Finite Group Databasebeta

← #28346654

Subgroups — #28346654

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#20293107C211yesmaximal, characteristic, complemented
2#20292943C211yesmaximal, characteristic, complemented
3#20292938C211yesmaximal, characteristic, complemented
4#20292931C211yesmaximal, characteristic, complemented
5#20292924C211yesmaximal, characteristic, complemented
6#20292824C211yesmaximal, characteristic, complemented
7#20292819C211yesmaximal, characteristic, complemented
8#20292770C211yesmaximal, characteristic, complemented
9#20292770C211yesmaximal, characteristic, complemented
10#20292737C211yesmaximal, characteristic, complemented
11#20292727C211yesmaximal, characteristic, complemented
12C4×#13133806C211yesmaximal, characteristic, complemented
13C4×#13133803C211yesmaximal, characteristic, complemented
14#20292688C211yesmaximal, characteristic, complemented
15#540×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133806C2211yescharacteristic
18C2×#13133806C2211yescharacteristic
19C2×#13133803C2211yescharacteristic
20C2×#13133803C2211yescharacteristic
21C4×Dic214C2211yescharacteristic
22C4×Dic214C2211yescharacteristic
23C4×D428C2211yescharacteristic
24C4×D428C2211yescharacteristic
25(C22⋊D107)⋊C4—21no—
26(C22⋊D107)⋊C4—21no—
27#16812067—21no—
28C2×C4⋊Dic107C2211yescharacteristic
29C4⋊C4×D107—21no—
30#16812042C2211yescharacteristic
31#16812042C2211yescharacteristic
32#16812040C2211yescharacteristic
33#16812040C2211yescharacteristic
34C4⋊(C107⋊C8)C2211yescharacteristic
35C4⋊(C107⋊C8)C2211yescharacteristic
36#16812032C2211yescharacteristic
37#16812032C2211yescharacteristic
38#16812030C2211yescharacteristic
39#16812030C2211yescharacteristic
40#16812030C2211yescharacteristic
41#16812030C2211yescharacteristic
42#16812029C2211yescharacteristic
43#16812029C2211yescharacteristic
44C22⋊(C107⋊C8)C2211yescharacteristic
45C22⋊(C107⋊C8)C2211yescharacteristic
46#16812020C2211yescharacteristic
47C4×C107⋊C8C2211yescharacteristic
48#127×C107C2211yescharacteristic
49#125×C107C2211yescharacteristic
50#123×C107—21no—
51#123×C107—21no—
52#121×C107—21no—
53#121×C107—21no—
54#121×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic
56C4×D4×C107C2211yescharacteristic
57C4×D4×C107C2211yescharacteristic
58#117×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—22no—
61C2×Dic214C2311yescharacteristic
62C2×D428C2311yescharacteristic
63C2×C22⋊D107—21no—
64C22×Dic107—21no—
65C2×C4×D107—21no—
66C2×C4×D107—21no—
67C2×C4×D107—21no—
68#13133806—22no—
69#13133806—22no—
70#13133803—22no—
71#13133803—22no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C2×C107⋊C8C2311yescharacteristic
76C4⋊Dic107—21no—
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81(C2×D107)⋊C4—21no—
82(C2×D107)⋊C4—21no—
83C4×Dic107—21no—
84C4×Dic107—21no—
85C2×D4×C107—21no—
86C2×D4×C107—21no—
87C2×D4×C107—21no—
88C2×D4×C107—21no—
89C2×D4×C107C2311yescharacteristic
90C2×D4×C107C2311yescharacteristic
91C22×C4×C107—21no—
92C22×C4×C107—21no—
93C22×C4×C107C2311yescharacteristic
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×C107—21no—
103C22⋊C4×C107—21no—
104C22⋊C4×C107D411yescharacteristic
105C22⋊C4×C107D411yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C23×C107—21no—
110C23×C107C2×D411yescharacteristic
111C22×D107—21no—
112D4×C107—21no—
113D4×C107—21no—
114D4×C107—21no—
115D4×C107—21no—
116D4×C107—81no—
117D4×C107—81no—
118D4×C107—81no—
119D4×C107—81no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
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—24no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—81no—
137D428—21no—
138D428#4112yes—
139C4×D107—24no—
