Finite Group Databasebeta

← #15760244

Subgroups — #15760244

Order 3328.

548 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 115 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×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C13×#435—24no—
9C13×#432—21no—
10C13×#407—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
30C2×C13×M16—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—
53C13×#97—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#9385—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—22no—
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—41no—
87C22×Dic13—41no—
88C22×Dic13—42no—
89C22×Dic13—81no—
90C2×Dic26—22no—
91C2×Dic26—81no—
92C13×M16—82no—
93C2×C8×C13—24no—
94C2×C8×C13—82no—
95C13×C4⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C42×C13—21no—
99C42×C13—21no—
100C22⋊Dic13—42no—
101C22⋊Dic13—42no—
102C22⋊Dic13—42no—
103C22⋊Dic13—42no—
104C22⋊Dic13—81no—
105C4⋊Dic13—22no—
106C4⋊Dic13—82no—
107#6101—42no—
108#6101—41no—
109#6101—41no—
110#6101—81no—
111#2973D1311yescharacteristic
112#2564—131no—
113#1799—131no—
114#1520—132no—
115#1294—132no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13#12112yes—
125C23×C13AGL(1,ℤ/8)11yescharacteristic
126C23×C13#13711yescharacteristic
127C23×C13#13712yes—
128D4×C13—42no—
129D4×C13—42no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13C4×D412yes—
144C2×C4×C13#12011yescharacteristic
145C2×C4×C13#12311yescharacteristic
146C2×Dic13—22no—
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—41no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161C2×Dic13—82no—
162C2×Dic13—82no—
163Dic26—82no—
164C8×C13—44no—
165C2×C22⋊Q8—131no—
166C2×C4×D4C2×D1311yescharacteristic
167#435—24no—
168#432—21no—
169C2×#99—261no—
170#407—21no—
171C2×C22⋊C8C2×D1312yes—
172#400—131no—
173#399—131no—
174#395—131no—
175#393—131no—
176#387—261no—
177#386—261no—
178#385—261no—
179#380—132no—
180#380—261no—
181C2×#95—131no—
182#342—261no—
183#328—264no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—81no—
196C22×C13#38611yescharacteristic
197C22×C13#41711yescharacteristic
198C22×C13#41911yescharacteristic
199C22×C13#46812yes—
200C22×C13#47012yes—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—21no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207Dic13—42no—
208Dic13—81no—
209Dic13—81no—
210Dic13—81no—
211Dic13—162no—
212C22×Q8—131no—
213C22×D4D5211yescharacteristic
214C23×C4—261no—
215C23×C4C22⋊D1311yescharacteristic
216C23×C4C22×D1311yescharacteristic
217C2×M16—22no—
218C22×C8—22no—
219C22⋊Q8—262no—
220C22⋊Q8—262no—
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4C4×D1311yescharacteristic
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4—262no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4C4×D1311yescharacteristic
234C2×C22⋊C4D5211yescharacteristic
235C2×C42C22⋊D1311yescharacteristic
236C4⋊C8—22no—
237#99—522no—
238C22⋊C8—22no—
239C22⋊C8—22no—
240C22⋊C8C22⋊D1314yes—
241#97—22no—
242#95—131no—
243#95—131no—
244#95—261no—
245#95—261no—
246#95—261no—
247#95—261no—
248#95—261no—
249#95—262no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—21no—
253C2×C13—22no—
254C2×C13—81no—
255C2×C13#188411yescharacteristic
256C2×C13#189411yescharacteristic
257C2×C13#191311yescharacteristic
258C24#610311yescharacteristic
259C24C2×D5211yescharacteristic
260C2×Q8—262no—
261C2×Q8—1041no—
262C2×D4—21no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—522no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4—522no—
278C22×C4—1041no—
279C22×C4#610311yescharacteristic
280C22×C4#610311yescharacteristic
281C22×C4#610311yescharacteristic
282C22×C4C2×C4×D1311yescharacteristic
283C22×C4#612712yes—
284C22×C4C2×C22⋊D1312yes—
285C22×C4C2×C22⋊D1311yescharacteristic
286M16—82no—
287C2×C8—24no—
288C2×C8—82no—
289C4⋊C4—22no—
290C4⋊C4—262no—
291C4⋊C4—522no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4—1041no—
295C4⋊C4—1042no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—522no—
299C22⋊C4—522no—
300C22⋊C4—522no—
301C22⋊C4—522no—
302C22⋊C4—1041no—
303C42—21no—
304C42—21no—
305C13#938511yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#8816211yescharacteristic
314C23#8816312yes—
315C23#8816311yescharacteristic
316C23C2×#610311yescharacteristic
317C23#8818412yes—
318Q8—1042no—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—262no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—1042no—
347C2×C4—1042no—
348C2×C4—1042no—
349C2×C4—1042no—
350C2×C4—1042no—
351C2×C4C4×C22⋊D1312yes—
352C2×C4#8818311yescharacteristic
353C2×C4#8820711yescharacteristic
354C8—44no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1171878111yescharacteristic
368C22#1171879411yescharacteristic
369C22#1171879512yes—
370C22#1171879812yes—
371C22#1171887411yescharacteristic
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—522no—
379C4—1041no—
380C4—1041no—
381C4—1041no—
382C4—2082no—
383C2—21no—
384C2—22no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#1311521911yescharacteristic
389C2#1311526911yescharacteristic
390C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2973D13
hypocenterC13#9385
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

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
305. C13#9385semidirect

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×#29732
#938513