Finite Group Databasebeta

← #15754562

Subgroups — #15754562

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88073C211yesmaximal, characteristic
2#13113438C212yesmaximal, complemented
3#13113283C212yesmaximal, complemented
4#13113177C211yesmaximal, characteristic
5C2×C13×#552C211yesmaximal, characteristic
6C13×#552—24no—
7C13×#552—24no—
8C2×C13×#126—21no—
9C2×C13×#125—21no—
10C2×C13×#125C2211yescharacteristic
11C2×C13×#123—21no—
12C2×C13×C22⋊Q8C411yescharacteristic
13C2×C13×C22⋊Q8C411yescharacteristic
14C2×C4×Q8×C13C2211yescharacteristic
15C2×C4×D4×C13C2211yescharacteristic
16C2×C13×#117—21no—
17C2×C13×#117C411yescharacteristic
18C22×C13×C4⋊C4C411yescharacteristic
19C2×#88073—21no—
20#11718587C2212yes—
21C4×#6099C2212yes—
22#11718135—24no—
23Q8⋊#1055—24no—
24#11718122—21no—
25#11718117—21no—
26#11718117—21no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13C2×C411yescharacteristic
32C13×#126—28no—
33C13×#125—28no—
34C13×#125—22no—
35C13×#125D414yes—
36C13×#123—28no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8—22no—
40C13×C22⋊Q8—22no—
41C4×Q8×C13—22no—
42C4×Q8×C13D414yes—
43C4×D4×C13—22no—
44C4×D4×C13—22no—
45C13×#117—28no—
46C13×#117—22no—
47C13×#117—22no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4D411yescharacteristic
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13C2311yescharacteristic
68C2×#6099—22no—
69#88073—24no—
70C22⋊#1055—22no—
71C4⋊#1055—22no—
72#88043—22no—
73#88043—22no—
74C4×#1055—22no—
75#8371—131nomaximal, Sylow
76C24×C13C22⋊C411yescharacteristic
77C24×C13C22⋊C411yescharacteristic
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C2×Q8×C13C22⋊C412yes—
81C2×D4×C13—22no—
82C2×D4×C13—22no—
83C2×D4×C13—41no—
84C22×C4×C13—24no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C22⋊C411yescharacteristic
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C13×C4⋊C4—24no—
103C13×C4⋊C4—24no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4C22⋊C412yes—
113C13×C4⋊C4C22⋊C412yes—
114C13×C4⋊C4C22⋊C412yes—
115C13×C22⋊C4—24no—
116C13×C22⋊C4—24no—
117C13×C22⋊C4—24no—
118C13×C22⋊C4—22no—
119C13×C22⋊C4—22no—
120C42×C13—24no—
121C42×C13—24no—
122C42×C13C2×D412yes—
123C42×C13C2×D412yes—
124#6099—24no—
125#6099—42no—
126C2×#1055—42no—
127C2×#1055—42no—
128C2×#552D1311yescharacteristic
129C4×#100—131no—
130#1528—132no—
131#1491—132no—
132#1466—131no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13#10412yes—
143C23×C13C2×C22⋊C411yescharacteristic
144Q8×C13—24no—
145Q8×C13—42no—
146D4×C13—44no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—22no—
150C2×C4×C13—21no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—48no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13C2×C22⋊C411yescharacteristic
171C2×C4×C13C2×C22⋊C411yescharacteristic
172C2×C4×C13#12012yes—
173C2×C4×C13#12012yes—
174#1055—44no—
175#1055—82no—
176#552—24no—
177#552—24no—
178C2×#126—21no—
179C2×#125—21no—
180C2×#125C2×D1311yescharacteristic
181C2×#123—21no—
182C2×C22⋊Q8Dic1311yescharacteristic
183C2×C22⋊Q8Dic1311yescharacteristic
184C2×C4×Q8C2×D1311yescharacteristic
185C2×C4×D4C2×D1311yescharacteristic
186C2×#117—21no—
187C2×#117Dic1311yescharacteristic
188C22×C4⋊C4Dic1311yescharacteristic
189#432—132no—
190C2×#100—261no—
191C4×M16—132no—
192#343—261no—
193#330—264no—
194Q8⋊C8—264no—
195#323—261no—
196#323—261no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—22no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—81no—
208C22×C13—81no—
