Finite Group Databasebeta

← #14672419

Subgroups — #14672419

Order 2816.

612 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 93 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#13071978C211yesmaximal, characteristic
2#13068602C211yesmaximal, characteristic
3#100×Dic11C211yesmaximal, characteristic
4#13066735C211yesmaximal, characteristic
5#13066734C211yesmaximal, characteristic
6#13066733C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8C23×Dic22C411yescharacteristic, complemented
9C2×D4×Dic11C2211yescharacteristic
10C2×#66931—21no—
11C2×C11×#100C2211yescharacteristic
12C2×C11×#99C2211yescharacteristic
13C11×#386C2211yescharacteristic
14#10622833C2211yescharacteristic
15C2×#66898C2211yescharacteristic
16C2×#66897C2211yescharacteristic
17#10622823C411yescharacteristic, complemented
18M16×Dic11—21no—
19#10622563C411yescharacteristic, complemented
20#10622560—21no—
21#10622555—21no—
22#10622555C411yescharacteristic, complemented
23#10622269—21no—
24#10622259—21no—
25#10622192—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C23×Dic11C2×C411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22—21no—
33C22×Dic22—21no—
34C22×Dic22—44no—
35C22×Dic22—41no—
36C22×Dic22—41no—
37C2×C11×M16—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11C2×C411yescharacteristic
44C2×C22⋊Dic11C2×C411yescharacteristic
45C2×C22⋊Dic11D411yescharacteristic
46D4×Dic11—41no—
47D4×Dic11—41no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—41no—
53C2×C4×Dic11D411yescharacteristic
54C2×#4318—21no—
55#66931—44no—
56C11×#100—21no—
57C11×#100Q812yescomplemented
58C11×#99—21no—
59C11×#99—21no—
60C11×#95—21no—
61#66898—21no—
62#66898—21no—
63#66897—21no—
64#66897Q812yescomplemented
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—41no—
70#66879—41no—
71C8×Dic11—41no—
72#13293—111nomaximal, Sylow
73C24×C11C22×C411yescharacteristic
74C24×C11C2×D411yescharacteristic
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11C2×Q811yescharacteristic
78C2×D4×C11C2×Q811yescharacteristic
79C2×D4×C11#4111yescharacteristic
80C2×D4×C11#4111yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—42no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C22×Dic11—41no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×Dic22—24no—
103C2×Dic22—42no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C2×Dic22—42no—
107C2×Dic22—44no—
108C2×Dic22—44no—
109C2×Dic22—44no—
110C2×Dic22—41no—
111C2×Dic22—41no—
112C2×Dic22—44no—
113C11×M16—22no—
114C11×M16—41no—
115C2×C8×C11—41no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C22⋊Dic11—42no—
125C22⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—42no—
128Dic11⋊C4—42no—
129Dic11⋊C4—42no—
130Dic11⋊C4—82no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133#4318—22no—
134#4318—41no—
135C2×C11⋊C8—41no—
136#2409—111no—
137#1799—111no—
138C4×#100—111no—
139#1390—111no—
140#1390—111no—
141#1390—111no—
142#1390D1111yescharacteristic
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C2×C22⋊C411yescharacteristic
152C23×C11C4×Q811yescharacteristic
153C23×C11C4×Q811yescharacteristic
154C23×C11#12411yescharacteristic
155C23×C11C4⋊Q811yescharacteristic
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×C4×C11C22⋊Q811yescharacteristic
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—42no—
183C2×Dic11—41no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197C2×Dic11#9911yescharacteristic
198C2×Dic11#9911yescharacteristic
199Dic22—44no—
200Dic22—48no—
201Dic22—44no—
202C8×C11—42no—
203C11⋊C8—42no—
204C23×Q8—111no—
205C2×C22⋊Q8—221no—
206C2×C4×D4—111no—
207C2×#100—111no—
208C2×#100C2×D1111yescharacteristic
209C2×#99—111no—
210C2×#99C2×D1111yescharacteristic
211C4×M16—221no—
212#395—221no—
213#393—221no—
214#391—221no—
215#386—111no—
216#386C2×D1111yescharacteristic
217#385—111no—
218#385—111no—
219#380—111no—
220#380—221no—
