Finite Group Databasebeta

← #14654179

Subgroups — #14654179

Order 2816.

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

normal subgroups only

This group has 654 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#13078564C211yesmaximal, characteristic, complemented
2#13073774C211yesmaximal, characteristic
3#13068715C211yesmaximal, characteristic, complemented
4#13067148C211yesmaximal, characteristic, complemented
5#13066943C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic, complemented
7C11×#2482C211yesmaximal, characteristic
8C2×C11×#117C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C11×#399—21no—
12C11×#397—21no—
13C11×#388—22no—
14C11×#385—21no—
15C11×#381C2211yescharacteristic
16C11×#379—21no—
17#10622860—21no—
18#10622824—21no—
19C4×C22⋊Dic11C2211yescharacteristic
20#10622820C2211yescharacteristic
21#10622820C2211yescharacteristic
22#10622617—21no—
23#10622609—22no—
24#10622608—21no—
25#10622584—21no—
26#10622583—21no—
27#10622566—21no—
28#10622560—21no—
29#10622558—22no—
30#10622170—22no—
31#10622163—22no—
32#10622090—22no—
33C25×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×Dic22D411yescharacteristic
37C11×#117—21no—
38C11×#117—21no—
39C11×#117—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—22no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11—21no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—22no—
59C2×C4⋊Dic11D411yescharacteristic
60#66977—21no—
61#66977—21no—
62#66977—21no—
63#66977—21no—
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11D412yes—
66C2×#4318—21no—
67C2×#4318—21no—
68C11×#95—22no—
69C11×#95—21no—
70C11×#95D412yes—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C11⋊#95—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)D412yes—
78#66874—22no—
79#66874—22no—
80#66872—22no—
81#66871—22no—
82#9944—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—42no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11C2×D411yescharacteristic
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—42no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—82no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—44no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—82no—
124C42×C11—41no—
125C42×C11—41no—
126C22⋊Dic11—42no—
127C22⋊Dic11—44no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—82no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—42no—
136#4318—42no—
137#4318—42no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—41no—
140#3095—111no—
141#2561—111no—
142#2482D1111yescharacteristic
143#1826—111no—
144#1511—111no—
145#1462—111no—
146#1284—111no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11—88no—
164C23×C11#12011yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11#12111yescharacteristic
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12711yescharacteristic
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195Dic22—42no—
196Dic22—81no—
197C11⋊C8—42no—
198C11⋊C8—81no—
199C2×C22⋊Q8—111no—
200C2×#117C2×D1111yescharacteristic
201C22×C22⋊C4C2×D1111yescharacteristic
202#485—222no—
203#484—221no—
204#483—221no—
205#428—221no—
206#419—221no—
207#407—111no—
208#407—111no—
209#399—21no—
210#397—21no—
211#397—221no—
212#393—221no—
213#388—22no—
214#388—222no—
215#385—21no—
216#381—221no—
217#381C2×D1111yescharacteristic
218#379—21no—
219#379—221no—
220C4×C22⋊C4—111no—
221#339—222no—
222#328—222no—
223#323—222no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—42no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#39211yescharacteristic
242C22×C11#45512yes—
243C22×C11#45812yes—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—82no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252Dic11—82no—
253Dic11—81no—
254Dic11—81no—
255C25C22⋊D1111yescharacteristic
256C22×Q8—111no—
257C23×C4C22⋊D1111yescharacteristic
258C23×C4C22×D1111yescharacteristic
259C2×M16—221no—
260C2×M16—221no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264C22⋊Q8—221no—
265#117—21no—
266#117—21no—
267#117—21no—
268#117—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C42—21no—
289C2×C42—112no—
290#107—222no—
291#106—222no—
292#103—222no—
293#103—222no—
294C22⋊C8—112no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298#95—22no—
299#95—21no—
300#95—222no—
301#95—222no—
302#95—221no—
303#95C22⋊D1112yes—
304C2×C11—22no—
305C2×C11—22no—
306C2×C11—41no—
307C2×C11—82no—
308C2×C11#200411yescharacteristic
309C2×C11#201011yescharacteristic
310C2×C11#202211yescharacteristic
311C24—21no—
312C24—21no—
313C24—21no—
314C24—42no—
315C24—42no—
316C24—42no—
317C24C2×C22⋊D1111yescharacteristic
318C2×Q8—221no—
319C2×Q8—221no—
320C2×Q8—442no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—222no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4#434111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338M16—442no—
339M16—442no—
340C2×C8—222no—
341C2×C8—441no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—82no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C22⋊C4—42no—
352C22⋊C4—44no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—82no—
360C22⋊C4—442no—
361C22⋊C4—444no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—882no—
365C42—41no—
366C42—41no—
367C42—442no—
368C11#994411yescharacteristic, complemented, Sylow
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—41no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—88no—
386C23#6699011yescharacteristic
387C23#6699211yescharacteristic
388C23#6700611yescharacteristic
389Q8—442no—
390Q8—881no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4#6699011yescharacteristic
416C2×C4#6699111yescharacteristic
417C2×C4#6699211yescharacteristic
418C2×C4#6699311yescharacteristic
419C8—442no—
420C8—881no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—82no—
433C22—82no—
434C22—82no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22#1062266612yes—
439C22#1062283611yescharacteristic
440C22#1062285512yes—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—82no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—882no—
450C4—881no—
451C4—881no—
452C2—22no—
453C2—22no—
454C2—41no—
455C2—82no—
456C2#1306964311yescharacteristic
457C2#1306968111yescharacteristic
458C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2482C2
socleC22×C11#392
prime radicalC25×C11D4
hypercenter#2482D11
hypocenterC11#9944
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. #13078564C2semidirect
3. #13068715C2semidirect
4. #13067148C2semidirect
6. #13066468C2semidirect
368. C11#9944semidirect

Maximal subgroups

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

subgroupindex
#130785642
#130737742
#130687152
#130671482
#130669432
#130664682
C11×#24822
#994411