Finite Group Databasebeta

← #28346662

Subgroups — #28346662

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#20293107C211yesmaximal, characteristic, complemented
3#20292946C211yesmaximal, characteristic, complemented
4#20292941C211yesmaximal, characteristic, complemented
5#20292935C211yesmaximal, characteristic, complemented
6#20292928C211yesmaximal, characteristic, complemented
7#20292828C211yesmaximal, characteristic, complemented
8#20292823C211yesmaximal, characteristic, complemented
9#20292774C211yesmaximal, characteristic, complemented
10#20292774C211yesmaximal, characteristic, complemented
11#20292740C211yesmaximal, characteristic, complemented
12#20292729C211yesmaximal, characteristic, complemented
13C4×#13133807C211yesmaximal, characteristic, complemented
14C4×D856C211yesmaximal, characteristic, complemented
15#433×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133807C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19C2×D856C2211yescharacteristic
20C2×D856C2211yescharacteristic
21#16812106C2211yescharacteristic
22#16812101C2211yescharacteristic
23#16812094—21no—
24#16812094—21no—
25#16812083C2211yescharacteristic
26#16812083C2211yescharacteristic
27#16812082—21no—
28#16812082—21no—
29C4×Dic214C2211yescharacteristic
30C4×Dic214C2211yescharacteristic
31C4×D428C2211yescharacteristic
32C4×D428C2211yescharacteristic
33C4×D428C2211yescharacteristic
34C4×D428C2211yescharacteristic
35(C22⋊D107)⋊C4—21no—
36(C22⋊D107)⋊C4—21no—
37#16812067—21no—
38C2×C4⋊Dic107C2211yescharacteristic
39C4⋊C4×D107—21no—
40#16812043C2211yescharacteristic
41#16812043C2211yescharacteristic
42#16812041C2211yescharacteristic
43#16812041C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812031C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic
51#16812031C2211yescharacteristic
52#117×C107C2211yescharacteristic
53C4⋊C8×C107C2211yescharacteristic
54C4⋊C8×C107C2211yescharacteristic
55C22⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57#97×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—22no—
61C2×Dic214C2311yescharacteristic
62C2×D428—21no—
63C2×D428—21no—
64C2×D428C2311yescharacteristic
65C2×D428C2311yescharacteristic
66C2×D428C2311yescharacteristic
67C2×C22⋊D107—21no—
68C2×C22⋊D107—21no—
69C2×C22⋊D107—21no—
70C22×Dic107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107—21no—
75C2×C4×D107—21no—
76#13133807—22no—
77#13133807—22no—
78D856—22no—
79D856—22no—
80C4⋊Dic107—21no—
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83C4⋊Dic107C2311yescharacteristic
84C4⋊Dic107C2311yescharacteristic
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C22×C4×C107C2311yescharacteristic
98C2×C8×C107C2311yescharacteristic
99C2×C8×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107D411yescharacteristic
103C4⋊C4×C107D411yescharacteristic
104C22⋊C4×C107D411yescharacteristic
105C22⋊C4×C107D411yescharacteristic
106C42×C107C2311yescharacteristic
107C42×C107C2311yescharacteristic
108C23×C107C2×D411yescharacteristic
109C22×D107—21no—
110C22×D107—21no—
111C22×D107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107C2×D411yescharacteristic
115C2×C4×C107C2×D411yescharacteristic
116C2×C4×C107C2×D411yescharacteristic
117C2×C4×C107C2×D411yescharacteristic
118C2×C4×C107C2×D411yescharacteristic
119C2×C4×C107C2411yescharacteristic
120C22⋊D107—24no—
121C22⋊D107—81no—
122C22⋊D107—81no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—81no—
129D428—21no—
130D428—21no—
131D428—21no—
132D428—21no—
133D428—21no—
134D428—81no—
135D428—81no—
136D428#4112yes—
137C4×D107—24no—
138C4×D107—81no—
139C4×D107—81no—
140C4×D107—81no—
141C4×D107—81no—
142Dic214—21no—
143Dic214#4112yes—
144C8×C107—21no—
145C8×C107—21no—
146C8×C107—21no—
147C8×C107—21no—
148C22×C107—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107C22×D411yescharacteristic
152C2×D107—22no—
153C2×D107—41no—
154C2×D107—41no—
155C2×D107—41no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C4×C107—21no—
162C4×C107—21no—
163C4×C107—21no—
164C4×C107—21no—
165C4×C107—21no—
