Finite Group Databasebeta

← #27207046

Subgroups — #27207046

Order 13184.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268487C211yesmaximal, characteristic, complemented
2#20268145C211yesmaximal, characteristic, complemented
3#20268129C211yesmaximal, characteristic, complemented
4#20268107C211yesmaximal, characteristic, complemented
5#20268098C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268003C211yesmaximal, characteristic, complemented
9#20267936C211yesmaximal, characteristic, complemented
10#20267930C211yesmaximal, characteristic, complemented
11C4×#13110092C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267787C211yesmaximal, characteristic, complemented
14C2×#15692945C211yesmaximal, characteristic, complemented
15#548×C103C211yesmaximal, characteristic, complemented
16C2×#13110092C2211yescharacteristic
17C2×#13110092C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C22×C103⋊C8C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic
21#15693016—21no—
22#15693013C2211yescharacteristic
23#15693003—21no—
24#15692995C2211yescharacteristic
25#15692995C2211yescharacteristic
26#15692993—21no—
27C4×D412C2211yescharacteristic
28(C22⋊D103)⋊C4—21no—
29#15692980C2211yescharacteristic
30C2×C4⋊Dic103C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35#15692945C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692945C2211yescharacteristic
39#15692945C2211yescharacteristic
40#15692945C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692942C2211yescharacteristic
43#15692942C2211yescharacteristic
44#15692941C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C2×#41×C103C2211yescharacteristic
49C22×Q8×C103C2211yescharacteristic
50#124×C103—21no—
51#124×C103C2211yescharacteristic
52C22⋊Q8×C103—21no—
53C22⋊Q8×C103C2211yescharacteristic
54#121×C103—21no—
55#121×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic
57C4×D4×C103—21no—
58C4×D4×C103C2211yescharacteristic
59C2×D412C2311yescharacteristic
60C2×C22⋊D103—21no—
61C2×C22⋊D103—21no—
62C22×Dic103—21no—
63C2×C4×D103—21no—
64#13110092—22no—
65#13110092—41no—
66#13110090—41no—
67C2×C103⋊C8—41no—
68C2×C103⋊C8—41no—
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C4⋊Dic103—21no—
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83C4×Dic103—21no—
84#41×C103—22no—
85#41×C103—41no—
86C2×Q8×C103—21no—
87C2×Q8×C103—22no—
88C2×Q8×C103—41no—
89C2×Q8×C103C2311yescharacteristic
90C2×Q8×C103C2311yescharacteristic
91C2×D4×C103—21no—
92C2×D4×C103—21no—
93C2×D4×C103D411yescharacteristic
94C2×D4×C103C2311yescharacteristic
95C22×C4×C103—21no—
96C22×C4×C103—21no—
97C22×C4×C103C2311yescharacteristic
98C22×C4×C103C2311yescharacteristic
99C4⋊C4×C103—21no—
100C4⋊C4×C103—21no—
101C4⋊C4×C103D411yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C22⋊C4×C103—21no—
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C22⋊C4×C103D411yescharacteristic
108C22⋊C4×C103D411yescharacteristic
109C42×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103C2×D411yescharacteristic
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115Q8×C103—21no—
116Q8×C103—21no—
117Q8×C103—21no—
118Q8×C103—42no—
119Q8×C103#4112yes—
120D4×C103—22no—
121D4×C103—21no—
122D4×C103—21no—
123D4×C103—42no—
124D4×C103—42no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103C2×D411yescharacteristic
135C2×C4×C103C2×D411yescharacteristic
136C2×C4×C103C2×D411yescharacteristic
137C2×C4×C103C2×D411yescharacteristic
138C2×C4×C103C2411yescharacteristic
139C22⋊D103—42no—
140C22⋊D103—81no—
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—81no—
145D412—21no—
146D412—21no—
147C4×D103—81no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103#13512yes—
161C22×C103C22×D411yescharacteristic
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C4×C103—21no—
166C4×C103—21no—
167C4×C103—22no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103C2×#4111yescharacteristic
173C4×C103H(5,𝔽2)11yescharacteristic
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177C2×C103—22no—
178C2×C103—41no—
179C2×C103—81no—
180C2×C103#54611yescharacteristic
