Finite Group Databasebeta

← #13072586

Subgroups — #13072586

Order 1408.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67000C211yesmaximal, characteristic, complemented
2C2×#66999C211yesmaximal, characteristic, complemented
3C2×#66947C211yesmaximal, characteristic, complemented
4C2×#66946C211yesmaximal, characteristic, complemented
5C11×#395C211yesmaximal, characteristic, complemented
6#10622607C211yesmaximal, characteristic, complemented
7#10622603C211yesmaximal, characteristic, complemented
8#10622602C211yesmaximal, characteristic, complemented
9#10622601C211yesmaximal, characteristic, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622284C211yesmaximal, characteristic
12#10622283C211yesmaximal, characteristic, complemented
13#10622282C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622262C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25#67000—24no—
26#66999—24no—
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
40C2×C4⋊Dic11C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×C4×Dic11C2211yescharacteristic
45C2×C4×Dic11C2211yescharacteristic
46C2×C4×Dic11C2211yescharacteristic
47#66947—24no—
48#66946—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—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—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4D414yescomplemented
104C4⋊Dic11—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4D414yescomplemented
108C4×Dic11—22no—
109C4×Dic11—22no—
110C4×Dic11—22no—
111#2461—111nomaximal, Sylow
112C23×C11C2411yescharacteristic
113C22×D11—21no—
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—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11C2×D412yes—
133C22×D11#4112yes—
134Q8×C11—44no—
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—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11C2×D412yes—
153C2×C4×C11C2×D412yes—
154C2×C4×C11#4112yes—
155C2×C4×C11#4112yes—
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—21no—
167C2×Dic11—21no—
168C2×Dic11C2×D412yes—
169C2×Dic11C2×D412yes—
170C2×Dic11C2×D412yes—
171D44—28no—
172D44—44no—
173D44—44no—
174C4×D11—44no—
175C4×D11—44no—
176C2×#124—111no—
177C2×#123—111no—
178C2×C22⋊Q8—111no—
179C2×C4×D4—111no—
180#396—111no—
181#395D1111yescharacteristic, complemented
182#394—111no—
183#392—111no—
184#390—111no—
185#388—111no—
186#388—111no—
187#388—111no—
188#386—111no—
189#385—111no—
190C4×C4⋊C4—111no—
191C22×C11C22×D411yescharacteristic
192C22×C11C22×D411yescharacteristic
193C22×C11C2×#4111yescharacteristic
194C22×C11C2×#4111yescharacteristic
195C22×C11C2×#4111yescharacteristic
196C22×C11H(5,𝔽2)11yescharacteristic
197C22×C112−1+411yescharacteristic
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—41no—
226Dic11—22no—
227Dic11—22no—
228Dic11—22no—
229Dic11—41no—
230Dic11—41no—
231C22×Q8C2×D1111yescharacteristic
232C22×D4—111no—
233C22×D4—111no—
234C22×D4—111no—
235C23×C4—111no—
236C23×C4—111no—
237#124—224no—
238#123—224no—
239C22⋊Q8—224no—
240C4×D4—224no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4C2×D1111yescharacteristic
246C2×C4⋊C4C2×D1111yescharacteristic
247C2×C4⋊C4C2×D1111yescharacteristic
248C2×C22⋊C4—111no—
249C2×C22⋊C4—111no—
250C2×C22⋊C4—111no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—111no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C42—111no—
262C2×C42—111no—
263C2×C42—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95C2×D1111yescharacteristic
268#95C2×D1111yescharacteristic
269#95C2×D1111yescharacteristic
270C2×C11#52511yescharacteristic
271C2×C11#53211yescharacteristic
272C2×C11#54211yescharacteristic
273C2×C11D4211yescharacteristic
274C2×C11#54711yescharacteristic
275C2×C11#54811yescharacteristic
276C2×C11#55111yescharacteristic
277D11—42no—
278D11—42no—
279D11—81no—
280C24—111no—
281C24—111no—
282C24—111no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—441no—
294C2×D4—441no—
295C22×C4—111no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4C22×D1111yescharacteristic
307C22×C4C22×D1111yescharacteristic
308C22×C4C22×D1111yescharacteristic
309C22×C4C22×D1111yescharacteristic
310C22×C4C22×D1111yescharacteristic
311C22×C4C22×D1111yescharacteristic
312C22×C4C22×D1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—114no—
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—222no—
320C22⋊C4—114no—
321C22⋊C4—222no—
322C22⋊C4—222no—
323C22⋊C4—222no—
324C22⋊C4—222no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C42—222no—
334C42—222no—
335C42—222no—
336C11#246111yescharacteristic, complemented, Sylow
337C23—112no—
338C23—112no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—221no—
345C23—221no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23C23×D1111yescharacteristic
359Q8—44no—
360D4—228no—
361D4—444no—
362D4—444no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—112no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—444no—
396C2×C4—444no—
397C2×C4D4×D1112yes—
398C2×C4D4×D1112yes—
399C2×C4#434312yes—
400C2×C4#434312yes—
401C22—222no—
402C22—222no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22—222no—
407C22—441no—
408C22—441no—
409C22—441no—
410C22—441no—
411C22—441no—
412C22—441no—
413C22—441no—
414C22—441no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22C2×D4×D1111yescharacteristic
423C22C2×D4×D1111yescharacteristic
424C22#6703711yescharacteristic
425C22C2×#434311yescharacteristic
426C22C2×#434311yescharacteristic
427C22#6704011yescharacteristic
428C22#41×D1111yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—222no—
437C4—222no—
438C4—222no—
439C4—441no—
440C4—441no—
441C2—442no—
442C2—442no—
443C2—881no—
444C2#1062312111yescharacteristic
445C2#1062315811yescharacteristic
446C2#1062316411yescharacteristic
447C2#1062316811yescharacteristic
448C2#1062325611yescharacteristic
449C2#1062325711yescharacteristic
450C2#1062326411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radical#10622284C2
hypercenter#395D11
hypocenterC11#2461
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#67000C2semidirect
2. C2×#66999C2semidirect
3. C2×#66947C2semidirect
4. C2×#66946C2semidirect
5. C11×#395C2semidirect
6. #10622607C2semidirect
7. #10622603C2semidirect
8. #10622602C2semidirect
9. #10622601C2semidirect
10. #10622285C2semidirect
12. #10622283C2semidirect
13. #10622282C2semidirect
14. #10622278C2semidirect
15. #10622262C2semidirect
103. (C2×D11)⋊C4D4semidirect
107. Dic11⋊C4D4semidirect
181. #395D11semidirect
336. C11#2461semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669992
C2×#669472
C2×#669462
C11×#3952
#106226072
#106226032
#106226022
#106226012
#106222852
#106222842
#106222832
#106222822
#106222782
#106222622
#246111