Finite Group Databasebeta

← #27197859

Subgroups — #27197859

Order 13184.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693020C211yesmaximal, characteristic
2C2×C4×Dic206C211yesmaximal, characteristic
3C2×#15692986C211yesmaximal, characteristic
4#20267695C211yesmaximal, characteristic
5#20267695C211yesmaximal, characteristic
6#20267678C211yesmaximal, characteristic
7#20267677C211yesmaximal, characteristic
8#20267676C211yesmaximal, characteristic
9#20267675C211yesmaximal, characteristic
10#20267674C211yesmaximal, characteristic
11#20267673C211yesmaximal, characteristic
12#20267672C211yesmaximal, characteristic
13#20267655C211yesmaximal, characteristic
14#20267636C211yesmaximal, characteristic
15#387×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C22×Dic206C2211yescharacteristic
18#15693020C418yescomplemented
19C4×Dic206—24no—
20#15692986—24no—
21C2×C4⋊Dic103C2211yescharacteristic
22C2×C4⋊Dic103C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×Dic103⋊C4C2211yescharacteristic
29C2×C4×Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C2×C4⋊C4×C103C2211yescharacteristic
48C2×C4⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C2×Dic206—22no—
55C2×Dic206—22no—
56C2×Dic206—22no—
57C2×Dic206—22no—
58C2×Dic206C2×C414yes—
59C2×Dic206C2×C414yes—
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C4⋊Dic103—22no—
69C4⋊Dic103C2×C414yes—
70Dic103⋊C4—22no—
71Dic103⋊C4—22no—
72Dic103⋊C4—22no—
73Dic103⋊C4—22no—
74Dic103⋊C4C2×C414yes—
75Dic103⋊C4C2×C414yes—
76C4×Dic103—22no—
77C4×Dic103—22no—
78C4×Dic103—22no—
79C4×Dic103—22no—
80C4×Dic103C2×C414yes—
81C4×Dic103D414yes—
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C22×C4×C103C2311yescharacteristic
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C4⋊C4×C103—22no—
90C4⋊C4×C103C2×C414yes—
91C42×C103—22no—
92C23×C103C2411yescharacteristic
93C2×C4×C103—21no—
94C2×C4×C103—21no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103C22×C412yes—
111C2×C4×C103C22×C412yes—
112C2×C4×C103C22×C412yes—
113C2×C4×C103C2×D412yes—
114C2×Dic103—21no—
115C2×Dic103—21no—
116C2×Dic103—21no—
117C2×Dic103—21no—
118C2×Dic103—21no—
119C2×Dic103—21no—
120C2×Dic103—21no—
121C2×Dic103—21no—
122C2×Dic103—21no—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103C22×C412yes—
132C2×Dic103C22×C412yes—
133C2×Dic103C22×C412yes—
134C2×Dic103C22×C412yes—
135C2×Dic103C2×D412yes—
136C2×Dic103C2×D412yes—
137C2×Dic103#4112yes—
138Dic206—28no—
139Dic206—28no—
140C22×C103C23×C411yescharacteristic
141C22×C103C22×D411yescharacteristic
142C22×C103C2×#4111yescharacteristic
143C22×C1032−1+411yescharacteristic
144C22×C1032−1+411yescharacteristic
145C22×C1032−1+411yescharacteristic
146C22×C1032−1+411yescharacteristic
147C4×C103—22no—
148C4×C103—22no—
149C4×C103—22no—
150C4×C103—22no—
151C4×C103—41no—
152C4×C103—41no—
153C4×C103—41no—
154Dic103—22no—
155Dic103—22no—
156Dic103—22no—
157Dic103—22no—
158Dic103—41no—
159Dic103—41no—
160Dic103—41no—
161Dic103C4×D414yes—
162C2×C103C2×C4×D411yescharacteristic
163C2×C103#51911yescharacteristic
164C2×C103#51911yescharacteristic
165C2×C103#53611yescharacteristic
166C2×C103#53611yescharacteristic
167C2×C103#54111yescharacteristic
168C2×C103#54111yescharacteristic
169#2327—1031nomaximal, Sylow
170C103#232711yescharacteristic, complemented, Sylow
171C2×C4⋊Q8—1031no—
172C2×C4×Q8—1031no—
173C2×C4×Q8—1031no—
174#391—1031no—
175#391—1031no—
