Finite Group Databasebeta

← #27206041

Subgroups — #27206041

Order 13184.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268369C211yesmaximal, characteristic, complemented
2#20268126C211yesmaximal, characteristic, complemented
3#20268124C211yesmaximal, characteristic, complemented
4#20268104C211yesmaximal, characteristic, complemented
5#20268102C211yesmaximal, characteristic, complemented
6#20268039C211yesmaximal, characteristic, complemented
7#20268035C211yesmaximal, characteristic, complemented
8#20268030C211yesmaximal, characteristic, complemented
9#20268025C211yesmaximal, characteristic, complemented
10#20267953C211yesmaximal, characteristic, complemented
11#20267951C211yesmaximal, characteristic, complemented
12#20267936C211yesmaximal, characteristic, complemented
13#20267934C211yesmaximal, characteristic, complemented
14#20267758C211yesmaximal, characteristic, complemented
15#537×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C2×#13110089C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic
23#15693000C2211yescharacteristic
24#15693000C2211yescharacteristic
25#15692997—21no—
26#15692995C2211yescharacteristic
27#15692995C2211yescharacteristic
28#15692993—21no—
29#15692993—21no—
30#15692992—21no—
31C2×C4⋊Dic103C2211yescharacteristic
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34#15692954C2211yescharacteristic
35#15692954C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692944C2211yescharacteristic
39#15692944C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C2×#41×C103C2211yescharacteristic
50C22⋊Q8×C103—21no—
51C22⋊Q8×C103C2211yescharacteristic
52C22⋊Q8×C103C2211yescharacteristic
53#121×C103—21no—
54#121×C103—21no—
55#121×C103—21no—
56#121×C103C2211yescharacteristic
57#121×C103C2211yescharacteristic
58C2×C4⋊C4×C103C2211yescharacteristic
59#13110105—41no—
60#13110105—41no—
61C2×Dic206C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C22×Dic103—21no—
67C2×C4×D103—21no—
68#13110095—41no—
69#13110093—41no—
70#13110092—41no—
71#13110090—41no—
72#13110089—41no—
73C2×C103⋊C8—41no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C4⋊Dic103—21no—
79C4⋊Dic103C2311yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83C22⋊Dic103—21no—
84C22⋊Dic103—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87#41×C103—41no—
88#41×C103—41no—
89#41×C103—41no—
90#41×C103—41no—
91C2×Q8×C103D411yescharacteristic
92C2×Q8×C103C2311yescharacteristic
93C2×D4×C103—21no—
94C2×D4×C103—21no—
95C2×D4×C103—21no—
96C2×D4×C103D411yescharacteristic
97C2×D4×C103D411yescharacteristic
98C2×D4×C103D411yescharacteristic
99C2×D4×C103C2311yescharacteristic
100C22×C4×C103—21no—
101C22×C4×C103—21no—
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—21no—
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C22⋊C4×C103—21no—
114C23×C103—21no—
115C23×C103C2×D411yescharacteristic
116C23×C103C2×D411yescharacteristic
117C23×C103C2×D411yescharacteristic
118C22×D103—21no—
119Q8×C103—21no—
120Q8×C103—21no—
121Q8×C103—41no—
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—41no—
125D4×C103—41no—
126D4×C103—41no—
127D4×C103—42no—
128D4×C103—81no—
129D4×C103—81no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—42no—
140C2×C4×C103—81no—
141C2×C4×C103C2×D411yescharacteristic
142C2×C4×C103C2×D411yescharacteristic
143C2×C4×C103C2×D411yescharacteristic
144C2×C4×C103C2411yescharacteristic
145C22⋊D103—42no—
146C22⋊D103—81no—
147C22⋊D103—81no—
148C2×Dic103—21no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103—81no—
152D412—21no—
153D412—21no—
154C4×D103—42no—
155Dic206—21no—
156Dic206—21no—
157C103⋊C8—21no—
158C103⋊C8—21no—
159C103⋊C8—21no—
160C103⋊C8—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—21no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103—21no—
168C22×C103—21no—
169C22×C103—21no—
170C22×C103—41no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103C22×D411yescharacteristic
174C2×D103—41no—
175C2×D103—41no—
176C2×D103—41no—
177C4×C103—21no—
178C4×C103—21no—
179C4×C103—21no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103—41no—
183C4×C103H(5,𝔽2)11yescharacteristic
184C4×C103H(5,𝔽2)11yescharacteristic
185Dic103—41no—
186Dic103—41no—
187Dic103—41no—
188C2×C103—41no—
189C2×C103—41no—
190C2×C103—41no—
191C2×C103—81no—
