Finite Group Databasebeta

← #28347873

Subgroups — #28347873

Order 13696.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293244C211yesmaximal, characteristic, complemented
2#20293230C211yesmaximal, characteristic, complemented
3#20292937C211yesmaximal, characteristic, complemented
4#20292925C211yesmaximal, characteristic, complemented
5#20292916C211yesmaximal, characteristic, complemented
6#20292905C211yesmaximal, characteristic, complemented
7#20292873C211yesmaximal, characteristic, complemented
8#20292861C211yesmaximal, characteristic, complemented
9#20292854C211yesmaximal, characteristic, complemented
10#20292841C211yesmaximal, characteristic, complemented
11#20292840C211yesmaximal, characteristic, complemented
12#20292826C211yesmaximal, characteristic, complemented
13#20292820C211yesmaximal, characteristic, complemented
14#20292655C211yesmaximal, characteristic, complemented
15#469×C107C211yesmaximal, characteristic, complemented
16C2×#13133807C2211yescharacteristic
17C2×#13133806C2211yescharacteristic
18C2×#13133803C2211yescharacteristic
19C22×C107⋊C8C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812105C2211yescharacteristic
22#16812102—21no—
23#16812100C2211yescharacteristic
24#16812096—21no—
25#16812096C2211yescharacteristic
26#16812093—21no—
27#16812091—21no—
28#16812090—21no—
29#16812088C2211yescharacteristic
30#16812086—21no—
31#16812083C2211yescharacteristic
32#16812081—21no—
33#16812080—21no—
34#16812074C2211yescharacteristic
35D4×Dic107C2211yescharacteristic
36D4×Dic107C2211yescharacteristic
37#16812071C2211yescharacteristic
38#16812068C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812040C2211yescharacteristic
42Dic107⋊C8C2211yescharacteristic
43Dic107⋊C8C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45Dic107⋊C8C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812032C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812030C2211yescharacteristic
50#16812030C2211yescharacteristic
51#16812029C2211yescharacteristic
52C2×D8×C107C2211yescharacteristic
53C2×M16×C107C2211yescharacteristic
54#121×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic
56#106×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic
59C2×Dic214—21no—
60C2×Dic214C2311yescharacteristic
61C2×D428C2311yescharacteristic
62C2×C22⋊D107—21no—
63C2×C22⋊D107—21no—
64C2×C22⋊D107—21no—
65C22×Dic107—21no—
66C22×Dic107—21no—
67C2×C4×D107—21no—
68#13133807—41no—
69#13133806—41no—
70#13133803—41no—
71C2×C107⋊C8—41no—
72C2×C107⋊C8C2311yescharacteristic
73C2×C107⋊C8C2311yescharacteristic
74C4⋊Dic107—21no—
75C4⋊Dic107D411yescharacteristic
76C4⋊Dic107D411yescharacteristic
77C4⋊Dic107C2311yescharacteristic
78C4⋊Dic107C2311yescharacteristic
79Dic107⋊C4—21no—
80Dic107⋊C4—21no—
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83C22⋊Dic107—21no—
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88C22⋊Dic107D411yescharacteristic
89C22⋊Dic107D411yescharacteristic
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92C4×Dic107—21no—
93C4×Dic107C2311yescharacteristic
94C4×Dic107C2311yescharacteristic
95C2×D4×C107—21no—
96C2×D4×C107—21no—
97C2×D4×C107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100D8×C107—41no—
101M16×C107—41no—
102C2×C8×C107C2311yescharacteristic
103C2×C8×C107C2311yescharacteristic
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C22⋊C4×C107—21no—
107C22⋊C4×C107—21no—
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—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2411yescharacteristic
124C22⋊D107—81no—
125C22⋊D107—81no—
126C22⋊D107—81no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107—21no—
130C2×Dic107—81no—
131C2×Dic107—81no—
132C2×Dic107C2×D411yescharacteristic
133C2×Dic107C2×D411yescharacteristic
134C2×Dic107C2×D411yescharacteristic
135C2×Dic107C2×D411yescharacteristic
136D428—21no—
137D428—21no—
138C4×D107—81no—
139Dic214—21no—
140Dic214—21no—
141Dic214—81no—
142C8×C107—21no—
143C8×C107—21no—
144C107⋊C8—21no—
145C107⋊C8—21no—
146C22×C107—21no—
147C22×C107—21no—
148C22×C107—21no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107C22×D411yescharacteristic
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C4×C107—21no—
160C4×C107—41no—
161C4×C107—41no—
162C4×C107H(5,𝔽2)11yescharacteristic
