Finite Group Databasebeta

← #14727967

Subgroups — #14727967

Order 2816.

950 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#10623031C211yesmaximal, characteristic
2#13079437C212yesmaximal
3#13067623C214yesmaximal, complemented
4#13067589C214yesmaximal, complemented
5#13067135C212yesmaximal
6#13066946C211yesmaximal, characteristic
7C11×#2583C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66979—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623031—22no—
14#10623031—24no—
15#10623031C2214yes—
16C2×#66943—22no—
17C2×#66941—22no—
18C11×#398C2212yes—
19C11×#395C2212yes—
20C11×#389—22no—
21C11×#385—21no—
22C11×#385—21no—
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622841C2214yes—
25#10622820C2212yes—
26#10622665—24no—
27#10622663—22no—
28#10622656—22no—
29#10622584C2214yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C22×Q8×C11C2311yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×Dic22—21no—
37C22×Dic22D412yes—
38C11×C22⋊Q8—22no—
39C11×C22⋊Q8—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11—21no—
51C2×C22⋊Dic11—22no—
52C2×#4326—24no—
53#66979—24no—
54#66979—24no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59#66977—24no—
60#66977—22no—
61#66977—22no—
62#66977—24no—
63#66977D414yes—
64#66977C2314yes—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×#4318—22no—
69#66943—28no—
70#66943—28no—
71#66941—28no—
72#66941—28no—
73C11×#95—22no—
74C11×#95—22no—
75C11×#95C2312yes—
76#66899—24no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66874—24no—
80#66872—24no—
81#18327—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—22no—
84C2×Q8×C11—81no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—24no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—81no—
94C22×C4×C11—81no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—22no—
103C2×Dic22—24no—
104C2×Dic22—22no—
105C2×Dic22—82no—
106C2×Dic22—82no—
107C2×Dic22C2×D414yes—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—44no—
113C11×C4⋊C4—82no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11—81no—
118C22⋊Dic11—24no—
119C22⋊Dic11—24no—
120#4326—84no—
121C4⋊Dic11—24no—
122C4⋊Dic11—24no—
123C4⋊Dic11—24no—
124C4⋊Dic11—22no—
125C4⋊Dic11C2×D414yes—
126Dic11⋊C4—28no—
127Dic11⋊C4—24no—
128Dic11⋊C4—24no—
129C4×Dic11—28no—
130#4318—82no—
131C2×C11⋊C8—24no—
132C2×#544—111no—
133#3195—112no—
134#2583D1111yescharacteristic
135#1611—114no—
136#1605—114no—
137#1508—112no—
138#1463—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11#12011yescharacteristic
143C23×C11#12011yescharacteristic
144C23×C11C22×D411yescharacteristic
145Q8×C11—44no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—81no—
165C2×C4×C11#12012yes—
166C2×C4×C11#13714yes—
167C2×C4×C11C22×D412yes—
168C2×Dic11—24no—
169C2×Dic11—24no—
170C2×Dic11—44no—
171C2×Dic11—44no—
172Dic22—44no—
173Dic22—82no—
174Dic22—84no—
175C11⋊C8—44no—
176#544—114no—
177#544—224no—
178#544—222no—
179C2×C4⋊Q8—222no—
180C2×#125—222no—
181C2×C22⋊Q8—112no—
182C2×C22⋊Q8—221no—
183C2×C22⋊Q8C2×D1111yescharacteristic
184C2×#117—221no—
185C22×C4⋊C4C2×D1111yescharacteristic
186#483—114no—
187#483—222no—
188#470—224no—
189#451—114no—
190#451—222no—
191#407—112no—
192#398C2×D1112yes—
193#395C2×D1112yes—
194#389—22no—
195#385—21no—
196#385—21no—
197C4×C22⋊C4C2×D1111yescharacteristic
198#328—118no—
199#324—114no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—44no—
208C22×C11#45612yes—
209C22×C11C2×#12011yescharacteristic
210C22×C11C2×#13712yes—
211C4×C11—24no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—44no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—81no—
218Dic11—44no—
219Dic11—44no—
220C22×Q8—112no—
221C22×Q8—221no—
222C22×Q8C22×D1111yescharacteristic
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22⋊D1111yescharacteristic
225C23×C4C22×D1111yescharacteristic
226C2×Q16—224no—
227C2×M16—222no—
228C4⋊Q8—228no—
229C4⋊Q8—228no—
230#125—228no—
231#125—228no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C22⋊Q8—114no—
235C22⋊Q8—114no—
236C22⋊Q8—224no—
237C22⋊Q8—222no—
238C22⋊Q8—222no—
239C22⋊Q8—224no—
240#117—224no—
241#117—224no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—222no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C22⋊D1112yes—
254C2×C4⋊C4C22×D1111yescharacteristic
255C2×C4⋊C4C22×D1112yes—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—222no—
259C2×C42—21no—
260C2×C42—222no—
261#106—224no—
262#103—224no—
263#103—224no—
264C22⋊C8—114no—
265C22⋊C8—222no—
266#95—22no—
267#95—22no—
268#95C22×D1112yes—
269C2×C11—22no—
270C2×C11—22no—
271C2×C11—41no—
272C2×C11#300411yescharacteristic
273C2×C11C2×#45611yescharacteristic
274C2×C11#302611yescharacteristic
275C24C2×C22⋊D1111yescharacteristic
276C2×Q8—22no—
277C2×Q8—81no—
278C2×Q8—114no—
279C2×Q8—224no—
280C2×Q8—222no—
281C2×Q8—882no—
282C2×Q8—882no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4D4×D1112yes—
296C22×C4D4×D1112yes—
297C22×C4C2×C22⋊D1112yes—
298C22×C4C2×C22⋊D1112yes—
299C22×C4C2×C22⋊D1111yescharacteristic
300C22×C4C23×D1111yescharacteristic
301Q16—884no—
302M16—882no—
303C2×C8—224no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—42no—
308C4⋊C4—44no—
309C4⋊C4—82no—
310C4⋊C4—114no—
311C4⋊C4—224no—
312C4⋊C4—224no—
313C4⋊C4—224no—
314C4⋊C4—228no—
315C4⋊C4—222no—
316C4⋊C4—224no—
317C4⋊C4—224no—
318C22⋊C4—24no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—224no—
322C22⋊C4—224no—
323C42—81no—
324C42—228no—
325C11#1832711yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—41no—
329C23#6699011yescharacteristic
330C23#6699011yescharacteristic
331C23C22×C22⋊D1111yescharacteristic
332Q8—44no—
333Q8—444no—
334Q8—882no—
335Q8—884no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—224no—
356C2×C4—224no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4#6699012yes—
360C2×C4#6700414yes—
361C2×C4C2×D4×D1112yes—
362C8—444no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22#1062270812yes—
372C22C2×#6699011yescharacteristic
373C22C2×#6700412yes—
374C4—24no—
375C4—22no—
376C4—22no—
377C4—44no—
378C4—42no—
379C4—81no—
380C4—81no—
381C4—444no—
382C4—444no—
383C2—22no—
384C2—22no—
385C2—41no—
386C2#1307784911yescharacteristic
387C2C2×#1062270811yescharacteristic
388C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2583C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#2583D11
hypocenterC11#18327
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #13067623C2semidirect
4. #13067589C2semidirect
325. C11#18327semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130794372
#130676232
#130675892
#130671352
#130669462
C11×#25832
#1832711