Finite Group Databasebeta

← #13120214

Subgroups — #13120214

Order 1664.

544 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C13×#389C211yesmaximal, characteristic, complemented
4#11718650C211yesmaximal, characteristic
5#11718650C211yesmaximal, characteristic
6#11718645C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718633C211yesmaximal, characteristic, complemented
9#11718633C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic
11#11718589C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic
13#11718329C211yesmaximal, characteristic
14#11718318C211yesmaximal, characteristic, complemented
15#11718317C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C42×C13C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88150—24no—
42C4⋊C4×D13—24no—
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C23×D13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13D414yes—
77C2×Dic26—22no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—41no—
84C42×C13—41no—
85#6103—22no—
86#6103—22no—
87#6103Q814yescomplemented
88#6103Q814yescomplemented
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92#6101—22no—
93#6101—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101—22no—
98#6101—41no—
99#6101—41no—
100C4×Dic13—41no—
101#2583—131nomaximal, Sylow
102C23×C13C2411yescharacteristic
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13C2×D412yes—
108C22×D13C2×Q812yes—
109C22×D13C2×Q812yes—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
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×C13C2×D412yes—
128C2×C4×C13C2×Q812yes—
129C2×C4×C13C2×Q812yes—
130C2×C4×C13#4112yes—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
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×Dic13C2×D412yes—
149C2×Dic13C2×Q812yes—
150C2×Dic13C2×Q812yes—
151C2×Dic13#4112yes—
152C4×D13—28no—
153C4×D13—44no—
154C4×D13—44no—
155Dic26—44no—
156C2×C22⋊Q8—131no—
157C22×C4⋊C4—131no—
158#398—131no—
159#398—131no—
160#395—131no—
161#395—131no—
162#389—131no—
163#389—131no—
164#389—131no—
165#389D1311yescharacteristic, complemented
166#385—131no—
167#385—131no—
168#385—131no—
169#385—131no—
170C4×C22⋊C4—131no—
171C22×C13C22×D411yescharacteristic
172C22×C13C22×Q811yescharacteristic
173C22×C13C22×Q811yescharacteristic
174C22×C13C2×#4111yescharacteristic
175C22×C13C2×#4111yescharacteristic
176C22×C13H(5,𝔽2)11yescharacteristic
177C22×C13H(5,𝔽2)11yescharacteristic
178C2×D13—22no—
179C2×D13—22no—
180C2×D13—22no—
181C2×D13—22no—
182C2×D13—22no—
183C2×D13—22no—
184C2×D13C4⋊Q814yes—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192Dic13—22no—
193Dic13—22no—
194Dic13—22no—
195Dic13—22no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C22×Q8—131no—
200C23×C4—131no—
201C23×C4—131no—
202C23×C4—131no—
203C22⋊Q8—264no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
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—264no—
216C2×C4⋊C4C2×D1311yescharacteristic
217C2×C4⋊C4C2×D1311yescharacteristic
218C2×C4⋊C4C2×D1311yescharacteristic
219C2×C4⋊C4C2×D1311yescharacteristic
220C2×C22⋊C4—131no—
221C2×C22⋊C4—131no—
222C2×C22⋊C4—131no—
223C2×C22⋊C4—131no—
224C2×C42—131no—
225C2×C42C2×D1311yescharacteristic
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95C2×D1311yescharacteristic
235#95C2×D1311yescharacteristic
236C2×C13#52511yescharacteristic
237C2×C13C2×C4⋊Q811yescharacteristic
238C2×C13#53411yescharacteristic
239C2×C13#55411yescharacteristic
240C2×C13#55411yescharacteristic
241C2×C13#55411yescharacteristic
242C2×C13#55411yescharacteristic
243D13—24no—
244C24—131no—
245C2×Q8—262no—
246C2×Q8—521no—
247C2×Q8—521no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—134no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—262no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266C22×C4C22×D1311yescharacteristic
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—262no—
276C4⋊C4—262no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C22⋊C4—134no—
287C22⋊C4—134no—
288C22⋊C4—262no—
289C22⋊C4—262no—
290C42—41no—
291C42—521no—
292C13#258311yescharacteristic, complemented, Sylow
293C23—132no—
294C23—132no—
295C23—132no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23—261no—
300C23C23×D1311yescharacteristic
301Q8—524no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
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—132no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—268no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
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—524no—
342C2×C4—524no—
343C2×C4#612712yes—
344C2×C4D4×D1312yes—
345C2×C4Q8×D1312yes—
346C2×C4Q8×D1312yes—
347C22—134no—
348C22—262no—
349C22—262no—
350C22—262no—
351C22—262no—
352C22—262no—
353C22—262no—
354C22C2×#612711yescharacteristic
355C22C2×D4×D1311yescharacteristic
356C22#8825111yescharacteristic
357C22C2×Q8×D1311yescharacteristic
358C22C2×Q8×D1311yescharacteristic
359C22#41×D1311yescharacteristic
360C22#8825611yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—262no—
369C4—262no—
370C4—262no—
371C4—262no—
372C4—521no—
373C4—521no—
374C4—521no—
375C2—264no—
376C2#1171921611yescharacteristic
377C2#1171925211yescharacteristic
378C2#1171928411yescharacteristic
379C2#1171931011yescharacteristic
380C2#1171934111yescharacteristic
381C2#1171939511yescharacteristic
382C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC23×D13C23
hypercenter#389D13
hypocenterC13#2583
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C13×#389C2semidirect
6. #11718645C2semidirect
7. #11718640C2semidirect
8. #11718633C2semidirect
9. #11718633C2semidirect
11. #11718589C2semidirect
14. #11718318C2semidirect
15. #11718317C2semidirect
87. #6103Q8semidirect
88. #6103Q8semidirect
165. #389D13semidirect
292. C13#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×C4⋊C4×D132
C13×#3892
#117186502
#117186452
#117186402
#117186332
C4×#61032
#117185892
#117183292
#117183182
#117183172
#258313