Finite Group Databasebeta

← #28373383

Subgroups — #28373383

Order 13952.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295653C211yesmaximal, characteristic, complemented
2#20295594C211yesmaximal, characteristic
3#20295391C211yesmaximal, characteristic, complemented
4#20295389C211yesmaximal, characteristic, complemented
5#20295387C211yesmaximal, characteristic, complemented
6#20295382C211yesmaximal, characteristic, complemented
7#20295380C211yesmaximal, characteristic, complemented
8#20295374C211yesmaximal, characteristic, complemented
9#20295371C211yesmaximal, characteristic, complemented
10#20295029C211yesmaximal, characteristic, complemented
11#20295026C211yesmaximal, characteristic, complemented
12#20295021C211yesmaximal, characteristic, complemented
13#102×D109C211yesmaximal, characteristic, complemented
14#20294983C211yesmaximal, characteristic, complemented
15#489×C109C211yesmaximal, characteristic, complemented
16C2×#13182030C2211yescharacteristic
17C2×D4×D109C2211yescharacteristic
18C2×#13182012C2211yescharacteristic
19C2×C8×D109C2211yescharacteristic
20#16812698C2211yescharacteristic, complemented
21#16812697—21no—
22#16812696C2211yescharacteristic
23#16812695C2211yescharacteristic
24#16812691C2211yescharacteristic, complemented
25#16812690C2211yescharacteristic, complemented
26#16812689—21no—
27#16812688C2211yescharacteristic
28#16812677—21no—
29#16812675—21no—
30#16812672—21no—
31#16812672—21no—
32#16812669—21no—
33#16812669—21no—
34#16812657C2211yescharacteristic
35#16812656C2211yescharacteristic
36C4⋊C4×D109C2211yescharacteristic
37#16812623C2211yescharacteristic, complemented
38#16812623C2211yescharacteristic, complemented
39#16812621C2211yescharacteristic
40#16812621C2211yescharacteristic
41#16812621C2211yescharacteristic, complemented
42#16812621C2211yescharacteristic, complemented
43#16812620C2211yescharacteristic
44#16812620C2211yescharacteristic
45#16812619C2211yescharacteristic
46#16812619C2211yescharacteristic
47#16812619C2211yescharacteristic, complemented
48#16812619C2211yescharacteristic, complemented
49#16812609C2211yescharacteristic, complemented
50C4×#11724784C2211yescharacteristic, complemented
51C8×Dic109C2211yescharacteristic, complemented
52C4⋊Q8×C109C2211yescharacteristic, complemented
53#124×C109C2211yescharacteristic
54#103×C109C2211yescharacteristic, complemented
55#103×C109C2211yescharacteristic, complemented
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic
58#97×C109C2211yescharacteristic, complemented
59C23×D109—21no—
60#13182030—22no—
61#13182030—22no—
62C2×Dic218—21no—
63C2×D436—21no—
64C2×D436—21no—
65C2×D436—21no—
66C2×D436C2311yescharacteristic
67C2×D436C2311yescharacteristic
68C2×C22⋊D109—21no—
69C2×C22⋊D109—21no—
70C2×C22⋊D109—21no—
71D4×D109—22no—
72D4×D109—22no—
73C2×C4×D109—21no—
74C2×C4×D109—21no—
75C2×C4×D109C2311yescharacteristic
76#13182012—22no—
77C2×#11724784C2311yescharacteristic
78C2×#11724784C2311yescharacteristic
79C8×D109—22no—
80C4⋊Dic109—21no—
81C4⋊Dic109C2311yescharacteristic
82C4⋊Dic109C2311yescharacteristic
83#13182008—21no—
84#13182008—21no—
85#13182008—21no—
86#13182008—21no—
87#13182008—21no—
88#13182008D411yescharacteristic
89#13182008D411yescharacteristic
90#13182006—21no—
91#13182006—21no—
92#13182006—21no—
93#13182006D411yescharacteristic
