Finite Group Databasebeta

← #28373294

Subgroups — #28373294

Order 13952.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295647C211yesmaximal, characteristic, complemented
2#20295361C211yesmaximal, characteristic, complemented
3#20295339C211yesmaximal, characteristic, complemented
4#20295321C211yesmaximal, characteristic, complemented
5#20295306C211yesmaximal, characteristic, complemented
6#20295248C211yesmaximal, characteristic, complemented
7#20295241C211yesmaximal, characteristic, complemented
8#20295188C211yesmaximal, characteristic, complemented
9#20295171C211yesmaximal, characteristic
10#20295126C211yesmaximal, characteristic, complemented
11#20295124C211yesmaximal, characteristic, complemented
12C4×#13182019C211yesmaximal, characteristic, complemented
13C4×#13182014C211yesmaximal, characteristic, complemented
14#20295087C211yesmaximal, characteristic, complemented
15#520×C109C211yesmaximal, characteristic, complemented
16C2×#13182019C2211yescharacteristic
17C2×#13182017C2211yescharacteristic
18C2×#13182016C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20#16812699C2211yescharacteristic
21#16812694—21no—
22#16812687C2211yescharacteristic
23#16812685—21no—
24#16812681—21no—
25#16812678C2211yescharacteristic
26#16812677—21no—
27#16812673C2211yescharacteristic
28C4×Dic218C2211yescharacteristic
29C4×D436C2211yescharacteristic
30#16812632C2211yescharacteristic
31#16812632C2211yescharacteristic
32#16812632C2211yescharacteristic
33#16812632C2211yescharacteristic
34C4⋊#11724784C2211yescharacteristic
35C4⋊#11724784C2211yescharacteristic
36#16812623C2211yescharacteristic
37#16812623C2211yescharacteristic
38#16812622C2211yescharacteristic
39#16812622C2211yescharacteristic
40#16812620C2211yescharacteristic
41#16812620C2211yescharacteristic
42#16812619C2211yescharacteristic
43#16812619C2211yescharacteristic
44C22⋊#11724784C2211yescharacteristic
45C22⋊#11724784C2211yescharacteristic
46#16812610C2211yescharacteristic
47C4×#11724784C2211yescharacteristic
48C2×#41×C109C2211yescharacteristic
49C4×Q8×C109C2211yescharacteristic
50C4×Q8×C109C2211yescharacteristic
51C4×D4×C109—21no—
52C4×D4×C109—21no—
53C4×D4×C109C2211yescharacteristic
54C4×D4×C109C2211yescharacteristic
55#117×C109—21no—
56#117×C109C2211yescharacteristic
57C2×C4⋊C4×C109—21no—
58C2×C4⋊C4×C109C2211yescharacteristic
59C2×Dic218—21no—
60C2×Dic218C2311yescharacteristic
61C2×D436C2311yescharacteristic
62C2×C22⋊D109—21no—
63C2×C4×D109—21no—
64#13182019—22no—
65#13182017—22no—
66#13182016—22no—
67#13182014—22no—
68C2×#11724784C2311yescharacteristic
69C2×#11724784C2311yescharacteristic
70C2×#11724784C2311yescharacteristic
71C2×#11724784C2311yescharacteristic
72C4⋊Dic109—21no—
73C4⋊Dic109C2311yescharacteristic
74C4⋊Dic109C2311yescharacteristic
75#13182008—21no—
76#13182008—21no—
77C22⋊Dic109—21no—
78#13182006—21no—
79#13182006—21no—
80#13182006—21no—
81#13182006—21no—
82C4×Dic109—21no—
83#41×C109—22no—
84#41×C109—22no—
85C2×Q8×C109C2311yescharacteristic
86C2×D4×C109—21no—
