Finite Group Databasebeta

← #28346653

Subgroups — #28346653

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#20293230C211yesmaximal, characteristic, complemented
2#20293110C211yesmaximal, characteristic, complemented
3#20292943C211yesmaximal, characteristic, complemented
4#20292941C211yesmaximal, characteristic, complemented
5#20292936C211yesmaximal, characteristic, complemented
6#20292925C211yesmaximal, characteristic, complemented
7#20292825C211yesmaximal, characteristic, complemented
8#20292820C211yesmaximal, characteristic, complemented
9#20292772C211yesmaximal, characteristic, complemented
10#20292736C211yesmaximal, characteristic, complemented
11#20292728C211yesmaximal, characteristic, complemented
12#20292712C211yesmaximal, characteristic, complemented
13D8×Dic107C211yesmaximal, characteristic, complemented
14#20292685C211yesmaximal, characteristic, complemented
15#449×C107C211yesmaximal, characteristic, complemented
16C2×#13133805C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18#16812105C2211yescharacteristic
19#16812100C2211yescharacteristic
20#16812093—21no—
21#16812091—21no—
22#16812083C2211yescharacteristic
23#16812081—21no—
24#16812080—21no—
25Q8×Dic107C2211yescharacteristic
26Q8×Dic107C2211yescharacteristic
27D4×Dic107—21no—
28D4×Dic107—21no—
29D4×Dic107C2211yescharacteristic
30D4×Dic107C2211yescharacteristic
31D4×Dic107C2211yescharacteristic
32#16812071C2211yescharacteristic
33#16812068—21no—
34#16812068C2211yescharacteristic
35C2×C4⋊Dic107—21no—
36C2×C4⋊Dic107C2211yescharacteristic
37#16812043C2211yescharacteristic
38#16812043C2211yescharacteristic
39#16812040C2211yescharacteristic
40#16812040C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42Dic107⋊C8C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812031C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812030C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic
50#16812019C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×#41×C107C2211yescharacteristic
53C2×SD16×C107C2211yescharacteristic
54C2×D8×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59C2×D428C2311yescharacteristic
60C2×C22⋊D107—21no—
61C2×C22⋊D107—21no—
62C2×C22⋊D107—21no—
63C22×Dic107—21no—
64C22×Dic107—21no—
65C22×Dic107—21no—
66C22×Dic107—21no—
67C2×C4×D107—21no—
68#13133805—22no—
69#13133803—22no—
70C2×C107⋊C8C2311yescharacteristic
71C2×C107⋊C8C2311yescharacteristic
72C4⋊Dic107—21no—
73C4⋊Dic107—21no—
74C4⋊Dic107—21no—
75C4⋊Dic107—21no—
76C4⋊Dic107D411yescharacteristic
77C4⋊Dic107D411yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79C4⋊Dic107C2311yescharacteristic
80C4⋊Dic107C2311yescharacteristic
81Dic107⋊C4—21no—
82C22⋊Dic107—21no—
83C22⋊Dic107—21no—
84C22⋊Dic107—21no—
85C22⋊Dic107D411yescharacteristic
86C22⋊Dic107D411yescharacteristic
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89C4×Dic107—21no—
90C4×Dic107—21no—
91C4×Dic107C2311yescharacteristic
92C4×Dic107C2311yescharacteristic
93#41×C107—22no—
94#41×C107—22no—
95C2×Q8×C107C2311yescharacteristic
96C2×D4×C107—21no—
97C2×D4×C107—21no—
98C2×D4×C107C2311yescharacteristic
99C2×D4×C107C2311yescharacteristic
100C22×C4×C107—21no—
101C22×C4×C107C2311yescharacteristic
102SD16×C107—22no—
103D8×C107—22no—
104C2×C8×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C22⋊C4×C107—21no—
108C23×C107—21no—
109C23×C107—21no—
110C23×C107C2×D411yescharacteristic
111C22×D107—21no—
112Q8×C107—21no—
113Q8×C107#4112yes—
114D4×C107—24no—
115D4×C107—21no—
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—81no—
119D4×C107#4112yes—
120C2×C4×C107—24no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107C2×D411yescharacteristic
126C2×C4×C107C2411yescharacteristic
127C22⋊D107—81no—
128C22⋊D107—81no—
129C22⋊D107—81no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—81no—
134C2×Dic107—81no—
135C2×Dic107—81no—
136C2×Dic107—81no—
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139C2×Dic107C2×D411yescharacteristic
140C2×Dic107C2×D411yescharacteristic
141D428—21no—
142D428—21no—
143C4×D107—81no—
144C8×C107—21no—
