Finite Group Databasebeta

← #14647771

Subgroups — #14647771

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068808C212yesmaximal
2C2×#10622166C211yesmaximal, characteristic
3#13066869C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C11×#2316C211yesmaximal, characteristic
6C2×C11×#117—21no—
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C11×#389—22no—
10C11×#389—22no—
11C11×#380—21no—
12C11×#380C2212yes—
13C2×C11⋊#95—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2212yes—
17C2×#66872—22no—
18#10622167—22no—
19#10622166C414yescomplemented
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C11×#117—42no—
26C11×#117—42no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C4⋊C4D412yes—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C4⋊C4Q812yes—
37C2×C11×C22⋊C4—22no—
38C2×C42×C11—22no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—42no—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—22no—
44C11⋊#95—22no—
45C11⋊#95—42no—
46C11⋊#95—42no—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)C2×C414yes—
49#66872—44no—
50#8857—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C4⋊C412yes—
65C22×C4×C11C4⋊C412yes—
66C22×C4×C11SD1612yes—
67C22×C4×C11SD1612yes—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×Q811yescharacteristic
71C22×C4×C11#4112yes—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—41no—
85C22×Dic11—41no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—42no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—42no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—42no—
96C42×C11—44no—
97C4⋊Dic11—24no—
98C4⋊Dic11—42no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8—42no—
101C2×C11⋊C8—42no—
102#2316D1111yescharacteristic
103#1853—112no—
104C2×#324—111no—
105#1441—111no—
106#1294—112no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11C2×C4⋊C411yescharacteristic
112C23×C11#12011yescharacteristic
113C23×C11#12311yescharacteristic
114C23×C11C2×SD1611yescharacteristic
115C23×C11C2×SD1611yescharacteristic
116C23×C11AGL(1,ℤ/8)11yescharacteristic
117C23×C11#13711yescharacteristic
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11#10614yescomplemented
141C2×C4×C11C4×D412yes—
142C2×C4×C11C22⋊Q812yes—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C11⋊C8—44no—
158C2×#117—21no—
159C22×C4⋊C4—111no—
160C22×C4⋊C4C2×D1111yescharacteristic
161C2×#106—222no—
162C2×C22⋊C8—112no—
163#389—22no—
164#389—22no—
165#380—21no—
166#380C2×D1112yes—
167C2×#95—111no—
168C2×#95—221no—
169C2×#95—221no—
170#340—222no—
171#324—114no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#38511yescharacteristic
185C22×C11C2×#10611yescharacteristic
186C22×C11#42811yescharacteristic
187C22×C11#44811yescharacteristic
188C22×C11#45011yescharacteristic
189C22×C11#45411yescharacteristic
190C22×C11#45611yescharacteristic
191C22×C11B(4,𝔽2)11yescharacteristic
192C22×C11#45811yescharacteristic
193C22×C11#48111yescharacteristic
194C22×C11#48311yescharacteristic
195C4×C11—24no—
196C4×C11—22no—
197C4×C11—22no—
198C4×C11—42no—
199C4×C11—82no—
200C4×C11—82no—
201Dic11—82no—
202Dic11—82no—
203C23×C4—221no—
204C23×C4—221no—
205C23×C4C22⋊D1111yescharacteristic
206C23×C4C22⋊D1111yescharacteristic
207C23×C4C22×D1111yescharacteristic
208C22×C8—222no—
209#117—42no—
210#117—42no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—442no—
219C2×C4⋊C4Dic2212yes—
220C2×C4⋊C4C4×D1112yes—
221C2×C4⋊C4C22⋊D1112yes—
222C2×C4⋊C4C22⋊D1112yes—
223C2×C22⋊C4—22no—
224C2×C42—22no—
225#106—444no—
226C22⋊C8—114no—
227C22⋊C8—222no—
228#95—22no—
229#95—22no—
230#95—222no—
231#95—442no—
232#95—442no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11#159911yescharacteristic
238C2×C11#160411yescharacteristic
239C2×C11#161111yescharacteristic
240C2×C11#161611yescharacteristic
241C2×C11#185311yescharacteristic
242C2×C11#185711yescharacteristic
243C2×C11#186711yescharacteristic
244C24C2×C22⋊D1111yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4Dic11⋊C412yes—
272C22×C4Dic11⋊C412yes—
273C22×C4#432412yes—
274C22×C4#432512yes—
275C22×C4C2×Dic2211yescharacteristic
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4#433912yes—
278C22×C4C2×C22⋊D1112yes—
279C2×C8—224no—
280C2×C8—442no—
281C2×C8—442no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—224no—
291C4⋊C4—442no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C42—44no—
295C11#885711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C2×Dic11⋊C411yescharacteristic
301C23#6698211yescharacteristic
302C23#6698511yescharacteristic
303C23C2×#432411yescharacteristic
304C23C2×#432511yescharacteristic
305C23#6699511yescharacteristic
306C23#6700611yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—442no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4#6687214yescomplemented
344C2×C4#6697712yes—
345C2×C4C4×C22⋊D1112yes—
346C8—444no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22C2×#6687211yescharacteristic
360C22#1062257711yescharacteristic
361C22#1062258111yescharacteristic
362C22#1062258411yescharacteristic
363C22#1062282311yescharacteristic
364C22#1062283111yescharacteristic
365C22#1062284011yescharacteristic
366C22#1062285611yescharacteristic
367C22#1062285711yescharacteristic
368C22#1062285811yescharacteristic
369C22#1062285911yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—82no—
375C4—82no—
376C4—882no—
377C4—882no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1306755611yescharacteristic
383C2#1306758511yescharacteristic
384C2#1306762411yescharacteristic
385C2#1306765311yescharacteristic
386C2#1306880911yescharacteristic
387C2#1306883111yescharacteristic
388C2#1306889711yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2316C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2316D11
hypocenterC11#8857
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
19. #10622166C4semidirect
140. C2×C4×C11#106semidirect
295. C11#8857semidirect
343. C2×C4#66872semidirect

Maximal subgroups

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

subgroupindex
#130688082
C2×#106221662
#130668692
#130664942
C11×#23162
#885711