Finite Group Databasebeta

← #15773263

Subgroups — #15773263

Order 3328.

486 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88074C211yesmaximal, characteristic, complemented
2#13113157C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2635C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#394—21no—
11C13×#394C411yescharacteristic, complemented
12C13×#392—21no—
13C13×#392C2211yescharacteristic
14C13×#388—21no—
15C13×#386—21no—
16C13×#381C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718586—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#121—41no—
30C13×#121—41no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4×Dic13—41no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—24no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11729—131nomaximal, Sylow
58C24×C13—21no—
59C24×C13C22⋊C411yescharacteristic
60C24×C13C2×D411yescharacteristic
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—42no—
66C2×D4×C13—42no—
67C2×D4×C13—81no—
68C2×D4×C13—81no—
69C2×D4×C13—81no—
70C2×D4×C13—81no—
71C2×D4×C13—81no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—81no—
80C22×C4×C13—81no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×Dic13—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—81no—
96C13×C22⋊C4—81no—
97C13×C22⋊C4—81no—
98C13×C22⋊C4—81no—
99C42×C13—21no—
100C42×C13—21no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103C4×Dic13—82no—
104C2×#1055—42no—
105#2635D1311yescharacteristic
106C4×#99—131no—
107#1460—131no—
108#1352—132no—
109#1343—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13C2×C22⋊C411yescharacteristic
127C23×C13#13512yes—
128D4×C13—44no—
129D4×C13—82no—
130D4×C13—84no—
131D4×C13—84no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13#9911yescharacteristic
155C2×C4×C13#9911yescharacteristic
156C2×C4×C13#10412yes—
157C2×Dic13—44no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160#1055—82no—
161C2×#121Dic1311yescharacteristic, complemented
162C2×C4×D4C2×D1311yescharacteristic
163#431—261no—
164C2×#99—261no—
165#400Dic1311yescharacteristic, complemented
166#399C2×D1311yescharacteristic
167#394—21no—
168#394Dic1311yescharacteristic, complemented
169#392—21no—
170#392C2×D1311yescharacteristic
171#388—21no—
172#386—21no—
173#381Dic1311yescharacteristic, complemented
174C4×C22⋊C4—261no—
175#342—132no—
176#323—132no—
177#323—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13C2×#9911yescharacteristic
198C22×C13#41611yescharacteristic
199C22×C13C2×#10411yescharacteristic
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—81no—
207C4×C13—81no—
208C4×C13—81no—
209Dic13—84no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2×Dic1311yescharacteristic
213C22×D4C22⋊D1311yescharacteristic
214C23×C4C2×Dic1311yescharacteristic
215C23×C4C22⋊D1311yescharacteristic
216#121—41no—
217#121—41no—
218C4×D4—41no—
219C4×D4—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C4⋊C4C2×Dic1311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—262no—
230C2×C22⋊C4C22⋊D1311yescharacteristic
231C2×C22⋊C4C22×D1311yescharacteristic
232C2×C42—521no—
233C2×C42C22⋊D1311yescharacteristic
234C4⋊C8—521no—
235#99—264no—
236C22⋊C8—262no—
237C4×C8—521no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—521no—
242#95C2×Dic1311yescharacteristic
243#95C2×Dic1311yescharacteristic
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—42no—
247C2×C13—81no—
248C2×C13—161no—
249C2×C13#150111yescharacteristic
250C2×C13#212111yescharacteristic
251C2×C13#212811yescharacteristic
252C24—21no—
253C24C22⋊Dic1311yescharacteristic
254C24C2×C22⋊D1311yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—81no—
264C2×D4—81no—
265C2×D4—81no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—522no—
276C22×C4C22⋊Dic1311yescharacteristic
277C22×C4C22⋊Dic1311yescharacteristic
278C22×C4C22⋊Dic1311yescharacteristic
279C22×C4C22×Dic1311yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281C2×C8—522no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C22⋊C4—264no—
295C22⋊C4—522no—
296C42—21no—
297C42—21no—
298C42—1042no—
299C13#1172911yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#8820412yes—
317C23C2×C22⋊Dic1311yescharacteristic
318D4—44no—
319D4—82no—
320D4—84no—
321D4—84no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—524no—
345C2×C4—1042no—
346C2×C4—1042no—
347C2×C4#8807411yescharacteristic
348C2×C4#8807411yescharacteristic
349C2×C4#8807712yes—
350C8—1042no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22C2×#8807411yescharacteristic
371C22#1171889411yescharacteristic
372C22C2×#8807711yescharacteristic
373C4—21no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—1044no—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—81no—
387C2—161no—
388C2#1311332711yescharacteristic
389C2#1311648211yescharacteristic
390C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2635C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2635D13
hypocenterC13#11729
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C4×#88074C2semidirect
2. #13113157C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
6. C2×C13×#121C4semidirect
8. C13×#400C4semidirect
11. C13×#394C4semidirect
16. C13×#381C4semidirect
161. C2×#121Dic13semidirect
165. #400Dic13semidirect
168. #394Dic13semidirect
173. #381Dic13semidirect
299. C13#11729semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131572
#131128602
#131128332
C13×#26352
#1172913