163C4×C1072−1+411yescharacteristic
164Dic107—21no—
165Dic107—21no—
166Dic107—21no—
167Dic107—21no—
168Dic107—41no—
169Dic107—41no—
170Dic107—41no—
171C2×C107—41no—
172C2×C107—81no—
173C2×C107—81no—
174C2×C107#53711yescharacteristic
175C2×C107#57611yescharacteristic
176C2×C107#57711yescharacteristic
177D107—81no—
178#3257—1071nomaximal, Sylow
179C107#325711yescharacteristic, complemented, Sylow
180#542—1071no—
181#540—1071no—
182#479—1071no—
183#478—1071no—
184#476—1071no—
185#474—1071no—
186#469D10711yescharacteristic, complemented
187#468—1071no—
188#466—1071no—
189#465—1071no—
190#463—1071no—
191#463—1071no—
192#460—1071no—
193#459—1071no—
194#424—1071no—
195C2×SD16—1071no—
196C2×SD16—1071no—
197C2×D8—1071no—
198C2×D8C2×D10711yescharacteristic
199C2×M16C2×D10711yescharacteristic
200C22×C8—1071no—
201C4⋊Q8—1071no—
202#127—1071no—
203#126—2141no—
204#125—1071no—
205#124—1071no—
206#124—2141no—
207#123—2141no—
208#123—2141no—
209#123—2141no—
210C22⋊Q8—1071no—
211C22⋊Q8—2141no—
212#121—1071no—
213#121—2141no—
214#121—2141no—
215#121C2×D10711yescharacteristic
216#121C2×D10711yescharacteristic
217C4×Q8—1071no—
218C4×D4—1071no—
219C4×D4—1071no—
220C4×D4—1071no—
221#117—1071no—
222#107—1071no—
223#107—1071no—
224#106—1071no—
225#106C2×D10711yescharacteristic
226C4⋊C8—1071no—
227C4⋊C8—1071no—
228C4⋊C8—1071no—
229C4⋊C8—1071no—
230#103—1071no—
231#103—1071no—
232#102—1071no—
233#102—1071no—
234#102—1071no—
235#102—1071no—
236#102C2×D10711yescharacteristic
237#102C2×D10711yescharacteristic
238C2×Q8—1071no—
239C2×Q8—2141no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1071no—
243C2×D4—2141no—
244C2×D4—2141no—
245C2×D4—2141no—
246C2×D4C22×D10711yescharacteristic
247C2×D4C22×D10711yescharacteristic
248C22×C4—2141no—
249C22×C4—2141no—
250C22×C4—2141no—
251C22×C4C22×D10711yescharacteristic
252SD16—4281no—
253SD16—4281no—
254D8—41no—
255D8—4281no—
256M16—41no—
257C2×C8—1071no—
258C2×C8—1071no—
259C2×C8—4281no—
260C2×C8C22×D10711yescharacteristic
261C2×C8C22×D10711yescharacteristic
262C4⋊C4—1071no—
263C4⋊C4—1071no—
264C4⋊C4—1071no—
265C4⋊C4—1071no—
266C4⋊C4—2141no—
267C4⋊C4—2141no—
268C4⋊C4—2141no—
269C4⋊C4—2141no—
270C4⋊C4—2141no—
271C4⋊C4C22×D10711yescharacteristic
272C4⋊C4C22×D10711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—1071no—
276C22⋊C4—1071no—
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C42—1071no—
285C42—1071no—
286C42—2141no—
287C23—21no—
288C23—21no—
289C23—2141no—
290C23D4×D10711yescharacteristic
291Q8—8561no—
292Q8—2141no—
293Q8—2141no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—8561no—
301D4—8561no—
302D4—8561no—
303D4—2141no—
304D4—2141no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—8561no—
310C2×C4—8561no—
311C2×C4—8561no—
312C2×C4—1071no—
313C2×C4—1071no—
314C2×C4—1071no—
315C2×C4—1071no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4D4×D10711yescharacteristic
320C2×C4C23×D10711yescharacteristic
321C8—21no—
322C8—21no—
323C8—2141no—
324C8—2141no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22C2×D4×D10711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—4281no—
342C4—4281no—
343C4—4281no—
344C4—2141no—
345C4—2141no—
346C4—2141no—
347C4—2141no—
348C4#1681215411yescharacteristic
349C4#1681215611yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—8561no—
354C2#2029320411yescharacteristic
355C2#2029343111yescharacteristic
356C2#2029343711yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#469×C107C2
socleC22×C107C22×D4
hypercenter#469D107
hypocenterC107#3257
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20293244C2semidirect
2. #20293230C2semidirect
3. #20292937C2semidirect
4. #20292925C2semidirect
5. #20292916C2semidirect
6. #20292905C2semidirect
7. #20292873C2semidirect
8. #20292861C2semidirect
9. #20292854C2semidirect
10. #20292841C2semidirect
11. #20292840C2semidirect
12. #20292826C2semidirect
13. #20292820C2semidirect
14. #20292655C2semidirect
15. #469×C107C2semidirect
179. C107#3257semidirect
186. #469D107semidirect

Maximal subgroups

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

subgroupindex
#202932442
#202932302
#202929372
#202929252
#202929162
#202929052
#202928732
#202928612
#202928542
#202928412
#202928402
#202928262
#202928202
#202926552
#469×C1072
#3257107