Finite Group Databasebeta

← #14753605

Subgroups — #14753605

Order 2816.

1470 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13068715C218yesmaximal, complemented
4#13068325C214yesmaximal, complemented
5C22×C11×#117C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#117—21no—
8C2×C11×#117—22no—
9C2×C11×#117—22no—
10C2×C11×#117—21no—
11C2×C11×#117C414yescomplemented
12C2×C11×#117C412yescomplemented
13C2×C11×#117C2212yes—
14C2×C11×#117C2214yes—
15C22×C11×C4⋊C4C412yescomplemented
16C22×C11×C22⋊C4—21no—
17C22×C42×C11—21no—
18C2×#66979C2212yes—
19C22×#4318C2212yes—
20#10622860—21no—
21#10622825—22no—
22#10622824—21no—
23C4×C22⋊Dic11C2214yes—
24#10622820—21no—
25#10622820—21no—
26#10622820C2214yes—
27C2×C22⋊(C11⋊C8)—22no—
28#10622170C22116yescomplemented
29C25×C11D411yescharacteristic
30C23×C4×C11—28no—
31C23×C4×C11—22no—
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C412yes—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D412yes—
37C23×C4×C11D412yes—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C11×#117—24no—
43C11×#117—24no—
44C11×#117—24no—
45C11×#117—24no—
46C11×#117—22no—
47C11×#117—24no—
48C11×#117—22no—
49C11×#117C2×C418yes—
50C11×#117C2×C414yes—
51C11×#117C2314yes—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—22no—
63C2×C42×C11—24no—
64C2×C42×C11—24no—
65C2×C42×C11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—24no—
68#66979—28no—
69C2×C4⋊Dic11—22no—
70C2×C4×Dic11C2314yes—
71C2×#4318—22no—
72C2×#4318—28no—
73C2×#4318C2314yes—
74C22×C11⋊C8—22no—
75C11⋊#95—24no—
76C22⋊(C11⋊C8)—24no—
77C22⋊(C11⋊C8)—24no—
78#20705—111nomaximal, Sylow
79C24×C11—24no—
80C24×C11—44no—
81C24×C11C22⋊C411yescharacteristic
82C24×C11C22⋊C412yes—
83C24×C11C22⋊C411yescharacteristic
84C24×C11C2×D412yes—
85C24×C11C2×D411yescharacteristic
86C22×C4×C11—24no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—28no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—28no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—48no—
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C22⋊C412yes—
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C412yes—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22⋊C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4118yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4C22×C418yes—
123C11×C22⋊C4—28no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C42×C11—28no—
127C42×C11—24no—
128C42×C11—24no—
129C22⋊Dic11—48no—
130C22⋊Dic11—44no—
131C4⋊Dic11—44no—
132C4×Dic11—28no—
133#4318—28no—
134#4318—44no—
135C2×C11⋊C8—24no—
136C2×C11⋊C8—44no—
137C22×#117D1111yescharacteristic
138C2×#407—111no—
139#2280—111no—
140#1826—118no—
141#1733—114no—
142C23×C11—22no—
143C23×C11—24no—
144C23×C11—24no—
145C23×C11—24no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—24no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—416no—
154C23×C11C2×C22⋊C412yes—
155C23×C11C2×C22⋊C411yescharacteristic
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11C2×C22⋊C412yes—
158C23×C11#12314yes—
159C23×C11C22×D411yescharacteristic
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—28no—
173C2×C4×C11—48no—
174C2×C4×C11—48no—
175C2×C4×C11—48no—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C2×C22⋊C412yes—
178C2×C4×C11C2×C22⋊C411yescharacteristic
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11#11714yes—
181C2×C4×C11#11714yes—
182C2×C4×C11#12314yes—
183C2×C4×C11#12314yes—
184C2×C4×C11#12314yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4114yes—
188C2×Dic11—48no—
189C2×Dic11—44no—
190C11⋊C8—44no—
191C24×C4C2×D1111yescharacteristic
192C22×M16—112no—
193C2×#117—22no—
194C2×#117—21no—
195C2×#117—22no—
196C2×#117—21no—
197C2×#117—112no—
198C2×#117Dic1114yescomplemented
199C2×#117Dic1112yescomplemented
200C2×#117C2×D1114yes—
201C2×#117C2×D1112yes—
202C22×C4⋊C4Dic1112yescomplemented
203C22×C22⋊C4—21no—
204C22×C42—21no—
205#407—114no—
206#407—221no—
207#407—221no—
208C2×C22⋊C8—222no—
209#381—221no—
210#380—222no—
211#379—221no—
212C4×C22⋊C4—114no—
213#339—1116no—
214C22×C11—28no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—44no—
224C22×C11—48no—
225C22×C11—48no—
226C22×C11—44no—
227C22×C11#38112yes—
228C22×C11#38112yes—
229C22×C11#42114yes—
230C22×C11C22×C22⋊C411yescharacteristic
231C22×C11C2×#12312yes—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—48no—
