Finite Group Databasebeta

← #28373596

Subgroups — #28373596

Order 13952.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295560C211yesmaximal, characteristic, complemented
2#20295425C211yesmaximal, characteristic, complemented
3#20295408C211yesmaximal, characteristic, complemented
4#20295383C211yesmaximal, characteristic, complemented
5#20295380C211yesmaximal, characteristic, complemented
6#20295265C211yesmaximal, characteristic, complemented
7#20295260C211yesmaximal, characteristic
8#20295257C211yesmaximal, characteristic, complemented
9#20295253C211yesmaximal, characteristic, complemented
10C4×#13182019C211yesmaximal, characteristic, complemented
11C4×#13182016C211yesmaximal, characteristic, complemented
12C4×#13182017C211yesmaximal, characteristic, complemented
13C4×#13182014C211yesmaximal, characteristic, complemented
14C2×C4×#11724784C211yesmaximal, characteristic, complemented
15#529×C109C211yesmaximal, characteristic, complemented
16C2×#13182019C2211yescharacteristic
17C2×#13182017C2211yescharacteristic
18C2×#13182016C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20C22×#11724784C2211yescharacteristic
21C22×#11724784C2211yescharacteristic
22#16812693—21no—
23#16812691C2211yescharacteristic
24#16812687C2211yescharacteristic
25#16812682—21no—
26#16812678C2211yescharacteristic
27#16812673C2211yescharacteristic
28C4×Dic218C2211yescharacteristic
29C4×D436C2211yescharacteristic
30C4×C22⋊D109—21no—
31#16812656—21no—
32#16812632C2211yescharacteristic
33#16812632C2211yescharacteristic
34#16812630C2211yescharacteristic
35#16812630C2211yescharacteristic
36#16812623C2211yescharacteristic
37#16812623C2211yescharacteristic
38#16812622C2211yescharacteristic
39#16812622C2211yescharacteristic
40#16812620C2211yescharacteristic
41#16812620C2211yescharacteristic
42#16812619C2211yescharacteristic
43#16812619C2211yescharacteristic
44C4×#11724784C2211yescharacteristic
45C4×#11724784C2211yescharacteristic
46C4×#11724784C2211yescharacteristic
47C4×#11724784C2211yescharacteristic
48#126×C109—21no—
49#125×C109C2211yescharacteristic
50#124×C109C2211yescharacteristic
51#123×C109—21no—
52C22⋊Q8×C109C2211yescharacteristic
53#121×C109C2211yescharacteristic
54C4×Q8×C109C2211yescharacteristic
55C4×D4×C109—21no—
56C4×D4×C109C2211yescharacteristic
57#117×C109—21no—
58C2×C42×C109C2211yescharacteristic
59C2×Dic218C2311yescharacteristic
60C2×D436C2311yescharacteristic
61C2×C22⋊D109—21no—
62C2×C4×D109—21no—
63#13182019—22no—
64#13182017—22no—
65#13182016—22no—
66#13182014—22no—
67C2×#11724784—22no—
68C2×#11724784—22no—
69C2×#11724784C2311yescharacteristic
70C2×#11724784C2311yescharacteristic
71C2×#11724784C2311yescharacteristic
72C2×#11724784C2311yescharacteristic
73C4⋊Dic109C2311yescharacteristic
74C4⋊Dic109C2311yescharacteristic
75#13182008—21no—
76#13182008—21no—
77#13182008—21no—
78#13182008—21no—
79C22⋊Dic109—21no—
80#13182006—21no—
81#13182006—21no—
82#13182006—21no—
83#13182006—21no—
84C4×Dic109—21no—
85C2×Q8×C109C2311yescharacteristic
