Finite Group Databasebeta

← #28346412

Subgroups — #28346412

Order 13696.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293193C211yesmaximal, characteristic
2#20293108C211yesmaximal, characteristic, complemented
3#20292954C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292949C211yesmaximal, characteristic, complemented
6#20292948C211yesmaximal, characteristic, complemented
7#20292945C211yesmaximal, characteristic, complemented
8#20292944C211yesmaximal, characteristic, complemented
9#20292942C211yesmaximal, characteristic, complemented
10#20292668C211yesmaximal, characteristic, complemented
11#20292664C211yesmaximal, characteristic, complemented
12#20292630C211yesmaximal, characteristic, complemented
13#102×D107C211yesmaximal, characteristic, complemented
14#20292592C211yesmaximal, characteristic, complemented
15#480×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×D4×D107C2211yescharacteristic
18C2×#13133801C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812105—21no—
21#16812095—21no—
22#16812084C2211yescharacteristic
23#16812083C2211yescharacteristic
24#16812080C2211yescharacteristic
25#16812079—21no—
26#16812077—21no—
27#16812074—21no—
28#16812071—21no—
29C4×C22⋊D107—21no—
30C4×C22⋊D107—21no—
31#16812068C2211yescharacteristic, complemented
32#16812067C2211yescharacteristic
33#16812067C2211yescharacteristic
34#16812067C2211yescharacteristic, complemented
35C4⋊C4×D107C2211yescharacteristic
36C4⋊C4×D107C2211yescharacteristic, complemented
37#16812043C2211yescharacteristic, complemented
38#16812042C2211yescharacteristic, complemented
39#16812041C2211yescharacteristic, complemented
40#16812040C2211yescharacteristic, complemented
41#16812040C2211yescharacteristic, complemented
42#16812040C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic
44#16812031C2211yescharacteristic
45#16812030C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic, complemented
50(C2×D107)⋊C8C2211yescharacteristic, complemented
51(C2×D107)⋊C8C2211yescharacteristic, complemented
52#121×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic, complemented
54#107×C107C2211yescharacteristic, complemented
55#107×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60#13133818—22no—
61#13133818—22no—
62C2×Dic214D411yescharacteristic
63C2×D428—21no—
64C2×D428D411yescharacteristic
65C2×D428C2311yescharacteristic
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C22⋊D107—21no—
69C2×C22⋊D107D411yescharacteristic
70C2×C22⋊D107D411yescharacteristic
71D4×D107—22no—
72D4×D107—22no—
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—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107—21no—
96C4×Dic107—21no—
97C2×D4×C107—21no—
98C2×D4×C107C2311yescharacteristic
99C22×C4×C107—21no—
100C22×C4×C107C2311yescharacteristic
101C2×C8×C107C2311yescharacteristic
102C2×C8×C107C2311yescharacteristic
103C4⋊C4×C107—21no—
104C4⋊C4×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C22⋊C4×C107—21no—
108C23×C107—21no—
109C23×C107C2×D411yescharacteristic
110C22×D107—21no—
111C22×D107—42no—
112C22×D107—81no—
113C22×D107—81no—
114C22×D107C2×D411yescharacteristic
115C22×D107C2×D411yescharacteristic
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—81no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—81no—
125C2×C4×C107C2×D411yescharacteristic
126C2×C4×C107C2411yescharacteristic
127C22⋊D107—22no—
128C22⋊D107—22no—
129C22⋊D107—42no—
130C22⋊D107—81no—
131C22⋊D107—81no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107C2×D411yescharacteristic
136C2×Dic107C2×D411yescharacteristic
137D428—22no—
138D428—21no—
139D428—21no—
140D428—81no—
141C4×D107—21no—
142C4×D107—21no—
143C4×D107—81no—
144C4×D107—81no—
145C4×D107#4112yes—
146C4×D107#4112yes—
147Dic214—22no—
148C8×C107—21no—
149C8×C107—21no—
150C107⋊C8—21no—
151C107⋊C8—21no—
152C22×C107—21no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107C22×D411yescharacteristic
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—21no—
162C2×D107—21no—
163C2×D107—21no—
164C2×D107—41no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—84no—
168C2×D107#12312yes—
169C4×C107—21no—
170C4×C107—41no—
171C4×C107—41no—
172C4×C107—41no—
173C4×C107C2×#4111yescharacteristic
174C4×C107C2×#4111yescharacteristic
175Dic107—21no—
176Dic107—41no—
177Dic107—41no—
178Dic107—41no—
179Dic107#12312yes—
180C2×C107—41no—
181C2×C107—81no—
182C2×C107C2×#12311yescharacteristic
183C2×C107#57611yescharacteristic
184C2×C107#57711yescharacteristic
185D107—22no—
186D107—41no—
187D107—81no—
188#3096—1071nomaximal, Sylow
189C107#309611yescharacteristic, complemented, Sylow
190#535—1071no—
191#520—1071no—
192#482—1071no—
193#482—1071no—
194#482—1071no—
195#482—1071no—
