Finite Group Databasebeta

← #27205406

Subgroups — #27205406

Order 13184.

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#20268412C211yesmaximal, characteristic, complemented
2#20268126C211yesmaximal, characteristic, complemented
3#20268104C211yesmaximal, characteristic, complemented
4#20268086C211yesmaximal, characteristic, complemented
5#20268071C211yesmaximal, characteristic, complemented
6#20268013C211yesmaximal, characteristic, complemented
7#20268006C211yesmaximal, characteristic, complemented
8#20267953C211yesmaximal, characteristic, complemented
9#20267936C211yesmaximal, characteristic
10#20267891C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110095C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#520×C103C211yesmaximal, characteristic, complemented
16C2×#13110095C2211yescharacteristic
17C2×#13110093C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20#15693021C2211yescharacteristic
21#15693016—21no—
22#15693009C2211yescharacteristic
23#15693007—21no—
24#15693003—21no—
25#15693000C2211yescharacteristic
26#15692999—21no—
27#15692995C2211yescharacteristic
28C4×Dic206C2211yescharacteristic
29C4×D412C2211yescharacteristic
30#15692954C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35C4⋊(C103⋊C8)C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692944C2211yescharacteristic
39#15692944C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C4×Q8×C103C2211yescharacteristic
50C4×Q8×C103C2211yescharacteristic
51C4×D4×C103—21no—
52C4×D4×C103—21no—
53C4×D4×C103C2211yescharacteristic
54C4×D4×C103C2211yescharacteristic
55#117×C103—21no—
56#117×C103C2211yescharacteristic
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C4×D103—21no—
64#13110095—22no—
65#13110093—22no—
66#13110092—22no—
67#13110090—22no—
68C2×C103⋊C8C2311yescharacteristic
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C4⋊Dic103—21no—
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77C22⋊Dic103—21no—
78(C2×D103)⋊C4—21no—
79(C2×D103)⋊C4—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82C4×Dic103—21no—
83#41×C103—22no—
84#41×C103—22no—
85C2×Q8×C103C2311yescharacteristic
86C2×D4×C103—21no—
87C2×D4×C103C2311yescharacteristic
88C22×C4×C103—21no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103D411yescharacteristic
97C4⋊C4×C103D411yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103D411yescharacteristic
103C22⋊C4×C103D411yescharacteristic
104C42×C103—21no—
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111Q8×C103—21no—
112Q8×C103#4112yes—
113D4×C103—24no—
114D4×C103—21no—
115D4×C103#4112yes—
116C2×C4×C103—24no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—81no—
123C2×C4×C103—81no—
124C2×C4×C103—81no—
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—81no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135D412—21no—
136D412—21no—
137C4×D103—81no—
138Dic206—21no—
139Dic206—21no—
140Dic206—81no—
141C103⋊C8—21no—
142C103⋊C8—21no—
143C103⋊C8—21no—
144C103⋊C8—21no—
145C22×C103—21no—
146C22×C103—22no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103C22×D411yescharacteristic
152C2×D103—41no—
153C2×D103—41no—
154C2×D103—41no—
155C4×C103—21no—
156C4×C103—22no—
157C4×C103—21no—
158C4×C103—21no—
159C4×C103—21no—
160C4×C103—21no—
161C4×C103—41no—
162C4×C103—41no—
163C4×C103C2×#4111yescharacteristic
164C4×C103C2×#4111yescharacteristic
165Dic103—41no—
166Dic103—41no—
167Dic103—41no—
168C2×C103—41no—
169C2×C103—42no—
170C2×C103#52511yescharacteristic
171C2×C103#57611yescharacteristic
172C2×C103#57811yescharacteristic
173D103—81no—
174#3124—1031nomaximal, Sylow
175C103#312411yescharacteristic, complemented, Sylow
176#542—1031no—
177#520D10311yescharacteristic, complemented
178#484—1031no—
179#480—1031no—
180#477—1031no—
181#474—1031no—
182#464—1031no—
183#463—1031no—
184#452—1031no—
