Finite Group Databasebeta

← #27205374

Subgroups — #27205374

Order 13184.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268414C211yesmaximal, characteristic
2#20268269C211yesmaximal, characteristic, complemented
3#20268129C211yesmaximal, characteristic, complemented
4#20268116C211yesmaximal, characteristic
5#20268084C211yesmaximal, characteristic, complemented
6#20268074C211yesmaximal, characteristic, complemented
7#20268015C211yesmaximal, characteristic, complemented
8#20268015C211yesmaximal, characteristic, complemented
9#20267930C211yesmaximal, characteristic
10#20267898C211yesmaximal, characteristic, complemented
11#20267894C211yesmaximal, characteristic, complemented
12Q16×Dic103C211yesmaximal, characteristic, complemented
13#20267876C211yesmaximal, characteristic, complemented
14#20267849C211yesmaximal, characteristic, complemented
15#451×C103C211yesmaximal, characteristic, complemented
16C2×#13110092C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18#15693020C2211yescharacteristic
19#15693016—21no—
20#15693010C2211yescharacteristic
21#15693007—21no—
22#15693003—21no—
23#15693001—21no—
24#15692995C2211yescharacteristic
25Q8×Dic103—21no—
26Q8×Dic103—21no—
27Q8×Dic103C2211yescharacteristic
28Q8×Dic103C2211yescharacteristic
29Q8×Dic103C2211yescharacteristic
30Q8×Dic103C2211yescharacteristic
31Q8×Dic103C2211yescharacteristic
32#15692983C2211yescharacteristic
33#15692980—21no—
34#15692980—21no—
35#15692980C2211yescharacteristic
36#15692980C2211yescharacteristic
37#15692955C2211yescharacteristic
38#15692954C2211yescharacteristic
39#15692953C2211yescharacteristic
40#15692952C2211yescharacteristic
41Dic103⋊C8C2211yescharacteristic
42Dic103⋊C8C2211yescharacteristic
43#15692945C2211yescharacteristic
44#15692945C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692945C2211yescharacteristic
47#15692943C2211yescharacteristic
48#15692943C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50#15692931C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C22×Q8×C103C2211yescharacteristic
53C2×Q16×C103C2211yescharacteristic
54C2×Q16×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58C22⋊C8×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×D412C2311yescharacteristic
61C2×C22⋊D103—21no—
62C2×C4×D103—21no—
63#13110092—22no—
64#13110092—22no—
65C2×C103⋊C8C2311yescharacteristic
66C2×C103⋊C8C2311yescharacteristic
67C4⋊Dic103—21no—
68C4⋊Dic103—21no—
69C4⋊Dic103—21no—
70C4⋊Dic103—21no—
71C4⋊Dic103—21no—
72C4⋊Dic103D411yescharacteristic
73C4⋊Dic103D411yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78C22⋊Dic103—21no—
79C22⋊Dic103D411yescharacteristic
80C22⋊Dic103D411yescharacteristic
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84(C2×D103)⋊C4—21no—
85C4×Dic103—21no—
86C4×Dic103—21no—
87C4×Dic103—21no—
88C4×Dic103—21no—
89C4×Dic103—21no—
90C4×Dic103—21no—
91C4×Dic103C2311yescharacteristic
92C4×Dic103C2311yescharacteristic
93C2×Q8×C103—22no—
94C2×Q8×C103—22no—
95C2×Q8×C103—21no—
96C2×Q8×C103C2311yescharacteristic
97C2×Q8×C103C2311yescharacteristic
98C2×Q8×C103C2311yescharacteristic
99C22×C4×C103—21no—
100C22×C4×C103C2311yescharacteristic
101Q16×C103—22no—
102Q16×C103—22no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C23×C103C2×D411yescharacteristic
109C22×D103—21no—
110Q8×C103—24no—
111Q8×C103—21no—
112Q8×C103—21no—
113Q8×C103—21no—
114Q8×C103—21no—
115Q8×C103#4112yes—
116Q8×C103#4112yes—
117C2×C4×C103—24no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—81no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103C2×D411yescharacteristic
131C2×Dic103C2×D411yescharacteristic
132C2×Dic103C2×D411yescharacteristic
133C2×Dic103C2×D411yescharacteristic
134D412—21no—
135D412—21no—
136C4×D103—81no—
137Dic206—81no—
138C8×C103—21no—
139C8×C103—21no—
140C103⋊C8—21no—
141C103⋊C8—21no—
142C22×C103—21no—
143C22×C103—21no—
144C22×C103—21no—
145C22×C103C22×D411yescharacteristic
146C2×D103—41no—
147C2×D103—41no—
148C2×D103—41no—
149C4×C103—22no—
150C4×C103—22no—
151C4×C103—21no—
152C4×C103—41no—
153C4×C103—41no—
154C4×C103C2×#4111yescharacteristic
155C4×C103C2×#4111yescharacteristic
156Dic103—21no—
157Dic103—21no—
