Finite Group Databasebeta

← #14654538

Subgroups — #14654538

Order 2816.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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#13078624C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13067179C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#2536C211yesmaximal, characteristic
8C2×C11×C22⋊Q8—21no—
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#398—21no—
13C11×#394—21no—
14C11×#388—22no—
15C11×#382C2211yescharacteristic
16C11×#380—21no—
17#10622838—21no—
18#10622831—21no—
19#10622635—22no—
20#10622634—21no—
21#10622633—21no—
22#10622632—21no—
23C4×#4324—22no—
24#10622621—21no—
25#10622584—21no—
26#10622577—21no—
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622090—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C11×C22⋊Q8—42no—
37C11×C22⋊Q8—42no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—21no—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4324—22no—
57#66979—21no—
58#66977—21no—
59#66977—21no—
60C2×#4318—21no—
61#66923—21no—
62#66922D411yescharacteristic
63#66922D411yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×#95—22no—
67C11×#95—21no—
68C11×#95D412yes—
69#66899—22no—
70#66899—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66874—22no—
75#66872—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8D412yes—
84#10001—111nomaximal, Sylow
85C24×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11SD1612yescomplemented
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—42no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C2×Dic22—21no—
109C2×Dic22—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—44no—
120C11×C22⋊C4—44no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C22⋊Dic11—41no—
130#4324—44no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138#4318—41no—
139#4318—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143#3101—111no—
144#3078—111no—
145#2536D1111yescharacteristic
146#1518—111no—
147#1486—111no—
148#1479—111no—
149#1286—111no—
150C23×C11—22no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11#12011yescharacteristic
158Q8×C11—22no—
159Q8×C11—22no—
160Q8×C11—41no—
161Q8×C11—41no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—41no—
165D4×C11—41no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11C2×SD1611yescharacteristic
190C2×C4×C11#13511yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11#13711yescharacteristic
193C2×Dic11—41no—
194C2×Dic11—41no—
195Dic22—42no—
196Dic22—81no—
197C11⋊C8—42no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200#533—111no—
201C2×C22⋊Q8—21no—
202C2×C4×Q8C2×D1111yescharacteristic
203C2×C4×D4C2×D1111yescharacteristic
204#483—221no—
205#479—222no—
206#477—221no—
207#476—221no—
208#475—221no—
209#461—221no—
210#450—221no—
211C4×SD16—222no—
212#431—111no—
213#431—111no—
214#428—221no—
215#423—111no—
216#419—221no—
217#398—21no—
218#394—21no—
219#388—22no—
220#382C2×D1111yescharacteristic
221#380—21no—
222#328—222no—
223Q8⋊C8—222no—
224D4⋊C8—222no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11#39211yescharacteristic
235C22×C11#45011yescharacteristic
236C22×C11#45211yescharacteristic
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11#44811yescharacteristic
246C4×C11#44911yescharacteristic
247C4×C11#46511yescharacteristic
248C4×C11#46811yescharacteristic
249Dic11—81no—
250Dic11—81no—
251C22×Q8C22⋊D1111yescharacteristic
252C22×D4C22⋊D1111yescharacteristic
253C23×C4—21no—
254C2×SD16—222no—
255C2×M16—221no—
256C4⋊Q8—111no—
257C4⋊Q8—111no—
258#125—221no—
259C22⋊Q8—42no—
260C22⋊Q8—42no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—221no—
268C4×Q8—221no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273#117—221no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—21no—
282C2×C42—21no—
283C2×C42C22×D1111yescharacteristic
284#107—222no—
285#106—222no—
286#106—222no—
287C4⋊C8—112no—
288C4⋊C8—221no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291#103—222no—
292#103—222no—
293#103—222no—
294#102—222no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C4×C8—112no—
298C4×C8—221no—
299#95—22no—
300#95—21no—
301#95C22⋊D1112yes—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—82no—
305C2×C11#200011yescharacteristic
306C2×C11#200911yescharacteristic
307C2×C11#201011yescharacteristic
308C24—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—221no—
315C2×Q8—221no—
316C2×Q8#432412yescomplemented
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—42no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334M16—441no—
335M16—441no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—441no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—44no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—441no—
359C42—41no—
360C42—41no—
361C42—441no—
362C42D4×D1111yescharacteristic
363C42D4×D1111yescharacteristic
364C42D4×D1111yescharacteristic
365C42#434111yescharacteristic
366C11#1000111yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#6700611yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—442no—
380Q8—881no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4#6698511yescharacteristic
405C2×C4C2×#432411yescharacteristic
406C2×C4#6699011yescharacteristic
407C2×C4#6699011yescharacteristic
408C2×C4#6699111yescharacteristic
409C2×C4#6699211yescharacteristic
410C2×C4#6699211yescharacteristic
411C2×C4#6699311yescharacteristic
412C2×C4#6700311yescharacteristic
413C2×C4#6700411yescharacteristic
414C8—442no—
415C8—442no—
416C8—881no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1062283111yescharacteristic
427C22#1062283611yescharacteristic
428C22#1062285211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—881no—
438C4—881no—
439C4#1062265011yescharacteristic
440C4#1062265311yescharacteristic
441C4#1062265411yescharacteristic
442C4#1062265511yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1306961911yescharacteristic
447C2#1306967611yescharacteristic
448C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2536C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#2536D11
hypocenterC11#10001
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
3. #13067179C2semidirect
5. #13067011C2semidirect
6. #13066474C2semidirect
91. C2×Q8×C11SD16semidirect
316. C2×Q8#4324semidirect
366. C11#10001semidirect

Maximal subgroups

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

subgroupindex
#130786242
#130784212
#130671792
#130670412
#130670112
#130664742
C11×#25362
#1000111