Finite Group Databasebeta

← #14663326

Subgroups — #14663326

Order 2816.

496 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073086C211yesmaximal, characteristic
2#13066944C211yesmaximal, characteristic, complemented
3D11×#324C211yesmaximal, characteristic, complemented
4#13066561C211yesmaximal, characteristic, complemented
5#13066561C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×C4⋊C4×D11C2211yescharacteristic
10C2×#66936—21no—
11C2×#66936—21no—
12C11×#390C2211yescharacteristic
13#10622834C411yescharacteristic
14#10622589C2211yescharacteristic
15#10622562—21no—
16#10622562—21no—
17C4×(C2×D11)⋊C4C411yescharacteristic
18#10622548C411yescharacteristic
19#10622339—21no—
20D11×C22⋊C8—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39#66991—41no—
40#66991—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4D411yescharacteristic
49C2×Dic11⋊C4D411yescharacteristic
50C2×C4×Dic11C2×C411yescharacteristic
51C2×#4313—41no—
52C2×C8×D11—41no—
53C4⋊C4×D11—41no—
54C4⋊C4×D11—41no—
55#66936—44no—
56#66936—44no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62(C2×D11)⋊C8—41no—
63(C2×D11)⋊C8—41no—
64#11549—111nomaximal, Sylow
65C24×C11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
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—21no—
92C2×C4×D11—41no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C42×C11—41no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104(C2×D11)⋊C4—24no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117#4313—82no—
118C8×D11—82no—
119#2501—111no—
120#1463—111no—
121C2×#324—111no—
122#1325—111no—
123#1325—111no—
124#1318—111no—
125#1318D1111yescharacteristic, complemented
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—22no—
137C22×D11—41no—
138C22×D11#9911yescharacteristic
139C22×D11#9911yescharacteristic
140D4×C11—81no—
141D4×C11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11#13111yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C22⋊D11—82no—
154C22⋊D11—82no—
155C2×Dic11—22no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C4×D11—41no—
169C4×D11—41no—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—81no—
175C4×D11—81no—
176C8×C11—81no—
177C8×C11—81no—
178C11⋊C8—81no—
179C11⋊C8—81no—
180C2×#123—221no—
181C2×#123—221no—
182C2×#121—111no—
183C22×C4⋊C4—111no—
184#407—221no—
185C2×C22⋊C8—221no—
186#399—221no—
187#399—221no—
188#390—111no—
189#390C2×D1111yescharacteristic
190#384—111no—
191#384—111no—
192C4×C22⋊C4—111no—
193#324—111no—
194#324—111no—
195#324—221no—
196#324—221no—
197#324C2×D1111yescharacteristic
198#324C2×D1111yescharacteristic
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#40811yescharacteristic
209C22×C11C2×#9911yescharacteristic
210C22×C11#41311yescharacteristic
211C2×D11—21no—
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—21no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11#35312yes—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—42no—
222C4×C11—41no—
223C4×C11—41no—
224Dic11—42no—
225Dic11—41no—
226Dic11—41no—
227Dic11—41no—
228Dic11—81no—
229C22×D4—221no—
230C22×D4C4×D1111yescharacteristic
231C23×C4—111no—
232C23×C4—111no—
233C23×C4—111no—
234C2×M16—441no—
235C22×C8—441no—
236#123—444no—
237#123—444no—
238#121—441no—
239#121—441no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—441no—
249C2×C4⋊C4—441no—
250C2×C4⋊C4C22×D1111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C42—111no—
258C2×C42C4×D1111yescharacteristic
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263C22⋊C8—441no—
264C22⋊C8—441no—
265#95—221no—
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—161no—
269C2×C11#146811yescharacteristic
270C2×C11C2×#35311yescharacteristic
271C2×C11#213311yescharacteristic
272D11—22no—
273D11—41no—
274C24—21no—
275C24—111no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—442no—
283C2×D4—442no—
284C22×C4—21no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—441no—
299C22×C4—442no—
300C22×C4—442no—
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4D4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304M16—882no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—882no—
310C4⋊C4—41no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—224no—
322C22⋊C4—442no—
323C22⋊C4—442no—
324C22⋊C4—442no—
325C42—41no—
326C42—221no—
327C42—221no—
328C11#1154911yescharacteristic, complemented, Sylow
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—111no—
337C23—111no—
338C23—222no—
339C23—221no—
340C23—221no—
341C23—441no—
342C23C22⋊C4×D1111yescharacteristic
343D4—81no—
344D4—81no—
345D4—882no—
346D4—882no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—222no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—881no—
376C2×C4—881no—
377C2×C4#6695411yescharacteristic
378C2×C4#6696011yescharacteristic
379C8—81no—
380C8—81no—
381C8—881no—
382C8—881no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—112no—
393C22—221no—
394C22—221no—
395C22—221no—
396C22—221no—
397C22—221no—
398C22—442no—
399C22—442no—
400C22#1062234011yescharacteristic
401C22D11×#9911yescharacteristic
402C22#1062235811yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—41no—
407C4—41no—
408C4—442no—
409C4—441no—
410C4—441no—
411C4—441no—
412C4—881no—
413C2—21no—
414C2—21no—
415C2—161no—
416C2—222no—
417C2—441no—
418C2#1306696111yescharacteristic
419C2D11×#35311yescharacteristic
420C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC2×#66991C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11549
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066944C2semidirect
3. D11×#324C2semidirect
4. #13066561C2semidirect
5. #13066561C2semidirect
6. #13066548C2semidirect
7. C11×#1318C2semidirect
125. #1318D11semidirect
328. C11#11549semidirect

Maximal subgroups

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

subgroupindex
#130730862
#130669442
D11×#3242
#130665612
#130665482
C11×#13182
#1154911