Finite Group Databasebeta

← #13121146

Subgroups — #13121146

Order 1664.

544 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic
3C2×#88198C211yesmaximal, characteristic, complemented
4C2×#88150C211yesmaximal, characteristic
5#11718892C211yesmaximal, characteristic
6#11718890C211yesmaximal, characteristic, complemented
7#11718653C211yesmaximal, characteristic
8#11718651C211yesmaximal, characteristic
9#11718650C211yesmaximal, characteristic
10#11718645C211yesmaximal, characteristic, complemented
11#11718642C211yesmaximal, characteristic, complemented
12#11718641C211yesmaximal, characteristic, complemented
13#11718640C211yesmaximal, characteristic, complemented
14#11718601C211yesmaximal, characteristic
15#11718594C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C13×C4⋊Q8—24no—
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C42×C13C2211yescharacteristic
26#88200—24no—
27#88198—24no—
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44#88150—24no—
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C23×D13C2311yescharacteristic
56C2×Q8×C13—22no—
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—22no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—41no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—41no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4D414yes—
86C42×C13—22no—
87#6103—22no—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—41no—
92#6103Q814yescomplemented
93C4⋊Dic13—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—41no—
101#6101D414yes—
102C4×Dic13—22no—
103#2677—131nomaximal, Sylow
104C23×C13C2411yescharacteristic
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13C2×Q812yes—
112Q8×C13—44no—
113Q8×C13—44no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13C2×D412yes—
131C2×C4×C13C2×D412yes—
132C2×C4×C13C2×D412yes—
133C2×C4×C13C2×D412yes—
134C2×C4×C13C2×Q812yes—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13C2×D412yes—
154C2×Dic13C2×D412yes—
155C2×Dic13C2×Q812yes—
156C4×D13—44no—
157Dic26—44no—
158C2×C4⋊Q8—131no—
159C2×C4⋊Q8D1311yescharacteristic, complemented
160C2×C22⋊Q8—131no—
161C2×C22⋊Q8—131no—
162#399—131no—
163#398—131no—
164#398—131no—
165#395—131no—
166#395—131no—
167#393—131no—
168#388—131no—
169#388—131no—
170#387—131no—
171#387—131no—
172#385—131no—
173C22×C13C22×D411yescharacteristic
174C22×C13C22×D411yescharacteristic
175C22×C13C22×Q811yescharacteristic
176C22×C13H(5,𝔽2)11yescharacteristic
177C22×C132−1+411yescharacteristic
178C22×C132−1+411yescharacteristic
179C22×C132−1+411yescharacteristic
180C2×D13—22no—
181C2×D13—22no—
182C2×D13—22no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—41no—
193C4×C13—41no—
194Dic13—22no—
195Dic13—22no—
196Dic13—22no—
197Dic13—41no—
198Dic13—41no—
199Dic13—41no—
200Dic13—41no—
201C22×Q8—131no—
202C22×Q8C2×D1311yescharacteristic
203C22×Q8C2×D1311yescharacteristic
204C23×C4—131no—
205C4⋊Q8—24no—
206C4⋊Q8—264no—
207C22⋊Q8—264no—
208C22⋊Q8—264no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4C2×D1311yescharacteristic
219C2×C4⋊C4C2×D1311yescharacteristic
220C2×C4⋊C4C2×D1311yescharacteristic
221C2×C4⋊C4C2×D1311yescharacteristic
222C2×C22⋊C4—131no—
223C2×C22⋊C4—131no—
224C2×C22⋊C4—131no—
225C2×C22⋊C4—131no—
226C2×C22⋊C4—131no—
227C2×C22⋊C4—131no—
228C2×C42—131no—
229C2×C42C2×D1311yescharacteristic
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95—131no—
235#95—131no—
236#95—131no—
237#95—131no—
238#95—131no—
239#95—131no—
240C2×C13#53611yescharacteristic
241C2×C13#53611yescharacteristic
242C2×C13#54411yescharacteristic
243C2×C13D4211yescharacteristic
244C2×C13D4×Q811yescharacteristic
245C2×C13D4×Q811yescharacteristic
246C2×C13#56311yescharacteristic
247D13—42no—
248C24—131no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—262no—
256C2×Q8—262no—
257C2×Q8—521no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—262no—
266C22×C4—262no—
267C22×C4—521no—
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C22×C4C22×D1311yescharacteristic
274C22×C4C22×D1311yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—134no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—521no—
287C4⋊C4C22⋊D1314yes—
288C22⋊C4—134no—
289C22⋊C4—262no—
290C22⋊C4—262no—
291C22⋊C4—262no—
292C22⋊C4—262no—
293C22⋊C4—521no—
294C42—22no—
295C42—262no—
296C13#267711yescharacteristic, complemented, Sylow
297C23—132no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23—261no—
302C23—261no—
303C23—261no—
304C23C23×D1311yescharacteristic
305Q8—44no—
306Q8—44no—
307Q8—524no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
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—132no—
325C2×C4—132no—
326C2×C4—132no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—524no—
346C2×C4D4×D1312yes—
347C2×C4Q8×D1312yes—
348C2×C4C2×C22⋊D1312yes—
349C2×C4C2×C22⋊D1312yes—
350C2×C4C2×C22⋊D1312yes—
351C22—262no—
352C22—262no—
353C22—262no—
354C22—521no—
355C22—521no—
356C22—521no—
357C22—521no—
358C22C2×D4×D1311yescharacteristic
359C22#8825111yescharacteristic
360C22C2×Q8×D1311yescharacteristic
361C22#8825411yescharacteristic
362C22#8825411yescharacteristic
363C22#8825411yescharacteristic
364C22C22×C22⋊D1311yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—262no—
373C4—262no—
374C4—262no—
375C4—521no—
376C4—521no—
377C4—521no—
378C4—521no—
379C2—522no—
380C2#1171942911yescharacteristic
381C2#1171943211yescharacteristic
382C2#1171943411yescharacteristic
383C2#1171944011yescharacteristic
384C2D4×C22⋊D1311yescharacteristic
385C2Q8×C22⋊D1311yescharacteristic
386C2#1171952111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C4⋊Q8C2
prime radicalC23×D13C23
hypercenterC2×C4⋊Q8D13
hypocenterC13#2677
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C4⋊Q8C2semidirect
3. C2×#88198C2semidirect
6. #11718890C2semidirect
10. #11718645C2semidirect
11. #11718642C2semidirect
12. #11718641C2semidirect
13. #11718640C2semidirect
15. #11718594C2semidirect
92. #6103Q8semidirect
159. C2×C4⋊Q8D13semidirect
296. C13#2677semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C4⋊Q82
C2×#882002
C2×#881982
C2×#881502
#117188922
#117188902
#117186532
#117186512
#117186502
#117186452
#117186422
#117186412
#117186402
#117186012
#117185942
#267713