Finite Group Databasebeta

← #27198313

Subgroups — #27198313

Order 13184.

520 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×#15693007C211yesmaximal, characteristic
2#20267697C211yesmaximal, characteristic, complemented
3#20267695C211yesmaximal, characteristic, complemented
4#20267682C211yesmaximal, characteristic, complemented
5#20267681C211yesmaximal, characteristic, complemented
6#20267679C211yesmaximal, characteristic, complemented
7#20267668C211yesmaximal, characteristic
8#20267667C211yesmaximal, characteristic
9#20267666C211yesmaximal, characteristic, complemented
10#20267665C211yesmaximal, characteristic, complemented
11#20267665C211yesmaximal, characteristic, complemented
12#20267663C211yesmaximal, characteristic, complemented
13#20267656C211yesmaximal, characteristic, complemented
14#20267655C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic, complemented
16C22×Dic206C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C23×Dic103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20#15693007C418yescomplemented
21C2×C4⋊Dic103C2211yescharacteristic
22C2×C4⋊Dic103C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×C22⋊Dic103C2211yescharacteristic
27C2×C22⋊Dic103C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
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
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×Dic206—41no—
54C2×Dic206—41no—
55C2×Dic206C2×C414yescomplemented
56C2×C22⋊D103—41no—
57C2×C22⋊D103—41no—
58C2×C22⋊D103C2×C414yes—
59C22×Dic103—41no—
60C22×Dic103—41no—
61C22×Dic103—41no—
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C22×Dic103C2311yescharacteristic
69C2×C4×D103—41no—
70C2×C4×D103—41no—
71C2×C4×D103—41no—
72C4⋊Dic103—41no—
73C4⋊Dic103—41no—
74Dic103⋊C4—41no—
75Dic103⋊C4—41no—
76Dic103⋊C4—41no—
77C22⋊Dic103—41no—
78C22⋊Dic103C2×C414yescomplemented
79(C2×D103)⋊C4—41no—
80(C2×D103)⋊C4—41no—
81(C2×D103)⋊C4—41no—
82(C2×D103)⋊C4C2×C414yescomplemented
83(C2×D103)⋊C4C2×C414yescomplemented
84C4×Dic103—41no—
85C4×Dic103C2×C414yescomplemented
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×C414yescomplemented
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—
155Dic206—44no—
156C22×C103—22no—
157C22×C103—22no—
158C22×C103—22no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103C23×C411yescharacteristic
164C22×C103H(5,𝔽2)11yescharacteristic
165C22×C103H(5,𝔽2)11yescharacteristic
166C22×C103H(5,𝔽2)11yescharacteristic
167C22×C103H(5,𝔽2)11yescharacteristic
168C22×C1032−1+411yescharacteristic
169C22×C1032−1+411yescharacteristic
170C2×D103—22no—
171C2×D103—22no—
172C2×D103—22no—
173C2×D103—41no—
174C2×D103—41no—
175C2×D103—41no—
176C2×D103—41no—
177C4×C103—22no—
178C4×C103—22no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103—41no—
183Dic103—22no—
184Dic103—22no—
185Dic103—22no—
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189Dic103—41no—
190C2×C103—42no—
191C2×C103#51811yescharacteristic
192C2×C103#52011yescharacteristic
193C2×C103#52011yescharacteristic
194C2×C103H(3,𝔽4)11yescharacteristic
195C2×C103#56211yescharacteristic
196C2×C103#56211yescharacteristic
197C2×C103#56311yescharacteristic
198D103—42no—
199#2379—1031nomaximal, Sylow
200C103#237911yescharacteristic, complemented, Sylow
201C2×#124—1031no—
202#391—1031no—
203#391—1031no—
204#388—1031no—
205#388—1031no—
206#388—1031no—
207#388D10311yescharacteristic, complemented
208#386—1031no—
209#386—1031no—
210#385—1031no—
211#385—1031no—
212#385—1031no—
213#385—1031no—
214#382—1031no—
215#382—1031no—
216C22×Q8—1031no—
217C22×D4—1031no—
218C23×C4—1031no—
219C23×C4—1031no—
220#124—1038no—
