Finite Group Databasebeta

← #27204104

Subgroups — #27204104

Order 13184.

412 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
1C4×#13110104C211yesmaximal, characteristic
2#20267920C211yesmaximal, characteristic, complemented
3#20267919C211yesmaximal, characteristic, complemented
4#20267867C211yesmaximal, characteristic, complemented
5#20267866C211yesmaximal, characteristic, complemented
6#20267863C211yesmaximal, characteristic, complemented
7#20267862C211yesmaximal, characteristic, complemented
8#20267859C211yesmaximal, characteristic, complemented
9#20267843C211yesmaximal, characteristic, complemented
10#20267841C211yesmaximal, characteristic, complemented
11#20267841C211yesmaximal, characteristic, complemented
12#20267743C211yesmaximal, characteristic, complemented
13M16×Dic103C211yesmaximal, characteristic, complemented
14C2×C8×Dic103C211yesmaximal, characteristic, complemented
15#435×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C411yescharacteristic
17C2×#13110089C2211yescharacteristic
18C2×#13110088C2211yescharacteristic
19C2×#13110088C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic
21C4×Dic206C2211yescharacteristic
22#15692986C411yescharacteristic
23D4×Dic103C411yescharacteristic
24C4×C22⋊D103C2211yescharacteristic
25C4×C22⋊D103C2211yescharacteristic
26(C22⋊D103)⋊C4C411yescharacteristic
27(C22⋊D103)⋊C4C411yescharacteristic
28#15692979C411yescharacteristic
29#15692977C411yescharacteristic
30#15692977C411yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C42×D103C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35Dic103⋊C8C2211yescharacteristic
36Dic103⋊C8C2211yescharacteristic
37Dic103⋊C8C2211yescharacteristic
38Dic103⋊C8C2211yescharacteristic
39C22⋊(C103⋊C8)C2211yescharacteristic
40C22⋊(C103⋊C8)C2211yescharacteristic
41(C2×D103)⋊C8C2211yescharacteristic
42(C2×D103)⋊C8C2211yescharacteristic
43#15692932C2211yescharacteristic
44#15692931C2211yescharacteristic
45#15692931C2211yescharacteristic
46C8×Dic103C2211yescharacteristic
47C8×Dic103C2211yescharacteristic
48C8×Dic103C2211yescharacteristic
49C8×Dic103C2211yescharacteristic
50C8×Dic103C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C2×M16×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54C4×D4×C103C2211yescharacteristic
55C4⋊C8×C103C2211yescharacteristic
56C22⋊C8×C103C2211yescharacteristic
57C22⋊C8×C103C2211yescharacteristic
58#97×C103C2211yescharacteristic
59#13110104—24no—
60C2×Dic206C2×C411yescharacteristic
61C2×C22⋊D103C2×C411yescharacteristic
62C2×C22⋊D103C2×C411yescharacteristic
63C22×Dic103C2×C411yescharacteristic
64C22×Dic103C2×C411yescharacteristic
65C22×Dic103C2×C411yescharacteristic
66C22×Dic103C2×C411yescharacteristic
67C2×C4×D103C2×C411yescharacteristic
68C2×C4×D103C2×C411yescharacteristic
69C2×C4×D103C2311yescharacteristic
70#13110089—22no—
71#13110088—22no—
72#13110088—22no—
73C2×C103⋊C8—22no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C4⋊Dic103C2×C411yescharacteristic
79Dic103⋊C4C2×C411yescharacteristic
80Dic103⋊C4C2×C411yescharacteristic
81Dic103⋊C4C2×C411yescharacteristic
82Dic103⋊C4C2×C411yescharacteristic
83C22⋊Dic103C2×C411yescharacteristic
84C22⋊Dic103C2×C411yescharacteristic
85(C2×D103)⋊C4C2×C411yescharacteristic
86(C2×D103)⋊C4C2×C411yescharacteristic
87C4×Dic103C2×C411yescharacteristic
88C4×Dic103C2×C411yescharacteristic
89C4×Dic103C2×C411yescharacteristic
