Finite Group Databasebeta

← #27205698

Subgroups — #27205698

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
1#20268343C211yesmaximal, characteristic, complemented
2#20268336C211yesmaximal, characteristic
3#20268188C211yesmaximal, characteristic, complemented
4#20268162C211yesmaximal, characteristic, complemented
5#20268140C211yesmaximal, characteristic, complemented
6#20268136C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268020C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267882C211yesmaximal, characteristic, complemented
11SD16×Dic103C211yesmaximal, characteristic, complemented
12#20267878C211yesmaximal, characteristic, complemented
13#20267876C211yesmaximal, characteristic, complemented
14C2×C8×Dic103C211yesmaximal, characteristic, complemented
15#465×C103C211yesmaximal, characteristic, complemented
16C2×#13110104—21no—
17C2×#13110094C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic
21#15693020C2211yescharacteristic
22#15693020C2211yescharacteristic
23#15693019C2211yescharacteristic
24#15693017C2211yescharacteristic
25#15693011—21no—
26#15693007—21no—
27#15693000C2211yescharacteristic
28#15692998—21no—
29#15692995C2211yescharacteristic
30#15692993—21no—
31Q8×Dic103C2211yescharacteristic
32#15692986—21no—
33#15692986C2211yescharacteristic
34D4×Dic103C2211yescharacteristic
35#15692983C2211yescharacteristic
36(C22⋊D103)⋊C4—21no—
37#15692977—21no—
38C2×C4×Dic103C2211yescharacteristic
39#15692953C2211yescharacteristic
40#15692952C2211yescharacteristic
41#15692952C2211yescharacteristic
42#15692946C2211yescharacteristic
43#15692945C2211yescharacteristic
44#15692944C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692941C2211yescharacteristic
48C8×Dic103C2211yescharacteristic
49C8×Dic103C2211yescharacteristic
50C8×Dic103C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C2×SD16×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59#13110104—44no—
60C2×Dic206—21no—
61C2×Dic206—21no—
62C2×Dic206C2311yescharacteristic
63C2×D412C2311yescharacteristic
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C22×Dic103—21no—
68C22×Dic103D411yescharacteristic
69C22×Dic103D411yescharacteristic
70C2×C4×D103—21no—
71#13110094—22no—
72#13110093—22no—
73#13110092—22no—
74C2×C103⋊C8—22no—
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C4⋊Dic103—21no—
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90C4×Dic103—21no—
91C4×Dic103—21no—
92C4×Dic103D411yescharacteristic
93C4×Dic103D411yescharacteristic
94C4×Dic103C2311yescharacteristic
95C4×Dic103C2311yescharacteristic
96C2×Q8×C103C2311yescharacteristic
97C2×D4×C103—21no—
98C2×D4×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100SD16×C103—22no—
101C2×C8×C103—22no—
102C2×C8×C103C2311yescharacteristic
103C2×C8×C103C2311yescharacteristic
104C4⋊C4×C103—21no—
105C4⋊C4×C103C2311yescharacteristic
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C22⋊C4×C103—21no—
109C23×C103—21no—
110C23×C103C2×D411yescharacteristic
111C22×D103—21no—
112Q8×C103—21no—
113Q8×C103—21no—
114D4×C103—21no—
115D4×C103—21no—
116D4×C103—42no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2411yescharacteristic
124C22⋊D103—42no—
125C22⋊D103—42no—
126C22⋊D103—42no—
127C2×Dic103—22no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—42no—
132C2×Dic103SD1614yescomplemented
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137D412—21no—
138D412—21no—
139C4×D103—42no—
140Dic206—21no—
141Dic206—21no—
142Dic206—42no—
143Dic206—42no—
144C8×C103—21no—
145C8×C103#4112yescomplemented
146C103⋊C8—21no—
147C103⋊C8#4112yescomplemented
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103C2×SD1612yes—
154C22×C103C22×D411yescharacteristic
155C2×D103—41no—
156C2×D103—41no—
157C2×D103—41no—
158C4×C103—21no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103C2×#4111yescharacteristic
163C4×C103C2×#4111yescharacteristic
164Dic103—21no—
165Dic103—41no—
166Dic103—41no—
167Dic103—41no—
168Dic103C2×SD1612yes—
169Dic103C2×SD1612yes—
170Dic103#13512yes—
171C2×C103—22no—
172C2×C103—81no—
173C2×C103#53211yescharacteristic
174C2×C103C22×SD1611yescharacteristic
175C2×C103C2×#13511yescharacteristic
176D103—81no—
