Finite Group Databasebeta

← #28374863

Subgroups — #28374863

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#20295711C211yesmaximal, characteristic, complemented
2#20295670C211yesmaximal, characteristic
3#20295379C211yesmaximal, characteristic, complemented
4#20295356C211yesmaximal, characteristic, complemented
5#20295348C211yesmaximal, characteristic, complemented
6#20295324C211yesmaximal, characteristic, complemented
7#20295267C211yesmaximal, characteristic, complemented
8#20295254C211yesmaximal, characteristic, complemented
9#20295247C211yesmaximal, characteristic, complemented
10#20295189C211yesmaximal, characteristic, complemented
11#20295177C211yesmaximal, characteristic, complemented
12#20295117C211yesmaximal, characteristic, complemented
13C8×C22⋊D109C211yesmaximal, characteristic, complemented
14#20295019C211yesmaximal, characteristic, complemented
15C2×#102×C109C211yesmaximal, characteristic, complemented
16C2×#13182028C2211yescharacteristic
17C2×Dic436C2211yescharacteristic, complemented
18C2×#13182017C2211yescharacteristic
19C2×#13182017C2211yescharacteristic
20C2×C8×D109C2211yescharacteristic, complemented
21#16812694—21no—
22#16812690C2211yescharacteristic, complemented
23#16812689—21no—
24#16812686C2211yescharacteristic
25#16812682—21no—
26#16812680—21no—
27#16812679C2211yescharacteristic, complemented
28#16812678C2211yescharacteristic
29#16812678C2211yescharacteristic
30#16812671—21no—
31#16812670C2211yescharacteristic
32#16812668—21no—
33#16812664C2211yescharacteristic, complemented
34D4×Dic109C2211yescharacteristic
35C4×C22⋊D109C2211yescharacteristic
36#16812658—21no—
37#16812657C2211yescharacteristic, complemented
38C2×C22⋊Dic109—21no—
39#16812633C2211yescharacteristic, complemented
40#16812630C2211yescharacteristic, complemented
41#16812630C2211yescharacteristic, complemented
42#16812628C2211yescharacteristic, complemented
43#16812624C2211yescharacteristic, complemented
44#16812624C2211yescharacteristic, complemented
45#16812622C2211yescharacteristic, complemented
46#16812622C2211yescharacteristic, complemented
47#16812620C2211yescharacteristic
48#16812620C2211yescharacteristic
49C22⋊#11724784C2211yescharacteristic
50#16812611C2211yescharacteristic, complemented
51C8×Dic109C2211yescharacteristic, complemented
52C22×D4×C109C2211yescharacteristic
53C22×C8×C109C2211yescharacteristic
54C2×C4⋊C4×C109C2211yescharacteristic
55#102×C109C2211yescharacteristic
56#102×C109C2211yescharacteristic
57#102×C109C2211yescharacteristic
58#102×C109C2211yescharacteristic
59#13182028—22no—
60#13182028—41no—
61C2×Dic218C2311yescharacteristic
62C2×Dic218C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C22⋊D109D411yescharacteristic
66C22×Dic109—21no—
67C22×Dic109—21no—
68C2×C4×D109C2311yescharacteristic
69Dic436—41no—
70#13182017—22no—
71#13182017—41no—
72C2×#11724784C2311yescharacteristic
73C2×#11724784C2311yescharacteristic
74C8×D109—41no—
75C4⋊Dic109—21no—
76C4⋊Dic109—21no—
77C4⋊Dic109C2311yescharacteristic
78C4⋊Dic109C2311yescharacteristic
79#13182008—21no—
80#13182008—21no—
81#13182008—21no—
82#13182008—21no—
83#13182008D411yescharacteristic
84C22⋊Dic109—21no—
85C22⋊Dic109—21no—
86C22⋊Dic109—21no—
