Finite Group Databasebeta

← #14647628

Subgroups — #14647628

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic
4C2×#10622117C211yesmaximal, characteristic, complemented
5#13066451C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#334C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8C411yescharacteristic
15C2×(C2×D11)⋊C8C411yescharacteristic
16C2×#66879—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20#10622448—22no—
21#10622448—22no—
22C11×#334—22no—
23#10622188—21no—
24#10622188C411yescharacteristic
25#10622188C411yescharacteristic
26#10622117—22no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11Q811yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4×Dic11C2×C411yescharacteristic
36C2×C4×Dic11D411yescharacteristic
37C2×C4×Dic11Q811yescharacteristic
38C22×C11⋊C8—21no—
39C22×C11⋊C8—21no—
40C22×C11⋊C8C2×C411yescharacteristic
41C22×C11⋊C8C2×C411yescharacteristic
42C42×D11—21no—
43C42×D11—21no—
44C42×D11—21no—
45C42×D11—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8D412yes—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52(C2×D11)⋊C8—24no—
53(C2×D11)⋊C8—22no—
54(C2×D11)⋊C8—22no—
55(C2×D11)⋊C8—42no—
56#66879—24no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63#8834—111nomaximal, Sylow
64C23×D11C4⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×Q811yescharacteristic
68C22×Dic11C4⋊C411yescharacteristic
69C22×Dic11C4⋊C411yescharacteristic
70C22×Dic11C4⋊C411yescharacteristic
71C2×C4×D11—22no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—41no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—22no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11M1612yes—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8M1612yes—
121C2×#432—111no—
122#1797—111no—
123C4×C22⋊C8—111no—
124C2×#335—111no—
125C2×#334D1111yescharacteristic, complemented
126#1277—111no—
127#1277—111no—
128C23×C11C2×C4⋊C411yescharacteristic
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11#10812yes—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11C2×M1611yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C4×D11—42no—
162C4×D11—42no—
163C4×D11—41no—
164C4×D11—41no—
165C4×D11—41no—
166C4×D11—41no—
167C4×D11—41no—
168C4×D11—41no—
169C4×D11—41no—
170C4×D11—41no—
171C8×C11—22no—
172C8×C11—41no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—22no—
176C11⋊C8—41no—
177C11⋊C8—42no—
178C11⋊C8—81no—
179C22×C42—111no—
180#432—222no—
181#432—222no—
182C2×C4⋊C8—111no—
183C2×C4⋊C8—111no—
184C2×C4⋊C8C2×D1111yescharacteristic
185C2×C4⋊C8C2×D1111yescharacteristic
186C2×C22⋊C8—111no—
187C2×C22⋊C8—111no—
188C2×C22⋊C8—221no—
189C2×C22⋊C8—221no—
190C2×#97—221no—
191C2×C4×C8—111no—
192C2×C4×C8C2×D1111yescharacteristic
193#336—111no—
194#336—111no—
195#336—221no—
196#335—222no—
197#334—22no—
198C22×C11#38511yescharacteristic
199C22×C11#42311yescharacteristic
200C22×C11#42411yescharacteristic
201C22×C11#42711yescharacteristic
202C22×C11#42811yescharacteristic
203C22×C11C2×#10811yescharacteristic
204C22×C11#43011yescharacteristic
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11#43511yescharacteristic
215C4×C11#43511yescharacteristic
216C4×C11#43611yescharacteristic
217C4×C11#43611yescharacteristic
218C4×C11#44911yescharacteristic
219C4×C11#45211yescharacteristic
220C4×C11#48211yescharacteristic
221C4×C11#48511yescharacteristic
222Dic11—41no—
223Dic11—41no—
224Dic11—41no—
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—111no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—111no—
231C22×C8—111no—
232C22×C8—221no—
233C22×C8—221no—
234C22×C8C4×D1111yescharacteristic
235C22×C8C4×D1111yescharacteristic
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—111no—
239C2×C42—221no—
240C2×C42—221no—
241C2×C42—221no—
242C2×C42—221no—
243C2×C42C22×D1111yescharacteristic
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251C4⋊C8C22⋊D1112yes—
252C22⋊C8—222no—
253C22⋊C8—224no—
254C22⋊C8—222no—
255C22⋊C8—442no—
256#97—224no—
257C4×C8—21no—
258C4×C8—21no—
259C4×C8—221no—
260C4×C8—221no—
261C2×C11#156811yescharacteristic
262C2×C11#156911yescharacteristic
263C2×C11#157211yescharacteristic
264C2×C11#157311yescharacteristic
265C2×C11#185111yescharacteristic
266C2×C11#185411yescharacteristic
267C2×C11#185511yescharacteristic
268D11—42no—
269C24—111no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—222no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4Q8×D1111yescharacteristic
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—112no—
304C2×C8—221no—
305C2×C8—221no—
306C2×C8—221no—
307C2×C8—221no—
308C2×C8—221no—
309C2×C8—222no—
310C2×C8—441no—
311C2×C8—441no—
312C2×C8—441no—
313C2×C8—441no—
314C2×C8—441no—
315C2×C8#431312yes—
316C42—221no—
317C42—221no—
318C42—221no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42#433911yescharacteristic
323C42D4×D1111yescharacteristic
324C42#434311yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C11#883411yescharacteristic, complemented, Sylow
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23C4⋊C4×D1111yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4#6694611yescharacteristic
357C2×C4#6694711yescharacteristic
358C2×C4#6694911yescharacteristic
359C2×C4C2×#431311yescharacteristic
360C2×C4#6695411yescharacteristic
361C2×C4M16×D1111yescharacteristic
362C2×C4#6696011yescharacteristic
363C2×C4#6696711yescharacteristic
364C2×C4#6696811yescharacteristic
365C2×C4#6696911yescharacteristic
366C2×C4#6696911yescharacteristic
367C2×C4C4×C22⋊D1111yescharacteristic
368C2×C4#6699011yescharacteristic
369C2×C4#6699911yescharacteristic
370C8—22no—
371C8—41no—
372C8—42no—
373C8—81no—
374C8—222no—
375C8—442no—
376C8—441no—
377C8—881no—
378C22—222no—
379C22—222no—
380C22—222no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22#1062245011yescharacteristic
386C22#1062245211yescharacteristic
387C22#1062247311yescharacteristic
388C22#1062247411yescharacteristic
389C22D11×#10811yescharacteristic
390C22#1062250611yescharacteristic
391C22#1062260211yescharacteristic
392C4—21no—
393C4—21no—
394C4—441no—
395C4—441no—
396C4—441no—
397C4#1062244911yescharacteristic
398C4#1062245111yescharacteristic
399C4#1062247911yescharacteristic
400C4#1062248011yescharacteristic
401C4#1062272411yescharacteristic
402C4#1062274111yescharacteristic
403C4#1062278511yescharacteristic
404C4#1062278611yescharacteristic
405C2—442no—
406C2#1306737611yescharacteristic
407C2#1306738011yescharacteristic
408C2#1306739311yescharacteristic
409C2#1306739811yescharacteristic
410C2#1306879711yescharacteristic
411C2#1306881411yescharacteristic
412C2#1306881911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socleC23×C11C2×C4⋊C4
prime radicalC23×D11C4⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#334D11
hypocenterC11#8834
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
4. C2×#10622117C2semidirect
5. #13066451C2semidirect
6. #13066450C2semidirect
7. C2×C11×#334C2semidirect
125. C2×#334D11semidirect
326. C11#8834semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
#130685932
C4×(C2×D11)⋊C82
C2×#106221172
#130664512
#130664502
C2×C11×#3342
#883411