177#3167—1031nomaximal, Sylow
178C103#316711yescharacteristic, complemented, Sylow
179#533—1031no—
180#532—1031no—
181#498—1031no—
182#492—1031no—
183#487—1031no—
184#486—1031no—
185#465—1031no—
186#465—1031no—
187#465—1031no—
188#465D10311yescharacteristic, complemented
189C4×SD16—1031no—
190C4×SD16—1031no—
191C4×SD16—1031no—
192C4×SD16—1031no—
193C2×C4×C8—1031no—
194C2×#41—2061no—
195C2×SD16—1031no—
196C2×SD16—1031no—
197C2×SD16—1031no—
198C2×SD16C2×D10311yescharacteristic
199C22×C8—1031no—
200C22×C8C2×D10311yescharacteristic
201C4⋊Q8—1031no—
202C4⋊Q8—1031no—
203C4⋊Q8—1031no—
204#127—1031no—
205#125—2061no—
206#124—2061no—
207C22⋊Q8—1031no—
208C22⋊Q8—2061no—
209C22⋊Q8C2×D10311yescharacteristic
210#121—1031no—
211#121—2061no—
212#121C2×D10311yescharacteristic
213C4×Q8—1031no—
214C4×Q8—1031no—
215C4×Q8—2061no—
216C4×D4—1031no—
217C4×D4—1031no—
218C4×D4—2061no—
219#117—2061no—
220C2×C42—1031no—
221#106—1031no—
222#106—1031no—
223#106—1031no—
224#106C2×D10311yescharacteristic
225#103—1031no—
226#103—1031no—
227#103—1031no—
228#103C2×D10311yescharacteristic
229#102—1031no—
230#102—1031no—
231#102—1031no—
232#102C2×D10311yescharacteristic
233C4×C8—1031no—
234C4×C8—1031no—
235C4×C8—1031no—
236C4×C8—1031no—
237#41—4124no—
238C2×Q8—1031no—
239C2×Q8—2061no—
240C2×Q8—2061no—
241C2×Q8C22×D10311yescharacteristic
242C2×D4—21no—
243C2×D4—1031no—
244C2×D4—2061no—
245C2×D4—2061no—
246C2×D4—2061no—
247C2×D4C22×D10311yescharacteristic
248C22×C4—1031no—
249C22×C4—1031no—
250C22×C4—2061no—
251C22×C4—2061no—
252C22×C4C22×D10311yescharacteristic
253SD16—22no—
254SD16—2062no—
255SD16—2062no—
256SD16—2062no—
257C2×C8—22no—
258C2×C8—1031no—
259C2×C8—1031no—
260C2×C8—2062no—
261C2×C8C22×D10311yescharacteristic
262C2×C8C22×D10311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—2061no—
267C4⋊C4—2061no—
268C4⋊C4—2061no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22×D10311yescharacteristic
274C4⋊C4C22×D10311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C42—1031no—
282C42—1031no—
283C42—1031no—
284C42—1031no—
285C42—2061no—
286C42—2061no—
287C23—21no—
288C23—2061no—
289C23D4×D10311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—4122no—
293Q8—4122no—
294Q8—2061no—
295Q8—2061no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—4122no—
300D4—4122no—
301D4—4122no—
302D4—2061no—
303D4—2061no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1031no—
310C2×C4—1031no—
311C2×C4—1031no—
312C2×C4—1034no—
313C2×C4—1031no—
314C2×C4—4122no—
315C2×C4—4122no—
316C2×C4—2062no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4D4×D10311yescharacteristic
321C2×C4C23×D10311yescharacteristic
322C8—21no—
323C8—1032no—
324C8—2061no—
325C8#1311010412yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—4121no—
332C22—4121no—
333C22—4121no—
334C22SD16×D10312yes—
335C22C2×D4×D10311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1032no—
341C4—1032no—
342C4—1032no—
343C4—4121no—
344C4—4121no—
345C4—4121no—
346C4—2061no—
347C4#41×D10311yescharacteristic
348C4C2×#1311010411yescharacteristic
349C2—22no—
350C2—81no—
351C2—8241no—
352C2#2026833611yescharacteristic
353C2C2×SD16×D10311yescharacteristic
354C2#135×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#465×C103C2
socleC22×C103C22×D4
prime radical#20268336C2
hypercenter#465D103
hypocenterC103#3167
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #20268343C2semidirect
3. #20268188C2semidirect
4. #20268162C2semidirect
5. #20268140C2semidirect
6. #20268136C2semidirect
7. #20268022C2semidirect
8. #20268020C2semidirect
9. #20268018C2semidirect
10. #20267882C2semidirect
11. SD16×Dic103C2semidirect
12. #20267878C2semidirect
13. #20267876C2semidirect
14. C2×C8×Dic103C2semidirect
15. #465×C103C2semidirect
132. C2×Dic103SD16semidirect
145. C8×C103#41semidirect
147. C103⋊C8#41semidirect
178. C103#3167semidirect
188. #465D103semidirect
325. C8#13110104semidirect

Maximal subgroups

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

subgroupindex
#202683432
#202683362
#202681882
#202681622
#202681402
#202681362
#202680222
#202680202
#202680182
#202678822
SD16×Dic1032
#202678782
#202678762
C2×C8×Dic1032
#465×C1032
#3167103