Finite Group Databasebeta

← #14664630

Subgroups — #14664630

Order 2816.

698 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 71 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#13071936C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic, complemented
3D11×#323C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic, complemented
9C2×#66935—21no—
10C2×C22⋊C4×D11C2211yescharacteristic
11C11×#393C2211yescharacteristic
12#10622844C411yescharacteristic, complemented
13#10622573C2211yescharacteristic
14#10622569—21no—
15#10622568—21no—
16D11×C22⋊C8—21no—
17#10622284C411yescharacteristic, complemented
18#10622278—21no—
19#10622278—21no—
20#10622277C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C22×C22⋊D11—21no—
30C2×#4343—41no—
31C2×#4343—41no—
32C2×#4343—44no—
33C22×D44—21no—
34C22×D44—21no—
35C22×D44C2×C411yescharacteristic
36C22×C4×D11—21no—
37C22×C4×D11C2×C411yescharacteristic
38C22×C4×D11D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11D411yescharacteristic
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—41no—
49C2×(C2×D11)⋊C4—41no—
50C2×(C2×D11)⋊C4C2×C411yescharacteristic
51C2×(C2×D11)⋊C4D411yescharacteristic
52C2×C8×D11—41no—
53#66935—44no—
54C22⋊C4×D11—41no—
55C22⋊C4×D11—41no—
56C11×C22⋊C8—21no—
57C11×#95—21no—
58C11×#95C2×C411yescharacteristic
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11839—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—41no—
72C23×D11—42no—
73C23×D11—81no—
74C23×D11C22⋊C411yescharacteristic
75C23×D11C22⋊C411yescharacteristic
76C2×Q8×C11—42no—
77C2×Q8×C11—41no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—42no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—81no—
87C22×Dic11—21no—
88C22×Dic11—41no—
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91#4343—44no—
92#4343—44no—
93#4343—44no—
94#4343—44no—
95C2×D44—24no—
96C2×D44—41no—
97C2×D44—42no—
98C2×D44—42no—
99C2×D44—42no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—81no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—81no—
113C2×C8×C11—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—42no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—81no—
126(C2×D11)⋊C4—81no—
127(C2×D11)⋊C4—82no—
128(C2×D11)⋊C4—82no—
129C2×C11⋊C8—41no—
130C8×D11—82no—
131#2404—111no—
132#1819—111no—
133C2×#323—111no—
134#1351—111no—
135#1351D1111yescharacteristic, complemented
136#1343—111no—
137#1343—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11#13511yescharacteristic
144C23×C11#13511yescharacteristic
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—22no—
148C22×D11—22no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—42no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—81no—
168C22×D11—81no—
169C22×D11—84no—
170C22×D11—82no—
171C22×D11—82no—
172C22×D11#9911yescharacteristic
173C22×D11#9911yescharacteristic
174Q8×C11—42no—
175Q8×C11—42no—
176C2×C4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C22⋊D11—82no—
190C22⋊D11—82no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—81no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201D44—44no—
202D44—42no—
203D44—42no—
204D44—44no—
205D44—84no—
206C4×D11—42no—
207C4×D11—42no—
208C4×D11—48no—
209C4×D11—42no—
210C4×D11—81no—
211C8×C11—81no—
212C11⋊C8—81no—
213C22×#41—111no—
214C2×#120—221no—
215C22×C22⋊C4—111no—
216C2×C22⋊C8—221no—
217#393—111no—
218#393C2×D1111yescharacteristic
219#392—111no—
220#392—111no—
221#386—221no—
222#386—221no—
223#386—221no—
224#381—111no—
225#379—221no—
226#342—111no—
227#342—221no—
228#342C2×D1111yescharacteristic
229#323—111no—
230#323—221no—
231#323C2×D1111yescharacteristic
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—81no—
241C22×C11C2×#9911yescharacteristic
242C22×C11#41611yescharacteristic
243C22×C11#42111yescharacteristic
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—21no—
247C2×D11—21no—
248C2×D11—21no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—41no—
255C2×D11—42no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—82no—