209C22×C13#37911yescharacteristic
210C22×C13C2×#10411yescharacteristic
211C22×C13#42111yescharacteristic
212C4×C13—22no—
213C4×C13—21no—
214C4×C13—22no—
215C4×C13—42no—
216C4×C13—41no—
217C4×C13—41no—
218C4×C13—42no—
219C4×C13—42no—
220C4×C13—42no—
221C4×C13#41312yes—
222C22×Q8C2×Dic1311yescharacteristic
223C22×D4C22⋊D1311yescharacteristic
224C23×C4—21no—
225C23×C4C2×Dic1311yescharacteristic
226C23×C4C2×Dic1311yescharacteristic
227C2×M16—262no—
228#126—28no—
229#125—28no—
230#125—22no—
231#125C22⋊D1314yes—
232#123—28no—
233C22⋊Q8—22no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8—22no—
237C4×Q8—22no—
238C4×Q8C22⋊D1314yes—
239C4×D4—22no—
240C4×D4—22no—
241#117—28no—
242#117—22no—
243#117—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4C2×Dic1311yescharacteristic
253C2×C4⋊C4C2×Dic1311yescharacteristic
254C2×C4⋊C4C2×Dic1311yescharacteristic
255C2×C4⋊C4C22⋊D1311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4C22⋊D1311yescharacteristic
260C2×C22⋊C4C22⋊D1311yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42C22×D1311yescharacteristic
264C4⋊C8—262no—
265#100—264no—
266C22⋊C8—262no—
267#97—262no—
268#97—262no—
269C4×C8—262no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—42no—
273C2×C13—81no—
274C2×C13#178511yescharacteristic
275C2×C13#178911yescharacteristic
276C2×C13#179611yescharacteristic
277C24C22⋊Dic1311yescharacteristic
278C24C22⋊Dic1311yescharacteristic
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8C22⋊Dic1312yes—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—41no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4C22⋊Dic1311yescharacteristic
299C22×C4C22⋊Dic1311yescharacteristic
300C22×C4C22×Dic1311yescharacteristic
301C22×C4C2×C22⋊D1311yescharacteristic
302C22×C4C2×C22⋊D1311yescharacteristic
303M16—264no—
304M16—522no—
305C2×C8—522no—
306C2×C8—522no—
307C4⋊C4—24no—
308C4⋊C4—24no—
309C4⋊C4—24no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4C22⋊Dic1312yes—
318C4⋊C4C22⋊Dic1312yes—
319C4⋊C4C22⋊Dic1312yes—
320C22⋊C4—24no—
321C22⋊C4—24no—
322C22⋊C4—24no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C42—24no—
326C42—24no—
327C42C2×C22⋊D1312yes—
328C42C2×C22⋊D1312yes—
329C13#837111yescharacteristic, complemented, Sylow
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23#8807712yes—
340C23C2×C22⋊Dic1311yescharacteristic
341Q8—24no—
342Q8—42no—
343D4—44no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—48no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4C2×C22⋊Dic1311yescharacteristic
368C2×C4C2×C22⋊Dic1311yescharacteristic
369C2×C4#8820712yes—
370C2×C4#8820712yes—
371C8—524no—
372C8—1042no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—42no—
377C22—42no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—81no—
385C22C2×#8807711yescharacteristic
386C22#1171889711yescharacteristic
387C22#1171890811yescharacteristic
388C4—21no—
389C4—22no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4#1171889812yes—
398C2—21no—
399C2—21no—
400C2—42no—
401C2—81no—
402C2#1311476411yescharacteristic
403C2#1311478011yescharacteristic
404C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#552C2
socleC22×C13#379
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenterC2×#552D13
hypocenterC13#8371
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13113438C2semidirect
3. #13113283C2semidirect
329. C13#8371semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131134382
#131132832
#131131772
C2×C13×#5522
#837113