Finite Group Databasebeta

← #14669252

Subgroups — #14669252

Order 2816.

1168 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10623361C211yesmaximal, characteristic
2C2×#10622113C214yesmaximal, complemented
3#13068534C211yesmaximal, characteristic, complemented
4C11×#1785C211yesmaximal, characteristic, complemented
5C22×C11×#41C2211yescharacteristic
6C23×D44C411yescharacteristic, complemented
7#10623361—28no—
8C2×#67000—21no—
9C2×#66993—21no—
10C2×#66990C412yescomplemented
11C2×#66990C2212yes—
12C2×#66983—21no—
13C2×#66983—21no—
14C2×#66979C411yescharacteristic, complemented
15C2×C11×#101—21no—
16C2×C11×#100C2212yes—
17C11×#407—21no—
18C2×#66898—21no—
19C2×#66898C2212yes—
20#10622824—21no—
21#10622113—28no—
22C24×D11C2×C412yes—
23C2×C11×#41—24no—
24C2×C11×#41—42no—
25C2×C11×#41—42no—
26C22×Q8×C11D411yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C22×D4×C11D411yescharacteristic
29C22×D4×C11C2311yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C22×C22⋊D11—22no—
34C22×C22⋊D11—22no—
35C22×D44—24no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—42no—
39C22×D44—42no—
40C2×C11×M16—22no—
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11C2×C412yes—
43#67000—28no—
44#66993—28no—
45#66990—24no—
46#66990—24no—
47#66990—24no—
48#66990D418yes—
49#66983—28no—
50#66983—28no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4—22no—
53#66979—24no—
54C2×C4⋊Dic11—21no—
55C2×C4×Dic11—21no—
56C11×#101—42no—
57C11×#100—24no—
58C11×C22⋊C8—42no—
59#66898—24no—
60#66898—42no—
61C11⋊#95—42no—
62#12691—111nomaximal, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22×C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C23×D11—22no—
67C23×D11—22no—
68C23×D11—42no—
69C23×D11—42no—
70C23×D11—84no—
71C23×D11C22⋊C414yes—
72C11×#41—416no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11C2×D414yes—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C2×C22⋊D11—28no—
99C2×C22⋊D11—28no—
100C2×C22⋊D11—84no—
101C2×C22⋊D11—84no—
102C22×Dic11—22no—
103C22×Dic11—42no—
104C2×D44—24no—
105C2×D44—24no—
106C2×D44—416no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—42no—
110C2×D44—42no—
111C11×M16—42no—
112C11×M16—42no—
113C2×C8×C11—42no—
114C22⋊Dic11—22no—
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11C22⋊C414yes—
118(C2×D11)⋊C4—28no—
119(C2×D11)⋊C4—28no—
120C4⋊Dic11—24no—
121C4×Dic11—24no—
122C2×#535—111no—
123C2×AΣL(1,𝔽16)—114no—
124#1785D1111yescharacteristic, complemented
125#1782—111no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11C2×C22⋊C412yes—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12012yes—
139C22×D11—24no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—44no—
146C22×D11—84no—
147C22×D11—84no—
148C22×D11—88no—
149C22×D11—88no—
150Q8×C11—44no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—44no—
154C2×C4×C11—28no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11#9912yes—
167C2×C4×C11#9912yes—
168C2×C4×C11#12012yes—
169C22⋊D11—88no—
170C22⋊D11—88no—
171C2×Dic11—24no—
172C2×Dic11—44no—
173C2×Dic11—82no—
174C2×Dic11—84no—
175D44—48no—
176D44—48no—
177C8×C11—82no—
178C22×#41C2×D1111yescharacteristic
179C23×D4—111no—
180#535—228no—
181C2×#127—221no—
182C2×#124—221no—
183C2×#121—221no—
184C2×#121—221no—
185C2×#120—112no—
186C2×#120—112no—
187C2×#117—111no—
188C2×#101—21no—
189C2×#100C2×D1112yes—
190C2×#99—112no—
191C2×#99—221no—
192#407—21no—
193#381—221no—
194AΣL(1,𝔽16)—228no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—42no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—41no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#37911yescharacteristic
209C22×C11C2×#9911yescharacteristic