140C4×D107—81no—
141C4×D107—81no—
142Dic214—21no—
143Dic214#4112yes—
144C107⋊C8—21no—
145C107⋊C8—21no—
146C107⋊C8—21no—
147C107⋊C8—21no—
148C22×C107—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107C22×D411yescharacteristic
158C2×D107—22no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107—21no—
164C4×C107—21no—
165C4×C107—21no—
166C4×C107—41no—
167C4×C107—41no—
168C4×C107C2×#4111yescharacteristic
169C4×C107C2×#4111yescharacteristic
170Dic107—22no—
171Dic107—41no—
172Dic107—41no—
173C2×C107—41no—
174C2×C107—81no—
175C2×C107—81no—
176C2×C107#52511yescharacteristic
177C2×C107#57611yescharacteristic
178C2×C107#57711yescharacteristic
179D107—42no—
180#3119—1071nomaximal, Sylow
181C107#311911yescharacteristic, complemented, Sylow
182#540D10711yescharacteristic, complemented
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#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#127C2×D10711yescharacteristic
203#125C2×D10711yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D10711yescharacteristic
209#121C2×D10711yescharacteristic
210C4×Q8—1071no—
211C4×Q8—1071no—
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—2141no—
215C4×D4—2141no—
216C4×D4C2×D10711yescharacteristic
217C4×D4C2×D10711yescharacteristic
218#117—2141no—
219#117C2×D10711yescharacteristic
220C2×C4⋊C4—1071no—
221C2×C4⋊C4—2141no—
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—2142no—
241#41—2142no—
242C2×Q8—1071no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—1071no—
248C2×D4—2141no—
249C2×D4C22×D10711yescharacteristic
250C2×D4C22×D10711yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—2141no—
254C22×C4—2141no—
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—1071no—
269C4⋊C4—1071no—
270C4⋊C4—2141no—
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—21no—
280C22⋊C4—21no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4C22⋊D10711yescharacteristic
284C22⋊C4C22⋊D10711yescharacteristic
285C42—2141no—
286C42—2141no—
287C42C22×D10711yescharacteristic
288C42C22×D10711yescharacteristic
289C23—21no—
290C23—21no—
291C23—2141no—
292C23C2×C22⋊D10711yescharacteristic
293Q8—1072no—
294Q8—2141no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—1072no—
304D4—2144no—
305D4—2141no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—8561no—
315C2×C4—2144no—
316C2×C4—2141no—
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—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—4281no—
339C22—4281no—
340C22—2142no—
341C22C22×C22⋊D10711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—4281no—
350C4—4281no—
351C4—2142no—
352C4#41×D10711yescharacteristic
353C4#41×D10711yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—4282no—
358C2#2029313411yescharacteristic
359C2#2029343011yescharacteristic
360C2#2029343811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#540×C107C2
socleC22×C107C22×D4
hypercenter#540D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20293107C2semidirect
2. #20292943C2semidirect
3. #20292938C2semidirect
4. #20292931C2semidirect
5. #20292924C2semidirect
6. #20292824C2semidirect
7. #20292819C2semidirect
8. #20292770C2semidirect
9. #20292770C2semidirect
10. #20292737C2semidirect
11. #20292727C2semidirect
12. C4×#13133806C2semidirect
13. C4×#13133803C2semidirect
14. #20292688C2semidirect
15. #540×C107C2semidirect
181. C107#3119semidirect
182. #540D107semidirect

Maximal subgroups

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

subgroupindex
#202931072
#202929432
#202929382
#202929312
#202929242
#202928242
#202928192
#202927702
#202927372
#202927272
C4×#131338062
C4×#131338032
#202926882
#540×C1072
#3119107