Finite Group Databasebeta

← #14654566

Subgroups — #14654566

Order 2816.

566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079806C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic
3#13069534C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067059C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#2562C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#400—21no—
12C11×#394—21no—
13C11×#388—22no—
14C11×#380—21no—
15C11×#380—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622830—21no—
18#10622680—21no—
19#10622679—22no—
20#10622678—21no—
21#10622628—21no—
22#10622627—22no—
23#10622621—21no—
24#10622581—21no—
25#10622581—21no—
26#10622580—21no—
27C2×#66869—22no—
28#10622539C2211yescharacteristic
29#10622539C2211yescharacteristic
30C4×#4318C2211yescharacteristic
31#10622181—22no—
32D4⋊(C11⋊C8)—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11—21no—
35C2×#4339—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11D412yes—
54C2×C42×C11C2311yescharacteristic
55C2×#4323—22no—
56#66983—21no—
57#66983—21no—
58C2×#4318—21no—
59#66928—21no—
60#66927D411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922D411yescharacteristic
64C11×#95—22no—
65C11×#95—22no—
66C11×#95—21no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66873—22no—
71#66873—22no—
72#66873—22no—
73#66872—22no—
74#66872—22no—
75#66871—22no—
76#66869—44no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yes—
79#66867—21no—
80#66867—21no—
81#66867D412yes—
82C4×C11⋊C8—21no—
83#10005—111nomaximal, Sylow
84C24×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100#4339—42no—
101#4339—42no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×C4×D11—41no—
106C2×Dic22—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—44no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—82no—
122C42×C11—42no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127#4323—44no—
128(C2×D11)⋊C4—41no—
129(C2×D11)⋊C4—41no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132#4318—22no—
133#4318—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—41no—
137#3234—111no—
138#3109—111no—
139#2562D1111yescharacteristic, complemented
140#1980—111no—
141#1528—111no—
142#1490—111no—
143#1285—111no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12011yescharacteristic
152C22×D11—41no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12711yescharacteristic
180C22⋊D11—81no—
181C22⋊D11—81no—
182C2×Dic11—41no—
183D44—42no—
184D44—42no—
185D44—42no—
186C4×D11—82no—
187Dic22—42no—
188C11⋊C8—42no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191#532—111no—
192C2×#125C2×D1111yescharacteristic
193C2×C4×D4C2×D1111yescharacteristic
194#501—221no—
195#490—221no—
196#481—221no—
197#481—221no—
198#480—221no—
199#478—222no—
200#476—221no—
201#459—221no—
202#447—221no—
203#442—222no—
204#432—111no—
205#432—111no—
206C2×#104—222no—
207C4×M16—111no—
208#400—21no—
209#394—21no—
210#388—22no—
211#380—21no—
212#380—21no—
213C4×C4⋊C4C2×D1111yescharacteristic
214#330—222no—
215D4⋊C8—222no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#39211yescharacteristic
226C22×C11#45311yescharacteristic
227C22×C11#45411yescharacteristic
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—82no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11#45412yes—
241Dic11—81no—
242C2×#41—221no—
243C22×D4C22⋊D1111yescharacteristic
244C23×C4—21no—
245C2×D8—222no—
246C2×M16—221no—
247C4⋊Q8—111no—
248#127—111no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#124—221no—
254#121—221no—
255#121—221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D1111yescharacteristic
266C2×C4⋊C4C22⋊D1111yescharacteristic
267C2×C4⋊C4C22⋊D1111yescharacteristic
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—22no—
271C2×C42C22⋊D1112yes—
272C2×C42C22×D1111yescharacteristic
273#107—222no—
274#106—222no—
275#106—222no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278#104—444no—
279#102—222no—
280#102—222no—
281#102—222no—
282#102—222no—
283C22⋊C8—221no—
284C22⋊C8—221no—
285#97—112no—
286#97—221no—
287#97—221no—
288C4×C8—221no—
289#95—22no—
290#95—22no—
291#95—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—82no—
295C2×C11#200311yescharacteristic
296C2×C11#200611yescharacteristic
297C2×C11#201011yescharacteristic
298D11—161no—
299C24—21no—
300#41—442no—
301#41—442no—
302C2×Q8—221no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—441no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—441no—
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322D8—444no—
323M16—222no—
324M16—441no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—441no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C22⋊C4—44no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—82no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—42no—
348C42D4×D1111yescharacteristic
349C42D4×D1111yescharacteristic
350C42D4×D1111yescharacteristic
351C42#434111yescharacteristic
352C11#1000511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—441no—
361C23#6700611yescharacteristic
362Q8—442no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367D4—442no—
368D4—442no—
369D4—442no—
370D4—881no—
371D4—881no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—441no—
390C2×C4—882no—
391C2×C4#6699011yescharacteristic
392C2×C4#6699011yescharacteristic
393C2×C4#6699111yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6699311yescharacteristic
397C8—442no—
398C8—442no—
399C8—442no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22#1062283611yescharacteristic
413C22#1062285411yescharacteristic
414C22#1062285811yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—881no—
425C4#1062267512yes—
426C2—21no—
427C2—21no—
428C2—82no—
429C2—1761no—
430C2#1306963811yescharacteristic
431C2#1306965811yescharacteristic
432C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2562C2
socleC22×C11#392
prime radical#13078707C2
hypercenter#2562D11
hypocenterC11#10005
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2562

Complements

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

NH ≅ G/Ntype
1. #13079806C2semidirect
3. #13069534C2semidirect
4. #13067218C2semidirect
5. #13067059C2semidirect
6. #13066472C2semidirect
7. C11×#2562C2semidirect
139. #2562D11semidirect
352. C11#10005semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130787072
#130695342
#130672182
#130670592
#130664722
C11×#25622
#1000511