Finite Group Databasebeta

← #14654535

Subgroups — #14654535

Order 2816.

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

normal subgroups only

This group has 568 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#13078417C211yesmaximal, characteristic, complemented
2#13073525C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic
5#13067012C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#3101C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66977—21no—
11C2×C4×Dic22C2211yescharacteristic
12C11×#483—21no—
13C11×#476—21no—
14C11×#461—21no—
15C11×#450—21no—
16C4×C11×SD16—22no—
17C11×#431C2211yescharacteristic
18#10622835—21no—
19#10622825—21no—
20#10622707—21no—
21#10622704—21no—
22#10622676—22no—
23#10622617—21no—
24#10622608—21no—
25#10622593—21no—
26#10622557—22no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622176—22no—
31D4⋊(C11⋊C8)—22no—
32#10622094—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C22×Dic22D411yescharacteristic
36C2×C11×SD16—22no—
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×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C11×#117—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D411yescharacteristic
56#66977—42no—
57#66977—42no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C2×#4318—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×#106—22no—
67C11×C4⋊C8—21no—
68C11×#103—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C4×C8×C11D412yes—
72C11⋊#95—22no—
73C11⋊#95—21no—
74C11⋊#95D412yes—
75C22⋊(C11⋊C8)—21no—
76#66874—22no—
77#66874—22no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4×C11⋊C8—21no—
84#10001—111nomaximal, Sylow
85C24×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—42no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22SD1612yescomplemented
110C11×SD16—44no—
111C2×C8×C11—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
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—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C22⋊Dic11—44no—
129C22⋊Dic11—44no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—44no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139#4318—41no—
140#4318—41no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143#3101D1111yescharacteristic
144#3078—111no—
145#2536—111no—
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—42no—
159Q8×C11—81no—
160D4×C11—22no—
161D4×C11—22no—
162D4×C11—41no—
163D4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12711yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11#13711yescharacteristic
185C2×Dic11—22no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193Dic22—22no—
194Dic22—22no—
195Dic22—41no—
196Dic22—41no—
197C8×C11—42no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200#533C2×D1111yescharacteristic
201C2×C22⋊Q8—221no—
202C2×C4×Q8—111no—
203C2×C4×D4C2×D1111yescharacteristic
204#483—21no—
205#479—222no—
206#477—221no—
207#476—21no—
208#475—221no—
209#461—21no—
210#450—21no—
211C4×SD16—22no—
212#431—111no—
213#431C2×D1111yescharacteristic
214#428—221no—
215#423—111no—
216#419—221no—
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—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—81no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11#44811yescharacteristic
245C4×C11#44911yescharacteristic
246C4×C11#46511yescharacteristic
247C4×C11#46811yescharacteristic
248Dic11—42no—
249Dic11—82no—
250Dic11—81no—
251C22×Q8—111no—
252C22×D4C22⋊D1111yescharacteristic
253C23×C4—21no—
254C2×SD16—22no—
255C2×M16—221no—
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—221no—
266C4×Q8—221no—
267C4×Q8—221no—
268C4×Q8—221no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273#117—21no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4C22⋊D1111yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—222no—
282C2×C42—221no—
283C2×C42C22×D1111yescharacteristic
284#107—222no—
285#106—22no—
286#106—222no—
287C4⋊C8—21no—
288C4⋊C8—112no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291#103—22no—
292#103—222no—
293#103—222no—
294#102—22no—
295C22⋊C8—21no—
296C22⋊C8—221no—
297C4×C8—221no—
298C4×C8C22⋊D1112yes—
299#95—112no—
300#95—222no—
301#95—221no—
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—112no—
312C2×Q8—221no—
313C2×Q8—221no—
314C2×Q8—221no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—42no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4—221no—
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—44no—
334M16—441no—
335M16—441no—
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—221no—
348C4⋊C4—221no—
349C4⋊C4—444no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—444no—
358C22⋊C4—444no—
359C42—41no—
360C42—441no—
361C42—441no—
362C42D4×D1111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#1000111yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#6699011yescharacteristic
375Q8—42no—
376Q8—81no—
377Q8—222no—
378Q8—222no—
379Q8—441no—
380Q8—441no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—222no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4SD16×D1111yescharacteristic
405C2×C4#6696711yescharacteristic
406C2×C4#6696811yescharacteristic
407C2×C4#6696911yescharacteristic
408C2×C4#6699011yescharacteristic
409C2×C4#6699111yescharacteristic
410C2×C4#6699211yescharacteristic
411C2×C4#6699211yescharacteristic
412C2×C4#6699311yescharacteristic
413C2×C4#6700611yescharacteristic
414C8—42no—
415C8—442no—
416C8—881no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1062278211yescharacteristic
427C22#1062278611yescharacteristic
428C22#1062283611yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—442no—
437C4—882no—
438C4—881no—
439C4#1062278311yescharacteristic
440C4#1062278411yescharacteristic
441C4#1062278511yescharacteristic
442C4#1062278711yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1306961611yescharacteristic
447C2#1306967311yescharacteristic
448C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3101C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3101D11
hypocenterC11#10001
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
1. #13078417C2semidirect
3. #13067180C2semidirect
5. #13067012C2semidirect
6. #13066475C2semidirect
109. C2×Dic22SD16semidirect
366. C11#10001semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130735252
#130671802
#130670412
#130670122
#130664752
C11×#31012
#1000111