90C4×Dic103C2×C411yescharacteristic
91C4×Dic103C2×C411yescharacteristic
92C4×Dic103C2×C411yescharacteristic
93C4×Dic103C2311yescharacteristic
94C4×Dic103C2311yescharacteristic
95C4×Dic103C2311yescharacteristic
96C2×D4×C103C2×C411yescharacteristic
97C22×C4×C103C2311yescharacteristic
98C22×C4×C103C2311yescharacteristic
99M16×C103—22no—
100C2×C8×C103—22no—
101C2×C8×C103C2311yescharacteristic
102C2×C8×C103C2311yescharacteristic
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103C2×C411yescharacteristic
106C22⋊C4×C103C2×C411yescharacteristic
107C22⋊C4×C103C2×C411yescharacteristic
108C42×C103C2311yescharacteristic
109C23×C103C22×C411yescharacteristic
110C23×C103C22×C411yescharacteristic
111C22×D103C22×C411yescharacteristic
112D4×C103—22no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103C22×C411yescharacteristic
118C2×C4×C103C22×C411yescharacteristic
119C2×C4×C103C22×C411yescharacteristic
120C2×C4×C103C22×C411yescharacteristic
121C2×C4×C103C2411yescharacteristic
122C22⋊D103—22no—
123C22⋊D103—22no—
124C2×Dic103—22no—
125C2×Dic103—22no—
126C2×Dic103—22no—
127C2×Dic103M1614yescomplemented
128C2×Dic103C22×C411yescharacteristic
129C2×Dic103C22×C411yescharacteristic
130C2×Dic103C22×C411yescharacteristic
131C2×Dic103C22×C411yescharacteristic
132C2×Dic103C22×C411yescharacteristic
133C2×Dic103C22×C411yescharacteristic
134C2×Dic103C22×C411yescharacteristic
135C4×D103—21no—
136C4×D103—21no—
137C4×D103—22no—
138C4×D103—22no—
139Dic206—22no—
140C8×C103—21no—
141C8×C103—21no—
142C8×C103—21no—
143C8×C103#4112yescomplemented
144C103⋊C8—21no—
145C103⋊C8—21no—
146C103⋊C8—21no—
147C103⋊C8#4112yescomplemented
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103—21no—
153C22×C103C2×M1612yes—
154C22×C103C23×C411yescharacteristic
155C2×D103—21no—
156C2×D103—21no—
157C2×D103—21no—
158C4×C103—21no—
159C4×C103—21no—
160C4×C103—21no—
161C4×C103—21no—
162C4×C103C2×#4111yescharacteristic
163C4×C103C2×#4111yescharacteristic
164Dic103—21no—
165Dic103—21no—
166Dic103—21no—
167Dic103—21no—
168Dic103C2×M1612yes—
169Dic103C2×M1612yes—
170Dic103#13112yes—
171C2×C103—22no—
172C2×C103—41no—
173C2×C103C4×#4111yescharacteristic
174C2×C103C22×M1611yescharacteristic
175C2×C103C2×#13111yescharacteristic
176D103—41no—
177#2965—1031nomaximal, Sylow
178C103#296511yescharacteristic, complemented, Sylow
179C4×#41—1031no—
180#446—1031no—
181#446—1031no—
182#436—1031no—
183#436—1031no—
184#435—1031no—
185#435—1031no—
186#435—1031no—
187#435D10311yescharacteristic, complemented
188#431—1031no—
189#431—1031no—
190#431—1031no—
191C4×M16—1031no—
192C4×M16—1031no—
193C2×C4×C8—1031no—
194C2×#41—1031no—
195C2×M16—1031no—
196C2×M16—1031no—
197C2×M16—1031no—
198C2×M16C2×D10311yescharacteristic
199C22×C8—1031no—
200C22×C8C2×D10311yescharacteristic
201C4×Q8—1031no—
202C4×Q8—1031no—
203C4×D4—1031no—
204C4×D4—1031no—
205C4×D4—1031no—
206C4×D4—1031no—
207C4×D4—1031no—
208C4×D4C2×D10311yescharacteristic
209#117—1031no—
210#117—1031no—
211#117—1031no—
212C2×C42—1031no—
213C2×C42—1031no—
214C2×C42—1031no—
215C4⋊C8—1031no—
216C4⋊C8—1031no—
217C4⋊C8—1031no—
218C4⋊C8—1031no—
219C4⋊C8—1031no—
220C4⋊C8C2×D10311yescharacteristic
221C22⋊C8—1031no—
222C22⋊C8—1031no—
223C22⋊C8—1031no—
224C22⋊C8—1031no—
225C22⋊C8C2×D10311yescharacteristic
226C22⋊C8C2×D10311yescharacteristic
227#97—1031no—
228#97—1031no—
229#97—1031no—
230#97C2×D10311yescharacteristic
