Finite Group Databasebeta

← #14664650

Subgroups — #14664650

Order 2816.

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

normal subgroups only

This group has 620 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#13073543C211yesmaximal, characteristic
2#13068689C211yesmaximal, characteristic, complemented
3D11×#323C211yesmaximal, 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×D11C2211yescharacteristic
12C11×#399C2211yescharacteristic
13#10622605C411yescharacteristic, complemented
14#10622601—21no—
15#10622573C2211yescharacteristic
16#10622570—21no—
17#10622568—21no—
18D11×C22⋊C8—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
32C22×C4×D11C2×C411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—41no—
47C2×(C2×D11)⋊C4—41no—
48C2×(C2×D11)⋊C4C2×C411yescharacteristic
49C2×(C2×D11)⋊C4D411yescharacteristic
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×C8×D11—41no—
53#66948—41no—
54#66948—41no—
55#66947—44no—
56#66935—44no—
57C22⋊C4×D11—41no—
58C22⋊C4×D11—41no—
59C11×C22⋊C8—21no—
60C11×#95C2×C411yescharacteristic
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11843—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
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×C22⋊D11—42no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—81no—
85C22×Dic11—21no—
86C22×Dic11—41no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C2×D44—42no—
90C2×D44—41no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—81no—
97C2×D44—81no—
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—42no—
103C2×C4×D11—81no—
104C2×C8×C11—41no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—42no—
118(C2×D11)⋊C4—42no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—82no—
122(C2×D11)⋊C4—82no—
123Dic11⋊C4—42no—
124C4×Dic11—81no—
125C2×C11⋊C8—41no—
126C8×D11—82no—
127#2539—111no—
128#1819—111no—
129C2×#323—111no—
130#1352—111no—
131#1352D1111yescharacteristic, complemented
132#1343—111no—
133#1343—111no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#13511yescharacteristic
140C23×C11#13511yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—22no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—42no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—42no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—81no—
164C22×D11—81no—
165C22×D11—84no—
166C22×D11—82no—
167C22×D11—82no—
168C22×D11#9911yescharacteristic
169C22×D11#9911yescharacteristic
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C22⋊D11—82no—
184C22⋊D11—82no—
185C2×Dic11—22no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195D44—84no—
196D44—82no—
197D44—82no—
198D44—82no—
199C4×D11—42no—
200C4×D11—81no—
201C4×D11—81no—
202C4×D11—81no—
203C8×C11—81no—
204C11⋊C8—81no—
205C2×#123—221no—
206C2×#121—111no—
207C2×#120—221no—
208C22×C22⋊C4—111no—
209C2×C22⋊C8—221no—
210#399—111no—
211#399C2×D1111yescharacteristic
212#392—111no—
213#392—111no—
214#390—221no—
215#390—221no—
216#379—221no—
217C4×C22⋊C4—111no—
218#342—111no—
219#342—221no—
220#342C2×D1111yescharacteristic
221#323—111no—
222#323—221no—
223#323C2×D1111yescharacteristic
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—81no—
233C22×C11C2×#9911yescharacteristic
234C22×C11#41611yescharacteristic
235C22×C11#42111yescharacteristic
236C2×D11—21no—
237C2×D11—21no—
238C2×D11—21no—
239C2×D11—21no—
240C2×D11—21no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—82no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11#35312yes—
260C4×C11—42no—
261C4×C11—41no—
262C4×C11—41no—
263C4×C11—81no—
264C4×C11—161no—
265Dic11—42no—
266Dic11—41no—
267Dic11—41no—
268Dic11—161no—
269C25—111no—
270C22×D4—111no—
271C22×D4—221no—
272C22×D4—221no—
273C22×D4—221no—
274C23×C4—111no—
275C23×C4—111no—
276C22×C8—441no—
277#123—444no—
278#121—441no—
279#121—441no—
280#120—444no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C4×D1111yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—441no—
296C2×C22⋊C4—441no—
297C2×C22⋊C4—441no—
298C2×C22⋊C4—441no—
299C2×C22⋊C4C22×D1111yescharacteristic
300C2×C42—221no—
301C22⋊C8—21no—
302C22⋊C8—221no—
303C22⋊C8—441no—
304#95—111no—
305#95C4×D1111yescharacteristic
306C2×C11—21no—
307C2×C11—21no—
308C2×C11—41no—
309C2×C11—41no—
310C2×C11#151611yescharacteristic
311C2×C11#212111yescharacteristic
312C2×C11C2×#35311yescharacteristic
313D11—22no—
314D11—41no—
315D11—81no—
316D11—161no—
317C24—111no—
318C24—111no—
319C24—221no—
320C24—221no—
321C24—221no—
322C24—221no—
323C24—221no—
324C24—441no—
325C24—442no—
326C24—881no—
327C24D4×D1111yescharacteristic
328C2×D4—441no—
329C2×D4—442no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—442no—
335C2×D4—442no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—881no—
339C2×D4—881no—
340C2×D4—881no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—442no—
352C22×C4—441no—
353C22×C4—881no—
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4D4×D1111yescharacteristic
356C2×C8—41no—
357C2×C8—441no—
358C2×C8—882no—
359C4⋊C4—41no—
360C4⋊C4—42no—
361C4⋊C4—442no—
362C22⋊C4—41no—
363C22⋊C4—42no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—224no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—442no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—882no—
377C22⋊C4—882no—
378C42—881no—
379C11#1184311yescharacteristic, complemented, Sylow
380C23—21no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23—111no—
385C23—111no—
386C23—222no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—442no—
404C23—442no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—881no—
409C23—881no—
410C23—882no—
411C23—882no—
412C23—884no—
413C23C22⋊C4×D1111yescharacteristic
414C23#6696911yescharacteristic
415C23#6697211yescharacteristic
416D4—884no—
417D4—882no—
418D4—882no—
419D4—882no—
420D4—882no—
421D4—882no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—222no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C8—81no—
450C8—881no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—112no—
461C22—221no—
462C22—221no—
463C22—221no—
464C22—221no—
465C22—221no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—441no—
470C22—441no—
471C22—441no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22—882no—
478C22—882no—
479C22—882no—
480C22—882no—
481C22—881no—
482C22—881no—
483C22—881no—
484C22D11×#9911yescharacteristic
485C22#1062241711yescharacteristic
486C22#1062243411yescharacteristic
487C4—42no—
488C4—41no—
489C4—41no—
490C4—81no—
491C4—161no—
492C4—442no—
493C4—441no—
494C4—441no—
495C4—1761no—
496C2—21no—
497C2—21no—
498C2—41no—
499C2—41no—
500C2—222no—
501C2—441no—
502C2—881no—
503C2—1761no—
504C2#1306717111yescharacteristic
505C2#1307026111yescharacteristic
506C2D11×#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#11843
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. #13068689C2semidirect
3. D11×#323C2semidirect
4. #13066640C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1352C2semidirect
8. C2×#66948C4semidirect
13. #10622605C4semidirect
19. #10622284C4semidirect
20. #10622279C4semidirect
131. #1352D11semidirect
379. C11#11843semidirect

Maximal subgroups

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

subgroupindex
#130735432
#130686892
D11×#3232
#130666402
#130666142
#130666122
C11×#13522
#1184311