221C2×C4⋊C4—1031no—
222C2×C4⋊C4—1031no—
223C2×C4⋊C4—1031no—
224C2×C4⋊C4—1031no—
225C2×C4⋊C4—1031no—
226C2×C4⋊C4C2×D10311yescharacteristic
227C2×C22⋊C4—1031no—
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⋊C4C2×D10311yescharacteristic
235C2×C22⋊C4C2×D10311yescharacteristic
236C2×C22⋊C4C2×D10311yescharacteristic
237C2×C42—1031no—
238C2×C42—1031no—
239C2×C42C2×D10311yescharacteristic
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
252C24—1031no—
253C24C22×D10311yescharacteristic
254C2×Q8—1034no—
255C2×Q8—4121no—
256C2×Q8—4121no—
257C2×D4—1034no—
258C2×D4—4121no—
259C2×D4—4121no—
260C22×C4—1031no—
261C22×C4—1031no—
262C22×C4—1031no—
263C22×C4—1031no—
264C22×C4—1031no—
265C22×C4—1031no—
266C22×C4—1031no—
267C22×C4—4121no—
268C22×C4—4121no—
269C22×C4—4121no—
270C22×C4—4121no—
271C22×C4—4121no—
272C22×C4—4121no—
273C22×C4C22×D10311yescharacteristic
274C22×C4C22×D10311yescharacteristic
275C22×C4C22×D10311yescharacteristic
276C22×C4C22×D10311yescharacteristic
277C22×C4C22×D10311yescharacteristic
278C22×C4C22×D10311yescharacteristic
279C4⋊C4—41no—
280C4⋊C4—4121no—
281C4⋊C4—4121no—
282C4⋊C4—4121no—
283C4⋊C4—4121no—
284C4⋊C4—4121no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—1034no—
288C22⋊C4—1034no—
289C22⋊C4—1034no—
290C22⋊C4—4121no—
291C22⋊C4—4121no—
292C22⋊C4—4121no—
293C22⋊C4—4121no—
294C22⋊C4C4×D10314yescomplemented
295C42—41no—
296C42—1034no—
297C42—4121no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1032no—
305C23—2061no—
306C23—2061no—
307C23—2061no—
308C23—2061no—
309C23—2061no—
310C23—2061no—
311C23C2×C4×D10312yes—
312C23C23×D10311yescharacteristic
313Q8—4124no—
314D4—4124no—
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—21no—
330C2×C4—21no—
331C2×C4—1032no—
332C2×C4—1032no—
333C2×C4—1032no—
334C2×C4—4124no—
335C2×C4—4124no—
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×C4C2×C4×D10312yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—4121no—
364C22—4121no—
365C22—4121no—
366C22—4121no—
367C22—2062no—
368C22—2062no—
369C22—2062no—
370C22C22×C4×D10311yescharacteristic
371C22#1569306611yescharacteristic
372C22#1569306611yescharacteristic
373C22#1569306711yescharacteristic
374C22#1569306711yescharacteristic
375C22#1569306811yescharacteristic
376C22#1569306811yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—4121no—
384C4—4121no—
385C4—4121no—
386C4—4121no—
387C4—2062no—
388C4—2062no—
389C4—2062no—
390C2—42no—
391C2—4122no—
392C2#2026826311yescharacteristic
393C2#2026827011yescharacteristic
394C2#2026827111yescharacteristic
395C2#2026853311yescharacteristic
396C2#2026853611yescharacteristic
397C2#2026853811yescharacteristic
398C2#2026854311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC22×C22⋊D103C22
hypercenter#388D103
hypocenterC103#2379
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20267697C2semidirect
3. #20267695C2semidirect
4. #20267682C2semidirect
5. #20267681C2semidirect
6. #20267679C2semidirect
9. #20267666C2semidirect
10. #20267665C2semidirect
11. #20267665C2semidirect
12. #20267663C2semidirect
13. #20267656C2semidirect
14. #20267655C2semidirect
15. #388×C103C2semidirect
20. #15693007C4semidirect
55. C2×Dic206C2×C4semidirect
78. C22⋊Dic103C2×C4semidirect
82. (C2×D103)⋊C4C2×C4semidirect
83. (C2×D103)⋊C4C2×C4semidirect
85. C4×Dic103C2×C4semidirect
96. C22⋊C4×C103C2×C4semidirect
200. C103#2379semidirect
207. #388D103semidirect
294. C22⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930072
#202676972
#202676952
#202676822
#202676812
#202676792
#202676682
#202676672
#202676662
#202676652
#202676632
#202676562
#202676552
#388×C1032
#2379103