Finite Group Databasebeta

← #27198172

Subgroups — #27198172

Order 13184.

576 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×#15692999C211yesmaximal, characteristic
2C2×C4×Dic206C211yesmaximal, characteristic, complemented
3C2×#15692978C211yesmaximal, characteristic
4#20267695C211yesmaximal, characteristic, complemented
5#20267686C211yesmaximal, characteristic, complemented
6#20267683C211yesmaximal, characteristic
7#20267682C211yesmaximal, characteristic
8#20267682C211yesmaximal, characteristic
9#20267681C211yesmaximal, characteristic
10#20267677C211yesmaximal, characteristic, complemented
11#20267675C211yesmaximal, characteristic, complemented
12C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
13#20267642C211yesmaximal, characteristic, complemented
14#20267638C211yesmaximal, characteristic
15C4×C4⋊C4×C103C211yesmaximal, characteristic, complemented
16C22×Dic206C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18#15692999C418yescomplemented
19C4×Dic206—24no—
20#15692978—24no—
21C2×C4⋊Dic103C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
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×C4⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50C2×C42×C103C2211yescharacteristic
51C2×C42×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C2×Dic206—22no—
56C2×Dic206—22no—
57C2×Dic206C2×C414yes—
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C2×C4×D103—22no—
66C2×C4×D103—22no—
67C2×C4×D103C2×C414yes—
68C4⋊Dic103—22no—
69Dic103⋊C4—22no—
70Dic103⋊C4—22no—
71Dic103⋊C4—22no—
72Dic103⋊C4C2×C414yes—
73Dic103⋊C4C2×C414yes—
74Dic103⋊C4D414yes—
75(C2×D103)⋊C4—22no—
76(C2×D103)⋊C4—22no—
77(C2×D103)⋊C4—22no—
78(C2×D103)⋊C4—22no—
79(C2×D103)⋊C4C2×C414yes—
80(C2×D103)⋊C4C2×C414yes—
81C4×Dic103—22no—
82C4×Dic103—22no—
83C4×Dic103—22no—
84C4×Dic103—22no—
85C4×Dic103—22no—
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—22no—
94C4⋊C4×C103C2×C414yes—
95C42×C103—22no—
96C42×C103—22no—
97C42×C103—22no—
98C23×C103C2411yescharacteristic
99C22×D103—21no—
100C22×D103—21no—
101C22×D103—21no—
102C22×D103—21no—
103C22×D103—21no—
104C22×D103—21no—
105C22×D103C22×C412yes—
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×C103C22×C412yes—
124C2×C4×C103C2×D412yes—
125C2×C4×C103#4112yes—
126C2×C4×C103#4112yes—
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×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103C22×C412yes—
143C2×Dic103C22×C412yes—
144C2×Dic103C22×C412yes—
145C2×Dic103C2×D412yes—
146C2×Dic103C2×D412yes—
147C2×Dic103#4112yes—
148C4×D103—28no—
149Dic206—28no—
150C22×C103C23×C411yescharacteristic
151C22×C103C22×D411yescharacteristic
152C22×C103C2×#4111yescharacteristic
153C22×C103C2×#4111yescharacteristic
154C22×C103C2×#4111yescharacteristic
155C22×C1032−1+411yescharacteristic
156C22×C1032−1+411yescharacteristic
157C2×D103—22no—
158C2×D103—22no—
159C2×D103—22no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—22no—
168C4×C103—22no—
169C4×C103—22no—
170C4×C103—41no—
171Dic103—22no—
172Dic103—22no—
173Dic103—22no—
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177Dic103C4×D414yes—
178C2×C103C2×C4×D411yescharacteristic
179C2×C103C4×#4111yescharacteristic
180C2×C103#51911yescharacteristic
181C2×C103#54711yescharacteristic
182C2×C103#54811yescharacteristic
183C2×C103#55211yescharacteristic
184C2×C103#55611yescharacteristic
