Finite Group Databasebeta

← #16788292

Subgroups — #16788292

Order 3328.

472 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130696C211yesmaximal, characteristic
2#13130075C211yesmaximal, characteristic
3#13129816C214yesmaximal, complemented
4#13119138C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic, complemented
6C2×#88183—21no—
7C2×C4×C22⋊D13C2211yescharacteristic
8C2×#88119—21no—
9#11719136—21no—
10#11719125—21no—
11#11718873C411yescharacteristic, complemented
12#11718872—21no—
13#11718654C2212yes—
14#11718648—21no—
15#11718641C412yescomplemented
16#11718634—21no—
17#11718305—21no—
18#11718289C2212yes—
19#11718287C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C22×C22⋊D13D411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C2×C22⋊#261—22no—
25C2×C4⋊#261—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13D411yescharacteristic
32#88183—42no—
33#88183—42no—
34C4×C22⋊D13—41no—
35C4×C22⋊D13—41no—
36C2×#6103—22no—
37C2×#6103C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×#6101—22no—
40C2×#6101C2×C411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C22⋊#1057—22no—
43#88119—42no—
44(C2×#261)⋊C4—41no—
45#88112—41no—
46C4×#1057—41no—
47#88071—22no—
48#88071—22no—
49#88071C2×C412yes—
50#11874—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C23×D13C2×D411yescharacteristic
53C22×#261—42no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C2×C22⋊D13—41no—
64C2×C22⋊D13—41no—
65C2×C22⋊D13D812yes—
66C2×C22⋊D13SD1612yes—
67C22×Dic13—22no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—42no—
74C22⋊#261—42no—
75C22⋊#261—42no—
76C2×#1057—42no—
77C4⋊#261—82no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C22⋊Dic13—41no—
82C22⋊Dic13—42no—
83#6103—41no—
84#6103—42no—
85#6103—42no—
86C4⋊Dic13—42no—
87#6101—41no—
88#6101—44no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91#2486—131no—
92#1799—131no—
93#1460—131no—
94#1344—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10212yes—
100C23×C13C2×C22⋊C411yescharacteristic
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—41no—
104C22×D13—41no—
105C22×D13C2×D811yescharacteristic
106C22×D13C2×SD1611yescharacteristic
107C2×#261—82no—
108C2×#261—82no—
109C2×#261—82no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—84no—
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#9911yescharacteristic
121C22⋊D13—42no—
122C22⋊D13—42no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13#10212yes—
133C4×D13—42no—
134C4×D13—81no—
135#1057—82no—
136C2×#123—261no—
137C2×C4×D4—131no—
138C22×C4⋊C4#26111yescharacteristic, complemented
139#431—261no—
140C2×#99—261no—
141#398—132no—
142#397—132no—
143#389—261no—
144#381—261no—
145#380—131no—
146#380—261no—
147#380—261no—
148#342—132no—
149#323—132no—
150#323—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13C2×#9911yescharacteristic
159C22×C13C2×#10211yescharacteristic
160C22×C13#42111yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—81no—
168#261—162no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—82no—
172C4×C13#35212yes—
173Dic13—22no—
174Dic13—41no—
175Dic13—41no—
176Dic13—82no—
177C22×D4—131no—
178C23×C4—21no—
179C23×C4—131no—
180C23×C4C2×#26111yescharacteristic
181#123—522no—
182#123—522no—
183C4×D4—521no—
184C4×D4—521no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—521no—
192C2×C4⋊C4C2×#26112yes—
193C2×C22⋊C4—131no—
194C2×C22⋊C4—131no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4—262no—
198C2×C42—131no—
199C4⋊C8—521no—
200#99—522no—
201C22⋊C8—262no—
202C4×C8—521no—
203#95—132no—
204#95—262no—
205#95—262no—
206#95—521no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—42no—
210C2×C13#151911yescharacteristic
211C2×C13C2×#35211yescharacteristic
212C2×C13#212911yescharacteristic
213D13—41no—
214D13—41no—
215C24—131no—
216C24C22⋊#26111yescharacteristic
217C2×D4—132no—
218C2×D4—132no—
219C2×D4—521no—
220C2×D4—521no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—262no—
234C22×C4—522no—
235C22×C4—522no—
236C22×C4C22⋊#26111yescharacteristic
237C22×C4C22×#26111yescharacteristic
238C2×C8—522no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—521no—
243C4⋊C4—522no—
244C4⋊C4—524no—
245C4⋊C4—1042no—
246C22⋊C4—521no—
247C22⋊C4—522no—
248C22⋊C4—522no—
249C22⋊C4—521no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C42—261no—
254C42—261no—
255C13#1187411yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—131no—
261C23—131no—
262C23—261no—
263C23—261no—
264C23—521no—
265C23—521no—
266C23#8811512yes—
267C23C2×C22⋊#26111yescharacteristic
268D4—522no—
269D4—522no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—84no—
279C2×C4—132no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—522no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—1041no—
291C2×C4—1042no—
292C2×C4—1042no—
293C2×C4—1042no—
294C2×C4#8811911yescharacteristic
295C2×C4#8811911yescharacteristic
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—261no—
305C22—261no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22—521no—
310C22—1041no—
311C22C2×#8811511yescharacteristic
312C22#1171914011yescharacteristic
313C22C2×#8811911yescharacteristic
314C4—21no—
315C4—41no—
316C4—82no—
317C4—262no—
318C4—521no—
319C4—521no—
320C4—1042no—
321C4—2082no—
322C4#1171828812yes—
323C2—21no—
324C2—21no—
325C2—42no—
326C2—521no—
327C2—521no—
328C2#1313027211yescharacteristic
329C2C2×#1171828811yescharacteristic
330C2#1313111811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radicalC22×C22⋊D13D4
cosocleC2×#6103C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11874
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129816C2semidirect
5. C22×C13×C4⋊C4C4semidirect
11. #11718873C4semidirect
15. #11718641C4semidirect
138. C22×C4⋊C4#261semidirect
255. C13#11874semidirect

Maximal subgroups

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

subgroupindex
#131306962
#131300752
#131298162
#131191382
#1187413