteristic
91C2×C4×C107—21no—
92C2×C4×C107—21no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—21no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107C22×C412yes—
106C2×C4×C107C22×C412yes—
107C2×C4×C107C22×C412yes—
108C2×C4×C107C2×Q812yes—
109C2×C4×C107#4112yes—
110C2×C4×C107#4112yes—
111C2×C4×C107#4112yes—
112C2×Dic107—21no—
113C2×Dic107—21no—
114C2×Dic107—21no—
115C2×Dic107—21no—
116C2×Dic107—21no—
117C2×Dic107—21no—
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—21no—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107C22×C412yes—
129C2×Dic107C22×C412yes—
130C2×Dic107C22×C412yes—
131C2×Dic107C22×C412yes—
132C2×Dic107C2×Q812yes—
133C2×Dic107C2×Q812yes—
134C2×Dic107#4112yes—
135C2×Dic107#4112yes—
136C22×C107C23×C411yescharacteristic
137C22×C107C22×Q811yescharacteristic
138C22×C107C2×#4111yescharacteristic
139C22×C107C2×#4111yescharacteristic
140C22×C107C2×#4111yescharacteristic
141C22×C107C2×#4111yescharacteristic
142C22×C107C2×#4111yescharacteristic
143C4×C107—22no—
144C4×C107—22no—
145C4×C107—22no—
146C4×C107—22no—
147C4×C107—41no—
148C4×C107—41no—
149C4×C107#12514yescomplemented
150Dic107—22no—
151Dic107—22no—
152Dic107—22no—
153Dic107—22no—
154Dic107—22no—
155Dic107—41no—
156Dic107—41no—
157Dic107C4×Q814yes—
158C2×C107C2×C4×Q811yescharacteristic
159C2×C107C4×#4111yescharacteristic
160C2×C107C4×#4111yescharacteristic
161C2×C107C2×#12511yescharacteristic
162C2×C107#52911yescharacteristic
163C2×C107#52911yescharacteristic
164C2×C107#53311yescharacteristic
165C4×#125—1071nomaximal, Sylow
166C107C4×#12511yescharacteristic, complemented, Sylow
167C2×#125—1071no—
168#389—1071no—
169#389—1071no—
170#387—1071no—
171#387—1071no—
172#387—1071no—
173#387—1071no—
174#382—1071no—
175C4×C4⋊C4—1071no—
176C4×C4⋊C4—1071no—
177C4×C4⋊C4—1071no—
178C4×C4⋊C4—1071no—
179C4×C4⋊C4—1071no—
180C4×C4⋊C4D10711yescharacteristic
181C43—1071no—
182#125—1078no—
183C2×C4⋊C4—1071no—
184C2×C4⋊C4—1071no—
185C2×C4⋊C4—1071no—
186C2×C4⋊C4—1071no—
187C2×C4⋊C4—1071no—
188C2×C4⋊C4—1071no—
189C2×C4⋊C4—1071no—
190C2×C4⋊C4—1071no—
191C2×C4⋊C4—1071no—
192C2×C4⋊C4—1071no—
193C2×C4⋊C4C2×D10711yescharacteristic
194C2×C4⋊C4C2×D10711yescharacteristic
195C2×C42—1071no—
196C2×C42—1071no—
197C2×C42—1071no—
198C2×C42—1071no—
199C2×C42—1071no—
200C2×C42—1071no—
201C2×C42—1071no—
202C2×C42—1071no—
203C2×C42C2×D10711yescharacteristic
204C2×C42C2×D10711yescharacteristic
205C2×C42C2×D10711yescharacteristic
206#95—1071no—
207#95—1071no—
208#95—1071no—
209#95—1071no—
210#95—1071no—
211#95—1071no—
212#95—1071no—
213#95—1071no—
214#95—1071no—
215#95—1071no—
216#95C2×D10711yescharacteristic
217#95C2×D10711yescharacteristic
218C22×C4—1071no—
219C22×C4—1071no—
220C22×C4—1071no—
221C22×C4—1071no—
222C22×C4—1071no—
223C22×C4—1071no—
224C22×C4—1071no—
225C22×C4—1071no—
226C22×C4C22×D10711yescharacteristic
227C22×C4C22×D10711yescharacteristic
228C22×C4C22×D10711yescharacteristic
229C22×C4C22×D10711yescharacteristic
230C22×C4C22×D10711yescharacteristic
231C22×C4C22×D10711yescharacteristic
232C22×C4C22×D10711yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—1074no—
235C4⋊C4—1074no—
236C4⋊C4—1074no—
237C4⋊C4—1074no—
238C4⋊C4—1074no—
239C4⋊C4—2142no—
240C4⋊C4—2142no—
241C4⋊C4—2142no—
242C4⋊C4—2142no—
243C4⋊C4—2142no—
244C4⋊C4C4×D10714yes—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—1074no—
249C42—1074no—
250C42—2142no—
251C42—2142no—
252C42—2142no—
253C42—2142no—
254C42—2142no—
255C42—2142no—
256C23C23×D10711yescharacteristic
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—1072no—
272C2×C4—1072no—
273C2×C4—1072no—
274C2×C4—1072no—
275C2×C4—1072no—
276C2×C4—1072no—
277C2×C4—1072no—
278C2×C4—1072no—
279C2×C4—2141no—
280C2×C4—2141no—
281C2×C4—2141no—
282C2×C4—2141no—
283C2×C4—2141no—
284C2×C4—2141no—
285C2×C4—2141no—
286C2×C4—2141no—
287C2×C4—2141no—
288C2×C4—2141no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4—2141no—
292C2×C4—2141no—
293C2×C4—2141no—
294C2×C4—2141no—
295C2×C4C2×C4×D10712yes—
296C2×C4C2×C4×D10712yes—
297C2×C4C2×C4×D10712yes—
298C2×C4Q8×D10712yes—
299C2×C4#1313381712yes—
300C2×C4#1313381812yes—
301C2×C4#1313381812yes—
302C22C22×C4×D10711yescharacteristic
303C22C2×Q8×D10711yescharacteristic
304C22#41×D10711yescharacteristic
305C22#41×D10711yescharacteristic
306C22C2×#1313381711yescharacteristic
307C22C2×#1313381811yescharacteristic
308C22C2×#1313381811yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—1074no—
316C4—4281no—
317C4—4281no—
318C4—2142no—
319C4—2142no—
320C4—2142no—
321C4—2142no—
322C4—2142no—
323C4#1681209914yesdirect product factor
324C2C4×Q8×D10711yescharacteristic
325C2C4×#1313381711yescharacteristic
326C2C4×#1313381811yescharacteristic
327C2C2×#1681209911yescharacteristic
328C2#2029315511yescharacteristic
329C2#2029315711yescharacteristic
330C2#2029318111yescharacteristic
subgroupG/H
centerC22×C4C22×D107
commutatorC22×C107C23×C4
FrattiniC23C23×D107
FittingC4×C4⋊C4×C107C2
socle, prime radical, cosocleC23×C107C24
hypercenterC4×C4⋊C4D107
hypocenterC107C4×#125
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #16812099C4direct (N × H)
149. C4×C107#125semidirect
166. C107C4×#125semidirect
323. C4#16812099direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168120992
#202925242
#202925222
#202925132
#202925122
#202925092
#202925082
#202924912
C4×Dic107⋊C42
C4×C4⋊Dic1072
C42×Dic1072
C4×C4⋊C4×C1072
C4×#125107