Finite Group Databasebeta

← #14650722

Subgroups — #14650722

Order 2816.

438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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#13079442C211yesmaximal, characteristic
2#13077678C211yesmaximal, characteristic
3#13067148C211yesmaximal, characteristic, complemented
4#13066979C211yesmaximal, characteristic, complemented
5#13066524C211yesmaximal, characteristic, complemented
6#13066493C211yesmaximal, characteristic, complemented
7C11×#1516C211yesmaximal, characteristic
8C11×#525C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#381C2211yescharacteristic
12#10622852—21no—
13#10622847—21no—
14#10622820C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17#10622665—21no—
18#10622663C411yescharacteristic, complemented
19#10622657C411yescharacteristic, complemented
20#10622655—21no—
21#10622653C411yescharacteristic, complemented
22#10622647C411yescharacteristic, complemented
23#10622625—21no—
24#10622625—21no—
25#10622624—21no—
26#10622624—21no—
27#10622613—21no—
28#10622609—21no—
29C11×#328—21no—
30C11×#327—21no—
31#10622107—21no—
32#10622107—21no—
33#10622090—21no—
34#10622090—21no—
35C2×C11×#41D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C22×C8×C11—21no—
39C11×#123—21no—
40C11×C22⋊Q8C2×C411yescharacteristic
41C11×C22⋊Q8D411yescharacteristic
42C11×#121C2×C411yescharacteristic
43C11×#121D411yescharacteristic
44C11×#120—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C11×#117D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C22⋊Dic11—21no—
50C2×#4326—21no—
51C2×#4324—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53#66977—21no—
54#66977—21no—
55#66977—21no—
56#66977—21no—
57C2×Dic11⋊C4—21no—
58C2×#4318—21no—
59C2×#4318—21no—
60C2×#4318—21no—
61C2×#4318—21no—
62C22×C11⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95—21no—
66C11×#95—21no—
67#66899—21no—
68#66896—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)C2×C411yescharacteristic
75C22⋊(C11⋊C8)C2×C411yescharacteristic
76C22⋊(C11⋊C8)D411yescharacteristic
77C22⋊(C11⋊C8)D411yescharacteristic
78C22⋊(C11⋊C8)D411yescharacteristic
79C22⋊(C11⋊C8)D411yescharacteristic
80#66874—21no—
81#66874—21no—
82#66872—21no—
83#66871—21no—
84C4⋊(C11⋊C8)—21no—
85C4⋊(C11⋊C8)—21no—
86#66867—21no—
87C4×C11⋊C8—21no—
88#9331—111nomaximal, Sylow
89C24×C11#4111yescharacteristic
90C11×#41—81no—
91C2×Q8×C11C22⋊C411yescharacteristic
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11C22⋊C411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—41no—
98C22×C4×C11—81no—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—81no—
110C2×C8×C11—41no—
111C2×C8×C11—81no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4C22⋊C411yescharacteristic
115C11×C4⋊C4C22⋊C411yescharacteristic
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—21no—
119C11×C22⋊C4—21no—
120C11×C22⋊C4—21no—
121C11×C22⋊C4—81no—
122C42×C11—21no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125#4326—81no—
126#4324—81no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131#4318—81no—
132#4318—81no—
133#4318—81no—
134#4318—81no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—81no—
142#3196—111no—
143#2978—111no—
144#1516D1111yescharacteristic
145#1511—111no—
146#1472—111no—
147#1306—111no—
148#1293—111no—
149C23×C11—21no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11C4×D411yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11#12311yescharacteristic
156Q8×C11—41no—
157D4×C11—41no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11C2×C22⋊C411yescharacteristic
176C2×C4×C11C4×D411yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—81no—
183Dic22—41no—
184Dic22—41no—
185Dic22—81no—
186C8×C11—81no—
187C11⋊C8—41no—
188C11⋊C8—41no—
189C11⋊C8—41no—
190C11⋊C8—41no—
191C11⋊C8—41no—
192C11⋊C8—41no—
193#525C2×D1111yescharacteristic
194C2×C22⋊Q8—111no—
195#485—221no—
196#484—111no—
197#481—111no—
198#470—221no—
199#468—221no—
200#452—221no—
201#451—111no—
202#448—111no—
203#436—221no—
