Finite Group Databasebeta

← #27198286

Subgroups — #27198286

Order 13184.

512 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693003C211yesmaximal, characteristic
2#20267691C211yesmaximal, characteristic
3#20267689C211yesmaximal, characteristic, complemented
4#20267688C211yesmaximal, characteristic, complemented
5#20267685C211yesmaximal, characteristic, complemented
6#20267683C211yesmaximal, characteristic, complemented
7#20267682C211yesmaximal, characteristic, complemented
8#20267674C211yesmaximal, characteristic, complemented
9#20267672C211yesmaximal, characteristic, complemented
10#20267668C211yesmaximal, characteristic
11#20267666C211yesmaximal, characteristic, complemented
12#20267663C211yesmaximal, characteristic, complemented
13#20267650C211yesmaximal, characteristic, complemented
14#20267648C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19#15693003C418yescomplemented
20C2×C4⋊Dic103C2211yescharacteristic
21C2×C4⋊Dic103C2211yescharacteristic
22C2×C4⋊Dic103C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×C22⋊Dic103C2211yescharacteristic
29C2×C22⋊Dic103C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×C4×Dic103C2211yescharacteristic
36C2×C4×Dic103C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C22⋊C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C23×D103C2311yescharacteristic
53C2×C22⋊D103—41no—
54C2×C22⋊D103—41no—
55C2×C22⋊D103C2×C414yes—
56C22×Dic103—41no—
57C22×Dic103—41no—
58C22×Dic103—41no—
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C2×C4×D103—41no—
67C2×C4×D103—41no—
68C2×C4×D103C2×C414yescomplemented
69C4⋊Dic103—41no—
70C4⋊Dic103—41no—
71C4⋊Dic103C2×C414yescomplemented
72Dic103⋊C4—41no—
73Dic103⋊C4—41no—
74Dic103⋊C4—41no—
75Dic103⋊C4—41no—
76Dic103⋊C4C2×C414yescomplemented
77C22⋊Dic103—41no—
78C22⋊Dic103C2×C414yes—
79(C2×D103)⋊C4—41no—
80(C2×D103)⋊C4—41no—
81(C2×D103)⋊C4—41no—
82(C2×D103)⋊C4—41no—
83(C2×D103)⋊C4C2×C414yescomplemented
84C4×Dic103—41no—
85C4×Dic103—41no—
86C24×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—41no—
94C22⋊C4×C103—41no—
95C22⋊C4×C103—41no—
96C22⋊C4×C103C2×C414yes—
97C42×C103—41no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103C22×C412yes—
105C23×C103C2411yescharacteristic
106C22×D103—21no—
107C22×D103—21no—
108C22×D103—21no—
109C22×D103—21no—
110C22×D103—21no—
111C22×D103—21no—
112C22×D103C22×C412yes—
113C2×C4×C103—21no—
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—21no—
128C2×C4×C103—21no—
129C2×C4×C103C22×C412yes—
130C2×C4×C103C22×C412yes—
131C22⋊D103—44no—
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—21no—
150C2×Dic103—44no—
151C2×Dic103C22×C412yes—
152C2×Dic103C22×C412yes—
153C2×Dic103C22×C412yes—
154C4×D103—44no—
155C22×C103—22no—
156C22×C103—22no—
157C22×C103—22no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103C23×C411yescharacteristic
163C22×C103H(5,𝔽2)11yescharacteristic
164C22×C103H(5,𝔽2)11yescharacteristic
165C22×C103H(5,𝔽2)11yescharacteristic
166C22×C103H(5,𝔽2)11yescharacteristic
167C22×C1032−1+411yescharacteristic
168C22×C1032−1+411yescharacteristic
169C2×D103—22no—
170C2×D103—22no—
171C2×D103—22no—
172C2×D103—41no—
173C2×D103—41no—
174C2×D103—41no—
175C2×D103—41no—
176C4×C103—22no—
177C4×C103—22no—
178C4×C103—41no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182Dic103—22no—
183Dic103—22no—
184Dic103—22no—
185Dic103—41no—
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189C2×C103—42no—
190C2×C103#51811yescharacteristic
191C2×C103#52011yescharacteristic
192C2×C103#52011yescharacteristic
193C2×C103#56011yescharacteristic
194C2×C103#56211yescharacteristic
195C2×C103#56211yescharacteristic
196C2×C103#56311yescharacteristic
197D103—42no—
198#2376—1031nomaximal, Sylow
199C103#237611yescharacteristic, complemented, Sylow
200C2×#123—1031no—
201#390—1031no—
202#389—1031no—
203#389—1031no—
204#388—1031no—
205#388—1031no—
206#388—1031no—
207#388D10311yescharacteristic, complemented
208#387—1031no—