235C4×C11#38112yes—
236C4×C11#38112yes—
237C4×C11C2×#11712yes—
238C4×C11C2×#12312yes—
239Dic11—84no—
240C25C22⋊D1111yescharacteristic
241C23×C4—28no—
242C23×C4—22no—
243C23×C4C2×Dic1111yescharacteristic
244C23×C4C2×Dic1112yes—
245C23×C4C2×Dic1111yescharacteristic
246C23×C4C22⋊D1112yes—
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22⋊D1112yes—
249C23×C4C22⋊D1111yescharacteristic
250C23×C4C22⋊D1111yescharacteristic
251C23×C4C22×D1112yes—
252C23×C4C22×D1111yescharacteristic
253C2×M16—114no—
254C2×M16—222no—
255C2×M16—228no—
256C22×C8—222no—
257#117—24no—
258#117—24no—
259#117—24no—
260#117—24no—
261#117—22no—
262#117—24no—
263#117—22no—
264#117—228no—
265#117C2×Dic1118yes—
266#117C2×Dic1114yes—
267#117C22×D1114yes—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4C2×Dic1114yes—
273C2×C4⋊C4C2×Dic1114yes—
274C2×C4⋊C4C2×Dic1114yes—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—224no—
281C2×C42—22no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—22no—
285C2×C42—114no—
286C22⋊C8—224no—
287C22⋊C8—224no—
288#95—224no—
289C2×C11—22no—
290C2×C11—22no—
291C2×C11—24no—
292C2×C11—22no—
293C2×C11—42no—
294C2×C11C2×#38111yescharacteristic
295C2×C11C2×#42112yes—
296C24—24no—
297C24—44no—
298C24C22⋊Dic1111yescharacteristic
299C24C22⋊Dic1112yes—
300C24C22⋊Dic1111yescharacteristic
301C24C2×C22⋊D1112yes—
302C24C2×C22⋊D1111yescharacteristic
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—28no—
307C22×C4—28no—
308C22×C4—28no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—28no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—48no—
316C22×C4—224no—
317C22×C4C22⋊Dic1111yescharacteristic
318C22×C4C22⋊Dic1112yes—
319C22×C4C22⋊Dic1111yescharacteristic
320C22×C4C22⋊Dic1112yes—
321C22×C4C22⋊Dic1112yes—
322C22×C4C22⋊Dic1112yes—
323C22×C4C22⋊Dic1112yes—
324C22×C4#433918yes—
325C22×C4C22×Dic1112yes—
326C22×C4C22×Dic1112yes—
327C22×C4C22×Dic1111yescharacteristic
328C22×C4C22×Dic1111yescharacteristic
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1112yes—
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C23×D1111yescharacteristic
336M16—228no—
337M16—444no—
338C2×C8—224no—
339C2×C8—444no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—444no—
344C4⋊C4C22×Dic1118yes—
345C22⋊C4—28no—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—448no—
349C22⋊C4—444no—
350C42—28no—
351C42—24no—
352C42—24no—
353C42—228no—
354C11#2070511yescharacteristic, complemented, Sylow
355C23—22no—
356C23—24no—
357C23—24no—
358C23—24no—
359C23—22no—
360C23—24no—
361C23—24no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—416no—
367C23#6698214yes—
368C23C2×C22⋊Dic1112yes—
369C23C2×C22⋊Dic1111yescharacteristic
370C23C2×C22⋊Dic1111yescharacteristic
371C23C2×C22⋊Dic1112yes—
372C23C22×C22⋊D1111yescharacteristic
373C2×C4—24no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—28no—
386C2×C4—48no—
387C2×C4—48no—
388C2×C4—48no—
389C2×C4—448no—
390C2×C4—444no—
391C2×C4#6697914yes—
392C2×C4#6697914yes—
393C2×C4#6698214yes—
394C2×C4#6698214yes—
395C2×C4#6698214yes—
396C2×C4C2×C22⋊Dic1112yes—
397C2×C4C2×C22⋊Dic1112yes—
398C2×C4C2×C22⋊Dic1111yescharacteristic
399C2×C4C2×C22⋊Dic1111yescharacteristic
400C2×C4C2×#433914yes—
401C2×C4C23×Dic1111yescharacteristic
402C2×C4C22×C22⋊D1111yescharacteristic
403C8—444no—
404C22—28no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—44no—
414C22—48no—
415C22—48no—
416C22—44no—
417C22#1062282412yes—
418C22#1062282412yes—
419C22#1062284914yes—
420C22C2×#6698212yes—
421C22C22×C22⋊Dic1111yescharacteristic
422C4—22no—
423C4—22no—
424C4—48no—
425C4—884no—
426C4#1062282412yes—
427C4#1062282412yes—
428C4C2×#6697912yes—
429C4C2×#6698212yes—
430C2—22no—
431C2—22no—
432C2—24no—
433C2—22no—
434C2—42no—
435C2C2×#1062282411yescharacteristic
436C2C2×#1062284912yes—
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#117C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×#117D11
hypocenterC11#20705
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #13068715C2semidirect
4. #13068325C2semidirect
11. C2×C11×#117C4semidirect
12. C2×C11×#117C4semidirect
15. C22×C11×C4⋊C4C4semidirect
28. #10622170C22semidirect
198. C2×#117Dic11semidirect
199. C2×#117Dic11semidirect
202. C22×C4⋊C4Dic11semidirect
354. C11#20705semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130687152
#130683252
C22×C11×#1172
#2070511