Finite Group Databasebeta

← #27198305

Subgroups — #27198305

Order 13184.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692997C211yesmaximal, characteristic
2#20267698C211yesmaximal, characteristic, complemented
3#20267688C211yesmaximal, characteristic, complemented
4#20267686C211yesmaximal, characteristic, complemented
5#20267683C211yesmaximal, characteristic
6#20267682C211yesmaximal, characteristic
7#20267681C211yesmaximal, characteristic
8#20267680C211yesmaximal, characteristic
9#20267676C211yesmaximal, characteristic, complemented
10#20267675C211yesmaximal, characteristic, complemented
11#20267674C211yesmaximal, characteristic, complemented
12#20267673C211yesmaximal, characteristic, complemented
13#20267653C211yesmaximal, characteristic
14#20267650C211yesmaximal, characteristic
15#391×C103C211yesmaximal, characteristic, complemented
16C22×C4×D103C2211yescharacteristic
17#15692997C418yescomplemented
18C2×C4⋊Dic103C2211yescharacteristic
19C2×C4⋊Dic103C2211yescharacteristic
20C2×Dic103⋊C4C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×(C2×D103)⋊C4C2211yescharacteristic
27C2×(C2×D103)⋊C4C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
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
45C22×Q8×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—41no—
61C2×C4×D103—41no—
62C2×C4×D103C2×C414yes—
63C4⋊Dic103—41no—
64C4⋊Dic103C2×C414yes—
65Dic103⋊C4—41no—
66Dic103⋊C4—41no—
67Dic103⋊C4—41no—
68Dic103⋊C4—41no—
69Dic103⋊C4C2×C414yes—
70Dic103⋊C4C2×C414yes—
71(C2×D103)⋊C4—41no—
72(C2×D103)⋊C4—41no—
73(C2×D103)⋊C4—41no—
74(C2×D103)⋊C4—41no—
75(C2×D103)⋊C4C2×C414yes—
76(C2×D103)⋊C4C2×C414yes—
77C4×Dic103—41no—
78C4×Dic103—41no—
79C4×Dic103—41no—
80C2×Q8×C103—41no—
81C2×Q8×C103—41no—
82C2×Q8×C103C2×C414yes—
83C22×C4×C103C2311yescharacteristic
84C22×C4×C103C2311yescharacteristic
85C22×C4×C103C2311yescharacteristic
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C4⋊C4×C103—41no—
91C42×C103—41no—
92C23×C103C2411yescharacteristic
93C22×D103—21no—
94C22×D103—21no—
95C22×D103—21no—
96C22×D103—21no—
97C22×D103—21no—
98C22×D103—21no—
99C22×D103C22×C412yes—
100Q8×C103—44no—
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×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103C22×C412yes—
120C2×C4×C103C22×C412yes—
121C2×C4×C103C22×C412yes—
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×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103C22×C412yes—
141C2×Dic103C22×C412yes—
142C2×Dic103C22×C412yes—
143C4×D103—44no—
144C22×C103C23×C411yescharacteristic
145C22×C103H(5,𝔽2)11yescharacteristic
146C22×C103H(5,𝔽2)11yescharacteristic
147C22×C103H(5,𝔽2)11yescharacteristic
148C22×C1032−1+411yescharacteristic
149C22×C1032−1+411yescharacteristic
150C22×C1032−1+411yescharacteristic
151C2×D103—22no—
152C2×D103—22no—
153C2×D103—22no—
154C2×D103—41no—
155C2×D103—41no—
156C2×D103—41no—
157C2×D103—41no—
158C4×C103—22no—
159C4×C103—22no—
160C4×C103—22no—
161C4×C103—41no—
162C4×C103—41no—
163C4×C103—41no—
164C4×C103—41no—
165Dic103—22no—
166Dic103—22no—
167Dic103—22no—
168Dic103—41no—
169Dic103—41no—
170Dic103—41no—
171Dic103—41no—
172C2×C103#51811yescharacteristic
173C2×C103#51911yescharacteristic
174C2×C103#52011yescharacteristic
175C2×C103#56211yescharacteristic
176C2×C103#56211yescharacteristic
177C2×C103#56311yescharacteristic
178C2×C103#56311yescharacteristic
179D103—42no—
180#2378—1031nomaximal, Sylow
181C103#237811yescharacteristic, complemented, Sylow
182C2×C22⋊Q8—1031no—
183#391—1031no—
184#391D10311yescharacteristic, complemented
185#389—1031no—