94#13182006D411yescharacteristic
95C4×Dic109—21no—
96C4×Dic109C2311yescharacteristic
97C2×Q8×C109—21no—
98C2×Q8×C109C2311yescharacteristic
99C2×D4×C109C2311yescharacteristic
100C2×C8×C109C2311yescharacteristic
101C2×C8×C109C2311yescharacteristic
102C4⋊C4×C109—21no—
103C4⋊C4×C109C2311yescharacteristic
104C4⋊C4×C109C2311yescharacteristic
105C22⋊C4×C109—21no—
106C22⋊C4×C109—21no—
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C22×D109—21no—
110C22×D109—21no—
111C22×D109—42no—
112C22×D109—81no—
113C22×D109—81no—
114C22×D109C2×D411yescharacteristic
115Q8×C109—21no—
116Q8×C109—21no—
117Q8×C109—81no—
118D4×C109—21no—
119D4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109C2×D411yescharacteristic
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2411yescharacteristic
126C22⋊D109—42no—
127C22⋊D109—81no—
128C22⋊D109—81no—
129C2×Dic109—21no—
130C2×Dic109—21no—
131C2×Dic109C2×D411yescharacteristic
132C2×Dic109C2×D411yescharacteristic
133C2×Dic109C2×D411yescharacteristic
134D436—21no—
135D436—21no—
136D436—21no—
137D436—21no—
138D436—42no—
139D436—81no—
140D436—81no—
141C4×D109—42no—
142C4×D109—81no—
143C4×D109#4112yes—
144C4×D109#4112yes—
145Dic218—81no—
146C8×C109—21no—
147C8×C109—21no—
148#11724784—21no—
149#11724784—21no—
150C22×C109—41no—
151C22×C109—41no—
152C22×C109—41no—
153C22×C109C22×D411yescharacteristic
154C2×D109—21no—
155C2×D109—21no—
156C2×D109—41no—
157C2×D109—41no—
158C2×D109—41no—
159C2×D109—41no—
160C2×D109—41no—
161C2×D109—41no—
162C2×D109—84no—
163C2×D109#12412yes—
164C4×C109—21no—
165C4×C109—21no—
166C4×C109—41no—
167C4×C109—41no—
168C4×C109—41no—
169C4×C109C2×#4111yescharacteristic
170C4×C109C2×#4111yescharacteristic
171Dic109—21no—
172Dic109—21no—
173Dic109—41no—
174Dic109—41no—
175Dic109#12412yes—
176C2×C109—81no—
177C2×C109C2×#12411yescharacteristic
178C2×C109#57611yescharacteristic
179C2×C109#57711yescharacteristic
180D109—22no—
181D109—81no—
182D109—81no—
183#3136—1091nomaximal, Sylow
184C109#313611yescharacteristic, complemented, Sylow
185#544—1091no—
186#535—1091no—
187#490—1091no—
188#490—1091no—
189#489—1091no—
190#489D10911yescharacteristic, complemented
191#488—1091no—
192#488—1091no—
193#486—1091no—
194#486—1091no—
195#418—1091no—
196#417—1091no—
197#416—1091no—
198C2×#102—1091no—
199#405—1091no—
200C2×#41—1091no—
201C22×D4—1091no—
202C2×M16—1091no—
203C22×C8—1091no—
204C4⋊Q8—1091no—
205C4⋊Q8—2181no—
206C4⋊Q8C2×D10911yescharacteristic, complemented
207#127—1091no—
208#127—1091no—
209#125—1091no—
210#125—1091no—
211#125—2181no—
212#124—1091no—
213#124C2×D10911yescharacteristic
214C22⋊Q8—2181no—
215C22⋊Q8—2181no—
216#121—2181no—
217#121—2181no—
218#120—2181no—
219#120—2181no—
220#117—1091no—
221#117—1091no—
222C2×C4⋊C4—1091no—
223#103—1091no—
224#103—1091no—
225#103C2×D10911yescharacteristic, complemented
226#103C2×D10911yescharacteristic, complemented
227#102—1091no—
228#102—1091no—
229#102—1091no—
230#102—1091no—
231#102—1091no—
232#102—1091no—
233#102—1091no—
234#102—1091no—
235#102—1091no—
236#102—1091no—
237#102C2×D10911yescharacteristic
238#102C2×D10911yescharacteristic
239#97—1091no—
240#97C2×D10911yescharacteristic, complemented
241C4×C8—1091no—
242C4×C8—1091no—
243C24—2181no—
244#41—2182no—
245#41—2182no—
246C2×Q8—21no—
247C2×Q8—2181no—
248C2×Q8C22×D10911yescharacteristic
249C2×D4—1091no—