192C2×C103#53411yescharacteristic
193C2×C103#57611yescharacteristic
194C2×C103#57811yescharacteristic
195D103—81no—
196#3203—1031nomaximal, Sylow
197C103#320311yescharacteristic, complemented, Sylow
198#537—1031no—
199#537D10311yescharacteristic, complemented
200#484—1031no—
201#484—1031no—
202#480—1031no—
203#480—1031no—
204#468—1031no—
205#468—1031no—
206#467—1031no—
207#466—1031no—
208#452—1031no—
209#452—1031no—
210#449—1031no—
211#449—1031no—
212#408—1031no—
213C2×#41—1031no—
214C2×#41C2×D10311yescharacteristic
215C2×#41C2×D10311yescharacteristic
216C2×Q16—1031no—
217C2×SD16—1031no—
218C2×SD16—1031no—
219C2×D8—1031no—
220C2×M16—1031no—
221C22×C8—1031no—
222C22⋊Q8—21no—
223C22⋊Q8—1031no—
224C22⋊Q8—1031no—
225C22⋊Q8—2061no—
226C22⋊Q8C2×D10311yescharacteristic
227C22⋊Q8C2×D10311yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—1031no—
232#121—1031no—
233#121—2061no—
234#121—2061no—
235#121—2061no—
236#121C2×D10311yescharacteristic
237#121C2×D10311yescharacteristic
238C2×C4⋊C4—1031no—
239C2×C4⋊C4C2×D10311yescharacteristic
240#107—1031no—
241#107—1031no—
242#107—1031no—
243#107—1031no—
244#103—1031no—
245#103—1031no—
246#103—1031no—
247#103—1031no—
248#102—1031no—
249#102—1031no—
250#102—1031no—
251#102—1031no—
252C22⋊C8—1031no—
253C22⋊C8—1031no—
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—4121no—
261#41—4121no—
262C2×Q8—1031no—
263C2×Q8C22⋊D10311yescharacteristic
264C2×Q8C22×D10311yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—1031no—
269C2×D4—2061no—
270C2×D4—2061no—
271C2×D4—2061no—
272C2×D4C22⋊D10311yescharacteristic
273C2×D4C22⋊D10311yescharacteristic
274C2×D4C22⋊D10311yescharacteristic
275C2×D4C22×D10311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2061no—
279C22×C4—2061no—
280C22×C4C22×D10311yescharacteristic
281C22×C4C22×D10311yescharacteristic
282C22×C4C22×D10311yescharacteristic
283Q16—4121no—
284SD16—4121no—
285SD16—4121no—
286D8—4121no—
287M16—4121no—
288C2×C8—1031no—
289C2×C8—1031no—
290C2×C8—1031no—
291C2×C8—1031no—
292C2×C8—4121no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—1031no—
297C4⋊C4—1031no—
298C4⋊C4—2061no—
299C4⋊C4—2061no—
300C4⋊C4—2061no—
301C4⋊C4C22×D10311yescharacteristic
302C4⋊C4C22×D10311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—2061no—
308C22⋊C4—2061no—
309C22⋊C4—2061no—
310C22⋊C4—2061no—
311C23—21no—
312C23—2061no—
313C23C2×C22⋊D10311yescharacteristic
314C23C2×C22⋊D10311yescharacteristic
315C23C2×C22⋊D10311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—2061no—
320Q8—2061no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—8241no—
330D4—8241no—
331D4—4122no—
332D4—2061no—
333D4—2061no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—8241no—
346C2×C4—4122no—
347C2×C4—2061no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4C2×C22⋊D10311yescharacteristic
351C2×C4C2×C22⋊D10311yescharacteristic
352C2×C4C2×C22⋊D10311yescharacteristic
353C2×C4C23×D10311yescharacteristic
354C8—2061no—
355C8—2061no—
356C8—2061no—
357C8—2061no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—4121no—
371C22—4121no—
372C22—4121no—
373C22C22×C22⋊D10311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4121no—
381C4—4121no—
382C4—4121no—
383C4#1569306611yescharacteristic
384C4#1569306611yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—8241no—
390C2#2026835011yescharacteristic
391C2#2026859411yescharacteristic
392C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#537×C103C2
socleC22×C103C22×D4
hypercenter#537D103
hypocenterC103#3203
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20268369C2semidirect
2. #20268126C2semidirect
3. #20268124C2semidirect
4. #20268104C2semidirect
5. #20268102C2semidirect
6. #20268039C2semidirect
7. #20268035C2semidirect
8. #20268030C2semidirect
9. #20268025C2semidirect
10. #20267953C2semidirect
11. #20267951C2semidirect
12. #20267936C2semidirect
13. #20267934C2semidirect
14. #20267758C2semidirect
15. #537×C103C2semidirect
197. C103#3203semidirect
199. #537D103semidirect

Maximal subgroups

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

subgroupindex
#202683692
#202681262
#202681242
#202681042
#202681022
#202680392
#202680352
#202680302
#202680252
#202679532
#202679512
#202679362
#202679342
#202677582
#537×C1032
#3203103