Finite Group Databasebeta

← #27198003

Subgroups — #27198003

Order 13184.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692979C211yesmaximal, characteristic
2#20267677C211yesmaximal, characteristic, complemented
3#20267676C211yesmaximal, characteristic, complemented
4#20267674C211yesmaximal, characteristic, complemented
5#20267665C211yesmaximal, characteristic
6#20267662C211yesmaximal, characteristic
7#20267658C211yesmaximal, characteristic, complemented
8#20267656C211yesmaximal, characteristic, complemented
9#20267653C211yesmaximal, characteristic
10C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
11C4×(C2×D103)⋊C4C211yesmaximal, characteristic
12#20267638C211yesmaximal, characteristic
13#20267636C211yesmaximal, characteristic, complemented
14#95×D103C211yesmaximal, characteristic
15#387×C103C211yesmaximal, characteristic, complemented
16C22×C4×D103C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19#15692979C418yescomplemented
20C2×C4⋊Dic103C2211yescharacteristic
21C2×C4⋊Dic103C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×(C2×D103)⋊C4C2211yescharacteristic
25C2×(C2×D103)⋊C4C2211yescharacteristic
26C2×(C2×D103)⋊C4C2211yescharacteristic
27C2×(C2×D103)⋊C4C2211yescharacteristic
28C2×C4×Dic103C2211yescharacteristic
29C2×C4×Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C103⋊#95C2211yescharacteristic
34C103⋊#95C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C42×C103C2211yescharacteristic
48#95×C103C2211yescharacteristic
49#95×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C23×D103C2311yescharacteristic
53C22×Dic103C2311yescharacteristic
54C22×Dic103C2311yescharacteristic
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C2×C4×D103—22no—
61C2×C4×D103—22no—
62C2×C4×D103—22no—
63C2×C4×D103—22no—
64C2×C4×D103—22no—
65C2×C4×D103—22no—
66C2×C4×D103—41no—
67C2×C4×D103—41no—
68C2×C4×D103C2×C414yes—
69C4⋊Dic103—41no—
70C4⋊Dic103C2×C414yescomplemented
71Dic103⋊C4—22no—
72Dic103⋊C4—22no—
73(C2×D103)⋊C4—22no—
74(C2×D103)⋊C4—22no—
75(C2×D103)⋊C4C2×C414yes—
76(C2×D103)⋊C4C2×C414yes—
77C4×Dic103—22no—
78C4×Dic103—22no—
79C4×Dic103—41no—
80C4×Dic103C2×C414yescomplemented
81C4×Dic103C2×C414yescomplemented
82C22×C4×C103C2311yescharacteristic
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C22×C4×C103C2311yescharacteristic
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C4⋊C4×C103—41no—
90C4⋊C4×C103C2×C414yescomplemented
91C42×C103—41no—
92C23×C103C2411yescharacteristic
93C22×D103—21no—
94C22×D103—21no—
95C22×D103—21no—
96C22×D103—21no—
97C22×D103C22×C412yes—
98C22×D103#4112yes—
99C22×D103#4112yes—
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×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103C22×C412yes—
118C2×C4×C103C22×C412yes—
119C2×C4×C103C22×C412yes—
120C2×C4×C103#4112yes—
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×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103C22×C412yes—
139C2×Dic103C22×C412yes—
140C2×Dic103C22×C412yes—
141C2×Dic103#4112yes—
142C4×D103—28no—
143C4×D103—44no—
144C4×D103—44no—
145C22×C103C23×C411yescharacteristic
146C22×C103C2×#4111yescharacteristic
147C22×C103C2×#4111yescharacteristic
148C22×C103C2×#4111yescharacteristic
149C22×C103C2×#4111yescharacteristic
150C22×C103H(5,𝔽2)11yescharacteristic
151C22×C1032−1+411yescharacteristic
152C2×D103—22no—
153C2×D103—22no—
154C2×D103—22no—
155C2×D103—22no—
156C2×D103—22no—
157C2×D103—22no—
158C2×D103#11714yes—
159C4×C103—22no—
160C4×C103—22no—
161C4×C103—22no—
162C4×C103—22no—
163C4×C103—41no—
164C4×C103—41no—
165C4×C103—41no—
166Dic103—22no—
167Dic103—22no—
168Dic103—22no—
169Dic103—22no—
170Dic103—41no—
171Dic103—41no—
172Dic103—41no—
173C2×C103C2×#11711yescharacteristic
174C2×C103C4×#4111yescharacteristic
175C2×C103#52011yescharacteristic
176C2×C103#55111yescharacteristic
177C2×C103#55111yescharacteristic
178C2×C103#55211yescharacteristic
179C2×C103#55211yescharacteristic
180D103—24no—
181#2343—1031nomaximal, Sylow
182C103#234311yescharacteristic, complemented, Sylow
