Finite Group Databasebeta

← #27197819

Subgroups — #27197819

Order 13184.

556 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692998C211yesmaximal, characteristic
2C2×#15692986C211yesmaximal, characteristic, complemented
3C2×#15692977C211yesmaximal, characteristic
4#20267695C211yesmaximal, characteristic, complemented
5#20267689C211yesmaximal, characteristic, complemented
6#20267688C211yesmaximal, characteristic, complemented
7#20267686C211yesmaximal, characteristic, complemented
8#20267685C211yesmaximal, characteristic
9#20267685C211yesmaximal, characteristic
10#20267684C211yesmaximal, characteristic
11#20267674C211yesmaximal, characteristic, complemented
12#20267673C211yesmaximal, characteristic, complemented
13#20267649C211yesmaximal, characteristic
14C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18#15692998C418yescomplemented
19#15692986—24no—
20#15692977—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×Dic103⋊C4C2211yescharacteristic
30C2×Dic103⋊C4C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
32C2×C22⋊Dic103C2211yescharacteristic
33C2×C22⋊Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C2×C4×Dic103C2211yescharacteristic
36C2×C4×Dic103C2211yescharacteristic
37C2×C4×Dic103C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C2×C4⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C42×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C2×Dic206—22no—
55C2×Dic206—22no—
56C2×Dic206C2×C414yes—
57C22×Dic103—22no—
58C22×Dic103—22no—
59C22×Dic103C2×C414yes—
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C4⋊Dic103—41no—
69C4⋊Dic103C2×C414yes—
70Dic103⋊C4—22no—
71Dic103⋊C4—22no—
72Dic103⋊C4—22no—
73Dic103⋊C4—22no—
74Dic103⋊C4—22no—
75Dic103⋊C4—41no—
76Dic103⋊C4C2×C414yes—
77Dic103⋊C4C2×C414yes—
78C22⋊Dic103—22no—
79C22⋊Dic103—41no—
80C22⋊Dic103C2×C414yes—
81C4×Dic103—22no—
82C4×Dic103—22no—
83C4×Dic103—22no—
84C4×Dic103—41no—
85C4×Dic103D414yes—
86C24×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—22no—
94C22⋊C4×C103—22no—
95C22⋊C4×C103—41no—
96C22⋊C4×C103C2×C414yes—
97C42×C103—41no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103C22×C412yes—
105C23×C103C2411yescharacteristic
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×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103C22×C412yes—
122C2×C4×C103C22×C412yes—
123C2×C4×C103C2×D412yes—
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—28no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103C22×C412yes—
143C2×Dic103C22×C412yes—
144C2×Dic103C22×C412yes—
145C2×Dic103C22×C412yes—
146C2×Dic103C2×D412yes—
147C2×Dic103C2×D412yes—
148C2×Dic103#4112yes—
149Dic206—28no—
150C22×C103—22no—
151C22×C103—22no—
152C22×C103—22no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103C23×C411yescharacteristic
158C22×C103C22×D411yescharacteristic
159C22×C103C2×#4111yescharacteristic
160C22×C103H(5,𝔽2)11yescharacteristic
161C22×C1032−1+411yescharacteristic
162C22×C1032−1+411yescharacteristic
163C22×C1032−1+411yescharacteristic
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170Dic103—22no—
171Dic103—22no—
172Dic103—22no—
173Dic103—22no—
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177Dic103C4×D414yes—
178C2×C103—42no—
179C2×C103C2×C4×D411yescharacteristic
180C2×C103#51911yescharacteristic
181C2×C103#52011yescharacteristic
182C2×C103#53611yescharacteristic
183C2×C103#53711yescharacteristic
184C2×C103#54111yescharacteristic
185C2×C103#54211yescharacteristic
186#2323—1031nomaximal, Sylow
187C103#232311yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—1031no—
189C2×C4×Q8—1031no—
190C2×#117—1031no—
191#391—1031no—
192#389—1031no—
193#389—1031no—
194#389—1031no—
195#388—1031no—