87C2×D4×C109C2311yescharacteristic
88C22×C4×C109—21no—
89C22×C4×C109—21no—
90C22×C4×C109—21no—
91C22×C4×C109—21no—
92C22×C4×C109C2311yescharacteristic
93C4⋊C4×C109—21no—
94C4⋊C4×C109—21no—
95C4⋊C4×C109—21no—
96C4⋊C4×C109D411yescharacteristic
97C4⋊C4×C109D411yescharacteristic
98C4⋊C4×C109C2311yescharacteristic
99C4⋊C4×C109C2311yescharacteristic
100C22⋊C4×C109—21no—
101C22⋊C4×C109—21no—
102C22⋊C4×C109D411yescharacteristic
103C22⋊C4×C109D411yescharacteristic
104C42×C109—21no—
105C42×C109—21no—
106C42×C109C2311yescharacteristic
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C23×C109C2×D411yescharacteristic
110C22×D109—21no—
111Q8×C109—21no—
112Q8×C109#4112yes—
113D4×C109—24no—
114D4×C109—21no—
115D4×C109#4112yes—
116C2×C4×C109—24no—
117C2×C4×C109—21no—
118C2×C4×C109—21no—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—81no—
123C2×C4×C109—81no—
124C2×C4×C109—81no—
125C2×C4×C109C2×D411yescharacteristic
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2×D411yescharacteristic
130C2×C4×C109C2411yescharacteristic
131C22⋊D109—81no—
132C2×Dic109—21no—
133C2×Dic109—21no—
134C2×Dic109—21no—
135D436—21no—
136D436—21no—
137C4×D109—81no—
138Dic218—21no—
139Dic218—21no—
140Dic218—81no—
141#11724784—21no—
142#11724784—21no—
143#11724784—21no—
144#11724784—21no—
145C22×C109—21no—
146C22×C109—22no—
147C22×C109—21no—
148C22×C109—21no—
149C22×C109—41no—
150C22×C109—41no—
151C22×C109C22×D411yescharacteristic
152C2×D109—41no—
153C2×D109—41no—
154C2×D109—41no—
155C4×C109—21no—
156C4×C109—22no—
157C4×C109—21no—
158C4×C109—21no—
159C4×C109—21no—
160C4×C109—21no—
161C4×C109—41no—
162C4×C109—41no—
163C4×C109C2×#4111yescharacteristic
164C4×C109C2×#4111yescharacteristic
165Dic109—41no—
166Dic109—41no—
167Dic109—41no—
168C2×C109—41no—
169C2×C109—42no—
170C2×C109#52511yescharacteristic
171C2×C109#57611yescharacteristic
172C2×C109#57811yescharacteristic
173D109—81no—
174#3124—1091nomaximal, Sylow
175C109#312411yescharacteristic, complemented, Sylow
176#542—1091no—
177#520D10911yescharacteristic, complemented
178#484—1091no—
179#480—1091no—
180#477—1091no—
181#474—1091no—
182#464—1091no—
183#463—1091no—
184#452—1091no—
185#449—1091no—
186#440—1091no—
187#440—1091no—
188C4×Q16—1091no—
189C4×D8—1091no—
190#433—1091no—
191C2×#41C2×D10911yescharacteristic
192C2×Q16—1091no—
193C2×SD16—1091no—
194C2×SD16—1091no—
195C2×D8—1091no—
196C4⋊Q8—1091no—
197#126—2181no—
198#124—1091no—
199#124—2181no—
200#123—2181no—
201C22⋊Q8—1091no—
202C22⋊Q8—2181no—
203#121—1091no—
204C4×Q8—1091no—
205C4×Q8C2×D10911yescharacteristic
206C4×Q8C2×D10911yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—1091no—
210C4×D4C2×D10911yescharacteristic
211C4×D4C2×D10911yescharacteristic
212#117—21no—
213#117C2×D10911yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D10911yescharacteristic
216#107—1091no—
217#107—1091no—
218#107—1091no—
219#107—1091no—
220C4⋊C8—1091no—
221C4⋊C8—1091no—
222#103—1091no—
223#103—1091no—
224#103—1091no—
225#103—1091no—
226#102—1091no—
