Finite Group Databasebeta

← #15760234

Subgroups — #15760234

Order 3328.

570 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 131 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#13120012C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13113409C212yesmaximal, complemented
4#13112716C212yesmaximal, complemented
5C13×#2972C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C8×D4×C13—24no—
9C13×#431—21no—
10C2×C13×C22⋊C8—21no—
11C2×C13×C22⋊C8C2212yes—
12#11718881—21no—
13C2×#88074—21no—
14#11718873C2212yes—
15#11718871—21no—
16C2×#88071C2211yescharacteristic
17#11718647C411yescharacteristic, complemented
18#11718640C411yescharacteristic, complemented
19#11718610C411yescharacteristic, complemented
20#11718608C411yescharacteristic, complemented
21#11718603—21no—
22#11718594—21no—
23#11718118—21no—
24#11718059—24no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C23×Dic13—21no—
29C22×Dic26C2×C411yescharacteristic
30C22×C8×C13—22no—
31C22×C8×C13—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—21no—
42C2×C4⋊Dic13—22no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44#88178—22no—
45#88178—22no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C13×C4⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×C22⋊C8D414yes—
53C4×C8×C13—22no—
54#88074—42no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—22no—
61#88071C2×C411yescharacteristic
62#88071C2×C411yescharacteristic
63#9383—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13SD1612yes—
69C2×D4×C13Q1612yes—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4112yes—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—42no—
86C22×Dic13—42no—
87C22×Dic13—42no—
88C22×Dic13—81no—
89C2×Dic26—22no—
90C2×Dic26—81no—
91C2×C8×C13—24no—
92C2×C8×C13—82no—
93C2×C8×C13—82no—
94C13×C4⋊C4—22no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C42×C13—21no—
98C42×C13—21no—
99C22⋊Dic13—42no—
100C22⋊Dic13—42no—
101C22⋊Dic13—42no—
102C22⋊Dic13—42no—
103C22⋊Dic13—81no—
104C4⋊Dic13—22no—
105C4⋊Dic13—82no—
106#6101—42no—
107#6101—41no—
108#6101—41no—
109#6101—81no—
110#2972D1311yescharacteristic
111#2564—131no—
112#1799—131no—
113#1520—132no—
114#1294—132no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13#10312yes—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#12112yes—
124C23×C13C2×SD1611yescharacteristic
125C23×C13C2×Q1611yescharacteristic
126C23×C13#13512yes—
127D4×C13—24no—
128D4×C13—24no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—81no—
141C2×C4×C13#10312yes—
142C2×C4×C13C4×D412yes—
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12311yescharacteristic
145C2×Dic13—22no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—84no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161Dic26—82no—
162C8×C13—44no—
163C2×C22⋊Q8—131no—
164C2×C4×D4C2×D1311yescharacteristic
165C8×D4—24no—
166#431—21no—
167C2×#99—261no—
168C2×C22⋊C8—21no—
169C2×C22⋊C8C2×D1312yes—
170#400—131no—
171#399—131no—
172#395—131no—
173#393—131no—
174#387—261no—
175#386—261no—
176#385—261no—
177#380—132no—
178#380—261no—
179C2×#95—131no—
180#342—261no—
181#328—264no—
182C22×C13—21no—
183C22×C13—22no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—42no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—81no—
194C22×C13#38611yescharacteristic
195C22×C13C2×#10311yescharacteristic
196C22×C13#41611yescharacteristic
197C22×C13#46512yes—
198C22×C13#46712yes—
199C4×C13—22no—
200C4×C13—21no—
201C4×C13—22no—
202C4×C13—21no—
203C4×C13—41no—
204C4×C13—41no—
205Dic13—42no—
206Dic13—81no—
207Dic13—81no—
208Dic13—81no—
209Dic13—162no—
210C22×Q8—131no—
211C22×D4D5211yescharacteristic
212C23×C4—261no—
213C23×C4C22⋊D1311yescharacteristic
214C23×C4C22×D1311yescharacteristic
215C22×C8—22no—
216C22×C8—22no—
217C22⋊Q8—262no—
218C22⋊Q8—262no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—262no—
226C2×C4⋊C4C4×D1311yescharacteristic
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C22⋊C4—262no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4C4×D1311yescharacteristic
232C2×C22⋊C4D5211yescharacteristic
233C2×C42C22⋊D1311yescharacteristic
234C4⋊C8—22no—
235#99—522no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238C22⋊C8C22⋊D1314yes—
239C4×C8—22no—
240#95—131no—
241#95—131no—
242#95—261no—
243#95—261no—
244#95—261no—
245#95—261no—
246#95—261no—
247#95—262no—
248C2×C13—21no—
249C2×C13—22no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—42no—
253C2×C13#188411yescharacteristic
254C2×C13#189211yescharacteristic
255C2×C13#191311yescharacteristic
256C24#610311yescharacteristic
257C24C2×D5211yescharacteristic
258C2×Q8—262no—
259C2×Q8—1041no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4#609512yes—
263C2×D4Dic5212yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—522no—
273C22×C4—522no—
274C22×C4—522no—
275C22×C4—1041no—
276C22×C4#610311yescharacteristic
277C22×C4#610311yescharacteristic
278C22×C4#610311yescharacteristic
279C22×C4C2×C4×D1311yescharacteristic
280C22×C4#612712yes—
281C22×C4C2×C22⋊D1312yes—
282C22×C4C2×C22⋊D1311yescharacteristic
283C2×C8—24no—
284C2×C8—82no—
285C2×C8—82no—
286C4⋊C4—22no—
287C4⋊C4—262no—
288C4⋊C4—522no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—1041no—
292C4⋊C4—1042no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—522no—
296C22⋊C4—522no—
297C22⋊C4—522no—
298C22⋊C4—522no—
299C22⋊C4—1041no—
300C42—21no—
301C42—21no—
302C13#938311yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#8805612yes—
310C23C2×#609511yescharacteristic
311C23#8815812yes—
312C23C2×Dic5211yescharacteristic
313C23C2×#610311yescharacteristic
314C23#8818412yes—
315Q8—1042no—
316D4—24no—
317D4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—262no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—1044no—
343C2×C4—1042no—
344C2×C4—1042no—
345C2×C4—1042no—
346C2×C4#8805612yes—
347C2×C4C4×C22⋊D1312yes—
348C2×C4#8818311yescharacteristic
349C2×C4#8820711yescharacteristic
350C8—44no—
351C22—21no—
352C22—22no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22C2×#8805611yescharacteristic
364C22#1171877411yescharacteristic
365C22#1171877512yes—
366C22#1171877712yes—
367C22#1171887411yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—22no—
372C4—41no—
373C4—41no—
374C4—522no—
375C4—1041no—
376C4—1041no—
377C4—1041no—
378C4—2082no—
379C2—21no—
380C2—22no—
381C2—21no—
382C2—22no—
383C2—42no—
384C2#1311521911yescharacteristic
385C2#1311525911yescharacteristic
386C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2972C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2972D13
hypocenterC13#9383
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #13113409C2semidirect
4. #13112716C2semidirect
17. #11718647C4semidirect
18. #11718640C4semidirect
19. #11718610C4semidirect
20. #11718608C4semidirect
302. C13#9383semidirect

Maximal subgroups

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

subgroupindex
#131200122
#131148242
#131134092
#131127162
C13×#29722
#938313