Finite Group Databasebeta

← #14664274

Subgroups — #14664274

Order 2816.

622 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622168C211yesmaximal, characteristic, complemented
2#13066946C211yesmaximal, characteristic, complemented
3#13066646C212yesmaximal, complemented
4#13066619C212yesmaximal, complemented
5C11×#2406C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic
7C2×C11×#123—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×#4318—21no—
10C11×#395C411yescharacteristic
11C11×#395C2211yescharacteristic
12C11×#394C411yescharacteristic
13C11×#394C2211yescharacteristic
14C11×#386—21no—
15C11×#385—21no—
16C11×#385—21no—
17C11×#381C411yescharacteristic
18#10622820—21no—
19#10622168—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C2×C11×#41—41no—
24C2×C11×#41—41no—
25C2×C11×#41—44no—
26C22×Q8×C11C2×C411yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C11×#123—44no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C4⋊C4—41no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4C2311yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×#4318—24no—
48C2×#4318—22no—
49C2×#4318—41no—
50C2×#4318—42no—
51C2×#4318—41no—
52C22×C11⋊C8—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11×#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11762—111nomaximal, Sylow
61C24×C11—21no—
62C24×C11C22⋊C411yescharacteristic
63C11×#41—44no—
64C11×#41—44no—
65C11×#41—44no—
66C11×#41—44no—
67C2×Q8×C11—42no—
68C2×Q8×C11—41no—
69C2×D4×C11—24no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110#4318—24no—
111#4318—44no—
112#4318—42no—
113#4318—82no—
114C2×C11⋊C8—44no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—42no—
117#2406D1111yescharacteristic
118C2×#343—111no—
119#1463—111no—
120#1354—112no—
121#1345—112no—
122C23×C11—22no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—22no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11#9911yescharacteristic
134C23×C11#9911yescharacteristic
135C23×C11C2×C22⋊C411yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138D4×C11—44no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—44no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—48no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—81no—
172C2×C4×C11#10412yes—
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C11⋊C8—44no—
176C11⋊C8—82no—
177C22×#41Dic1111yescharacteristic
178C22×M16—221no—
179C2×#123—21no—
180C22×C4⋊C4C2×D1111yescharacteristic
181#407—221no—
182#395Dic1111yescharacteristic
183#395C2×D1111yescharacteristic
184#394Dic1111yescharacteristic
185#394C2×D1111yescharacteristic
186#386—21no—
187#385—21no—
188#385—21no—
189#381Dic1111yescharacteristic
190#343—112no—
191#343—221no—
192#324—112no—
193#324—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11AΣL(1,𝔽16)12yes—
211C22×C11C2×#9911yescharacteristic
212C22×C11#41711yescharacteristic
213C22×C11C2×#10411yescharacteristic
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—41no—
218C4×C11—42no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—81no—
223C4×C11—81no—
224C2×#41—41no—
225C2×#41—41no—
226C2×#41—44no—
227C22×Q8C2×Dic1111yescharacteristic
228C22×D4—21no—
229C22×D4C2×Dic1111yescharacteristic
230C23×C4—21no—
231C23×C4C2×Dic1111yescharacteristic
232C23×C4C22⋊D1111yescharacteristic
233C23×C4C22⋊D1111yescharacteristic
234C2×M16—224no—
235C2×M16—222no—
236C2×M16—441no—
237C2×M16—442no—
238C2×M16—441no—
239C22×C8—441no—
240#123—44no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4—41no—
245C2×C4⋊C4C2×Dic1111yescharacteristic
246C2×C4⋊C4C22⋊D1111yescharacteristic
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C4⋊C4C22×D1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C22⋊C8—222no—
255C22⋊C8—441no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95C2×Dic1111yescharacteristic
260#95C2×Dic1111yescharacteristic
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—22no—
264C2×C11—41no—
265C2×C11—82no—
266C2×C11#150411yescharacteristic
267C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
268C2×C11#213311yescharacteristic
269C24—21no—
270C24C22⋊Dic1111yescharacteristic
271#41—44no—
272#41—44no—
273#41—44no—
274#41—44no—
275C2×Q8—42no—
276C2×Q8—41no—
277C2×D4—24no—
278C2×D4—41no—
279C2×D4—42no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4C22⋊Dic1111yescharacteristic
301C22×C4C22⋊Dic1111yescharacteristic
302C22×C4C22⋊Dic1111yescharacteristic
303C22×C4C22×Dic1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306M16—224no—
307M16—444no—
308M16—442no—
309M16—882no—
310C2×C8—444no—
311C2×C8—442no—
312C2×C8—442no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C11#1176211yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—22no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23#6689811yescharacteristic
338C23#6689811yescharacteristic
339C23C2×C22⋊Dic1111yescharacteristic
340Q8—42no—
341Q8—42no—
342D4—44no—
343D4—42no—
344D4—42no—
345D4—44no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—48no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4#6690112yes—
377C2×C4#6700211yescharacteristic
378C2×C4#6700411yescharacteristic
379C8—444no—
380C8—882no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22#1062217412yes—
398C22C2×#6689811yescharacteristic
399C22#1062284511yescharacteristic
400C22C2×#6690111yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—41no—
405C4—41no—
406C4—42no—
407C4—41no—
408C4—41no—
409C4—81no—
410C4—81no—
411C2—21no—
412C2—21no—
413C2—22no—
414C2—41no—
415C2—82no—
416C2#1306712011yescharacteristic
417C2C2×#1062217411yescharacteristic
418C2#1307030511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2406C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2406D11
hypocenterC11#11762
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
1. C2×#10622168C2semidirect
2. #13066946C2semidirect
3. #13066646C2semidirect
4. #13066619C2semidirect
325. C11#11762semidirect

Maximal subgroups

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

subgroupindex
C2×#106221682
#130669462
#130666462
#130666192
C11×#24062
#1176211