Finite Group Databasebeta

← #14649452

Subgroups — #14649452

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622448C211yesmaximal, characteristic
2#13076969C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622119C211yesmaximal, characteristic, complemented
5C2×#10622119C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66950C412yes—
9C2×C42×D11C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×#66879—21no—
17#10622600—21no—
18#10622600—21no—
19#10622598—21no—
20#10622598—21no—
21#10622587C412yes—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622448—22no—
25#10622448—22no—
26#10622188—21no—
27#10622119—22no—
28#10622119—22no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×Dic22C2×C412yes—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—22no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48#66950—44no—
49C42×D11—21no—
50C42×D11—21no—
51C42×D11—21no—
52C42×D11—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11⋊#95—22no—
62C11⋊#95—22no—
63(C2×D11)⋊C8—24no—
64(C2×D11)⋊C8—42no—
65#66879—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70#9136—111nomaximal, Sylow
71C23×D11C22⋊C411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—22no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C2×C4×D11—22no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—41no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115(C2×D11)⋊C4—44no—
116C4⋊Dic11—44no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×#432—111no—
134#2857—111no—
135#1797—111no—
136C2×#333—111no—
137C2×#333—111no—
138#1296—111no—
139#1296D1111yescharacteristic, complemented
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11#10012yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×C4×C11#13711yescharacteristic
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C4×D11—42no—
180C4×D11—42no—
181C4×D11—41no—
182C4×D11—41no—
183C4×D11—41no—
184C4×D11—41no—
185C4×D11—41no—
186C4×D11—41no—
187C4×D11—41no—
188C4×D11—41no—
189Dic22—82no—
190Dic22—82no—
191C8×C11—42no—
192C8×C11—81no—
193C11⋊C8—42no—
194C11⋊C8—81no—
195C2×C4⋊Q8—111no—
196C2×C22⋊Q8—112no—
197C22×C42—111no—
198#432—222no—
199#432—222no—
200C2×C4⋊C8—111no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8C2×D1111yescharacteristic
203C2×C4⋊C8C2×D1111yescharacteristic
204C2×C22⋊C8—221no—
205C2×C22⋊C8—221no—
206C2×#97—221no—
207#391—112no—
208#389—221no—
209#389—221no—
210#384C2×D1111yescharacteristic
211#380—221no—
212#380—221no—
213#336—221no—
214#333—222no—
215#333—222no—
216C22×C11#38611yescharacteristic
217C22×C11C2×#10011yescharacteristic
218C22×C11#41311yescharacteristic
219C22×C11#41611yescharacteristic
220C22×C11#41711yescharacteristic
221C22×C11#41911yescharacteristic
222C22×C11#41911yescharacteristic
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—82no—
233C4×C11#45211yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#46811yescharacteristic
236C4×C11#46811yescharacteristic
237C4×C11#47011yescharacteristic
238C4×C11#47011yescharacteristic
239C4×C11#48511yescharacteristic
240C4×C11#48511yescharacteristic
241Dic11—41no—
242Dic11—41no—
243Dic11—41no—
244Dic11—82no—
245C22×Q8—112no—
246C23×C4—111no—
247C23×C4—111no—
248C23×C4—111no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—221no—
252C22×C8—221no—
253C4⋊Q8—221no—
254C4⋊Q8—221no—
255C4⋊Q8—221no—
256C4⋊Q8—221no—
257C22⋊Q8—444no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4C4×D1112yes—
264C2×C22⋊C4—222no—
265C2×C42—111no—
266C2×C42—111no—
267C2×C42—111no—
268C2×C42—221no—
269C2×C42—221no—
270C2×C42—221no—
271C2×C42—221no—
272C2×C42C22×D1111yescharacteristic
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280C4⋊C8D4412yes—
281C22⋊C8—224no—
282C22⋊C8—442no—
283#97—224no—
284#95—222no—
285#95—222no—
286C2×C11#155111yescharacteristic
287C2×C11#155411yescharacteristic
288C2×C11#155811yescharacteristic
289C2×C11#155911yescharacteristic
290C2×C11#187311yescharacteristic
291C2×C11#189411yescharacteristic
292C2×C11#190011yescharacteristic
293D11—42no—
294C24—111no—
295C2×Q8—222no—
296C2×Q8—222no—
297C2×Q8—442no—
298C2×Q8—442no—
299C22×C4—22no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—222no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—222no—
319C22×C4—441no—
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—222no—
330C2×C8—441no—
331C2×C8—441no—
332C2×C8—441no—
333C2×C8—441no—
334C2×C8—441no—
335C4⋊C4—42no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—444no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—444no—
346C42—221no—
347C42—221no—
348C42—221no—
349C42—221no—
350C42—221no—
351C42—221no—
352C42C2×D4411yescharacteristic
353C42#433911yescharacteristic
354C42D4×D1111yescharacteristic
355C42#434311yescharacteristic
356C11#913611yescharacteristic, complemented, Sylow
357C23—112no—
358C23—221no—
359C23—221no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23C22⋊C4×D1111yescharacteristic
365Q8—882no—
366Q8—882no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4C4×D4411yescharacteristic
395C2×C4#6693511yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4#6694611yescharacteristic
398C2×C4#6694711yescharacteristic
399C2×C4#6694811yescharacteristic
400C2×C4#6696411yescharacteristic
401C2×C4#6696511yescharacteristic
402C2×C4#6696811yescharacteristic
403C2×C4#6696811yescharacteristic
404C2×C4#6696811yescharacteristic
405C2×C4#6696911yescharacteristic
406C2×C4#6697111yescharacteristic
407C2×C4#6697111yescharacteristic
408C8—42no—
409C8—81no—
410C8—442no—
411C8—881no—
412C22—222no—
413C22—222no—
414C22—222no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22#1062227811yescharacteristic
420C22D11×#10011yescharacteristic
421C22#1062236411yescharacteristic
422C22#1062238411yescharacteristic
423C22#1062238511yescharacteristic
424C22#1062241511yescharacteristic
425C22#1062241511yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—441no—
430C4—441no—
431C4—441no—
432C4—882no—
433C4#1062239311yescharacteristic
434C4#1062239611yescharacteristic
435C4#1062242311yescharacteristic
436C4#1062242911yescharacteristic
437C4#1062248011yescharacteristic
438C4#1062248111yescharacteristic
439C4#1062249911yescharacteristic
440C4#1062250111yescharacteristic
441C2—442no—
442C2#1306730811yescharacteristic
443C2#1306732311yescharacteristic
444C2#1306734011yescharacteristic
445C2#1306734511yescharacteristic
446C2#1306892711yescharacteristic
447C2#1306904811yescharacteristic
448C2#1306907811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9136
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#10622119C2semidirect
5. C2×#10622119C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
139. #1296D11semidirect
356. C11#9136semidirect

Maximal subgroups

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

subgroupindex
C2×#106224482
#130769692
#130685932
C2×#106221192
#130664992
C11×#12962
#913611