259C2×D11—82no—
260C2×D11—82no—
261C2×D11—82no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11AΣL(1,𝔽16)12yes—
268C4×C11—42no—
269C4×C11—41no—
270C4×C11—41no—
271C4×C11—81no—
272C4×C11—161no—
273Dic11—41no—
274Dic11—41no—
275Dic11—81no—
276Dic11—161no—
277C25—111no—
278C2×#41—441no—
279C2×#41—441no—
280C2×#41—444no—
281C22×Q8C4×D1111yescharacteristic
282C22×D4—111no—
283C22×D4—221no—
284C22×D4—221no—
285C22×D4—221no—
286C23×C4—111no—
287C23×C4—111no—
288C23×C4—221no—
289C22×C8—441no—
290#120—444no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—441no—
302C2×C22⋊C4—441no—
303C2×C22⋊C4—441no—
304C2×C22⋊C4—441no—
305C2×C22⋊C4C22×D1111yescharacteristic
306C22⋊C8—21no—
307C22⋊C8—221no—
308C22⋊C8—441no—
309#95—21no—
310#95—111no—
311#95—221no—
312#95—221no—
313#95C4×D1111yescharacteristic
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—41no—
317C2×C11—41no—
318C2×C11#151611yescharacteristic
319C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
320C2×C11#212711yescharacteristic
321D11—22no—
322D11—41no—
323D11—81no—
324D11—82no—
325C24—111no—
326C24—111no—
327C24—221no—
328C24—221no—
329C24—221no—
330C24—221no—
331C24—221no—
332C24—441no—
333C24—442no—
334C24—881no—
335C24D4×D1111yescharacteristic
336#41—444no—
337#41—444no—
338#41—444no—
339#41—444no—
340C2×Q8—42no—
341C2×Q8—41no—
342C2×D4—224no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—442no—
347C2×D4—442no—
348C2×D4—442no—
349C2×D4—442no—
350C2×D4—442no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—881no—
354C2×D4—881no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—441no—
370C22×C4—881no—
371C22×C4C2×C4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C2×C8—41no—
374C2×C8—441no—
375C2×C8—882no—
376C22⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—881no—
388C22⋊C4—881no—
389C22⋊C4—882no—
390C22⋊C4—882no—
391C11#1183911yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—41no—
395C23—41no—
396C23—111no—
397C23—111no—
398C23—222no—
399C23—222no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—442no—
416C23—442no—
417C23—441no—
418C23—441no—
419C23—441no—
420C23—881no—
421C23—881no—
422C23—882no—
423C23—882no—
424C23—884no—
425C23C22⋊C4×D1111yescharacteristic
426C23#6696911yescharacteristic
427C23#6697211yescharacteristic
428Q8—42no—
429Q8—42no—
430D4—444no—
431D4—444no—
432D4—442no—
433D4—442no—
434D4—884no—
435D4—882no—
436D4—882no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—448no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4—881no—
464C2×C4—881no—
465C8—81no—
466C8—881no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—112no—
477C22—221no—
478C22—221no—
479C22—221no—
480C22—221no—
481C22—221no—
482C22—442no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—441no—
488C22—442no—
489C22—441no—
490C22—441no—
491C22—881no—
492C22—881no—
493C22—881no—
494C22—882no—
495C22—882no—
496C22—882no—
497C22—882no—
498C22—881no—
499C22—881no—
500C22D11×#9911yescharacteristic
501C22#1062241711yescharacteristic
502C22#1062243411yescharacteristic
503C4—42no—
504C4—41no—
505C4—41no—
506C4—81no—
507C4—161no—
508C4—441no—
509C4—441no—
510C4—881no—
511C4—1761no—
512C2—21no—
513C2—21no—
514C2—41no—
515C2—41no—
516C2—222no—
517C2—441no—
518C2—881no—
519C2—882no—
520C2#1306717111yescharacteristic
521C2D11×AΣL(1,𝔽16)11yescharacteristic
522C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radical#13071936C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11839
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #13068689C2semidirect
3. D11×#323C2semidirect
4. #13066637C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1351C2semidirect
8. C22×#4343C4semidirect
12. #10622844C4semidirect
17. #10622284C4semidirect
20. #10622277C4semidirect
135. #1351D11semidirect
391. C11#11839semidirect

Maximal subgroups

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

subgroupindex
#130719362
#130686892
D11×#3232
#130666372
#130666142
#130666122
C11×#13512
#1183911