Finite Group Databasebeta

← #14662950

Subgroups — #14662950

Order 2816.

562 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 115 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#13071228C211yesmaximal, characteristic
2C2×#10622163C211yesmaximal, characteristic
3#13066565C212yesmaximal, complemented
4#13066563C212yesmaximal, complemented
5C2×C11×#323C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic11C411yescharacteristic
8C22×C22⋊Dic11C411yescharacteristic
9C2×C11×C22⋊C8—21no—
10#10622823—21no—
11#10622823—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622559C411yescharacteristic
14#10622559C411yescharacteristic
15#10622559C2211yescharacteristic
16#10622559C2211yescharacteristic
17#10622555—21no—
18#10622555—21no—
19C11×#323—21no—
20C11×#323C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C23×Dic11C2×C411yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C22×C8×C11—41no—
30C2×C11×C22⋊C4—41no—
31C2×C11×C22⋊C4—41no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—41no—
41C2×C22⋊Dic11—41no—
42C2×C22⋊Dic11C814yescomplemented
43C2×C22⋊Dic11C2×C411yescharacteristic
44C2×C22⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—41no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11453—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—22no—
62C24×C11—81no—
63C24×C11—81no—
64C24×C11C22⋊C411yescharacteristic
65C24×C11C22⋊C411yescharacteristic
66C24×C11C2×C812yes—
67C24×C11M1612yes—
68C24×C11C22×C411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—81no—
74C22×C4×C11—81no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—24no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86C22×Dic11—81no—
87C22×Dic11—81no—
88C22×Dic11—81no—
89C22×Dic11—81no—
90C2×C8×C11—42no—
91C2×C8×C11—82no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C22⋊Dic11—24no—
97C22⋊Dic11—21no—
98C22⋊Dic11—21no—
99C22⋊Dic11—42no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11C2×C812yescomplemented
103C22⋊Dic11C2×C812yescomplemented
104Dic11⋊C4—81no—
105Dic11⋊C4—81no—
106Dic11⋊C4—81no—
107Dic11⋊C4—81no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—82no—
110#2315—111no—
111C2×#323—111no—
112C2×#323D1111yescharacteristic
113#1326—112no—
114#1326—112no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11—84no—
136C23×C11C22⋊C812yes—
137C23×C11C22⋊C812yes—
138C23×C11#9911yescharacteristic
139C23×C11#9911yescharacteristic
140C23×C11#10112yes—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11C22×C811yescharacteristic
143C23×C11C2×M1611yescharacteristic
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—84no—
169C2×Dic11—82no—
170C2×Dic11—82no—
171C8×C11—82no—
172C11⋊C8—82no—
173C22×C22⋊C4—111no—
174C22×C22⋊C4—111no—
175C22×C22⋊C4C2×D1111yescharacteristic
176C2×C22⋊C8—21no—
177C2×C22⋊C8—221no—
178#385—111no—
179#385—111no—
180#385—111no—
181#385—111no—
182#385—221no—
183#385—221no—
184#380—221no—
185#380—221no—
186#323—21no—
187#323—112no—
188#323—221no—
189#323C2×D1112yes—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—22no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11—82no—
214C22×C11#32412yes—
215C22×C11#32412yes—
216C22×C11C2×C22⋊C811yescharacteristic
217C22×C11C2×#9911yescharacteristic
218C22×C11C2×#10111yescharacteristic
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223Dic11—42no—
224Dic11—42no—
225Dic11—81no—
226Dic11—81no—
227C25C4×D1111yescharacteristic
228C23×C4—111no—
229C23×C4—111no—
230C23×C4—221no—
231C23×C4D4411yescharacteristic
232C23×C4C22⋊D1111yescharacteristic
233C22×C8—41no—
234C22×C8—441no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—114no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—441no—
249C2×C22⋊C4—441no—
250C2×C22⋊C4C4×D1111yescharacteristic
251C2×C22⋊C4D4411yescharacteristic
252C2×C22⋊C4C22⋊D1111yescharacteristic
253C2×C22⋊C4C22×D1111yescharacteristic
254C22⋊C8—22no—
255C22⋊C8—41no—
256C22⋊C8—222no—
257C22⋊C8—441no—
258#95—221no—
259#95—221no—
260#95—221no—
261#95—221no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—22no—
265C2×C11—22no—
266C2×C11—42no—
267C2×C11—41no—
268C2×C11—41no—
269C2×C11C2×#32411yescharacteristic
270C2×C11#212111yescharacteristic
271C2×C11#212111yescharacteristic
272C24—21no—
273C24—21no—
274C24—22no—
275C24—81no—
276C24—81no—
277C24C8×D1112yes—
278C24#431312yes—
279C24(C2×D11)⋊C411yescharacteristic
280C24(C2×D11)⋊C411yescharacteristic
281C24C2×C4×D1111yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—224no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—881no—
296C22×C4—881no—
297C22×C4—881no—
298C22×C4—881no—
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4C2×D4411yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303C2×C8—42no—
304C2×C8—82no—
305C2×C8—442no—
306C2×C8—882no—
307C4⋊C4—881no—
308C4⋊C4—881no—
309C4⋊C4—881no—
310C4⋊C4—881no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—112no—
316C22⋊C4—112no—
317C22⋊C4—224no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—442no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C11#1145311yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—82no—
343C23—82no—
344C23—84no—
345C23#6687011yescharacteristic
346C23#6687011yescharacteristic
347C23(C2×D11)⋊C812yes—
348C23(C2×D11)⋊C812yes—
349C23#6688812yes—
350C23C2×C8×D1111yescharacteristic
351C23C2×#431311yescharacteristic
352C23C2×(C2×D11)⋊C411yescharacteristic
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—884no—
378C2×C4—882no—
379C2×C4—882no—
380C8—82no—
381C8—882no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—82no—
403C22—82no—
404C22—82no—
405C22—82no—
406C22#1062210712yes—
407C22#1062210712yes—
408C22C2×#6687011yescharacteristic
409C22C2×(C2×D11)⋊C811yescharacteristic
410C22C2×#6688811yescharacteristic
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—442no—
416C4—442no—
417C4—881no—
418C4—881no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—22no—
423C2—42no—
424C2—41no—
425C2—41no—
426C2C2×#1062210711yescharacteristic
427C2#1307026011yescharacteristic
428C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC23×C11C22×C8
FrattiniC2×C22⋊C4C22×D11
FittingC2×C11×#323C2
socleC22×C11C2×#99
prime radicalC25×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenterC2×#323D11
hypocenterC11#11453
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #13066565C2semidirect
4. #13066563C2semidirect
42. C2×C22⋊Dic11C8semidirect
102. C22⋊Dic11C2×C8semidirect
103. C22⋊Dic11C2×C8semidirect
323. C11#11453semidirect

Maximal subgroups

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

subgroupindex
#130712282
C2×#106221632
#130665652
#130665632
C2×C11×#3232
#1145311