Finite Group Databasebeta

← #27205337

Subgroups — #27205337

Order 13184.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268271C211yesmaximal, characteristic, complemented
2#20268107C211yesmaximal, characteristic, complemented
3#20268102C211yesmaximal, characteristic, complemented
4#20268095C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20267988C211yesmaximal, characteristic, complemented
7#20267983C211yesmaximal, characteristic, complemented
8#20267934C211yesmaximal, characteristic, complemented
9#20267934C211yesmaximal, characteristic, complemented
10#20267901C211yesmaximal, characteristic, complemented
11#20267891C211yesmaximal, characteristic, complemented
12C4×#13110093C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#540×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110093C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C4×Dic206C2211yescharacteristic
22C4×Dic206C2211yescharacteristic
23C4×D412C2211yescharacteristic
24C4×D412C2211yescharacteristic
25(C22⋊D103)⋊C4—21no—
26(C22⋊D103)⋊C4—21no—
27#15692979—21no—
28C2×C4⋊Dic103C2211yescharacteristic
29C4⋊C4×D103—21no—
30#15692954C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35C4⋊(C103⋊C8)C2211yescharacteristic
36#15692944C2211yescharacteristic
37#15692944C2211yescharacteristic
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48#127×C103C2211yescharacteristic
49#125×C103C2211yescharacteristic
50#123×C103—21no—
51#123×C103—21no—
52#121×C103—21no—
53#121×C103—21no—
54#121×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56C4×D4×C103C2211yescharacteristic
57C4×D4×C103C2211yescharacteristic
58#117×C103C2211yescharacteristic
59#13110105—22no—
60#13110105—22no—
61C2×Dic206C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C22×Dic103—21no—
65C2×C4×D103—21no—
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68#13110093—22no—
69#13110093—22no—
70#13110090—22no—
71#13110090—22no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83C4×Dic103—21no—
84C4×Dic103—21no—
85C2×D4×C103—21no—
86C2×D4×C103—21no—
87C2×D4×C103—21no—
88C2×D4×C103—21no—
89C2×D4×C103C2311yescharacteristic
90C2×D4×C103C2311yescharacteristic
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103C2311yescharacteristic
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103D411yescharacteristic
97C4⋊C4×C103D411yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103—21no—
103C22⋊C4×C103—21no—
104C22⋊C4×C103D411yescharacteristic
105C22⋊C4×C103D411yescharacteristic
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103—21no—
110C23×C103C2×D411yescharacteristic
111C22×D103—21no—
112D4×C103—21no—
113D4×C103—21no—
114D4×C103—21no—
115D4×C103—21no—
116D4×C103—81no—
117D4×C103—81no—
118D4×C103—81no—
119D4×C103—81no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—81no—
125C2×C4×C103—81no—
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2×D411yescharacteristic
131C2×C4×C103C2411yescharacteristic
132C22⋊D103—24no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—81no—
137D412—21no—
138D412#4112yes—
139C4×D103—24no—
140C4×D103—81no—
141C4×D103—81no—
142Dic206—21no—
143Dic206#4112yes—
144C103⋊C8—21no—
145C103⋊C8—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103C22×D411yescharacteristic
158C2×D103—22no—
159C2×D103—41no—
160C2×D103—41no—
161C4×C103—21no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103C2×#4111yescharacteristic
169C4×C103C2×#4111yescharacteristic
170Dic103—22no—
171Dic103—41no—
172Dic103—41no—
173C2×C103—41no—
174C2×C103—81no—
175C2×C103—81no—
176C2×C103#52511yescharacteristic
177C2×C103#57611yescharacteristic
178C2×C103#57711yescharacteristic
179D103—42no—
180#3119—1031nomaximal, Sylow
181C103#311911yescharacteristic, complemented, Sylow
182#540D10311yescharacteristic, complemented
183#520—1031no—
184#481—1031no—
185#480—1031no—
