Finite Group Databasebeta

← #27198132

Subgroups — #27198132

Order 13184.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15693004C211yesmaximal, characteristic
2C2×C4×C22⋊D103C211yesmaximal, characteristic
3C2×#15692980C211yesmaximal, characteristic, complemented
4#20267688C211yesmaximal, characteristic, complemented
5#20267683C211yesmaximal, characteristic, complemented
6#20267680C211yesmaximal, characteristic, complemented
7#20267678C211yesmaximal, characteristic, complemented
8#20267673C211yesmaximal, characteristic, complemented
9#20267670C211yesmaximal, characteristic
10#20267665C211yesmaximal, characteristic, complemented
11#20267664C211yesmaximal, characteristic, complemented
12#20267642C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
14#20267638C211yesmaximal, characteristic, complemented
15C2×#95×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18#15693004C418yescomplemented
19C4×C22⋊D103—24no—
20#15692980—24no—
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×C22⋊Dic103C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×C4×Dic103C2211yescharacteristic
37C2×C4×Dic103C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C2×C4×Dic103C2211yescharacteristic
40C2×C4×Dic103C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C23×C4×C103C2211yescharacteristic
48C23×C4×C103C2211yescharacteristic
49C23×C4×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C2×C22⋊D103—22no—
56C2×C22⋊D103—22no—
57C2×C22⋊D103C2×C414yes—
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C2×C4×D103—22no—
66C2×C4×D103—22no—
67C2×C4×D103—41no—
68C4⋊Dic103—22no—
69C4⋊Dic103—22no—
70Dic103⋊C4—22no—
71Dic103⋊C4—22no—
72Dic103⋊C4—41no—
73Dic103⋊C4C2×C414yescomplemented
74Dic103⋊C4C2×C414yescomplemented
75C22⋊Dic103—22no—
76C22⋊Dic103C2×C414yescomplemented
77C22⋊Dic103D414yes—
78(C2×D103)⋊C4—22no—
79(C2×D103)⋊C4—22no—
80(C2×D103)⋊C4—41no—
81(C2×D103)⋊C4C2×C414yescomplemented
82(C2×D103)⋊C4C2×C414yescomplemented
83C4×Dic103—22no—
84C4×Dic103—22no—
85C4×Dic103—22no—
86C4×Dic103—22no—
87C4×Dic103—41no—
88C24×C103C2311yescharacteristic
89C22×C4×C103—22no—
90C22×C4×C103—22no—
91C22×C4×C103—22no—
92C22×C4×C103—22no—
93C22×C4×C103—22no—
94C22×C4×C103—22no—
95C22×C4×C103—41no—
96C22×C4×C103—41no—
97C22×C4×C103C2×C414yescomplemented
98C22×C4×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C23×C103—21no—
105C23×C103—21no—
106C23×C103—21no—
107C23×C103—21no—
108C23×C103C22×C412yes—
109C23×C103C2×D412yes—
110C23×C103#4112yes—
111C23×C103C2411yescharacteristic
112C22×D103—21no—
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—21no—
117C22×D103—21no—
118C22×D103C22×C412yes—
119C2×C4×C103—28no—
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×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—44no—
135C2×C4×C103—44no—
136C2×C4×C103C22×C412yes—
137C2×C4×C103C22×C412yes—
138C2×C4×C103#4112yes—
139C2×C4×C103#4112yes—
140C22⋊D103—28no—
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—21no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—21no—
