Finite Group Databasebeta

← #15773665

Subgroups — #15773665

Order 3328.

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

normal subgroups only

This group has 386 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#13120649C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112865C212yesmaximal, complemented
4#13112862C212yesmaximal, complemented
5C13×#1821C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C13×#407—21no—
9#11718873C411yescharacteristic
10#11718872—21no—
11#11718871—21no—
12#11718868—21no—
13#11718647C411yescharacteristic
14#11718647C2211yescharacteristic
15#11718645—21no—
16#11718645—21no—
17#11718640C411yescharacteristic
18#11718640C2211yescharacteristic
19C13×#343—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—22no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38#88178—41no—
39#88178—41no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6099—41no—
44C13×C22⋊C8—41no—
45C13×C22⋊C8—41no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11817—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—41no—
66C22×C4×C13—81no—
67C22×C4×C13—81no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—41no—
79C2×Dic26—81no—
80C13×M16—42no—
81C13×M16—42no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C22⋊Dic13—42no—
88C22⋊Dic13—41no—
89C22⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—81no—
92#6101—42no—
93#6101—81no—
94#6101—81no—
95#6099—82no—
96C2×#1055—42no—
97#2627—131no—
98#1821D1311yescharacteristic
99#1463—131no—
100#1354—132no—
101#1353—132no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13#9911yescharacteristic
107C23×C13#9911yescharacteristic
108C23×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13#13712yes—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—42no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140Dic26—82no—
141C8×C13—82no—
142#1055—82no—
143C2×C22⋊Q8—131no—
144C22×C4⋊C4C2×D1311yescharacteristic
145#407—21no—
146#407—261no—
147#400—131no—
148#400—131no—
149#398—261no—
150#398—261no—
151#395—131no—
152#395—131no—
153#385—261no—
154#381—261no—
155#380—131no—
156#343—21no—
157#343C2×D1312yes—
158#324—132no—
159#324—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13C2×#9911yescharacteristic
171C22×C13#41911yescharacteristic
172C22×C13#42111yescharacteristic
173C4×C13—22no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179Dic13—81no—
180Dic13—81no—
181Dic13—81no—
182Dic13—81no—
183C22×Q8—131no—
184C23×C4C4×D1311yescharacteristic
185C23×C4D5211yescharacteristic
186C23×C4C22⋊D1311yescharacteristic
187C2×M16—22no—
188C2×M16—521no—
189C22⋊Q8—521no—
190C22⋊Q8—521no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4C4×D1311yescharacteristic
199C2×C4⋊C4D5211yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C4⋊C4C22×D1311yescharacteristic
202C2×C22⋊C4—261no—
203C2×C22⋊C4—261no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206C22⋊C8—262no—
207C22⋊C8—521no—
208#95—131no—
209#95—131no—
210#95—261no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—41no—
219C2×C13—41no—
220C2×C13#151111yescharacteristic
221C2×C13#212111yescharacteristic
222C2×C13#213311yescharacteristic
223C24#610311yescharacteristic
224C2×Q8—521no—
225C2×Q8—1041no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—81no—
235C22×C4—81no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4C2×C4×D1311yescharacteristic
244C22×C4C2×D5211yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—42no—
247M16—42no—
248M16—1042no—
249C2×C8—42no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—521no—
256C4⋊C4—522no—
257C4⋊C4—1041no—
258C4⋊C4—1041no—
259C4⋊C4—1041no—
260C22⋊C4—522no—
261C22⋊C4—521no—
262C22⋊C4—521no—
263C13#1181711yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—41no—
267C23—41no—
268C23#8804611yescharacteristic
269C23#8804611yescharacteristic
270C23C2×#610311yescharacteristic
271Q8—1042no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—522no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4#8820512yes—
303C8—82no—
304C8—1042no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22C2×#8804611yescharacteristic
316C22#1171866511yescharacteristic
317C22#1171866611yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1041no—
325C4—1041no—
326C4—1041no—
327C4—1041no—
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2#1311336811yescharacteristic
333C2#1311648311yescharacteristic
334C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1821C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1821D13
hypocenterC13#11817
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13112865C2semidirect
4. #13112862C2semidirect
263. C13#11817semidirect

Maximal subgroups

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

subgroupindex
#131206492
#131131662
#131128652
#131128622
C13×#18212
#1181713