Finite Group Databasebeta

← #14673454

Subgroups — #14673454

Order 2816.

484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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#13076559C211yesmaximal, characteristic
2#13068899C211yesmaximal, characteristic
3#13068896C211yesmaximal, characteristic
4#13068828C211yesmaximal, characteristic
5#13066740C211yesmaximal, characteristic
6#13066735C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8#10623329C2211yescharacteristic
9C2×C11×#100C2211yescharacteristic
10C2×C11×#99C2211yescharacteristic
11C11×#386C2211yescharacteristic
12#10622834C2211yescharacteristic
13#10622833C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15#10622823—21no—
16#10622823—21no—
17#10622734—21no—
18#10622563—21no—
19#10622560—21no—
20#10622560—21no—
21#10622559—21no—
22#10622273—21no—
23#10622259—21no—
24#10622193—21no—
25#10622165—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42D4×Dic11—41no—
43D4×Dic11—41no—
44#66979—21no—
45C2×C4⋊Dic11—41no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—41no—
50C2×C4×Dic11D411yescharacteristic
51C11×#100—21no—
52C11×#100Q812yescomplemented
53C11×#99—21no—
54C11×#99Q812yescomplemented
55C11×#95—21no—
56#66898—21no—
57#66898Q812yescomplemented
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—41no—
65C11⋊#95—41no—
66#66882—41no—
67#66881—41no—
68#13463—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11C2×Q811yescharacteristic
74C2×D4×C11C2×Q811yescharacteristic
75C2×D4×C11C2×Q811yescharacteristic
76C2×D4×C11#4111yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—81no—
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—81no—
94C2×Dic22—42no—
95C2×Dic22—81no—
96C2×Dic22—81no—
97C11×M16—22no—
98C11×M16—41no—
99C2×C8×C11—41no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C22⋊Dic11—22no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—42no—
110C22⋊Dic11—42no—
111C22⋊Dic11—41no—
112C22⋊Dic11—81no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—82no—
117Dic11⋊C4—81no—
118Dic11⋊C4—81no—
119Dic11⋊C4—82no—
120C4×Dic11—41no—
121C4×Dic11—41no—
122#2804—111no—
123#1867—111no—
124#1867—111no—
125#1856—111no—
126#1393—111no—
127#1390—111no—
128#1390D1111yescharacteristic
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11#12011yescharacteristic
138C23×C11C22⋊Q811yescharacteristic
139C23×C11C22⋊Q811yescharacteristic
140C23×C11C4⋊Q811yescharacteristic
141C23×C11C4⋊Q811yescharacteristic
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11C22⋊Q811yescharacteristic
160C2×C4×C11C4⋊Q811yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184Dic22—84no—
185C8×C11—42no—
186#518—111no—
187#428—221no—
188C2×#100C2×D1111yescharacteristic
189C2×#99—111no—
190C2×#99C2×D1111yescharacteristic
191#400—221no—
192#393—221no—
193#393—221no—
194#391—221no—
195#390—111no—
196#386—111no—
197#386C2×D1111yescharacteristic
198#385—221no—
199#385—221no—
200#385—221no—
201#385—221no—
202#342—221no—
203#342—221no—
204#339—221no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#39511yescharacteristic
222C22×C11B(4,𝔽2)11yescharacteristic
223C22×C11#45811yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11—82no—
228C4×C11—81no—
229Dic11—42no—
230Dic11—81no—
231Dic11—82no—
232Dic11—81no—
233Dic11—81no—
234Dic11—81no—
235Dic11—81no—
236C22×Q8—221no—
237C22×D4C22×D1111yescharacteristic
238C23×C4—111no—
239C23×C4D4411yescharacteristic
240C2×M16—21no—
241C4×D4—441no—
242C4×D4—441no—
243#117—221no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—441no—
248C2×C4⋊C4—441no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4D4411yescharacteristic
259C2×C42—111no—
260#107—441no—
261#106—441no—
262#100—21no—
263#100Dic2212yescomplemented
264#99—21no—
265#99—112no—
266#99—221no—
267#99Dic2212yescomplemented
268#95—21no—
269#95—221no—
270#95—221no—
271#95—221no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—441no—
276#95—441no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11—41no—
282C2×C11—41no—
283C2×C11#206211yescharacteristic
284C2×C11#219811yescharacteristic
285C2×C11#219911yescharacteristic
286C24C2×D4411yescharacteristic
287C24D4×D1111yescharacteristic
288C2×Q8—442no—
289C2×Q8—881no—
290C2×Q8—881no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4C2×Dic2211yescharacteristic
294C2×D4C2×Dic2211yescharacteristic
295C2×D4#434111yescharacteristic
296C2×D4Q8×D1111yescharacteristic
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—81no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—881no—
313C22×C4D4×D1111yescharacteristic
314M16—22no—
315M16—41no—
316C2×C8—41no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—441no—
320C4⋊C4—881no—
321C4⋊C4—881no—
322C4⋊C4—882no—
323C4⋊C4—882no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—81no—
328C22⋊C4—222no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—881no—
337C42—441no—
338C42—441no—
339C11#1346311yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23#6692211yescharacteristic
349C23#6693111yescharacteristic
350C23#6693511yescharacteristic
351C23#6694111yescharacteristic
352C23#6695011yescharacteristic
353Q8—884no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—41no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—442no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—442no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4#6693111yescharacteristic
395C2×C4#6694111yescharacteristic
396C8—42no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1062226911yescharacteristic
414C22#1062235411yescharacteristic
415C22#1062235511yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—82no—
420C4—81no—
421C4—442no—
422C4—881no—
423C4—882no—
424C4—881no—
425C4—881no—
426C4—881no—
427C4—881no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—41no—
433C2—41no—
434C2#1306997011yescharacteristic
435C2#1307061311yescharacteristic
436C2#1307061811yescharacteristic
subgroupG/H
centerC22#10622354
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1390C2
socleC22×C11B(4,𝔽2)
hypercenter#1390D11
hypocenterC11#13463
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
52. C11×#100Q8semidirect
54. C11×#99Q8semidirect
57. #66898Q8semidirect
263. #100Dic22semidirect
267. #99Dic22semidirect
339. C11#13463semidirect

Maximal subgroups

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

subgroupindex
#130765592
#130688992
#130688962
#130688282
#130667402
#130667352
C11×#13902
#1346311