Finite Group Databasebeta

← #28346440

Subgroups — #28346440

Order 13696.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293207C211yesmaximal, characteristic
2#20293108C211yesmaximal, characteristic, complemented
3#20292966C211yesmaximal, characteristic, complemented
4#20292965C211yesmaximal, characteristic, complemented
5#20292961C211yesmaximal, characteristic, complemented
6#20292954C211yesmaximal, characteristic, complemented
7#20292952C211yesmaximal, characteristic, complemented
8#20292942C211yesmaximal, characteristic, complemented
9#20292940C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#107×D107C211yesmaximal, characteristic, complemented
12#20292627C211yesmaximal, characteristic, complemented
13#20292622C211yesmaximal, characteristic, complemented
14#20292592C211yesmaximal, characteristic, complemented
15#484×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133818C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812087—21no—
21#16812085C2211yescharacteristic
22#16812084—21no—
23#16812084C2211yescharacteristic
24#16812083C2211yescharacteristic
25#16812082—21no—
26#16812082—21no—
27#16812074—21no—
28#16812071—21no—
29C4×C22⋊D107—21no—
30C4×C22⋊D107—21no—
31#16812068C2211yescharacteristic
32#16812067C2211yescharacteristic
33#16812067C2211yescharacteristic
34C4⋊C4×D107C2211yescharacteristic
35C4⋊C4×D107C2211yescharacteristic
36C4⋊C4×D107C2211yescharacteristic
37#16812043C2211yescharacteristic
38#16812042C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812042C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812040C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51(C2×D107)⋊C8C2211yescharacteristic
52C22⋊Q8×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#107×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#103×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133819—22no—
60#13133819—22no—
61#13133818—22no—
62#13133818—22no—
63C2×Dic214D411yescharacteristic
64C2×D428—21no—
65C2×D428—21no—
66C2×D428D411yescharacteristic
67C2×D428C2311yescharacteristic
68C2×C22⋊D107—21no—
69C2×C22⋊D107D411yescharacteristic
70C2×C22⋊D107D411yescharacteristic
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107—21no—
75C2×C4×D107C2311yescharacteristic
76C2×C4×D107C2311yescharacteristic
77#13133801—22no—
78C2×C107⋊C8C2311yescharacteristic
79C2×C107⋊C8C2311yescharacteristic
80C8×D107—22no—
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83C4⋊Dic107C2311yescharacteristic
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88C22⋊Dic107—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—
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C2×Q8×C107C2311yescharacteristic
98C22×C4×C107—21no—
99C22×C4×C107C2311yescharacteristic
100C2×C8×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C4⋊C4×C107—21no—
103C4⋊C4×C107—21no—
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C22⋊C4×C107—21no—
108C23×C107C2×D411yescharacteristic
109C22×D107—21no—
110C22×D107C2×D411yescharacteristic
111C22×D107C2×D411yescharacteristic
112Q8×C107—21no—
113Q8×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—81no—
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2411yescharacteristic
123C22⋊D107—22no—
124C22⋊D107—22no—
125C22⋊D107—81no—
126C2×Dic107—21no—
127C2×Dic107—21no—
128C2×Dic107—21no—
129C2×Dic107C2×D411yescharacteristic
130C2×Dic107C2×D411yescharacteristic
131D428—22no—
132D428—21no—
133D428—21no—
134D428—42no—
135D428—81no—
136C4×D107—21no—
137C4×D107—21no—
138C4×D107—42no—
139C4×D107—81no—
140C4×D107—81no—
141C4×D107—81no—
142C4×D107#4112yes—
143C4×D107#4112yes—
144Dic214—22no—
145C8×C107—21no—
146C8×C107—21no—
147C107⋊C8—21no—
148C107⋊C8—21no—
149C22×C107—21no—
150C22×C107—21no—
151C22×C107—21no—
152C22×C107C22×D411yescharacteristic
153C2×D107—21no—
154C2×D107—21no—
155C2×D107—21no—
156C2×D107—21no—
157C2×D107—21no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C2×D107#12312yes—
162C4×C107—21no—
163C4×C107—41no—
164C4×C107—41no—
165C4×C107—41no—
166C4×C107—41no—
167C4×C107C2×#4111yescharacteristic
168C4×C107C2×#4111yescharacteristic
169Dic107—21no—
170Dic107—41no—
171Dic107—41no—
172Dic107—41no—
173Dic107#12312yes—
174C2×C107—41no—
175C2×C107C2×#12311yescharacteristic
176C2×C107#57611yescharacteristic