87C22⋊Dic109—21no—
88C22⋊Dic109—21no—
89C22⋊Dic109—21no—
90C22⋊Dic109D411yescharacteristic
91#13182006—21no—
92#13182006—21no—
93#13182006D411yescharacteristic
94C4×Dic109—21no—
95C4×Dic109—21no—
96C4×Dic109C2311yescharacteristic
97C24×C109—21no—
98C2×D4×C109—22no—
99C2×D4×C109—21no—
100C2×D4×C109—41no—
101C2×D4×C109C2311yescharacteristic
102C2×D4×C109C2311yescharacteristic
103C22×C4×C109—21no—
104C22×C4×C109C2311yescharacteristic
105C2×C8×C109—41no—
106C2×C8×C109C2311yescharacteristic
107C2×C8×C109C2311yescharacteristic
108C4⋊C4×C109—21no—
109C4⋊C4×C109C2311yescharacteristic
110C4⋊C4×C109C2311yescharacteristic
111C23×C109—21no—
112C23×C109—21no—
113C23×C109—42no—
114C23×C109—42no—
115C23×C109—81no—
116C23×C109C2×D411yescharacteristic
117C22×D109C2×D411yescharacteristic
118D4×C109—21no—
119D4×C109—21no—
120D4×C109—21no—
121D4×C109—42no—
122D4×C109#4112yes—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—21no—
126C2×C4×C109—21no—
127C2×C4×C109—42no—
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2411yescharacteristic
130C22⋊D109—22no—
131C22⋊D109—42no—
132C22⋊D109—81no—
133C2×Dic109—21no—
134C2×Dic109—21no—
135C2×Dic109—21no—
136C2×Dic109—21no—
137C2×Dic109—42no—
138C2×Dic109—81no—
139C2×Dic109C2×D411yescharacteristic
140C2×Dic109C2×D411yescharacteristic
141C2×Dic109C2×D411yescharacteristic
142C4×D109—21no—
143C4×D109—21no—
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—22no—
155C22×C109—41no—
156C22×C109—41no—
157C22×C109—41no—
158C22×C109—41no—
159C22×C109—41no—
160C22×C109—84no—
161C22×C109#13512yes—
162C22×C109C22×D411yescharacteristic
163C2×D109—21no—
164C2×D109—21no—
165C2×D109—21no—
166C4×C109—21no—
167C4×C109—41no—
168C4×C109—41no—
169C4×C109C2×#4111yescharacteristic
170C4×C109H(5,𝔽2)11yescharacteristic
171Dic109—21no—
172Dic109—21no—
173Dic109—21no—
174Dic109—41no—
175Dic109—41no—
176Dic109—41no—
177Dic109—41no—
178C2×C109—22no—
179C2×C109—42no—
180C2×C109—81no—
181C2×C109#54611yescharacteristic
182C2×C109C2×#13511yescharacteristic
183C2×C109#57711yescharacteristic
184D109—41no—
185#3296—1091nomaximal, Sylow
186C109#329611yescharacteristic, complemented, Sylow
187#552—1091no—
188#546—1091no—
189#488—1091no—
190#483—1091no—
191#482—1091no—
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×#102D10911yescharacteristic, complemented
202C2×#41—1091no—
203C22×D4C2×D10911yescharacteristic
204C2×Q16—1091no—
205C2×SD16—1091no—
206C2×SD16—1091no—
207C22×C8—1091no—
208C22×C8C2×D10911yescharacteristic
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—1091no—
219#121—2181no—
220#120—2181no—
221C4×Q8—1091no—
222C4×D4—1091no—
223C4×D4—1091no—
224#117—1091no—
225#117—2181no—
226C2×C4⋊C4C2×D10911yescharacteristic
227C2×C22⋊C4—2181no—
228#107—1091no—
229#106—1091no—
230#106—1091no—
231C4⋊C8—1091no—
232#103—1091no—
233#103—1091no—
234#103—1091no—
235#103—1091no—
236#102—1091no—
237#102—1091no—
238#102C2×D10911yescharacteristic
239#102C2×D10911yescharacteristic
240#102C2×D10911yescharacteristic
241#102C2×D10911yescharacteristic
242C22⋊C8—1091no—
243C22⋊C8—1091no—
244C4×C8—1091no—
245C24—21no—
246#41—4361no—
247#41—2182no—
248C2×Q8—1091no—
249C2×Q8—1091no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—1091no—
