Finite Group Databasebeta

← #14654508

Subgroups — #14654508

Order 2816.

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

normal subgroups only

This group has 622 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#13078612C211yesmaximal, characteristic
2#13073521C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic, complemented
5#13067011C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#3037C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C11×#532C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#464—22no—
14C11×#462—21no—
15C11×#460—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622700—21no—
19#10622685—21no—
20#10622649—21no—
21#10622646—21no—
22C4×#4323—22no—
23#10622604—21no—
24#10622600—21no—
25#10622596—21no—
26#10622553—22no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622175—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622121—22no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C11×#137—42no—
38C11×#137—42no—
39C2×C11×Q16—22no—
40C2×C11×SD16—22no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic
43C11×#127D411yescharacteristic
44C11×#124—21no—
45C11×#121—21no—
46C11×#121—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#66999—42no—
58#66999—42no—
59C2×#4323—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×Dic11⋊C4—22no—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44—21no—
69C4×D44—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×#103—22no—
73C11×#102—22no—
74#66896—22no—
75C11⋊#95—22no—
76C11⋊#95—21no—
77C11⋊#95D412yes—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80#66873—22no—
81#66871—22no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4×C11⋊C8—21no—
85C4×C11⋊C8D412yes—
86#9997—111nomaximal, Sylow
87C23×D11—21no—
88C11×#41—41no—
89C11×#41—41no—
90C11×#41—41no—
91C11×#41—41no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11D812yescomplemented
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—42no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C11×Q16—44no—
121C11×SD16—44no—
122C11×M16—41no—
123C11×M16—41no—
124C2×C8×C11—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139#4323—44no—
140(C2×D11)⋊C4—44no—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—41no—
147C4⋊Dic11—41no—
148Dic11⋊C4—44no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—41no—
151#3100—111no—
152#3037D1111yescharacteristic, complemented
153#2536—111no—
154#1517—111no—
155#1486—111no—
156#1479—111no—
157#1286—111no—
158C23×C11—41no—
159C23×C11#12011yescharacteristic
160C22×D11—22no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167Q8×C11—22no—
168Q8×C11—22no—
169Q8×C11—41no—
170Q8×C11—41no—
171Q8×C11—41no—
172Q8×C11—41no—
173D4×C11—42no—
174D4×C11—41no—
175D4×C11—41no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11—81no—
179C2×C4×C11—22no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12711yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11#13511yescharacteristic
197C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205D44—22no—
206D44—22no—
207D44—41no—
208D44—41no—
209C4×D11—81no—
210C4×D11—81no—
211C4×D11—81no—
212C4×D11—81no—
213C8×C11—42no—
214C11⋊C8—42no—
215C11⋊C8—81no—
216C2×#137—21no—
217#532C2×D1111yescharacteristic
218C2×C22⋊Q8—221no—
219C2×C4×Q8C2×D1111yescharacteristic
220C2×C4×D4—111no—
221#480—221no—
222#474—221no—
223#464—22no—
224#462—21no—
225#460—21no—
226#459—221no—
227#447—221no—
228C4×D8—222no—
229#431—111no—
230#431—111no—
231#423C2×D1111yescharacteristic
232#417—21no—
233#398—221no—
234#394—221no—
235#388—222no—
236#382—111no—
237#380—221no—
238#327—222no—
239Q8⋊C8—222no—
240D4⋊C8—222no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#39211yescharacteristic
247C22×C11#44711yescharacteristic
248C22×C11#44911yescharacteristic
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—81no—
262C4×C11—81no—
263C4×C11#44711yescharacteristic
264C4×C11#44911yescharacteristic
265C4×C11#46611yescharacteristic
266C4×C11#46911yescharacteristic
267Dic11—82no—
268Dic11—81no—
269C2×#41—21no—
270C22×Q8C22⋊D1111yescharacteristic
271C22×D4—111no—
272C23×C4—221no—
273#137—42no—
274#137—42no—
275C2×Q16—22no—
276C2×SD16—22no—
277C2×D8—222no—
278C2×M16—21no—
279C4⋊Q8C22⋊D1111yescharacteristic
280#127C22⋊D1111yescharacteristic
281#124—21no—
282C22⋊Q8—442no—
283C22⋊Q8—442no—
284#121—21no—
285#121—21no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—221no—
293C4×D4—221no—
294C4×D4—221no—
295C4×D4—221no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4C22⋊D1111yescharacteristic
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—221no—
304C2×C42—21no—
305C2×C42C22×D1111yescharacteristic
306#107—222no—
307C4⋊C8—21no—
308C4⋊C8—221no—
309C4⋊C8—221no—
310C4⋊C8C22⋊D1112yes—
311#103—22no—
312#102—22no—
313#102—222no—
314#102—222no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317C4×C8—112no—
318C4×C8—221no—
319#95—112no—
320#95—222no—
321#95—221no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—161no—
325C2×C11#199911yescharacteristic
326C2×C11#200911yescharacteristic
327C2×C11#201011yescharacteristic
328D11—82no—
329C24—221no—
330#41—41no—
331#41—41no—
332#41—41no—
333#41—41no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8#432312yescomplemented
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—442no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362Q16—44no—
363SD16—44no—
364D8—444no—
365M16—41no—
366M16—41no—
367C2×C8—22no—
368C2×C8—222no—
369C2×C8—441no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—444no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—444no—
384C22⋊C4—444no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—41no—
388C42—41no—
389C42D4×D1111yescharacteristic
390C42#434111yescharacteristic
391C42C2×C22⋊D1111yescharacteristic
392C42C2×C22⋊D1111yescharacteristic
393C11#999711yescharacteristic, complemented, Sylow
394C23—41no—
395C23—222no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23#6699011yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409D4—42no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—81no—
414D4—81no—
415D4—222no—
416D4—222no—
417D4—441no—
418D4—441no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—881no—
436C2×C4—881no—
437C2×C4—881no—
438C2×C4—881no—
439C2×C4C2×#432311yescharacteristic
440C2×C4#6698511yescharacteristic
441C2×C4#6699011yescharacteristic
442C2×C4#6699111yescharacteristic
443C2×C4#6699211yescharacteristic
444C2×C4#6699211yescharacteristic
445C2×C4#6699311yescharacteristic
446C2×C4#6700211yescharacteristic
447C2×C4#6700311yescharacteristic
448C2×C4#6700611yescharacteristic
449C8—42no—
450C8—442no—
451C8—881no—
452C22—21no—
453C22—21no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22—881no—
464C22#1062264911yescharacteristic
465C22#1062265011yescharacteristic
466C22#1062283611yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—81no—
473C4—81no—
474C4—882no—
475C4—881no—
476C4#1062265111yescharacteristic
477C4#1062265211yescharacteristic
478C4#1062283011yescharacteristic
479C4#1062285111yescharacteristic
480C2—21no—
481C2—21no—
482C2—161no—
483C2—882no—
484C2#1306961211yescharacteristic
485C2#1306967411yescharacteristic
486C2#1306968011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3037C2
socleC22×C11#392
prime radical#13078612C2
hypercenter#3037D11
hypocenterC11#9997
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. #13073521C2semidirect
3. #13067176C2semidirect
4. #13067040C2semidirect
5. #13067011C2semidirect
6. #13066476C2semidirect
7. C11×#3037C2semidirect
98. C2×Q8×C11D8semidirect
152. #3037D11semidirect
340. C2×Q8#4323semidirect
393. C11#9997semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130735212
#130671762
#130670402
#130670112
#130664762
C11×#30372
#999711