Finite Group Databasebeta

← C4×#16812102 #28339010

Subgroups — C4×#16812102 #28339010

Order 13696.

516 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812102C211yesmaximal, characteristic
2#20292521C211yesmaximal, characteristic
3#20292520C211yesmaximal, characteristic
4#20292515C211yesmaximal, characteristic
5#20292514C211yesmaximal, characteristic, complemented
6#20292512C211yesmaximal, characteristic, complemented
7#20292509C211yesmaximal, characteristic, complemented
8#20292494C211yesmaximal, characteristic, complemented
9C4×Dic107⋊C4C211yesmaximal, characteristic, complemented
10C4×Dic107⋊C4C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic107C211yesmaximal, characteristic, complemented
12C4×C22⋊Dic107C211yesmaximal, characteristic
13C4×C22⋊Dic107C211yesmaximal, characteristic
14C42×Dic107C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C107C211yesmaximal, characteristic
16#16812102C418yesdirect product factor
17C2×C4⋊Dic107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×C22⋊Dic107C2211yescharacteristic
24C2×C22⋊Dic107C2211yescharacteristic
25C2×C22⋊Dic107C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
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
45C23×C4×C107C2211yescharacteristic
46C2×C22⋊C4×C107C2211yescharacteristic
47C2×C22⋊C4×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×C414yescomplemented
62Dic107⋊C4—22no—
63Dic107⋊C4—22no—
64Dic107⋊C4C2×C414yescomplemented
65Dic107⋊C4C2×C414yescomplemented
66C22⋊Dic107—22no—
67C22⋊Dic107—22no—
68C22⋊Dic107C2×C414yes—
69C22⋊Dic107C2×C414yes—
70C4×Dic107—22no—
71C4×Dic107—22no—
72C4×Dic107—22no—
73C4×Dic107—22no—
74C4×Dic107—22no—
75C4×Dic107—22no—
76C4×Dic107—22no—
77C4×Dic107C2×C414yescomplemented
78C24×C107C2311yescharacteristic
79C22×C4×C107—22no—
80C22×C4×C107—22no—
81C22×C4×C107—22no—
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C22⋊C4×C107—22no—
89C22⋊C4×C107C2×C414yes—
90C42×C107—22no—
91C42×C107—22no—
92C23×C107—21no—
93C23×C107—21no—
94C23×C107—21no—
95C23×C107—21no—
96C23×C107—21no—
97C23×C107—21no—
98C23×C107C22×C412yes—
99C23×C107C2411yescharacteristic
100C2×C4×C107—21no—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
108C2×C4×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—44no—
113C2×C4×C107C22×C412yes—
114C2×C4×C107C22×C412yes—
115C2×C4×C107#4112yes—
116C2×C4×C107#4112yes—
117C2×C4×C107#4112yes—
118C2×C4×C107#4112yes—
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×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107C22×C412yes—
138C2×Dic107C22×C412yes—
139C2×Dic107C22×C412yes—
140C2×Dic107C22×C412yes—
141C2×Dic107#4112yes—
142C2×Dic107#4112yes—
143C22×C107—22no—
144C22×C107—22no—
145C22×C107—22no—
146C22×C107—41no—
147C22×C107—41no—
148C22×C107—41no—
149C22×C107—41no—
150C22×C107C23×C411yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107C2×#4111yescharacteristic
153C22×C107C2×#4111yescharacteristic
154C22×C107C2×#4111yescharacteristic
155C22×C107C2×#4111yescharacteristic
156C22×C107C2×#4111yescharacteristic
157C4×C107—22no—
158C4×C107—22no—
159C4×C107—22no—
160C4×C107—41no—
161C4×C107—41no—
162C4×C107#12614yescomplemented
163Dic107—22no—
164Dic107—22no—
165Dic107—22no—
166Dic107—22no—
167Dic107—22no—
168Dic107—22no—
169Dic107—41no—
170Dic107—41no—
171C2×C107—42no—
172C2×C107C4×#4111yescharacteristic
173C2×C107C4×#4111yescharacteristic
174C2×C107C4×#4111yescharacteristic
175C2×C107C2×#12611yescharacteristic
176C2×C107#52911yescharacteristic
177C2×C107#52911yescharacteristic
178C2×C107#52911yescharacteristic
179C4×#126—1071nomaximal, Sylow
180C107C4×#12611yescharacteristic, complemented, Sylow
181C2×#126—1071no—
182#388—1071no—
183#388—1071no—
184#388—1071no—
185#387—1071no—
186#387—1071no—
187#387—1071no—
188#383—1071no—
189C4×C4⋊C4—1071no—
190C4×C4⋊C4—1071no—
191C4×C4⋊C4—1071no—
192C4×C22⋊C4—1071no—
193C4×C22⋊C4—1071no—
194C4×C22⋊C4D10711yescharacteristic
195C43—1071no—
