Finite Group Databasebeta

← #28347898

Subgroups — #28347898

Order 13696.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293231C211yesmaximal, characteristic, complemented
2#20293228C211yesmaximal, characteristic, complemented
3#20292929C211yesmaximal, characteristic, complemented
4#20292928C211yesmaximal, characteristic, complemented
5#20292927C211yesmaximal, characteristic, complemented
6#20292925C211yesmaximal, characteristic, complemented
7#20292879C211yesmaximal, characteristic, complemented
8#20292877C211yesmaximal, characteristic, complemented
9#20292862C211yesmaximal, characteristic, complemented
10#20292860C211yesmaximal, characteristic, complemented
11#20292820C211yesmaximal, characteristic, complemented
12#20292820C211yesmaximal, characteristic, complemented
13#20292819C211yesmaximal, characteristic, complemented
14#20292652C211yesmaximal, characteristic, complemented
15#459×C107C211yesmaximal, characteristic, complemented
16C2×#13133803C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812105C2211yescharacteristic
21#16812101C2211yescharacteristic
22#16812100C2211yescharacteristic
23#16812092—21no—
24#16812091—21no—
25#16812090—21no—
26#16812090—21no—
27#16812084C2211yescharacteristic
28#16812083—21no—
29#16812082—21no—
30#16812081—21no—
31#16812081—21no—
32#16812080C2211yescharacteristic
33#16812080C2211yescharacteristic
34#16812080C2211yescharacteristic
35C4×D428C2211yescharacteristic
36D4×Dic107C2211yescharacteristic
37D4×Dic107C2211yescharacteristic
38#16812066C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43C4⋊(C107⋊C8)C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812030C2211yescharacteristic
50#16812030C2211yescharacteristic
51#16812030C2211yescharacteristic
52C2×D8×C107C2211yescharacteristic
53C2×D8×C107C2211yescharacteristic
54#127×C107C2211yescharacteristic
55C4×D4×C107C2211yescharacteristic
56C4⋊C8×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59C2×D428—21no—
60C2×D428C2311yescharacteristic
61C2×C22⋊D107—21no—
62C2×C22⋊D107—21no—
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66C22×Dic107—21no—
67C22×Dic107—21no—
68C2×C4×D107—21no—
69C2×C4×D107C2311yescharacteristic
70#13133803—41no—
71#13133803—41no—
72#13133801—41no—
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C8×D107—41no—
76C4⋊Dic107—21no—
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79C4⋊Dic107C2311yescharacteristic
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84Dic107⋊C4D411yescharacteristic
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88C22⋊Dic107—21no—
89C22⋊Dic107—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4D411yescharacteristic
93(C2×D107)⋊C4D411yescharacteristic
94C4×Dic107C2311yescharacteristic
95C2×D4×C107—21no—
96C2×D4×C107—21no—
97C2×D4×C107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C2×D4×C107C2311yescharacteristic
100C22×C4×C107—21no—
101D8×C107—41no—
102D8×C107—41no—
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C42×C107C2311yescharacteristic
108C23×C107—21no—
109C23×C107—21no—
110C23×C107—21no—
111C22×D107—21no—
112C22×D107C2×D411yescharacteristic
113D4×C107—21no—
114D4×C107—21no—
115D4×C107—21no—
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—21no—
119D4×C107—81no—
120D4×C107—81no—
121C2×C4×C107—21no—
122C2×C4×C107—81no—
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2411yescharacteristic
126C22⋊D107—81no—
127C22⋊D107—81no—
128C22⋊D107—81no—
129C22⋊D107—81no—
130C22⋊D107—81no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—81no—
135C2×Dic107—81no—
136C2×Dic107C2×D411yescharacteristic
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139D428—21no—
140D428—21no—
141D428—81no—
142C4×D107—21no—
143C4×D107—21no—
144C4×D107—81no—
145C8×C107—21no—
146C8×C107—21no—
147C107⋊C8—21no—
148C107⋊C8—21no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107C22×D411yescharacteristic
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—21no—
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—41no—
165C4×C107—21no—
166C4×C107—21no—
167C4×C107—41no—
168C4×C107H(5,𝔽2)11yescharacteristic
169C4×C1072−1+411yescharacteristic
170Dic107—21no—
171Dic107—21no—
172Dic107—21no—
173Dic107—41no—
174Dic107—41no—
175Dic107—41no—
176C2×C107—81no—
177C2×C107—81no—
178C2×C107—81no—
