Finite Group Databasebeta

← #27205821

Subgroups — #27205821

Order 13184.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268396C211yesmaximal, characteristic, complemented
2#20268197C211yesmaximal, characteristic, complemented
3#20268181C211yesmaximal, characteristic, complemented
4#20268145C211yesmaximal, characteristic, complemented
5#20268139C211yesmaximal, characteristic, complemented
6#20268042C211yesmaximal, characteristic, complemented
7#20268039C211yesmaximal, characteristic, complemented
8#20268025C211yesmaximal, characteristic, complemented
9#20268022C211yesmaximal, characteristic, complemented
10#20267901C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110092C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14#20267747C211yesmaximal, characteristic, complemented
15#542×C103C211yesmaximal, characteristic, complemented
16C2×#13110092C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C2×#13110089C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22#15693018C2211yescharacteristic
23#15693013C2211yescharacteristic
24#15693006—21no—
25#15693006—21no—
26#15692995C2211yescharacteristic
27#15692995C2211yescharacteristic
28#15692994—21no—
29#15692994—21no—
30C4×D412C2211yescharacteristic
31C4×D412C2211yescharacteristic
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34#15692952C2211yescharacteristic
35#15692952C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692941C2211yescharacteristic
41#15692941C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692932C2211yescharacteristic
45#15692932C2211yescharacteristic
46C4×C103⋊C8C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C4⋊Q8×C103C2211yescharacteristic
49#126×C103—21no—
50#124×C103—21no—
51#124×C103C2211yescharacteristic
52#123×C103—21no—
53C22⋊Q8×C103—21no—
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic
57C4×D4×C103C2211yescharacteristic
58#117×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—
71#13110089—22no—
72C2×C103⋊C8—22no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84(C2×D103)⋊C4—21no—
85C2×Q8×C103—21no—
86C2×Q8×C103C2311yescharacteristic
87C2×D4×C103—21no—
88C2×D4×C103C2311yescharacteristic
89C22×C4×C103—21no—
90C22×C4×C103C2311yescharacteristic
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103D411yescharacteristic
95C4⋊C4×C103D411yescharacteristic
96C4⋊C4×C103C2311yescharacteristic
97C4⋊C4×C103C2311yescharacteristic
98C22⋊C4×C103—21no—
99C22⋊C4×C103—21no—
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103—21no—
103C22⋊C4×C103D411yescharacteristic
104C22⋊C4×C103D411yescharacteristic
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111C22×D103—21no—
112Q8×C103—21no—
113Q8×C103—21no—
114Q8×C103—81no—
115D4×C103—21no—
116D4×C103—21no—
117D4×C103—81no—
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×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—81no—
131C22⋊D103—81no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134D412—21no—
135D412—21no—
136D412—21no—
137D412—21no—
138D412—81no—
139D412—81no—
140C4×D103—81no—
141C4×D103—81no—
142C103⋊C8—21no—
143C103⋊C8—21no—
144C103⋊C8#4112yes—
145C103⋊C8#4112yes—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103C22×D411yescharacteristic
153C2×D103—41no—
154C2×D103—41no—
155C2×D103—41no—
156C2×D103—41no—
157C2×D103—41no—
158C2×D103—41no—
159C4×C103—21no—
160C4×C103—21no—
161C4×C103—21no—
162C4×C103—21no—
163C4×C103—21no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—41no—
167C4×C103C2×#4111yescharacteristic
168C4×C103C2×#4111yescharacteristic
169Dic103—41no—
170Dic103—41no—
171C2×C103—41no—
172C2×C103—81no—
173C2×C103#53211yescharacteristic
174C2×C103#57611yescharacteristic
175C2×C103#57711yescharacteristic
176D103—81no—
177D103—81no—
178#3179—1031nomaximal, Sylow
179C103#317911yescharacteristic, complemented, Sylow
180#542D10311yescharacteristic, complemented
181#540—1031no—
182#501—1031no—
183#496—1031no—