231C4×C8—1031no—
232C4×C8—1031no—
233C4×C8—1031no—
234C4×C8—1031no—
235C4×C8—1031no—
236C4×C8—1031no—
237#41—2064no—
238C2×Q8—1031no—
239C2×D4—1031no—
240C2×D4—1031no—
241C2×D4C4×D10311yescharacteristic
242C22×C4—1031no—
243C22×C4—1031no—
244C22×C4—1031no—
245C22×C4—1031no—
246C22×C4—1031no—
247C22×C4—1031no—
248C22×C4—1031no—
249C22×C4C22×D10311yescharacteristic
250C22×C4C22×D10311yescharacteristic
251M16—22no—
252M16—2062no—
253M16—2062no—
254M16—2062no—
255C2×C8—22no—
256C2×C8—1031no—
257C2×C8—1031no—
258C2×C8—1031no—
259C2×C8—1031no—
260C2×C8—2062no—
261C2×C8C22×D10311yescharacteristic
262C2×C8C22×D10311yescharacteristic
263C2×C8C22×D10311yescharacteristic
264C2×C8C22×D10311yescharacteristic
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4C4×D10311yescharacteristic
271C22⋊C4—1031no—
272C22⋊C4—1031no—
273C22⋊C4—1031no—
274C22⋊C4—1031no—
275C22⋊C4C4×D10311yescharacteristic
276C22⋊C4C4×D10311yescharacteristic
277C42—1031no—
278C42—1031no—
279C42—1031no—
280C42—1031no—
281C42—1031no—
282C42—1031no—
283C42—1031no—
284C42—1031no—
285C42—1031no—
286C42C22×D10311yescharacteristic
287C23—1031no—
288C23C2×C4×D10311yescharacteristic
289C23C2×C4×D10311yescharacteristic
290Q8—2062no—
291D4—22no—
292D4—2062no—
293D4—2062no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1034no—
299C2×C4—1031no—
300C2×C4—1031no—
301C2×C4—1031no—
302C2×C4—1031no—
303C2×C4—1031no—
304C2×C4—1031no—
305C2×C4—1031no—
306C2×C4—2062no—
307C2×C4—2062no—
308C2×C4—2062no—
309C2×C4—2062no—
310C2×C4—2062no—
311C2×C4—2061no—
312C2×C4—2061no—
313C2×C4C2×C4×D10311yescharacteristic
314C2×C4C2×C4×D10311yescharacteristic
315C2×C4C2×C4×D10311yescharacteristic
316C2×C4C2×C4×D10311yescharacteristic
317C2×C4C23×D10311yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—1032no—
322C8—2061no—
323C8—2061no—
324C8—2061no—
325C8#1311010412yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—2061no—
332C22—2061no—
333C22—2061no—
334C22M16×D10312yes—
335C22C22×C4×D10311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—1032no—
341C4—1032no—
342C4—1032no—
343C4—2061no—
344C4—2061no—
345C4—2061no—
346C4—2061no—
347C4#41×D10311yescharacteristic
348C4C2×#1311010411yescharacteristic
349C2—22no—
350C2—41no—
351C2—4121no—
352C2C4×#1311010411yescharacteristic
353C2C2×M16×D10311yescharacteristic
354C2#131×D10311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D103
commutator, socleC22×C103C23×C4
Fitting#435×C103C2
prime radicalC2×#13110104C4
cosocleC2×C4×C103C24
hypercenter#435D103
hypocenterC103#2965
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #20267920C2semidirect
3. #20267919C2semidirect
4. #20267867C2semidirect
5. #20267866C2semidirect
6. #20267863C2semidirect
7. #20267862C2semidirect
8. #20267859C2semidirect
9. #20267843C2semidirect
10. #20267841C2semidirect
11. #20267841C2semidirect
12. #20267743C2semidirect
13. M16×Dic103C2semidirect
14. C2×C8×Dic103C2semidirect
15. #435×C103C2semidirect
127. C2×Dic103M16semidirect
143. C8×C103#41semidirect
147. C103⋊C8#41semidirect
178. C103#2965semidirect
187. #435D103semidirect
325. C8#13110104semidirect

Maximal subgroups

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

subgroupindex
C4×#131101042
#202679202
#202679192
#202678672
#202678662
#202678632
#202678622
#202678592
#202678432
#202678412
#202677432
M16×Dic1032
C2×C8×Dic1032
#435×C1032
#2965103