254C2×D4—2181no—
255C2×D4—2181no—
256C2×D4C22×D10911yescharacteristic
257C2×D4C22×D10911yescharacteristic
258C22×C4—21no—
259C22×C4—1091no—
260C22×C4—2181no—
261C22×C4—2181no—
262C22×C4C22×D10911yescharacteristic
263Q16—4361no—
264SD16—4361no—
265SD16—2182no—
266C2×C8—41no—
267C2×C8—1091no—
268C2×C8—1091no—
269C2×C8—4361no—
270C2×C8C22×D10911yescharacteristic
271C2×C8C22×D10911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1091no—
274C4⋊C4—1091no—
275C4⋊C4—1091no—
276C4⋊C4—2181no—
277C4⋊C4—2181no—
278C4⋊C4—2181no—
279C4⋊C4—2181no—
280C4⋊C4—2181no—
281C4⋊C4—2181no—
282C4⋊C4C22×D10911yescharacteristic
283C4⋊C4C22×D10911yescharacteristic
284C22⋊C4—1091no—
285C22⋊C4—1091no—
286C22⋊C4—2181no—
287C22⋊C4—2181no—
288C22⋊C4—2181no—
289C22⋊C4—2181no—
290C22⋊C4—2181no—
291C22⋊C4—2181no—
292C22⋊C4—2181no—
293C22⋊C4—2181no—
294C42—1091no—
295C42—2181no—
296C42—2181no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—1091no—
303C23D4×D10911yescharacteristic
304Q8—2181no—
305Q8—2181no—
306Q8—2181no—
307Q8—2181no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—8721no—
313D4—4362no—
314D4—2182no—
315D4#1318202912yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—8721no—
322C2×C4—1091no—
323C2×C4—1091no—
324C2×C4—1091no—
325C2×C4—4362no—
326C2×C4—2181no—
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—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—2181no—
348C22—2181no—
349C22—2181no—
350C22#1681271812yes—
351C22C2×D4×D10911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—4361no—
356C4—4361no—
357C4—4361no—
358C4—4361no—
359C4—2181no—
360C4—2181no—
361C4—2181no—
362C4C2×#1318202911yescharacteristic
363C4#1681274411yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—4361no—
368C2#2029566611yescharacteristic
369C2C2×#1681271811yescharacteristic
370C2#2029583211yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#102×C109C2
socleC22×C109C22×D4
prime radical#20295670C2
hypercenterC2×#102D109
hypocenterC109#3296
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20295711C2semidirect
3. #20295379C2semidirect
4. #20295356C2semidirect
5. #20295348C2semidirect
6. #20295324C2semidirect
7. #20295267C2semidirect
8. #20295254C2semidirect
9. #20295247C2semidirect
10. #20295189C2semidirect
11. #20295177C2semidirect
12. #20295117C2semidirect
13. C8×C22⋊D109C2semidirect
14. #20295019C2semidirect
15. C2×#102×C109C2semidirect
17. C2×Dic436C22semidirect
20. C2×C8×D109C22semidirect
22. #16812690C22semidirect
27. #16812679C22semidirect
33. #16812664C22semidirect
37. #16812657C22semidirect
39. #16812633C22semidirect
40. #16812630C22semidirect
41. #16812630C22semidirect
42. #16812628C22semidirect
43. #16812624C22semidirect
44. #16812624C22semidirect
45. #16812622C22semidirect
46. #16812622C22semidirect
50. #16812611C22semidirect
51. C8×Dic109C22semidirect
186. C109#3296semidirect
201. C2×#102D109semidirect

Maximal subgroups

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

subgroupindex
#202957112
#202956702
#202953792
#202953562
#202953482
#202953242
#202952672
#202952542
#202952472
#202951892
#202951772
#202951172
C8×C22⋊D1092
#202950192
C2×#102×C1092
#3296109