Finite Group Databasebeta

← #14727678

Subgroups — #14727678

Order 2816.

1282 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1282 conjugacy classes of subgroups — too many to draw. Only its 187 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×#10623041C211yesmaximal, characteristic, complemented
2#13079367C212yesmaximal, complemented
3#13074358C211yesmaximal, characteristic, complemented
4#13067621C214yesmaximal, complemented
5#13067553C214yesmaximal, complemented
6#13067185C212yesmaximal, complemented
7C2×C11×#324C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983—21no—
11C2×#66983C2212yes—
12C2×#66983C2211yescharacteristic
13C2×#66982—21no—
14#10623041—22no—
15#10623041—24no—
16#10623041C2214yes—
17C2×#66950—22no—
18C2×#66948—22no—
19C2×C11×C22⋊C8C2212yes—
20#10622826—21no—
21#10622825C2211yescharacteristic
22#10622728—24no—
23#10622607—22no—
24#10622604C2212yescomplemented
25#10622596C2212yescomplemented
26#10622349—22no—
27#10622349C2214yescomplemented
28#10622345—22no—
29#10622345C2214yescomplemented
30C11×#324C2214yescomplemented
31#10622108C2218yescomplemented
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C2×#4339—24no—
38C2×#4339—24no—
39C2×#4339—44no—
40C2×#4339—44no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44D412yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—22no—
46C22×Dic22—21no—
47C22×C8×C11—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C22⋊Dic11—21no—
53#66983—24no—
54#66983—22no—
55#66983—22no—
56#66983—24no—
57#66983—22no—
58#66983—22no—
59#66983D414yes—
60#66983C2314yes—
61#66982—44no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D412yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—22no—
72C2×D88—24no—
73#66950—28no—
74#66950—28no—
75#66948—28no—
76#66948—28no—
77C11×C22⋊C8—22no—
78C11×C22⋊C8C2314yes—
79C11⋊#95—22no—
80C11⋊#95C2312yes—
81#66885—24no—
82#66885—24no—
83#66882—24no—
84#18292—111nomaximal, Sylow
85C24×C11C2×D411yescharacteristic
86C23×D11—22no—
87C23×D11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—81no—
94C22×C4×C11—81no—
95C22×C4×C11D814yescomplemented
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—24no—
103C2×C22⋊D11—24no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—44no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—44no—
109C2×C22⋊D11—42no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113#4339—48no—
114#4339—416no—
115#4339—48no—
116C2×D44—24no—
117C2×D44—24no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—44no—
121C2×D44—81no—
122C2×D44—82no—
123C2×D44—82no—
124C2×D44C2×D414yes—
125C2×C4×D11—28no—
126C2×C4×D11—48no—
127C2×Dic22—24no—
128C2×Dic22—44no—
129C2×C8×C11—24no—
130C2×C8×C11—82no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C22⋊Dic11—42no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—24no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—24no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—81no—
144C4⋊Dic11C2×D414yes—
145Dic11⋊C4—44no—
146D88—84no—
147C2×#537—111no—
148#3186—112no—
149#2618—111no—
150#1610—114no—
151#1598—114no—
152#1519—112no—
153C2×#324D1111yescharacteristic, complemented
154C23×C11—41no—
155C23×C11—41no—
156C23×C11#12011yescharacteristic
157C23×C11#12011yescharacteristic
158C23×C11C2×D812yes—
159C23×C11AGL(1,ℤ/8)12yes—
160C23×C11C22×D411yescharacteristic
161C22×D11—24no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—42no—
166C22×D11—42no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—81no—
182C2×C4×C11#12012yes—
183C2×C4×C11C2×D814yes—
184C2×C4×C11C22×D412yes—
185C22⋊D11—44no—
186C22⋊D11—44no—
187C22⋊D11—48no—
188C22⋊D11—82no—
189C22⋊D11—82no—
190C2×Dic11—24no—
191C2×Dic11—44no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198D44—44no—
199D44—48no—
200D44—44no—
201D44—82no—
202D44—84no—
203C4×D11—416no—
204Dic22—48no—
205C8×C11—44no—
206C22×#41—221no—
207#537—114no—
208#537—224no—
209#537—222no—
210C2×#123—221no—
211C2×C22⋊Q8—222no—
212C2×#121—112no—
213C2×#121—111no—
214C2×#121—222no—
215C2×#121—221no—
216C22×C4⋊C4C2×D1111yescharacteristic
217#480—114no—
218#480—222no—
219#466—224no—
220#447—114no—
221#447—222no—
222C2×C22⋊C8C2×D1112yes—
223#398—112no—
224#396—222no—
225#394—112no—
226#386—221no—
227#380—111no—
228#327—118no—
229#324C2×D1114yescomplemented
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11#44712yes—
239C22×C11#44712yes—
240C22×C11C2×#12011yescharacteristic
241C22×C11C22×D811yescharacteristic
