Finite Group Databasebeta

← #27207040

Subgroups — #27207040

Order 13184.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268450C211yesmaximal, characteristic, complemented
2#20268148C211yesmaximal, characteristic, complemented
3#20268132C211yesmaximal, characteristic, complemented
4#20268109C211yesmaximal, characteristic, complemented
5#20268095C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268018C211yesmaximal, characteristic, complemented
8#20268006C211yesmaximal, characteristic, complemented
9#20267934C211yesmaximal, characteristic, complemented
10#20267929C211yesmaximal, characteristic, complemented
11C4×#13110093C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267785C211yesmaximal, characteristic, complemented
14C2×#15692944C211yesmaximal, characteristic, complemented
15#553×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×Dic206C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic
23#15693009C2211yescharacteristic
24#15693007—21no—
25#15693000C2211yescharacteristic
26#15692999—21no—
27#15692995C2211yescharacteristic
28#15692993—21no—
29C4×Dic206C2211yescharacteristic
30(C22⋊D103)⋊C4—21no—
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35#15692944C2211yescharacteristic
36#15692944C2211yescharacteristic
37#15692944C2211yescharacteristic
38#15692944C2211yescharacteristic
39#15692944C2211yescharacteristic
40#15692944C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692941C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48#126×C103—21no—
49#125×C103C2211yescharacteristic
50#123×C103—21no—
51#121×C103—21no—
52#121×C103C2211yescharacteristic
53#121×C103C2211yescharacteristic
54C4×D4×C103—21no—
55C4×D4×C103C2211yescharacteristic
56C4×D4×C103C2211yescharacteristic
57#117×C103C2211yescharacteristic
58C2×C4⋊C4×C103C2211yescharacteristic
59#13110105—22no—
60#13110105—41no—
61C2×Dic206—22no—
62C2×Dic206—21no—
63C2×Dic206—41no—
64C2×Dic206C2311yescharacteristic
65C2×Dic206C2311yescharacteristic
66C2×D412C2311yescharacteristic
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C22×Dic103—21no—
70C2×C4×D103—21no—
71#13110093—22no—
72#13110093—41no—
73#13110090—41no—
74C2×C103⋊C8—41no—
75C2×C103⋊C8—41no—
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83C22⋊Dic103—21no—
84(C2×D103)⋊C4—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87C4×Dic103—21no—
88C2×D4×C103—21no—
89C2×D4×C103—21no—
90C2×D4×C103D411yescharacteristic
91C2×D4×C103C2311yescharacteristic
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103C2311yescharacteristic
95C22×C4×C103C2311yescharacteristic
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103D411yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C22⋊C4×C103—21no—
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C22⋊C4×C103D411yescharacteristic
108C22⋊C4×C103D411yescharacteristic
109C42×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103C2×D411yescharacteristic
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115D4×C103—22no—
116D4×C103—21no—
117D4×C103—21no—
118D4×C103—42no—
119D4×C103—81no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—81no—
128C2×C4×C103—81no—
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2×D411yescharacteristic
132C2×C4×C103C2×D411yescharacteristic
133C2×C4×C103C2411yescharacteristic
134C22⋊D103—42no—
135C22⋊D103—42no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—42no—
140D412—21no—
141D412—21no—
142C4×D103—42no—
143Dic206—21no—
144Dic206—21no—
145Dic206—21no—
146Dic206—42no—
147Dic206#4112yes—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103#13512yes—
161C22×C103C22×D411yescharacteristic
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C4×C103—21no—
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—21no—
169C4×C103—41no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103C2×#4111yescharacteristic
173C4×C103H(5,𝔽2)11yescharacteristic
174Dic103—22no—
175Dic103—41no—
176Dic103—41no—
177C2×C103—22no—
178C2×C103—41no—
179C2×C103—81no—
180C2×C103#54611yescharacteristic
181C2×C103C2×#13511yescharacteristic
182C2×C103#57711yescharacteristic
