Finite Group Databasebeta

← #15757989

Subgroups — #15757989

Order 3328.

534 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123865C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13113283C212yesmaximal, complemented
4#13112729C212yesmaximal, complemented
5C13×#2398C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400—21no—
9C13×#397C411yescharacteristic
10C13×#397C411yescharacteristic
11C13×#394—21no—
12C13×#393C411yescharacteristic
13C13×#393C411yescharacteristic
14C4×C13×C22⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C13×#376C2211yescharacteristic
17C2×#88073—21no—
18#11718868—21no—
19C2×C22⋊#1055—21no—
20#11718672—24no—
21#11718587C2212yes—
22C4×#6099C2212yes—
23Q8⋊#1055—24no—
24#11718122—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C4×Q8×C13—22no—
30C4×Q8×C13—22no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6099—22no—
46C2×#6099—22no—
47C22×#1055—22no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55#88073—24no—
56C22⋊#1055—22no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C4⋊#1055D414yes—
60#88043—22no—
61#88043—22no—
62C4×#1055—22no—
63#9029—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—42no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—42no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C42×C13—42no—
96C42×C13—41no—
97C42×C13—41no—
98C42×C13C2×D412yes—
99C42×C13#4112yes—
100#6099—24no—
101#6099—42no—
102#6099—82no—
103C2×#1055—24no—
104C2×#1055—42no—
105C2×#1055—82no—
106#2973—131no—
107#2398D1311yescharacteristic
108C4×#100—131no—
109#1491—132no—
110#1300—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#10412yes—
121C23×C13C2×C22⋊C411yescharacteristic
122Q8×C13—24no—
123Q8×C13—42no—
124D4×C13—44no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
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—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13C4×D412yes—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12112yes—
152C2×C4×C13#12311yescharacteristic
153#1055—44no—
154#1055—44no—
155C2×C4×Q8C2×D1311yescharacteristic
156C2×C4×D4C2×D1311yescharacteristic
157#435—264no—
158#432—132no—
159C2×#100—261no—
160#407—261no—
161C2×C22⋊C8—261no—
162C4×M16—132no—
163#400—21no—
164#397Dic1311yescharacteristic
165#397Dic1311yescharacteristic
166#394—21no—
167#393Dic1311yescharacteristic
168#393Dic1311yescharacteristic
169C4×C22⋊C4—21no—
170C4×C22⋊C4—21no—
171#376C2×D1311yescharacteristic
172#343—261no—
173Q8⋊C8—264no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#38611yescharacteristic
187C22×C13C2×#10411yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—42no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13#45512yes—
199C22×Q8C2×Dic1311yescharacteristic
200C22×D4C22⋊D1311yescharacteristic
201C23×C4C22⋊D1311yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C2×M16—262no—
204C2×M16—262no—
205C22×C8—262no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4C2×Dic1311yescharacteristic
218C2×C22⋊C4C2×Dic1311yescharacteristic
219C2×C42—21no—
220C2×C42—21no—
221C2×C42C22×D1311yescharacteristic
222C4⋊C8—134no—
223#100—264no—
224C22⋊C8—262no—
225C22⋊C8—262no—
226C22⋊C8—262no—
227#97—262no—
228#97—262no—
229C4×C8—262no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95C2×Dic1311yescharacteristic
236#95C2×Dic1311yescharacteristic
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—42no—
240C2×C13—81no—
241C2×C13#187111yescharacteristic
242C2×C13#188511yescharacteristic
243C2×C13#189111yescharacteristic
244C24C22⋊Dic1311yescharacteristic
245C24C22⋊Dic1311yescharacteristic
246C2×Q8—22no—
247C2×Q8—42no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22×Dic1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266M16—264no—
267M16—522no—
268M16—1042no—
269C2×C8—264no—
270C2×C8—522no—
271C2×C8—1042no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—42no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C42—42no—
282C42—41no—
283C42—41no—
284C42D4×D1312yes—
285C42#612912yes—
286C13#902911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#8807712yes—
297C23C2×C22⋊Dic1311yescharacteristic
298Q8—24no—
299Q8—42no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
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—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4D4×Dic1312yes—
326C2×C4#8818911yescharacteristic
327C2×C4#8819111yescharacteristic
328C2×C4#8819312yes—
329C8—524no—
330C8—524no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1171888111yescharacteristic
344C22C2×#8807711yescharacteristic
345C22#1171889711yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4#1171872212yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#1311513911yescharacteristic
361C2#1311522511yescharacteristic
362C2#1311525511yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2398C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2398D13
hypocenterC13#9029
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
3. #13113283C2semidirect
4. #13112729C2semidirect
286. C13#9029semidirect

Maximal subgroups

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

subgroupindex
#131238652
C4×#880732
#131132832
#131127292
C13×#23982
#902913