Finite Group Databasebeta

← #14664248

Subgroups — #14664248

Order 2816.

700 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073543C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic, complemented
3#13066941C211yesmaximal, characteristic, complemented
4#13066640C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic, complemented
9C2×#66947—21no—
10C2×#66935—21no—
11C2×C22⋊C4×D11—21no—
12C2×C22⋊C4×D11C2211yescharacteristic
13C11×#399C2211yescharacteristic
14#10622605C411yescharacteristic, complemented
15#10622601—21no—
16#10622573C2211yescharacteristic
17#10622570—21no—
18#10622339—21no—
19#10622284C411yescharacteristic, complemented
20#10622279C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44C2×C411yescharacteristic, complemented
32C22×C4×D11—41no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—41no—
48C2×(C2×D11)⋊C4C2×C411yescharacteristic
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×#4313—41no—
53#66948—41no—
54#66948—41no—
55#66947—44no—
56#66935—44no—
57C22⋊C4×D11—24no—
58C22⋊C4×D11—41no—
59C22⋊C4×D11—41no—
60C22⋊C4×D11—42no—
61C11×C22⋊C8—21no—
62C11×#95C2×C411yescharacteristic, complemented
63C11⋊#95C2×C411yescharacteristic, complemented
64C22⋊(C11⋊C8)—21no—
65(C2×D11)⋊C8—41no—
66#11757—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C23×D11—21no—
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—22no—
73C23×D11—21no—
74C23×D11—42no—
75C23×D11—81no—
76C23×D11C22⋊C411yescharacteristic
77C23×D11C22⋊C411yescharacteristic
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
91C2×D44—42no—
92C2×D44—41no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—42no—
98C2×D44—81no—
99C2×D44—81no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—42no—
105C2×C4×D11—44no—
106C2×C4×D11—81no—
107C2×C4×D11—82no—
108C2×C4×D11—82no—
109C2×C8×C11—41no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—41no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119(C2×D11)⋊C4—24no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—44no—
124(C2×D11)⋊C4—42no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127Dic11⋊C4—42no—
128C4×Dic11—81no—
129C2×C11⋊C8—41no—
130#4313—82no—
131#2539—111no—
132C2×#342—111no—
133#1462—111no—
134#1352—111no—
135#1352D1111yescharacteristic, complemented
136#1343—111no—
137#1343—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11AGL(1,ℤ/8)11yescharacteristic
144C23×C11#13711yescharacteristic
145C22×D11—22no—
146C22×D11—22no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—22no—
151C22×D11—22no—
152C22×D11—21no—
153C22×D11—22no—
154C22×D11—41no—
155C22×D11—42no—
156C22×D11—42no—
157C22×D11—41no—
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—81no—
167C22×D11—81no—
168C22×D11—84no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11#9911yescharacteristic
172C22×D11#9911yescharacteristic
173C22×D11#10412yes—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C22⋊D11—82no—
188C22⋊D11—82no—
189C2×Dic11—22no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199D44—84no—
200D44—82no—
201D44—82no—
202D44—82no—
203C4×D11—42no—
204C4×D11—81no—
205C4×D11—81no—
206C4×D11—81no—
207C4×D11—88no—
208C8×C11—81no—
209C11⋊C8—81no—
210C2×#123—221no—
211C2×#121—111no—
212C2×#120—221no—
213C22×C22⋊C4—111no—
214C22×C22⋊C4—221no—
215#407—221no—
216#399—111no—
217#399C2×D1111yescharacteristic
218#392—111no—
219#392—111no—
220#390—221no—
221#390—221no—
222C4×C22⋊C4—111no—
223#342—111no—
224#342—221no—
225#342C2×D1111yescharacteristic
226#323—111no—
227#323—221no—
228#323C2×D1111yescharacteristic
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—81no—
238C22×C11C2×#9911yescharacteristic
239C22×C11#41711yescharacteristic
240C22×C11C2×#10411yescharacteristic
241C2×D11—21no—
242C2×D11—21no—
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—22no—
247C2×D11—42no—
248C2×D11—42no—
249C2×D11—44no—
250C2×D11—44no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—42no—
254C2×D11—81no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C2×D11—81no—
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11#35312yes—
265C4×C11—42no—
266C4×C11—41no—
267C4×C11—41no—
268C4×C11—82no—
269C4×C11—81no—
270Dic11—42no—
271Dic11—41no—
272Dic11—41no—
273Dic11—82no—
274C25—111no—
275C22×D4—111no—