196#388—1031no—
197#388—1031no—
198#388D10311yescharacteristic
199#387—1031no—
200#387—1031no—
201#380—1031no—
202C4×C4⋊C4—1031no—
203C22×Q8—1031no—
204C23×C4—1031no—
205C22⋊Q8—1038no—
206C4×Q8—2064no—
207#117—2064no—
208C2×C4⋊C4—1031no—
209C2×C4⋊C4—1031no—
210C2×C4⋊C4—1031no—
211C2×C4⋊C4—1031no—
212C2×C4⋊C4—1031no—
213C2×C4⋊C4—1031no—
214C2×C4⋊C4—1031no—
215C2×C4⋊C4—1031no—
216C2×C4⋊C4—1031no—
217C2×C4⋊C4—1031no—
218C2×C4⋊C4C2×D10311yescharacteristic
219C2×C22⋊C4—1031no—
220C2×C22⋊C4—1031no—
221C2×C22⋊C4—1031no—
222C2×C22⋊C4C2×D10311yescharacteristic
223C2×C22⋊C4C2×D10311yescharacteristic
224C2×C22⋊C4C2×D10311yescharacteristic
225C2×C42—1031no—
226C2×C42—1031no—
227C2×C42—1031no—
228C2×C42—1031no—
229C2×C42—1031no—
230C2×C42C2×D10311yescharacteristic
231#95—1031no—
232#95—1031no—
233#95—1031no—
234#95—1031no—
235#95—1031no—
236#95—1031no—
237#95—1031no—
238#95—1031no—
239#95C2×D10311yescharacteristic
240#95C2×D10311yescharacteristic
241C24C22×D10311yescharacteristic
242C2×Q8—1034no—
243C2×Q8—2062no—
244C2×Q8—2062no—
245C22×C4—1031no—
246C22×C4—1034no—
247C22×C4—1031no—
248C22×C4—1031no—
249C22×C4—1031no—
250C22×C4—1031no—
251C22×C4—1031no—
252C22×C4—1031no—
253C22×C4—1031no—
254C22×C4—2062no—
255C22×C4—2062no—
256C22×C4C22×D10311yescharacteristic
257C22×C4C22×D10311yescharacteristic
258C22×C4C22×D10311yescharacteristic
259C22×C4C22×D10311yescharacteristic
260C22×C4C22×D10311yescharacteristic
261C22×C4C22×D10311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—1034no—
264C4⋊C4—1034no—
265C4⋊C4—1034no—
266C4⋊C4—4121no—
267C4⋊C4—4121no—
268C4⋊C4—2062no—
269C4⋊C4—2062no—
270C4⋊C4—2062no—
271C4⋊C4—2062no—
272C4⋊C4—2062no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—1034no—
276C22⋊C4—4121no—
277C22⋊C4—2062no—
278C22⋊C4C4×D10314yes—
279C42—41no—
280C42—1034no—
281C42—4121no—
282C42—2062no—
283C42—2062no—
284C42—2062no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23C2×C4×D10312yes—
292C23C23×D10311yescharacteristic
293Q8—2068no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1032no—
312C2×C4—1032no—
313C2×C4—1032no—
314C2×C4—1032no—
315C2×C4—1032no—
316C2×C4—2068no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2061no—
323C2×C4—2061no—
324C2×C4—2061no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4—2061no—
333C2×C4—2061no—
334C2×C4C2×C4×D10312yes—
335C2×C4C2×C4×D10312yes—
336C2×C4D4×D10312yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C22×C4×D10311yescharacteristic
345C22C2×D4×D10311yescharacteristic
346C22#41×D10311yescharacteristic
347C22#1569306611yescharacteristic
348C22#1569306811yescharacteristic
349C22#1569306811yescharacteristic
350C22#1569306811yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1034no—
358C4—4121no—
359C4—4121no—
360C4—4121no—
361C4—2062no—
362C4—2062no—
363C4—2062no—
364C4—2062no—
365C2—42no—
366C2C4×D4×D10311yescharacteristic
367C2#2026826811yescharacteristic
368C2#2026827011yescharacteristic
369C2#2026836111yescharacteristic
370C2#2026836811yescharacteristic
371C2#2026839811yescharacteristic
372C2#2026840911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC24×C103C23
hypercenter#388D103
hypocenterC103#2323
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#15692986C2semidirect
4. #20267695C2semidirect
5. #20267689C2semidirect
6. #20267688C2semidirect
7. #20267686C2semidirect
11. #20267674C2semidirect
12. #20267673C2semidirect
14. C4×Dic103⋊C4C2semidirect
18. #15692998C4semidirect
187. C103#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#156929982
C2×#156929862
C2×#156929772
#202676952
#202676892
#202676882
#202676862
#202676852
#202676842
#202676742
#202676732
#202676492
C4×Dic103⋊C42
#388×C1032
#2323103