185D103—42no—
186#2362—1031nomaximal, Sylow
187C103#236211yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—1031no—
189C2×C4×Q8—1031no—
190C2×#117—1031no—
191#391—1031no—
192#389—1031no—
193#388—1031no—
194#388—1031no—
195#388—1031no—
196#388—1031no—
197#387—1031no—
198#387—1031no—
199C4×C4⋊C4—1031no—
200C4×C4⋊C4—1031no—
201C4×C4⋊C4D10311yescharacteristic, complemented
202C4×C22⋊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⋊C4C2×D10311yescharacteristic
216C2×C4⋊C4C2×D10311yescharacteristic
217C2×C22⋊C4—1031no—
218C2×C22⋊C4—1031no—
219C2×C22⋊C4—1031no—
220C2×C22⋊C4—1031no—
221C2×C22⋊C4—1031no—
222C2×C22⋊C4—1031no—
223C2×C42—1031no—
224C2×C42—1031no—
225C2×C42—1031no—
226C2×C42—1031no—
227C2×C42—1031no—
228C2×C42C2×D10311yescharacteristic
229C2×C42C2×D10311yescharacteristic
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
241C24—1031no—
242C2×Q8—1034no—
243C2×Q8—2062no—
244C2×Q8—2062no—
245C22×C4—1031no—
246C22×C4—1031no—
247C22×C4—1031no—
248C22×C4—1031no—
249C22×C4—1034no—
250C22×C4—1031no—
251C22×C4—1031no—
252C22×C4—1031no—
253C22×C4—2062no—
254C22×C4—2062no—
255C22×C4C22×D10311yescharacteristic
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—2062no—
267C4⋊C4—2062no—
268C4⋊C4—2062no—
269C4⋊C4—2062no—
270C4⋊C4C4×D10314yes—
271C22⋊C4—1034no—
272C22⋊C4—1034no—
273C22⋊C4—2062no—
274C22⋊C4—2062no—
275C22⋊C4—2062no—
276C22⋊C4—2062no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—2062no—
281C42—2062no—
282C42—2062no—
283C42—2062no—
284C42—2062no—
285C23—1032no—
286C23—2061no—
287C23—2061no—
288C23—2061no—
289C23—2061no—
290C23—2061no—
291C23—2061no—
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—2068no—
316C2×C4—2061no—
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×C4C2×C4×D10312yes—
332C2×C4C2×C4×D10312yes—
333C2×C4C2×C4×D10312yes—
334C2×C4D4×D10312yes—
335C2×C4#1311010512yes—
336C2×C4#1311010512yes—
337C22—4121no—
338C22—4121no—
339C22—4121no—
340C22—4121no—
341C22—2062no—
342C22—2062no—
343C22—2062no—
344C22C22×C4×D10311yescharacteristic
345C22C2×D4×D10311yescharacteristic
346C22#41×D10311yescharacteristic
347C22C2×#1311010511yescharacteristic
348C22C2×#1311010511yescharacteristic
349C22#1569306811yescharacteristic
350C22#1569306911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—1034no—
359C4—4121no—
360C4—4121no—
361C4—4121no—
362C4—2062no—
363C4—2062no—
364C4—2062no—
365C2—4122no—
366C2C4×D4×D10311yescharacteristic
367C2C4×#1311010511yescharacteristic
368C2#2026826711yescharacteristic
369C2#2026844211yescharacteristic
370C2#2026845011yescharacteristic
371C2#2026847411yescharacteristic
372C2#2026851311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC4×C4⋊C4×C103C2
socle, cosocleC23×C103C24
prime radicalC23×D103C23
hypercenterC4×C4⋊C4D103
hypocenterC103#2362
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic206C2semidirect
4. #20267695C2semidirect
5. #20267686C2semidirect
10. #20267677C2semidirect
11. #20267675C2semidirect
12. C4×Dic103⋊C4C2semidirect
13. #20267642C2semidirect
15. C4×C4⋊C4×C103C2semidirect
18. #15692999C4semidirect
187. C103#2362semidirect
201. C4×C4⋊C4D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929992
C2×C4×Dic2062
C2×#156929782
#202676952
#202676862
#202676832
#202676822
#202676812
#202676772
#202676752
C4×Dic103⋊C42
#202676422
#202676382
C4×C4⋊C4×C1032
#2362103