Finite Group Databasebeta

← #15756405

Subgroups — #15756405

Order 3328.

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

normal subgroups only

This group has 450 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#13117316C211yesmaximal, characteristic
2#13113168C211yesmaximal, characteristic
3#13113168C211yesmaximal, characteristic
4#13112693C211yesmaximal, characteristic, complemented
5#13112692C211yesmaximal, characteristic, complemented
6#13112691C211yesmaximal, characteristic, complemented
7C13×#1285C211yesmaximal, characteristic, complemented
8C2×#88126C411yescharacteristic
9C2×#88126C2211yescharacteristic
10C2×C42×D13C411yescharacteristic
11C13×#432C2211yescharacteristic
12C13×#432C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14#11718650—21no—
15#11718633—21no—
16C4×C4⋊Dic13C2211yescharacteristic
17C4×#6101C411yescharacteristic
18C4×#6101C411yescharacteristic
19#11718587C2211yescharacteristic
20#11718587C2211yescharacteristic
21#11718329—21no—
22#11718308—21no—
23#11718061—21no—
24#11718061—21no—
25#11718060—21no—
26#11718060—21no—
27C22×C4×D13—21no—
28C22×C4×D13C2×C411yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×#6103—21no—
34C2×#6103D411yescharacteristic
35C2×#6103D411yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101D411yescharacteristic
41C2×#6101D411yescharacteristic
42C2×C4×Dic13—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46#88126—21no—
47#88126—21no—
48#88126—21no—
49#88126—21no—
50#88126—42no—
51C42×D13—42no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#97—21no—
57C13×#97—21no—
58C13×#95—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66#88043—21no—
67#88043—21no—
68#8742—131nomaximal, Sylow
69C23×D13C22⋊C411yescharacteristic
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C22⋊C411yescharacteristic
79C22×Dic13C22⋊C411yescharacteristic
80C2×C4×D13—22no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—22no—
84C2×C4×D13—42no—
85C2×C4×D13—42no—
86C2×C4×D13—42no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—42no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C42×C13#4111yescharacteristic
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—42no—
101C4⋊Dic13—42no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101—42no—
107#6101—42no—
108#6101—42no—
109C4×Dic13—21no—
110C4×Dic13—21no—
111C4×Dic13—42no—
112C4×Dic13—41no—
113C4×Dic13—41no—
114C2×#1055—41no—
115C2×#1055—41no—
116#2296—131no—
117#1464—131no—
118#1464—131no—
119#1285—131no—
120#1285—131no—
121#1285—131no—
122#1285D1311yescharacteristic, complemented
123C23×C13C2×C22⋊C411yescharacteristic
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13#10012yes—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—22no—
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#11711yescharacteristic
140C2×C4×C13#11711yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×C4×C13#12311yescharacteristic
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—22no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13#10112yes—
158C4×D13—24no—
159C4×D13—24no—
160C4×D13—48no—
161C8×C13—81no—
162C8×C13—81no—
163#1055—81no—
164#1055—81no—
165C2×#117—131no—
166C2×#117—131no—
167C22×C42—131no—
168#432—131no—
169#432—131no—
170#432C2×D1311yescharacteristic
171#432C2×D1311yescharacteristic
172#389—261no—
173#389—261no—
174#385—261no—
175#385—261no—
176C4×C4⋊C4—131no—
177C4×C4⋊C4—131no—
178C4×C4⋊C4—131no—
179C4×C4⋊C4C2×D1311yescharacteristic
180#324—261no—
181#324—261no—
182#323—261no—
183#323—261no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13#38111yescharacteristic
187C22×C13C2×#10011yescharacteristic
188C22×C13C2×#10111yescharacteristic
189C2×D13—22no—
190C2×D13—42no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—42no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—42no—
201C4×C13—81no—
202Dic13—22no—
203Dic13—42no—
204Dic13—41no—
205Dic13—41no—
206Dic13—81no—
207C23×C4—131no—
208C23×C4—261no—
209#117—261no—
210#117—261no—
211#117—261no—
212#117—261no—
213#117—522no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C22⋊C4—131no—
222C2×C22⋊C4—131no—
223C2×C22⋊C4—261no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—261no—
228C2×C42—522no—
229C2×C42C4×D1311yescharacteristic
230C2×C42C4×D1311yescharacteristic
231C2×C42C22×D1311yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—261no—
239C22⋊C8—261no—
240#97—21no—
241#97—21no—
242#97—261no—
243#97—261no—
244#95—21no—
245#95—261no—
246#95—261no—
247#95—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13#182111yescharacteristic
251C2×C13#182711yescharacteristic
252C2×C13#182711yescharacteristic
253D13—42no—
254C24—131no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—522no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4D4×D1311yescharacteristic
271C22×C4D4×D1311yescharacteristic
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—521no—
275C2×C8—521no—
276C4⋊C4—42no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—522no—
290C42—41no—
291C42—41no—
292C42—261no—
293C42—261no—
294C42—521no—
295C42—521no—
296C42—522no—
297C42#612711yescharacteristic
298C42#612711yescharacteristic
299C42#612911yescharacteristic
300C42#613111yescharacteristic
301C13#874211yescharacteristic, complemented, Sylow
302C23—132no—
303C23—261no—
304C23—261no—
305C23—521no—
306C23—521no—
307C23C22⋊C4×D1311yescharacteristic
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—132no—
319C2×C4—264no—
320C2×C4—264no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—262no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—528no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4#8812611yescharacteristic
335C2×C4#8813711yescharacteristic
336C2×C4#8813711yescharacteristic
337C2×C4#8814611yescharacteristic
338C2×C4#8814811yescharacteristic
339C2×C4#8814811yescharacteristic
340C8—81no—
341C8—81no—
342C8—1041no—
343C8—1041no—
344C22—21no—
345C22—21no—
346C22—262no—
347C22—522no—
348C22—522no—
349C22—521no—
350C22—521no—
351C22#1171832511yescharacteristic
352C22D13×#10011yescharacteristic
353C22D13×#10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—262no—
363C4—522no—
364C4—521no—
365C4—521no—
366C4—1041no—
367C2—21no—
368C2—21no—
369C2—522no—
370C2#1311491511yescharacteristic
371C2#1311493811yescharacteristic
372C2#1311493911yescharacteristic
subgroupG/H
centerC22#11718325
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1285C2
socleC22×C13#381
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1285D13
hypocenterC13#8742
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
4. #13112693C2semidirect
5. #13112692C2semidirect
6. #13112691C2semidirect
7. C13×#1285C2semidirect
122. #1285D13semidirect
301. C13#8742semidirect

Maximal subgroups

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

subgroupindex
#131173162
#131131682
#131126932
#131126922
#131126912
C13×#12852
#874213