Finite Group Databasebeta

← #28346665

Subgroups — #28346665

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#20293233C211yesmaximal, characteristic, complemented
2#20293106C211yesmaximal, characteristic, complemented
3#20292947C211yesmaximal, characteristic, complemented
4#20292942C211yesmaximal, characteristic, complemented
5#20292931C211yesmaximal, characteristic, complemented
6#20292828C211yesmaximal, characteristic, complemented
7#20292822C211yesmaximal, characteristic, complemented
8#20292773C211yesmaximal, characteristic, complemented
9#20292773C211yesmaximal, characteristic, complemented
10#20292736C211yesmaximal, characteristic, complemented
11#20292726C211yesmaximal, characteristic, complemented
12#20292714C211yesmaximal, characteristic, complemented
13#20292707C211yesmaximal, characteristic, complemented
14#20292687C211yesmaximal, characteristic, complemented
15#478×C107C211yesmaximal, characteristic, complemented
16C2×#13133817C2211yescharacteristic
17C2×#13133807C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20C2×#13133803C2211yescharacteristic
21#16812106C2211yescharacteristic
22#16812094—21no—
23#16812094—21no—
24#16812084—21no—
25#16812084—21no—
26#16812084C2211yescharacteristic
27#16812084C2211yescharacteristic
28C4×Dic214C2211yescharacteristic
29#16812074C2211yescharacteristic
30D4×Dic107C2211yescharacteristic
31#16812071C2211yescharacteristic
32#16812071C2211yescharacteristic
33C4×C22⋊D107—21no—
34(C22⋊D107)⋊C4—21no—
35#16812066C2211yescharacteristic
36#16812065—21no—
37C2×Dic107⋊C4—21no—
38C4⋊C4×D107C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812040C2211yescharacteristic
41C4⋊(C107⋊C8)C2211yescharacteristic
42#16812032C2211yescharacteristic
43#16812032C2211yescharacteristic
44#16812031C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812029C2211yescharacteristic
47#16812029C2211yescharacteristic
48(C2×D107)⋊C8C2211yescharacteristic
49(C2×D107)⋊C8C2211yescharacteristic
50#16812019C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52#125×C107C2211yescharacteristic
53C4×D4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#106×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59#13133817—22no—
60#13133817—22no—
61C2×Dic214C2311yescharacteristic
62C2×D428—21no—
63C2×D428—21no—
64C2×D428—21no—
65C2×D428—21no—
66C2×D428C2311yescharacteristic
67C2×D428C2311yescharacteristic
68C2×C22⋊D107—21no—
69C22×Dic107—21no—
70C22×Dic107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107C2311yescharacteristic
75#13133807—22no—
76#13133807—22no—
77#13133803—22no—
78#13133803—22no—
79C2×C107⋊C8C2311yescharacteristic
80C2×C107⋊C8C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
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×Dic107—21no—
96C4×Dic107C2311yescharacteristic
97C2×D4×C107C2311yescharacteristic
98C22×C4×C107—21no—
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C4⋊C4×C107—21no—
102C4⋊C4×C107—21no—
103C4⋊C4×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C22×D107—21no—
110C22×D107—21no—
111C22×D107C2×D411yescharacteristic
112D4×C107—21no—
113D4×C107#4112yes—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—81no—
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2×D411yescharacteristic
120C2×C4×C107C2411yescharacteristic
121C22⋊D107—24no—
122C2×Dic107—24no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—81no—
126C2×Dic107C2×D411yescharacteristic
127C2×Dic107C2×D411yescharacteristic
128C2×Dic107C2×D411yescharacteristic
129D428—21no—
130D428—21no—
131D428—21no—
132D428—21no—
133D428—81no—
134D428—81no—
135D428—81no—
136D428—81no—
137C4×D107—21no—
138C4×D107—21no—
139C4×D107—81no—
140C4×D107—81no—
141C4×D107—81no—
142Dic214—21no—
