Finite Group Databasebeta

← #28374870

Subgroups — #28374870

Order 13952.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295715C211yesmaximal, characteristic, complemented
2#20295673C211yesmaximal, characteristic
3#20295379C211yesmaximal, characteristic, complemented
4#20295358C211yesmaximal, characteristic, complemented
5#20295329C211yesmaximal, characteristic, complemented
6#20295268C211yesmaximal, characteristic, complemented
7#20295253C211yesmaximal, characteristic, complemented
8#20295247C211yesmaximal, characteristic, complemented
9#20295190C211yesmaximal, characteristic, complemented
10#20295178C211yesmaximal, characteristic, complemented
11#20295113C211yesmaximal, characteristic, complemented
12#20295089C211yesmaximal, characteristic, complemented
13#20295020C211yesmaximal, characteristic, complemented
14#102×D109C211yesmaximal, characteristic, complemented
15#482×C109C211yesmaximal, characteristic, complemented
16C2×#13182029C2211yescharacteristic
17C2×D4×D109C2211yescharacteristic
18C2×Dic436C2211yescharacteristic, complemented
19C2×#13182018C2211yescharacteristic
20C2×#13182017C2211yescharacteristic
21C22×#11724784C2211yescharacteristic, complemented
22C2×C8×D109C2211yescharacteristic
23#16812692—21no—
24#16812691—21no—
25#16812690C2211yescharacteristic, complemented
26#16812686C2211yescharacteristic
27#16812681—21no—
28#16812681—21no—
29#16812679C2211yescharacteristic
30#16812679C2211yescharacteristic
31#16812678C2211yescharacteristic, complemented
32#16812670—21no—
33#16812667—21no—
34#16812664C2211yescharacteristic, complemented
35#16812661C2211yescharacteristic
36C4×C22⋊D109C2211yescharacteristic
37#16812656—21no—
38C4⋊C4×D109C2211yescharacteristic
39C22⋊C4×D109—21no—
40#16812630C2211yescharacteristic, complemented
41#16812628C2211yescharacteristic, complemented
42#16812624C2211yescharacteristic, complemented
43#16812622C2211yescharacteristic, complemented
44#16812622C2211yescharacteristic, complemented
45#16812622C2211yescharacteristic, complemented
46#16812621C2211yescharacteristic
47#16812620C2211yescharacteristic
48#16812619C2211yescharacteristic
49#16812619C2211yescharacteristic
50#16812611C2211yescharacteristic
51C8×Dic109C2211yescharacteristic, complemented
52#121×C109C2211yescharacteristic
53#117×C109C2211yescharacteristic, complemented
54#107×C109C2211yescharacteristic, complemented
55#106×C109C2211yescharacteristic, complemented
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic
58C22⋊C8×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60#13182029—22no—
61#13182029—41no—
62C2×Dic218C2311yescharacteristic
63C2×Dic218C2311yescharacteristic
64C2×D436C2311yescharacteristic
65C2×C22⋊D109—21no—
66C2×C22⋊D109—21no—
67C2×C22⋊D109D411yescharacteristic
68D4×D109—22no—
69D4×D109—41no—
70C2×C4×D109—21no—
71C2×C4×D109—21no—
72C2×C4×D109—21no—
73C2×C4×D109C2311yescharacteristic
74Dic436—41no—
75#13182018—22no—
76#13182017—41no—
77C2×#11724784—41no—
78C2×#11724784C2311yescharacteristic
79C2×#11724784C2311yescharacteristic
80C8×D109—41no—
81C4⋊Dic109—21no—
82C4⋊Dic109—21no—
83C4⋊Dic109—21no—
84C4⋊Dic109C2311yescharacteristic
85#13182008—21no—
86#13182008—21no—
87#13182008—21no—
88#13182008—21no—
89#13182008D411yescharacteristic
90C22⋊Dic109—21no—
91C22⋊Dic109—21no—
92C22⋊Dic109—21no—
93C22⋊Dic109D411yescharacteristic
94#13182006—21no—
95#13182006—21no—
96#13182006—21no—