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C2×D11—44no—
244C2×D11—44no—
245C2×D11—44no—
246C2×D11—88no—
247C2×D11—82no—
248C2×D11—82no—
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—24no—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—42no—
256Dic11—44no—
257Dic11—82no—
258Dic11—81no—
259C2×#41—224no—
260C2×#41—224no—
261C2×#41—444no—
262C2×#41—444no—
263C22×Q8—221no—
264C22×D4—112no—
265C22×D4—111no—
266C22×D4—221no—
267C22×D4—221no—
268C22×D4—222no—
269C22×D4—221no—
270C23×C4—222no—
271C23×C4D4411yescharacteristic
272C23×C4D4411yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C2×D8—224no—
275C22×C8—22no—
276#123—444no—
277C22⋊Q8—228no—
278C22⋊Q8—228no—
279#121—114no—
280#121—114no—
281#121—228no—
282#121—228no—
283#121—224no—
284#121—222no—
285#121—224no—
286#121—222no—
287#121—222no—
288#121—222no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4D4412yes—
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304#107—224no—
305#102—224no—
306#102—224no—
307C22⋊C8—22no—
308C22⋊C8C22×D1114yes—
309#95—112no—
310#95—222no—
311C2×C11—21no—
312C2×C11—22no—
313C2×C11—21no—
314C2×C11—22no—
315C2×C11C2×#44711yescharacteristic
316C2×C11#302011yescharacteristic
317C2×C11#302611yescharacteristic
318D11—84no—
319D11—161no—
320C24—222no—
321C24—221no—
322C24C2×D4411yescharacteristic
323#41—448no—
324#41—4416no—
325#41—448no—
326C2×Q8—224no—
327C2×Q8—444no—
328C2×D4—114no—
329C2×D4—224no—
330C2×D4—224no—
331C2×D4—224no—
332C2×D4—224no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—444no—
336C2×D4—444no—
337C2×D4—444no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—442no—
341C2×D4—442no—
342C2×D4—881no—
343C2×D4—882no—
344C2×D4—882no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—81no—
351C22×C4—81no—
352C22×C4—228no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—221no—
356C22×C4—448no—
357C22×C4D8814yescomplemented
358C22×C4C2×D4412yes—
359C22×C4C2×D4412yes—
360C22×C4C2×D4411yescharacteristic
361C22×C4D4×D1112yes—
362C22×C4D4×D1112yes—
363C22×C4C23×D1111yescharacteristic
364D8—884no—
365C2×C8—24no—
366C2×C8—82no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C4⋊C4—114no—
370C4⋊C4—224no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—444no—
374C4⋊C4—881no—
375C22⋊C4—228no—
376C22⋊C4—224no—
377C22⋊C4—224no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C22⋊C4—444no—
381C22⋊C4—882no—
382C11#1829211yescharacteristic, complemented, Sylow
383C23—41no—
384C23—41no—
385C23—224no—
386C23—444no—
387C23—444no—
388C23—442no—
389C23—442no—
390C23—444no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23#6693511yescharacteristic
395C23#6693511yescharacteristic
396C23C2×D8812yes—
397C23#6696112yes—
398C23C22×D4411yescharacteristic
399Q8—448no—
400D4—444no—
401D4—448no—
402D4—444no—
403D4—444no—
404D4—444no—
405D4—448no—
406D4—882no—
407D4—884no—
408D4—882no—
409D4—882no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—81no—
422C2×C4—224no—
423C2×C4—4416no—
424C2×C4—444no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4#6693512yes—
432C2×C4C2×D8814yes—
433C2×C4C2×D4×D1112yes—
434C8—44no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—444no—
444C22—444no—
445C22—444no—
446C22—888no—
447C22—882no—
448C22—882no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22#1062234512yes—
453C22#1062234512yes—
454C22C2×#6693511yescharacteristic
455C22C22×D8811yescharacteristic
456C22C2×#6696111yescharacteristic
457C4—24no—
458C4—22no—
459C4—22no—
460C4—42no—
461C4—444no—
462C4—882no—
463C4—881no—
464C2—21no—
465C2—22no—
466C2—21no—
467C2—22no—
468C2—884no—
469C2—1761no—
470C2C2×#1062234511yescharacteristic
471C2#1307798311yescharacteristic
472C2#1307801511yescharacteristic
subgroupG/H
centerC22C2×#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC22×C11C2×#120
hypercenterC2×#324D11
hypocenterC11#18292
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. #13079367C2semidirect
3. #13074358C2semidirect
4. #13067621C2semidirect
5. #13067553C2semidirect
6. #13067185C2semidirect
7. C2×C11×#324C2semidirect
24. #10622604C22semidirect
25. #10622596C22semidirect
27. #10622349C22semidirect
29. #10622345C22semidirect
30. C11×#324C22semidirect
31. #10622108C22semidirect
95. C22×C4×C11D8semidirect
153. C2×#324D11semidirect
229. #324C2×D11semidirect
357. C22×C4D88semidirect
382. C11#18292semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130793672
#130743582
#130676212
#130675532
#130671852
C2×C11×#3242
#1829211