Finite Group Databasebeta

← #14648225

Subgroups — #14648225

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069578C211yesmaximal, characteristic
2#13069379C211yesmaximal, characteristic
3#13069374C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic
7C11×#2365C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11—21no—
10C11×#391—21no—
11C11×#389—21no—
12C11×#387—22no—
13C4×C11×C4⋊C4—21no—
14C4×C11×C4⋊C4C2211yescharacteristic
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×#66872—21no—
17C2×#66871—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622185C414yescomplemented
23#10622167—22no—
24#10622167—21no—
25#10622167—21no—
26C22×Q8×C11—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8C2×C412yes—
30C11×C4⋊Q8Q812yes—
31C4×Q8×C11—42no—
32C4×Q8×C11—42no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D412yes—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—22no—
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50C11×#95—22no—
51C11×#95—22no—
52C11×#95—21no—
53C11×#95—21no—
54#66872—42no—
55#66871—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)C2×C412yes—
59C4⋊(C11⋊C8)C2×C412yes—
60C4×C11⋊C8—21no—
61C4×C11⋊C8—21no—
62#8926—111nomaximal, Sylow
63C2×Q8×C11—22no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—41no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—44no—
88C11×C4⋊C4C4⋊C414yes—
89C11×C4⋊C4SD1612yes—
90C11×C4⋊C4Q1612yes—
91C42×C11—44no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11—41no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×Q811yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C4⋊Dic11—42no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2365D1111yescharacteristic
115#1990—111no—
116#1948—111no—
117#1947—111no—
118C2×#332—111no—
119#1279—111no—
120#1279—111no—
121C23×C11#12011yescharacteristic
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—42no—
125Q8×C11—42no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—24no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C4⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11C2×Q1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11#13511yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C11⋊C8—42no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164C2×C4×Q8—21no—
165C2×#107—221no—
166C2×#106—221no—
167C2×C4⋊C8—111no—
168C2×C4⋊C8—111no—
169C2×C4×C8—111no—
170#391—21no—
171#389—21no—
172#387—22no—
173#384—111no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4C2×D1111yescharacteristic
176C4×C4⋊C4C2×D1111yescharacteristic
177#340—221no—
178#340—221no—
179#340—222no—
180#332—114no—
181C22×C11#38511yescharacteristic
182C22×C11#44911yescharacteristic
183C22×C11#44911yescharacteristic
184C22×C11#45011yescharacteristic
185C22×C11#45111yescharacteristic
186C22×C11#45411yescharacteristic
187C22×C11#45611yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—44no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11C4×SD1611yescharacteristic
196C4×C11C4×Q1611yescharacteristic
197C4×C11#44011yescharacteristic
198C4×C11#44211yescharacteristic
199C4×C11#47611yescharacteristic
200C4×C11#47711yescharacteristic
201C4×C11#47811yescharacteristic
202C4×C11#47911yescharacteristic
203Dic11—161no—
204C22×Q8—21no—
205C22×C8—221no—
206C22×C8—221no—
207C22×C8—221no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8Dic2212yes—
211C4⋊Q8C4×D1112yes—
212C4×Q8—42no—
213C4×Q8—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4C22⋊D1111yescharacteristic
220C2×C4⋊C4C22⋊D1111yescharacteristic
221C2×C4⋊C4C22⋊D1112yes—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C42—22no—
225C2×C42—21no—
226C2×C42—21no—
227C2×C42C22×D1111yescharacteristic
228#107—442no—
229#106—442no—
230C4⋊C8—112no—
231C4⋊C8—112no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4×C8—221no—
235C4×C8—221no—
236#95—22no—
237#95—22no—
238#95—21no—
239#95—21no—
240C2×C11#162811yescharacteristic
241C2×C11#163711yescharacteristic
242C2×C11#164811yescharacteristic
243C2×C11#165411yescharacteristic
244C2×C11#185711yescharacteristic
245C2×C11#186311yescharacteristic
246C2×C11#186411yescharacteristic
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—441no—
259C22×C4C2×C22⋊D1111yescharacteristic
260C22×C4C2×C22⋊D1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—44no—
281C4⋊C4—442no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4Dic11⋊C414yes—
287C4⋊C4#432412yes—
288C4⋊C4#432612yes—
289C42—44no—
290C42—41no—
291C42—41no—
292C42—41no—
293C42—41no—
294C42C2×Dic2211yescharacteristic
295C42C2×C4×D1111yescharacteristic
296C42#433911yescharacteristic
297C42#433911yescharacteristic
298C11#892611yescharacteristic, complemented, Sylow
299C23#6700611yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—42no—
303Q8—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4C2×Dic11⋊C411yescharacteristic
325C2×C4#6697711yescharacteristic
326C2×C4#6697711yescharacteristic
327C2×C4C4×C22⋊D1111yescharacteristic
328C2×C4C4×C22⋊D1111yescharacteristic
329C2×C4#6698211yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4C2×#432411yescharacteristic
332C2×C4#6699511yescharacteristic
333C2×C4C2×#432611yescharacteristic
334C2×C4#6700211yescharacteristic
335C2×C4#6700211yescharacteristic
336C2×C4#6700311yescharacteristic
337C2×C4#6700311yescharacteristic
338C8—442no—
339C8—442no—
340C8—442no—
341C22#1062282311yescharacteristic
342C22#1062283111yescharacteristic
343C22#1062284111yescharacteristic
344C22#1062285111yescharacteristic
345C22#1062285111yescharacteristic
346C22#1062285811yescharacteristic
347C22#1062285911yescharacteristic
348C4—21no—
349C4—21no—
350C4—42no—
351C4—44no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—1761no—
356C4#1062262111yescharacteristic
357C4#1062262211yescharacteristic
358C4#1062262711yescharacteristic
359C4C4×#432411yescharacteristic
360C4#1062263411yescharacteristic
361C4#1062263511yescharacteristic
362C4#1062263911yescharacteristic
363C4C4×#432611yescharacteristic
364C2#1306772611yescharacteristic
365C2#1306778111yescharacteristic
366C2#1306785811yescharacteristic
367C2#1306790011yescharacteristic
368C2#1306883111yescharacteristic
369C2#1306887011yescharacteristic
370C2#1306887711yescharacteristic
subgroupG/H
centerC23#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2365C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#2365D11
hypocenterC11#8926
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2365

Complements

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

NH ≅ G/Ntype
22. #10622185C4semidirect
298. C11#8926semidirect

Maximal subgroups

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

subgroupindex
#130695782
#130693792
#130693742
C2×#106221852
#130664572
C11×#23652
#892611