158Dic103—21no—
159Dic103—21no—
160Dic103—41no—
161Dic103—41no—
162Dic103—41no—
163C2×C103—41no—
164C2×C103#52511yescharacteristic
165C2×C103#57711yescharacteristic
166C2×C103#57811yescharacteristic
167D103—81no—
168#3121—1031nomaximal, Sylow
169C103#312111yescharacteristic, complemented, Sylow
170#542—1031no—
171#519—1031no—
172#485—1031no—
173#482—1031no—
174#477—1031no—
175#475—1031no—
176#464—1031no—
177#464—1031no—
178#451D10311yescharacteristic, complemented
179#448—1031no—
180#441—1031no—
181#440—1031no—
182C4×Q16—1031no—
183C4×SD16—1031no—
184#433—1031no—
185C22×Q8C2×D10311yescharacteristic
186C2×Q16C2×D10311yescharacteristic
187C2×Q16C2×D10311yescharacteristic
188C2×SD16—1031no—
189C2×SD16—1031no—
190C4⋊Q8—1031no—
191#126—2061no—
192#124—1031no—
193#124—2061no—
194#123—2061no—
195C22⋊Q8—2061no—
196C22⋊Q8C2×D10311yescharacteristic
197#121—1031no—
198C4×Q8—1031no—
199C4×Q8—1031no—
200C4×Q8—1031no—
201C4×Q8—1031no—
202C4×Q8—1031no—
203C4×Q8—2061no—
204C4×Q8—2061no—
205C4×D4—1031no—
206#117—1031no—
207#117—1031no—
208#117—2061no—
209#117—2061no—
210#107—1031no—
211#107—1031no—
212#106—1031no—
213#106—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216#103—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103C2×D10311yescharacteristic
221#103C2×D10311yescharacteristic
222#102—1031no—
223#102—1031no—
224C22⋊C8—1031no—
225C22⋊C8C2×D10311yescharacteristic
226#97—1031no—
227C4×C8—1031no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—2061no—
232C2×Q8C22×D10311yescharacteristic
233C2×Q8C22×D10311yescharacteristic
234C2×Q8C22×D10311yescharacteristic
235C2×D4—1031no—
236C2×D4—2061no—
237C22×C4—21no—
238C22×C4—2061no—
239C22×C4C22×D10311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—2062no—
243SD16—2062no—
244C2×C8—1031no—
245C2×C8—1031no—
246C2×C8C22×D10311yescharacteristic
247C2×C8C22×D10311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—1031no—
250C4⋊C4—1031no—
251C4⋊C4—1031no—
252C4⋊C4—1031no—
253C4⋊C4—1031no—
254C4⋊C4—2061no—
255C4⋊C4—2061no—
256C4⋊C4—2061no—
257C4⋊C4—2061no—
258C4⋊C4—2061no—
259C4⋊C4—2061no—
260C4⋊C4C22×D10311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—1031no—
263C22⋊C4—1031no—
264C22⋊C4—2061no—
265C22⋊C4—2061no—
266C22⋊C4—2061no—
267C22⋊C4—2061no—
268C22⋊C4—2061no—
269C42—1031no—
270C42—1031no—
271C42—2061no—
272C42—2061no—
273C42—2061no—
274C42—2061no—
275C42—2061no—
276C42—2061no—
277C23—2061no—
278C23D4×D10311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—8241no—
285Q8#1311010412yes—
286Q8#1311010412yes—
287D4—8241no—
288D4—2061no—
289D4—2061no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—8241no—
298C2×C4—1031no—
299C2×C4—1031no—
300C2×C4—1031no—
301C2×C4—1031no—
302C2×C4—2061no—
303C2×C4—2061no—
304C2×C4—2061no—
305C2×C4D4×D10311yescharacteristic
306C2×C4C23×D10311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2061no—
310C8—2061no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4121no—
315C22—4121no—
316C22—4121no—
317C22C2×D4×D10311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—4121no—
324C4—4121no—
325C4—4121no—
326C4—2061no—
327C4—2061no—
328C4—2061no—
329C4—2061no—
330C4C2×#1311010411yescharacteristic
331C4C2×#1311010411yescharacteristic
332C2—41no—
333C2—8241no—
334C2#2026829711yescharacteristic
335C2#2026860011yescharacteristic
336C2#2026860411yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#451×C103C2
socleC22×C103C22×D4
prime radical#15692995C22
hypercenter#451D103
hypocenterC103#3121
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #20268269C2semidirect
3. #20268129C2semidirect
5. #20268084C2semidirect
6. #20268074C2semidirect
7. #20268015C2semidirect
8. #20268015C2semidirect
10. #20267898C2semidirect
11. #20267894C2semidirect
12. Q16×Dic103C2semidirect
13. #20267876C2semidirect
14. #20267849C2semidirect
15. #451×C103C2semidirect
169. C103#3121semidirect
178. #451D103semidirect

Maximal subgroups

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

subgroupindex
#202684142
#202682692
#202681292
#202681162
#202680842
#202680742
#202680152
#202679302
#202678982
#202678942
Q16×Dic1032
#202678762
#202678492
#451×C1032
#3121103