Finite Group Databasebeta

← #14654536

Subgroups — #14654536

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#13078620C211yesmaximal, characteristic
2#13073521C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic
5#13067011C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#3078C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#479—22no—
13C11×#477—21no—
14C11×#475—21no—
15C11×#428—21no—
16C11×#423C2211yescharacteristic
17C11×#419—21no—
18#10622697—21no—
19#10622696—21no—
20#10622659—21no—
21#10622656—21no—
22C4×#4325—22no—
23#10622604—21no—
24#10622600—21no—
25#10622596—21no—
26#10622553—22no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622176—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622121—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C2×C11×M16—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53#66999—42no—
54#66999—42no—
55C2×#4325—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×Dic11⋊C4—22no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44—21no—
66C11×#107—22no—
67C11×#106—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×#103—22no—
71C11×#103—22no—
72#66899—22no—
73C11⋊#95—22no—
74C11⋊#95—21no—
75C11⋊#95D412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78#66873—22no—
79#66872—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8D412yes—
84#10001—111nomaximal, Sylow
85C23×D11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11SD1612yescomplemented
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—42no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131#4325—44no—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—44no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140Dic11⋊C4—44no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143#3101—111no—
144#3078D1111yescharacteristic, complemented
145#2536—111no—
146#1518—111no—
147#1486—111no—
148#1479—111no—
149#1286—111no—
150C23×C11#12011yescharacteristic
151C22×D11—22no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158Q8×C11—22no—
159Q8×C11—22no—
160Q8×C11—42no—
161Q8×C11—41no—
162Q8×C11—41no—
163Q8×C11—81no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×C4×C11C2×SD1611yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189D44—22no—
190D44—22no—
191D44—41no—
192D44—41no—
193C4×D11—81no—
194C4×D11—81no—
195C4×D11—81no—
196C4×D11—81no—
197C8×C11—42no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200#533C2×D1111yescharacteristic
201C2×C22⋊Q8—221no—
202C2×C4×Q8C2×D1111yescharacteristic
203C2×C4×D4—111no—
204#483—221no—
205#479—22no—
206#477—21no—
207#476—221no—
208#475—21no—
209#461—221no—
210#450—221no—
211C4×SD16—222no—
212#431—111no—
213#431—111no—
214#428—21no—
215#423C2×D1111yescharacteristic
216#419—21no—
217#398—221no—
218#394—221no—
219#388—222no—
220#382—111no—
221#380—221no—
222#328—222no—
223Q8⋊C8—222no—
224D4⋊C8—222no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11#39211yescharacteristic
228C22×C11#45011yescharacteristic
229C22×C11#45211yescharacteristic
230C2×D11—42no—
231C2×D11—42no—
232C2×D11—42no—
233C2×D11—81no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—81no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11#44811yescharacteristic
246C4×C11#44911yescharacteristic
247C4×C11#46511yescharacteristic
248C4×C11#46811yescharacteristic
249Dic11—82no—
250Dic11—81no—
251C22×Q8C22⋊D1111yescharacteristic
252C22×D4—111no—
253C23×C4—221no—
254C2×SD16—222no—
255C2×M16—21no—
256C4⋊Q8C22⋊D1111yescharacteristic
257C4⋊Q8C22⋊D1111yescharacteristic
258#125—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—442no—
262C22⋊Q8—442no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—221no—
270C4×D4—221no—
271C4×D4—221no—
272C4×D4—221no—
273#117—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—221no—
282C2×C42—21no—
283C2×C42C22×D1111yescharacteristic
284#107—22no—
285#106—22no—
286#106—222no—
287C4⋊C8—21no—
288C4⋊C8—221no—
289C4⋊C8—221no—
290C4⋊C8C22⋊D1112yes—
291#103—22no—
292#103—22no—
293#103—222no—
294#102—222no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C4×C8—112no—
298C4×C8—221no—
299#95—112no—
300#95—222no—
301#95—221no—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11#200011yescharacteristic
305C2×C11#200911yescharacteristic
306C2×C11#201011yescharacteristic
307D11—82no—
308C24—221no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8#432512yescomplemented
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—442no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—222no—
323C22×C4—221no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—222no—
338C2×C8—441no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—444no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C22⋊C4—41no—
355C22⋊C4—444no—
356C22⋊C4—444no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42D4×D1111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#1000111yescharacteristic, complemented, Sylow
367C23—222no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23#6699011yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—42no—
378Q8—41no—
379Q8—41no—
380Q8—81no—
381D4—222no—
382D4—222no—
383D4—441no—
384D4—441no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4#6699011yescharacteristic
405C2×C4#6699111yescharacteristic
406C2×C4#6699211yescharacteristic
407C2×C4#6699211yescharacteristic
408C2×C4#6699311yescharacteristic
409C2×C4C2×#432511yescharacteristic
410C2×C4#6699511yescharacteristic
411C2×C4#6700211yescharacteristic
412C2×C4#6700311yescharacteristic
413C2×C4#6700611yescharacteristic
414C8—42no—
415C8—442no—
416C8—881no—
417C22—21no—
418C22—21no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062265911yescharacteristic
427C22#1062266011yescharacteristic
428C22#1062283611yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—882no—
438C4—881no—
439C4#1062266111yescharacteristic
440C4#1062266211yescharacteristic
441C4#1062284011yescharacteristic
442C4#1062285111yescharacteristic
443C2—21no—
444C2—21no—
445C2—882no—
446C2#1306961711yescharacteristic
447C2#1306967411yescharacteristic
448C2#1306968011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3078D11
hypocenterC11#10001
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #13067180C2semidirect
5. #13067011C2semidirect
6. #13066476C2semidirect
7. C11×#3078C2semidirect
93. C2×Q8×C11SD16semidirect
144. #3078D11semidirect
316. C2×Q8#4325semidirect
366. C11#10001semidirect

Maximal subgroups

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

subgroupindex
#130786202
#130735212
#130671802
#130670402
#130670112
#130664762
C11×#30782
#1000111