Finite Group Databasebeta

← #27205343

Subgroups — #27205343

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#20268396C211yesmaximal, characteristic, complemented
2#20268109C211yesmaximal, characteristic, complemented
3#20268104C211yesmaximal, characteristic, complemented
4#20268098C211yesmaximal, characteristic, complemented
5#20268091C211yesmaximal, characteristic, complemented
6#20267991C211yesmaximal, characteristic, complemented
7#20267986C211yesmaximal, characteristic, complemented
8#20267936C211yesmaximal, characteristic, complemented
9#20267936C211yesmaximal, characteristic, complemented
10#20267901C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110092C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#520×C103C211yesmaximal, characteristic, complemented
16C2×#13110092C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20#15693018C2211yescharacteristic
21#15693013C2211yescharacteristic
22#15693006—21no—
23#15693006—21no—
24#15692995C2211yescharacteristic
25#15692995C2211yescharacteristic
26#15692994—21no—
27#15692994—21no—
28C4×D412C2211yescharacteristic
29C4×D412C2211yescharacteristic
30#15692954C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35C4⋊(C103⋊C8)C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692941C2211yescharacteristic
41#15692941C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C4×Q8×C103C2211yescharacteristic
50C4×Q8×C103C2211yescharacteristic
51C4×D4×C103—21no—
52C4×D4×C103—21no—
53C4×D4×C103C2211yescharacteristic
54C4×D4×C103C2211yescharacteristic
55#117×C103—21no—
56#117×C103C2211yescharacteristic
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103C2211yescharacteristic
59C2×D412—21no—
60C2×D412—21no—
61C2×D412C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C4×D103—21no—
66C2×C4×D103—21no—
67#13110092—22no—
68#13110092—22no—
69#13110090—22no—
70#13110090—22no—
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79(C2×D103)⋊C4—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83#41×C103—22no—
84#41×C103—22no—
85C2×Q8×C103C2311yescharacteristic
86C2×D4×C103—21no—
87C2×D4×C103C2311yescharacteristic
88C22×C4×C103—21no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—21no—
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×C103D411yescharacteristic
103C22⋊C4×C103D411yescharacteristic
104C42×C103—21no—
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111C22×D103—21no—
112Q8×C103—21no—
113Q8×C103#4112yes—
114D4×C103—24no—
115D4×C103—21no—
116D4×C103#4112yes—
117C2×C4×C103—24no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—81no—
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—81no—
133C22⋊D103—81no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136D412—21no—
137D412—21no—
138D412—21no—
139D412—21no—
140D412—81no—
141D412—81no—
142C4×D103—81no—
143C4×D103—81no—
144C103⋊C8—21no—
145C103⋊C8—21no—
146C103⋊C8—21no—
147C103⋊C8—21no—
148C22×C103—21no—
149C22×C103—22no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103C22×D411yescharacteristic
155C2×D103—41no—
156C2×D103—41no—
157C2×D103—41no—
158C2×D103—41no—
159C2×D103—41no—
160C2×D103—41no—
161C4×C103—21no—
162C4×C103—22no—
163C4×C103—21no—
164C4×C103—21no—
165C4×C103—21no—
166C4×C103—21no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103C2×#4111yescharacteristic
170C4×C103C2×#4111yescharacteristic
171Dic103—41no—
172Dic103—41no—
173C2×C103—41no—
174C2×C103—42no—
175C2×C103#52511yescharacteristic
176C2×C103#57611yescharacteristic
177C2×C103#57711yescharacteristic
178D103—81no—
179D103—81no—
180#3119—1031nomaximal, Sylow
181C103#311911yescharacteristic, complemented, Sylow
182#540—1031no—
183#520D10311yescharacteristic, complemented
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×#41C2×D10311yescharacteristic
198C2×SD16—1031no—
199C2×SD16—1031no—
200C2×D8—1031no—
201C2×D8—1031no—
202#127—1031no—
203#125—1031no—
204#123—2061no—
205#123—2061no—
206#121—1031no—
207#121—1031no—
208#121—2061no—
209#121—2061no—
210C4×Q8C2×D10311yescharacteristic
211C4×Q8C2×D10311yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1031no—
215C4×D4—1031no—
216C4×D4C2×D10311yescharacteristic
217C4×D4C2×D10311yescharacteristic
218#117—21no—
219#117C2×D10311yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D10311yescharacteristic
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—22no—
241#41—22no—
242C2×Q8C22×D10311yescharacteristic
243C2×D4—21no—
244C2×D4—1031no—
245C2×D4—1031no—
246C2×D4—2061no—
247C2×D4—2061no—
248C2×D4—2061no—
249C2×D4—2061no—
250C2×D4C22×D10311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
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—21no—
269C4⋊C4—1031no—
270C4⋊C4—1031no—
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—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4—2061no—
283C22⋊C4C22⋊D10311yescharacteristic
284C22⋊C4C22⋊D10311yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D10311yescharacteristic
288C42C22×D10311yescharacteristic
289C23—21no—
290C23—2061no—
291C23—2061no—
292C23C2×C22⋊D10311yescharacteristic
293Q8—21no—
294Q8#1311010512yes—
295D4—24no—
296D4—21no—
297D4—8241no—
298D4—8241no—
299D4—8241no—
300D4—8241no—
301D4—2061no—
302D4—2061no—
303D4—2061no—
304D4—2061no—
305D4#1311010512yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—8241no—
316C2×C4—8241no—
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—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—4121no—
336C22—4121no—
337C22—4121no—
338C22—4121no—
339C22—4121no—
340C22—4121no—
341C22C22×C22⋊D10311yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—4121no—
351C4—4121no—
352C4C2×#1311010511yescharacteristic
353C4C2×#1311010511yescharacteristic
354C2—41no—
355C2—42no—
356C2—8241no—
357C2—8241no—
358C2#2026830211yescharacteristic
359C2#2026859411yescharacteristic
360C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#520×C103C2
socleC22×C103C22×D4
hypercenter#520D103
hypocenterC103#3119
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20268396C2semidirect
2. #20268109C2semidirect
3. #20268104C2semidirect
4. #20268098C2semidirect
5. #20268091C2semidirect
6. #20267991C2semidirect
7. #20267986C2semidirect
8. #20267936C2semidirect
9. #20267936C2semidirect
10. #20267901C2semidirect
11. #20267889C2semidirect
12. C4×#13110092C2semidirect
13. C4×#13110090C2semidirect
14. #20267852C2semidirect
15. #520×C103C2semidirect
181. C103#3119semidirect
183. #520D103semidirect

Maximal subgroups

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

subgroupindex
#202683962
#202681092
#202681042
#202680982
#202680912
#202679912
#202679862
#202679362
#202679012
#202678892
C4×#131100922
C4×#131100902
#202678522
#520×C1032
#3119103