177C2×C107#57811yescharacteristic
178D107—22no—
179D107—41no—
180D107—81no—
181#3098—1071nomaximal, Sylow
182C107#309811yescharacteristic, complemented, Sylow
183#537—1071no—
184#520—1071no—
185#485—1071no—
186#485—1071no—
187#484—1071no—
188#484D10711yescharacteristic, complemented
189#482—1071no—
190#482—1071no—
191#480—1071no—
192#480—1071no—
193#428—1071no—
194C2×#107—1071no—
195#417—1071no—
196#416—1071no—
197#408—1071no—
198C2×#41—1071no—
199C2×#41—1071no—
200C2×M16—1071no—
201C22×C8—1071no—
202C22⋊Q8—1071no—
203C22⋊Q8—2141no—
204C22⋊Q8C2×D10711yescharacteristic
205#121—1071no—
206#121—1071no—
207#121—2141no—
208#121—2141no—
209#121—2141no—
210C4×Q8—2141no—
211C4×D4—2141no—
212C4×D4—2141no—
213C4×D4—2141no—
214#117—1071no—
215#117—1071no—
216#117—1071no—
217C2×C4⋊C4—1071no—
218C2×C4⋊C4—1071no—
219C2×C4⋊C4—1071no—
220C2×C4⋊C4C2×D10711yescharacteristic
221#107—1071no—
222#107—1071no—
223#107—1071no—
224#107—1071no—
225#107C2×D10711yescharacteristic
226#107C2×D10711yescharacteristic
227#106—1071no—
228#106—1071no—
229#103—1071no—
230#103—1071no—
231#103C2×D10711yescharacteristic
232#103C2×D10711yescharacteristic
233#102—1071no—
234#102—1071no—
235#102—1071no—
236#102—1071no—
237C22⋊C8—1071no—
238C22⋊C8—1071no—
239C22⋊C8—1071no—
240C22⋊C8C2×D10711yescharacteristic
241#41—2142no—
242#41—2142no—
243#41—2142no—
244#41—2142no—
245C2×Q8—1071no—
246C2×Q8C22×D10711yescharacteristic
247C2×D4—1071no—
248C2×D4—1071no—
249C2×D4—1071no—
250C2×D4—1071no—
251C2×D4—2141no—
252C2×D4—2141no—
253C2×D4—2141no—
254C22×C4—21no—
255C22×C4—1071no—
256C22×C4—1071no—
257C22×C4—2141no—
258C22×C4—2141no—
259C22×C4—2141no—
260C22×C4—2141no—
261C22×C4C22×D10711yescharacteristic
262M16—2142no—
263C2×C8—1071no—
264C2×C8—1071no—
265C2×C8—2142no—
266C2×C8C22×D10711yescharacteristic
267C2×C8C22×D10711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—1071no—
271C4⋊C4—1071no—
272C4⋊C4—1071no—
273C4⋊C4—2141no—
274C4⋊C4—2141no—
275C4⋊C4—2141no—
276C4⋊C4—2141no—
277C4⋊C4C22×D10711yescharacteristic
278C4⋊C4C22×D10711yescharacteristic
279C4⋊C4C22×D10711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2141no—
282C22⋊C4—2141no—
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C22⋊C4—2141no—
287C42—2141no—
288C42—2141no—
289C42—2141no—
290C23—1071no—
291C23—1071no—
292C23—2141no—
293C23D4×D10711yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—2142no—
297D4—8561no—
298D4—8561no—
299D4—4282no—
300D4—2142no—
301D4—2142no—
302D4—2142no—
303D4—2141no—
304D4—2141no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—8561no—
313C2×C4—8561no—
314C2×C4—8561no—
315C2×C4—1071no—
316C2×C4—1072no—
317C2×C4—1072no—
318C2×C4—1071no—
319C2×C4—4282no—
320C2×C4—2141no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4D4×D10711yescharacteristic
326C2×C4C23×D10711yescharacteristic
327C8—21no—
328C8—21no—
329C8—2141no—
330C8—2141no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—1072no—
335C22—4281no—
336C22—4281no—
337C22—4281no—
338C22—2141no—
339C22—2141no—
340C22—2141no—
341C22—2141no—
342C22—2141no—
343C22C2×D4×D10711yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1072no—
350C4—4281no—
351C4—4281no—
352C4—4281no—
353C4—2141no—
354C4#41×D10711yescharacteristic
355C4#41×D10711yescharacteristic
356C2—41no—
357C2—8561no—
358C2—4281no—
359C2—2142no—
360C2#123×D10711yescharacteristic
361C2#2029343111yescharacteristic
362C2#2029344011yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#484×C107C2
socleC22×C107C22×D4
prime radical#20293207C2
hypercenter#484D107
hypocenterC107#3098
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #20293108C2semidirect
3. #20292966C2semidirect
4. #20292965C2semidirect
5. #20292961C2semidirect
6. #20292954C2semidirect
7. #20292952C2semidirect
8. #20292942C2semidirect
9. #20292940C2semidirect
10. #20292668C2semidirect
11. #107×D107C2semidirect
12. #20292627C2semidirect
13. #20292622C2semidirect
14. #20292592C2semidirect
15. #484×C107C2semidirect
182. C107#3098semidirect
188. #484D107semidirect

Maximal subgroups

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

subgroupindex
#202932072
#202931082
#202929662
#202929652
#202929612
#202929542
#202929522
#202929422
#202929402
#202926682
#107×D1072
#202926272
#202926222
#202925922
#484×C1072
#3098107