157C2×Dic103C22×C412yes—
158C2×Dic103C22×C412yes—
159C2×Dic103C22×C412yes—
160C2×Dic103C2×D412yes—
161C2×Dic103C2×D412yes—
162C4×D103—44no—
163C22×C103—22no—
164C22×C103—22no—
165C22×C103—22no—
166C22×C103—22no—
167C22×C103—22no—
168C22×C103—22no—
169C22×C103C4×D414yes—
170C22×C103C23×C411yescharacteristic
171C22×C103C22×D411yescharacteristic
172C22×C103C2×#4111yescharacteristic
173C22×C103C2×#4111yescharacteristic
174C22×C103C2×#4111yescharacteristic
175C22×C103H(5,𝔽2)11yescharacteristic
176C22×C1032−1+411yescharacteristic
177C2×D103—22no—
178C2×D103—22no—
179C2×D103—22no—
180C2×D103—41no—
181C2×D103—41no—
182C2×D103—41no—
183C2×D103—41no—
184C4×C103—22no—
185C4×C103—22no—
186C4×C103—22no—
187C4×C103—22no—
188C4×C103—41no—
189C4×C103—41no—
190Dic103—22no—
191Dic103—22no—
192Dic103—22no—
193Dic103—22no—
194Dic103—22no—
195Dic103—41no—
196Dic103—41no—
197C2×C103—24no—
198C2×C103C2×C4×D411yescharacteristic
199C2×C103C4×#4111yescharacteristic
200C2×C103#52011yescharacteristic
201C2×C103#54611yescharacteristic
202C2×C103#54711yescharacteristic
203C2×C103#55111yescharacteristic
204C2×C103#55211yescharacteristic
205D103—42no—
206#2359—1031nomaximal, Sylow
207C103#235911yescharacteristic, complemented, Sylow
208C2×#123—1031no—
209C2×C4×D4—1031no—
210C2×#117—1031no—
211#389—1031no—
212#388—1031no—
213#388—1031no—
214#387—1031no—
215#387—1031no—
216#386—1031no—
217#385—1031no—
218#385—1031no—
219C4×C4⋊C4—1031no—
220C4×C22⋊C4—1031no—
221C4×C22⋊C4—1031no—
222C2×#95D10311yescharacteristic, complemented
223C22×D4—1031no—
224C23×C4—1031no—
225C23×C4C2×D10311yescharacteristic
226C23×C4C2×D10311yescharacteristic
227C23×C4C2×D10311yescharacteristic
228#123—1038no—
229C4×D4—2064no—
230#117—2064no—
231C2×C4⋊C4—1031no—
232C2×C4⋊C4—1031no—
233C2×C4⋊C4—1031no—
234C2×C4⋊C4—1031no—
235C2×C4⋊C4—1031no—
236C2×C4⋊C4—1031no—
237C2×C4⋊C4—1031no—
238C2×C22⋊C4—1031no—
239C2×C22⋊C4—1031no—
240C2×C22⋊C4—1031no—
241C2×C22⋊C4—1031no—
242C2×C22⋊C4—1031no—
243C2×C22⋊C4—1031no—
244C2×C22⋊C4—1031no—
245C2×C22⋊C4—1031no—
246C2×C42—1031no—
247C2×C42—1031no—
248C2×C42—1031no—
249C2×C42—1031no—
250C2×C42—1031no—
251#95—1031no—
252#95—1031no—
253#95—1031no—
254#95—1031no—
255#95—1031no—
256#95—1031no—
257#95C2×D10311yescharacteristic
258#95C2×D10311yescharacteristic
259#95C2×D10311yescharacteristic
260#95C2×D10311yescharacteristic
261C24—1031no—
262C24C22×D10311yescharacteristic
263C2×D4—1034no—
264C2×D4—2062no—
265C2×D4—2062no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—1031no—
275C22×C4—1031no—
276C22×C4—1031no—
277C22×C4—1031no—
278C22×C4—1031no—
279C22×C4—1031no—
280C22×C4—1031no—
281C22×C4—4121no—
282C22×C4—2062no—
283C22×C4—2062no—
284C22×C4C4×D10314yescomplemented
285C22×C4C22×D10311yescharacteristic
286C22×C4C22×D10311yescharacteristic
287C22×C4C22×D10311yescharacteristic
288C22×C4C22×D10311yescharacteristic
289C22×C4C22×D10311yescharacteristic
290C22×C4C22×D10311yescharacteristic
291C4⋊C4—1034no—
292C4⋊C4—1034no—
293C4⋊C4—4121no—
