Finite Group Databasebeta

← #14663300

Subgroups — #14663300

Order 2816.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#13072894C211yesmaximal, characteristic
2C2×#10622163C211yesmaximal, characteristic
3#13066563C212yesmaximal, complemented
4#13066545C212yesmaximal, complemented
5C11×#1462C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic11C411yescharacteristic
8C11×#407—21no—
9#10622860C411yescharacteristic
10#10622824—21no—
11#10622823—21no—
12C2×C22⋊(C11⋊C8)—21no—
13#10622565—21no—
14#10622565—21no—
15#10622559C411yescharacteristic
16#10622559C2211yescharacteristic
17#10622556C411yescharacteristic
18#10622556C2211yescharacteristic
19C11×#323—21no—
20C11×#323C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C2×C11×M16—41no—
29C2×C11×C22⋊C4—41no—
30C2×C11×C22⋊C4—41no—
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—41no—
40C2×C22⋊Dic11—41no—
41C2×C22⋊Dic11C2×C411yescharacteristic
42C2×C22⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—41no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—41no—
56#11543—111nomaximal, Sylow
57C24×C11—21no—
58C24×C11—21no—
59C24×C11—22no—
60C24×C11—41no—
61C24×C11—42no—
62C24×C11—81no—
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22⋊C411yescharacteristic
65C24×C11C22×C411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—42no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—22no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—81no—
85C11×M16—82no—
86C2×C8×C11—42no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C22⋊Dic11—22no—
92C22⋊Dic11—41no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—82no—
102#2483—111no—
103#1462D1111yescharacteristic
104C2×#323—111no—
105#1326—112no—
106#1317—112no—
107C23×C11—22no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—42no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—42no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11—84no—
127C23×C11—84no—
128C23×C11#9911yescharacteristic
129C23×C11#9911yescharacteristic
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#13112yes—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—82no—
157C2×Dic11—82no—
158C8×C11—82no—
159C11⋊C8—82no—
160C22×C22⋊C4—111no—
161C22×C22⋊C4C2×D1111yescharacteristic
162#407—21no—
163C2×C22⋊C8—221no—
164#397—221no—
165#397—221no—
166#385—111no—
167#385—111no—
168#385—221no—
169#381—111no—
170#381—111no—
171#381—221no—
172#379—111no—
173#323—21no—
174#323—112no—
175#323—221no—
176#323C2×D1112yes—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—22no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—84no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—84no—
198C22×C11#35212yes—
199C22×C11#40811yescharacteristic
200C22×C11C2×#9911yescharacteristic
201C22×C11#41311yescharacteristic
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206Dic11—81no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210C25C4×D1111yescharacteristic
211C23×C4—111no—
212C23×C4—111no—
213C23×C4D4411yescharacteristic
214C23×C4C22⋊D1111yescharacteristic
215C2×M16—41no—
216C22×C8—441no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C22⋊C4—41no—
220C2×C22⋊C4—41no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—441no—
228C2×C22⋊C4—441no—
229C2×C22⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4D4411yescharacteristic
231C2×C22⋊C4C22⋊D1111yescharacteristic
232C2×C22⋊C4C22×D1111yescharacteristic
233C22⋊C8—22no—
234C22⋊C8—41no—
235C22⋊C8—222no—
236C22⋊C8—441no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11—22no—
246C2×C11—41no—
247C2×C11—42no—
248C2×C11—81no—
249C2×C11#146811yescharacteristic
250C2×C11C2×#35211yescharacteristic
251C2×C11#212111yescharacteristic
252C24—21no—
253C24—21no—
254C24—22no—
255C24—41no—
256C24—42no—
257C24—81no—
258C24(C2×D11)⋊C411yescharacteristic
259C24(C2×D11)⋊C411yescharacteristic
260C24C2×C4×D1111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—42no—
266C22×C4—81no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4—881no—
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4C2×D4411yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280M16—82no—
281C2×C8—42no—
282C2×C8—442no—
283C2×C8—882no—
284C4⋊C4—881no—
285C4⋊C4—881no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—222no—
291C22⋊C4—442no—
292C22⋊C4—442no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C22⋊C4—881no—
297C11#1154311yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#6687011yescharacteristic
320C23#6687011yescharacteristic
321C23#6696012yes—
322C23C2×(C2×D11)⋊C411yescharacteristic
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—882no—
348C2×C4—882no—
349C8—82no—
350C8—882no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#1062211412yes—
373C22C2×#6687011yescharacteristic
374C22#1062274211yescharacteristic
375C22#1062274511yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—881no—
381C4—881no—
382C4—881no—
383C4—881no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#1306696511yescharacteristic
391C2C2×#1062211411yescharacteristic
392C2#1307026011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1462C2
socleC22×C11C2×#99
prime radicalC25×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1462D11
hypocenterC11#11543
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #13066563C2semidirect
4. #13066545C2semidirect
297. C11#11543semidirect

Maximal subgroups

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

subgroupindex
#130728942
C2×#106221632
#130665632
#130665452
C11×#14622
#1154311