Finite Group Databasebeta

← #15758885

Subgroups — #15758885

Order 3328.

530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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#13123877C211yesmaximal, characteristic
2#13120753C211yesmaximal, characteristic
3#13113355C212yesmaximal, complemented
4#13112689C212yesmaximal, complemented
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C2×C13×#99—21no—
9C4×C13×C22⋊C4C2212yes—
10#11718883—21no—
11#11718872C2211yescharacteristic
12#11718871—21no—
13#11718868—21no—
14#11718868C2212yes—
15#11718673—24no—
16#11718644C411yescharacteristic, complemented
17#11718640C411yescharacteristic, complemented
18#11718614C411yescharacteristic, complemented
19#11718613—21no—
20#11718608C411yescharacteristic, complemented
21#11718594—21no—
22#11718586—21no—
23C13×#342—21no—
24#11718044—24no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13—22no—
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42#88178—22no—
43#88178—22no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6099—22no—
48C2×#6099—22no—
49C13×#99—24no—
50C13×#95—22no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055D414yes—
61C4⋊#1055—22no—
62C4×#1055—22no—
63#9184—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—42no—
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×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13#4112yes—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C2×Dic26—22no—
86C2×Dic26—81no—
87C13×C4⋊C4—22no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—42no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—82no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C22⋊Dic13—81no—
98C22⋊Dic13—81no—
99C4⋊Dic13—22no—
100#6101—42no—
101#6101—41no—
102#6101—41no—
103#6101—81no—
104#6099—82no—
105#6099—82no—
106C2×#1055—24no—
107#2975—131no—
108#2638—131no—
109C4×#99D1311yescharacteristic
110#1508—132no—
111#1284—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13#12112yes—
123D4×C13—44no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—44no—
136C2×C4×C13—81no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×C4×C13#10412yes—
140C2×C4×C13C4×D412yes—
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
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—
155Dic26—82no—
156#1055—44no—
157C2×C22⋊Q8—131no—
158C2×C4×D4C2×D1311yescharacteristic
159#436—264no—
160#431—261no—
161C2×#99—21no—
162#407—132no—
163#407—261no—
164#398—131no—
165#397—131no—
166#397—261no—
167#395—131no—
168#394—261no—
169#393—131no—
170#387—261no—
171#385—261no—
172#381—131no—
173C4×C22⋊C4C2×D1312yes—
174#342—21no—
175#328—264no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#38611yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13#42111yescharacteristic
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—84no—
198Dic13—81no—
199Dic13—81no—
200Dic13—81no—
201Dic13—81no—
202C22×Q8—131no—
203C22×D4C22⋊D1311yescharacteristic
204C23×C4D5211yescharacteristic
205C23×C4C22×D1311yescharacteristic
206C2×M16—262no—
207C2×M16—262no—
208C22⋊Q8—262no—
209C22⋊Q8—262no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4C4×D1311yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4C4×D1311yescharacteristic
223C2×C22⋊C4C22⋊D1311yescharacteristic
224C2×C42—22no—
225C2×C42D5211yescharacteristic
226C4⋊C8—262no—
227#99—24no—
228C22⋊C8—134no—
229C22⋊C8—262no—
230C22⋊C8—262no—
231C4×C8—262no—
232#95—22no—
233#95—131no—
234#95—131no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—261no—
239#95—261no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—42no—
243C2×C13—81no—
244C2×C13#187111yescharacteristic
245C2×C13#190911yescharacteristic
246C2×C13#191311yescharacteristic
247C24#610311yescharacteristic
248C24C2×C22⋊D1311yescharacteristic
249C2×Q8—262no—
250C2×Q8—1041no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4C2×C4×D1311yescharacteristic
267C22×C4C2×D5211yescharacteristic
268C22×C4D4×D1312yes—
269C22×C4#612912yes—
270M16—1042no—
271M16—1042no—
272C2×C8—264no—
273C4⋊C4—22no—
274C4⋊C4—262no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—522no—
278C4⋊C4—1041no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—24no—
282C22⋊C4—42no—
283C22⋊C4—522no—
284C22⋊C4—522no—
285C22⋊C4—1041no—
286C22⋊C4—1041no—
287C42—21no—
288C42—21no—
289C42—82no—
290C13#918411yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23C2×#610311yescharacteristic
301C23#8819312yes—
302Q8—1042no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—44no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4#8804512yes—
332C2×C4#8813512yes—
333C2×C4#8813611yescharacteristic
334C2×C4#8814011yescharacteristic
335C8—524no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22C2×#8804511yescharacteristic
349C22#1171861911yescharacteristic
350C22#1171866611yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—1041no—
359C4—1041no—
360C4—1041no—
361C4—1041no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2#1311513611yescharacteristic
367C2#1311535611yescharacteristic
368C2#1311537611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×#99C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenterC4×#99D13
hypocenterC13#9184
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13113355C2semidirect
4. #13112689C2semidirect
16. #11718644C4semidirect
17. #11718640C4semidirect
18. #11718614C4semidirect
20. #11718608C4semidirect
290. C13#9184semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131207532
#131133552
#131126892
C4×C13×#992
#918413