86C2×D4×C109—21no—
87C2×D4×C109C2311yescharacteristic
88C22×C4×C109—21no—
89C22×C4×C109D411yescharacteristic
90C22×C4×C109D411yescharacteristic
91C22×C4×C109C2311yescharacteristic
92C4⋊C4×C109—21no—
93C4⋊C4×C109—21no—
94C4⋊C4×C109—21no—
95C4⋊C4×C109—21no—
96C4⋊C4×C109C2311yescharacteristic
97C4⋊C4×C109C2311yescharacteristic
98C22⋊C4×C109—21no—
99C22⋊C4×C109—21no—
100C22⋊C4×C109—21no—
101C22⋊C4×C109—21no—
102C22⋊C4×C109—21no—
103C42×C109—21no—
104C42×C109D411yescharacteristic
105C42×C109D411yescharacteristic
106C42×C109C2311yescharacteristic
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C23×C109C2×D411yescharacteristic
110C22×D109—21no—
111Q8×C109—21no—
112Q8×C109—21no—
113D4×C109—21no—
114D4×C109—21no—
115D4×C109—42no—
116C2×C4×C109—22no—
117C2×C4×C109—22no—
118C2×C4×C109—21no—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—42no—
124C2×C4×C109C2×D411yescharacteristic
125C2×C4×C109C2×D411yescharacteristic
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2411yescharacteristic
130C22⋊D109—42no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133C2×Dic109—21no—
134D436—21no—
135D436—21no—
136C4×D109—42no—
137Dic218—21no—
138Dic218—21no—
139#11724784—21no—
140#11724784—21no—
141#11724784#4112yes—
142#11724784#4112yes—
143C22×C109—21no—
144C22×C109—21no—
145C22×C109—41no—
146C22×C109—41no—
147C22×C109—41no—
148C22×C109#13512yes—
149C22×C109C22×D411yescharacteristic
150C2×D109—41no—
151C2×D109—41no—
152C2×D109—41no—
153C4×C109—21no—
154C4×C109—21no—
155C4×C109—21no—
156C4×C109—21no—
157C4×C109—41no—
158C4×C109—41no—
159C4×C109—41no—
160C4×C109#13512yes—
161C4×C109C2×#4111yescharacteristic
162C4×C109C2×#4111yescharacteristic
163Dic109—41no—
164Dic109—41no—
165Dic109—41no—
166C2×C109—22no—
167C2×C109—81no—
168C2×C109#53211yescharacteristic
169C2×C109C2×#13511yescharacteristic
170C2×C109C2×#13511yescharacteristic
171D109—81no—
172#3168—1091nomaximal, Sylow
173C109#316811yescharacteristic, complemented, Sylow
174#529—1091no—
175#529D10911yescharacteristic, complemented
176#499—1091no—
177#495—1091no—
178#488—1091no—
179#488—1091no—
180#467—1091no—
181#466—1091no—
182#465—1091no—
183#465—1091no—
184C4×Q16—1091no—
185C4×SD16—1091no—
186C4×SD16—1091no—
187C4×D8—1091no—
188C2×C4×C8—1091no—
189C2×Q16—1091no—
190C2×SD16—1091no—
191C2×SD16—1091no—
192C2×D8—1091no—
193C22×C8—1091no—
194C22×C8—1091no—
195#126—21no—
196#126—2181no—
197#125—1091no—
198#125C2×D10911yescharacteristic
199#124—1091no—
200#124C2×D10911yescharacteristic
201#123—21no—
202#123—2181no—
203C22⋊Q8—1091no—
204C22⋊Q8C2×D10911yescharacteristic
205#121—1091no—
206#121C2×D10911yescharacteristic
207C4×Q8—1091no—
208C4×Q8C2×D10911yescharacteristic
209C4×D4—21no—
210C4×D4—1091no—
211C4×D4—2181no—
212C4×D4C2×D10911yescharacteristic
213#117—21no—
214#117—2181no—
215C2×C42C2×D10911yescharacteristic
216#107—1091no—
217#107—1091no—
218#106—1091no—
219#106—1091no—
220#103—1091no—
221#103—1091no—
222#103—1091no—
223#103—1091no—
224#102—1091no—
225#102—1091no—
226#102—1091no—
