Finite Group Databasebeta

← #14664795

Subgroups — #14664795

Order 2816.

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

normal subgroups only

This group has 536 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
1#13073513C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066615C212yesmaximal, complemented
4#13066612C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66991—21no—
8C2×C4×D44C411yescharacteristic, complemented
9C2×C11×#99—21no—
10C11×#380—21no—
11#10622826—21no—
12#10622826—21no—
13C2×C22⋊(C11⋊C8)—21no—
14#10622600—21no—
15#10622573C411yescharacteristic, complemented
16#10622573C2211yescharacteristic
17#10622566C411yescharacteristic, complemented
18#10622566C2211yescharacteristic
19#10622549C411yescharacteristic, complemented
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40#66991—42no—
41#66991—42no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C22×C11⋊C8—41no—
48C4×D44—41no—
49C4×D44—41no—
50C11×#99—42no—
51C11×#95—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—22no—
58C22⋊(C11⋊C8)—41no—
59#11875—111nomaximal, Sylow
60C24×C11C22⋊C411yescharacteristic
61C24×C11C2×D411yescharacteristic
62C23×D11—21no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11D812yes—
66C2×D4×C11SD1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—42no—
72C22×C4×C11—81no—
73C22×C4×C11—81no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—81no—
85C2×C22⋊D11—81no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×D44—41no—
90C2×D44—42no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—42no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—82no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C42×C11—21no—
101C42×C11—21no—
102C22⋊Dic11—42no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—81no—
108(C2×D11)⋊C4—81no—
109C4⋊Dic11—41no—
110C4⋊Dic11—42no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—82no—
113#2535—111no—
114#1799D1111yescharacteristic, complemented
115#1459—111no—
116#1344—112no—
117#1343—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11#10212yes—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11C2×D811yescharacteristic
129C23×C11C2×SD1611yescharacteristic
130C22×D11—22no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137D4×C11—42no—
138D4×C11—42no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11#9911yescharacteristic
156C2×C4×C11#9911yescharacteristic
157C2×C4×C11#10212yes—
158C22⋊D11—84no—
159C22⋊D11—82no—
160C22⋊D11—82no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170D44—42no—
171D44—42no—
172C4×D11—84no—
173C11⋊C8—82no—
174C2×#121—221no—
175C2×C4×D4—111no—
176C2×C4×D4C2×D1111yescharacteristic
177C2×#99—21no—
178C2×C22⋊C8—221no—
179#397—111no—
180#397—111no—
181#392—111no—
182#392—111no—
183#386—221no—
184#386—221no—
185#382—111no—
186#380—21no—
187#380—221no—
188#342C2×D1112yes—
189#324—221no—
190#323—112no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—22no—
195C22×C11—21no—
196C22×C11—42no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11C2×#9911yescharacteristic
206C22×C11C2×#10211yescharacteristic
207C22×C11#42111yescharacteristic
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—22no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—162no—
222Dic11—81no—
223Dic11—81no—
224Dic11—81no—
225C22×D4—111no—
226C22×D4—221no—
227C22×D4—221no—
228C22×D4C22⋊D1111yescharacteristic
229C23×C4—221no—
230C23×C4D4411yescharacteristic
231C23×C4C22⋊D1111yescharacteristic
232C22×C8—441no—
233#121—442no—
234#121—442no—
235C4×D4—41no—
236C4×D4—41no—
237C4×D4—441no—
238C4×D4—441no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4D4411yescharacteristic
243C2×C22⋊C4—22no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4C4×D1111yescharacteristic
250C2×C22⋊C4C22×D1111yescharacteristic
251C2×C42C4×D1111yescharacteristic
252#99—42no—
253C22⋊C8—222no—
254C22⋊C8—441no—
255#95—41no—
256#95—111no—
257#95—111no—
258#95—221no—
259#95—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—41no—
264C2×C11—42no—
265C2×C11—41no—
266C2×C11#151911yescharacteristic
267C2×C11#212011yescharacteristic
268C2×C11#212711yescharacteristic
269D11—82no—
270C24—221no—
271C24(C2×D11)⋊C411yescharacteristic
272C24C2×C22⋊D1111yescharacteristic
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—441no—
276C2×D4—442no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4—442no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—881no—
283C2×D4—881no—
284C2×D4#432312yes—
285C2×D4#432512yes—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C2×C8—442no—
305C2×C8—882no—
306C4⋊C4—41no—
307C4⋊C4—82no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—442no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—881no—
320C22⋊C4—881no—
321C42—21no—
322C42—21no—
323C11#1187511yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—222no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23#6687312yes—
340C23C2×(C2×D11)⋊C411yescharacteristic
341C23C2×#432311yescharacteristic
342C23C2×#432511yescharacteristic
343D4—42no—
344D4—42no—
345D4—442no—
346D4—442no—
347D4—884no—
348D4—882no—
349D4—882no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—884no—
376C2×C4#6687011yescharacteristic
377C2×C4#6687011yescharacteristic
378C2×C4#6687312yes—
379C8—882no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—42no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—81no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22—881no—
398C22—881no—
399C22—881no—
400C22—881no—
401C22C2×#6687011yescharacteristic
402C22C2×#6687311yescharacteristic
403C22#1062261811yescharacteristic
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—162no—
411C4—881no—
412C4—881no—
413C4—881no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—42no—
418C2—41no—
419C2—882no—
420C2#1306718311yescharacteristic
421C2#1307025511yescharacteristic
422C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radical#13073513C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1799D11
hypocenterC11#11875
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066615C2semidirect
4. #13066612C2semidirect
5. C11×#1799C2semidirect
8. C2×C4×D44C4semidirect
15. #10622573C4semidirect
17. #10622566C4semidirect
19. #10622549C4semidirect
114. #1799D11semidirect
323. C11#11875semidirect

Maximal subgroups

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

subgroupindex
#130735132
#130669342
#130666152
#130666122
C11×#17992
#1187511