Finite Group Databasebeta

← #14664631

Subgroups — #14664631

Order 2816.

698 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 91 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#13068690C211yesmaximal, characteristic, complemented
2C2×#10622163C211yesmaximal, characteristic, complemented
3#13066637C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2404C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic, complemented
7C2×C11×#120—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C11×#393C411yescharacteristic, complemented
10C11×#393C2211yescharacteristic
11C11×#392C411yescharacteristic, complemented
12C11×#392C2211yescharacteristic
13C11×#386—21no—
14C11×#386—21no—
15C11×#386—21no—
16C11×#381C411yescharacteristic, complemented
17#10622860—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622164—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11D411yescharacteristic
24C2×C11×#41—41no—
25C2×C11×#41—41no—
26C2×C11×#41—44no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C11×#120—44no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—41no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—41no—
49C2×C22⋊Dic11—41no—
50C22×C11⋊C8—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11×#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11839—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—21no—
62C24×C11—22no—
63C24×C11—41no—
64C24×C11—42no—
65C24×C11—81no—
66C24×C11C22⋊C411yescharacteristic
67C24×C11C22⋊C411yescharacteristic
68C24×C11C2×D411yescharacteristic
69C11×#41—44no—
70C11×#41—44no—
71C11×#41—44no—
72C11×#41—44no—
73C2×Q8×C11—42no—
74C2×Q8×C11—41no—
75C2×D4×C11—24no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—42no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—81no—
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C22⋊C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×Dic11—42no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C22⋊Dic11—42no—
114C22⋊Dic11—42no—
115C22⋊Dic11—82no—
116C22⋊Dic11—82no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—82no—
119#2404D1111yescharacteristic
120#1819—111no—
121C2×#323—111no—
122#1351—112no—
123#1343—112no—
124C23×C11—22no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—84no—
151C23×C11—84no—
152C23×C11#9911yescharacteristic
153C23×C11#9911yescharacteristic
154C23×C11C2×C22⋊C411yescharacteristic
155C23×C11#13512yes—
156Q8×C11—42no—
157Q8×C11—42no—
158D4×C11—44no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—44no—
162D4×C11—84no—
163D4×C11—84no—
164C2×C4×C11—22no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—48no—
173C2×C4×C11—42no—
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—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×Dic11—82no—
187C2×Dic11—82no—
188C2×Dic11—82no—
189C11⋊C8—82no—
190C22×#41Dic1111yescharacteristic, complemented
191C2×#120—21no—
192C22×C22⋊C4C2×D1111yescharacteristic
193C2×C22⋊C8—221no—
194#393Dic1111yescharacteristic, complemented
195#393C2×D1111yescharacteristic
196#392Dic1111yescharacteristic, complemented
197#392C2×D1111yescharacteristic
198#386—21no—
199#386—21no—
200#386—21no—
201#381Dic1111yescharacteristic, complemented
202#379—221no—
203#342—112no—
204#342—221no—
205#323—112no—
206#323—221no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—81no—
228C22×C11—84no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—84no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11AΣL(1,𝔽16)12yes—
236C22×C11C2×#9911yescharacteristic
237C22×C11#41611yescharacteristic
238C22×C11#42111yescharacteristic
239C4×C11—41no—
240C4×C11—42no—
241C4×C11—41no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11—81no—
245C4×C11—81no—
246Dic11—162no—
247C25C22⋊D1111yescharacteristic
248C2×#41—41no—
249C2×#41—41no—
250C2×#41—44no—
251C22×Q8C2×Dic1111yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4C2×Dic1111yescharacteristic
256C23×C4—21no—
257C23×C4C2×Dic1111yescharacteristic
258C23×C4C22⋊D1111yescharacteristic
259C22×C8—441no—
260#120—44no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—41no—
267C2×C22⋊C4—41no—
268C2×C22⋊C4—222no—
269C2×C22⋊C4—441no—
270C2×C22⋊C4—441no—
271C2×C22⋊C4C2×Dic1111yescharacteristic
272C2×C22⋊C4C22⋊D1111yescharacteristic
273C2×C22⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4C22×D1111yescharacteristic
275C22⋊C8—222no—
276C22⋊C8—441no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95C2×Dic1111yescharacteristic
281#95C2×Dic1111yescharacteristic
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—42no—
286C2×C11—41no—
287C2×C11—81no—
288C2×C11—82no—
289C2×C11#151611yescharacteristic
290C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
291C2×C11#212711yescharacteristic
292C24—21no—
293C24—21no—
294C24—21no—
295C24—22no—
296C24—41no—
297C24—42no—
298C24—81no—
299C24C22⋊Dic1111yescharacteristic
300C24C22⋊Dic1111yescharacteristic
301C24C2×C22⋊D1111yescharacteristic
302#41—44no—
303#41—44no—
304#41—44no—
305#41—44no—
306C2×Q8—42no—
307C2×Q8—41no—
308C2×D4—24no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—81no—
319C2×D4—81no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—81no—
332C22×C4—442no—
333C22×C4C22⋊Dic1111yescharacteristic
334C22×C4C22⋊Dic1111yescharacteristic
335C22×C4C22×Dic1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C2×C8—442no—
338C2×C8—882no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—81no—
347C22⋊C4—81no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—882no—
351C22⋊C4—882no—
352C11#1183911yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—41no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—81no—
378C23—81no—
379C23—84no—
380C23—84no—
381C23#6689811yescharacteristic
382C23#6689811yescharacteristic
383C23#6700312yes—
384C23C2×C22⋊Dic1111yescharacteristic
385Q8—42no—
386Q8—42no—
387D4—44no—
388D4—42no—
389D4—42no—
390D4—44no—
391D4—84no—
392D4—84no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—48no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—882no—
416C2×C4—882no—
417C2×C4—882no—
418C8—882no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—42no—
437C22—41no—
438C22—41no—
439C22—81no—
440C22—84no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—84no—
445C22—81no—
446C22—81no—
447C22#1062217412yes—
448C22C2×#6689811yescharacteristic
449C22#1062284611yescharacteristic
450C22#1062284911yescharacteristic
451C4—41no—
452C4—42no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—1762no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2—41no—
464C2—81no—
465C2—82no—
466C2#1306717211yescharacteristic
467C2C2×#1062217411yescharacteristic
468C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2404C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2404D11
hypocenterC11#11839
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. #13068690C2semidirect
2. C2×#10622163C2semidirect
3. #13066637C2semidirect
4. #13066613C2semidirect
6. C22×C11×#41C4semidirect
9. C11×#393C4semidirect
11. C11×#392C4semidirect
16. C11×#381C4semidirect
190. C22×#41Dic11semidirect
194. #393Dic11semidirect
196. #392Dic11semidirect
201. #381Dic11semidirect
352. C11#11839semidirect

Maximal subgroups

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

subgroupindex
#130686902
C2×#106221632
#130666372
#130666132
C11×#24042
#1183911