Finite Group Databasebeta

← #28346658

Subgroups — #28346658

Order 13696.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293228C211yesmaximal, characteristic, complemented
2#20293109C211yesmaximal, characteristic, complemented
3#20292944C211yesmaximal, characteristic, complemented
4#20292942C211yesmaximal, characteristic, complemented
5#20292932C211yesmaximal, characteristic, complemented
6#20292930C211yesmaximal, characteristic, complemented
7#20292825C211yesmaximal, characteristic, complemented
8#20292821C211yesmaximal, characteristic, complemented
9#20292775C211yesmaximal, characteristic, complemented
10#20292771C211yesmaximal, characteristic, complemented
11#20292740C211yesmaximal, characteristic, complemented
12C4×#13133805C211yesmaximal, characteristic, complemented
13C4×#13133803C211yesmaximal, characteristic, complemented
14#20292689C211yesmaximal, characteristic, complemented
15#440×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133805C2211yescharacteristic
18C2×D856C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20#16812105C2211yescharacteristic
21#16812100C2211yescharacteristic
22#16812092—21no—
23#16812091—21no—
24#16812084C2211yescharacteristic
25#16812083—21no—
26#16812082—21no—
27#16812080C2211yescharacteristic
28Q8×Dic107C2211yescharacteristic
29C4×D428—21no—
30C4×D428C2211yescharacteristic
31C4×D428C2211yescharacteristic
32#16812071—21no—
33#16812071C2211yescharacteristic
34#16812066—21no—
35#16812066C2211yescharacteristic
36C4⋊C4×D107—21no—
37C4⋊C4×D107C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812041C2211yescharacteristic
40#16812040C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42Dic107⋊C8C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812031C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic
49(C2×D107)⋊C8C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C4×C107⋊C8C2211yescharacteristic
52C2×SD16×C107C2211yescharacteristic
53C4×Q8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55#107×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58#97×C107C2211yescharacteristic
59#13133819—22no—
60#13133819—22no—
61C2×D428—21no—
62C2×D428—21no—
63C2×D428C2311yescharacteristic
64C2×D428C2311yescharacteristic
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C4×D107—21no—
69C2×C4×D107—21no—
70C2×C4×D107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107C2311yescharacteristic
74#13133805—22no—
75D856—22no—
76#13133803—22no—
77C2×C107⋊C8C2311yescharacteristic
78C2×C107⋊C8C2311yescharacteristic
79C4⋊Dic107—21no—
80C4⋊Dic107—21no—
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83Dic107⋊C4—21no—
84Dic107⋊C4—21no—
85Dic107⋊C4D411yescharacteristic
86Dic107⋊C4D411yescharacteristic
87C22⋊Dic107—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4D411yescharacteristic
93(C2×D107)⋊C4D411yescharacteristic
94C4×Dic107—21no—
95C4×Dic107C2311yescharacteristic
96C2×Q8×C107C2311yescharacteristic
97C2×D4×C107C2311yescharacteristic
98C22×C4×C107—21no—
99SD16×C107—22no—
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107—21no—
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C22⋊C4×C107—21no—
106C42×C107—21no—
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C22×D107—21no—
110C22×D107—21no—
111C22×D107C2×D411yescharacteristic
112Q8×C107—21no—
113Q8×C107#4112yes—
114D4×C107—21no—
115D4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—81no—
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2411yescharacteristic
123C22⋊D107—81no—
124C22⋊D107—81no—
125C22⋊D107—81no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107C2×D411yescharacteristic
129C2×Dic107C2×D411yescharacteristic
130C2×Dic107C2×D411yescharacteristic
131D428—24no—
132D428—21no—
133D428—21no—
134D428—21no—
135D428—81no—
136D428#4112yes—
137C4×D107—24no—
138C4×D107—21no—
139C4×D107—21no—
140C4×D107—81no—
141C4×D107—81no—
142C4×D107—81no—
143C4×D107—81no—
144C8×C107—21no—
145C8×C107—21no—
146C107⋊C8—21no—
147C107⋊C8—21no—
148C22×C107—41no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107C22×D411yescharacteristic
152C2×D107—21no—
153C2×D107—22no—
154C2×D107—21no—
155C2×D107—21no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—22no—
162C4×C107—21no—
163C4×C107—21no—
164C4×C107—41no—
165C4×C107—41no—
