Finite Group Databasebeta

← #14786224

Subgroups — #14786224

Order 2816.

1474 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1474 conjugacy classes of subgroups — too many to draw. Only its 199 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
1#13076906C212yesmaximal, complemented
2C2×#10622556C211yesmaximal, characteristic, complemented
3#13069782C212yesmaximal, complemented
4#13069745C212yesmaximal, complemented
5#13069070C212yesmaximal, complemented
6#13069029C214yesmaximal, complemented
7#13068690C211yesmaximal, characteristic, complemented
8C11×#3490C211yesmaximal, characteristic
9C24×Dic11C2211yescharacteristic
10C11×#551—24no—
11C11×#546—24no—
12C11×#543C2211yescharacteristic
13C11×#538—22no—
14C11×#534C2211yescharacteristic
15C11×#525—22no—
16C2×C11×#120C2212yes—
17C11×#518C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C2×#66988C2214yes—
21#10622860C2212yes—
22#10622833—24no—
23C2×#66898C2214yes—
24C2×C11⋊#95—22no—
25#10622559—24no—
26#10622556—22no—
27#10622556C2212yes—
28#10622556C2212yes—
29#10622556C2214yes—
30#10622164C2214yes—
31#10622164C2212yes—
32#10622164C2212yes—
33C25×C11C2311yescharacteristic
34C2×C11×#41—22no—
35C22×D4×C11D414yes—
36C22×D4×C11C2312yes—
37C23×C4×C11D412yes—
38C23×Dic11—21no—
39C23×Dic11—21no—
40C23×Dic11—24no—
41C23×Dic11—24no—
42C23×Dic11—21no—
43C23×Dic11—42no—
44C23×Dic11C2312yes—
45C11×#126—24no—
46C11×#124—24no—
47C11×#123—24no—
48C11×#123—24no—
49C11×#123—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×#121—22no—
54C11×#121—24no—
55C11×#121—22no—
56C11×#120—22no—
57C11×#120—22no—
58C11×#120—24no—
59C11×#120—22no—
60C4×D4×C11—24no—
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C11×#117—22no—
64C11×#117—22no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C11×C22⋊C4D414yes—
69C2×C11×C22⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4C2312yes—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2312yes—
77C2×C22⋊Dic11C2314yes—
78#66988—28no—
79#66988—44no—
80C2×Dic11⋊C4—24no—
81#66898—44no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—28no—
85#23985—111nomaximal, Sylow
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—44no—
89C24×C11C2×D411yescharacteristic
90C24×C11C2×D414yes—
91C24×C11C2×D412yes—
92C24×C11C2×D411yescharacteristic
93C24×C11C2411yescharacteristic
94C11×#41—84no—
95C2×Q8×C11—22no—
96C2×D4×C11—24no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—48no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—44no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D414yes—
111C22×C4×C11C2×D412yes—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—22no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—24no—
120C22×Dic11—416no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11—44no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11#4114yescomplemented
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C42×C11—24no—
142C22⋊Dic11—24no—
143C22⋊Dic11—24no—
144C22⋊Dic11—24no—
145C22⋊Dic11—48no—
146C22⋊Dic11—48no—
147C22⋊Dic11—42no—
148Dic11⋊C4—48no—
149#3490D1111yescharacteristic
150#2849—112no—
151C2×#381—111no—
152#2030—112no—
153#2022—112no—
154#1898—112no—
155#1890—114no—
156#1819—111no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—24no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—28no—
163C23×C11—28no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—42no—
167C23×C11—44no—
168C23×C11—42no—
169C23×C11—48no—
170C23×C11—48no—
171C23×C11—44no—
172C23×C11#12012yes—
173C23×C11#12012yes—
174C23×C11C22×D411yescharacteristic
175C23×C11C22×D412yes—
176C23×C11C2×#4112yes—
177C23×C11H(5,𝔽2)12yes—
178Q8×C11—82no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—44no—
182D4×C11—48no—
183D4×C11—84no—
184D4×C11—82no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—44no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—44no—
194C2×C4×C11—82no—
195C2×C4×C11—84no—
196C2×Dic11—24no—
197C2×Dic11—28no—
198C2×Dic11—48no—
199C2×Dic11—48no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—44no—
203C2×Dic11—48no—
204C2×Dic11—44no—
205C2×Dic11—42no—
206C2×Dic11—44no—
207C2×Dic11—84no—
208C24×C4—111no—
209#551—24no—
210#546—24no—
211#543C2×D1111yescharacteristic
212#538—22no—
213#534C2×D1111yescharacteristic
214#525—22no—
215C2×#123—114no—
216C2×#120C2×D1112yes—
217#518C2×D1112yes—
218C22×C22⋊C4—111no—
219C22×C22⋊C4C2×D1111yescharacteristic
220C2×#99—114no—
221#386—224no—
222#385—224no—
223#381—114no—
224#381—112no—
225#381—112no—
226#381—222no—
227#379—112no—
228C2×#95—222no—
229#342—112no—
230#342—112no—