227#102—1091no—
228#102—1091no—
229#102—1091no—
230C22⋊C8—1091no—
231C22⋊C8—1091no—
232#97—1091no—
233C4×C8—1091no—
234#41—22no—
235#41—22no—
236C2×Q8—1091no—
237C2×Q8—2181no—
238C2×Q8C22×D10911yescharacteristic
239C2×D4—21no—
240C2×D4—1091no—
241C2×D4—2181no—
242C2×D4C22×D10911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2181no—
248C22×C4C22×D10911yescharacteristic
249Q16—2182no—
250SD16—2182no—
251SD16—2182no—
252D8—2182no—
253C2×C8—1091no—
254C2×C8—1091no—
255C2×C8—1091no—
256C2×C8—1091no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1091no—
261C4⋊C4—1091no—
262C4⋊C4—2181no—
263C4⋊C4—2181no—
264C4⋊C4—2181no—
265C4⋊C4C22⋊D10911yescharacteristic
266C4⋊C4C22⋊D10911yescharacteristic
267C4⋊C4C22×D10911yescharacteristic
268C4⋊C4C22×D10911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2181no—
272C22⋊C4—2181no—
273C22⋊C4—2181no—
274C22⋊C4—2181no—
275C22⋊C4—2181no—
276C22⋊C4C22⋊D10911yescharacteristic
277C22⋊C4C22⋊D10911yescharacteristic
278C42—21no—
279C42—21no—
280C42—2181no—
281C42C22×D10911yescharacteristic
282C42C22×D10911yescharacteristic
283C23—21no—
284C23—2181no—
285C23C2×C22⋊D10911yescharacteristic
286Q8—21no—
287Q8—8721no—
288Q8—2181no—
289Q8—2181no—
290Q8#1318202912yes—
291D4—24no—
292D4—21no—
293D4—8721no—
294D4—2181no—
295D4—2181no—
296D4#1318202912yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—8721no—
307C2×C4—2181no—
308C2×C4—2181no—
309C2×C4—2181no—
310C2×C4C2×C22⋊D10911yescharacteristic
311C2×C4C2×C22⋊D10911yescharacteristic
312C2×C4C2×C22⋊D10911yescharacteristic
313C2×C4C2×C22⋊D10911yescharacteristic
314C2×C4C2×C22⋊D10911yescharacteristic
315C2×C4C23×D10911yescharacteristic
316C8—2181no—
317C8—2181no—
318C8—2181no—
319C8—2181no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—4361no—
327C22—4361no—
328C22—4361no—
329C22C22×C22⋊D10911yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—4361no—
339C4—4361no—
340C4—4361no—
341C4C2×#1318202911yescharacteristic
342C4C2×#1318202911yescharacteristic
343C2—41no—
344C2—42no—
345C2—8721no—
346C2#2029553711yescharacteristic
347C2#2029582911yescharacteristic
348C2#2029584111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#520×C109C2
socleC22×C109C22×D4
prime radical#20295171C2
hypercenter#520D109
hypocenterC109#3124
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20295647C2semidirect
2. #20295361C2semidirect
3. #20295339C2semidirect
4. #20295321C2semidirect
5. #20295306C2semidirect
6. #20295248C2semidirect
7. #20295241C2semidirect
8. #20295188C2semidirect
10. #20295126C2semidirect
11. #20295124C2semidirect
12. C4×#13182019C2semidirect
13. C4×#13182014C2semidirect
14. #20295087C2semidirect
15. #520×C109C2semidirect
175. C109#3124semidirect
177. #520D109semidirect

Maximal subgroups

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

subgroupindex
#202956472
#202953612
#202953392
#202953212
#202953062
#202952482
#202952412
#202951882
#202951712
#202951262
#202951242
C4×#131820192
C4×#131820142
#202950872
#520×C1092
#3124109