Finite Group Databasebeta

← #14656165

Subgroups — #14656165

Order 2816.

578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079734C211yesmaximal, characteristic
2#13073601C211yesmaximal, characteristic, complemented
3#13067289C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66997—21no—
12C2×#66922C2211yescharacteristic
13C11×#464—22no—
14C11×#462—21no—
15C11×#460—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622691—21no—
19#10622683—21no—
20#10622646—22no—
21#10622620—22no—
22#10622596—22no—
23#10622587—21no—
24C4×C4⋊Dic11C2211yescharacteristic
25#10622541—22no—
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29Q8⋊(C11⋊C8)—22no—
30#10622120—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×Dic22—21no—
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—22no—
37C2×C11×SD16—22no—
38C2×C11×M16—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54#66997—42no—
55#66997—42no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11D412yes—
59C2×Dic11⋊C4—24no—
60C2×C4×Dic11—21no—
61#66922—21no—
62#66922—21no—
63#66922—21no—
64#66922—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#102—22no—
69#66896—24no—
70C11⋊#95—24no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66871—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10243—111nomaximal, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11D812yes—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—22no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×Dic22—41no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C11×Q16—44no—
110C11×SD16—44no—
111C11×M16—41no—
112C11×M16—41no—
113C2×C8×C11—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133Dic11⋊C4—48no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138#3226—111no—
139#3037D1111yescharacteristic
140#2546—111no—
141#1546—111no—
142#1502—111no—
143#1479—111no—
144#1303—111no—
145C23×C11—41no—
146C23×C11#12011yescharacteristic
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—41no—
150Q8×C11—41no—
151Q8×C11—41no—
152Q8×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—42no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×Dic11—24no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185Dic22—81no—
186Dic22—81no—
187Dic22—81no—
188Dic22—81no—
189C8×C11—42no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C2×#137—21no—
193#532C2×D1111yescharacteristic
194C2×C4⋊Q8—111no—
195C2×C4⋊Q8—221no—
196C2×C4×Q8C2×D1111yescharacteristic
197#500—221no—
198#486—221no—
199#480—222no—
200#474—222no—
201#464—22no—
202#462—21no—
203#460—21no—
204#431—111no—
205#431—111no—
206#423C2×D1111yescharacteristic
207#417—21no—
208#398—222no—
209#391—221no—
210#389—222no—
211C4×C4⋊C4—111no—
212#332—222no—
213#327—222no—
214Q8⋊C8—222no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39211yescharacteristic
221C22×C11#44711yescharacteristic
222C22×C11#44911yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11#44711yescharacteristic
230C4×C11#44911yescharacteristic
231C4×C11#45612yes—
232C4×C11#46611yescharacteristic
233C4×C11#46911yescharacteristic
234Dic11—44no—
235Dic11—82no—
236C2×#41—21no—
237C22×Q8—221no—
238C22×Q8C22⋊D1111yescharacteristic
239#137—42no—
240#137—42no—
241C2×Q16—22no—
242C2×SD16—22no—
243C2×M16—21no—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—442no—
249C4⋊Q8—442no—
250C4⋊Q8C22⋊D1111yescharacteristic
251#127C22⋊D1111yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×D4—21no—
260C4×D4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—112no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—224no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4C22⋊D1111yescharacteristic
267C2×C42—21no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—224no—
271C4⋊C8—21no—
272C4⋊C8—112no—
273C4⋊C8—221no—
274C4⋊C8C22⋊D1112yes—
275#103—22no—
276#102—22no—
277#102—224no—
278C22⋊C8—221no—
279C22⋊C8—221no—
280C4×C8—221no—
281C4×C8—221no—
282#95—112no—
283#95—224no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—161no—
287C2×C11#199911yescharacteristic
288C2×C11#200511yescharacteristic
289C2×C11#200911yescharacteristic
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×Q8—441no—
306C2×Q8#432312yes—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319Q16—44no—
320SD16—44no—
321M16—41no—
322M16—41no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—224no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—448no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C42—41no—
341C42—41no—
342C42—441no—
343C42—441no—
344C42D4×D1111yescharacteristic
345C42#434111yescharacteristic
346C42C2×C22⋊D1111yescharacteristic
347C42C2×C22⋊D1111yescharacteristic
348C11#1024311yescharacteristic, complemented, Sylow
349C23—41no—
350C23#6699011yescharacteristic
351Q8—22no—
352Q8—22no—
353Q8—41no—
354Q8—41no—
355Q8—41no—
356Q8—41no—
357Q8—881no—
358Q8—881no—
359Q8—881no—
360Q8—881no—
361D4—42no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366D4—81no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—224no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4C2×#432311yescharacteristic
384C2×C4#6698511yescharacteristic
385C2×C4#6699011yescharacteristic
386C2×C4#6699111yescharacteristic
387C2×C4#6699211yescharacteristic
388C2×C4#6699211yescharacteristic
389C2×C4#6699311yescharacteristic
390C2×C4#6700211yescharacteristic
391C2×C4#6700311yescharacteristic
392C2×C4#6700611yescharacteristic
393C8—42no—
394C8—442no—
395C8—881no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22#1062264911yescharacteristic
402C22#1062265011yescharacteristic
403C22#1062283611yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—81no—
409C4—81no—
410C4—444no—
411C4—882no—
412C4#1062265111yescharacteristic
413C4#1062265211yescharacteristic
414C4#1062281812yes—
415C4#1062283011yescharacteristic
416C4#1062285111yescharacteristic
417C2—21no—
418C2—21no—
419C2—161no—
420C2#1306961211yescharacteristic
421C2#1306964911yescharacteristic
422C2#1306967311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3037D11
hypocenterC11#10243
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #13073601C2semidirect
3. #13067289C2semidirect
5. #13067011C2semidirect
6. #13066517C2semidirect
348. C11#10243semidirect

Maximal subgroups

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

subgroupindex
#130797342
#130736012
#130672892
#130671112
#130670112
#130665172
C11×#30372
#1024311