196#481—1071no—
197#481—1071no—
198#480—1071no—
199#480D10711yescharacteristic, complemented
200#428—1071no—
201#427—1071no—
202#418—1071no—
203C2×#102—1071no—
204#408—1071no—
205C2×#41—1071no—
206C22×D4—1071no—
207C2×M16—1071no—
208C22×C8—1071no—
209#127—2141no—
210#124—2141no—
211#121—1071no—
212#121—1071no—
213#121—1071no—
214#121C2×D10711yescharacteristic
215#120—2141no—
216#120—2141no—
217C4×Q8—2141no—
218C4×D4—2141no—
219C4×D4—2141no—
220C4×D4—2141no—
221#117—1071no—
222#117—1071no—
223#117—1071no—
224#117—1071no—
225C2×C4⋊C4—1071no—
226C2×C4⋊C4—1071no—
227C2×C4⋊C4C2×D10711yescharacteristic, complemented
228#107—1071no—
229#107—1071no—
230#107C2×D10711yescharacteristic, complemented
231#107C2×D10711yescharacteristic, complemented
232#106—1071no—
233#106—1071no—
234#106—1071no—
235#106—1071no—
236#102—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102—1071no—
241#102—1071no—
242#102C2×D10711yescharacteristic
243#102C2×D10711yescharacteristic
244C22⋊C8—1071no—
245C22⋊C8—1071no—
246C22⋊C8—1071no—
247C22⋊C8C2×D10711yescharacteristic, complemented
248C24—2141no—
249#41—2142no—
250#41—2142no—
251C2×Q8—1071no—
252C2×D4—21no—
253C2×D4—1071no—
254C2×D4—1071no—
255C2×D4—1071no—
256C2×D4—1071no—
257C2×D4—2141no—
258C2×D4—2142no—
259C2×D4—2142no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4—2141no—
263C2×D4C22×D10711yescharacteristic
264C22×C4—21no—
265C22×C4—1071no—
266C22×C4—1071no—
267C22×C4—2141no—
268C22×C4—2141no—
269C22×C4C22×D10711yescharacteristic
270M16—2142no—
271C2×C8—1071no—
272C2×C8—1071no—
273C2×C8—2142no—
274C2×C8C22×D10711yescharacteristic
275C2×C8C22×D10711yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—1071no—
278C4⋊C4—1071no—
279C4⋊C4—1071no—
280C4⋊C4—2141no—
281C4⋊C4—2141no—
282C4⋊C4C22×D10711yescharacteristic
283C4⋊C4C22×D10711yescharacteristic
284C4⋊C4C22×D10711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—2141no—
287C22⋊C4—2141no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C22⋊C4—2141no—
292C22⋊C4—2141no—
293C42—2141no—
294C42—2141no—
295C42—2141no—
296C42—2141no—
297C23—21no—
298C23—8561no—
299C23—8561no—
300C23—1071no—
301C23—1071no—
302C23—4282no—
303C23—2141no—
304C23D4×D10711yescharacteristic
305Q8—2142no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—8561no—
310D4—8561no—
311D4—8561no—
312D4—4282no—
313D4—2142no—
314D4—2142no—
315D4—2142no—
316D4—2141no—
317D4—2141no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—8561no—
325C2×C4—8561no—
326C2×C4—1071no—
327C2×C4—1072no—
328C2×C4—1072no—
329C2×C4—1071no—
330C2×C4—2141no—
331C2×C4—2141no—
332C2×C4—2141no—
333C2×C4—2141no—
334C2×C4—2141no—
335C2×C4D4×D10711yescharacteristic
336C2×C4C23×D10711yescharacteristic
337C8—21no—
338C8—21no—
339C8—2141no—
340C8—2141no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—8564no—
348C22—1072no—
349C22—4281no—
350C22—4281no—
351C22—4281no—
352C22—2141no—
353C22—2141no—
354C22—2141no—
355C22—2141no—
356C22—2141no—
357C22C2×D4×D10711yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—1072no—
363C4—4281no—
364C4—4281no—
365C4—4281no—
366C4—2141no—
367C4#41×D10711yescharacteristic
368C4#41×D10711yescharacteristic
369C2—41no—
370C2—81no—
371C2—8561no—
372C2—4281no—
373C2—2142no—
374C2#123×D10711yescharacteristic
375C2#2029342811yescharacteristic
376C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#480×C107C2
socleC22×C107C22×D4
prime radical#20293193C2
hypercenter#480D107
hypocenterC107#3096
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #20293108C2semidirect
3. #20292954C2semidirect
4. #20292952C2semidirect
5. #20292949C2semidirect
6. #20292948C2semidirect
7. #20292945C2semidirect
8. #20292944C2semidirect
9. #20292942C2semidirect
10. #20292668C2semidirect
11. #20292664C2semidirect
12. #20292630C2semidirect
13. #102×D107C2semidirect
14. #20292592C2semidirect
15. #480×C107C2semidirect
31. #16812068C22semidirect
34. #16812067C22semidirect
36. C4⋊C4×D107C22semidirect
37. #16812043C22semidirect
38. #16812042C22semidirect
39. #16812041C22semidirect
40. #16812040C22semidirect
41. #16812040C22semidirect
42. #16812040C22semidirect
49. C22⋊(C107⋊C8)C22semidirect
50. (C2×D107)⋊C8C22semidirect
51. (C2×D107)⋊C8C22semidirect
53. C2×C4⋊C4×C107C22semidirect
54. #107×C107C22semidirect
55. #107×C107C22semidirect
58. C22⋊C8×C107C22semidirect
189. C107#3096semidirect
199. #480D107semidirect
227. C2×C4⋊C4C2×D107semidirect
230. #107C2×D107semidirect
231. #107C2×D107semidirect
247. C22⋊C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931932
#202931082
#202929542
#202929522
#202929492
#202929482
#202929452
#202929442
#202929422
#202926682
#202926642
#202926302
#102×D1072
#202925922
#480×C1072
#3096107