97#13182006D411yescharacteristic
98C4×Dic109—21no—
99C4×Dic109C2311yescharacteristic
100C2×D4×C109—21no—
101C2×D4×C109C2311yescharacteristic
102C22×C4×C109C2311yescharacteristic
103C2×C8×C109C2311yescharacteristic
104C2×C8×C109C2311yescharacteristic
105C4⋊C4×C109C2311yescharacteristic
106C4⋊C4×C109C2311yescharacteristic
107C4⋊C4×C109C2311yescharacteristic
108C22⋊C4×C109—21no—
109C22⋊C4×C109—21no—
110C42×C109—21no—
111C23×C109—21no—
112C23×C109C2×D411yescharacteristic
113C22×D109—21no—
114C22×D109—42no—
115C22×D109—42no—
116C22×D109—81no—
117C22×D109C2×D411yescharacteristic
118D4×C109—21no—
119D4×C109—21no—
120D4×C109—81no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—21no—
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2411yescharacteristic
128C22⋊D109—22no—
129C22⋊D109—42no—
130C22⋊D109—42no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133C2×Dic109—21no—
134C2×Dic109C2×D411yescharacteristic
135C2×Dic109C2×D411yescharacteristic
136C2×Dic109C2×D411yescharacteristic
137D436—21no—
138D436#4112yes—
139C4×D109—21no—
140C4×D109—21no—
141C4×D109—42no—
142C4×D109—42no—
143C4×D109—81no—
144Dic218—21no—
145Dic218—21no—
146Dic218—21no—
147Dic218—21no—
148C8×C109—21no—
149C8×C109—21no—
150#11724784—21no—
151#11724784—21no—
152C22×C109—21no—
153C22×C109—21no—
154C22×C109—21no—
155C22×C109—41no—
156C22×C109—41no—
157C22×C109—41no—
158C22×C109C22×D411yescharacteristic
159C2×D109—21no—
160C2×D109—21no—
161C2×D109—22no—
162C2×D109—41no—
163C2×D109—41no—
164C2×D109—84no—
165C2×D109#13512yes—
166C4×C109—21no—
167C4×C109—41no—
168C4×C109—41no—
169C4×C109—41no—
170C4×C109C2×#4111yescharacteristic
171C4×C109H(5,𝔽2)11yescharacteristic
172Dic109—21no—
173Dic109—21no—
174Dic109—21no—
175Dic109—41no—
176Dic109—41no—
177Dic109—41no—
178C2×C109—41no—
179C2×C109—81no—
180C2×C109#54611yescharacteristic
181C2×C109C2×#13511yescharacteristic
182C2×C109#57711yescharacteristic
183D109—22no—
184D109—42no—
185#3296—1091nomaximal, Sylow
186C109#329611yescharacteristic, complemented, Sylow
187#552—1091no—
188#546—1091no—
189#488—1091no—
190#483—1091no—
191#482D10911yescharacteristic, complemented
192#478—1091no—
193#467—1091no—
194#465—1091no—
195#464—1091no—
196#452—1091no—
197#450—1091no—
198C4×SD16—1091no—
199C8×D4—1091no—
200#416—1091no—
201C2×#102—1091no—
202C2×#41—1091no—
203C22×D4—1091no—
204C2×Q16—1091no—
205C2×SD16—1091no—
206C2×SD16—1091no—
207C22×C8—1091no—
208C22×C8—1091no—
209#126—2181no—
210#125—1091no—
211#125—2181no—
212#124—1091no—
213#123—2181no—
214#123—2181no—
215C22⋊Q8—1091no—
216C22⋊Q8—1091no—
217C22⋊Q8—1091no—
218#121—2181no—
219#121C2×D10911yescharacteristic
220#120—2181no—
221C4×Q8—1091no—
222C4×D4—1091no—
223C4×D4—1091no—
224#117—2181no—
225#117C2×D10911yescharacteristic, complemented
226C2×C4⋊C4—1091no—
227C2×C22⋊C4—2181no—
228#107C2×D10911yescharacteristic, complemented
229#106—1091no—
230#106C2×D10911yescharacteristic, complemented
231C4⋊C8—1091no—
232#103—1091no—
233#103—1091no—
234#103—1091no—
235#103—1091no—
236#102—1091no—
237#102—1091no—
238#102—1091no—
239#102—1091no—
240#102C2×D10911yescharacteristic
241#102C2×D10911yescharacteristic
242C22⋊C8—1091no—
243C22⋊C8C2×D10911yescharacteristic, complemented
244C4×C8—1091no—
245C24—2181no—
246#41—4361no—
247#41—2182no—
248C2×Q8—1091no—
249C2×Q8—1091no—
250C2×D4—21no—
251C2×D4—1091no—
252C2×D4—1091no—
253C2×D4—4361no—
254C2×D4—2181no—
