Finite Group Databasebeta

← #14672441

Subgroups — #14672441

Order 2816.

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

normal subgroups only

This group has 556 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#13073567C211yesmaximal, characteristic
2#13068602C211yesmaximal, characteristic
3#99×Dic11C211yesmaximal, characteristic
4#13066741C211yesmaximal, characteristic
5#13066740C211yesmaximal, characteristic
6#13066740C211yesmaximal, characteristic
7C11×#1393C211yesmaximal, characteristic
8C2×D4×Dic11C2211yescharacteristic
9C2×#66941C411yescharacteristic, complemented
10C2×#66931—21no—
11C2×#66931—21no—
12C2×C11×#99C2211yescharacteristic
13C2×C11×#99C2211yescharacteristic
14C11×#390C2211yescharacteristic
15#10622834C2211yescharacteristic
16C2×#66898C2211yescharacteristic
17C2×#66898C2211yescharacteristic
18#10622589C411yescharacteristic, complemented
19#10622562—21no—
20#10622562—21no—
21#10622555—21no—
22C22⋊C4×Dic11—21no—
23#10622548C411yescharacteristic, complemented
24C4×Dic11⋊C4C411yescharacteristic, complemented
25#10622165—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×Dic11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×Dic22—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43D4×Dic11—41no—
44D4×Dic11—41no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—41no—
54C2×C4×Dic11—41no—
55C2×C4×Dic11C2×C411yescharacteristic
56C2×C4×Dic11C2×C411yescharacteristic
57#66941—41no—
58#66941—41no—
59#66931—44no—
60#66931—44no—
61C11×#99—21no—
62C11×#99—21no—
63C11×#99—21no—
64C11×#99Q812yescomplemented
65#66898—21no—
66#66898—21no—
67#66898—21no—
68#66898Q812yescomplemented
69C11⋊#95—21no—
70C11⋊#95—41no—
71C11⋊#95—41no—
72#13298—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
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—41no—
84C22×C4×C11—41no—
85C22×C4×C11C22×C411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C2×Dic22—42no—
101C2×Dic22—42no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C22⋊Dic11—22no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—42no—
118C22⋊Dic11—42no—
119C22⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—42no—
123C4⋊Dic11—42no—
124Dic11⋊C4—24no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128Dic11⋊C4—82no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—41no—
132C4×Dic11—82no—
133#2542—111no—
134#1799—111no—
135C4×#99—111no—
136#1393—111no—
137#1393—111no—
138#1393—111no—
139#1393D1111yescharacteristic
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11C2×C22⋊C411yescharacteristic
149C23×C11C22⋊Q811yescharacteristic
150C23×C11C22⋊Q811yescharacteristic
151C23×C11#12411yescharacteristic
152C23×C11C4⋊Q811yescharacteristic
153D4×C11—41no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—41no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11C4×Q811yescharacteristic
172C2×C4×C11C4×Q811yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195C2×Dic11—81no—
196C2×Dic11#9911yescharacteristic
197C2×Dic11#9911yescharacteristic
198Dic22—82no—
199Dic22—82no—
200C2×C4⋊Q8—111no—
201C2×C22⋊Q8—221no—
202C2×C22⋊Q8—221no—
203C2×C4×D4—111no—
204C2×#99—111no—
205C2×#99—111no—
206C2×#99C2×D1111yescharacteristic
207C2×#99C2×D1111yescharacteristic
208#399—221no—
209#399—221no—
210#390—111no—
211#390C2×D1111yescharacteristic
212#384—111no—
213#384—111no—
214#380—221no—
215C4×C4⋊C4—111no—
216C4×C22⋊C4—221no—
217#342—221no—
218#342—221no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11#39111yescharacteristic
236C22×C11C2×#9911yescharacteristic
237C22×C11#41011yescharacteristic
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—42no—
241C4×C11—82no—
242C4×C11—81no—
243C4×C11—161no—
244Dic11—21no—
245Dic11—42no—
246Dic11—41no—
247Dic11—41no—
248Dic11—41no—
249Dic11—82no—
250Dic11—81no—
251Dic11—161no—
252Dic11#35312yes—
253C22×Q8—221no—
254C22×D4C22×D1111yescharacteristic
255C23×C4—111no—
256C23×C4—111no—
257C4⋊Q8—441no—
258C4⋊Q8—441no—
259C22⋊Q8—444no—
260C22⋊Q8—444no—
261C4×D4—441no—
262C4×D4—441no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—441no—
272C2×C4⋊C4C4×D1111yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42—441no—
286C2×C42C4×D1111yescharacteristic
287#99—21no—
288#99—21no—
289#99—21no—
290#99—112no—
291#99—221no—
292#99—221no—
293#99—221no—
294#99Dic2212yescomplemented
295#95—221no—
296#95—441no—
297#95—441no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—41no—
301C2×C11—41no—
302C2×C11—41no—
303C2×C11—41no—
304C2×C11#199611yescharacteristic
305C2×C11C2×#35311yescharacteristic
306C2×C11#212911yescharacteristic
307C24D4×D1111yescharacteristic
308C24D4×D1111yescharacteristic
309C2×Q8—441no—
310C2×Q8—441no—
311C2×Q8—442no—
312C2×Q8—442no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4C2×Dic2211yescharacteristic
316C2×D4#433911yescharacteristic
317C2×D4#434111yescharacteristic
318C2×D4Q8×D1111yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—221no—
333C22×C4—442no—
334C22×C4—442no—
335C22×C4—441no—
336C22×C4—441no—
337C22×C4C2×C4×D1111yescharacteristic
338C4⋊C4—41no—
339C4⋊C4—224no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—442no—
343C4⋊C4—442no—
344C4⋊C4—442no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4—882no—
348C22⋊C4—22no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—222no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—442no—
358C22⋊C4—442no—
359C22⋊C4—441no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C42—41no—
363C42—221no—
364C42—221no—
365C42—441no—
366C42—882no—
367C11#1329811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23#6693111yescharacteristic
377C23C22⋊C4×D1111yescharacteristic
378C23#6693811yescharacteristic
379C23#6694111yescharacteristic
380C23#6694911yescharacteristic
381Q8—882no—
382Q8—882no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—111no—
402C2×C4—111no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4—881no—
426C2×C4C4×Dic2211yescharacteristic
427C2×C4#6694011yescharacteristic
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—81no—
443C22—81no—
444C22#1062225911yescharacteristic
445C22#1062235311yescharacteristic
446C22D11×#9911yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—112no—
453C4—161no—
454C4—221no—
455C4—442no—
456C4—441no—
457C4—441no—
458C4—441no—
459C4—882no—
460C4—881no—
461C4—1761no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—41no—
467C2—41no—
468C2#1306959911yescharacteristic
469C2D11×#35311yescharacteristic
470C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1393C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1393D11
hypocenterC11#13298
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
9. C2×#66941C4semidirect
18. #10622589C4semidirect
23. #10622548C4semidirect
24. C4×Dic11⋊C4C4semidirect
64. C11×#99Q8semidirect
68. #66898Q8semidirect
294. #99Dic22semidirect
367. C11#13298semidirect

Maximal subgroups

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

subgroupindex
#130735672
#130686022
#99×Dic112
#130667412
#130667402
C11×#13932
#1329811