250C2×D4—1091no—
251C2×D4—2181no—
252C2×D4—2182no—
253C2×D4—2182no—
254C2×D4—2181no—
255C2×D4—2181no—
256C2×D4—2181no—
257C2×D4—2181no—
258C2×D4—2181no—
259C2×D4C22×D10911yescharacteristic
260C22×C4—1091no—
261C22×C4—2181no—
262C22×C4—2181no—
263M16—2182no—
264C2×C8—1091no—
265C2×C8—1091no—
266C2×C8—2182no—
267C2×C8C22×D10911yescharacteristic
268C2×C8C22×D10911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—1091no—
271C4⋊C4—1091no—
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⋊C4C22×D10911yescharacteristic
281C4⋊C4C22×D10911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1091no—
285C22⋊C4—1091no—
286C22⋊C4—2181no—
287C22⋊C4—2181no—
288C22⋊C4—2181no—
289C42—1091no—
290C42—2181no—
291C42C22×D10911yescharacteristic
292C23—21no—
293C23—8721no—
294C23—8721no—
295C23—1091no—
296C23—4362no—
297C23—2181no—
298C23—2181no—
299Q8—21no—
300Q8—21no—
301Q8—81no—
302Q8—8721no—
303D4—21no—
304D4—21no—
305D4—8721no—
306D4—8721no—
307D4—8721no—
308D4—8721no—
309D4—4362no—
310D4—4362no—
311D4—2181no—
312D4—2181no—
313D4—2181no—
314D4—2181no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—8721no—
319C2×C4—1091no—
320C2×C4—1092no—
321C2×C4—1092no—
322C2×C4—1091no—
323C2×C4—1091no—
324C2×C4—4362no—
325C2×C4—2181no—
326C2×C4—2181no—
327C2×C4D4×D10911yescharacteristic
328C2×C4D4×D10911yescharacteristic
329C2×C4C23×D10911yescharacteristic
330C8—21no—
331C8—21no—
332C8—2181no—
333C8—2181no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—8724no—
338C22—1092no—
339C22—4361no—
340C22—4361no—
341C22—4361no—
342C22—4361no—
343C22—4361no—
344C22—4361no—
345C22—2181no—
346C22—2181no—
347C22C2×D4×D10911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1092no—
354C4—4361no—
355C4—4361no—
356C4—2181no—
357C4—2181no—
358C4#41×D10911yescharacteristic
359C4#41×D10911yescharacteristic
360C2—81no—
361C2—8721no—
362C2—8721no—
363C2—2182no—
364C2#124×D10911yescharacteristic
365C2#2029583011yescharacteristic
366C2#2029583511yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#489×C109C2
socleC22×C109C22×D4
prime radical#20295594C2
hypercenter#489D109
hypocenterC109#3136
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #20295653C2semidirect
3. #20295391C2semidirect
4. #20295389C2semidirect
5. #20295387C2semidirect
6. #20295382C2semidirect
7. #20295380C2semidirect
8. #20295374C2semidirect
9. #20295371C2semidirect
10. #20295029C2semidirect
11. #20295026C2semidirect
12. #20295021C2semidirect
13. #102×D109C2semidirect
14. #20294983C2semidirect
15. #489×C109C2semidirect
20. #16812698C22semidirect
24. #16812691C22semidirect
25. #16812690C22semidirect
37. #16812623C22semidirect
38. #16812623C22semidirect
41. #16812621C22semidirect
42. #16812621C22semidirect
47. #16812619C22semidirect
48. #16812619C22semidirect
49. #16812609C22semidirect
50. C4×#11724784C22semidirect
51. C8×Dic109C22semidirect
52. C4⋊Q8×C109C22semidirect
54. #103×C109C22semidirect
55. #103×C109C22semidirect
58. #97×C109C22semidirect
184. C109#3136semidirect
190. #489D109semidirect
206. C4⋊Q8C2×D109semidirect
225. #103C2×D109semidirect
226. #103C2×D109semidirect
240. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202956532
#202955942
#202953912
#202953892
#202953872
#202953822
#202953802
#202953742
#202953712
#202950292
#202950262
#202950212
#102×D1092
#202949832
#489×C1092
#3136109