Finite Group Databasebeta

← #14669251

Subgroups — #14669251

Order 2816.

1168 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622174C214yesmaximal, complemented
2#13068544C211yesmaximal, characteristic, complemented
3#13068534C211yesmaximal, characteristic, complemented
4C2×C11×#535C211yesmaximal, characteristic
5C22×C11×#41C2211yescharacteristic
6C23×D4×C11C411yescharacteristic, complemented
7C11×#535—28no—
8C2×C11×#127—21no—
9C2×C11×#124—21no—
10C2×C11×#121—21no—
11C2×C11×#121—21no—
12C2×C11×#120C412yescomplemented
13C2×C11×#120C2212yes—
14C2×C11×#117C411yescharacteristic, complemented
15C2×#66900—21no—
16C2×#66898—21no—
17C2×#66898C2212yes—
18C2×#66897C2212yes—
19#10622824—21no—
20#10622820—21no—
21#10622174—28no—
22C25×C11C2×C412yes—
23C2×C11×#41—24no—
24C2×C11×#41—42no—
25C2×C11×#41—42no—
26C22×Q8×C11D411yescharacteristic
27C22×D4×C11—24no—
28C22×D4×C11—22no—
29C22×D4×C11—22no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—42no—
33C22×D4×C11—42no—
34C22×D4×C11C2×C411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C22×D4×C11C2311yescharacteristic
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C11×#127—28no—
41C11×#124—28no—
42C11×#121—28no—
43C11×#121—28no—
44C11×#120—24no—
45C11×#120—24no—
46C11×#120—24no—
47C11×#120D418yes—
48C11×#117—24no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4C2×C412yes—
53C2×C42×C11—21no—
54C2×C22⋊Dic11—22no—
55C2×#4318—22no—
56#66900—42no—
57#66898—24no—
58#66898—42no—
59#66897—24no—
60C11⋊#95—42no—
61C22⋊(C11⋊C8)—42no—
62#12691—111nomaximal, Sylow
63C24×C11—22no—
64C24×C11—22no—
65C24×C11—42no—
66C24×C11—42no—
67C24×C11—84no—
68C24×C11C22⋊C411yescharacteristic
69C24×C11C22⋊C414yes—
70C24×C11C22×C411yescharacteristic
71C24×C11C2×D411yescharacteristic
72C11×#41—416no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—28no—
81C2×D4×C11—28no—
82C2×D4×C11—22no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—416no—
89C2×D4×C11—42no—
90C2×D4×C11—42no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—84no—
94C2×D4×C11—84no—
95C2×D4×C11C2×D414yes—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×Dic11—42no—
111C11×C4⋊C4—24no—
112C11×C22⋊C4—28no—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—28no—
115C11×C22⋊C4C22⋊C414yes—
116C42×C11—24no—
117C22⋊Dic11—42no—
118C22⋊Dic11—42no—
119#4318—42no—
120#4318—42no—
121C2×C11⋊C8—42no—
122C2×#535D1111yescharacteristic
123C2×AΣL(1,𝔽16)—114no—
124#1785—111no—
125#1782—111no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—24no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—44no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—84no—
144C23×C11—84no—
145C23×C11—88no—
146C23×C11—88no—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11C2×C22⋊C412yes—
149C23×C11#12012yes—
150Q8×C11—44no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—48no—
154D4×C11—48no—
155D4×C11—44no—
156D4×C11—88no—
157D4×C11—88no—
158C2×C4×C11—28no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—24no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11#9912yes—
173C2×C4×C11#9912yes—
174C2×C4×C11#12012yes—
175C2×Dic11—82no—
176C2×Dic11—84no—
177C11⋊C8—82no—
178C22×#41C2×D1111yescharacteristic
179C23×D4Dic1111yescharacteristic, complemented
180#535—28no—
181C2×#127—21no—
182C2×#124—21no—
183C2×#121—21no—
184C2×#121—21no—
185C2×#120Dic1112yescomplemented
186C2×#120C2×D1112yes—
187C2×#117Dic1111yescharacteristic, complemented
188C2×#101—221no—
189C2×#100—112no—
190C2×#99—112no—
191C2×#99—221no—
192#407—221no—
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—44no—
203C22×C11—44no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11—41no—
208C22×C11—44no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—84no—
212C22×C11—88no—
213C22×C11—88no—
214C22×C11—84no—
215C22×C11#37911yescharacteristic
216C22×C11C2×#9911yescharacteristic