221#343—221no—
222#342—221no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—81no—
239C22×C11#39111yescharacteristic
240C22×C11C2×#9911yescharacteristic
241C22×C11#41011yescharacteristic
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—42no—
245C4×C11—81no—
246C4×C11—161no—
247Dic11—21no—
248Dic11—42no—
249Dic11—41no—
250Dic11—41no—
251Dic11—41no—
252Dic11—81no—
253Dic11—161no—
254Dic11AΣL(1,𝔽16)12yes—
255C22×Q8—221no—
256C22×Q8—221no—
257C22×Q8—441no—
258C22×Q8—441no—
259C22×Q8—444no—
260C22×D4C22×D1111yescharacteristic
261C23×C4—111no—
262C23×C4—111no—
263C23×C4—111no—
264C23×C4C4×D1111yescharacteristic
265C2×M16—21no—
266C2×M16—221no—
267C22⋊Q8—444no—
268C4×D4—441no—
269C4×D4—441no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—441no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4C4×D1111yescharacteristic
283C2×C42—111no—
284#100—21no—
285#100—112no—
286#100—221no—
287#100Dic2212yescomplemented
288#99—21no—
289#99—21no—
290#99—221no—
291#99—221no—
292#97—441no—
293C4×C8—441no—
294#95—21no—
295#95—221no—
296#95—221no—
297#95—221no—
298#95—221no—
299#95—441no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—41no—
303C2×C11—41no—
304C2×C11—41no—
305C2×C11—41no—
306C2×C11#199611yescharacteristic
307C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
308C2×C11#212311yescharacteristic
309C24C2×C4×D1111yescharacteristic
310C24D4×D1111yescharacteristic
311C2×Q8—224no—
312C2×Q8—442no—
313C2×Q8—441no—
314C2×Q8—441no—
315C2×Q8—442no—
316C2×Q8—442no—
317C2×Q8—442no—
318C2×Q8—444no—
319C2×Q8—444no—
320C2×Q8—444no—
321C2×Q8—444no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4C2×Dic2211yescharacteristic
325C2×D4#433911yescharacteristic
326C2×D4#434111yescharacteristic
327C2×D4Q8×D1111yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—442no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349M16—22no—
350M16—41no—
351M16—222no—
352M16—441no—
353C2×C8—41no—
354C2×C8—441no—
355C4⋊C4—441no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—882no—
360C22⋊C4—42no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—442no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—221no—
371C42—221no—
372C11#1329311yescharacteristic, complemented, Sylow
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23C4×Dic2211yescharacteristic
382C23C22⋊C4×D1111yescharacteristic
383C23#6693811yescharacteristic
384C23#6694011yescharacteristic
385C23#6694111yescharacteristic
386Q8—444no—
387Q8—444no—
388Q8—448no—
389D4—41no—
390D4—41no—
391D4—41no—
392D4—41no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—111no—
407C2×C4—111no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—442no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4#6693111yescharacteristic
431C2×C4#6694911yescharacteristic
432C8—42no—
433C8—442no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—81no—
450C22#1062225911yescharacteristic
451C22#1062235311yescharacteristic
452C22D11×#9911yescharacteristic
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—112no—
458C4—161no—
459C4—221no—
460C4—442no—
461C4—441no—
462C4—441no—
463C4—441no—
464C4—881no—
465C4—1761no—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2#1306959911yescharacteristic
473C2D11×AΣL(1,𝔽16)11yescharacteristic
474C2#1307026811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1390C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1390D11
hypocenterC11#13293
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
8. C23×Dic22C4semidirect
17. #10622823C4semidirect
19. #10622563C4semidirect
22. #10622555C4semidirect
57. C11×#100Q8semidirect
64. #66897Q8semidirect
287. #100Dic22semidirect
372. C11#13293semidirect

Maximal subgroups

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

subgroupindex
#130719782
#130686022
#100×Dic112
#130667352
#130667342
#130667332
C11×#13902
#1329311