Finite Group Databasebeta

← #14803547

Subgroups — #14803547

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078998C211yesmaximal, characteristic, complemented
2#13078409C211yesmaximal, characteristic
3C2×#10622454C211yesmaximal, characteristic
4#13069982C212yesmaximal, complemented
5#13069879C212yesmaximal
6#13069519C212yesmaximal
7#13069460C211yesmaximal, characteristic, complemented
8#13069392C211yesmaximal, characteristic, complemented
9#13069271C212yesmaximal, complemented
10C4×#66887C211yesmaximal, characteristic
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C22×#4314C2212yes—
14C2×C4×D44C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#446—22no—
17C11×#446—21no—
18C8×Q8×C11—21no—
19C11×#424C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#405C2212yes—
22C4×C11×M16C2211yescharacteristic
23C2×#66888C2212yes—
24C2×#66888C2212yes—
25C2×#66887C2211yescharacteristic
26C2×#66887C2211yescharacteristic
27C2×#66883C2212yes—
28C2×#66880C2212yes—
29#10622706—21no—
30#10622706—21no—
31#10622700—21no—
32#10622697—21no—
33#10622682—22no—
34#10622679—22no—
35#10622617C2212yes—
36#10622617C2212yes—
37#10622614C2212yes—
38#10622608C2212yes—
39#10622537C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622454—21no—
42#10622454—22no—
43#10622454—21no—
44#10622192C2211yescharacteristic
45#10622192C2211yescharacteristic
46#10622190C2212yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2312yes—
50C2×C11×M16C2311yescharacteristic
51C2×C11×M16C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#125D412yes—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C11×#117C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×#4318C2311yescharacteristic
67C2×#4318C2312yes—
68C2×#4318C2311yescharacteristic
69C2×#4314—24no—
70C2×#4314—22no—
71C2×#4314—22no—
72C2×#4314—42no—
73C4×D44—21no—
74C4×D44—21no—
75C4×D44—21no—
76C4×D44—21no—
77#66922—21no—
78#66922—21no—
79#66922—21no—
80#66922—21no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8D411yescharacteristic
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8D412yes—
86C11×#97—22no—
87C11×#97—21no—
88C4×C8×C11—22no—
89C4×C8×C11—21no—
90#66888—24no—
91#66888—42no—
92#66887—22no—
93#66887—22no—
94#66883—42no—
95#66880—22no—
96#66880—22no—
97#66874—22no—
98#66874—22no—
99#66874—22no—
100#66874—22no—
101#66873—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107#66867—21no—
108C4×C11⋊C8—21no—
109#25313—111nomaximal, Sylow
110C23×D11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44#4112yes—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—82no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C11×M16—21no—
134C11×M16—21no—
135C11×M16—21no—
136C11×M16#4112yes—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—22no—
150C42×C11—22no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163#4318—21no—
164#4318—21no—
165#4318—22no—
166#4318—21no—
167#4318—22no—
168#4318—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172#4314—44no—
173#4314—44no—
174#3139—111no—
175#3077—111no—
176C2×#461—111no—
177#2962D1111yescharacteristic, complemented
178#2064—112no—
179#2046—112no—
180#1977—112no—
181#1966—111no—
182#1950—111no—
183#1930—112no—
184C4×#100—111no—
185C23×C11C2×#4111yescharacteristic
186C22×D11—22no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—81no—
190C22×D11—81no—
191Q8×C11—42no—
192Q8×C11—81no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—81no—
212D44—22no—
213D44—22no—
214D44—41no—
215D44—41no—
216C4×D11—82no—
217C4×D11—82no—
218Dic22—42no—
219Dic22—42no—
220Dic22—42no—
221Dic22—42no—
222C8×C11—22no—
223C8×C11—22no—
224C8×C11—22no—
225C8×C11—41no—
226C11⋊C8—41no—
227C11⋊C8—41no—
228C11⋊C8—42no—
229C22×SD16—112no—
230#533C2×D1111yescharacteristic
231C2×C4⋊Q8—111no—
232C2×C4×D4—111no—
233#491—222no—
234#487—221no—
235#487—221no—
236#478—222no—
237#476—221no—
238#474—221no—
239#461—221no—
240#461—222no—
241#461—221no—
242#446—22no—
243#446—21no—
244C8×Q8—21no—
245C2×#108—112no—
246#428—112no—
247#424C2×D1112yes—
248#423—111no—
249C2×C4⋊C8C2×D1111yescharacteristic
250#419—112no—
251#419—112no—
252#418—112no—
253C2×#103—112no—
254C2×#101—112no—
255C2×#101—112no—
256C2×#100—111no—
257C2×#100—111no—
258#405C2×D1112yes—
259C4×M16—111no—
260C4×M16C2×D1111yescharacteristic
261#343—111no—
262#343—111no—
