Finite Group Databasebeta

← #14650721

Subgroups — #14650721

Order 2816.

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

normal subgroups only

This group has 438 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#13079446C211yesmaximal, characteristic
2#13077676C211yesmaximal, characteristic
3#13067170C211yesmaximal, characteristic
4#13066980C211yesmaximal, characteristic, complemented
5#13066524C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#1511C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9#10623322C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12#10622841C411yescharacteristic, complemented
13#10622840C411yescharacteristic, complemented
14#10622820C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622741—21no—
18#10622740—21no—
19#10622665—21no—
20#10622662—21no—
21#10622660—21no—
22#10622658—21no—
23#10622583C411yescharacteristic, complemented
24#10622581C411yescharacteristic, complemented
25#10622342—21no—
26#10622341—21no—
27#10622340—21no—
28#10622333—21no—
29C11×#328—21no—
30C11×#328—21no—
31#10622166—21no—
32#10622166—21no—
33#10622090—21no—
34#10622089—21no—
35C22×Q8×C11C2×C411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C2×#4339D411yescharacteristic
38C2×C11×M16—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47#67006—21no—
48C2×#4326—21no—
49C2×#4325—21no—
50#66983C2×C411yescharacteristic
51#66983D411yescharacteristic
52#66982—21no—
53C4×C22⋊D11—21no—
54C4×C22⋊D11—21no—
55#66979D411yescharacteristic
56#66977C2×C411yescharacteristic
57#66977D411yescharacteristic
58C2×#4318—21no—
59C2×#4318—21no—
60C22×C11⋊C8—21no—
61C2×#4313—21no—
62C2×C8×D11—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D411yescharacteristic
65C11×C22⋊C8D411yescharacteristic
66C11×#95—21no—
67C11×#95—21no—
68#66899—21no—
69#66899—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
78(C2×D11)⋊C8—21no—
79(C2×D11)⋊C8—21no—
80#66879—21no—
81Dic11⋊C8—21no—
82Dic11⋊C8—21no—
83C8×Dic11—21no—
84#66874—21no—
85#66873—21no—
86#66872—21no—
87#66871—21no—
88#9331—111nomaximal, Sylow
89C24×C11#4111yescharacteristic
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—81no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—81no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×C22⋊D11—21no—
104C2×C22⋊D11—21no—
105C2×C22⋊D11—21no—
106#4339—81no—
107C2×D44C22⋊C411yescharacteristic
108C2×C4×D11—21no—
109C2×Dic22C22⋊C411yescharacteristic
110C11×M16—81no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—81no—
120C22⋊Dic11—21no—
121C22⋊Dic11—21no—
122C22⋊Dic11—21no—
123#4326—81no—
124#4325—81no—
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127C4⋊Dic11C22⋊C411yescharacteristic
128C4⋊Dic11C22⋊C411yescharacteristic
129Dic11⋊C4—21no—
130Dic11⋊C4—21no—
131C4×Dic11—21no—
132#4318—81no—
133#4318—81no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—81no—
140#4313—81no—
141C8×D11—81no—
142#3196—111no—
143#2978—111no—
144#1516—111no—
145#1511D1111yescharacteristic, complemented
146#1472—111no—
147#1306—111no—
148#1293—111no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C4×D411yescharacteristic
153C23×C11#12111yescharacteristic
154C23×C11#12311yescharacteristic
155C22×D11—21no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—81no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C22⋊D11—81no—
177C22⋊D11—81no—
178C22⋊D11—81no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182D44—41no—
183C4×D11—41no—
184C4×D11—41no—
185Dic22—41no—
186C8×C11—41no—
187C8×C11—41no—
188C11⋊C8—41no—
189C11⋊C8—41no—
190C11⋊C8—41no—
191C11⋊C8—41no—
192C11⋊C8—81no—
193#525—111no—
194C2×C22⋊Q8C2×D1111yescharacteristic
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#407C2×D1111yescharacteristic
212C2×C22⋊C8—111no—
213#381C2×D1111yescharacteristic
214#328—21no—
215#328—21no—
216#328—221no—
217#327—221no—
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—82no—
230C22×C11#38611yescharacteristic
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11—161no—
241Dic11—41no—
242Dic11—41no—
243Dic11—41no—
244C2×#41—111no—
245C22×Q8C4×D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C2×Q16—221no—
248C2×SD16—221no—
249C2×M16—21no—
250C2×M16—221no—
251C2×M16—221no—
252C2×M16—221no—
253C22×C8—221no—
254C22×C8—221no—
255#123—221no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—111no—
261C22⋊Q8—111no—
262#121—111no—
263#121—111no—
264#120—221no—
265C4×D4—221no—
266C4×D4—221no—
267#117—111no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
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—111no—
282C22⋊C8—111no—
283C22⋊C8—111no—
284C22⋊C8—111no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C22⋊C8C22⋊D1111yescharacteristic
292C22⋊C8C22⋊D1111yescharacteristic
293#97—221no—
294C4×C8—221no—
295#95—21no—
296#95—21no—
297C2×C11—41no—
298C2×C11—41no—
299C2×C11—41no—
300C2×C11#188111yescharacteristic
301C2×C11#190211yescharacteristic
302C2×C11#191311yescharacteristic
303D11—81no—
304C24#434111yescharacteristic
305#41—881no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—81no—
309C2×Q8—111no—
310C2×D4—111no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—221no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—81no—
318C22×C4—221no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4#433911yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325Q16—881no—
326SD16—881no—
327M16—81no—
328M16—881no—
329M16—881no—
330M16—881no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—441no—
338C2×C8—881no—
339C2×C8—881no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—111no—
345C4⋊C4—111no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—81no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C42—221no—
357C11#933111yescharacteristic, complemented, Sylow
358C23—41no—
359C23—41no—
360C23—41no—
361C23—221no—
362C23(C22⋊D11)⋊C411yescharacteristic
363C23#6693611yescharacteristic
364C23#6699111yescharacteristic
365Q8—41no—
366Q8—41no—
367Q8—81no—
368Q8—441no—
369D4—441no—
370D4—881no—
371D4—881no—
372D4—881no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4C22⋊C4×D1111yescharacteristic
392C2×C4#6693711yescharacteristic
393C2×C4C4×C22⋊D1111yescharacteristic
394C2×C4#6699011yescharacteristic
395C8—41no—
396C8—41no—
397C8—441no—
398C8—441no—
399C8—441no—
400C8—441no—
401C8—881no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—82no—
412C22—441no—
413C22—441no—
414C22—441no—
415C22#1062256911yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—81no—
421C4—81no—
422C4—161no—
423C4—441no—
424C4—441no—
425C4—441no—
426C2—41no—
427C2—41no—
428C2—41no—
429C2—881no—
430C2#1306897511yescharacteristic
431C2#1306908611yescharacteristic
432C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1511C2
socleC22×C11#386
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1511D11
hypocenterC11#9331
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
4. #13066980C2semidirect
5. #13066524C2semidirect
6. #13066492C2semidirect
7. C11×#1511C2semidirect
12. #10622841C4semidirect
13. #10622840C4semidirect
23. #10622583C4semidirect
24. #10622581C4semidirect
145. #1511D11semidirect
357. C11#9331semidirect

Maximal subgroups

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

subgroupindex
#130794462
#130776762
#130671702
#130669802
#130665242
#130664922
C11×#15112
#933111