143Dic214#4112yes—
144C8×C107—21no—
145C8×C107—21no—
146C107⋊C8—21no—
147C107⋊C8—21no—
148C22×C107—22no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107C22×D411yescharacteristic
152C2×D107—21no—
153C2×D107—21no—
154C2×D107—21no—
155C2×D107—41no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107—41no—
164C4×C107—41no—
165C4×C107—41no—
166C4×C107C2×#4111yescharacteristic
167C4×C107C2×#4111yescharacteristic
168Dic107—22no—
169Dic107—21no—
170Dic107—21no—
171Dic107—21no—
172Dic107—41no—
173C2×C107—42no—
174C2×C107#52511yescharacteristic
175C2×C107#57611yescharacteristic
176C2×C107#57711yescharacteristic
177D107—41no—
178D107—81no—
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#478D10711yescharacteristic, complemented
188#460—1071no—
189#459—1071no—
190#449—1071no—
191#449—1071no—
192#442—1071no—
193#440—1071no—
194C4×SD16—1071no—
195C4×D8—1071no—
196#433—1071no—
197C2×#41—1071no—
198C2×SD16—1071no—
199C2×SD16—1071no—
200C2×D8—1071no—
201C2×D8—1071no—
202#127—1071no—
203#125C2×D10711yescharacteristic
204#123—2141no—
205#123—2141no—
206#121—1071no—
207#121—1071no—
208#121—2141no—
209#121—2141no—
210C4×Q8—1071no—
211C4×Q8—1071no—
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#106C2×D10711yescharacteristic
226C4⋊C8—1071no—
227C4⋊C8C2×D10711yescharacteristic
228#103—1071no—
229#103—1071no—
230#102—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102C2×D10711yescharacteristic
235#102C2×D10711yescharacteristic
236C22⋊C8—1071no—
237C22⋊C8—1071no—
238#97—1071no—
239C4×C8—1071no—
240#41—2142no—
241#41—2142no—
242C2×Q8—1071no—
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—2142no—
259SD16—2142no—
260D8—2142no—
261D8—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1071no—
269C4⋊C4—1071no—
270C4⋊C4—1071no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4C22×D10711yescharacteristic
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—1071no—
286C42—2141no—
287C42—2141no—
288C42C22×D10711yescharacteristic
289C23—21no—
290C23—1071no—
291C23—2141no—
292C23—2141no—
293Q8—1072no—
294Q8—2141no—
295D4—21no—
296D4—8561no—
297D4—8561no—
298D4—8561no—
299D4—8561no—
300D4—2144no—
301D4—2141no—
302D4—2141no—
303D4—2141no—
304D4—2141no—
305D4#1313381912yes—
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—2141no—
318C2×C4—2144no—
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—22no—
330C22—41no—
331C22—41no—
332C22—4281no—
333C22—4281no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22—4281no—
338C22—2141no—
339C22—2141no—
340C22—2141no—
341C22C2×D4×D10711yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—4281no—
348C4—2141no—
349C4—2142no—
350C4—2141no—
351C4—2141no—
352C4#41×D10711yescharacteristic
353C4C2×#1313381911yescharacteristic
354C2—42no—
355C2—8561no—
356C2—8561no—
357C2—4281no—
358C2#2029314011yescharacteristic
359C2#2029343111yescharacteristic
360C2#2029343411yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#478×C107C2
socleC22×C107C22×D4
hypercenter#478D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20293233C2semidirect
2. #20293106C2semidirect
3. #20292947C2semidirect
4. #20292942C2semidirect
5. #20292931C2semidirect
6. #20292828C2semidirect
7. #20292822C2semidirect
8. #20292773C2semidirect
9. #20292773C2semidirect
10. #20292736C2semidirect
11. #20292726C2semidirect
12. #20292714C2semidirect
13. #20292707C2semidirect
14. #20292687C2semidirect
15. #478×C107C2semidirect
181. C107#3119semidirect
187. #478D107semidirect

Maximal subgroups

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

subgroupindex
#202932332
#202931062
#202929472
#202929422
#202929312
#202928282
#202928222
#202927732
#202927362
#202927262
#202927142
#202927072
#202926872
#478×C1072
#3119107