Finite Group Databasebeta

← #15773713

Subgroups — #15773713

Order 3328.

418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120704C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112859C212yesmaximal, complemented
4#13112835C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C13×#380—21no—
10#11718883—21no—
11#11718871—21no—
12#11718871—21no—
13#11718868—21no—
14#11718641—21no—
15#11718614C411yescharacteristic, complemented
16#11718614C2211yescharacteristic
17#11718610C411yescharacteristic, complemented
18#11718610C2211yescharacteristic
19#11718598C411yescharacteristic, complemented
20C13×#342C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4C2311yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6099—41no—
45#88124—41no—
46#88124—41no—
47C13×#99—42no—
48C13×#95—41no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11827—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—42no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—81no—
92C22⋊Dic13—81no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95#6101—42no—
96#6101—41no—
97#6101—41no—
98#6101—81no—
99#6101—81no—
100#6099—82no—
101C2×#1055—42no—
102#2633—131no—
103#1799D1311yescharacteristic
104#1465—131no—
105#1352—132no—
106#1344—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117C23×C13AGL(1,ℤ/8)11yescharacteristic
118C23×C13#13711yescharacteristic
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—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×C4×C13—82no—
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13#9911yescharacteristic
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152#1055—82no—
153C2×#125—131no—
154C2×C4×D4C2×D1311yescharacteristic
155C2×#99—21no—
156#407—261no—
157#399—131no—
158#399—131no—
159#398—261no—
160#397—131no—
161#397—131no—
162#394—261no—
163#385—261no—
164#385—261no—
165#383—131no—
166#380—21no—
167#342C2×D1312yes—
168#324—261no—
169#323—132no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
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—162no—
194Dic13—81no—
195Dic13—81no—
196Dic13—81no—
197Dic13—81no—
198C22×D4C22⋊D1311yescharacteristic
199C23×C4D5211yescharacteristic
200C23×C4C22⋊D1311yescharacteristic
201C2×M16—521no—
202#125—521no—
203#125—521no—
204C4×D4—41no—
205C4×D4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4D5211yescharacteristic
214C2×C22⋊C4—22no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4C4×D1311yescharacteristic
220C2×C22⋊C4C22×D1311yescharacteristic
221C2×C42C4×D1311yescharacteristic
222#99—42no—
223C22⋊C8—262no—
224C22⋊C8—521no—
225#95—41no—
226#95—131no—
227#95—131no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—41no—
235C2×C13—41no—
236C2×C13—81no—
237C2×C13#151311yescharacteristic
238C2×C13#212311yescharacteristic
239C2×C13#212711yescharacteristic
240C24#610311yescharacteristic
241C24C2×C22⋊D1311yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4C2×C4×D1311yescharacteristic
261C22×C4C2×D5211yescharacteristic
262M16—1042no—
263C2×C8—522no—
264C4⋊C4—41no—
265C4⋊C4—82no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—522no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—1041no—
272C4⋊C4—1041no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—522no—
278C22⋊C4—521no—
279C22⋊C4—521no—
280C22⋊C4—1041no—
281C22⋊C4—1041no—
282C42—21no—
283C42—21no—
284C13#1182711yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23C2×#610311yescharacteristic
295C23#8818611yescharacteristic
296C23#8819611yescharacteristic
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—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4#8804611yescharacteristic
329C2×C4#8804611yescharacteristic
330C8—1042no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22C2×#8804611yescharacteristic
346C22#1171862711yescharacteristic
347C22#1171866611yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—162no—
355C4—1041no—
356C4—1041no—
357C4—1041no—
358C4—1041no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#1311337711yescharacteristic
365C2#1311648911yescharacteristic
366C2#1311650311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1799D13
hypocenterC13#11827
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13112859C2semidirect
4. #13112835C2semidirect
7. C2×#88124C4semidirect
15. #11718614C4semidirect
17. #11718610C4semidirect
19. #11718598C4semidirect
284. C13#11827semidirect

Maximal subgroups

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

subgroupindex
#131207042
#131131742
#131128592
#131128352
C13×#17992
#1182713