Finite Group Databasebeta

← #27203960

Subgroups — #27203960

Order 13184.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693053C211yesmaximal, characteristic
2C4×#13110106C211yesmaximal, characteristic
3C4×Q8×D103C211yesmaximal, characteristic, complemented
4#20267896C211yesmaximal, characteristic, complemented
5#20267893C211yesmaximal, characteristic, complemented
6#20267889C211yesmaximal, characteristic, complemented
7Q16×Dic103C211yesmaximal, characteristic, complemented
8#20267883C211yesmaximal, characteristic, complemented
9#20267878C211yesmaximal, characteristic, complemented
10#20267876C211yesmaximal, characteristic, complemented
11#20267830C211yesmaximal, characteristic, complemented
12#20267798C211yesmaximal, characteristic, complemented
13#20267791C211yesmaximal, characteristic
14#20267743C211yesmaximal, characteristic, complemented
15#441×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×Q8×D103C2211yescharacteristic
18#15693053C418yescomplemented
19C2×#13110095C2211yescharacteristic
20C2×#13110094C2211yescharacteristic
21C2×#13110092C2211yescharacteristic
22C2×#13110088C2211yescharacteristic
23C2×#13110088C2211yescharacteristic
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
36C4⋊C4×D103—21no—
37C4⋊C4×D103C2211yescharacteristic
38C42×D103—21no—
39C42×D103—21no—
40C42×D103C2211yescharacteristic
41#15692955C2211yescharacteristic
42#15692954C2211yescharacteristic
43#15692952C2211yescharacteristic
44#15692946C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692945C2211yescharacteristic
47#15692944C2211yescharacteristic
48#15692943C2211yescharacteristic
49#15692941C2211yescharacteristic
50#15692932C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C8×Dic103C2211yescharacteristic
53C2×Q16×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic
55C4×Q8×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#103×C103C2211yescharacteristic
59#97×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×D103D411yescharacteristic
74C2×C4×D103D411yescharacteristic
75C2×C4×D103C2311yescharacteristic
76#13110095C2×C414yescomplemented
77#13110094C2×C414yescomplemented
78#13110092C2×C414yescomplemented
79#13110088—22no—
80#13110088C2×C414yescomplemented
81C2×C103⋊C8C2311yescharacteristic
82C2×C103⋊C8C2311yescharacteristic
83C4⋊Dic103—21no—
84C4⋊Dic103—21no—
85C4⋊Dic103C2311yescharacteristic
86C4⋊Dic103C2311yescharacteristic
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93C4×Dic103—21no—
94C4×Dic103—21no—
95C4×Dic103—21no—
96C4×Dic103—21no—
97C4×Dic103—21no—
98C4×Dic103D411yescharacteristic
99C4×Dic103D411yescharacteristic
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—22no—
138C4×D103—41no—
139C4×D103—42no—
140C4×D103—42no—
141C4×D103—42no—
142C4×D103C22×C412yes—
143C4×D103#4112yes—
144Dic206—21no—
145Dic206—24no—
146Dic206C22×C412yes—
147C8×C103—21no—
148C8×C103C22×C412yes—
149C103⋊C8—21no—
150C103⋊C8C22×C412yes—
151C22×C103C22×D411yescharacteristic
152C2×D103—21no—
153C2×D103—21no—
154C2×D103—22no—
155C2×D103—41no—
156C2×D103—41no—
157C2×D103C4×D412yes—
158C4×C103—22no—
159C4×C103—22no—
160C4×C103—21no—
161C4×C103—21no—
162C4×C103—41no—
163C4×C103—41no—
164C4×C103C23×C411yescharacteristic
165C4×C103C2×#4111yescharacteristic
166Dic103—22no—
167Dic103—21no—
168Dic103—41no—
169Dic103—41no—
170Dic103C4×D412yes—
171Dic103#13712yescomplemented
172C2×C103C2×C4×D411yescharacteristic
173C2×C103C2×#13711yescharacteristic
174C2×C103#57511yescharacteristic
175D103—22no—
176D103—42no—
177C4×#137—1031nomaximal, Sylow
178C103C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1031no—
180C4×#41—1031no—
181C2×C4×Q8—1031no—
182#441—1031no—
183#441D10311yescharacteristic, complemented
184#440—1031no—
185#440—1031no—
186C4×Q16—1031no—
187C4×Q16—1031no—
188C4×SD16—1031no—
189C4×SD16—1031no—
190#428—1031no—
191#419—1031no—
192#417—1031no—
193C4×M16—1031no—
194C2×#41—1031no—
195C22×Q8—1031no—
196#137—1038no—