263#341—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11C2×#12111yescharacteristic
267C22×C11#52911yescharacteristic
268C22×C11#54211yescharacteristic
269C2×D11—42no—
270C2×D11—82no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—82no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11#47112yes—
280C4×C11#54611yescharacteristic
281C4×C11#54811yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11#55011yescharacteristic
284Dic11—82no—
285Dic11—81no—
286C22×Q8—112no—
287C22×D4—111no—
288C23×C4—221no—
289C2×SD16—224no—
290C2×SD16—222no—
291C2×SD16—222no—
292C2×SD16—442no—
293C2×M16—111no—
294C2×M16—112no—
295C2×M16—111no—
296C2×M16C22×D1111yescharacteristic
297C2×M16C22×D1111yescharacteristic
298C22×C8C22×D1112yes—
299C4⋊Q8—221no—
300C4⋊Q8—221no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303C4⋊Q8D4411yescharacteristic
304C4⋊Q8D4411yescharacteristic
305#125D4412yes—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314#117C22×D1112yes—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C42C22×D1111yescharacteristic
320#108—442no—
321#107—222no—
322#106—222no—
323C4⋊C8—22no—
324C4⋊C8—22no—
325C4⋊C8—221no—
326C4⋊C8—221no—
327C4⋊C8C22⋊D1111yescharacteristic
328C4⋊C8C22⋊D1111yescharacteristic
329C4⋊C8C22⋊D1112yes—
330#103—222no—
331#103—222no—
332#103—222no—
333#103—222no—
334#103—222no—
335#103—222no—
336#102—222no—
337#102—222no—
338#101—224no—
339#101—442no—
340#100—222no—
341#100—222no—
342#97—22no—
343#97—21no—
344#97—221no—
345C4×C8—22no—
346C4×C8—21no—
347C4×C8—221no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11#242611yescharacteristic
351C2×C11C2×#47111yescharacteristic
352C2×C11#306911yescharacteristic
353D11—82no—
354C24—221no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×D4—112no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C22×C4—222no—
370C22×C4—221no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—882no—
374C22×C4#433911yescharacteristic
375C22×C4#433911yescharacteristic
376C22×C4C23×D1111yescharacteristic
377SD16—444no—
378SD16—444no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—221no—
383M16—222no—
384M16—221no—
385M16—221no—
386M16—222no—
387M16—221no—
388M16#434312yes—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—222no—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4C2×D4412yes—
409C4⋊C4C2×D4412yes—
410C22⋊C4—22no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—22no—
414C42C2×D4411yescharacteristic
415C42C2×D4411yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C11#2531311yescharacteristic, complemented, Sylow
419C23—222no—
420C23—441no—
421C23—441no—
422C23—881no—
423C23—881no—
424C23C2×#433911yescharacteristic
425Q8—42no—
426Q8—81no—
427Q8—442no—
428Q8—442no—
429Q8—442no—
430Q8—442no—
431D4—222no—
432D4—222no—
433D4—441no—
434D4—441no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4—881no—
446C2×C4#6698311yescharacteristic
447C2×C4#6698311yescharacteristic
448C2×C4#6698311yescharacteristic
449C2×C4#6698311yescharacteristic
450C2×C4C22×D4411yescharacteristic
451C2×C4C2×#434311yescharacteristic
452C2×C4#6704011yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704211yescharacteristic
455C2×C4C22×C22⋊D1111yescharacteristic
456C8—22no—
457C8—22no—
458C8—22no—
459C8—41no—
460C8—441no—
461C8—441no—
462C8—442no—
463C22—21no—
464C22—21no—
465C22—442no—
466C22—882no—
467C22—882no—
468C22—881no—
469C22—881no—
470C22#1062311111yescharacteristic
471C22#1062311311yescharacteristic
472C22C2×#6698311yescharacteristic
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—881no—
479C4—882no—
480C4#1062275412yes—
481C4#1062310711yescharacteristic
482C4#1062310811yescharacteristic
483C4#1062334811yescharacteristic
484C4#1062336011yescharacteristic
485C2—21no—
486C2—21no—
487C2—882no—
488C2#1307217611yescharacteristic
489C2C2×#1062275411yescharacteristic
490C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radicalC22×D44C23
hypercenter#2962D11
hypocenterC11#25313
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #13078998C2semidirect
4. #13069982C2semidirect
7. #13069460C2semidirect
8. #13069392C2semidirect
9. #13069271C2semidirect
11. C11×#2962C2semidirect
177. #2962D11semidirect
418. C11#25313semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130784092
C2×#106224542
#130699822
#130698792
#130695192
#130694602
#130693922
#130692712
C4×#668872
C11×#29622
#2531311