Finite Group Databasebeta

← #13118705

Subgroups — #13118705

Order 1664.

548 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic, complemented
3C13×#385C211yesmaximal, characteristic, complemented
4#11718873C211yesmaximal, characteristic, complemented
5#11718655C211yesmaximal, characteristic, complemented
6#11718650C211yesmaximal, characteristic, complemented
7C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
8#11718618C211yesmaximal, characteristic
9#11718618C211yesmaximal, characteristic
10#11718610C211yesmaximal, characteristic, complemented
11#11718609C211yesmaximal, characteristic, complemented
12#11718338C211yesmaximal, characteristic, complemented
13#11718328C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C23×C4×C13C2211yescharacteristic
17C22×C22⋊D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C4×C22⋊D13—24no—
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45C2×C4×Dic13C2211yescharacteristic
46#88143—24no—
47C13×#95C2211yescharacteristic
48C13×#95C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C23×D13C2311yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—22no—
65C2×C22⋊D13—22no—
66C2×C22⋊D13Q814yes—
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—41no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—41no—
81C22⋊Dic13—22no—
82C22⋊Dic13—41no—
83C22⋊Dic13—41no—
84#6103—22no—
85#6103—22no—
86#6103—41no—
87#6103—41no—
88#6103—41no—
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101—41no—
98#6101—41no—
99#6101D414yes—
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—22no—
103#2454—131nomaximal, Sylow
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13C2×Q812yes—
111C23×C13C2411yescharacteristic
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13C2×Q812yes—
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×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—44no—
135C2×C4×C13C2×D412yes—
136C2×C4×C13#4112yes—
137C2×C4×C13#4112yes—
138C22⋊D13—28no—
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×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13C2×D412yes—
157C2×Dic13C2×D412yes—
158C2×Dic13C2×Q812yes—
159C2×Dic13#4112yes—
160C4×D13—44no—
161C2×#125—131no—
162C2×C4×D4—131no—
163#399—131no—
164#399—131no—
165#396—131no—
166#396—131no—
167#390—131no—
168#390—131no—
169#389—131no—
170#389—131no—
171#385—131no—
172#385D1311yescharacteristic, complemented
173#380—131no—
174#380—131no—
175C4×C4⋊C4—131no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13C22×D411yescharacteristic
184C22×C13C22×Q811yescharacteristic
185C22×C13C2×#4111yescharacteristic
186C22×C13C2×#4111yescharacteristic
187C22×C13C2×#4111yescharacteristic
188C22×C13H(5,𝔽2)11yescharacteristic
189C22×C13H(5,𝔽2)11yescharacteristic
190C2×D13—22no—
191C2×D13—22no—
192C2×D13—22no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—22no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—41no—
203Dic13—22no—
204Dic13—41no—
205Dic13—41no—
206Dic13—41no—
207Dic13—41no—
208Dic13—41no—
209Dic13C22⋊Q814yes—
210C22×D4—131no—
211C23×C4—131no—
212C23×C4C2×D1311yescharacteristic
213#125—264no—
214C4×D4—264no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4C2×D1311yescharacteristic
227C2×C4⋊C4C2×D1311yescharacteristic
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4C2×D1311yescharacteristic
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95C2×D1311yescharacteristic
246#95C2×D1311yescharacteristic
247C2×C13—42no—
248C2×C13C2×C22⋊Q811yescharacteristic
249C2×C13#52911yescharacteristic
250C2×C13#54011yescharacteristic
251C2×C13#54611yescharacteristic
252C2×C13#55011yescharacteristic
253C2×C13#55411yescharacteristic
254C2×C13#55411yescharacteristic
255D13—42no—
256C24—131no—
257C24C22×D1311yescharacteristic
258C2×D4—134no—
259C2×D4—262no—
260C2×D4—262no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—262no—
272C22×C4—262no—
273C22×C4—521no—
274C22×C4C22×D1311yescharacteristic
275C22×C4C22×D1311yescharacteristic
276C22×C4C22×D1311yescharacteristic
277C22×C4C22×D1311yescharacteristic
278C22×C4C22×D1311yescharacteristic
279C22×C4C22×D1311yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—134no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—262no—
296C22⋊C4—262no—
297C22⋊C4—262no—
298C22⋊C4—521no—
299C22⋊C4—521no—
300C22⋊C4—521no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C42—262no—
304C42—262no—
305C42—262no—
306C13#245411yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—132no—
314C23—261no—
315C23—261no—
316C23—261no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23Q8×D1312yes—
321C23C23×D1311yescharacteristic
322D4—268no—
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—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—44no—
339C2×C4—132no—
340C2×C4—132no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—524no—
361C2×C4#612712yes—
362C2×C4D4×D1312yes—
363C2×C4#612912yes—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—262no—
372C22—262no—
373C22—262no—
374C22—521no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22C2×#612711yescharacteristic
379C22C2×D4×D1311yescharacteristic
380C22C2×#612911yescharacteristic
381C22#8825111yescharacteristic
382C22C2×Q8×D1311yescharacteristic
383C22#41×D1311yescharacteristic
384C22#8825611yescharacteristic
385C4—22no—
386C4—22no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—134no—
392C4—262no—
393C4—521no—
394C4—521no—
395C4—521no—
396C4—521no—
397C4—521no—
398C2—42no—
399C2—522no—
400C2#1171921611yescharacteristic
401C2#1171924311yescharacteristic
402C2#1171925811yescharacteristic
403C2#1171929611yescharacteristic
404C2D13×C22⋊Q811yescharacteristic
405C2#1171934011yescharacteristic
406C2#1171936811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#385C2
prime radicalC22×C22⋊D13C22
hypercenter#385D13
hypocenterC13#2454
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#88143C2semidirect
3. C13×#385C2semidirect
4. #11718873C2semidirect
5. #11718655C2semidirect
6. #11718650C2semidirect
7. C4⋊C4×Dic13C2semidirect
10. #11718610C2semidirect
11. #11718609C2semidirect
12. #11718338C2semidirect
13. #11718328C2semidirect
14. #11718308C2semidirect
15. #11718308C2semidirect
172. #385D13semidirect
306. C13#2454semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C2×#881432
C13×#3852
#117188732
#117186552
#117186502
C4⋊C4×Dic132
#117186182
#117186102
#117186092
#117183382
#117183282
#117183082
#245413