209#387—1031no—
210#386—1031no—
211#385—1031no—
212#385—1031no—
213#380—1031no—
214#380—1031no—
215C22×D4—1031no—
216C23×C4—1031no—
217C23×C4—1031no—
218#123—1038no—
219C2×C4⋊C4—1031no—
220C2×C4⋊C4—1031no—
221C2×C4⋊C4—1031no—
222C2×C4⋊C4—1031no—
223C2×C4⋊C4—1031no—
224C2×C4⋊C4—1031no—
225C2×C4⋊C4—1031no—
226C2×C4⋊C4—1031no—
227C2×C4⋊C4C2×D10311yescharacteristic
228C2×C22⋊C4—1031no—
229C2×C22⋊C4—1031no—
230C2×C22⋊C4—1031no—
231C2×C22⋊C4—1031no—
232C2×C22⋊C4—1031no—
233C2×C22⋊C4—1031no—
234C2×C22⋊C4—1031no—
235C2×C22⋊C4C2×D10311yescharacteristic
236C2×C22⋊C4C2×D10311yescharacteristic
237C2×C22⋊C4C2×D10311yescharacteristic
238C2×C42—1031no—
239C2×C42—1031no—
240C2×C42C2×D10311yescharacteristic
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#95C2×D10311yescharacteristic
250#95C2×D10311yescharacteristic
251C24—1031no—
252C24C22×D10311yescharacteristic
253C2×D4—1034no—
254C2×D4—4121no—
255C2×D4—4121no—
256C22×C4—1031no—
257C22×C4—1031no—
258C22×C4—1031no—
259C22×C4—1034no—
260C22×C4—1031no—
261C22×C4—1031no—
262C22×C4—1031no—
263C22×C4—1031no—
264C22×C4—4121no—
265C22×C4—4121no—
266C22×C4—4121no—
267C22×C4—4121no—
268C22×C4—4121no—
269C22×C4C22×D10311yescharacteristic
270C22×C4C22×D10311yescharacteristic
271C22×C4C22×D10311yescharacteristic
272C22×C4C22×D10311yescharacteristic
273C22×C4C22×D10311yescharacteristic
274C22×C4C22×D10311yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—1034no—
277C4⋊C4—1034no—
278C4⋊C4—4121no—
279C4⋊C4—4121no—
280C4⋊C4—4121no—
281C4⋊C4—4121no—
282C4⋊C4—4121no—
283C4⋊C4—4121no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—1034no—
287C22⋊C4—1034no—
288C22⋊C4—4121no—
289C22⋊C4—4121no—
290C22⋊C4—4121no—
291C22⋊C4—4121no—
292C22⋊C4—4121no—
293C22⋊C4C4×D10314yes—
294C42—41no—
295C42—4121no—
296C42—4121no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—1032no—
304C23—2061no—
305C23—2061no—
306C23—2061no—
307C23—2061no—
308C23—2061no—
309C23—2061no—
310C23C2×C4×D10312yes—
311C23C23×D10311yescharacteristic
312D4—4124no—
313C2×C4—21no—
314C2×C4—21no—
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—21no—
329C2×C4—1032no—
330C2×C4—1032no—
331C2×C4—1032no—
332C2×C4—4124no—
333C2×C4—4124no—
334C2×C4—2061no—
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×C4C2×C4×D10312yes—
353C2×C4C2×C4×D10312yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—4121no—
362C22—4121no—
363C22—4121no—
364C22—4121no—
365C22—2062no—
366C22—2062no—
367C22—2062no—
368C22C22×C4×D10311yescharacteristic
369C22#1569306611yescharacteristic
370C22#1569306611yescharacteristic
371C22#1569306711yescharacteristic
372C22#1569306711yescharacteristic
373C22#1569306811yescharacteristic
374C22#1569306811yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—4121no—
382C4—4121no—
383C4—4121no—
384C4—4121no—
385C4—2062no—
386C4—2062no—
387C4—2062no—
388C2—42no—
389C2—4122no—
390C2#2026826311yescharacteristic
391C2#2026827011yescharacteristic
392C2#2026827111yescharacteristic
393C2#2026853111yescharacteristic
394C2#2026853511yescharacteristic
395C2#2026853611yescharacteristic
396C2#2026854311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC22×C22⋊D103C22
hypercenter#388D103
hypocenterC103#2376
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #20267689C2semidirect
4. #20267688C2semidirect
5. #20267685C2semidirect
6. #20267683C2semidirect
7. #20267682C2semidirect
8. #20267674C2semidirect
9. #20267672C2semidirect
11. #20267666C2semidirect
12. #20267663C2semidirect
13. #20267650C2semidirect
14. #20267648C2semidirect
15. #388×C103C2semidirect
19. #15693003C4semidirect
68. C2×C4×D103C2×C4semidirect
71. C4⋊Dic103C2×C4semidirect
76. Dic103⋊C4C2×C4semidirect
83. (C2×D103)⋊C4C2×C4semidirect
199. C103#2376semidirect
207. #388D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930032
#202676912
#202676892
#202676882
#202676852
#202676832
#202676822
#202676742
#202676722
#202676682
#202676662
#202676632
#202676502
#202676482
#388×C1032
#2376103