Finite Group Databasebeta

← #27203982

Subgroups — #27203982

Order 13184.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693053C211yesmaximal, characteristic
2#20268273C211yesmaximal, characteristic
3#20268267C211yesmaximal, characteristic, complemented
4#20267898C211yesmaximal, characteristic, complemented
5#20267896C211yesmaximal, characteristic, complemented
6#20267890C211yesmaximal, characteristic, complemented
7#20267889C211yesmaximal, characteristic, complemented
8#20267883C211yesmaximal, characteristic, complemented
9C4×#13110094C211yesmaximal, characteristic, complemented
10#20267876C211yesmaximal, characteristic, complemented
11#20267832C211yesmaximal, characteristic, complemented
12#20267786C211yesmaximal, characteristic
13#103×D103C211yesmaximal, characteristic, complemented
14#20267745C211yesmaximal, characteristic, complemented
15C4×Q16×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×Q8×D103C2211yescharacteristic
18#15693053C418yescomplemented
19C2×#13110095C2211yescharacteristic
20C2×#13110094C2211yescharacteristic
21C2×#13110092C2211yescharacteristic
22C2×#13110088C2211yescharacteristic
23C2×C8×D103C2211yescharacteristic
24Q8×Dic103C2211yescharacteristic
25Q8×Dic103C2211yescharacteristic
26C4×Dic206—21no—
27C4×Dic206C2211yescharacteristic
28#15692986—21no—
29#15692986C2211yescharacteristic
30C4×D412—21no—
31C4×D412C2211yescharacteristic
32#15692983—21no—
33#15692983C2211yescharacteristic
34#15692979—21no—
35#15692979C2211yescharacteristic
36#15692978—21no—
37#15692978—21no—
38#15692978C2211yescharacteristic
39C4⋊C4×D103—21no—
40C4⋊C4×D103C2211yescharacteristic
41#15692954C2211yescharacteristic
42#15692953C2211yescharacteristic
43#15692952C2211yescharacteristic
44#15692946C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692945C2211yescharacteristic
47#15692944C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692941C2211yescharacteristic
50#15692932C2211yescharacteristic
51#15692931C2211yescharacteristic
52C8×Dic103C2211yescharacteristic
53C2×Q16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic
55C4×Q8×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#103×C103C2211yescharacteristic
59C4×C8×C103C2211yescharacteristic
60#13110106—22no—
61#13110106C2×C414yes—
62C2×Dic206—21no—
63C2×Dic206C2311yescharacteristic
64Q8×D103—22no—
65Q8×D103C2×C414yescomplemented
66C2×D412—21no—
67C2×D412C2311yescharacteristic
68C2×C4×D103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103C2311yescharacteristic
74#13110095C2×C414yescomplemented
75#13110094C2×C414yescomplemented
76#13110092C2×C414yescomplemented
77#13110088C2×C414yescomplemented
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C8×D103—22no—
81C4⋊Dic103—21no—
82C4⋊Dic103—21no—
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4D411yescharacteristic
89Dic103⋊C4D411yescharacteristic
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103—21no—
100C4×Dic103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C2×Q8×C103C2311yescharacteristic
103Q16×C103C2×C414yescomplemented
104C2×C8×C103C2311yescharacteristic
105C2×C8×C103C2311yescharacteristic
106C4⋊C4×C103—21no—
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C42×C103—21no—
111C42×C103—21no—
112C42×C103C2311yescharacteristic
113C22×D103—21no—
114C22×D103C2×D411yescharacteristic
115Q8×C103—21no—
116Q8×C103—21no—
117Q8×C103C22×C412yes—
118Q8×C103C22×C412yes—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103C2×D411yescharacteristic
130C2×Dic103C2×D411yescharacteristic
131C2×Dic103C2×D411yescharacteristic
132D412—24no—
133D412—21no—
134D412C22×C412yes—
135C4×D103—24no—
136C4×D103—24no—
137C4×D103—81no—
138C4×D103—81no—
139C4×D103—81no—
140C4×D103C22×C412yes—
141C4×D103#4112yes—
142Dic206—21no—
143Dic206—24no—
144Dic206C22×C412yes—
145C8×C103—21no—
146C8×C103C22×C412yes—
147C103⋊C8—21no—
148C103⋊C8C22×C412yes—
149C22×C103C22×D411yescharacteristic
150C2×D103—21no—
151C2×D103—21no—
152C2×D103—22no—
153C2×D103—41no—
154C2×D103—41no—
155C2×D103C4×D412yes—
156C4×C103—22no—
157C4×C103—22no—
158C4×C103—21no—
159C4×C103—21no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103C23×C411yescharacteristic
163C4×C103C2×#4111yescharacteristic
164Dic103—22no—
165Dic103—21no—
166Dic103—21no—
167Dic103—41no—
168Dic103—41no—
169Dic103C4×D412yes—
170C2×C103C2×C4×D411yescharacteristic