185#449—1031no—
186#440—1031no—
187#440—1031no—
188C4×Q16—1031no—
189C4×D8—1031no—
190#433—1031no—
191C2×#41C2×D10311yescharacteristic
192C2×Q16—1031no—
193C2×SD16—1031no—
194C2×SD16—1031no—
195C2×D8—1031no—
196C4⋊Q8—1031no—
197#126—2061no—
198#124—1031no—
199#124—2061no—
200#123—2061no—
201C22⋊Q8—1031no—
202C22⋊Q8—2061no—
203#121—1031no—
204C4×Q8—1031no—
205C4×Q8C2×D10311yescharacteristic
206C4×Q8C2×D10311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—1031no—
210C4×D4C2×D10311yescharacteristic
211C4×D4C2×D10311yescharacteristic
212#117—21no—
213#117C2×D10311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D10311yescharacteristic
216#107—1031no—
217#107—1031no—
218#107—1031no—
219#107—1031no—
220C4⋊C8—1031no—
221C4⋊C8—1031no—
222#103—1031no—
223#103—1031no—
224#103—1031no—
225#103—1031no—
226#102—1031no—
227#102—1031no—
228#102—1031no—
229#102—1031no—
230C22⋊C8—1031no—
231C22⋊C8—1031no—
232#97—1031no—
233C4×C8—1031no—
234#41—22no—
235#41—22no—
236C2×Q8—1031no—
237C2×Q8—2061no—
238C2×Q8C22×D10311yescharacteristic
239C2×D4—21no—
240C2×D4—1031no—
241C2×D4—2061no—
242C2×D4C22×D10311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2061no—
248C22×C4C22×D10311yescharacteristic
249Q16—2062no—
250SD16—2062no—
251SD16—2062no—
252D8—2062no—
253C2×C8—1031no—
254C2×C8—1031no—
255C2×C8—1031no—
256C2×C8—1031no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1031no—
261C4⋊C4—1031no—
262C4⋊C4—2061no—
263C4⋊C4—2061no—
264C4⋊C4—2061no—
265C4⋊C4C22⋊D10311yescharacteristic
266C4⋊C4C22⋊D10311yescharacteristic
267C4⋊C4C22×D10311yescharacteristic
268C4⋊C4C22×D10311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2061no—
272C22⋊C4—2061no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4C22⋊D10311yescharacteristic
277C22⋊C4C22⋊D10311yescharacteristic
278C42—21no—
279C42—21no—
280C42—2061no—
281C42C22×D10311yescharacteristic
282C42C22×D10311yescharacteristic
283C23—21no—
284C23—2061no—
285C23C2×C22⋊D10311yescharacteristic
286Q8—21no—
287Q8—8241no—
288Q8—2061no—
289Q8—2061no—
290Q8#1311010512yes—
291D4—24no—
292D4—21no—
293D4—8241no—
294D4—2061no—
295D4—2061no—
296D4#1311010512yes—
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—8241no—
307C2×C4—2061no—
308C2×C4—2061no—
309C2×C4—2061no—
310C2×C4C2×C22⋊D10311yescharacteristic
311C2×C4C2×C22⋊D10311yescharacteristic
312C2×C4C2×C22⋊D10311yescharacteristic
313C2×C4C2×C22⋊D10311yescharacteristic
314C2×C4C2×C22⋊D10311yescharacteristic
315C2×C4C23×D10311yescharacteristic
316C8—2061no—
317C8—2061no—
318C8—2061no—
319C8—2061no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—4121no—
327C22—4121no—
328C22—4121no—
329C22C22×C22⋊D10311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—4121no—
339C4—4121no—
340C4—4121no—
341C4C2×#1311010511yescharacteristic
342C4C2×#1311010511yescharacteristic
343C2—41no—
344C2—42no—
345C2—8241no—
346C2#2026830211yescharacteristic
347C2#2026859411yescharacteristic
348C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#520×C103C2
socleC22×C103C22×D4
prime radical#20267936C2
hypercenter#520D103
hypocenterC103#3124
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20268412C2semidirect
2. #20268126C2semidirect
3. #20268104C2semidirect
4. #20268086C2semidirect
5. #20268071C2semidirect
6. #20268013C2semidirect
7. #20268006C2semidirect
8. #20267953C2semidirect
10. #20267891C2semidirect
11. #20267889C2semidirect
12. C4×#13110095C2semidirect
13. C4×#13110090C2semidirect
14. #20267852C2semidirect
15. #520×C103C2semidirect
175. C103#3124semidirect
177. #520D103semidirect

Maximal subgroups

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

subgroupindex
#202684122
#202681262
#202681042
#202680862
#202680712
#202680132
#202680062
#202679532
#202679362
#202678912
#202678892
C4×#131100952
C4×#131100902
#202678522
#520×C1032
#3124103