Finite Group Databasebeta

← #14646518

Subgroups — #14646518

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C11×#1434C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C2×C4×Dic22C411yescharacteristic, complemented
9C2×C11×#95—21no—
10C2×C11×#95—21no—
11C2×C11×#95C2212yes—
12#10622825C2211yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17#10622546—21no—
18C4×Dic11⋊C4—21no—
19#10622542C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×C4⋊(C11⋊C8)—21no—
22#10622162—21no—
23#10622090—24no—
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C42×C11—42no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39#66977—21no—
40#66977—21no—
41#66977D412yes—
42#66977Q812yes—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C22×C11⋊C8—22no—
49C4×Dic22—42no—
50C11×#95—24no—
51C11×#95—22no—
52C11×#95—22no—
53C11×#95—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—42no—
62#8576—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×Q811yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22C4⋊C412yes—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—41no—
100C42×C11—41no—
101C22⋊Dic11—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—42no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11C4⋊C412yes—
108Dic11⋊C4—22no—
109Dic11⋊C4—22no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—42no—
113C4×Dic11—42no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—42no—
117C4×C22⋊Q8—111no—
118#1797—111no—
119C2×#328—112no—
120#1434D1111yescharacteristic
121#1294—112no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#12111yescharacteristic
128C23×C11C22⋊Q811yescharacteristic
129C23×C11#13512yes—
130C23×C11#13712yes—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11—82no—
157C2×C4×C11—82no—
158C2×C4×C11#9912yes—
159C2×C4×C11#10412yes—
160C2×C4×C11C2×C4⋊C411yescharacteristic
161C2×C4×C11#11711yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C22⋊Q811yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176Dic22—42no—
177Dic22—42no—
178C11⋊C8—82no—
179C2×C22⋊Q8—111no—
180C2×C4×Q8—111no—
181C22×C42C2×D1111yescharacteristic
182C2×C4⋊C8—221no—
183C2×C22⋊C8—112no—
184#391—111no—
185#389—111no—
186#387—221no—
187#385—221no—
188#380—111no—
189C4×C4⋊C4—111no—
190C4×C4⋊C4—221no—
191C4×C22⋊C4—221no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95C2×D1112yes—
195#336—221no—
196#328—224no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#38011yescharacteristic
206C22×C11C2×#9911yescharacteristic
207C22×C11#41011yescharacteristic
208C22×C11#41611yescharacteristic
209C22×C11#41911yescharacteristic
210C22×C11C2×#10411yescharacteristic
211C22×C11#42111yescharacteristic
212C22×C11#46412yes—
213C22×C11#47912yes—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—84no—
223Dic11—42no—
224Dic11—42no—
225Dic11—81no—
226Dic11—81no—
227C22×Q8—111no—
228C23×C4—22no—
229C23×C4C22⋊D1111yescharacteristic
230C23×C4C22⋊D1111yescharacteristic
231C23×C4C22×D1111yescharacteristic
232C22×C8—222no—
233C22⋊Q8—112no—
234C22⋊Q8—112no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C4×Q8—442no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—42no—
247C2×C42—221no—
248C2×C42—221no—
249C2×C42C4×D1111yescharacteristic
250C2×C42C4×D1111yescharacteristic
251C2×C42D4411yescharacteristic
252C2×C42D4411yescharacteristic
253C4⋊C8—442no—
254C22⋊C8—222no—
255C22⋊C8—222no—
256#95—24no—
257#95—22no—
258#95—22no—
259#95—42no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95—221no—
265C2×C11—22no—
266C2×C11—22no—
267C2×C11#150111yescharacteristic
268C2×C11#150611yescharacteristic
269C2×C11#151111yescharacteristic
270C2×C11#152111yescharacteristic
271C2×C11#179911yescharacteristic
272C2×C11#180511yescharacteristic
273C2×C11#180611yescharacteristic
274C24C2×C22⋊D1111yescharacteristic
275C2×Q8—112no—
276C2×Q8—221no—
277C2×Q8—441no—
278C2×Q8—441no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4(C2×D11)⋊C411yescharacteristic
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4#434111yescharacteristic
306C22×C4Q8×D1111yescharacteristic
307C22×C4#434311yescharacteristic
308C2×C8—442no—
309C2×C8—442no—
310C2×C8—442no—
311C4⋊C4—112no—
312C4⋊C4—221no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C22⋊C4—222no—
320C22⋊C4—222no—
321C22⋊C4—442no—
322C42—22no—
323C42—22no—
324C42—41no—
325C42—41no—
326C42—442no—
327C42—442no—
328C11#857611yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23C2×(C2×D11)⋊C411yescharacteristic
334C23#6699111yescharacteristic
335C23#6699911yescharacteristic
336C23#6700312yes—
337C23#6700412yes—
338Q8—442no—
339Q8—442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4#6686912yes—
380C2×C4#6687012yes—
381C2×C4C4⋊C4×D1111yescharacteristic
382C2×C4#6694511yescharacteristic
383C2×C4#6694811yescharacteristic
384C2×C4#6695011yescharacteristic
385C8—882no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22C2×#6686911yescharacteristic
395C22C2×#6687011yescharacteristic
396C22#1062260011yescharacteristic
397C22#1062261511yescharacteristic
398C22#1062261711yescharacteristic
399C22#1062261811yescharacteristic
400C22#1062261911yescharacteristic
401C22#1062266712yes—
402C22#1062267612yes—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—41no—
410C4—41no—
411C4—84no—
412C4—442no—
413C4—442no—
414C4—881no—
415C4—881no—
416C2—22no—
417C2—22no—
418C2#1306710511yescharacteristic
419C2#1306712711yescharacteristic
420C2#1306714811yescharacteristic
421C2#1306719111yescharacteristic
422C2#1306860111yescharacteristic
423C2#1306862811yescharacteristic
424C2#1306863711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#8576
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic22C4semidirect
16. C4×C4⋊Dic11C4semidirect
19. #10622542C4semidirect
20. #10622541C4semidirect
328. C11#8576semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130685962
C2×#106220902
#130664952
C11×#14342
#857611