Finite Group Databasebeta

← #28347017

Subgroups — #28347017

Order 13696.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293181C211yesmaximal, characteristic, complemented
2#20293174C211yesmaximal, characteristic
3#20293024C211yesmaximal, characteristic, complemented
4#20292998C211yesmaximal, characteristic, complemented
5#20292976C211yesmaximal, characteristic, complemented
6#20292972C211yesmaximal, characteristic, complemented
7#20292859C211yesmaximal, characteristic, complemented
8#20292857C211yesmaximal, characteristic, complemented
9#20292855C211yesmaximal, characteristic, complemented
10#20292853C211yesmaximal, characteristic, complemented
11C4×#13133807C211yesmaximal, characteristic, complemented
12C4×#13133805C211yesmaximal, characteristic, complemented
13C4×#13133806C211yesmaximal, characteristic, complemented
14C4×C8×D107C211yesmaximal, characteristic, complemented
15C4×SD16×C107C211yesmaximal, characteristic, complemented
16C2×#13133818—21no—
17C2×#13133807C2211yescharacteristic
18C2×#13133806C2211yescharacteristic
19C2×#13133805C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21C2×C8×D107C2211yescharacteristic
22#16812108C2211yescharacteristic
23#16812108C2211yescharacteristic
24#16812107C2211yescharacteristic
25#16812105C2211yescharacteristic
26#16812099—21no—
27#16812095—21no—
28#16812089C2211yescharacteristic
29#16812087—21no—
30#16812085C2211yescharacteristic
31#16812084C2211yescharacteristic
32#16812082—21no—
33#16812080C2211yescharacteristic
34C4×Dic214—21no—
35C4×Dic214C2211yescharacteristic
36C4×D428C2211yescharacteristic
37C4×C22⋊D107—21no—
38#16812066—21no—
39C42×D107C2211yescharacteristic
40#16812041C2211yescharacteristic
41#16812040C2211yescharacteristic
42#16812040C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812032C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812029C2211yescharacteristic
49C4×C107⋊C8C2211yescharacteristic
50C8×Dic107C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×SD16×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59#13133818—44no—
60C2×Dic214—21no—
61C2×Dic214—21no—
62C2×Dic214C2311yescharacteristic
63C2×D428—21no—
64C2×D428C2311yescharacteristic
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C4×D107—21no—
69C2×C4×D107D411yescharacteristic
70C2×C4×D107D411yescharacteristic
71C2×C4×D107C2311yescharacteristic
72#13133807—22no—
73#13133806—22no—
74#13133805—22no—
75C2×C107⋊C8C2311yescharacteristic
76C2×C107⋊C8C2311yescharacteristic
77C8×D107—22no—
78C8×D107—22no—
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88C22⋊Dic107—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93C4×Dic107—21no—
94C4×Dic107D411yescharacteristic
95C4×Dic107D411yescharacteristic
96C4×Dic107C2311yescharacteristic
97C2×Q8×C107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C22×C4×C107—21no—
100SD16×C107—22no—
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C4⋊C4×C107—21no—
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C42×C107—21no—
108C42×C107C2311yescharacteristic
109C23×C107—21no—
110C22×D107—21no—
111C22×D107C2×D411yescharacteristic
112Q8×C107—21no—
113Q8×C107—21no—
114D4×C107—21no—
115D4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—42no—
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2411yescharacteristic
123C22⋊D107—42no—
124C22⋊D107—42no—
125C22⋊D107—42no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107C2×D411yescharacteristic
130C2×Dic107C2×D411yescharacteristic
131C2×Dic107C2×D411yescharacteristic
132D428—21no—
133D428—21no—
134D428—42no—
135C4×D107—21no—
136C4×D107—21no—
137C4×D107—22no—
138C4×D107—42no—
139C4×D107SD1614yescomplemented
140Dic214—21no—
141Dic214—21no—
142Dic214—42no—
143Dic214—42no—
144C8×C107—21no—
145C8×C107#4112yescomplemented
146C107⋊C8—21no—
147C107⋊C8#4112yescomplemented
148C22×C107—41no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107C22×D411yescharacteristic
152C2×D107—21no—
153C2×D107—21no—
154C2×D107—41no—
155C2×D107—41no—
156C2×D107—41no—
157C2×D107C2×SD1612yes—
158C4×C107—21no—
159C4×C107—41no—
160C4×C107—41no—
161C4×C107—41no—
162C4×C107C2×SD1612yes—
163C4×C107C2×#4111yescharacteristic
164C4×C107C2×#4111yescharacteristic
165Dic107—21no—
166Dic107—41no—
167Dic107—41no—
168Dic107—41no—
169Dic107C2×SD1612yes—
170Dic107#13512yes—
171C2×C107—81no—
172C2×C107#53211yescharacteristic
173C2×C107C22×SD1611yescharacteristic
