Finite Group Databasebeta

← #13121206

Subgroups — #13121206

Order 1664.

592 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic, complemented
3C2×#88178C211yesmaximal, characteristic, complemented
4C2×#88150C211yesmaximal, characteristic, complemented
5#11718890C211yesmaximal, characteristic, complemented
6#11718874C211yesmaximal, characteristic
7#11718655C211yesmaximal, characteristic, complemented
8#11718655C211yesmaximal, characteristic, complemented
9#11718646C211yesmaximal, characteristic, complemented
10#11718640C211yesmaximal, characteristic, complemented
11#11718633C211yesmaximal, characteristic, complemented
12#11718618C211yesmaximal, characteristic
13#11718617C211yesmaximal, characteristic
14#11718609C211yesmaximal, characteristic, complemented
15#11718609C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×Dic26C2211yescharacteristic
21C13×C22⋊Q8—24no—
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30#88200—24no—
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39#88178—24no—
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×#6101C2211yescharacteristic
45C2×#6101C2211yescharacteristic
46C2×#6101C2211yescharacteristic
47C2×C4×Dic13C2211yescharacteristic
48#88150—24no—
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C23×D13C2311yescharacteristic
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—41no—
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—41no—
70C2×C22⋊D13—41no—
71C2×C22⋊D13Q814yescomplemented
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—41no—
82C2×Dic26—22no—
83C2×Dic26—22no—
84C2×Dic26—41no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4D414yescomplemented
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C22⋊Dic13—22no—
91C22⋊Dic13—22no—
92C22⋊Dic13—41no—
93#6103—22no—
94#6103—22no—
95#6103—22no—
96#6103—22no—
97#6103—41no—
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100C4⋊Dic13—41no—
101#6101—22no—
102#6101—22no—
103#6101—22no—
104#6101—22no—
105#6101—41no—
106#6101—41no—
107#6101D414yescomplemented
108C4×Dic13—41no—
109#2683—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13C2×Q812yes—
117C23×C13C2411yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13C2×Q812yes—
125Q8×C13—44no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—44no—
141C2×C4×C13C2×D412yes—
142C2×C4×C13C2×D412yes—
143C2×C4×C13C2×D412yes—
144C2×C4×C13C2×D412yes—
145C22⋊D13—44no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13C2×D412yes—
165C2×Dic13C2×D412yes—
166C2×Dic13C2×Q812yes—
167C4×D13—44no—
168Dic26—44no—
169C2×C22⋊Q8—131no—
170C2×C22⋊Q8—131no—
171C2×C22⋊Q8—131no—
172C2×C22⋊Q8D1311yescharacteristic, complemented
173#396—131no—
174#396—131no—
175#396—131no—
176#396—131no—
177#395—131no—
178#395—131no—
179#390—131no—
180#389—131no—
181#389—131no—
182#386—131no—
183#386—131no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13C22×D411yescharacteristic
192C22×C13C22×D411yescharacteristic
193C22×C13C22×Q811yescharacteristic
194C22×C13H(5,𝔽2)11yescharacteristic
195C22×C13H(5,𝔽2)11yescharacteristic
196C22×C132−1+411yescharacteristic
197C22×C132−1+411yescharacteristic
198C2×D13—22no—
199C2×D13—22no—
200C2×D13—22no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C2×D13—41no—
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—22no—
208C4×C13—22no—
209C4×C13—41no—
210C4×C13—41no—
211Dic13—22no—
212Dic13—22no—
213Dic13—22no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217Dic13—41no—
218C22×Q8—131no—
219C22×Q8C2×D1311yescharacteristic
220C22×D4—131no—
221C23×C4—131no—
222C23×C4C2×D1311yescharacteristic
223C22⋊Q8—24no—
224C22⋊Q8—264no—
225C22⋊Q8—264no—