197C2×Q16—1031no—
198C2×Q16C2×D10311yescharacteristic
199C2×SD16—1031no—
200C2×SD16—1031no—
201C2×M16—1031no—
202C2×M16—1031no—
203C4×Q8—1031no—
204C4×Q8—1031no—
205C4×Q8—1031no—
206C4×Q8—1031no—
207C4×Q8—2061no—
208C4×Q8—2061no—
209C4×Q8C2×D10311yescharacteristic
210C4×Q8C2×D10311yescharacteristic
211C4×D4—1031no—
212C4×D4—1031no—
213C4×D4—2061no—
214C4×D4—2061no—
215#117—1031no—
216#117—2061no—
217C2×C4⋊C4—1031no—
218C2×C4⋊C4—2061no—
219C2×C42—1031no—
220C2×C42—2061no—
221C2×C42—2061no—
222#107—1031no—
223#107—1031no—
224#106—1031no—
225#106C2×D10311yescharacteristic
226#103—1031no—
227#103—1031no—
228#103—1031no—
229#103—1031no—
230#103C2×D10311yescharacteristic
231#103C2×D10311yescharacteristic
232#102—1031no—
233#102—1031no—
234#97—1031no—
235#97C2×D10311yescharacteristic
236C4×C8—1031no—
237C4×C8—1031no—
238#41—1034no—
239#41—2062no—
240C2×Q8—1034no—
241C2×Q8—1031no—
242C2×Q8—2061no—
243C2×Q8—2062no—
244C2×Q8C22×D10311yescharacteristic
245C2×Q8C22×D10311yescharacteristic
246C2×D4—1031no—
247C2×D4—2061no—
248C22×C4—1031no—
249C22×C4—1031no—
250C22×C4—1031no—
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256Q16—1034no—
257Q16C4×D10314yescomplemented
258SD16—1034no—
259SD16—1034no—
260M16—1034no—
261M16—2062no—
262C2×C8—1031no—
263C2×C8—1031no—
264C2×C8C22×D10311yescharacteristic
265C2×C8C22×D10311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4—2061no—
274C4⋊C4—2061no—
275C4⋊C4C22×D10311yescharacteristic
276C4⋊C4C22×D10311yescharacteristic
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C42—21no—
281C42—21no—
282C42—1031no—
283C42—1031no—
284C42—1031no—
285C42—2061no—
286C42—2061no—
287C42—2061no—
288C42—2061no—
289C42—2061no—
290C42C22×D10311yescharacteristic
291C23—1031no—
292C23—2061no—
293Q8—21no—
294Q8—21no—
295Q8—1032no—
296Q8—2064no—
297Q8—2061no—
298Q8C2×C4×D10312yes—
299Q8C2×C4×D10312yes—
300D4—1032no—
301D4—2064no—
302D4—2061no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1031no—
308C2×C4—1031no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1031no—
312C2×C4—4122no—
313C2×C4—4121no—
314C2×C4—4122no—
315C2×C4—4122no—
316C2×C4—2062no—
317C2×C4—2064no—
318C2×C4—2064no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4D4×D10311yescharacteristic
323C2×C4D4×D10311yescharacteristic
324C2×C4C23×D10311yescharacteristic
325C8—21no—
326C8—1032no—
327C8—2061no—
328C8C2×C4×D10312yes—
329C22—1032no—
330C22—4121no—
331C22—4121no—
332C22—2062no—
333C22—2061no—
334C22—2061no—
335C22C2×D4×D10311yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—1032no—
343C4—1032no—
344C4—4121no—
345C4—4121no—
346C4—2061no—
347C4—2062no—
348C4C22×C4×D10311yescharacteristic
349C4#41×D10311yescharacteristic
350C2—4122no—
351C2—2062no—
352C2C4×D4×D10311yescharacteristic
353C2#137×D10311yescharacteristic
354C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutatorC4×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#441×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110106C22
cosocleC2×C4×C103C24
hypercenter#441D103
hypocenterC103C4×#137
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D103C2semidirect
4. #20267896C2semidirect
5. #20267893C2semidirect
6. #20267889C2semidirect
7. Q16×Dic103C2semidirect
8. #20267883C2semidirect
9. #20267878C2semidirect
10. #20267876C2semidirect
11. #20267830C2semidirect
12. #20267798C2semidirect
14. #20267743C2semidirect
15. #441×C103C2semidirect
18. #15693053C4semidirect
65. Q8×D103C2×C4semidirect
76. #13110095C2×C4semidirect
77. #13110094C2×C4semidirect
78. #13110092C2×C4semidirect
80. #13110088C2×C4semidirect
103. Q16×C103C2×C4semidirect
171. Dic103#137semidirect
178. C103C4×#137semidirect
183. #441D103semidirect
257. Q16C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930532
C4×#131101062
C4×Q8×D1032
#202678962
#202678932
#202678892
Q16×Dic1032
#202678832
#202678782
#202678762
#202678302
#202677982
#202677912
#202677432
#441×C1032
C4×#137103