Finite Group Databasebeta

← #28346660

Subgroups — #28346660

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#20293232C211yesmaximal, characteristic, complemented
2#20292945C211yesmaximal, characteristic, complemented
3#20292940C211yesmaximal, characteristic, complemented
4#20292934C211yesmaximal, characteristic, complemented
5#20292927C211yesmaximal, characteristic, complemented
6#20292827C211yesmaximal, characteristic, complemented
7#20292822C211yesmaximal, characteristic, complemented
8#20292772C211yesmaximal, characteristic, complemented
9#20292772C211yesmaximal, characteristic, complemented
10#20292737C211yesmaximal, characteristic, complemented
11#20292725C211yesmaximal, characteristic, complemented
12C4×#13133805C211yesmaximal, characteristic, complemented
13C4×#13133803C211yesmaximal, characteristic, complemented
14#20292688C211yesmaximal, characteristic, complemented
15#520×C107C211yesmaximal, characteristic, complemented
16C2×#13133805C2211yescharacteristic
17C2×#13133805C2211yescharacteristic
18C2×#13133803C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20#16812106C2211yescharacteristic
21#16812101C2211yescharacteristic
22#16812094—21no—
23#16812094—21no—
24#16812083C2211yescharacteristic
25#16812083C2211yescharacteristic
26#16812082—21no—
27#16812082—21no—
28C4×D428C2211yescharacteristic
29C4×D428C2211yescharacteristic
30#16812042C2211yescharacteristic
31#16812042C2211yescharacteristic
32#16812040C2211yescharacteristic
33#16812040C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35C4⋊(C107⋊C8)C2211yescharacteristic
36#16812033C2211yescharacteristic
37#16812033C2211yescharacteristic
38#16812030C2211yescharacteristic
39#16812030C2211yescharacteristic
40#16812029C2211yescharacteristic
41#16812029C2211yescharacteristic
42#16812029C2211yescharacteristic
43#16812029C2211yescharacteristic
44C22⋊(C107⋊C8)C2211yescharacteristic
45C22⋊(C107⋊C8)C2211yescharacteristic
46#16812020C2211yescharacteristic
47C4×C107⋊C8C2211yescharacteristic
48C2×#41×C107C2211yescharacteristic
49C4×Q8×C107C2211yescharacteristic
50C4×Q8×C107C2211yescharacteristic
51C4×D4×C107—21no—
52C4×D4×C107—21no—
53C4×D4×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55#117×C107—21no—
56#117×C107C2211yescharacteristic
57C2×C4⋊C4×C107—21no—
58C2×C4⋊C4×C107C2211yescharacteristic
59C2×D428—21no—
60C2×D428—21no—
61C2×D428C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67#13133805—22no—
68#13133805—22no—
69#13133803—22no—
70#13133803—22no—
71C2×C107⋊C8C2311yescharacteristic
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C4⋊Dic107C2311yescharacteristic
76C4⋊Dic107C2311yescharacteristic
77Dic107⋊C4—21no—
78Dic107⋊C4—21no—
79(C2×D107)⋊C4—21no—
80(C2×D107)⋊C4—21no—
81(C2×D107)⋊C4—21no—
82(C2×D107)⋊C4—21no—
83#41×C107—22no—
84#41×C107—22no—
85C2×Q8×C107C2311yescharacteristic
86C2×D4×C107—21no—
87C2×D4×C107C2311yescharacteristic
88C22×C4×C107—21no—
89C22×C4×C107—21no—
90C22×C4×C107—21no—
91C22×C4×C107—21no—
92C22×C4×C107C2311yescharacteristic
93C4⋊C4×C107—21no—
94C4⋊C4×C107—21no—
95C4⋊C4×C107—21no—
96C4⋊C4×C107D411yescharacteristic
97C4⋊C4×C107D411yescharacteristic
98C4⋊C4×C107C2311yescharacteristic
99C4⋊C4×C107C2311yescharacteristic
100C22⋊C4×C107—21no—
101C22⋊C4×C107—21no—
102C22⋊C4×C107D411yescharacteristic
103C22⋊C4×C107D411yescharacteristic
104C42×C107—21no—
105C42×C107—21no—
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C23×C107C2×D411yescharacteristic
110C22×D107—21no—
111C22×D107—21no—
112Q8×C107—21no—
113Q8×C107#4112yes—
114D4×C107—24no—
115D4×C107—21no—
116D4×C107#4112yes—
117C2×C4×C107—24no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—81no—
124C2×C4×C107—81no—
125C2×C4×C107—81no—
126C2×C4×C107C2×D411yescharacteristic
127C2×C4×C107C2×D411yescharacteristic
128C2×C4×C107C2×D411yescharacteristic
129C2×C4×C107C2×D411yescharacteristic
130C2×C4×C107C2×D411yescharacteristic
131C2×C4×C107C2411yescharacteristic
132C22⋊D107—81no—
133C22⋊D107—81no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136D428—21no—
137D428—21no—
138D428—21no—
139D428—21no—
140D428—81no—
141D428—81no—
142C4×D107—81no—
143C4×D107—81no—
144C107⋊C8—21no—
145C107⋊C8—21no—
146C107⋊C8—21no—
147C107⋊C8—21no—
148C22×C107—21no—
149C22×C107—22no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107C22×D411yescharacteristic