294C4⋊C4—2062no—
295C4⋊C4—2062no—
296C4⋊C4—2062no—
297C4⋊C4—2062no—
298C22⋊C4—1034no—
299C22⋊C4—1034no—
300C22⋊C4—1034no—
301C22⋊C4—1034no—
302C22⋊C4—4121no—
303C22⋊C4—2062no—
304C22⋊C4—2062no—
305C22⋊C4—2062no—
306C42—4121no—
307C42—2062no—
308C42—2062no—
309C42—2062no—
310C42—2062no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—1032no—
316C23—2061no—
317C23—2061no—
318C23—2061no—
319C23—2061no—
320C23—2061no—
321C23—2061no—
322C23C2×C4×D10312yes—
323C23D4×D10312yes—
324C23#1311010412yes—
325C23C23×D10311yescharacteristic
326D4—2068no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—28no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—1032no—
345C2×C4—1032no—
346C2×C4—1032no—
347C2×C4—1032no—
348C2×C4—1032no—
349C2×C4—4124no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4—2061no—
353C2×C4—2061no—
354C2×C4—2061no—
355C2×C4—2061no—
356C2×C4—2061no—
357C2×C4—2061no—
358C2×C4—2061no—
359C2×C4—2061no—
360C2×C4—2061no—
361C2×C4—2061no—
362C2×C4—2061no—
363C2×C4—2061no—
364C2×C4—2061no—
365C2×C4—2061no—
366C2×C4C2×C4×D10312yes—
367C2×C4C2×C4×D10312yes—
368C2×C4#1311010512yes—
369C2×C4#1311010512yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—4121no—
377C22—4121no—
378C22—4121no—
379C22—4121no—
380C22—2062no—
381C22—2062no—
382C22—2062no—
383C22(C22⋊D103)⋊C414yes—
384C22C22×C4×D10311yescharacteristic
385C22C2×D4×D10311yescharacteristic
386C22C2×#1311010411yescharacteristic
387C22C2×#1311010511yescharacteristic
388C22C2×#1311010511yescharacteristic
389C22#1569306611yescharacteristic
390C22#1569306911yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—4121no—
398C4—4121no—
399C4—2062no—
400C4—2062no—
401C4—2062no—
402C4—2062no—
403C4—2062no—
404C2—24no—
405C2—4122no—
406C2C2×(C22⋊D103)⋊C411yescharacteristic
407C2C4×#1311010511yescharacteristic
408C2#2026827211yescharacteristic
409C2#2026843111yescharacteristic
410C2#2026844211yescharacteristic
411C2#2026846711yescharacteristic
412C2#2026847611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC2×#95×C103C2
socle, cosocleC23×C103C24
prime radicalC22×C22⋊D103C22
hypercenterC2×#95D103
hypocenterC103#2359
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×#15692980C2semidirect
4. #20267688C2semidirect
5. #20267683C2semidirect
6. #20267680C2semidirect
7. #20267678C2semidirect
8. #20267673C2semidirect
10. #20267665C2semidirect
11. #20267664C2semidirect
12. #20267642C2semidirect
13. C4×C22⋊Dic103C2semidirect
14. #20267638C2semidirect
15. C2×#95×C103C2semidirect
18. #15693004C4semidirect
73. Dic103⋊C4C2×C4semidirect
74. Dic103⋊C4C2×C4semidirect
76. C22⋊Dic103C2×C4semidirect
81. (C2×D103)⋊C4C2×C4semidirect
82. (C2×D103)⋊C4C2×C4semidirect
97. C22×C4×C103C2×C4semidirect
207. C103#2359semidirect
222. C2×#95D103semidirect
284. C22×C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930042
C2×C4×C22⋊D1032
C2×#156929802
#202676882
#202676832
#202676802
#202676782
#202676732
#202676702
#202676652
#202676642
#202676422
C4×C22⋊Dic1032
#202676382
C2×#95×C1032
#2359103