Finite Group Databasebeta

← #27197953

Subgroups — #27197953

Order 13184.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693008C211yesmaximal, characteristic
2#20267695C211yesmaximal, characteristic, complemented
3#20267695C211yesmaximal, characteristic, complemented
4#20267685C211yesmaximal, characteristic, complemented
5#20267685C211yesmaximal, characteristic, complemented
6#20267679C211yesmaximal, characteristic, complemented
7#20267679C211yesmaximal, characteristic, complemented
8#20267671C211yesmaximal, characteristic
9#20267664C211yesmaximal, characteristic, complemented
10#20267663C211yesmaximal, characteristic, complemented
11#20267658C211yesmaximal, characteristic, complemented
12#20267642C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic103C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
15#386×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18#15693008C418yescomplemented
19C2×Dic103⋊C4C2211yescharacteristic
20C2×Dic103⋊C4C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×C22⋊Dic103C2211yescharacteristic
24C2×C22⋊Dic103C2211yescharacteristic
25C2×C22⋊Dic103C2211yescharacteristic
26C2×C22⋊Dic103C2211yescharacteristic
27C2×C22⋊Dic103C2211yescharacteristic
28C2×C22⋊Dic103C2211yescharacteristic
29C2×C22⋊Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C22×D4×C103C2211yescharacteristic
46C23×C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C2×Dic206—41no—
53C2×Dic206—41no—
54C2×Dic206C2×C414yescomplemented
55C22×Dic103—22no—
56C22×Dic103—41no—
57C22×Dic103—41no—
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66Dic103⋊C4—22no—
67Dic103⋊C4—22no—
68Dic103⋊C4—41no—
69Dic103⋊C4—41no—
70C22⋊Dic103—22no—
71C22⋊Dic103—41no—
72C22⋊Dic103—41no—
73C22⋊Dic103C2×C414yescomplemented
74C22⋊Dic103C2×C414yescomplemented
75C22⋊Dic103C2×C414yescomplemented
76C22⋊Dic103C2×C414yescomplemented
77C4×Dic103—41no—
78C4×Dic103—41no—
79C4×Dic103—41no—
80C4×Dic103—41no—
81C4×Dic103C2×C414yescomplemented
82C24×C103C2311yescharacteristic
83C24×C103C2311yescharacteristic
84C2×D4×C103—41no—
85C2×D4×C103—41no—
86C2×D4×C103C2×C414yes—
87C22×C4×C103—22no—
88C22×C4×C103—41no—
89C22×C4×C103—41no—
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C22×C4×C103C2311yescharacteristic
94C22×C4×C103C2311yescharacteristic
95C22⋊C4×C103—22no—
96C22⋊C4×C103—41no—
97C22⋊C4×C103—41no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103—21no—
105C23×C103—21no—
106C23×C103—21no—
107C23×C103—21no—
108C23×C103—21no—
109C23×C103—21no—
110C23×C103C22×C412yes—
111C23×C103C22×C412yes—
112C23×C103C2411yescharacteristic
113D4×C103—44no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—44no—
128C2×C4×C103C22×C412yes—
129C2×C4×C103#4112yes—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—21no—
146C2×Dic103—21no—
147C2×Dic103—21no—
148C2×Dic103—21no—
149C2×Dic103—44no—
150C2×Dic103C22×C412yes—
151C2×Dic103C22×C412yes—
152C2×Dic103C22×C412yes—
153C2×Dic103C22×C412yes—
154C2×Dic103#4112yes—
155Dic206—44no—
156C22×C103—22no—
157C22×C103—22no—
158C22×C103—22no—
159C22×C103—22no—
160C22×C103—22no—
161C22×C103—22no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103—41no—
167C22×C103—41no—
168C22×C103—41no—
169C22×C103—41no—
170C22×C103C23×C411yescharacteristic
171C22×C103C2×#4111yescharacteristic
172C22×C103C2×#4111yescharacteristic
173C22×C103H(5,𝔽2)11yescharacteristic
174C22×C103H(5,𝔽2)11yescharacteristic
175C22×C103H(5,𝔽2)11yescharacteristic
176C22×C1032−1+411yescharacteristic
177C4×C103—22no—
178C4×C103—22no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182Dic103—22no—
183Dic103—22no—
184Dic103—22no—
185Dic103—22no—
186Dic103—22no—
187Dic103—41no—
188Dic103—41no—
189Dic103—41no—
190C2×C103—42no—
191C2×C103—42no—
192C2×C103C4×#4111yescharacteristic
193C2×C103#51811yescharacteristic
194C2×C103#52011yescharacteristic
195C2×C103#53811yescharacteristic
196C2×C103#53811yescharacteristic
197C2×C103#54211yescharacteristic
198C2×C103#54211yescharacteristic
199#2337—1031nomaximal, Sylow
200C103#233711yescharacteristic, complemented, Sylow
201C2×#124—1031no—
202#391—1031no—
203#391—1031no—
204#388—1031no—
205#388—1031no—
206#388—1031no—