174C2×C107C2×#13511yescharacteristic
175D107—22no—
176D107—81no—
177#3167—1071nomaximal, Sylow
178C107#316711yescharacteristic, complemented, Sylow
179#533—1071no—
180#532—1071no—
181#498—1071no—
182#492—1071no—
183#487—1071no—
184#486—1071no—
185#465—1071no—
186#465—1071no—
187#465—1071no—
188#465—1071no—
189C4×SD16—1071no—
190C4×SD16—1071no—
191C4×SD16—1071no—
192C4×SD16D10711yescharacteristic, complemented
193C2×C4×C8—1071no—
194C2×#41—2141no—
195C2×SD16—1071no—
196C2×SD16—1071no—
197C2×SD16—1071no—
198C2×SD16C2×D10711yescharacteristic
199C22×C8—1071no—
200C22×C8—1071no—
201C4⋊Q8—1071no—
202C4⋊Q8—1071no—
203C4⋊Q8—1071no—
204#127—1071no—
205#125—2141no—
206#124—2141no—
207C22⋊Q8—1071no—
208C22⋊Q8—1071no—
209C22⋊Q8—2141no—
210#121—1071no—
211#121—1071no—
212#121—2141no—
213C4×Q8—1071no—
214C4×Q8—2141no—
215C4×Q8C2×D10711yescharacteristic
216C4×D4—1071no—
217C4×D4—2141no—
218C4×D4C2×D10711yescharacteristic
219#117—2141no—
220C2×C42—1071no—
221#106—1071no—
222#106—1071no—
223#106—1071no—
224#106C2×D10711yescharacteristic
225#103—1071no—
226#103—1071no—
227#103—1071no—
228#103C2×D10711yescharacteristic
229#102—1071no—
230#102—1071no—
231#102—1071no—
232#102C2×D10711yescharacteristic
233C4×C8—1071no—
234C4×C8—1071no—
235C4×C8—1071no—
236C4×C8C2×D10711yescharacteristic
237#41—4284no—
238C2×Q8—1071no—
239C2×Q8—2141no—
240C2×Q8—2141no—
241C2×Q8C22×D10711yescharacteristic
242C2×D4—1071no—
243C2×D4—2141no—
244C2×D4—2141no—
245C2×D4—2141no—
246C2×D4—2141no—
247C2×D4C22×D10711yescharacteristic
248C22×C4—21no—
249C22×C4—1071no—
250C22×C4—1071no—
251C22×C4—1071no—
252C22×C4—2141no—
253SD16—22no—
254SD16—2142no—
255SD16—2142no—
256SD16—2142no—
257C2×C8—1071no—
258C2×C8—1071no—
259C2×C8—2142no—
260C2×C8—2142no—
261C2×C8C22×D10711yescharacteristic
262C2×C8C22×D10711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1071no—
265C4⋊C4—1071no—
266C4⋊C4—2141no—
267C4⋊C4—2141no—
268C4⋊C4—2141no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4C22×D10711yescharacteristic
274C4⋊C4C22×D10711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2141no—
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C42—21no—
282C42—1071no—
283C42—1071no—
284C42—1071no—
285C42—2141no—
286C42C22×D10711yescharacteristic
287C23—21no—
288C23—1071no—
289C23—2141no—
290Q8—21no—
291Q8—21no—
292Q8—4282no—
293Q8—4282no—
294Q8—2141no—
295Q8—2141no—
296D4—21no—
297D4—21no—
298D4—4282no—
299D4—4282no—
300D4—4282no—
301D4—4282no—
302D4—2141no—
303D4—2141no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—1071no—
309C2×C4—1071no—
310C2×C4—1074no—
311C2×C4—1071no—
312C2×C4—4282no—
313C2×C4—2142no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4D4×D10711yescharacteristic
320C2×C4D4×D10711yescharacteristic
321C2×C4C23×D10711yescharacteristic
322C8—21no—
323C8—1072no—
324C8—2141no—
325C8#1313381812yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1072no—
330C22—4281no—
331C22—4281no—
332C22—4281no—
333C22—2141no—
334C22—2141no—
335C22C2×D4×D10711yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1072no—
341C4—1072no—
342C4—4281no—
343C4—4281no—
344C4—4281no—
345C4—2141no—
346C4SD16×D10712yes—
347C4#41×D10711yescharacteristic
348C4C2×#1313381811yescharacteristic
349C2—81no—
350C2—8561no—
351C2—2142no—
352C2#2029317411yescharacteristic
353C2C2×SD16×D10711yescharacteristic
354C2#135×D10711yescharacteristic
subgroupG/H
centerC2×C4D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×SD16×C107C2
socleC22×C107C22×D4
prime radical#20293174C2
hypercenterC4×SD16D107
hypocenterC107#3167
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20293181C2semidirect
3. #20293024C2semidirect
4. #20292998C2semidirect
5. #20292976C2semidirect
6. #20292972C2semidirect
7. #20292859C2semidirect
8. #20292857C2semidirect
9. #20292855C2semidirect
10. #20292853C2semidirect
11. C4×#13133807C2semidirect
12. C4×#13133805C2semidirect
13. C4×#13133806C2semidirect
14. C4×C8×D107C2semidirect
15. C4×SD16×C107C2semidirect
139. C4×D107SD16semidirect
145. C8×C107#41semidirect
147. C107⋊C8#41semidirect
178. C107#3167semidirect
192. C4×SD16D107semidirect
325. C8#13133818semidirect

Maximal subgroups

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

subgroupindex
#202931812
#202931742
#202930242
#202929982
#202929762
#202929722
#202928592
#202928572
#202928552
#202928532
C4×#131338072
C4×#131338052
C4×#131338062
C4×C8×D1072
C4×SD16×C1072
#3167107