210C22×C11C2×#9911yescharacteristic
211C2×D11—44no—
212C2×D11—44no—
213C2×D11—44no—
214C2×D11—84no—
215C2×D11—88no—
216C2×D11—84no—
217C2×D11—88no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222Dic11—44no—
223Dic11—162no—
224C25—112no—
225C2×#41—24no—
226C2×#41—42no—
227C2×#41—42no—
228C22×Q8C22⋊D1111yescharacteristic
229C22×D4—224no—
230C22×D4—222no—
231C22×D4—222no—
232C22×D4—221no—
233C22×D4—221no—
234C22×D4—442no—
235C22×D4—442no—
236C22×D4C4×D1111yescharacteristic
237C22×D4D4411yescharacteristic
238C22×D4C22×D1111yescharacteristic
239C23×C4C4×D1111yescharacteristic
240C23×C4D4411yescharacteristic
241C23×C4C22⋊D1111yescharacteristic
242C2×M16—22no—
243#127—228no—
244#124—228no—
245#121—228no—
246#121—228no—
247#120—118no—
248#120—224no—
249#120—224no—
250#120—224no—
251#117—224no—
252C2×C4⋊C4—221no—
253C2×C22⋊C4—112no—
254C2×C22⋊C4—222no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—222no—
257C2×C42—221no—
258#101—42no—
259#100—24no—
260#99—224no—
261#99—442no—
262C22⋊C8—42no—
263#95—442no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—42no—
267C2×C11—42no—
268C2×C11—81no—
269C2×C11#178111yescharacteristic
270C2×C11#212212yes—
271D11—84no—
272C24—114no—
273C24—222no—
274C24—222no—
275C24—442no—
276C24—442no—
277C24—884no—
278C24(C2×D11)⋊C411yescharacteristic
279C24C2×C4×D1111yescharacteristic
280C24C2×D4411yescharacteristic
281#41—416no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—224no—
294C2×D4—224no—
295C2×D4—228no—
296C2×D4—228no—
297C2×D4—4416no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—884no—
303C2×D4—884no—
304C2×D4D4×D1114yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—222no—
315C22×C4—442no—
316C22×C4(C2×D11)⋊C411yescharacteristic
317C22×C4(C2×D11)⋊C411yescharacteristic
318C22×C4(C2×D11)⋊C411yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320M16—42no—
321M16—42no—
322C2×C8—42no—
323C4⋊C4—224no—
324C22⋊C4—114no—
325C22⋊C4—228no—
326C22⋊C4—222no—
327C22⋊C4—228no—
328C22⋊C4—442no—
329C22⋊C4—442no—
330C42—224no—
331C11#1269111yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—224no—
343C23—444no—
344C23—444no—
345C23—444no—
346C23—444no—
347C23—442no—
348C23—442no—
349C23—884no—
350C23—884no—
351C23—888no—
352C23—888no—
353C23C22⋊C4×D1112yes—
354C23#6693512yes—
355C23C2×(C2×D11)⋊C411yescharacteristic
356Q8—44no—
357D4—44no—
358D4—44no—
359D4—44no—
360D4—448no—
361D4—448no—
362D4—888no—
363D4—888no—
364C2×C4—28no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—224no—
377C2×C4—444no—
378C2×C4—882no—
379C2×C4—884no—
380C2×C4#6687012yes—
381C2×C4#6687012yes—
382C2×C4#6699012yes—
383C8—82no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—81no—
396C22—81no—
397C22—444no—
398C22—444no—
399C22—444no—
400C22—884no—
401C22—888no—
402C22—888no—
403C22—884no—
404C22C2×#6687011yescharacteristic
405C22C2×#6687011yescharacteristic
406C22#1062256811yescharacteristic
407C4—22no—
408C4—22no—
409C4—22no—
410C4—41no—
411C4—444no—
412C4—1762no—
413C2—21no—
414C2—21no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2—884no—
419C2#1306853011yescharacteristic
420C2#1307026712yes—
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1785C2
socleC22×C11C2×#99
prime radicalC2×#10623361C2
cosocleC22×D4×C11C23
hypercenter#1785D11
hypocenterC11#12691
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
2. C2×#10622113C2semidirect
3. #13068534C2semidirect
4. C11×#1785C2semidirect
6. C23×D44C4semidirect
10. C2×#66990C4semidirect
14. C2×#66979C4semidirect
124. #1785D11semidirect
331. C11#12691semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106221132
#130685342
C11×#17852
#1269111