Finite Group Databasebeta

← #14657448

Subgroups — #14657448

Order 2816.

460 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 101 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#13068608C211yesmaximal, characteristic, complemented
2#13067374C211yesmaximal, characteristic, complemented
3#13067293C211yesmaximal, characteristic, complemented
4#13067067C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#463—22no—
12C11×#461—21no—
13C11×#459—21no—
14C11×#423C2211yescharacteristic
15C11×#417—21no—
16C2×#66897—21no—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622185—21no—
22#10622182—21no—
23D4⋊(C11⋊C8)—21no—
24D4⋊(C11⋊C8)—21no—
25D4⋊(C11⋊C8)—21no—
26D4⋊(C11⋊C8)—21no—
27#10622168—21no—
28#10622117—22no—
29C2×C11×#41—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C11×AGL(1,ℤ/8)—42no—
33C11×AGL(1,ℤ/8)—42no—
34C2×C11×SD16—22no—
35C2×C11×D8—22no—
36C2×C11×M16—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4318—21no—
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D412yes—
57C11×#103—22no—
58C11×#102—22no—
59#66897—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8D411yescharacteristic
68C4×C11⋊C8D411yescharacteristic
69#10456—111nomaximal, Sylow
70C24×C11—21no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11D812yes—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—81no—
91C22×C4×C11—81no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C11×SD16—44no—
96C11×D8—44no—
97C11×M16—41no—
98C11×M16—41no—
99C2×C8×C11—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4318—41no—
113#4318—41no—
114#4318—41no—
115#4318—41no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—81no—
123#3036D1111yescharacteristic
124#1800—111no—
125#1567—111no—
126#1547—111no—
127#1492—111no—
128C2×D4⋊C8—111no—
129#1292—111no—
130C23×C11—22no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12311yescharacteristic
137Q8×C11—41no—
138Q8×C11—41no—
139D4×C11—22no—
140D4×C11—22no—
141D4×C11—41no—
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—41no—
147D4×C11—81no—
148D4×C11—81no—
149D4×C11—81no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—82no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12411yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C8×C11—42no—
172C11⋊C8—22no—
173C11⋊C8—41no—
174C11⋊C8—81no—
175C11⋊C8—81no—
176C11⋊C8—81no—
177C2×AGL(1,ℤ/8)—21no—
178#532C2×D1111yescharacteristic
179C2×C4×D4C2×D1111yescharacteristic
180#463—22no—
181#461—21no—
182#459—21no—
183#423—111no—
184#423—111no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187#417—21no—
188C2×#100—221no—
189C2×C4×C8—111no—
190#343—221no—
191#335—222no—
192#332—221no—
193#331—221no—
194D4⋊C8—221no—
195D4⋊C8—221no—
196D4⋊C8—221no—
197D4⋊C8—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—42no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39411yescharacteristic
209C22×C11#48011yescharacteristic
210C22×C11#48211yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11#44711yescharacteristic
217C4×C11#45211yescharacteristic
218C4×C11#46611yescharacteristic
219C4×C11#46811yescharacteristic
220C4×C11#47111yescharacteristic
221C4×C11#47211yescharacteristic
222C2×#41—21no—
223C22×D4C22⋊D1111yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—42no—
226AGL(1,ℤ/8)—42no—
227C2×SD16—22no—
228C2×D8—22no—
229C2×M16—21no—
230C2×M16—221no—
231C2×M16—221no—
232C22×C8—221no—
233C22×C8—221no—
234C4⋊Q8C22⋊D1111yescharacteristic
235#127C22⋊D1111yescharacteristic
236#124—21no—
237#121—21no—
238#121—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C2×C4⋊C4C22⋊D1111yescharacteristic
246C2×C22⋊C4—21no—
247C2×C42C22×D1111yescharacteristic
248C4⋊C8—21no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8C22⋊D1112yes—
256#103—22no—
257#102—22no—
258#100—442no—
259C4×C8—111no—
260C4×C8—111no—
261C4×C8—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—82no—
265C2×C11—161no—
266C2×C11#203311yescharacteristic
267C2×C11#205011yescharacteristic
268C2×C11#205111yescharacteristic
269C24—21no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4#432312yes—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—81no—
290C22×C4—81no—
291C22×C4#434111yescharacteristic
292C22×C4#434111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294SD16—44no—
295D8—44no—
296M16—41no—
297M16—41no—
298M16—441no—
299M16—441no—
300M16—441no—
301M16—441no—
302C2×C8—22no—
303C2×C8—221no—
304C2×C8—221no—
305C2×C8—442no—
306C2×C8—441no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—881no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C42D4×D1111yescharacteristic
319C42#434111yescharacteristic
320C42C2×C22⋊D1111yescharacteristic
321C42C2×C22⋊D1111yescharacteristic
322C11#1045611yescharacteristic, complemented, Sylow
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—81no—
328C23—81no—
329C23#6698811yescharacteristic
330Q8—41no—
331Q8—41no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C2×#432311yescharacteristic
355C2×C4#6698511yescharacteristic
356C2×C4#6698811yescharacteristic
357C2×C4#6698911yescharacteristic
358C2×C4#6699111yescharacteristic
359C2×C4#6699211yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4#6700311yescharacteristic
362C2×C4#6700411yescharacteristic
363C2×C4#6700611yescharacteristic
364C8—42no—
365C8—222no—
366C8—441no—
367C8—881no—
368C8—881no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—82no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22#1062264611yescharacteristic
381C22#1062264811yescharacteristic
382C22#1062283511yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—81no—
388C4#1062265111yescharacteristic
389C4#1062265511yescharacteristic
390C4#1062281211yescharacteristic
391C4#1062281311yescharacteristic
392C4#1062283011yescharacteristic
393C4#1062285211yescharacteristic
394C2—21no—
395C2—21no—
396C2—82no—
397C2—161no—
398C2#1306979511yescharacteristic
399C2#1306990011yescharacteristic
400C2#1306990511yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3036C2
socleC22×C11#394
hypercenter#3036D11
hypocenterC11#10456
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13068608C2semidirect
2. #13067374C2semidirect
3. #13067293C2semidirect
4. #13067067C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. #13066490C2semidirect
322. C11#10456semidirect

Maximal subgroups

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

subgroupindex
#130686082
#130673742
#130672932
#130670672
C2×D4⋊(C11⋊C8)2
#130664902
C11×#30362
#1045611