204#436—221no—
205#435—221no—
206#435—221no—
207#433—221no—
208#408—221no—
209#407—111no—
210#407—111no—
211#407—111no—
212C2×C22⋊C8C2×D1111yescharacteristic
213#381C2×D1111yescharacteristic
214#328—21no—
215#328—221no—
216#328—221no—
217#327—21no—
218#324—221no—
219#324—221no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—82no—
233C22×C11#38611yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—161no—
242Dic11—81no—
243Dic11—81no—
244C2×#41D4411yescharacteristic
245C22×Q8—111no—
246C23×C4C22×D1111yescharacteristic
247C2×Q16—221no—
248C2×SD16—221no—
249C2×M16—221no—
250C2×M16—221no—
251C2×M16—221no—
252C2×M16—221no—
253C22×C8—21no—
254C22×C8—221no—
255#123—21no—
256C22⋊Q8—221no—
257C22⋊Q8—221no—
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8C4×D1111yescharacteristic
261C22⋊Q8C22⋊D1111yescharacteristic
262#121C4×D1111yescharacteristic
263#121C22⋊D1111yescharacteristic
264#120—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117D4411yescharacteristic
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—221no—
272#107—221no—
273#106—221no—
274C4⋊C8—221no—
275C4⋊C8—221no—
276#103—221no—
277#103—221no—
278#103—221no—
279#102—221no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—111no—
283C22⋊C8—111no—
284C22⋊C8—111no—
285C22⋊C8—111no—
286C22⋊C8—111no—
287C22⋊C8—111no—
288C22⋊C8—221no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C22⋊C8—221no—
292C22⋊C8—221no—
293#97—221no—
294C4×C8—221no—
295#95—21no—
296#95—21no—
297C2×C11—41no—
298C2×C11—41no—
299C2×C11—41no—
300C2×C11—81no—
301C2×C11#188111yescharacteristic
302C2×C11#190211yescharacteristic
303C2×C11#191311yescharacteristic
304C24#434111yescharacteristic
305#41—81no—
306C2×Q8—221no—
307C2×Q8—221no—
308C2×Q8—881no—
309C2×Q8(C2×D11)⋊C411yescharacteristic
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4(C2×D11)⋊C411yescharacteristic
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—81no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4C2×D4411yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—881no—
326SD16—881no—
327M16—881no—
328M16—881no—
329M16—881no—
330M16—881no—
331C2×C8—41no—
332C2×C8—81no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—881no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4(C2×D11)⋊C411yescharacteristic
347C4⋊C4(C2×D11)⋊C411yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—81no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C42—21no—
357C11#933111yescharacteristic, complemented, Sylow
358C23—21no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23(C22⋊D11)⋊C411yescharacteristic
363C23#6693911yescharacteristic
364C23#6699211yescharacteristic
365Q8—41no—
366Q8—441no—
367Q8—441no—
368Q8—881no—
369D4—41no—
370D4—81no—
371D4—81no—
372D4—81no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—881no—
391C2×C4(C22⋊D11)⋊C411yescharacteristic
392C2×C4#6693511yescharacteristic
393C2×C4C2×(C2×D11)⋊C411yescharacteristic
394C2×C4#6699211yescharacteristic
395C8—81no—
396C8—441no—
397C8—441no—
398C8—441no—
399C8—441no—
400C8—441no—
401C8—441no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22#1062257111yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—161no—
424C4—881no—
425C4—881no—
426C2—41no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2#1306897611yescharacteristic
431C2#1306908711yescharacteristic
432C2#1306915611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1516C2
socleC22×C11#386
prime radicalC11×#525C22
cosocleC23×C4×C11C23
hypercenter#1516D11
hypocenterC11#9331
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
3. #13067148C2semidirect
4. #13066979C2semidirect
5. #13066524C2semidirect
6. #13066493C2semidirect
18. #10622663C4semidirect
19. #10622657C4semidirect
21. #10622653C4semidirect
22. #10622647C4semidirect
357. C11#9331semidirect

Maximal subgroups

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

subgroupindex
#130794422
#130776782
#130671482
#130669792
#130665242
#130664932
C11×#15162
#933111