Finite Group Databasebeta

← #14663296

Subgroups — #14663296

Order 2816.

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

normal subgroups only

This group has 492 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#13072895C211yesmaximal, characteristic
2#13066941C211yesmaximal, characteristic
3D11×#323C211yesmaximal, characteristic
4#13066565C211yesmaximal, characteristic, complemented
5#13066563C211yesmaximal, characteristic, complemented
6#13066546C211yesmaximal, characteristic, complemented
7C11×#1317C211yesmaximal, characteristic, complemented
8C22×(C2×D11)⋊C4C411yescharacteristic
9C2×C22⋊C4×D11C2211yescharacteristic
10C11×#381C2211yescharacteristic
11#10622824C411yescharacteristic
12#10622568C411yescharacteristic
13#10622563C411yescharacteristic
14#10622559C2211yescharacteristic
15#10622339—21no—
16D11×C22⋊C8—21no—
17#10622288—21no—
18#10622287—21no—
19#10622281—21no—
20#10622277—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C24×D11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11C2×C411yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—41no—
41C2×(C2×D11)⋊C4—41no—
42C2×(C2×D11)⋊C4D411yescharacteristic
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×#4313—41no—
47C2×C8×D11—41no—
48C22⋊C4×D11—41no—
49C22⋊C4×D11—41no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11543—111nomaximal, Sylow
63C24×C11C22×C411yescharacteristic
64C23×D11—21no—
65C23×D11—21no—
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—41no—
69C23×D11—42no—
70C23×D11—81no—
71C23×D11C22⋊C411yescharacteristic
72C23×D11C22⋊C411yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C22×Dic11—81no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—42no—
92C2×C4×D11—81no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—42no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—81no—
107C4⋊Dic11—81no—
108Dic11⋊C4—81no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#4313—82no—
112C8×D11—82no—
113#2483—111no—
114#1462—111no—
115C2×#323—111no—
116#1326—111no—
117#1326—111no—
118#1317—111no—
119#1317D1111yescharacteristic, complemented
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11C2×C22⋊C411yescharacteristic
125C23×C11#13111yescharacteristic
126C23×C11#13111yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—22no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—81no—
143C22×D11—81no—
144C22×D11—84no—
145C22×D11—82no—
146C22×D11—82no—
147C22×D11#9911yescharacteristic
148C22×D11#9911yescharacteristic
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—82no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—81no—
175C4×D11—81no—
176C8×C11—81no—
177C8×C11—81no—
178C11⋊C8—81no—
179C11⋊C8—81no—
180C22×C22⋊C4—111no—
181C22×C22⋊C4—111no—
182#407—221no—
183C2×C22⋊C8—221no—
184#397—221no—
185#397—221no—
186#385—111no—
187#385—111no—
188#385—221no—
189#381—111no—
190#381—221no—
191#381C2×D1111yescharacteristic
192#379—111no—
193#323—111no—
194#323—111no—
195#323—221no—
196#323—221no—
197#323C2×D1111yescharacteristic
198#323C2×D1111yescharacteristic
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—42no—
206C22×C11—41no—
207C22×C11—41no—
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—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—82no—
224C2×D11—82no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11#35212yes—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—81no—
231C4×C11—81no—
232Dic11—41no—
233Dic11—41no—
234Dic11—81no—
235Dic11—81no—
236C25—111no—
237C23×C4—111no—
238C23×C4—111no—
239C23×C4—111no—
240C23×C4C4×D1111yescharacteristic
241C2×M16—441no—
242C22×C8—441no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4—111no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—441no—
254C2×C22⋊C4—441no—
255C2×C22⋊C4—441no—
256C2×C22⋊C4—441no—
257C2×C22⋊C4C4×D1111yescharacteristic
258C2×C22⋊C4C22×D1111yescharacteristic
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263C22⋊C8—441no—
264C22⋊C8—441no—
265#95—21no—
266#95—21no—
267#95—221no—
268#95—221no—
269#95—221no—
270#95—221no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—41no—
274C2×C11—41no—
275C2×C11#146811yescharacteristic
276C2×C11C2×#35211yescharacteristic
277C2×C11#212111yescharacteristic
278D11—22no—
279D11—41no—
280D11—81no—
281C24—111no—
282C24—111no—
283C24—221no—
284C24—221no—
285C24—221no—
286C24—221no—
287C24—441no—
288C24—442no—
289C24—881no—
290C24C2×C4×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—442no—
306C22×C4—441no—
307C22×C4—881no—
308C22×C4—881no—
309C22×C4D4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311M16—882no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—441no—
315C2×C8—441no—
316C2×C8—882no—
317C4⋊C4—881no—
318C4⋊C4—881no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—441no—
330C22⋊C4—881no—
331C11#1154311yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—41no—
335C23—41no—
336C23—111no—
337C23—111no—
338C23—222no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23—442no—
352C23—442no—
353C23—881no—
354C23—881no—
355C23—882no—
356C23—882no—
357C23—884no—
358C23C22⋊C4×D1111yescharacteristic
359C23#6695411yescharacteristic
360C23#6696011yescharacteristic
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4—882no—
388C8—81no—
389C8—81no—
390C8—881no—
391C8—881no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—112no—
402C22—221no—
403C22—221no—
404C22—221no—
405C22—221no—
406C22—221no—
407C22—442no—
408C22—442no—
409C22—441no—
410C22—441no—
411C22—441no—
412C22—881no—
413C22—881no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—882no—
418C22#1062234011yescharacteristic
419C22D11×#9911yescharacteristic
420C22#1062235811yescharacteristic
421C4—41no—
422C4—41no—
423C4—81no—
424C4—81no—
425C4—441no—
426C4—441no—
427C4—881no—
428C4—881no—
429C2—21no—
430C2—21no—
431C2—41no—
432C2—41no—
433C2—222no—
434C2—441no—
435C2—881no—
436C2#1306696111yescharacteristic
437C2D11×#35211yescharacteristic
438C2#1307026111yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11C2×#99
prime radicalC24×D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1317D11
hypocenterC11#11543
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
4. #13066565C2semidirect
5. #13066563C2semidirect
6. #13066546C2semidirect
7. C11×#1317C2semidirect
119. #1317D11semidirect
331. C11#11543semidirect

Maximal subgroups

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

subgroupindex
#130728952
#130669412
D11×#3232
#130665652
#130665632
#130665462
C11×#13172
#1154311