179C2×C107#53711yescharacteristic
180C2×C107#57611yescharacteristic
181C2×C107#57611yescharacteristic
182D107—41no—
183D107—81no—
184#3259—1071nomaximal, Sylow
185C107#325911yescharacteristic, complemented, Sylow
186#540—1071no—
187#540—1071no—
188#478—1071no—
189#478—1071no—
190#478—1071no—
191#478—1071no—
192#469—1071no—
193#469—1071no—
194#466—1071no—
195#466—1071no—
196#459—1071no—
197#459—1071no—
198#459—1071no—
199#459D10711yescharacteristic, complemented
200#424—1071no—
201C2×D8—1071no—
202C2×D8—1071no—
203C2×D8C2×D10711yescharacteristic
204C2×D8C2×D10711yescharacteristic
205C2×M16—1071no—
206C22×C8—1071no—
207#127—1071no—
208#127C2×D10711yescharacteristic
209#125—1071no—
210#125—1071no—
211#123—2141no—
212#123—2141no—
213#123—2141no—
214#123—2141no—
215#121—1071no—
216#121—1071no—
217#121—1071no—
218#121—1071no—
219#121—2141no—
220#121—2141no—
221#121—2141no—
222#121—2141no—
223C4×D4—1071no—
224C4×D4—1071no—
225C4×D4—1071no—
226C4×D4C2×D10711yescharacteristic
227#117—1071no—
228#107—1071no—
229#107—1071no—
230#106—1071no—
231#106—1071no—
232C4⋊C8—1071no—
233C4⋊C8—1071no—
234C4⋊C8—1071no—
235C4⋊C8C2×D10711yescharacteristic
236#102—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102—1071no—
241#102—1071no—
242#102C2×D10711yescharacteristic
243#102C2×D10711yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—1071no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4—2141no—
250C2×D4—2141no—
251C2×D4—2141no—
252C2×D4—2141no—
253C2×D4C22×D10711yescharacteristic
254C2×D4C22×D10711yescharacteristic
255C2×D4C22×D10711yescharacteristic
256C22×C4—21no—
257C22×C4—1071no—
258C22×C4—2141no—
259C22×C4—2141no—
260C22×C4—2141no—
261D8—41no—
262D8—41no—
263D8—4281no—
264D8—4281no—
265M16—4281no—
266C2×C8—1071no—
267C2×C8—1071no—
268C2×C8—4281no—
269C2×C8C22×D10711yescharacteristic
270C2×C8C22×D10711yescharacteristic
271C4⋊C4—1071no—
272C4⋊C4—1071no—
273C4⋊C4—1071no—
274C4⋊C4—1071no—
275C4⋊C4—1071no—
276C4⋊C4—2141no—
277C4⋊C4—2141no—
278C4⋊C4—2141no—
279C4⋊C4—2141no—
280C4⋊C4C22×D10711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—1071no—
283C22⋊C4—1071no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C22⋊C4—2141no—
287C22⋊C4—2141no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C42—1071no—
292C42C22×D10711yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23—1071no—
297C23—2141no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—8561no—
307D4—8561no—
308D4—8561no—
309D4—8561no—
310D4—8561no—
311D4—8561no—
312D4—2141no—
313D4—2141no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—8561no—
317C2×C4—8561no—
318C2×C4—8561no—
319C2×C4—1071no—
320C2×C4—1071no—
321C2×C4—1071no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4—2141no—
326C2×C4—2141no—
327C2×C4D4×D10711yescharacteristic
328C2×C4D4×D10711yescharacteristic
329C2×C4C23×D10711yescharacteristic
330C8—21no—
331C8—21no—
332C8—2141no—
333C8—2141no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—4281no—
344C22—4281no—
345C22—4281no—
346C22—2141no—
347C22—2141no—
348C22—2141no—
349C22C2×D4×D10711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—4281no—
354C4—4281no—
355C4—4281no—
356C4—2141no—
357C4—2141no—
358C4—2141no—
359C4#1681215411yescharacteristic
360C4#1681215611yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—8561no—
365C2—4281no—
366C2#2029320611yescharacteristic
367C2#2029342811yescharacteristic
368C2#2029343111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#459×C107C2
socleC22×C107C22×D4
hypercenter#459D107
hypocenterC107#3259
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20293231C2semidirect
2. #20293228C2semidirect
3. #20292929C2semidirect
4. #20292928C2semidirect
5. #20292927C2semidirect
6. #20292925C2semidirect
7. #20292879C2semidirect
8. #20292877C2semidirect
9. #20292862C2semidirect
10. #20292860C2semidirect
11. #20292820C2semidirect
12. #20292820C2semidirect
13. #20292819C2semidirect
14. #20292652C2semidirect
15. #459×C107C2semidirect
185. C107#3259semidirect
199. #459D107semidirect

Maximal subgroups

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

subgroupindex
#202932312
#202932282
#202929292
#202929282
#202929272
#202929252
#202928792
#202928772
#202928622
#202928602
#202928202
#202928192
#202926522
#459×C1072
#3259107