Finite Group Databasebeta

← #14803569

Subgroups — #14803569

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic
2#13078417C211yesmaximal, characteristic, complemented
3C2×#10622461C211yesmaximal, characteristic
4#13069975C212yesmaximal, complemented
5#13069879C212yesmaximal, complemented
6#13069519C212yesmaximal, complemented
7#13069456C211yesmaximal, characteristic
8#13069392C211yesmaximal, characteristic, complemented
9#13069278C212yesmaximal, complemented
10C4×#66888C211yesmaximal, characteristic, complemented
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C22×#4314C2212yes—
14C2×#66927C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C11×#446—22no—
17C11×#446—21no—
18C8×Q8×C11—21no—
19C11×#424C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#405C2212yes—
22C4×C11×M16C2211yescharacteristic
23C2×#66888C2211yescharacteristic
24C2×#66888C2211yescharacteristic
25C2×#66887C2212yes—
26C2×#66887C2212yes—
27C2×#66885C2212yes—
28C2×#66883C2212yes—
29#10622707—21no—
30#10622704—21no—
31#10622701—21no—
32#10622701—21no—
33#10622680—22no—
34#10622676—22no—
35#10622617C2212yes—
36#10622614C2212yes—
37#10622614C2212yes—
38#10622608C2212yes—
39#10622537C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622461—21no—
42#10622461—22no—
43#10622461—21no—
44#10622192C2211yescharacteristic
45#10622192C2211yescharacteristic
46#10622190C2212yes—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44C2312yes—
50C22×Dic22C2311yescharacteristic
51C2×C11×M16C2311yescharacteristic
52C2×C11×M16C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8D411yescharacteristic
56C11×#125D412yes—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C11×#117C2312yes—
62C2×C42×C11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11—21no—
66C2×#4318C2311yescharacteristic
67C2×#4318C2312yes—
68C2×#4318C2311yescharacteristic
69C2×#4314—24no—
70C2×#4314—22no—
71C2×#4314—22no—
72C2×#4314—42no—
73#66927—21no—
74#66927—21no—
75#66927—21no—
76#66927—21no—
77C4×Dic22—21no—
78C4×Dic22—21no—
79C4×Dic22—21no—
80C4×Dic22—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—22no—
91#66888—22no—
92#66887—24no—
93#66887—42no—
94#66885—22no—
95#66885—22no—
96#66883—42no—
97#66874—22no—
98#66874—22no—
99#66873—22no—
100#66873—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#25315—111nomaximal, Sylow
110C23×D11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—41no—
125C2×D44—41no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—82no—
129C2×D44—82no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22#4112yes—
136C11×M16—21no—
137C11×M16—21no—
138C11×M16—21no—
139C11×M16#4112yes—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—22no—
153C42×C11—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164#4318—22no—
165#4318—21no—
166#4318—21no—
167#4318—21no—
168#4318—22no—
169#4318—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173#4314—44no—
174#4314—44no—
175#3138—111no—
176#3078—111no—
177C2×#460—111no—
178#2962D1111yescharacteristic, complemented
179#2063—112no—
180#2046—112no—
181#1977—112no—
182#1965—111no—
183#1950—111no—
184#1931—112no—
185C4×#101—111no—
186C23×C11C2×#4111yescharacteristic
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—82no—
191C22×D11—82no—
192Q8×C11—42no—
193Q8×C11—81no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—81no—
213D44—42no—
214D44—42no—
215D44—42no—
216D44—42no—
217D44—82no—
218D44—82no—
219D44—82no—
220D44—82no—
221Dic22—22no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—22no—
226C8×C11—22no—
227C8×C11—22no—
228C8×C11—41no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8—42no—
232C22×SD16—112no—
233#533C2×D1111yescharacteristic
234C2×#127—111no—
235C2×C4×Q8—111no—
236#490—222no—
237#486—221no—
238#486—221no—
239#479—222no—
240#477—221no—
241#475—221no—
242#460—221no—
243#460—222no—
244#460—221no—
245#446—22no—
246#446—21no—
247C8×Q8—21no—
248C2×#108—112no—
249#428—112no—
250#424C2×D1112yes—
251#423—111no—
252C2×C4⋊C8C2×D1111yescharacteristic
253#419—112no—
254#418—112no—
255#418—112no—
256C2×#102—112no—
257C2×#101—111no—
258C2×#101—111no—
259C2×#100—112no—
260C2×#100—112no—
261#405C2×D1112yes—
262C4×M16—111no—
263C4×M16C2×D1111yescharacteristic
264#343—111no—
265#343—111no—
266#341—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#52911yescharacteristic
271C22×C11#54211yescharacteristic