227#102—1091no—
228C4×C8—1091no—
229C4×C8—1091no—
230C4×C8—1091no—
231C4×C8—1091no—
232C2×Q8—1091no—
233C2×Q8C22×D10911yescharacteristic
234C2×D4—21no—
235C2×D4—1091no—
236C2×D4—2181no—
237C2×D4C22×D10911yescharacteristic
238C22×C4—21no—
239C22×C4—2181no—
240C22×C4C22⋊D10911yescharacteristic
241C22×C4C22⋊D10911yescharacteristic
242C22×C4C22×D10911yescharacteristic
243Q16—2182no—
244SD16—2182no—
245SD16—2182no—
246D8—2182no—
247C2×C8—1091no—
248C2×C8—1091no—
249C2×C8—1091no—
250C2×C8—1091no—
251C2×C8—2182no—
252C2×C8—2182no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—1091no—
258C4⋊C4—1091no—
259C4⋊C4—2181no—
260C4⋊C4—2181no—
261C4⋊C4—2181no—
262C4⋊C4—2181no—
263C4⋊C4C22×D10911yescharacteristic
264C4⋊C4C22×D10911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2181no—
271C22⋊C4—2181no—
272C22⋊C4—2181no—
273C22⋊C4—2181no—
274C22⋊C4—2181no—
275C42—21no—
276C42—2181no—
277C42C22⋊D10911yescharacteristic
278C42C22⋊D10911yescharacteristic
279C42C22×D10911yescharacteristic
280C42C22×D10911yescharacteristic
281C23—21no—
282C23—2181no—
283C23C2×C22⋊D10911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—2181no—
287Q8—2181no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—4362no—
292D4—2181no—
293D4—2181no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—4362no—
303C2×C4—2181no—
304C2×C4—2181no—
305C2×C4—2181no—
306C2×C4C2×C22⋊D10911yescharacteristic
307C2×C4C2×C22⋊D10911yescharacteristic
308C2×C4C2×C22⋊D10911yescharacteristic
309C2×C4C2×C22⋊D10911yescharacteristic
310C2×C4C2×C22⋊D10911yescharacteristic
311C2×C4C23×D10911yescharacteristic
312C8—1092no—
313C8—1092no—
314C8—2181no—
315C8—2181no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4361no—
322C22—4361no—
323C22—4361no—
324C22#1681271912yes—
325C22C22×C22⋊D10911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4361no—
334C4—4361no—
335C4—4361no—
336C4#1681271912yes—
337C4#41×D10911yescharacteristic
338C4#41×D10911yescharacteristic
339C2—22no—
340C2—81no—
341C2—8721no—
342C2#2029557211yescharacteristic
343C2C2×#1681271911yescharacteristic
344C2C2×#1681271911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#529×C109C2
socleC22×C109C22×D4
prime radical#20295260C2
hypercenter#529D109
hypocenterC109#3168
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20295560C2semidirect
2. #20295425C2semidirect
3. #20295408C2semidirect
4. #20295383C2semidirect
5. #20295380C2semidirect
6. #20295265C2semidirect
8. #20295257C2semidirect
9. #20295253C2semidirect
10. C4×#13182019C2semidirect
11. C4×#13182016C2semidirect
12. C4×#13182017C2semidirect
13. C4×#13182014C2semidirect
14. C2×C4×#11724784C2semidirect
15. #529×C109C2semidirect
173. C109#3168semidirect
175. #529D109semidirect

Maximal subgroups

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

subgroupindex
#202955602
#202954252
#202954082
#202953832
#202953802
#202952652
#202952602
#202952572
#202952532
C4×#131820192
C4×#131820162
C4×#131820172
C4×#131820142
C2×C4×#117247842
#529×C1092
#3168109