Finite Group Databasebeta

← #14663299

Subgroups — #14663299

Order 2816.

492 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 91 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#13066943C211yesmaximal, characteristic
2C2×#10622163C211yesmaximal, characteristic
3#13066564C212yesmaximal, complemented
4#13066546C212yesmaximal, complemented
5C11×#2483C211yesmaximal, characteristic
6C22×C11×C22⋊C4C411yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C11×#397—21no—
9C11×#397—21no—
10C11×#385—21no—
11C11×#385C411yescharacteristic
12C11×#385C2211yescharacteristic
13C11×#381—21no—
14C11×#381C411yescharacteristic
15C11×#381C2211yescharacteristic
16C11×#379C411yescharacteristic
17#10622820—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622163—21no—
20#10622163—21no—
21#10622163C2212yes—
22#10622163C2212yes—
23C25×C11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—41no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4—41no—
37C2×C11×C22⋊C4—41no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4D411yescharacteristic
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×#4318—41no—
45C22×C11⋊C8—41no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—41no—
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—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—81no—
80C22×C4×C11—81no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×C4⋊C4—81no—
86C11×C4⋊C4—81no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—42no—
93C11×C22⋊C4—42no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—81no—
98#4318—82no—
99C2×C11⋊C8—42no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—82no—
102#2483D1111yescharacteristic
103#1462—111no—
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—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×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C11⋊C8—82no—
159C11⋊C8—82no—
160C22×C22⋊C4Dic1111yescharacteristic
161C22×C22⋊C4C2×D1111yescharacteristic
162#407—221no—
163C2×C22⋊C8—221no—
164#397—21no—
165#397—21no—
166#385—21no—
167#385Dic1111yescharacteristic
168#385C2×D1111yescharacteristic
169#381—21no—
170#381Dic1111yescharacteristic
171#381C2×D1111yescharacteristic
172#379Dic1111yescharacteristic
173#323—112no—
174#323—112no—
175#323—221no—
176#323—221no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—22no—
184C22×C11—21no—
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—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210C25C2×Dic1111yescharacteristic
211C23×C4C2×Dic1111yescharacteristic
212C23×C4C2×Dic1111yescharacteristic
213C23×C4C22⋊D1111yescharacteristic
214C23×C4C22⋊D1111yescharacteristic
215C2×M16—441no—
216C22×C8—441no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—41no—
224C2×C22⋊C4—41no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4C2×Dic1111yescharacteristic
228C2×C22⋊C4C2×Dic1111yescharacteristic
229C2×C22⋊C4C2×Dic1111yescharacteristic
230C2×C22⋊C4C22⋊D1111yescharacteristic
231C2×C22⋊C4C22⋊D1111yescharacteristic
232C2×C22⋊C4C22×D1111yescharacteristic
233C22⋊C8—222no—
234C22⋊C8—222no—
235C22⋊C8—441no—
236C22⋊C8—441no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
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—
258C24C22⋊Dic1111yescharacteristic
259C24C22⋊Dic1111yescharacteristic
260C24C22×Dic1111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4C22⋊Dic1111yescharacteristic
277C22×C4C22⋊Dic1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280M16—882no—
281C2×C8—442no—
282C2×C8—442no—
283C2×C8—882no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—81no—
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#6689811yescharacteristic
320C23#6689811yescharacteristic
321C23#6700112yes—
322C23C2×C22⋊Dic1111yescharacteristic
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—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C8—882no—
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#1062217712yes—
373C22C2×#6689811yescharacteristic
374C22#1062284711yescharacteristic
375C22#1062285011yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2#1306696411yescharacteristic
391C2C2×#1062217711yescharacteristic
392C2#1307026211yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2483C2
socleC22×C11C2×#99
prime radicalC25×C11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#2483D11
hypocenterC11#11543
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2483

Complements

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

NH ≅ G/Ntype
3. #13066564C2semidirect
4. #13066546C2semidirect
297. C11#11543semidirect

Maximal subgroups

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

subgroupindex
#130669432
C2×#106221632
#130665642
#130665462
C11×#24832
#1154311