145C8×C107—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×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107C22×D411yescharacteristic
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—21no—
162C4×C107—22no—
163C4×C107—41no—
164C4×C107C2×#4111yescharacteristic
165C4×C107C2×#4111yescharacteristic
166Dic107—21no—
167Dic107—21no—
168Dic107—21no—
169Dic107—21no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173C2×C107—41no—
174C2×C107—42no—
175C2×C107—81no—
176C2×C107#52511yescharacteristic
177C2×C107#57611yescharacteristic
178C2×C107#57711yescharacteristic
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#449D10711yescharacteristic, complemented
192#442—1071no—
193#440—1071no—
194C4×SD16—1071no—
195C4×D8—1071no—
196#433—1071no—
197C2×#41C2×D10711yescharacteristic
198C2×SD16—1071no—
199C2×SD16C2×D10711yescharacteristic
200C2×D8—1071no—
201C2×D8C2×D10711yescharacteristic
202#127—1071no—
203#125—1071no—
204#123—2141no—
205#123—2141no—
206#121—1071no—
207#121—2141no—
208#121—2141no—
209#121C2×D10711yescharacteristic
210C4×Q8—1071no—
211C4×Q8—1071no—
212C4×D4—1071no—
213C4×D4—1071no—
214C4×D4—1071no—
215C4×D4—1071no—
216C4×D4—2141no—
217C4×D4—2141no—
218#117—1071no—
219#117—2141no—
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#103C2×D10711yescharacteristic
230#102—1071no—
231#102—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102C2×D10711yescharacteristic
236C22⋊C8—1071no—
237C22⋊C8C2×D10711yescharacteristic
238#97—1071no—
239C4×C8—1071no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D10711yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—1071no—
246C2×D4—2141no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4C22×D10711yescharacteristic
250C2×D4C22×D10711yescharacteristic
251C22×C4—21no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4—2141no—
257C22×C4C22×D10711yescharacteristic
258SD16—22no—
259SD16—2142no—
260D8—22no—
261D8—2142no—
262C2×C8—1071no—
263C2×C8—1071no—
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—1071no—
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⋊C4—2141no—
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—1071no—
287C42—2141no—
288C42—2141no—
289C23—21no—
290C23—21no—
291C23—2141no—
292C23D4×D10711yescharacteristic
293Q8—21no—
294Q8#1313381712yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—8561no—
301D4—8561no—
302D4—8561no—
303D4—2141no—
304D4—2141no—
305D4#1313381712yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—8561no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—8561no—
315C2×C4—8561no—
316C2×C4—1071no—
317C2×C4—1071no—
318C2×C4—1071no—
319C2×C4—1071no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4D4×D10711yescharacteristic
324C2×C4C23×D10711yescharacteristic
325C8—21no—
326C8—21no—
327C8—2141no—
328C8—2141no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—4281no—
339C22—4281no—
340C22—4281no—
341C22C2×D4×D10711yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—4281no—
346C4—4281no—
347C4—4281no—
348C4—2141no—
349C4—2141no—
350C4—2141no—
351C4—2141no—
352C4C2×#1313381711yescharacteristic
353C4C2×#1313381711yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—8561no—
358C2#2029313311yescharacteristic
359C2#2029342911yescharacteristic
360C2#2029343711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#449×C107C2
socleC22×C107C22×D4
hypercenter#449D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20293230C2semidirect
2. #20293110C2semidirect
3. #20292943C2semidirect
4. #20292941C2semidirect
5. #20292936C2semidirect
6. #20292925C2semidirect
7. #20292825C2semidirect
8. #20292820C2semidirect
9. #20292772C2semidirect
10. #20292736C2semidirect
11. #20292728C2semidirect
12. #20292712C2semidirect
13. D8×Dic107C2semidirect
14. #20292685C2semidirect
15. #449×C107C2semidirect
181. C107#3119semidirect
191. #449D107semidirect

Maximal subgroups

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

subgroupindex
#202932302
#202931102
#202929432
#202929412
#202929362
#202929252
#202928252
#202928202
#202927722
#202927362
#202927282
#202927122
D8×Dic1072
#202926852
#449×C1072
#3119107