171C2×C103#57711yescharacteristic
172C2×C103#57811yescharacteristic
173D103—22no—
174D103—42no—
175#2947—1031nomaximal, Sylow
176C103#294711yescharacteristic, complemented, Sylow
177C2×#137—1031no—
178#520—1031no—
179#519—1031no—
180#441—1031no—
181#441—1031no—
182#440—1031no—
183#440—1031no—
184C4×Q16—1031no—
185C4×Q16D10311yescharacteristic, complemented
186C4×SD16—1031no—
187C4×SD16—1031no—
188#428—1031no—
189#416—1031no—
190C2×#103—1031no—
191#405—1031no—
192C2×#41—1031no—
193C22×Q8—1031no—
194#137—1038no—
195C2×Q16—1031no—
196C2×Q16C2×D10311yescharacteristic
197C2×SD16—1031no—
198C2×SD16—1031no—
199C2×M16—1031no—
200C22×C8—1031no—
201C4×Q8—1031no—
202C4×Q8—1031no—
203C4×Q8—1031no—
204C4×Q8—1031no—
205C4×Q8—2061no—
206C4×Q8—2061no—
207C4×Q8C2×D10311yescharacteristic
208C4×Q8C2×D10311yescharacteristic
209C4×D4—1031no—
210C4×D4—1031no—
211C4×D4—2061no—
212C4×D4—2061no—
213#117—1031no—
214#117—1031no—
215#117—2061no—
216#117—2061no—
217#117—2061no—
218C2×C4⋊C4—1031no—
219C2×C4⋊C4—2061no—
220#107—1031no—
221#107C2×D10311yescharacteristic
222#106—1031no—
223#106—1031no—
224#103—1031no—
225#103—1031no—
226#103—1031no—
227#103—1031no—
228#103C2×D10311yescharacteristic
229#103C2×D10311yescharacteristic
230#102—1031no—
231#102—1031no—
232#97—1031no—
233#97—1031no—
234C4×C8—1031no—
235C4×C8C2×D10311yescharacteristic
236#41—1034no—
237#41—2062no—
238C2×Q8—1034no—
239C2×Q8—1031no—
240C2×Q8—2061no—
241C2×Q8—2062no—
242C2×Q8C22×D10311yescharacteristic
243C2×Q8C22×D10311yescharacteristic
244C2×D4—1031no—
245C2×D4—2061no—
246C22×C4—1031no—
247C22×C4—2061no—
248C22×C4—2061no—
249C22×C4—2061no—
250C22×C4—2061no—
251C22×C4—2061no—
252Q16—1034no—
253Q16C4×D10314yescomplemented
254SD16—1034no—
255SD16—1034no—
256M16—1034no—
257C2×C8—1031no—
258C2×C8—1031no—
259C2×C8—2062no—
260C2×C8C22×D10311yescharacteristic
261C2×C8C22×D10311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—2061no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22×D10311yescharacteristic
274C4⋊C4C22×D10311yescharacteristic
275C22⋊C4—1031no—
276C22⋊C4—1031no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C42—21no—
281C42—21no—
282C42—1031no—
283C42—2061no—
284C42—2061no—
285C42—2061no—
286C42—2061no—
287C42—2061no—
288C42C22×D10311yescharacteristic
289C23—1031no—
290C23—2061no—
291Q8—21no—
292Q8—21no—
293Q8—1032no—
294Q8—2064no—
295Q8—2061no—
296Q8C2×C4×D10312yes—
297Q8C2×C4×D10312yes—
298D4—1032no—
299D4—2064no—
300D4—2061no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—8241no—
306C2×C4—8241no—
307C2×C4—8241no—
308C2×C4—1031no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1031no—
312C2×C4—1031no—
313C2×C4—2064no—
314C2×C4—2064no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4D4×D10311yescharacteristic
319C2×C4D4×D10311yescharacteristic
320C2×C4C23×D10311yescharacteristic
321C8—21no—
322C8—1032no—
323C8—2061no—
324C8C2×C4×D10312yes—
325C22—1032no—
326C22—4121no—
327C22—4121no—
328C22—2062no—
329C22—2061no—
330C22—2061no—
331C22C2×D4×D10311yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—1032no—
339C4—4121no—
340C4—4121no—
341C4—2061no—
342C4—2061no—
343C4—2062no—
344C4C22×C4×D10311yescharacteristic
345C4#41×D10311yescharacteristic
346C2—4122no—
347C2—2062no—
348C2C4×D4×D10311yescharacteristic
349C2#2026859811yescharacteristic
350C2#2026860411yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
FittingC4×Q16×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110106C22
cosocleC2×C4×C103C24
hypercenterC4×Q16D103
hypocenterC103#2947
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #20268267C2semidirect
4. #20267898C2semidirect
5. #20267896C2semidirect
6. #20267890C2semidirect
7. #20267889C2semidirect
8. #20267883C2semidirect
9. C4×#13110094C2semidirect
10. #20267876C2semidirect
11. #20267832C2semidirect
13. #103×D103C2semidirect
14. #20267745C2semidirect
15. C4×Q16×C103C2semidirect
18. #15693053C4semidirect
65. Q8×D103C2×C4semidirect
74. #13110095C2×C4semidirect
75. #13110094C2×C4semidirect
76. #13110092C2×C4semidirect
77. #13110088C2×C4semidirect
103. Q16×C103C2×C4semidirect
176. C103#2947semidirect
185. C4×Q16D103semidirect
253. Q16C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930532
#202682732
#202682672
#202678982
#202678962
#202678902
#202678892
#202678832
C4×#131100942
#202678762
#202678322
#202677862
#103×D1032
#202677452
C4×Q16×C1032
#2947103