Finite Group Databasebeta

← #27206026

Subgroups — #27206026

Order 13184.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268369C211yesmaximal, characteristic
2#20268132C211yesmaximal, characteristic, complemented
3#20268124C211yesmaximal, characteristic, complemented
4#20268119C211yesmaximal, characteristic, complemented
5#20268115C211yesmaximal, characteristic, complemented
6#20268047C211yesmaximal, characteristic, complemented
7#20268039C211yesmaximal, characteristic, complemented
8#20268030C211yesmaximal, characteristic, complemented
9#20268022C211yesmaximal, characteristic, complemented
10#20267951C211yesmaximal, characteristic, complemented
11#20267951C211yesmaximal, characteristic, complemented
12#20267947C211yesmaximal, characteristic, complemented
13#20267930C211yesmaximal, characteristic, complemented
14#20267758C211yesmaximal, characteristic, complemented
15#536×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110095C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110092C2211yescharacteristic
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#15692952C2211yescharacteristic
35#15692952C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692945C2211yescharacteristic
39#15692945C2211yescharacteristic
40#15692944C2211yescharacteristic
41#15692944C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic
47C22⋊(C103⋊C8)C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C22×Q8×C103C2211yescharacteristic
50C4⋊Q8×C103—21no—
51#124×C103—21no—
52#123×C103—21no—
53#123×C103—21no—
54C22⋊Q8×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56C22⋊Q8×C103C2211yescharacteristic
57C22⋊Q8×C103C2211yescharacteristic
58#117×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#13110095—41no—
70#13110092—41no—
71#13110092—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—
89C2×Q8×C103—21no—
90C2×Q8×C103—41no—
91C2×Q8×C103—41no—
92C2×Q8×C103D411yescharacteristic
93C2×Q8×C103C2311yescharacteristic
94C2×Q8×C103C2311yescharacteristic
95C2×D4×C103D411yescharacteristic
96C2×D4×C103D411yescharacteristic
97C2×D4×C103D411yescharacteristic
98C22×C4×C103—21no—
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C4⋊C4×C103—21no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C4⋊C4×C103C2311yescharacteristic
108C22⋊C4×C103—21no—
109C22⋊C4×C103—21no—
110C22⋊C4×C103—21no—
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C42×C103—21no—
114C23×C103C2×D411yescharacteristic
115C23×C103C2×D411yescharacteristic
116C23×C103C2×D411yescharacteristic
117C22×D103—21no—
118Q8×C103—21no—
119Q8×C103—21no—
120Q8×C103—21no—
121Q8×C103—21no—
122Q8×C103—41no—
123Q8×C103—42no—
124D4×C103—41no—
125D4×C103—41no—
126D4×C103—41no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
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—42no—
138C2×C4×C103C2×D411yescharacteristic
139C2×C4×C103C2×D411yescharacteristic
140C2×C4×C103C2×D411yescharacteristic
141C2×C4×C103C2411yescharacteristic
142C22⋊D103—42no—
143C22⋊D103—81no—
144C22⋊D103—81no—
145C2×Dic103—21no—
146C2×Dic103—21no—
147C2×Dic103—21no—
148C2×Dic103—81no—
149D412—21no—
150D412—21no—
151C4×D103—42no—
152Dic206—21no—
153Dic206—21no—
154C103⋊C8—21no—
155C103⋊C8—21no—
156C103⋊C8—21no—
157C103⋊C8—21no—
158C22×C103—21no—
159C22×C103—21no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—21no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103C22×D411yescharacteristic
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—41no—
171C4×C103—21no—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—41no—
175C4×C103—41no—
176C4×C103—41no—
177C4×C103—41no—
178C4×C103H(5,𝔽2)11yescharacteristic
179C4×C103H(5,𝔽2)11yescharacteristic
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—41no—
184C2×C103—41no—
185C2×C103—41no—
186C2×C103#53411yescharacteristic
187C2×C103#57711yescharacteristic
188C2×C103#57811yescharacteristic
189D103—81no—
190#3201—1031nomaximal, Sylow
191C103#320111yescharacteristic, complemented, Sylow
192#537—1031no—
193#536D10311yescharacteristic, complemented
