Finite Group Databasebeta

← #14664293

Subgroups — #14664293

Order 2816.

488 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 73 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#13074092C211yesmaximal, characteristic
2D11×#343C211yesmaximal, characteristic, complemented
3#13066944C211yesmaximal, characteristic, complemented
4#13066643C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×#66948C411yescharacteristic
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#400C2211yescharacteristic
12#10622604C2211yescharacteristic
13#10622595C411yescharacteristic
14#10622339—21no—
15#10622285C411yescharacteristic
16#10622283—21no—
17#10622282—21no—
18#10622279C411yescharacteristic
19#10622278—21no—
20#10622278—21no—
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D44—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4C2×C411yescharacteristic
43C2×Dic11⋊C4D411yescharacteristic
44C2×C4×Dic11—21no—
45C2×#4318—21no—
46M16×D11—24no—
47M16×D11—42no—
48C2×#4313—41no—
49C2×#4313—41no—
50C2×C8×D11—41no—
51#66948—41no—
52#66948—41no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95C2×C411yescharacteristic
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11766—111nomaximal, Sylow
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C2×D44—41no—
77C2×D44—42no—
78C2×D44—42no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—81no—
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—22no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—81no—
105(C2×D11)⋊C4—81no—
106C4⋊Dic11—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—81no—
110#4318—22no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#4313—44no—
115#4313—82no—
116C8×D11—44no—
117#2591—111no—
118C2×#343—111no—
119#1463—111no—
120#1353—111no—
121#1353D1111yescharacteristic, complemented
122#1345—111no—
123#1345—111no—
124C23×C11C2×C22⋊C411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—22no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11#9911yescharacteristic
137C22×D11#9911yescharacteristic
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11#10412yes—
162D44—82no—
163D44—82no—
164D44—82no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—22no—
169C4×D11—42no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C22×M16—221no—
178C2×#121—111no—
179C22×C4⋊C4—111no—
180#407—221no—
181#400—111no—
182#400C2×D1111yescharacteristic
183#394—111no—
184#394—111no—
185#388—221no—
186#388—221no—
187#386—221no—
188#386—221no—
189C4×C22⋊C4—111no—
190#343—111no—
191#343—221no—
192#343C2×D1111yescharacteristic
193#324—111no—
194#324—221no—
195#324C2×D1111yescharacteristic
196C22×C11—21no—
197C22×C11—21no—
198C22×C11C2×#9911yescharacteristic
199C22×C11#41711yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—21no—
205C2×D11—21no—
206C2×D11—42no—
207C2×D11—42no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11#35512yes—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—81no—
221C4×C11—81no—
222Dic11—22no—
223Dic11—41no—
224Dic11—41no—
225Dic11—81no—
226C22×D4—111no—
227C22×D4—221no—
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—111no—
231C2×M16—21no—
232C2×M16—224no—
233C2×M16—221no—
234C2×M16—441no—
235C2×M16—441no—
236C2×M16—442no—
237C22×C8—441no—
238#121—441no—
239#121—441no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—441no—
244C2×C4⋊C4—441no—
245C2×C4⋊C4C4×D1111yescharacteristic
246C2×C4⋊C4C22×D1111yescharacteristic
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C42—221no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256C22⋊C8—441no—
257#95—21no—
258#95—21no—
259#95—111no—
260#95—221no—
261#95—221no—
262#95C4×D1111yescharacteristic
263C2×C11—21no—
264C2×C11—21no—
265C2×C11#150411yescharacteristic
266C2×C11#212111yescharacteristic
267C2×C11C2×#35511yescharacteristic
268D11—22no—
269D11—41no—
270D11—161no—
271C24—111no—
272C24—221no—
273C2×D4—441no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—881no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—222no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—881no—
295C22×C4—881no—
296C22×C4C2×C4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299M16—22no—
300M16—41no—
301M16—222no—
302M16—444no—
303M16—441no—
304M16—882no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—444no—
308C2×C8—441no—
309C2×C8—441no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C22⋊C4—442no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—881no—
321C22⋊C4—881no—
322C42—881no—
323C11#1176611yescharacteristic, complemented, Sylow
324C23—111no—
325C23—111no—
326C23—222no—
327C23—221no—
328C23—221no—
329C23—441no—
330C23—441no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23C22⋊C4×D1111yescharacteristic
338D4—882no—
339D4—882no—
340D4—882no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—112no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—442no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4#6696711yescharacteristic
372C2×C4#6697111yescharacteristic
373C8—42no—
374C8—81no—
375C8—442no—
376C8—881no—
377C22—21no—
378C22—21no—
379C22—112no—
380C22—221no—
381C22—221no—
382C22—221no—
383C22—221no—
384C22—221no—
385C22—442no—
386C22—442no—
387C22—881no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22D11×#9911yescharacteristic
395C22#1062241611yescharacteristic
396C22D11×#10411yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—81no—
402C4—81no—
403C4—222no—
404C4—441no—
405C4—441no—
406C4—881no—
407C2—21no—
408C2—21no—
409C2—222no—
410C2—441no—
411C2—1761no—
412C2#1306711911yescharacteristic
413C2#1307026111yescharacteristic
414C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radicalC2×#66948C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11766
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. D11×#343C2semidirect
3. #13066944C2semidirect
4. #13066643C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1353C2semidirect
121. #1353D11semidirect
323. C11#11766semidirect

Maximal subgroups

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

subgroupindex
#130740922
D11×#3432
#130669442
#130666432
#130666202
#130666182
C11×#13532
#1176611