186#389—1031no—
187#388—1031no—
188#388—1031no—
189#388—1031no—
190#388—1031no—
191#387—1031no—
192#387—1031no—
193#387—1031no—
194#387—1031no—
195#381—1031no—
196#380—1031no—
197C22×Q8C2×D10311yescharacteristic
198C23×C4—1031no—
199C22⋊Q8—1038no—
200C2×C4⋊C4—1031no—
201C2×C4⋊C4—1031no—
202C2×C4⋊C4—1031no—
203C2×C4⋊C4—1031no—
204C2×C4⋊C4—1031no—
205C2×C4⋊C4—1031no—
206C2×C4⋊C4—1031no—
207C2×C4⋊C4—1031no—
208C2×C4⋊C4C2×D10311yescharacteristic
209C2×C22⋊C4—1031no—
210C2×C22⋊C4—1031no—
211C2×C22⋊C4—1031no—
212C2×C22⋊C4—1031no—
213C2×C22⋊C4—1031no—
214C2×C22⋊C4—1031no—
215C2×C42—1031no—
216C2×C42—1031no—
217C2×C42—1031no—
218C2×C42C2×D10311yescharacteristic
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#95C2×D10311yescharacteristic
230#95C2×D10311yescharacteristic
231#95C2×D10311yescharacteristic
232#95C2×D10311yescharacteristic
233C24—1031no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8C4×D10314yes—
237C22×C4—1031no—
238C22×C4—1031no—
239C22×C4—1031no—
240C22×C4—1034no—
241C22×C4—1031no—
242C22×C4—1031no—
243C22×C4—1031no—
244C22×C4—1031no—
245C22×C4—4121no—
246C22×C4—4121no—
247C22×C4C22×D10311yescharacteristic
248C22×C4C22×D10311yescharacteristic
249C22×C4C22×D10311yescharacteristic
250C22×C4C22×D10311yescharacteristic
251C22×C4C22×D10311yescharacteristic
252C22×C4C22×D10311yescharacteristic
253C22×C4C22×D10311yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—1034no—
256C4⋊C4—1034no—
257C4⋊C4—1034no—
258C4⋊C4—4121no—
259C4⋊C4—4121no—
260C4⋊C4—4121no—
261C4⋊C4—4121no—
262C4⋊C4—4121no—
263C22⋊C4—1034no—
264C22⋊C4—1034no—
265C22⋊C4—4121no—
266C22⋊C4—4121no—
267C22⋊C4—4121no—
268C22⋊C4—4121no—
269C42—41no—
270C42—4121no—
271C42—4121no—
272C42—4121no—
273C23—1032no—
274C23—2061no—
275C23—2061no—
276C23—2061no—
277C23—2061no—
278C23—2061no—
279C23—2061no—
280C23C23×D10311yescharacteristic
281Q8—44no—
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—21no—
300C2×C4—1032no—
301C2×C4—1032no—
302C2×C4—1032no—
303C2×C4—4124no—
304C2×C4—2061no—
305C2×C4—2061no—
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×C4C2×C4×D10312yes—
323C2×C4C2×C4×D10312yes—
324C2×C4C2×C4×D10312yes—
325C22—4121no—
326C22—4121no—
327C22—4121no—
328C22—4121no—
329C22—2062no—
330C22—2062no—
331C22—2062no—
332C22C22×C4×D10311yescharacteristic
333C22#1569306611yescharacteristic
334C22#1569306611yescharacteristic
335C22#1569306711yescharacteristic
336C22#1569306811yescharacteristic
337C22#1569306911yescharacteristic
338C22#1569306911yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4121no—
347C4—4121no—
348C4—4121no—
349C4—4121no—
350C4—2062no—
351C4—2062no—
352C4—2062no—
353C2—4122no—
354C2#2026826411yescharacteristic
355C2#2026826711yescharacteristic
356C2#2026827311yescharacteristic
357C2#2026853511yescharacteristic
358C2#2026853711yescharacteristic
359C2#2026854011yescharacteristic
360C2#2026854211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#391×C103C2
socle, cosocleC23×C103C24
prime radicalC23×D103C23
hypercenter#391D103
hypocenterC103#2378
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #20267698C2semidirect
3. #20267688C2semidirect
4. #20267686C2semidirect
9. #20267676C2semidirect
10. #20267675C2semidirect
11. #20267674C2semidirect
12. #20267673C2semidirect
15. #391×C103C2semidirect
17. #15692997C4semidirect
181. C103#2378semidirect
184. #391D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929972
#202676982
#202676882
#202676862
#202676832
#202676822
#202676812
#202676802
#202676762
#202676752
#202676742
#202676732
#202676532
#202676502
#391×C1032
#2378103