155C2×D107—41no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—21no—
162C4×C107—22no—
163C4×C107—21no—
164C4×C107—21no—
165C4×C107—21no—
166C4×C107—21no—
167C4×C107—41no—
168C4×C107—41no—
169C4×C107C2×#4111yescharacteristic
170C4×C107C2×#4111yescharacteristic
171Dic107—41no—
172Dic107—41no—
173C2×C107—41no—
174C2×C107—42no—
175C2×C107#52511yescharacteristic
176C2×C107#57611yescharacteristic
177C2×C107#57711yescharacteristic
178D107—81no—
179D107—81no—
180#3119—1071nomaximal, Sylow
181C107#311911yescharacteristic, complemented, Sylow
182#540—1071no—
183#520D10711yescharacteristic, complemented
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#440—1071no—
194C4×SD16—1071no—
195C4×D8—1071no—
196#433—1071no—
197C2×#41C2×D10711yescharacteristic
198C2×SD16—1071no—
199C2×SD16—1071no—
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×Q8C2×D10711yescharacteristic
211C4×Q8C2×D10711yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1071no—
215C4×D4—1071no—
216C4×D4C2×D10711yescharacteristic
217C4×D4C2×D10711yescharacteristic
218#117—21no—
219#117C2×D10711yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D10711yescharacteristic
222#107—1071no—
223#107—1071no—
224#106—1071no—
225#106—1071no—
226C4⋊C8—1071no—
227C4⋊C8—1071no—
228#103—1071no—
229#103—1071no—
230#102—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102—1071no—
236C22⋊C8—1071no—
237C22⋊C8—1071no—
238#97—1071no—
239C4×C8—1071no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D10711yescharacteristic
243C2×D4—21no—
244C2×D4—1071no—
245C2×D4—1071no—
246C2×D4—2141no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4—2141no—
250C2×D4C22×D10711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2141no—
256C22×C4—2141no—
257C22×C4C22×D10711yescharacteristic
258SD16—2142no—
259SD16—2142no—
260D8—2142no—
261D8—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8—1071no—
265C2×C8—1071no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—1071no—
270C4⋊C4—1071no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4C22⋊D10711yescharacteristic
274C4⋊C4C22⋊D10711yescharacteristic
275C4⋊C4C22×D10711yescharacteristic
276C4⋊C4C22×D10711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4C22⋊D10711yescharacteristic
284C22⋊C4C22⋊D10711yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D10711yescharacteristic
288C42C22×D10711yescharacteristic
289C23—21no—
290C23—2141no—
291C23—2141no—
292C23C2×C22⋊D10711yescharacteristic
293Q8—21no—
294Q8#1313381812yes—
295D4—24no—
296D4—21no—
297D4—8561no—
298D4—8561no—
299D4—8561no—
300D4—8561no—
301D4—2141no—
302D4—2141no—
303D4—2141no—
304D4—2141no—
305D4#1313381812yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—8561no—
316C2×C4—8561no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4C2×C22⋊D10711yescharacteristic
320C2×C4C2×C22⋊D10711yescharacteristic
321C2×C4C2×C22⋊D10711yescharacteristic
322C2×C4C2×C22⋊D10711yescharacteristic
323C2×C4C2×C22⋊D10711yescharacteristic
324C2×C4C23×D10711yescharacteristic
325C8—2141no—
326C8—2141no—
327C8—2141no—
328C8—2141no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—4281no—
336C22—4281no—
337C22—4281no—
338C22—4281no—
339C22—4281no—
340C22—4281no—
341C22C22×C22⋊D10711yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—4281no—
351C4—4281no—
352C4C2×#1313381811yescharacteristic
353C4C2×#1313381811yescharacteristic
354C2—41no—
355C2—42no—
356C2—8561no—
357C2—8561no—
358C2#2029313811yescharacteristic
359C2#2029343011yescharacteristic
360C2#2029343511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#520×C107C2
socleC22×C107C22×D4
hypercenter#520D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20293232C2semidirect
2. #20292945C2semidirect
3. #20292940C2semidirect
4. #20292934C2semidirect
5. #20292927C2semidirect
6. #20292827C2semidirect
7. #20292822C2semidirect
8. #20292772C2semidirect
9. #20292772C2semidirect
10. #20292737C2semidirect
11. #20292725C2semidirect
12. C4×#13133805C2semidirect
13. C4×#13133803C2semidirect
14. #20292688C2semidirect
15. #520×C107C2semidirect
181. C107#3119semidirect
183. #520D107semidirect

Maximal subgroups

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

subgroupindex
#202932322
#202929452
#202929402
#202929342
#202929272
#202928272
#202928222
#202927722
#202927372
#202927252
C4×#131338052
C4×#131338032
#202926882
#520×C1072
#3119107