Finite Group Databasebeta

← #13072721

Subgroups — #13072721

Order 1408.

582 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×C11×#117C211yesmaximal, characteristic, complemented
2C2×#66947C211yesmaximal, characteristic, complemented
3#10622826C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic, complemented
5#10622606C211yesmaximal, characteristic, complemented
6#10622605C211yesmaximal, characteristic, complemented
7#10622594C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic
9#10622570C211yesmaximal, characteristic, complemented
10#10622569C211yesmaximal, characteristic, complemented
11#10622561C211yesmaximal, characteristic, complemented
12#10622553C211yesmaximal, characteristic, complemented
13#10622552C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15#10622546C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C11×#117—24no—
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C42×C11C2211yescharacteristic
27C2×C42×C11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×C4⋊Dic11C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44#66947—24no—
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C23×D11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C2×C22⋊D11—22no—
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—41no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—41no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4D414yescomplemented
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C42×C11—22no—
88C42×C11—22no—
89C22⋊Dic11—41no—
90C22⋊Dic11—41no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95(C2×D11)⋊C4—22no—
96(C2×D11)⋊C4—22no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103Dic11⋊C4—41no—
104C4×Dic11—41no—
105#2471—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11#4112yes—
113C23×C11C2411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11#4112yes—
128C2×C4×C11—28no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
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×C11C2×D412yes—
144C2×C4×C11C2×D412yes—
145C2×C4×C11C2×D412yes—
146C2×C4×C11#4112yes—
147C22⋊D11—44no—
148C22⋊D11—44no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
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—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11#4112yes—
167D44—44no—
168C4×D11—44no—
169C2×#123—111no—
170C2×#117D1111yescharacteristic, complemented
171#399—111no—
172#397—111no—
173#396—111no—
174#392—111no—
175#390—111no—
176#390—111no—
177#388—111no—
178#387—111no—
179#387—111no—
180#386—111no—
181#386—111no—
182#386—111no—
183C4×C22⋊C4—111no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11C22×D411yescharacteristic
192C22×C11C2×#4111yescharacteristic
193C22×C11C2×#4111yescharacteristic
194C22×C11C2×#4111yescharacteristic
195C22×C11C2×#4111yescharacteristic
196C22×C11H(5,𝔽2)11yescharacteristic
197C22×C11H(5,𝔽2)11yescharacteristic
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11—41no—
218Dic11—22no—
219Dic11—41no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224C22×D4—111no—
225C22×D4—111no—
226C22×D4—111no—
227C23×C4—111no—
228C23×C4C2×D1111yescharacteristic
229#123—224no—
230#117—24no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4C2×D1111yescharacteristic
236C2×C4⋊C4C2×D1111yescharacteristic
237C2×C22⋊C4—111no—
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—111no—
247C2×C22⋊C4—111no—
248C2×C22⋊C4C2×D1111yescharacteristic
249C2×C22⋊C4C2×D1111yescharacteristic
250C2×C42—111no—
251C2×C42C2×D1111yescharacteristic
252C2×C42C2×D1111yescharacteristic
253#95—111no—
254#95—111no—
255#95—111no—
256#95—111no—
257#95—111no—
258#95—111no—
259#95—111no—
260#95—111no—
261C2×C11—42no—
262C2×C11#52511yescharacteristic
263C2×C11#52911yescharacteristic
264C2×C11#54011yescharacteristic
265C2×C11#54611yescharacteristic
266C2×C11#55011yescharacteristic
267C2×C11#55111yescharacteristic
268C2×C11#55111yescharacteristic
269D11—42no—
270D11—81no—
271C24—111no—
272C24—111no—
273C24C22×D1111yescharacteristic
274C2×D4—222no—
275C2×D4—222no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—222no—
293C22×C4—222no—
294C22×C4—441no—
295C22×C4C22×D1111yescharacteristic
296C22×C4C22×D1111yescharacteristic
297C22×C4C22×D1111yescharacteristic
298C22×C4C22×D1111yescharacteristic
299C22×C4C22×D1111yescharacteristic
300C22×C4C22×D1111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4C22⋊D1114yescomplemented
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—222no—
310C22⋊C4—222no—
311C22⋊C4—222no—
312C22⋊C4—222no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C42—22no—
321C42—22no—
322C42—441no—
323C11#247111yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—112no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23—221no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23#433912yes—
345C23C23×D1111yescharacteristic
346D4—444no—
347D4—444no—
348D4—444no—
349C2×C4—28no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—112no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
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—221no—
382C2×C4—444no—
383C2×C4#433912yes—
384C2×C4C2×C22⋊D1112yes—
385C2×C4C2×C22⋊D1112yes—
386C2×C4C2×C22⋊D1112yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—222no—
395C22—222no—
396C22—222no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22C2×#433911yescharacteristic
409C22C2×#433911yescharacteristic
410C22#41×D1111yescharacteristic
411C22#41×D1111yescharacteristic
412C22#6704211yescharacteristic
413C22#6704211yescharacteristic
414C22C22×C22⋊D1111yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—41no—
421C4—222no—
422C4—441no—
423C4—441no—
424C4—441no—
425C4—441no—
426C4—441no—
427C2—42no—
428C2—442no—
429C2—881no—
430C2#1062305811yescharacteristic
431C2#1062305811yescharacteristic
432C2#1062305911yescharacteristic
433C2#1062306611yescharacteristic
434C2#1062332211yescharacteristic
435C2#1062336011yescharacteristic
436C2#1062336511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#117C2
prime radical#10622573C2
hypercenterC2×#117D11
hypocenterC11#2471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C11×#117C2semidirect
2. C2×#66947C2semidirect
3. #10622826C2semidirect
4. #10622826C2semidirect
5. #10622606C2semidirect
6. #10622605C2semidirect
7. #10622594C2semidirect
9. #10622570C2semidirect
10. #10622569C2semidirect
11. #10622561C2semidirect
12. #10622553C2semidirect
13. #10622552C2semidirect
14. C4×(C2×D11)⋊C4C2semidirect
15. #10622546C2semidirect
84. C11×C4⋊C4D4semidirect
170. C2×#117D11semidirect
306. C4⋊C4C22⋊D11semidirect
323. C11#2471semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
C2×#669472
#106228262
#106226062
#106226052
#106225942
#106225732
#106225702
#106225692
#106225612
#106225532
#106225522
C4×(C2×D11)⋊C42
#106225462
#247111