183C2×#117—1031no—
184#387—1031no—
185#387—1031no—
186#387—1031no—
187#387D10311yescharacteristic, complemented
188#385—1031no—
189#385—1031no—
190#383—1031no—
191#382—1031no—
192#381—1031no—
193C4×C4⋊C4—1031no—
194C4×C22⋊C4—1031no—
195C4×C22⋊C4—1031no—
196#376—1031no—
197C2×#95—1031no—
198C23×C4—1031no—
199C23×C4—1031no—
200C23×C4—1031no—
201#117—1038no—
202C2×C4⋊C4—1031no—
203C2×C4⋊C4—1031no—
204C2×C4⋊C4—1031no—
205C2×C4⋊C4—1031no—
206C2×C4⋊C4C2×D10311yescharacteristic
207C2×C4⋊C4C2×D10311yescharacteristic
208C2×C22⋊C4—1031no—
209C2×C22⋊C4—1031no—
210C2×C22⋊C4—1031no—
211C2×C22⋊C4—1031no—
212C2×C42—1031no—
213C2×C42—1031no—
214C2×C42—1031no—
215C2×C42—1031no—
216C2×C42—1031no—
217C2×C42C2×D10311yescharacteristic
218#95—1031no—
219#95—1031no—
220#95—1031no—
221#95—1031no—
222#95—1031no—
223#95—1031no—
224#95—1031no—
225#95—1031no—
226#95—1031no—
227#95—1031no—
228#95—1031no—
229#95—1031no—
230#95C2×D10311yescharacteristic
231#95C2×D10311yescharacteristic
232#95C2×D10311yescharacteristic
233#95C2×D10311yescharacteristic
234C24—1031no—
235C22×C4—1031no—
236C22×C4—1031no—
237C22×C4—1031no—
238C22×C4—1031no—
239C22×C4—1034no—
240C22×C4—1031no—
241C22×C4—1031no—
242C22×C4—1031no—
243C22×C4—4121no—
244C22×C4—4121no—
245C22×C4—2062no—
246C22×C4—2062no—
247C22×C4—2062no—
248C22×C4—2062no—
249C22×C4—2062no—
250C22×C4—2062no—
251C22×C4C22×D10311yescharacteristic
252C22×C4C22×D10311yescharacteristic
253C22×C4C22×D10311yescharacteristic
254C22×C4C22×D10311yescharacteristic
255C22×C4C22×D10311yescharacteristic
256C22×C4C22×D10311yescharacteristic
257C22×C4C22×D10311yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—1034no—
260C4⋊C4—4121no—
261C4⋊C4—2062no—
262C4⋊C4—2062no—
263C4⋊C4C4×D10314yescomplemented
264C22⋊C4—1034no—
265C22⋊C4—1034no—
266C22⋊C4—2062no—
267C22⋊C4—2062no—
268C42—41no—
269C42—1034no—
270C42—1034no—
271C42—4121no—
272C42—2062no—
273C42—2062no—
274C23—1032no—
275C23—1032no—
276C23—1032no—
277C23—2061no—
278C23—2061no—
279C23—2061no—
280C23—2061no—
281C23C23×D10311yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—1032no—
300C2×C4—1032no—
301C2×C4—1032no—
302C2×C4—1032no—
303C2×C4—4124no—
304C2×C4—4124no—
305C2×C4—2068no—
306C2×C4—2061no—
307C2×C4—2061no—
308C2×C4—2061no—
309C2×C4—2061no—
310C2×C4—2061no—
311C2×C4—2061no—
312C2×C4—2061no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2061no—
323C2×C4C2×C4×D10312yes—
324C2×C4C2×C4×D10312yes—
325C2×C4C2×C4×D10312yes—
326C2×C4#1311010612yes—
327C22—1034no—
328C22—2062no—
329C22—2062no—
330C22—2062no—
331C22—2062no—
332C22—2062no—
333C22—2062no—
334C22C22×C4×D10311yescharacteristic
335C22#41×D10311yescharacteristic
336C22#41×D10311yescharacteristic
337C22#41×D10311yescharacteristic
338C22C2×#1311010611yescharacteristic
339C22#1569306611yescharacteristic
340C22#1569306811yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—4121no—
349C4—4121no—
350C4—4121no—
351C4—2062no—
352C4—2062no—
353C4—2062no—
354C4—2062no—
355C2—2064no—
356C2#117×D10311yescharacteristic
357C2C4×#1311010611yescharacteristic
358C2#2026827011yescharacteristic
359C2#2026846811yescharacteristic
360C2#2026846911yescharacteristic
361C2#2026847711yescharacteristic
362C2#2026847911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, cosocleC23×C103C24
prime radicalC23×D103C23
hypercenter#387D103
hypocenterC103#2343
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20267677C2semidirect
3. #20267676C2semidirect
4. #20267674C2semidirect
7. #20267658C2semidirect
8. #20267656C2semidirect
10. C4×Dic103⋊C4C2semidirect
13. #20267636C2semidirect
15. #387×C103C2semidirect
19. #15692979C4semidirect
70. C4⋊Dic103C2×C4semidirect
80. C4×Dic103C2×C4semidirect
81. C4×Dic103C2×C4semidirect
90. C4⋊C4×C103C2×C4semidirect
182. C103#2343semidirect
187. #387D103semidirect
263. C4⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929792
#202676772
#202676762
#202676742
#202676652
#202676622
#202676582
#202676562
#202676532
C4×Dic103⋊C42
C4×(C2×D103)⋊C42
#202676382
#202676362
#95×D1032
#387×C1032
#2343103