166C4×C107C2×#4111yescharacteristic
167C4×C107C2×#4111yescharacteristic
168Dic107—22no—
169Dic107—41no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173C2×C107—41no—
174C2×C107#52511yescharacteristic
175C2×C107#57611yescharacteristic
176C2×C107#57711yescharacteristic
177D107—42no—
178D107—81no—
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#449—1071no—
192#442—1071no—
193#440—1071no—
194C4×SD16—1071no—
195C4×D8—1071no—
196#433D10711yescharacteristic, complemented
197C2×#41—1071no—
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×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—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⋊C8C2×D10711yescharacteristic
227C4⋊C8C2×D10711yescharacteristic
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⋊C8C2×D10711yescharacteristic
237C22⋊C8C2×D10711yescharacteristic
238#97C2×D10711yescharacteristic
239C4×C8C2×D10711yescharacteristic
240#41—2142no—
241#41—2142no—
242C2×Q8—1071no—
243C2×D4—1071no—
244C2×D4—1071no—
245C2×D4—1071no—
246C2×D4—2141no—
247C2×D4—2141no—
248C2×D4—2141no—
249C2×D4—2141no—
250C2×D4—2141no—
251C22×C4—2141no—
252C22×C4—2141no—
253C22×C4—2141no—
254C22×C4—2141no—
255C22×C4—2141no—
256C22×C4—2141no—
257C22×C4C22×D10711yescharacteristic
258SD16—2142no—
259SD16—2142no—
260D8—2142no—
261D8—2142no—
262C2×C8C22×D10711yescharacteristic
263C2×C8C22×D10711yescharacteristic
264C2×C8C22×D10711yescharacteristic
265C2×C8C22×D10711yescharacteristic
266C4⋊C4—1071no—
267C4⋊C4—1071no—
268C4⋊C4—1071no—
269C4⋊C4—1071no—
270C4⋊C4—2141no—
271C4⋊C4—2141no—
272C4⋊C4—2141no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4D42811yescharacteristic
276C4⋊C4D42811yescharacteristic
277C22⋊C4—2141no—
278C22⋊C4—2141no—
279C22⋊C4—2141no—
280C22⋊C4—2141no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4D42811yescharacteristic
284C22⋊C4D42811yescharacteristic
285C42—2141no—
286C42—2141no—
287C42C22×D10711yescharacteristic
288C42C22×D10711yescharacteristic
289C23—2141no—
290C23—2141no—
291C23—2141no—
292C23C2×D42811yescharacteristic
293Q8—1072no—
294Q8—2141no—
295D4—8561no—
296D4—8561no—
297D4—8561no—
298D4—8561no—
299D4—1072no—
300D4—2144no—
301D4—2141no—
302D4—2141no—
303D4—2141no—
304D4—2141no—
305D4—2141no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—8561no—
309C2×C4—8561no—
310C2×C4—8561no—
311C2×C4—8561no—
312C2×C4—8561no—
313C2×C4—2144no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4C2×D42811yescharacteristic
320C2×C4C2×D42811yescharacteristic
321C2×C4C2×D42811yescharacteristic
322C2×C4C2×D42811yescharacteristic
323C2×C4C2×D42811yescharacteristic
324C2×C4C23×D10711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—4281no—
333C22—4281no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22—4281no—
338C22—4281no—
339C22—4281no—
340C22—2142no—
341C22C22×D42811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—4281no—
348C4—4281no—
349C4—4281no—
350C4—4281no—
351C4—2142no—
352C4#41×D10711yescharacteristic
353C4#41×D10711yescharacteristic
354C2—41no—
355C2—8561no—
356C2—8561no—
357C2—4282no—
358C2#2029313911yescharacteristic
359C2#2029343211yescharacteristic
360C2#2029343911yescharacteristic
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#433×C107C2
socleC22×C107C22×D4
hypercenter#433D107
hypocenterC107#3119
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20293232C2semidirect
2. #20293107C2semidirect
3. #20292946C2semidirect
4. #20292941C2semidirect
5. #20292935C2semidirect
6. #20292928C2semidirect
7. #20292828C2semidirect
8. #20292823C2semidirect
9. #20292774C2semidirect
10. #20292774C2semidirect
11. #20292740C2semidirect
12. #20292729C2semidirect
13. C4×#13133807C2semidirect
14. C4×D856C2semidirect
15. #433×C107C2semidirect
181. C107#3119semidirect
196. #433D107semidirect

Maximal subgroups

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

subgroupindex
#202932322
#202931072
#202929462
#202929412
#202929352
#202929282
#202928282
#202928232
#202927742
#202927402
#202927292
C4×#131338072
C4×D8562
#433×C1072
#3119107