176#387—1031no—
177#387—1031no—
178#387—1031no—
179#387—1031no—
180#387—1031no—
181#387—1031no—
182#387—1031no—
183#387D10311yescharacteristic
184#382—1031no—
185#376—1031no—
186C22×Q8—1031no—
187C22×Q8—1031no—
188C4⋊Q8—1038no—
189C4×Q8—2064no—
190C4×Q8—2064no—
191C2×C4⋊C4—1031no—
192C2×C4⋊C4—1031no—
193C2×C4⋊C4—1031no—
194C2×C4⋊C4—1031no—
195C2×C4⋊C4—1031no—
196C2×C4⋊C4—1031no—
197C2×C4⋊C4—1031no—
198C2×C4⋊C4—1031no—
199C2×C4⋊C4C2×D10311yescharacteristic
200C2×C4⋊C4C2×D10311yescharacteristic
201C2×C42—1031no—
202C2×C42—1031no—
203C2×C42—1031no—
204C2×C42—1031no—
205C2×C42—1031no—
206C2×C42—1031no—
207C2×C42C2×D10311yescharacteristic
208#95—1031no—
209#95—1031no—
210#95—1031no—
211#95—1031no—
212#95—1031no—
213#95—1031no—
214#95—1031no—
215#95—1031no—
216#95—1031no—
217#95—1031no—
218#95—1031no—
219#95—1031no—
220#95C2×D10311yescharacteristic
221#95C2×D10311yescharacteristic
222#95C2×D10311yescharacteristic
223#95C2×D10311yescharacteristic
224C2×Q8—1034no—
225C2×Q8—1034no—
226C2×Q8—2062no—
227C2×Q8—2062no—
228C2×Q8—2062no—
229C2×Q8—2062no—
230C22×C4—1031no—
231C22×C4—1031no—
232C22×C4—1031no—
233C22×C4—1031no—
234C22×C4—1031no—
235C22×C4—1031no—
236C22×C4—1031no—
237C22×C4—1031no—
238C22×C4C22×D10311yescharacteristic
239C22×C4C22×D10311yescharacteristic
240C22×C4C22×D10311yescharacteristic
241C22×C4C22×D10311yescharacteristic
242C22×C4C22×D10311yescharacteristic
243C22×C4C22×D10311yescharacteristic
244C22×C4C22×D10311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—1034no—
247C4⋊C4—1034no—
248C4⋊C4—1034no—
249C4⋊C4—2062no—
250C4⋊C4—2062no—
251C4⋊C4—2062no—
252C4⋊C4—2062no—
253C4⋊C4—2062no—
254C4⋊C4C4×D10314yes—
255C42—22no—
256C42—1034no—
257C42—1034no—
258C42—2062no—
259C42—2062no—
260C42—2062no—
261C42—2062no—
262C23C23×D10311yescharacteristic
263Q8—2068no—
264Q8—2068no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—1032no—
283C2×C4—1032no—
284C2×C4—1032no—
285C2×C4—1032no—
286C2×C4—1032no—
287C2×C4—1032no—
288C2×C4—1032no—
289C2×C4—2061no—
290C2×C4—2061no—
291C2×C4—2061no—
292C2×C4—2061no—
293C2×C4—2061no—
294C2×C4—2061no—
295C2×C4—2061no—
296C2×C4—2061no—
297C2×C4—2061no—
298C2×C4—2061no—
299C2×C4—2061no—
300C2×C4—2061no—
301C2×C4—2061no—
302C2×C4—2061no—
303C2×C4—2061no—
304C2×C4—2061no—
305C2×C4—2061no—
306C2×C4C2×C4×D10312yes—
307C2×C4C2×C4×D10312yes—
308C2×C4C2×C4×D10312yes—
309C2×C4D4×D10312yes—
310C22C22×C4×D10311yescharacteristic
311C22C2×D4×D10311yescharacteristic
312C22#41×D10311yescharacteristic
313C22#1569306811yescharacteristic
314C22#1569306811yescharacteristic
315C22#1569306811yescharacteristic
316C22#1569306911yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1034no—
325C4—4121no—
326C4—4121no—
327C4—4121no—
328C4—2062no—
329C4—2062no—
330C4—2062no—
331C4—2062no—
332C2C4×D4×D10311yescharacteristic
333C2#2026826711yescharacteristic
334C2#2026826811yescharacteristic
335C2#2026836311yescharacteristic
336C2#2026836411yescharacteristic
337C2#2026839811yescharacteristic
338C2#2026840011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#387D103
hypocenterC103#2327
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #15693020C4semidirect
170. C103#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#156930202
C2×C4×Dic2062
C2×#156929862
#202676952
#202676782
#202676772
#202676762
#202676752
#202676742
#202676732
#202676722
#202676552
#202676362
#387×C1032
#2327103