Finite Group Databasebeta

← #15773710

Subgroups — #15773710

Order 3328.

414 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13114824C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112857C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2638C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#398C411yescharacteristic, complemented
9C13×#397—21no—
10C13×#397C2211yescharacteristic
11C13×#395C411yescharacteristic, complemented
12C13×#394—21no—
13C13×#393C2211yescharacteristic
14C13×#387—21no—
15C13×#385—21no—
16C13×#381C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
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⋊C4D411yescharacteristic
41C2×C13×C22⋊C4C2311yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4⋊Dic13—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—42no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11826—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—81no—
94C13×C22⋊C4—81no—
95C42×C13—21no—
96C42×C13—21no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C4⋊Dic13—82no—
100C2×#1055—42no—
101#2638D1311yescharacteristic
102#1799—131no—
103#1466—131no—
104#1351—132no—
105#1344—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13AGL(1,ℤ/8)11yescharacteristic
117C23×C13#13711yescharacteristic
118Q8×C13—82no—
119D4×C13—42no—
120D4×C13—42no—
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—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13#9911yescharacteristic
148C2×C4×C13#9911yescharacteristic
149C2×Dic13—82no—
150C2×Dic13—82no—
151C2×Dic13—82no—
152#1055—82no—
153C2×C22⋊Q8Dic1311yescharacteristic, complemented
154C2×C4×D4C2×D1311yescharacteristic
155#432—261no—
156C2×#99—261no—
157#398Dic1311yescharacteristic, complemented
158#397—21no—
159#397C2×D1311yescharacteristic
160#395Dic1311yescharacteristic, complemented
161#394—21no—
162#393C2×D1311yescharacteristic
163#387—21no—
164#385—21no—
165#381Dic1311yescharacteristic, complemented
166#380—261no—
167#342—132no—
168#323—132no—
169#323—261no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13C2×#9911yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13#42111yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197Dic13—162no—
198C22×Q8C2×Dic1311yescharacteristic
199C22×D4C22⋊D1311yescharacteristic
200C23×C4C2×Dic1311yescharacteristic
201C23×C4C22⋊D1311yescharacteristic
202C22⋊Q8—41no—
203C22⋊Q8—41no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—521no—
210C2×C4⋊C4C2×Dic1311yescharacteristic
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—262no—
217C2×C22⋊C4C22⋊D1311yescharacteristic
218C2×C22⋊C4C22×D1311yescharacteristic
219C2×C42C22⋊D1311yescharacteristic
220C4⋊C8—521no—
221#99—522no—
222C22⋊C8—262no—
223#97—521no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—521no—
230#95C2×Dic1311yescharacteristic
231#95C2×Dic1311yescharacteristic
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—41no—
235C2×C13—41no—
236C2×C13—81no—
237C2×C13#151311yescharacteristic
238C2×C13#212111yescharacteristic
239C2×C13#212911yescharacteristic
240C24C22⋊Dic1311yescharacteristic
241C24C2×C22⋊D1311yescharacteristic
242C2×Q8—41no—
243C2×Q8—81no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—522no—
259C22×C4C22⋊Dic1311yescharacteristic
260C22×C4C22⋊Dic1311yescharacteristic
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22×Dic1311yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264C2×C8—522no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—81no—
271C4⋊C4—1042no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—81no—
278C22⋊C4—81no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C42—21no—
282C42—21no—
283C13#1182611yescharacteristic, complemented, Sylow
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23#8820311yescharacteristic
294C23#8820511yescharacteristic
295C23C2×C22⋊Dic1311yescharacteristic
296Q8—82no—
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—1042no—
326C2×C4—1042no—
327C2×C4—1042no—
328C2×C4#8807411yescharacteristic
329C2×C4#8807411yescharacteristic
330C8—1042no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×#8807411yescharacteristic
346C22#1171889311yescharacteristic
347C22#1171889711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—2082no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#1311337911yescharacteristic
365C2#1311648211yescharacteristic
366C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2638C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2638D13
hypocenterC13#11826
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #13112857C2semidirect
4. #13112836C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
8. C13×#398C4semidirect
11. C13×#395C4semidirect
16. C13×#381C4semidirect
153. C2×C22⋊Q8Dic13semidirect
157. #398Dic13semidirect
160. #395Dic13semidirect
165. #381Dic13semidirect
283. C13#11826semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131772
#131128572
#131128362
C13×#26382
#1182613