186#479—1031no—
187#478—1031no—
188#460—1031no—
189#459—1031no—
190#449—1031no—
191#449—1031no—
192#442—1031no—
193#440—1031no—
194C4×SD16—1031no—
195C4×D8—1031no—
196#433—1031no—
197C2×#41—1031no—
198C2×SD16—1031no—
199C2×SD16—1031no—
200C2×D8—1031no—
201C2×D8—1031no—
202#127C2×D10311yescharacteristic
203#125C2×D10311yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D10311yescharacteristic
209#121C2×D10311yescharacteristic
210C4×Q8—1031no—
211C4×Q8—1031no—
212C4×D4—1031no—
213C4×D4—1031no—
214C4×D4—2061no—
215C4×D4—2061no—
216C4×D4C2×D10311yescharacteristic
217C4×D4C2×D10311yescharacteristic
218#117—2061no—
219#117C2×D10311yescharacteristic
220C2×C4⋊C4—1031no—
221C2×C4⋊C4—2061no—
222#107—1031no—
223#107—1031no—
224#106—1031no—
225#106—1031no—
226C4⋊C8—1031no—
227C4⋊C8—1031no—
228#103—1031no—
229#103—1031no—
230#102—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#102—1031no—
235#102—1031no—
236C22⋊C8—1031no—
237C22⋊C8—1031no—
238#97—1031no—
239C4×C8—1031no—
240#41—2062no—
241#41—2062no—
242C2×Q8—1031no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—1031no—
248C2×D4—2061no—
249C2×D4C22×D10311yescharacteristic
250C2×D4C22×D10311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—2061no—
254C22×C4—2061no—
255C22×C4—2061no—
256C22×C4—2061no—
257C22×C4C22×D10311yescharacteristic
258SD16—2062no—
259SD16—2062no—
260D8—2062no—
261D8—2062no—
262C2×C8—1031no—
263C2×C8—1031no—
264C2×C8—1031no—
265C2×C8—1031no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1031no—
269C4⋊C4—1031no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4C22⋊D10311yescharacteristic
274C4⋊C4C22⋊D10311yescharacteristic
275C4⋊C4C22×D10311yescharacteristic
276C4⋊C4C22×D10311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4C22⋊D10311yescharacteristic
284C22⋊C4C22⋊D10311yescharacteristic
285C42—2061no—
286C42—2061no—
287C42C22×D10311yescharacteristic
288C42C22×D10311yescharacteristic
289C23—21no—
290C23—21no—
291C23—2061no—
292C23C2×C22⋊D10311yescharacteristic
293Q8—1032no—
294Q8—2061no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—1032no—
304D4—2064no—
305D4—2061no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—8241no—
313C2×C4—8241no—
314C2×C4—8241no—
315C2×C4—2064no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4C2×C22⋊D10311yescharacteristic
320C2×C4C2×C22⋊D10311yescharacteristic
321C2×C4C2×C22⋊D10311yescharacteristic
322C2×C4C2×C22⋊D10311yescharacteristic
323C2×C4C2×C22⋊D10311yescharacteristic
324C2×C4C23×D10311yescharacteristic
325C8—2061no—
326C8—2061no—
327C8—2061no—
328C8—2061no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—4121no—
339C22—4121no—
340C22—2062no—
341C22C22×C22⋊D10311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—4121no—
350C4—4121no—
351C4—2062no—
352C4#41×D10311yescharacteristic
353C4#41×D10311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—4122no—
358C2#2026829811yescharacteristic
359C2#2026859411yescharacteristic
360C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#540×C103C2
socleC22×C103C22×D4
hypercenter#540D103
hypocenterC103#3119
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20268271C2semidirect
2. #20268107C2semidirect
3. #20268102C2semidirect
4. #20268095C2semidirect
5. #20268088C2semidirect
6. #20267988C2semidirect
7. #20267983C2semidirect
8. #20267934C2semidirect
9. #20267934C2semidirect
10. #20267901C2semidirect
11. #20267891C2semidirect
12. C4×#13110093C2semidirect
13. C4×#13110090C2semidirect
14. #20267852C2semidirect
15. #540×C103C2semidirect
181. C103#3119semidirect
182. #540D103semidirect

Maximal subgroups

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

subgroupindex
#202682712
#202681072
#202681022
#202680952
#202680882
#202679882
#202679832
#202679342
#202679012
#202678912
C4×#131100932
C4×#131100902
#202678522
#540×C1032
#3119103