184#488—1031no—
185#486—1031no—
186#469—1031no—
187#468—1031no—
188#466—1031no—
189#465—1031no—
190#442—1031no—
191#440—1031no—
192C4×SD16—1031no—
193C4×D8—1031no—
194#405—1031no—
195C2×SD16—1031no—
196C2×SD16—1031no—
197C2×D8—1031no—
198C2×D8—1031no—
199C2×M16—1031no—
200C22×C8—1031no—
201C4⋊Q8C2×D10311yescharacteristic
202#127—1031no—
203#126—21no—
204#125—1031no—
205#124—21no—
206#124C2×D10311yescharacteristic
207#123—21no—
208#123—2061no—
209#123—2061no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D10311yescharacteristic
212#121—1031no—
213#121—1031no—
214#121—2061no—
215#121—2061no—
216#121C2×D10311yescharacteristic
217C4×Q8C2×D10311yescharacteristic
218C4×D4—1031no—
219C4×D4—1031no—
220C4×D4C2×D10311yescharacteristic
221#117C2×D10311yescharacteristic
222#107—1031no—
223#107—1031no—
224#106—1031no—
225#106—1031no—
226#103—1031no—
227#103—1031no—
228#102—1031no—
229#102—1031no—
230#102—1031no—
231#102—1031no—
232#102—1031no—
233#102—1031no—
234#97—1031no—
235#97—1031no—
236C4×C8—1031no—
237C4×C8—1031no—
238C2×Q8—21no—
239C2×Q8C22×D10311yescharacteristic
240C2×D4—21no—
241C2×D4—1031no—
242C2×D4—1031no—
243C2×D4—2061no—
244C2×D4—2061no—
245C2×D4—2061no—
246C2×D4—2061no—
247C2×D4C22×D10311yescharacteristic
248C22×C4—21no—
249C22×C4—2061no—
250C22×C4—2061no—
251C22×C4C22×D10311yescharacteristic
252SD16—2062no—
253SD16—2062no—
254D8—2062no—
255D8—2062no—
256M16—2062no—
257C2×C8—1031no—
258C2×C8—1031no—
259C2×C8—1031no—
260C2×C8—1031no—
261C2×C8—2062no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—2061no—
268C4⋊C4—2061no—
269C4⋊C4C22⋊D10311yescharacteristic
270C4⋊C4C22⋊D10311yescharacteristic
271C4⋊C4C22×D10311yescharacteristic
272C4⋊C4C22×D10311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—2061no—
279C22⋊C4—2061no—
280C22⋊C4—2061no—
281C22⋊C4—2061no—
282C22⋊C4C22⋊D10311yescharacteristic
283C22⋊C4C22⋊D10311yescharacteristic
284C42—21no—
285C42C22×D10311yescharacteristic
286C42C22×D10311yescharacteristic
287C23—21no—
288C23—2061no—
289C23—2061no—
290C23C2×C22⋊D10311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—8241no—
298D4—8241no—
299D4—8241no—
300D4—8241no—
301D4—2061no—
302D4—2061no—
303D4—2061no—
304D4—2061no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—8241no—
312C2×C4—8241no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4C2×C22⋊D10311yescharacteristic
316C2×C4C2×C22⋊D10311yescharacteristic
317C2×C4C2×C22⋊D10311yescharacteristic
318C2×C4C2×C22⋊D10311yescharacteristic
319C2×C4C2×C22⋊D10311yescharacteristic
320C2×C4C23×D10311yescharacteristic
321C8—1032no—
322C8—1032no—
323C8—2061no—
324C8—2061no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—4121no—
332C22—4121no—
333C22—4121no—
334C22—4121no—
335C22—4121no—
336C22—4121no—
337C22C22×C22⋊D10311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4121no—
347C4—4121no—
348C4#41×D10311yescharacteristic
349C4#41×D10311yescharacteristic
350C2—41no—
351C2—81no—
352C2—8241no—
353C2—8241no—
354C2#2026833711yescharacteristic
355C2#2026859411yescharacteristic
356C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#542×C103C2
socleC22×C103C22×D4
hypercenter#542D103
hypocenterC103#3179
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20268396C2semidirect
2. #20268197C2semidirect
3. #20268181C2semidirect
4. #20268145C2semidirect
5. #20268139C2semidirect
6. #20268042C2semidirect
7. #20268039C2semidirect
8. #20268025C2semidirect
9. #20268022C2semidirect
10. #20267901C2semidirect
11. #20267889C2semidirect
12. C4×#13110092C2semidirect
13. C4×#13110090C2semidirect
14. #20267747C2semidirect
15. #542×C103C2semidirect
179. C103#3179semidirect
180. #542D103semidirect

Maximal subgroups

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

subgroupindex
#202683962
#202681972
#202681812
#202681452
#202681392
#202680422
#202680392
#202680252
#202680222
#202679012
#202678892
C4×#131100922
C4×#131100902
#202677472
#542×C1032
#3179103