181C2×C103C2×#13511yescharacteristic
182C2×C103#57711yescharacteristic
183D103—81no—
184#3301—1031nomaximal, Sylow
185C103#330111yescharacteristic, complemented, Sylow
186#553—1031no—
187#548D10311yescharacteristic, complemented
188#488—1031no—
189#485—1031no—
190#481—1031no—
191#479—1031no—
192#466—1031no—
193#465—1031no—
194#463—1031no—
195#449—1031no—
196#448—1031no—
197C4×SD16—1031no—
198C8×D4—1031no—
199#416—1031no—
200C2×#103—1031no—
201C2×#41C2×D10311yescharacteristic
202C22×Q8C2×D10311yescharacteristic
203C2×SD16—1031no—
204C2×SD16—1031no—
205C2×D8—1031no—
206C22×C8—1031no—
207C22×C8—1031no—
208#126—2061no—
209#125—1031no—
210#124—21no—
211#124C2×D10311yescharacteristic
212#123—2061no—
213C22⋊Q8—21no—
214C22⋊Q8C2×D10311yescharacteristic
215#121—21no—
216#121—1031no—
217#121—1031no—
218#121—2061no—
219#121C2×D10311yescharacteristic
220C4×Q8C2×D10311yescharacteristic
221C4×D4—21no—
222C4×D4—1031no—
223C4×D4—2061no—
224C4×D4C2×D10311yescharacteristic
225#117—1031no—
226C2×C4⋊C4—1031no—
227#107—1031no—
228#106—1031no—
229#106—1031no—
230C4⋊C8—1031no—
231#103—1031no—
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#103—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241C22⋊C8—1031no—
242C22⋊C8—1031no—
243C4×C8—1031no—
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D10311yescharacteristic
250C2×Q8C22×D10311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—1031no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4C22⋊D10311yescharacteristic
257C2×D4C22×D10311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263C22×C4C22×D10311yescharacteristic
264SD16—4121no—
265SD16—2062no—
266D8—4121no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—1031no—
270C2×C8—1031no—
271C2×C8—4121no—
272C2×C8—4121no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—1031no—
276C4⋊C4—1031no—
277C4⋊C4—1031no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4C22⋊D10311yescharacteristic
282C4⋊C4C22×D10311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4C22⋊D10311yescharacteristic
292C22⋊C4C22⋊D10311yescharacteristic
293C42—21no—
294C42—2061no—
295C42C22×D10311yescharacteristic
296C23—21no—
297C23—2061no—
298C23C2×C22⋊D10311yescharacteristic
299C23C2×C22⋊D10311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1311010412yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—8241no—
311D4—4122no—
312D4—2061no—
313D4—2061no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—8241no—
324C2×C4—8241no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4C2×C22⋊D10311yescharacteristic
329C2×C4C2×C22⋊D10311yescharacteristic
330C2×C4C2×C22⋊D10311yescharacteristic
331C2×C4C2×C22⋊D10311yescharacteristic
332C2×C4C23×D10311yescharacteristic
333C8—2061no—
334C8—2061no—
335C8—2061no—
336C8—2061no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—4121no—
346C22—4121no—
347C22—4121no—
348C22#1569304112yes—
349C22C22×C22⋊D10311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—4121no—
358C4—4121no—
359C4—4121no—
360C4C2×#1311010411yescharacteristic
361C4#1569306611yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—8241no—
366C2#2026843511yescharacteristic
367C2C2×#1569304111yescharacteristic
368C2#2026859911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#548×C103C2
socleC22×C103C22×D4
hypercenter#548D103
hypocenterC103#3301
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #20268487C2semidirect
2. #20268145C2semidirect
3. #20268129C2semidirect
4. #20268107C2semidirect
5. #20268098C2semidirect
6. #20268025C2semidirect
7. #20268022C2semidirect
8. #20268003C2semidirect
9. #20267936C2semidirect
10. #20267930C2semidirect
11. C4×#13110092C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267787C2semidirect
14. C2×#15692945C2semidirect
15. #548×C103C2semidirect
185. C103#3301semidirect
187. #548D103semidirect

Maximal subgroups

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

subgroupindex
#202684872
#202681452
#202681292
#202681072
#202680982
#202680252
#202680222
#202680032
#202679362
#202679302
C4×#131100922
D4×C103⋊C82
#202677872
C2×#156929452
#548×C1032
#3301103