196C23×C4C2×D10711yescharacteristic
197#126—1078no—
198C2×C4⋊C4—1071no—
199C2×C4⋊C4—1071no—
200C2×C4⋊C4—1071no—
201C2×C4⋊C4—1071no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4—1071no—
204C2×C22⋊C4—1071no—
205C2×C22⋊C4—1071no—
206C2×C22⋊C4—1071no—
207C2×C22⋊C4—1071no—
208C2×C22⋊C4C2×D10711yescharacteristic
209C2×C22⋊C4C2×D10711yescharacteristic
210C2×C42—1071no—
211C2×C42—1071no—
212C2×C42—1071no—
213C2×C42—1071no—
214C2×C42—1071no—
215C2×C42—1071no—
216C2×C42—1071no—
217C2×C42—1071no—
218C2×C42C2×D10711yescharacteristic
219C2×C42C2×D10711yescharacteristic
220#95—1071no—
221#95—1071no—
222#95—1071no—
223#95—1071no—
224#95—1071no—
225#95—1071no—
226#95—1071no—
227#95—1071no—
228#95—1071no—
229#95—1071no—
230#95C2×D10711yescharacteristic
231#95C2×D10711yescharacteristic
232C24C22×D10711yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—1071no—
237C22×C4—1071no—
238C22×C4—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1071no—
243C22×C4—1071no—
244C22×C4C22×D10711yescharacteristic
245C22×C4C22×D10711yescharacteristic
246C22×C4C22×D10711yescharacteristic
247C22×C4C22×D10711yescharacteristic
248C22×C4C22×D10711yescharacteristic
249C22×C4C22×D10711yescharacteristic
250C4⋊C4—1074no—
251C4⋊C4—1074no—
252C4⋊C4—1074no—
253C4⋊C4—2142no—
254C4⋊C4—2142no—
255C4⋊C4—2142no—
256C22⋊C4—22no—
257C22⋊C4—1074no—
258C22⋊C4—1074no—
259C22⋊C4—2142no—
260C22⋊C4—2142no—
261C22⋊C4C4×D10714yes—
262C42—22no—
263C42—22no—
264C42—1074no—
265C42—2142no—
266C42—2142no—
267C42—2142no—
268C42—2142no—
269C42—2142no—
270C42—2142no—
271C42—2142no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D10712yes—
279C23C23×D10711yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—1072no—
294C2×C4—1072no—
295C2×C4—1072no—
296C2×C4—1072no—
297C2×C4—1072no—
298C2×C4—1072no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4—2141no—
302C2×C4—2141no—
303C2×C4—2141no—
304C2×C4—2141no—
305C2×C4—2141no—
306C2×C4—2141no—
307C2×C4—2141no—
308C2×C4—2141no—
309C2×C4—2141no—
310C2×C4—2141no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4—2141no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4C2×C4×D10712yes—
318C2×C4C2×C4×D10712yes—
319C2×C4#1313381712yes—
320C2×C4#1313381712yes—
321C2×C4#1313381812yes—
322C2×C4#1313381812yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D10711yescharacteristic
331C22#41×D10711yescharacteristic
332C22#41×D10711yescharacteristic
333C22C2×#1313381711yescharacteristic
334C22C2×#1313381711yescharacteristic
335C22C2×#1313381811yescharacteristic
336C22C2×#1313381811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—4281no—
343C4—4281no—
344C4—2142no—
345C4—2142no—
346C4—2142no—
347C4—2142no—
348C4—2142no—
349C4—2142no—
350C4#1681210214yesdirect product factor
351C2—42no—
352C2C4×#1313381711yescharacteristic
353C2C4×#1313381711yescharacteristic
354C2C4×#1313381811yescharacteristic
355C2C2×#1681210211yescharacteristic
356C2#2029315511yescharacteristic
357C2#2029315711yescharacteristic
358C2#2029315911yescharacteristic
subgroupG/H
centerC22×C4C22×D107
commutatorC22×C107C23×C4
FrattiniC23C23×D107
FittingC4×C22⋊C4×C107C2
socle, cosocleC23×C107C24
prime radicalC24×C107C23
hypercenterC4×C22⋊C4D107
hypocenterC107C4×#126
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #20292514C2semidirect
6. #20292512C2semidirect
7. #20292509C2semidirect
8. #20292494C2semidirect
9. C4×Dic107⋊C4C2semidirect
10. C4×Dic107⋊C4C2semidirect
11. C4×C4⋊Dic107C2semidirect
14. C42×Dic107C2semidirect
16. #16812102C4direct (N × H)
61. C4⋊Dic107C2×C4semidirect
64. Dic107⋊C4C2×C4semidirect
65. Dic107⋊C4C2×C4semidirect
77. C4×Dic107C2×C4semidirect
162. C4×C107#126semidirect
180. C107C4×#126semidirect
350. C4#16812102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168121022
#202925212
#202925202
#202925152
#202925142
#202925122
#202925092
#202924942
C4×Dic107⋊C42
C4×C4⋊Dic1072
C4×C22⋊Dic1072
C42×Dic1072
C4×C22⋊C4×C1072
C4×#126107