217C22×C11C2×#9911yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—44no—
222C4×C11—41no—
223Dic11—162no—
224C25C2×Dic1112yes—
225C2×#41—24no—
226C2×#41—42no—
227C2×#41—42no—
228C22×Q8C22⋊D1111yescharacteristic
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—21no—
233C22×D4—21no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4C2×Dic1111yescharacteristic
237C22×D4C22⋊D1111yescharacteristic
238C22×D4C22×D1111yescharacteristic
239C23×C4C2×Dic1111yescharacteristic
240C23×C4C22⋊D1111yescharacteristic
241C23×C4C22⋊D1111yescharacteristic
242C2×M16—222no—
243#127—28no—
244#124—28no—
245#121—28no—
246#121—28no—
247#120—24no—
248#120—24no—
249#120—24no—
250#120C22⋊D1118yes—
251#117—24no—
252C2×C4⋊C4—21no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4C2×Dic1112yes—
257C2×C42—21no—
258#101—442no—
259#100—224no—
260#99—224no—
261#99—442no—
262C22⋊C8—442no—
263#95—442no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—42no—
267C2×C11—42no—
268C2×C11—81no—
269C2×C11—84no—
270C2×C11#178111yescharacteristic
271C2×C11#212212yes—
272C24—22no—
273C24—22no—
274C24—42no—
275C24—42no—
276C24—84no—
277C24C22⋊Dic1111yescharacteristic
278C24C22⋊Dic1114yes—
279C24C22×Dic1111yescharacteristic
280C24C2×C22⋊D1111yescharacteristic
281#41—416no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×D4—24no—
286C2×D4—24no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—28no—
290C2×D4—28no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—416no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—84no—
303C2×D4—84no—
304C2×D4C2×C22⋊D1114yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—442no—
316C22×C4C22⋊Dic1111yescharacteristic
317C22×C4C22⋊Dic1111yescharacteristic
318C22×C4C22⋊Dic1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320M16—442no—
321M16—442no—
322C2×C8—442no—
323C4⋊C4—24no—
324C22⋊C4—28no—
325C22⋊C4—22no—
326C22⋊C4—28no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4C22⋊Dic1114yes—
330C42—24no—
331C11#1269111yescharacteristic, complemented, Sylow
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—24no—
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—44no—
344C23—44no—
345C23—44no—
346C23—44no—
347C23—42no—
348C23—42no—
349C23—84no—
350C23—84no—
351C23—88no—
352C23—88no—
353C23C2×C22⋊Dic1111yescharacteristic
354C23C2×C22⋊Dic1112yes—
355C23#6700612yes—
356Q8—44no—
357D4—44no—
358D4—44no—
359D4—48no—
360D4—48no—
361D4—44no—
362D4—88no—
363D4—88no—
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—24no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—882no—
379C2×C4—884no—
380C2×C4#6689812yes—
381C2×C4#6689812yes—
382C2×C4#6700612yes—
383C8—882no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—44no—
392C22—44no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—41no—
397C22—44no—
398C22—81no—
399C22—81no—
400C22—84no—
401C22—88no—
402C22—88no—
403C22—84no—
404C22C2×#6689811yescharacteristic
405C22C2×#6689811yescharacteristic
406C22#1062286011yescharacteristic
407C4—22no—
408C4—22no—
409C4—22no—
410C4—44no—
411C4—41no—
412C4—1762no—
413C2—21no—
414C2—21no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2—84no—
419C2#1306853111yescharacteristic
420C2#1307026612yes—
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC2×C11×#535C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenterC2×#535D11
hypocenterC11#12691
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10622174C2semidirect
2. #13068544C2semidirect
3. #13068534C2semidirect
6. C23×D4×C11C4semidirect
12. C2×C11×#120C4semidirect
14. C2×C11×#117C4semidirect
179. C23×D4Dic11semidirect
185. C2×#120Dic11semidirect
187. C2×#117Dic11semidirect
331. C11#12691semidirect

Maximal subgroups

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

subgroupindex
C2×#106221742
#130685442
#130685342
C2×C11×#5352
#1269111