276C22×D4—221no—
277C22×D4—221no—
278C22×D4—221no—
279C23×C4—111no—
280C23×C4—111no—
281C23×C4—441no—
282C2×M16—441no—
283#123—444no—
284#121—441no—
285#121—441no—
286#120—444no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C4×D1111yescharacteristic, complemented
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—224no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—441no—
303C2×C22⋊C4—441no—
304C2×C22⋊C4—442no—
305C2×C22⋊C4—441no—
306C2×C22⋊C4C22×D1111yescharacteristic
307C2×C42—221no—
308C22⋊C8—21no—
309C22⋊C8—221no—
310C22⋊C8—441no—
311#95—111no—
312#95C4×D1111yescharacteristic, complemented
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—41no—
316C2×C11—41no—
317C2×C11#150411yescharacteristic
318C2×C11#212111yescharacteristic
319C2×C11C2×#35311yescharacteristic
320D11—22no—
321D11—41no—
322D11—42no—
323D11—161no—
324C24—111no—
325C24—111no—
326C24—221no—
327C24—222no—
328C24—221no—
329C24—221no—
330C24—221no—
331C24—221no—
332C24—442no—
333C24—881no—
334C24D4×D1111yescharacteristic
335C2×D4—441no—
336C2×D4—442no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—442no—
340C2×D4—442no—
341C2×D4—442no—
342C2×D4—442no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—881no—
346C2×D4—881no—
347C2×D4—881no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—442no—
359C22×C4—444no—
360C22×C4—441no—
361C22×C4—881no—
362C22×C4—882no—
363C22×C4—882no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366M16—882no—
367C2×C8—41no—
368C2×C8—441no—
369C4⋊C4—41no—
370C4⋊C4—42no—
371C4⋊C4—442no—
372C22⋊C4—22no—
373C22⋊C4—41no—
374C22⋊C4—42no—
375C22⋊C4—41no—
376C22⋊C4—224no—
377C22⋊C4—222no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—442no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C22⋊C4—444no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—881no—
388C11#1175711yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—111no—
394C23—111no—
395C23—112no—
396C23—222no—
397C23—222no—
398C23—222no—
399C23—222no—
400C23—222no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23—442no—
413C23—442no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—881no—
418C23—881no—
419C23—882no—
420C23—882no—
421C23—884no—
422C23C22⋊C4×D1111yescharacteristic
423C23#6696711yescharacteristic
424C23#6697111yescharacteristic
425D4—884no—
426D4—882no—
427D4—882no—
428D4—882no—
429D4—882no—
430D4—882no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—222no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—442no—
453C2×C4—881no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—888no—
457C2×C4—881no—
458C2×C4—881no—
459C8—81no—
460C8—881no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—81no—
470C22—112no—
471C22—221no—
472C22—221no—
473C22—221no—
474C22—222no—
475C22—221no—
476C22—221no—
477C22—442no—
478C22—442no—
479C22—442no—
480C22—444no—
481C22—444no—
482C22—441no—
483C22—441no—
484C22—881no—
485C22—881no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22—882no—
490C22—882no—
491C22—881no—
492C22—881no—
493C22—881no—
494C22D11×#9911yescharacteristic
495C22#1062241611yescharacteristic
496C22D11×#10411yescharacteristic
497C4—42no—
498C4—41no—
499C4—41no—
500C4—82no—
501C4—81no—
502C4—442no—
503C4—441no—
504C4—441no—
505C4—882no—
506C2—21no—
507C2—21no—
508C2—41no—
509C2—41no—
510C2—222no—
511C2—441no—
512C2—442no—
513C2—1761no—
514C2#1306711911yescharacteristic
515C2#1307026111yescharacteristic
516C2D11×#35311yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radical#13073543C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11757
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
2. D11×#342C2semidirect
3. #13066941C2semidirect
4. #13066640C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1352C2semidirect
8. C2×#66948C4semidirect
14. #10622605C4semidirect
19. #10622284C4semidirect
20. #10622279C4semidirect
31. C22×D44C2×C4semidirect
36. C2×C11×C4⋊C4C2×C4semidirect
62. C11×#95C2×C4semidirect
63. C11⋊#95C2×C4semidirect
135. #1352D11semidirect
289. C2×C4⋊C4C4×D11semidirect
312. #95C4×D11semidirect
388. C11#11757semidirect

Maximal subgroups

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

subgroupindex
#130735432
D11×#3422
#130669412
#130666402
#130666142
#130666122
C11×#13522
#1175711