183D103—81no—
184#3301—1031nomaximal, Sylow
185C103#330111yescharacteristic, complemented, Sylow
186#553D10311yescharacteristic, complemented
187#548—1031no—
188#488—1031no—
189#485—1031no—
190#481—1031no—
191#479—1031no—
192#466—1031no—
193#465—1031no—
194#463—1031no—
195#449—1031no—
196#448—1031no—
197C4×SD16—1031no—
198C8×D4—1031no—
199#416—1031no—
200C2×#103—1031no—
201C2×#41—1031no—
202C22×Q8—1031no—
203C2×SD16—1031no—
204C2×SD16—1031no—
205C2×D8—1031no—
206C22×C8—1031no—
207C22×C8—1031no—
208#126—21no—
209#125C2×D10311yescharacteristic
210#124—1031no—
211#124—2061no—
212#123—21no—
213C22⋊Q8—1031no—
214C22⋊Q8—2061no—
215#121—21no—
216#121—1031no—
217#121—2061no—
218#121C2×D10311yescharacteristic
219#121C2×D10311yescharacteristic
220C4×Q8—1031no—
221C4×D4—21no—
222C4×D4—2061no—
223C4×D4C2×D10311yescharacteristic
224C4×D4C2×D10311yescharacteristic
225#117C2×D10311yescharacteristic
226C2×C4⋊C4C2×D10311yescharacteristic
227#107—1031no—
228#106—1031no—
229#106—1031no—
230C4⋊C8—1031no—
231#103—1031no—
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#103—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241C22⋊C8—1031no—
242C22⋊C8—1031no—
243C4×C8—1031no—
244#41—4121no—
245#41—2062no—
246C2×Q8—1031no—
247C2×Q8—1031no—
248C2×Q8—4121no—
249C2×Q8—2062no—
250C2×Q8—2061no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—1031no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4C22⋊D10311yescharacteristic
257C2×D4C22×D10311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263C22×C4C22×D10311yescharacteristic
264SD16—4121no—
265SD16—2062no—
266D8—4121no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—1031no—
270C2×C8—1031no—
271C2×C8—4121no—
272C2×C8—4121no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1031no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4C22⋊D10311yescharacteristic
280C4⋊C4C22×D10311yescharacteristic
281C4⋊C4C22×D10311yescharacteristic
282C4⋊C4C22×D10311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4C22⋊D10311yescharacteristic
292C22⋊C4C22⋊D10311yescharacteristic
293C42—21no—
294C42—2061no—
295C42C22×D10311yescharacteristic
296C23—21no—
297C23—2061no—
298C23C2×C22⋊D10311yescharacteristic
299C23C2×C22⋊D10311yescharacteristic
300Q8—1032no—
301Q8—4122no—
302Q8—2061no—
303Q8—2061no—
304Q8—2061no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—4122no—
311D4—4122no—
312D4—2061no—
313D4—2061no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—4122no—
324C2×C4—4122no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4C2×C22⋊D10311yescharacteristic
329C2×C4C2×C22⋊D10311yescharacteristic
330C2×C4C2×C22⋊D10311yescharacteristic
331C2×C4C2×C22⋊D10311yescharacteristic
332C2×C4C23×D10311yescharacteristic
333C8—2061no—
334C8—2061no—
335C8—2061no—
336C8—2061no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—4121no—
346C22—4121no—
347C22—4121no—
348C22#1569304112yes—
349C22C22×C22⋊D10311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4121no—
358C4—4121no—
359C4—2062no—
360C4#41×D10311yescharacteristic
361C4#1569306711yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—8241no—
366C2#2026842911yescharacteristic
367C2C2×#1569304111yescharacteristic
368C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#553×C103C2
socleC22×C103C22×D4
hypercenter#553D103
hypocenterC103#3301
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20268450C2semidirect
2. #20268148C2semidirect
3. #20268132C2semidirect
4. #20268109C2semidirect
5. #20268095C2semidirect
6. #20268025C2semidirect
7. #20268018C2semidirect
8. #20268006C2semidirect
9. #20267934C2semidirect
10. #20267929C2semidirect
11. C4×#13110093C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267785C2semidirect
14. C2×#15692944C2semidirect
15. #553×C103C2semidirect
185. C103#3301semidirect
186. #553D103semidirect

Maximal subgroups

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

subgroupindex
#202684502
#202681482
#202681322
#202681092
#202680952
#202680252
#202680182
#202680062
#202679342
#202679292
C4×#131100932
D4×C103⋊C82
#202677852
C2×#156929442
#553×C1032
#3301103