255C2×D4—2182no—
256C2×D4—2181no—
257C2×D4C22×D10911yescharacteristic
258C22×C4—1091no—
259C22×C4—2181no—
260C22×C4—2181no—
261C22×C4—2181no—
262C22×C4C22×D10911yescharacteristic
263Q16—4361no—
264SD16—4361no—
265SD16—2182no—
266C2×C8—1091no—
267C2×C8—1091no—
268C2×C8—4361no—
269C2×C8—4361no—
270C2×C8C22×D10911yescharacteristic
271C2×C8C22×D10911yescharacteristic
272C4⋊C4—1091no—
273C4⋊C4—1091no—
274C4⋊C4—2181no—
275C4⋊C4—2181no—
276C4⋊C4—2181no—
277C4⋊C4—2181no—
278C4⋊C4—2181no—
279C4⋊C4—2181no—
280C4⋊C4—2181no—
281C4⋊C4C22×D10911yescharacteristic
282C4⋊C4C22×D10911yescharacteristic
283C4⋊C4C22×D10911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1091no—
287C22⋊C4—1091no—
288C22⋊C4—2181no—
289C22⋊C4—2181no—
290C22⋊C4—2181no—
291C22⋊C4—2181no—
292C22⋊C4—2181no—
293C22⋊C4—2181no—
294C42—21no—
295C42—1091no—
296C42—2181no—
297C23—21no—
298C23—8721no—
299C23—1091no—
300C23—4362no—
301C23—4362no—
302C23—2181no—
303C23D4×D10911yescharacteristic
304Q8—2181no—
305Q8—2181no—
306Q8—2181no—
307Q8—2181no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—1092no—
312D4—4362no—
313D4—4362no—
314D4—2182no—
315D4—2181no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—8721no—
322C2×C4—1091no—
323C2×C4—1091no—
324C2×C4—1091no—
325C2×C4—4362no—
326C2×C4—4362no—
327C2×C4—2181no—
328C2×C4—2181no—
329C2×C4—2181no—
330C2×C4—2181no—
331C2×C4—2181no—
332C2×C4D4×D10911yescharacteristic
333C2×C4C23×D10911yescharacteristic
334C8—21no—
335C8—21no—
336C8—2181no—
337C8—2181no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—8724no—
345C22—1092no—
346C22—4361no—
347C22—4361no—
348C22—2182no—
349C22—2181no—
350C22—2181no—
351C22C2×D4×D10911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—4361no—
357C4—4361no—
358C4—4361no—
359C4—2181no—
360C4—2181no—
361C4—2181no—
362C4#41×D10911yescharacteristic
363C4#1681274511yescharacteristic
364C2—41no—
365C2—81no—
366C2—4362no—
367C2—2182no—
368C2#2029566811yescharacteristic
369C2#135×D10911yescharacteristic
370C2#2029583611yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#482×C109C2
socleC22×C109C22×D4
prime radical#20295673C2
hypercenter#482D109
hypocenterC109#3296
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20295715C2semidirect
3. #20295379C2semidirect
4. #20295358C2semidirect
5. #20295329C2semidirect
6. #20295268C2semidirect
7. #20295253C2semidirect
8. #20295247C2semidirect
9. #20295190C2semidirect
10. #20295178C2semidirect
11. #20295113C2semidirect
12. #20295089C2semidirect
13. #20295020C2semidirect
14. #102×D109C2semidirect
15. #482×C109C2semidirect
18. C2×Dic436C22semidirect
21. C22×#11724784C22semidirect
25. #16812690C22semidirect
31. #16812678C22semidirect
34. #16812664C22semidirect
40. #16812630C22semidirect
41. #16812628C22semidirect
42. #16812624C22semidirect
43. #16812622C22semidirect
44. #16812622C22semidirect
45. #16812622C22semidirect
51. C8×Dic109C22semidirect
53. #117×C109C22semidirect
54. #107×C109C22semidirect
55. #106×C109C22semidirect
58. C22⋊C8×C109C22semidirect
186. C109#3296semidirect
191. #482D109semidirect
225. #117C2×D109semidirect
228. #107C2×D109semidirect
230. #106C2×D109semidirect
243. C22⋊C8C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202957152
#202956732
#202953792
#202953582
#202953292
#202952682
#202952532
#202952472
#202951902
#202951782
#202951132
#202950892
#202950202
#102×D1092
#482×C1092
#3296109