194#485—1031no—
195#484—1031no—
196#483—1031no—
197#482—1031no—
198#470—1031no—
199#468—1031no—
200#467—1031no—
201#465—1031no—
202#452—1031no—
203#452—1031no—
204#451—1031no—
205#448—1031no—
206#408—1031no—
207C2×#41—1031no—
208C2×#41C2×D10311yescharacteristic
209C22×Q8C2×D10311yescharacteristic
210C2×Q16—1031no—
211C2×Q16—1031no—
212C2×SD16—1031no—
213C2×SD16—1031no—
214C2×M16—1031no—
215C22×C8—1031no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—1031no—
221C22⋊Q8—1031no—
222C22⋊Q8—2061no—
223C22⋊Q8C2×D10311yescharacteristic
224C22⋊Q8C2×D10311yescharacteristic
225C22⋊Q8C2×D10311yescharacteristic
226C22⋊Q8C2×D10311yescharacteristic
227#121—1031no—
228#121—1031no—
229#121—2061no—
230#121—2061no—
231#121—2061no—
232#117C2×D10311yescharacteristic
233C2×C4⋊C4—1031no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237#106—1031no—
238#103—1031no—
239#103—1031no—
240#103—1031no—
241#103—1031no—
242#103—1031no—
243#103—1031no—
244#102—1031no—
245#102—1031no—
246C22⋊C8—1031no—
247C22⋊C8—1031no—
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250#41—41no—
251#41—41no—
252#41—4121no—
253#41—4121no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—1031no—
258C2×Q8C22⋊D10311yescharacteristic
259C2×Q8C22×D10311yescharacteristic
260C2×Q8C22×D10311yescharacteristic
261C2×D4—1031no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4C22⋊D10311yescharacteristic
266C2×D4C22⋊D10311yescharacteristic
267C2×D4C22⋊D10311yescharacteristic
268C22×C4—21no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4C22×D10311yescharacteristic
272C22×C4C22×D10311yescharacteristic
273C22×C4C22×D10311yescharacteristic
274Q16—4121no—
275Q16—4121no—
276SD16—4121no—
277SD16—4121no—
278M16—4121no—
279C2×C8—1031no—
280C2×C8—1031no—
281C2×C8—1031no—
282C2×C8—1031no—
283C2×C8—4121no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—1031no—
289C4⋊C4—1031no—
290C4⋊C4—2061no—
291C4⋊C4—2061no—
292C4⋊C4—2061no—
293C4⋊C4C22×D10311yescharacteristic
294C4⋊C4C22×D10311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2061no—
301C22⋊C4—2061no—
302C22⋊C4—2061no—
303C22⋊C4—2061no—
304C42—21no—
305C23—2061no—
306C23C2×C22⋊D10311yescharacteristic
307C23C2×C22⋊D10311yescharacteristic
308C23C2×C22⋊D10311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—2061no—
316Q8—2061no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—8241no—
321D4—8241no—
322D4—4122no—
323D4—2061no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—8241no—
337C2×C4—4122no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4C2×C22⋊D10311yescharacteristic
342C2×C4C2×C22⋊D10311yescharacteristic
343C2×C4C2×C22⋊D10311yescharacteristic
344C2×C4C23×D10311yescharacteristic
345C8—2061no—
346C8—2061no—
347C8—2061no—
348C8—2061no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—4121no—
359C22—4121no—
360C22—4121no—
361C22C22×C22⋊D10311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4121no—
370C4—4121no—
371C4—4121no—
372C4#1569306611yescharacteristic
373C4#1569306611yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—8241no—
378C2#2026835011yescharacteristic
379C2#2026859911yescharacteristic
380C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#536×C103C2
socleC22×C103C22×D4
prime radical#20268369C2
hypercenter#536D103
hypocenterC103#3201
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20268132C2semidirect
3. #20268124C2semidirect
4. #20268119C2semidirect
5. #20268115C2semidirect
6. #20268047C2semidirect
7. #20268039C2semidirect
8. #20268030C2semidirect
9. #20268022C2semidirect
10. #20267951C2semidirect
11. #20267951C2semidirect
12. #20267947C2semidirect
13. #20267930C2semidirect
14. #20267758C2semidirect
15. #536×C103C2semidirect
191. C103#3201semidirect
193. #536D103semidirect

Maximal subgroups

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

subgroupindex
#202683692
#202681322
#202681242
#202681192
#202681152
#202680472
#202680392
#202680302
#202680222
#202679512
#202679472
#202679302
#202677582
#536×C1032
#3201103