Finite Group Databasebeta

← #14664249

Subgroups — #14664249

Order 2816.

700 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622164C211yesmaximal, characteristic, complemented
2#13066943C211yesmaximal, characteristic, complemented
3#13066640C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2539C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C2×C11×#121C411yescharacteristic, complemented
8C2×C11×#120—21no—
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11—21no—
11C11×#399C411yescharacteristic, complemented
12C11×#399C2211yescharacteristic
13C11×#392C411yescharacteristic, complemented
14C11×#392C2211yescharacteristic
15C11×#390—21no—
16C11×#390—21no—
17C4×C11×C22⋊C4C411yescharacteristic, complemented
18#10622820—21no—
19#10622164—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11D411yescharacteristic
24C22×D4×C11—21no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic, complemented
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×Dic11—41no—
31C11×#123—44no—
32C11×#121—41no—
33C11×#121—41no—
34C11×#120—44no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—41no—
45C2×C11×C22⋊C4—41no—
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4D411yescharacteristic
48C2×C11×C22⋊C4D411yescharacteristic
49C2×C11×C22⋊C4C2311yescharacteristic
50C2×C42×C11—21no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—41no—
54C2×C22⋊Dic11—42no—
55C2×#4318—41no—
56C11×#95C2×C411yescharacteristic, complemented
57C11×#95C2×C411yescharacteristic, complemented
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11757—111nomaximal, Sylow
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—22no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—42no—
68C24×C11—81no—
69C24×C11C22⋊C411yescharacteristic
70C24×C11C22⋊C411yescharacteristic
71C24×C11C2×D411yescharacteristic
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—81no—
83C2×D4×C11—81no—
84C2×D4×C11—81no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—42no—
93C22×C4×C11—81no—
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—44no—
99C22×Dic11—42no—
100C22×Dic11—82no—
101C22×Dic11—82no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C42×C11—81no—
116C22⋊Dic11—24no—
117C22⋊Dic11—44no—
118C22⋊Dic11—42no—
119#4318—82no—
120C2×C11⋊C8—42no—
121#2539D1111yescharacteristic
122C2×#342—111no—
123#1462—111no—
124#1352—112no—
125#1343—112no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—84no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11#9911yescharacteristic
157C23×C11#9911yescharacteristic
158C23×C11#10412yes—
159C23×C11C2×C22⋊C411yescharacteristic
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C23×C11#13711yescharacteristic
162D4×C11—84no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—82no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
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—41no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×Dic11—44no—
190C2×Dic11—88no—
191C2×Dic11—82no—
192C2×Dic11—82no—
193C11⋊C8—82no—
194C2×#123—21no—
195C2×#121Dic1111yescharacteristic, complemented
196C2×#120—21no—
197C22×C22⋊C4—221no—
198C22×C22⋊C4C2×D1111yescharacteristic
199#407—221no—
200#399Dic1111yescharacteristic, complemented
201#399C2×D1111yescharacteristic
202#392Dic1111yescharacteristic, complemented
203#392C2×D1111yescharacteristic
204#390—21no—
205#390—21no—
206C4×C22⋊C4Dic1111yescharacteristic, complemented
207#342—112no—
208#342—221no—
209#323—112no—
210#323—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—22no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#35312yes—
244C22×C11C2×#9911yescharacteristic
245C22×C11#41711yescharacteristic
246C22×C11C2×#10411yescharacteristic
247C4×C11—42no—
248C4×C11—42no—
249C4×C11—41no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11—41no—
253C4×C11—81no—
254Dic11—84no—
255C25C22⋊D1111yescharacteristic
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4C2×Dic1111yescharacteristic, complemented
260C23×C4—441no—
261C23×C4C2×Dic1111yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C2×M16—441no—
264#123—44no—
265#121—41no—
266#121—41no—
267#120—44no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—41no—
278C2×C22⋊C4—41no—
279C2×C22⋊C4—224no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—441no—
282C2×C22⋊C4—442no—
283C2×C22⋊C4C2×Dic1111yescharacteristic
284C2×C22⋊C4C22⋊D1111yescharacteristic
285C2×C22⋊C4C22⋊D1111yescharacteristic
286C2×C22⋊C4C22×D1111yescharacteristic
287C2×C42—21no—
288C22⋊C8—222no—
289C22⋊C8—441no—
290#95C2×Dic1111yescharacteristic, complemented
291#95C2×Dic1111yescharacteristic, complemented
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—22no—
295C2×C11—41no—
296C2×C11—41no—
297C2×C11—42no—
298C2×C11—41no—
299C2×C11—161no—
300C2×C11#150411yescharacteristic
301C2×C11#212111yescharacteristic
302C2×C11C2×#35311yescharacteristic
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—21no—
308C24—21no—
309C24—42no—
310C24—81no—
311C24C22⋊Dic1111yescharacteristic
312C24C22⋊Dic1111yescharacteristic
313C24C2×C22⋊D1111yescharacteristic
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4—81no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—444no—
337C22×C4—442no—
338C22×C4—882no—
339C22×C4—882no—
340C22×C4C22⋊Dic1111yescharacteristic
341C22×C4C22⋊Dic1111yescharacteristic
342C22×C4C22×Dic1111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344M16—882no—
345C2×C8—442no—
346C4⋊C4—41no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C22⋊C4—24no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—224no—
360C22⋊C4—444no—
361C22⋊C4—442no—
362C42—81no—
363C11#1175711yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23—84no—
392C23—82no—
393C23—82no—
394C23#6689811yescharacteristic
395C23#6689811yescharacteristic
396C23#6690112yes—
397C23#6700211yescharacteristic
398C23#6700411yescharacteristic
399C23C2×C22⋊Dic1111yescharacteristic
400D4—84no—
401D4—82no—
402D4—82no—
403D4—82no—
404D4—82no—
405D4—82no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—444no—
428C2×C4—888no—
429C2×C4—882no—
430C2×C4—882no—
431C8—882no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—44no—
448C22—44no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—82no—
460C22—82no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22#1062218312yes—
465C22C2×#6689811yescharacteristic
466C22#1062284511yescharacteristic
467C22C2×#6690111yescharacteristic
468C4—42no—
469C4—42no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—81no—
475C4—884no—
476C2—21no—
477C2—21no—
478C2—22no—
479C2—41no—
480C2—41no—
481C2—42no—
482C2—41no—
483C2—161no—
484C2#1306712011yescharacteristic
485C2#1307026211yescharacteristic
486C2C2×#1062218311yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2539C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2539D11
hypocenterC11#11757
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#10622164C2semidirect
2. #13066943C2semidirect
3. #13066640C2semidirect
4. #13066613C2semidirect
7. C2×C11×#121C4semidirect
11. C11×#399C4semidirect
13. C11×#392C4semidirect
17. C4×C11×C22⋊C4C4semidirect
27. C22×D4×C11C2×C4semidirect
37. C2×C11×C4⋊C4C2×C4semidirect
56. C11×#95C2×C4semidirect
57. C11×#95C2×C4semidirect
195. C2×#121Dic11semidirect
200. #399Dic11semidirect
202. #392Dic11semidirect
206. C4×C22⋊C4Dic11semidirect
259. C22×D4C2×Dic11semidirect
270. C2×C4⋊C4C2×Dic11semidirect
290. #95C2×Dic11semidirect
291. #95C2×Dic11semidirect
363. C11#11757semidirect

Maximal subgroups

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

subgroupindex
C2×#106221642
#130669432
#130666402
#130666132
C11×#25392
#1175711