226C22⋊Q8—264no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237C2×C4⋊C4C2×D1311yescharacteristic
238C2×C4⋊C4C2×D1311yescharacteristic
239C2×C4⋊C4C2×D1311yescharacteristic
240C2×C22⋊C4—131no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4—131no—
247C2×C22⋊C4—131no—
248C2×C22⋊C4C2×D1311yescharacteristic
249C2×C22⋊C4C2×D1311yescharacteristic
250C2×C42—131no—
251#95—131no—
252#95—131no—
253#95—131no—
254#95—131no—
255#95—131no—
256#95—131no—
257C2×C13—42no—
258C2×C13#53711yescharacteristic
259C2×C13#53711yescharacteristic
260C2×C13#54311yescharacteristic
261C2×C13D4211yescharacteristic
262C2×C13D4×Q811yescharacteristic
263C2×C13D4×Q811yescharacteristic
264C2×C13#56311yescharacteristic
265D13—42no—
266C24—131no—
267C24C22×D1311yescharacteristic
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—262no—
272C2×Q8—262no—
273C2×Q8—521no—
274C2×D4—134no—
275C2×D4—521no—
276C2×D4—521no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—41no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—262no—
288C22×C4—262no—
289C22×C4—521no—
290C22×C4C22×D1311yescharacteristic
291C22×C4C22×D1311yescharacteristic
292C22×C4C22×D1311yescharacteristic
293C22×C4C22×D1311yescharacteristic
294C22×C4C22×D1311yescharacteristic
295C22×C4C22×D1311yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—134no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—521no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C4⋊C4C22⋊D1314yescomplemented
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—262no—
312C22⋊C4—262no—
313C22⋊C4—262no—
314C22⋊C4—262no—
315C22⋊C4—262no—
316C22⋊C4—262no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C42—521no—
320C13#268311yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—132no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23Q8×D1312yes—
335C23C23×D1311yescharacteristic
336Q8—44no—
337Q8—524no—
338D4—524no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—44no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—524no—
376C2×C4D4×D1312yes—
377C2×C4C2×C22⋊D1312yes—
378C2×C4C2×C22⋊D1312yes—
379C2×C4C2×C22⋊D1312yes—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—262no—
388C22—262no—
389C22—262no—
390C22—521no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22C2×D4×D1311yescharacteristic
395C22#8825111yescharacteristic
396C22C2×Q8×D1311yescharacteristic
397C22#8825411yescharacteristic
398C22#8825611yescharacteristic
399C22#8825711yescharacteristic
400C22C22×C22⋊D1311yescharacteristic
401C4—22no—
402C4—22no—
403C4—22no—
404C4—22no—
405C4—41no—
406C4—41no—
407C4—262no—
408C4—262no—
409C4—262no—
410C4—521no—
411C4—521no—
412C4—521no—
413C4—521no—
414C2—42no—
415C2—522no—
416C2#1171933411yescharacteristic
417C2#1171933711yescharacteristic
418C2#1171933911yescharacteristic
419C2#1171935111yescharacteristic
420C2D4×C22⋊D1311yescharacteristic
421C2Q8×C22⋊D1311yescharacteristic
422C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC22×C22⋊D13C22
hypercenterC2×C22⋊Q8D13
hypocenterC13#2683
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
2. C2×#88200C2semidirect
3. C2×#88178C2semidirect
4. C2×#88150C2semidirect
5. #11718890C2semidirect
7. #11718655C2semidirect
8. #11718655C2semidirect
9. #11718646C2semidirect
10. #11718640C2semidirect
11. #11718633C2semidirect
14. #11718609C2semidirect
15. #11718609C2semidirect
71. C2×C22⋊D13Q8semidirect
87. C13×C4⋊C4D4semidirect
107. #6101D4semidirect
172. C2×C22⋊Q8D13semidirect
308. C4⋊C4C22⋊D13semidirect
320. C13#2683semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#882002
C2×#881782
C2×#881502
#117188902
#117188742
#117186552
#117186462
#117186402
#117186332
#117186182
#117186172
#117186092
#268313