231#342—114no—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—24no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—24no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—416no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—44no—
247C22×C11—84no—
248C22×C11#45814yes—
249C22×C11C2×#12011yescharacteristic
250C22×C11#52511yescharacteristic
251C22×C11#53511yescharacteristic
252C22×C11#54614yes—
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—44no—
257Dic11—44no—
258Dic11—84no—
259Dic11—82no—
260C25C22×D1111yescharacteristic
261C2×#41—22no—
262C22×D4C22⋊D1114yes—
263C22×D4C22×D1112yes—
264C23×C4—112no—
265C23×C4—224no—
266C23×C4—221no—
267C23×C4—221no—
268C23×C4—221no—
269C23×C4—224no—
270C23×C4—442no—
271C23×C4C22⋊D1112yes—
272#126—24no—
273#124—24no—
274#123—24no—
275#123—24no—
276#123—22no—
277#123—228no—
278#123—444no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—24no—
282#121—22no—
283#121—24no—
284#121—22no—
285#120—22no—
286#120—22no—
287#120—24no—
288#120—22no—
289C4×D4—24no—
290C4×D4—24no—
291C4×D4—24no—
292#117—22no—
293#117—22no—
294C2×C4⋊C4—224no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—112no—
298C2×C22⋊C4—114no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—224no—
301C2×C22⋊C4—224no—
302C2×C22⋊C4—442no—
303C2×C22⋊C4C22⋊D1112yes—
304C2×C22⋊C4C22⋊D1114yes—
305C2×C22⋊C4C22×D1111yescharacteristic
306C2×C22⋊C4C22×D1111yescharacteristic
307C2×C22⋊C4C22×D1112yes—
308#99—444no—
309#95—224no—
310#95—224no—
311#95—228no—
312C2×C11—21no—
313C2×C11—24no—
314C2×C11—21no—
315C2×C11—24no—
316C2×C11—42no—
317C2×C11—82no—
318C2×C11#240411yescharacteristic
319C2×C11C2×#45812yes—
320C24—22no—
321C24—22no—
322C24—44no—
323C24C2×C22⋊D1111yescharacteristic
324C24C2×C22⋊D1114yes—
325C24C2×C22⋊D1112yes—
326C24C2×C22⋊D1111yescharacteristic
327C24C23×D1111yescharacteristic
328#41—84no—
329C2×Q8—22no—
330C2×D4—24no—
331C2×D4—24no—
332C2×D4—24no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—24no—
337C2×D4—48no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—44no—
342C22×C4—114no—
343C22×C4—224no—
344C22×C4—224no—
345C22×C4—222no—
346C22×C4—224no—
347C22×C4—222no—
348C22×C4—224no—
349C22×C4—222no—
350C22×C4—224no—
351C22×C4—4416no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—442no—
356C22×C4—442no—
357C22×C4—444no—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1114yes—
361C22×C4C2×C22⋊D1112yes—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—448no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—224no—
377C22⋊C4—224no—
378C22⋊C4—224no—
379C22⋊C4—448no—
380C22⋊C4—442no—
381C22⋊C4—448no—
382C42—24no—
383C11#2398511yescharacteristic, complemented, Sylow
384C23—21no—
385C23—21no—
386C23—24no—
387C23—21no—
388C23—28no—
389C23—21no—
390C23—28no—
391C23—22no—
392C23—24no—
393C23—42no—
394C23—44no—
395C23—42no—
396C23—48no—
397C23—48no—
398C23—44no—
399C23#6700612yes—
400C23#6700612yes—
401C23#41×D1112yes—
402C23#6704212yes—
403C23C22×C22⋊D1111yescharacteristic
404C23C22×C22⋊D1112yes—
405Q8—82no—
406D4—42no—
407D4—44no—
408D4—42no—
409D4—48no—
410D4—84no—
411D4—82no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—82no—
422C2×C4—84no—
423C2×C4—224no—
424C2×C4—228no—
425C2×C4—448no—
426C2×C4—448no—
427C2×C4—444no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—448no—
431C2×C4—444no—
432C2×C4—444no—
433C2×C4—442no—
434C2×C4—884no—
435C22—24no—
436C22—24no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—22no—
441C22—22no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—416no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—44no—
450C22—84no—
451C22#1062285614yes—
452C22#1062335911yescharacteristic
453C22#1062336014yes—
454C22#1062336111yescharacteristic
455C22C2×#6700611yescharacteristic
456C4—42no—
457C4—42no—
458C4—42no—
459C4—44no—
460C4—444no—
461C4—882no—
462C4—884no—
463C2—21no—
464C2—24no—
465C2—21no—
466C2—24no—
467C2—42no—
468C2—82no—
469C2#1307193111yescharacteristic
470C2C2×#1062285612yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
Fitting, prime radicalC11×#3490C2
socleC22×C11C2×#120
hypercenter#3490D11
hypocenterC11#23985
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #13076906C2semidirect
2. C2×#10622556C2semidirect
3. #13069782C2semidirect
4. #13069745C2semidirect
5. #13069070C2semidirect
6. #13069029C2semidirect
7. #13068690C2semidirect
127. C22×Dic11#41semidirect
383. C11#23985semidirect

Maximal subgroups

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

subgroupindex
#130769062
C2×#106225562
#130697822
#130697452
#130690702
#130690292
#130686902
C11×#34902
#2398511