Finite Group Databasebeta

← #14654540

Subgroups — #14654540

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#13078625C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13073521C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic, complemented
5#13067042C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999—21no—
10C2×C4×D44C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622838—21no—
15#10622635—22no—
16#10622634—21no—
17#10622633—21no—
18#10622604—21no—
19#10622600—21no—
20#10622596—21no—
21#10622577—21no—
22#10622553—22no—
23#10622549C2211yescharacteristic
24#10622537C2211yescharacteristic
25#10622455—21no—
26#10622454—21no—
27#10622344—21no—
28#10622334—21no—
29C4×#4314—22no—
30C11×Q8⋊C8—22no—
31#10622105—22no—
32#10622097—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#66999—42no—
45#66999—42no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—21no—
49#66979—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52#66977—21no—
53#66977—21no—
54C2×Dic11⋊C4—22no—
55C2×#4318—21no—
56C2×#4314—22no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61#66923—21no—
62#66922D411yescharacteristic
63#66922D411yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C4×C8×C11—21no—
71C4×C8×C11D412yes—
72#66899—22no—
73#66899—22no—
74C11⋊#95—22no—
75C11⋊#95—21no—
76C11⋊#95D412yes—
77#66885—22no—
78#66881—22no—
79#66880—22no—
80#66872—22no—
81#66871—22no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)D412yes—
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×C11SD1612yescomplemented
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—42no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C22⋊Dic11—41no—
123(C2×D11)⋊C4—44no—
124(C2×D11)⋊C4—44no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135Dic11⋊C4—44no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C4×Dic11—41no—
139#4318—41no—
140#4318—41no—
141C2×C11⋊C8—22no—
142#4314—44no—
143#3101—111no—
144#3078—111no—
145#2536—111no—
146#1518—111no—
147#1486—111no—
148#1479D1111yescharacteristic, complemented
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—41no—
161Q8×C11—41no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
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×SD1611yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187D44—22no—
188D44—22no—
189D44—41no—
190D44—41no—
191C4×D11—81no—
192C4×D11—81no—
193C4×D11—81no—
194C4×D11—81no—
195Dic22—42no—
196Dic22—81no—
197C8×C11—42no—
198C8×C11—81no—
199C11⋊C8—42no—
200#533—111no—
201C2×C22⋊Q8—221no—
202C2×C4×Q8C2×D1111yescharacteristic
203C2×C4×D4—111no—
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#431C2×D1111yescharacteristic
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—22no—
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#44811yescharacteristic
244C4×C11#44911yescharacteristic
245C4×C11#46511yescharacteristic
246C4×C11#46811yescharacteristic
247Dic11—82no—
248Dic11—81no—
249Dic11—81no—
250Dic11—81no—
251C22×Q8D4411yescharacteristic
252C22×D4—111no—
253C23×C4—221no—
254C2×SD16—222no—
255C2×M16—221no—
256C4⋊Q8—111no—
257C4⋊Q8—111no—
258#125—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—442no—
262C22⋊Q8—442no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×Q8—21no—
267C4×Q8—221no—
268C4×Q8—221no—
269C4×D4—221no—
270C4×D4—221no—
271C4×D4—221no—
272C4×D4—221no—
273#117—221no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4D4411yescharacteristic
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—221no—
282C2×C42—21no—
283C2×C42C22×D1111yescharacteristic
284#107—222no—
285#106—222no—
286#106—222no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—112no—
290C4⋊C8—221no—
291#103—222no—
292#103—222no—
293#103—222no—
294#102—222no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8C22⋊D1112yes—
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—221no—
315C2×Q8—221no—
316C2×Q8#431412yescomplemented
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×C4C2×D4411yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333SD16—444no—
334M16—441no—
335M16—441no—
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—222no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—444no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C22⋊C4—444no—
355C22⋊C4—444no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—41no—
360C42—41no—
361C42—441no—
362C42#433911yescharacteristic
363C42D4×D1111yescharacteristic
364C42D4×D1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#1000111yescharacteristic, complemented, Sylow
367C23—222no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23#6693511yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—442no—
380Q8—881no—
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—442no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
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#6693511yescharacteristic
405C2×C4#6693711yescharacteristic
406C2×C4#6693711yescharacteristic
407C2×C4C2×#431411yescharacteristic
408C2×C4#6695711yescharacteristic
409C2×C4#6696111yescharacteristic
410C2×C4#6696211yescharacteristic
411C2×C4#6698311yescharacteristic
412C2×C4#6699011yescharacteristic
413C2×C4#6699311yescharacteristic
414C8—42no—
415C8—81no—
416C8—442no—
417C22—21no—
418C22—21no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062234411yescharacteristic
427C22#1062234611yescharacteristic
428C22#1062257311yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—81no—
435C4—882no—
436C4—881no—
437C4—881no—
438C4—881no—
439C4#1062234711yescharacteristic
440C4#1062235111yescharacteristic
441C4#1062272711yescharacteristic
442C4#1062274711yescharacteristic
443C2—21no—
444C2—21no—
445C2—882no—
446C2#1306962111yescharacteristic
447C2#1306967811yescharacteristic
448C2#1306968211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1479D11
hypocenterC11#10001
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
4. #13067181C2semidirect
6. #13066475C2semidirect
7. C11×#1479C2semidirect
91. C2×Q8×C11SD16semidirect
148. #1479D11semidirect
316. C2×Q8#4314semidirect
366. C11#10001semidirect

Maximal subgroups

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

subgroupindex
#130786252
#130784212
#130735212
#130671812
#130670422
#130664752
C11×#14792
#1000111