Finite Group Databasebeta

← #13119753

Subgroups — #13119753

Order 1664.

620 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic, complemented
2C2×#88141C211yesmaximal, characteristic, complemented
3C2×#88135C211yesmaximal, characteristic
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#396C211yesmaximal, characteristic, complemented
6#11718655C211yesmaximal, characteristic, complemented
7#11718655C211yesmaximal, characteristic, complemented
8#11718637C211yesmaximal, characteristic, complemented
9#11718633C211yesmaximal, characteristic, complemented
10#11718618C211yesmaximal, characteristic
11#11718618C211yesmaximal, characteristic
12#11718609C211yesmaximal, characteristic, complemented
13#11718603C211yesmaximal, characteristic, complemented
14#11718328C211yesmaximal, characteristic, complemented
15#11718308C211yesmaximal, characteristic, complemented
16C22×C22⋊D13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×C4×Dic13C2211yescharacteristic
45C2×C4×Dic13C2211yescharacteristic
46C2×C4×Dic13C2211yescharacteristic
47#88150—24no—
48#88141—24no—
49#88135—24no—
50#88132—24no—
51C13×#95C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C23×D13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—22no—
64C2×C22⋊D13—22no—
65C2×C22⋊D13Q814yescomplemented
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
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—22no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26D414yescomplemented
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—41no—
88C22⋊Dic13—22no—
89C22⋊Dic13—41no—
90#6103—22no—
91#6103—22no—
92#6103—22no—
93#6103—41no—
94#6103—41no—
95C4⋊Dic13—22no—
96C4⋊Dic13—41no—
97#6101—22no—
98#6101—22no—
99#6101—22no—
100#6101—22no—
101#6101—22no—
102#6101—22no—
103#6101—22no—
104#6101—22no—
105#6101—22no—
106C4×Dic13—22no—
107C4×Dic13—22no—
108C4×Dic13D414yes—
109#2538—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—
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—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13C2×D412yes—
142C2×C4×C13C2×D412yes—
143C22⋊D13—28no—
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×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—44no—
159C2×Dic13C2×D412yes—
160C2×Dic13C2×D412yes—
161C2×Dic13C2×D412yes—
162C2×Dic13C2×D412yes—
163C2×Dic13C2×Q812yes—
164C2×Dic13#4112yes—
165C2×Dic13#4112yes—
166C4×D13—44no—
167Dic26—28no—
168C2×C22⋊Q8—131no—
169C2×C22⋊Q8—131no—
170C2×C4×Q8—131no—
171C2×C4×D4—131no—
172#396—131no—
173#396—131no—
174#396—131no—
175#396D1311yescharacteristic, complemented
176#390—131no—
177#390—131no—
178#389—131no—
179#389—131no—
180#384—131no—
181#380—131no—
182#380—131no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13C22×D411yescharacteristic
191C22×C13C22×D411yescharacteristic
192C22×C13C22×Q811yescharacteristic
193C22×C13C2×#4111yescharacteristic
194C22×C13C2×#4111yescharacteristic
195C22×C13H(5,𝔽2)11yescharacteristic
196C22×C132−1+411yescharacteristic
197C2×D13—22no—
198C2×D13—22no—
199C2×D13—22no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—41no—
204C4×C13—22no—
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210Dic13—22no—
211Dic13—41no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13#12114yes—
216Dic13C22⋊Q814yescomplemented
217C22×Q8—131no—
218C22×D4—131no—
219C23×C4—131no—
220C23×C4—131no—
221C22⋊Q8—264no—
222C22⋊Q8—264no—
223C4×Q8—264no—
224C4×D4—264no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
237C2×C4⋊C4C2×D1311yescharacteristic
238C2×C4⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
247C2×C22⋊C4C2×D1311yescharacteristic
248C2×C22⋊C4C2×D1311yescharacteristic
249C2×C42—131no—
250C2×C42—131no—
251C2×C42—131no—
252#95—131no—
253#95—131no—
254#95—131no—
255#95C2×D1311yescharacteristic
256C2×C13—42no—
257C2×C13C2×#12111yescharacteristic
258C2×C13C2×C22⋊Q811yescharacteristic
259C2×C13#53711yescharacteristic
260C2×C13D4×Q811yescharacteristic
261C2×C13#55011yescharacteristic
262C2×C13#55411yescharacteristic
263C2×C13#55611yescharacteristic
264D13—42no—
265C24—131no—
266C24C22×D1311yescharacteristic
267C2×Q8—134no—
268C2×Q8—262no—
269C2×Q8—262no—
270C2×D4—134no—
271C2×D4—262no—
272C2×D4—262no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—262no—
284C22×C4—262no—
285C22×C4—262no—
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C22×C4C22×D1311yescharacteristic
290C22×C4C22×D1311yescharacteristic
291C22×C4C22×D1311yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—262no—
296C4⋊C4—262no—
297C4⋊C4—262no—
298C4⋊C4—262no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—262no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—521no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—262no—
310C22⋊C4—262no—
311C22⋊C4—262no—
312C22⋊C4—262no—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42—134no—
317C42—262no—
318C42—262no—
319C13#253811yescharacteristic, complemented, Sylow
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—132no—
327C23—261no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23Q8×D1312yes—
334C23C23×D1311yescharacteristic
335Q8—268no—
336D4—268no—
337C2×C4—21no—
338C2×C4—21no—
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—132no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—132no—
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—524no—
375C2×C4—524no—
376C2×C4D4×D1312yes—
377C2×C4D4×D1312yes—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—262no—
386C22—262no—
387C22—262no—
388C22—521no—
389C22—521no—
390C22—521no—
391C22—521no—
392C22C2×D4×D1311yescharacteristic
393C22C2×D4×D1311yescharacteristic
394C22#8825111yescharacteristic
395C22C2×Q8×D1311yescharacteristic
396C22#41×D1311yescharacteristic
397C22#41×D1311yescharacteristic
398C22#8825711yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—134no—
406C4—134no—
407C4—262no—
408C4—521no—
409C4—521no—
410C4—521no—
411C4—521no—
412C2—42no—
413C2—522no—
414C2#1171930211yescharacteristic
415C2#1171930411yescharacteristic
416C2D13×#12111yescharacteristic
417C2D13×C22⋊Q811yescharacteristic
418C2#1171933711yescharacteristic
419C2#1171934111yescharacteristic
420C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#396C2
prime radicalC22×C22⋊D13C22
hypercenter#396D13
hypocenterC13#2538
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
2. C2×#88141C2semidirect
4. C2×#88132C2semidirect
5. C13×#396C2semidirect
6. #11718655C2semidirect
7. #11718655C2semidirect
8. #11718637C2semidirect
9. #11718633C2semidirect
12. #11718609C2semidirect
13. #11718603C2semidirect
14. #11718328C2semidirect
15. #11718308C2semidirect
65. C2×C22⋊D13Q8semidirect
81. C2×Dic26D4semidirect
175. #396D13semidirect
216. Dic13C22⋊Q8semidirect
319. C13#2538semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881412
C2×#881352
C2×#881322
C13×#3962
#117186552
#117186372
#117186332
#117186182
#117186092
#117186032
#117183282
#117183082
#253813