207#388—1031no—
208#386—1031no—
209#386D10311yescharacteristic
210#385—1031no—
211#385—1031no—
212#383—1031no—
213C4×C4⋊C4—1031no—
214C4×C22⋊C4—1031no—
215C4×C22⋊C4—1031no—
216C22×Q8—1031no—
217C22×D4C2×D10311yescharacteristic
218C23×C4—1031no—
219C23×C4C2×D10311yescharacteristic
220#124—1038no—
221C2×C4⋊C4—1031no—
222C2×C4⋊C4—1031no—
223C2×C4⋊C4—1031no—
224C2×C4⋊C4—1031no—
225C2×C22⋊C4—1031no—
226C2×C22⋊C4—1031no—
227C2×C22⋊C4—1031no—
228C2×C22⋊C4—1031no—
229C2×C22⋊C4—1031no—
230C2×C22⋊C4—1031no—
231C2×C22⋊C4—1031no—
232C2×C22⋊C4C2×D10311yescharacteristic
233C2×C22⋊C4C2×D10311yescharacteristic
234C2×C22⋊C4C2×D10311yescharacteristic
235C2×C42—1031no—
236C2×C42—1031no—
237C2×C42—1031no—
238C2×C42—1031no—
239C2×C42—1031no—
240#95—1031no—
241#95—1031no—
242#95—1031no—
243#95—1031no—
244#95—1031no—
245#95—1031no—
246#95—1031no—
247#95—1031no—
248#95—1031no—
249#95—1031no—
250#95C2×D10311yescharacteristic
251#95C2×D10311yescharacteristic
252C24C22×D10311yescharacteristic
253C24C22×D10311yescharacteristic
254C2×Q8—1034no—
255C2×Q8—4121no—
256C2×Q8—4121no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4C4×D10314yes—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—1031no—
264C22×C4—1031no—
265C22×C4—1031no—
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—1031no—
270C22×C4—1031no—
271C22×C4—4121no—
272C22×C4—4121no—
273C22×C4—2062no—
274C22×C4C22×D10311yescharacteristic
275C22×C4C22×D10311yescharacteristic
276C22×C4C22×D10311yescharacteristic
277C22×C4C22×D10311yescharacteristic
278C22×C4C22×D10311yescharacteristic
279C4⋊C4—4121no—
280C4⋊C4—4121no—
281C4⋊C4—2062no—
282C4⋊C4—2062no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—1034no—
287C22⋊C4—1034no—
288C22⋊C4—1034no—
289C22⋊C4—1034no—
290C22⋊C4—4121no—
291C22⋊C4—4121no—
292C22⋊C4—2062no—
293C42—1034no—
294C42—4121no—
295C42—4121no—
296C42—4121no—
297C42—4121no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23C2×C4×D10312yes—
311C23C2×C4×D10312yes—
312C23C23×D10311yescharacteristic
313Q8—4124no—
314D4—44no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—44no—
329C2×C4—1032no—
330C2×C4—1032no—
331C2×C4—1032no—
332C2×C4—1032no—
333C2×C4—1032no—
334C2×C4—4124no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4—2061no—
342C2×C4—2061no—
343C2×C4—2061no—
344C2×C4—2061no—
345C2×C4—2061no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4—2061no—
353C2×C4—2061no—
354C2×C4C2×C4×D10312yes—
355C2×C4#1311010412yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C22×C4×D10311yescharacteristic
371C22#41×D10311yescharacteristic
372C22C2×#1311010411yescharacteristic
373C22#1569306611yescharacteristic
374C22#1569306611yescharacteristic
375C22#1569306611yescharacteristic
376C22#1569306811yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—4121no—
383C4—4121no—
384C4—4121no—
385C4—2062no—
386C4—2062no—
387C4—2062no—
388C4—2062no—
389C4—2062no—
390C2—42no—
391C2—42no—
392C2C4×#1311010411yescharacteristic
393C2#2026826411yescharacteristic
394C2#2026827011yescharacteristic
395C2#2026837311yescharacteristic
396C2#2026837611yescharacteristic
397C2#2026840811yescharacteristic
398C2#2026840911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#386×C103C2
socle, cosocleC23×C103C24
prime radicalC22×D4×C103C22
hypercenter#386D103
hypocenterC103#2337
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. #20267695C2semidirect
3. #20267695C2semidirect
4. #20267685C2semidirect
5. #20267685C2semidirect
6. #20267679C2semidirect
7. #20267679C2semidirect
9. #20267664C2semidirect
10. #20267663C2semidirect
11. #20267658C2semidirect
12. #20267642C2semidirect
13. C22⋊C4×Dic103C2semidirect
14. C4×C22⋊Dic103C2semidirect
18. #15693008C4semidirect
54. C2×Dic206C2×C4semidirect
73. C22⋊Dic103C2×C4semidirect
74. C22⋊Dic103C2×C4semidirect
75. C22⋊Dic103C2×C4semidirect
76. C22⋊Dic103C2×C4semidirect
81. C4×Dic103C2×C4semidirect
200. C103#2337semidirect

Maximal subgroups

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

subgroupindex
C2×#156930082
#202676952
#202676852
#202676792
#202676712
#202676642
#202676632
#202676582
#202676422
C22⋊C4×Dic1032
C4×C22⋊Dic1032
#386×C1032
#2337103