Finite Group Databasebeta

← #13121339

Subgroups — #13121339

Order 1664.

536 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88200C211yesmaximal, characteristic, complemented
2C2×#88151C211yesmaximal, characteristic, complemented
3C13×#395C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718655C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718650C211yesmaximal, characteristic, complemented
8#11718649C211yesmaximal, characteristic
9#11718645C211yesmaximal, characteristic, complemented
10#11718334C211yesmaximal, characteristic, complemented
11#11718328C211yesmaximal, characteristic, complemented
12#11718326C211yesmaximal, characteristic
13#11718326C211yesmaximal, characteristic
14#11718315C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×C4×D13C2211yescharacteristic
20C22×Dic26C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24#88200—24no—
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×#6103C2211yescharacteristic
30C2×#6103C2211yescharacteristic
31C2×#6103C2211yescharacteristic
32C2×#6103C2211yescharacteristic
33C2×#6103C2211yescharacteristic
34C2×#6103C2211yescharacteristic
35C2×C4⋊Dic13C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42#88151—24no—
43C13×#95C2211yescharacteristic
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C23×D13C2311yescharacteristic
54C23×D13C2311yescharacteristic
55C2×Q8×C13—22no—
56C2×Q8×C13—41no—
57C2×Q8×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C2×D52—41no—
72C2×D52—41no—
73C2×D52Q814yescomplemented
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×Dic26—22no—
81C2×Dic26—22no—
82C2×Dic26—41no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86#6103—22no—
87#6103—22no—
88#6103—22no—
89#6103—22no—
90#6103—22no—
91#6103—41no—
92#6103—41no—
93#6103—41no—
94#6103—41no—
95#6103—41no—
96C4⋊Dic13—22no—
97C4⋊Dic13D414yescomplemented
98#6101—22no—
99#6101—22no—
100#6101—41no—
101#6101—41no—
102C4×Dic13—41no—
103#2692—131nomaximal, Sylow
104C23×C13C2411yescharacteristic
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13C2×Q812yes—
118C22×D13C2×Q812yes—
119Q8×C13—44no—
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—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13C2×D412yes—
139C2×C4×C13C2×Q812yes—
140C2×C4×C13#4112yes—
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×Dic13—21no—
157C2×Dic13C2×D412yes—
158C2×Dic13C2×D412yes—
159D52—44no—
160C4×D13—44no—
161C4×D13—44no—
162Dic26—44no—
163C2×C22⋊Q8—131no—
164C2×C22⋊Q8—131no—
165#399—131no—
166#398—131no—
167#396—131no—
168#395D1311yescharacteristic, complemented
169#393—131no—
170#393—131no—
171#391—131no—
172#390—131no—
173#387—131no—
174#386—131no—
175#386—131no—
176#385—131no—
177#380—131no—
178C22×C13C22×D411yescharacteristic
179C22×C13C22×Q811yescharacteristic
180C22×C13C2×#4111yescharacteristic
181C22×C13H(5,𝔽2)11yescharacteristic
182C22×C13H(5,𝔽2)11yescharacteristic
183C22×C13H(5,𝔽2)11yescharacteristic
184C22×C132−1+411yescharacteristic
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—22no—
189C2×D13—22no—
190C2×D13—22no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C2×D13—41no—
198C2×D13—41no—
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206Dic13—22no—
207Dic13—22no—
208Dic13—41no—
209Dic13—41no—
210Dic13—41no—
211Dic13—41no—
212C22×Q8—131no—
213C22×Q8C2×D1311yescharacteristic
214C22×D4—131no—
215C23×C4—131no—
216C23×C4—131no—
217C22⋊Q8—264no—
218C22⋊Q8—264no—
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⋊C4C2×D1311yescharacteristic
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⋊C4—131no—
237C2×C22⋊C4—131no—
238C2×C42—131no—
239#95—131no—
240#95—131no—
241#95—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95C2×D1311yescharacteristic
247#95C2×D1311yescharacteristic
248#95C2×D1311yescharacteristic
249C2×C13#53511yescharacteristic
250C2×C13#54211yescharacteristic
251C2×C13#54311yescharacteristic
252C2×C13#54611yescharacteristic
253C2×C13D4×Q811yescharacteristic
254C2×C13#55411yescharacteristic
255C2×C13#56211yescharacteristic
256D13—42no—
257D13—42no—
258C24—131no—
259C24—131no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—262no—
264C2×Q8—262no—
265C2×Q8—521no—
266C2×D4—134no—
267C2×D4—521no—
268C2×D4—521no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4C22×D1311yescharacteristic
282C22×C4C22×D1311yescharacteristic
283C22×C4C22×D1311yescharacteristic
284C22×C4C22×D1311yescharacteristic
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—134no—
292C4⋊C4—262no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—262no—
301C22⋊C4—262no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C42—521no—
308C13#269211yescharacteristic, complemented, Sylow
309C23—132no—
310C23—132no—
311C23—261no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23—261no—
316C23—261no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23—261no—
323C23C23×D1311yescharacteristic
324Q8—44no—
325Q8—524no—
326D4—524no—
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—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—132no—
346C2×C4—132no—
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—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—524no—
364C2×C4—524no—
365C2×C4D4×D1312yes—
366C2×C4Q8×D1312yes—
367C2×C4#613112yes—
368C22—262no—
369C22—262no—
370C22—262no—
371C22—262no—
372C22—262no—
373C22—262no—
374C22—521no—
375C22—521no—
376C22—521no—
377C22—521no—
378C22—521no—
379C22—521no—
380C22—521no—
381C22—521no—
382C22C2×D4×D1311yescharacteristic
383C22#8825111yescharacteristic
384C22#8825111yescharacteristic
385C22C2×Q8×D1311yescharacteristic
386C22C2×#613111yescharacteristic
387C22#8825411yescharacteristic
388C22#8825611yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—262no—
397C4—262no—
398C4—521no—
399C4—521no—
400C4—521no—
401C4—521no—
402C2—522no—
403C2—522no—
404C2#1171929711yescharacteristic
405C2#1171933511yescharacteristic
406C2#1171933911yescharacteristic
407C2#1171935211yescharacteristic
408C2#1171943211yescharacteristic
409C2#1171943511yescharacteristic
410C2#1171943811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC22×D52C22
hypercenter#395D13
hypocenterC13#2692
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
2. C2×#88151C2semidirect
3. C13×#395C2semidirect
4. #11718892C2semidirect
5. #11718655C2semidirect
6. #11718653C2semidirect
7. #11718650C2semidirect
9. #11718645C2semidirect
10. #11718334C2semidirect
11. #11718328C2semidirect
14. #11718315C2semidirect
15. #11718307C2semidirect
73. C2×D52Q8semidirect
97. C4⋊Dic13D4semidirect
168. #395D13semidirect
308. C13#2692semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×#881512
C13×#3952
#117188922
#117186552
#117186532
#117186502
#117186492
#117186452
#117183342
#117183282
#117183262
#117183152
#117183072
#269213