166C4×C107C2×#4111yescharacteristic
167C4×C107C2×#4111yescharacteristic
168Dic107—21no—
169Dic107—21no—
170Dic107—21no—
171Dic107—41no—
172Dic107—41no—
173C2×C107—81no—
174C2×C107#52511yescharacteristic
175C2×C107#57611yescharacteristic
176C2×C107#57711yescharacteristic
177D107—41no—
178D107—42no—
179D107—81no—
180#3119—1071nomaximal, Sylow
181C107#311911yescharacteristic, complemented, Sylow
182#540—1071no—
183#520—1071no—
184#481—1071no—
185#480—1071no—
186#479—1071no—
187#478—1071no—
188#460—1071no—
189#459—1071no—
190#449—1071no—
191#449—1071no—
192#442—1071no—
193#440D10711yescharacteristic, complemented
194C4×SD16—1071no—
195C4×D8—1071no—
196#433—1071no—
197C2×#41—1071no—
198C2×SD16—1071no—
199C2×SD16C2×D10711yescharacteristic
200C2×D8—1071no—
201C2×D8—1071no—
202#127—1071no—
203#125—1071no—
204#123—2141no—
205#123—2141no—
206#121—1071no—
207#121—1071no—
208#121—2141no—
209#121—2141no—
210C4×Q8—1071no—
211C4×Q8C2×D10711yescharacteristic
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—1071no—
215C4×D4—2141no—
216C4×D4—2141no—
217C4×D4C2×D10711yescharacteristic
218#117—1071no—
219#117—2141no—
220C2×C4⋊C4—1071no—
221C2×C4⋊C4—2141no—
222#107—1071no—
223#107C2×D10711yescharacteristic
224#106—1071no—
225#106—1071no—
226C4⋊C8—1071no—
227C4⋊C8—1071no—
228#103—1071no—
229#103C2×D10711yescharacteristic
230#102—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102C2×D10711yescharacteristic
236C22⋊C8—1071no—
237C22⋊C8—1071no—
238#97C2×D10711yescharacteristic
239C4×C8—1071no—
240#41—2142no—
241#41—2142no—
242C2×Q8C22×D10711yescharacteristic
243C2×D4—1071no—
244C2×D4—1071no—
245C2×D4—2141no—
246C2×D4—2141no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4—2141no—
250C2×D4C22×D10711yescharacteristic
251C22×C4—21no—
252C22×C4—1071no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4—2141no—
257C22×C4—2141no—
258SD16—22no—
259SD16—2142no—
260D8—2142no—
261D8—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—1071no—
270C4⋊C4—1071no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4C22×D10711yescharacteristic
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1071no—
279C22⋊C4—1071no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C42—21no—
286C42—1071no—
287C42—2141no—
288C42C22×D10711yescharacteristic
289C23—21no—
290C23—1071no—
291C23—2141no—
292C23—2141no—
293Q8—21no—
294Q8#1313381812yes—
295D4—21no—
296D4—21no—
297D4—8561no—
298D4—8561no—
299D4—8561no—
300D4—8561no—
301D4—1072no—
302D4—2144no—
303D4—2141no—
304D4—2141no—
305D4—2141no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—8561no—
311C2×C4—8561no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—1071no—
315C2×C4—1071no—
316C2×C4—1071no—
317C2×C4—2144no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4D4×D10711yescharacteristic
323C2×C4D4×D10711yescharacteristic
324C2×C4C23×D10711yescharacteristic
325C8—21no—
326C8—21no—
327C8—2141no—
328C8—2141no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—4281no—
333C22—4281no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22—2142no—
338C22—2141no—
339C22—2141no—
340C22—2141no—
341C22C2×D4×D10711yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—4281no—
348C4—4281no—
349C4—2141no—
350C4—2141no—
351C4—2141no—
352C4#41×D10711yescharacteristic
353C4C2×#1313381811yescharacteristic
354C2—81no—
355C2—8561no—
356C2—4282no—
357C2—4281no—
358C2#2029313611yescharacteristic
359C2#2029343111yescharacteristic
360C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#440×C107C2
socleC22×C107C22×D4
hypercenter#440D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20293228C2semidirect
2. #20293109C2semidirect
3. #20292944C2semidirect
4. #20292942C2semidirect
5. #20292932C2semidirect
6. #20292930C2semidirect
7. #20292825C2semidirect
8. #20292821C2semidirect
9. #20292775C2semidirect
10. #20292771C2semidirect
11. #20292740C2semidirect
12. C4×#13133805C2semidirect
13. C4×#13133803C2semidirect
14. #20292689C2semidirect
15. #440×C107C2semidirect
181. C107#3119semidirect
193. #440D107semidirect

Maximal subgroups

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

subgroupindex
#202932282
#202931092
#202929442
#202929422
#202929322
#202929302
#202928252
#202928212
#202927752
#202927712
#202927402
C4×#131338052
C4×#131338032
#202926892
#440×C1072
#3119107