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—162no—
276C2×D11—162no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11#47112yes—
283C4×C11#54611yescharacteristic
284C4×C11#54811yescharacteristic
285C4×C11#54811yescharacteristic
286C4×C11#55011yescharacteristic
287Dic11—42no—
288Dic11—81no—
289C22×Q8—111no—
290C22×D4—112no—
291C22×D4—221no—
292C22×D4—221no—
293C2×SD16—224no—
294C2×SD16—222no—
295C2×SD16—222no—
296C2×SD16—442no—
297C2×M16—111no—
298C2×M16—112no—
299C2×M16—111no—
300C2×M16C22×D1111yescharacteristic
301C2×M16C22×D1111yescharacteristic
302C22×C8C22×D1112yes—
303C4⋊Q8D4411yescharacteristic
304C4⋊Q8D4411yescharacteristic
305#127—221no—
306#127—221no—
307#127—221no—
308#127—221no—
309#125D4412yes—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—221no—
318#117C22×D1112yes—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C42—221no—
322C2×C42C22×D1111yescharacteristic
323#108—442no—
324#107—222no—
325#106—222no—
326C4⋊C8—22no—
327C4⋊C8—22no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330C4⋊C8C22⋊D1111yescharacteristic
331C4⋊C8C22⋊D1111yescharacteristic
332C4⋊C8C22⋊D1112yes—
333#103—222no—
334#103—222no—
335#102—222no—
336#102—222no—
337#102—222no—
338#102—222no—
339#102—222no—
340#102—222no—
341#101—222no—
342#101—222no—
343#100—224no—
344#100—442no—
345#97—22no—
346#97—21no—
347#97—221no—
348C4×C8—22no—
349C4×C8—21no—
350C4×C8—221no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11#242611yescharacteristic
354C2×C11C2×#47111yescharacteristic
355C2×C11#306811yescharacteristic
356D11—162no—
357C24—222no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—112no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—882no—
377C2×D4—882no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4#433911yescharacteristic
381C22×C4#433911yescharacteristic
382C22×C4C23×D1111yescharacteristic
383SD16—444no—
384SD16—444no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—222no—
389M16—221no—
390M16—221no—
391M16—221no—
392M16—222no—
393M16—221no—
394M16#434312yes—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8C2×C22⋊D1112yes—
403C2×C8C2×C22⋊D1112yes—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4C2×D4412yes—
413C4⋊C4C2×D4412yes—
414C22⋊C4—22no—
415C42—22no—
416C42—441no—
417C42—441no—
418C42C2×D4411yescharacteristic
419C42C2×D4411yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C11#2531511yescharacteristic, complemented, Sylow
423C23—442no—
424C23—442no—
425C23—442no—
426C23—882no—
427C23—882no—
428C23C2×#433911yescharacteristic
429Q8—42no—
430Q8—81no—
431Q8—222no—
432Q8—222no—
433Q8—441no—
434Q8—441no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—442no—
439D4—882no—
440D4—882no—
441D4—882no—
442D4—882no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—222no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—881no—
452C2×C4#6698311yescharacteristic
453C2×C4#6698311yescharacteristic
454C2×C4#6698311yescharacteristic
455C2×C4#6698311yescharacteristic
456C2×C4C22×D4411yescharacteristic
457C2×C4C2×#434311yescharacteristic
458C2×C4#6704011yescharacteristic
459C2×C4#41×D1111yescharacteristic
460C2×C4#6704211yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—22no—
463C8—22no—
464C8—22no—
465C8—41no—
466C8—441no—
467C8—441no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—882no—
472C22—882no—
473C22—882no—
474C22—1762no—
475C22—1762no—
476C22#1062311111yescharacteristic
477C22#1062311311yescharacteristic
478C22C2×#6698311yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—442no—
485C4—881no—
486C4#1062275412yes—
487C4#1062310711yescharacteristic
488C4#1062310811yescharacteristic
489C4#1062334811yescharacteristic
490C4#1062336011yescharacteristic
491C2—21no—
492C2—21no—
493C2—1762no—
494C2#1307217611yescharacteristic
495C2C2×#1062275411yescharacteristic
496C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#2962D11
hypocenterC11#25315
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
2. #13078417C2semidirect
4. #13069975C2semidirect
5. #13069879C2semidirect
6. #13069519C2semidirect
8. #13069392C2semidirect
9. #13069278C2semidirect
10. C4×#66888C2semidirect
11. C11×#2962C2semidirect
178. #2962D11semidirect
422. C11#25315semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130784172
C2×#106224612
#130699752
#130698792
#130695192
#130694562
#130693922
#130692782
C4×#668882
C11×#29622
#2531511