Finite Group Databasebeta

← #13072192

Subgroups — #13072192

Order 1408.

660 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
2C2×#66949C211yesmaximal, characteristic, complemented
3C2×#66938C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic
5C11×#380C211yesmaximal, characteristic, complemented
6#10622826C211yesmaximal, characteristic, complemented
7#10622606C211yesmaximal, characteristic, complemented
8#10622604C211yesmaximal, characteristic, complemented
9#10622585C211yesmaximal, characteristic, complemented
10#10622572C211yesmaximal, characteristic, complemented
11#10622565C211yesmaximal, characteristic, complemented
12#10622280C211yesmaximal, characteristic, complemented
13#10622279C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C22×C4×D11C2211yescharacteristic
22C22×Dic22C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C4×C22⋊D11—24no—
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×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
43C2×C4×Dic11C2211yescharacteristic
44#66949—24no—
45#66938—24no—
46#66937—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11D414yes—
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2311yescharacteristic
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—41no—
82C2×C4×D11—22no—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—22no—
87C2×C4×D11—41no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C22⋊Dic11—22no—
96C22⋊Dic11—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)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105Dic11⋊C4—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—41no—
108Dic11⋊C4D414yescomplemented
109C4×Dic11—22no—
110C4×Dic11—22no—
111#2427—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11C2×D412yes—
119C23×C11C2411yescharacteristic
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—
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×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—44no—
151C2×C4×C11C2×D412yes—
152C2×C4×C11#4112yes—
153C22⋊D11—28no—
154C22⋊D11—44no—
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—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11C2×D412yes—
170C2×Dic11C2×D412yes—
171C2×Dic11C2×D412yes—
172C2×Dic11#4112yes—
173D44—44no—
174C4×D11—44no—
175C4×D11—44no—
176Dic22—44no—
177C2×#124—111no—
178C2×C22⋊Q8—111no—
179C2×#121—111no—
180C2×C4×D4—111no—
181#397—111no—
182#397—111no—
183#394—111no—
184#394—111no—
185#391—111no—
186#389—111no—
187#386—111no—
188#386—111no—
189#380—111no—
190#380D1111yescharacteristic, complemented
191C4×C22⋊C4—111no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11C22×D411yescharacteristic
200C22×C11C22×D411yescharacteristic
201C22×C11C2×#4111yescharacteristic
202C22×C11C2×#4111yescharacteristic
203C22×C11C2×#4111yescharacteristic
204C22×C11H(5,𝔽2)11yescharacteristic
205C22×C112−1+411yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—22no—
211C2×D11—22no—
212C2×D11—41no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—41no—
226Dic11—22no—
227Dic11—41no—
228Dic11—41no—
229Dic11—41no—
230Dic11—41no—
231Dic11#12114yes—
232C22×Q8—111no—
233C22×D4—111no—
234C22×D4—111no—
235C22×D4—111no—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4C2×D1111yescharacteristic
239#124—224no—
240C22⋊Q8—224no—
241#121—224no—
242C4×D4—224no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4C2×D1111yescharacteristic
248C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
260C2×C22⋊C4C2×D1111yescharacteristic
261C2×C42—111no—
262C2×C42—111no—
263#95—111no—
264#95—111no—
265#95—111no—
266#95—111no—
267#95—111no—
268#95—111no—
269#95C2×D1111yescharacteristic
270#95C2×D1111yescharacteristic
271C2×C11—42no—
272C2×C11C2×#12111yescharacteristic
273C2×C11#52911yescharacteristic
274C2×C11#54211yescharacteristic
275C2×C11#54611yescharacteristic
276C2×C11#54611yescharacteristic
277C2×C11#54711yescharacteristic
278C2×C11#54811yescharacteristic
279D11—42no—
280D11—42no—
281C24—111no—
282C24—111no—
283C24C22×D1111yescharacteristic
284C2×Q8—222no—
285C2×Q8—222no—
286C2×Q8—222no—
287C2×D4—114no—
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—222no—
294C2×D4—441no—
295C2×D4—441no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—441no—
311C22×C4C22×D1111yescharacteristic
312C22×C4C22×D1111yescharacteristic
313C22×C4C22×D1111yescharacteristic
314C22×C4C22×D1111yescharacteristic
315C22×C4C22×D1111yescharacteristic
316C22×C4C22×D1111yescharacteristic
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—114no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—441no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C22⋊C4—222no—
334C22⋊C4—222no—
335C42—222no—
336C42—222no—
337C11#242711yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—112no—
345C23—112no—
346C23—221no—
347C23—221no—
348C23—221no—
349C23—221no—
350C23—221no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23D4×D1112yes—
359C23C23×D1111yescharacteristic
360Q8—444no—
361D4—228no—
362D4—444no—
363D4—444no—
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—44no—
381C2×C4—112no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—112no—
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—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4#433912yes—
402C2×C4D4×D1112yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—222no—
411C22—222no—
412C22—222no—
413C22—222no—
414C22—222no—
415C22—222no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22C2×#433911yescharacteristic
425C22C2×D4×D1111yescharacteristic
426C22C2×D4×D1111yescharacteristic
427C22#6703711yescharacteristic
428C22#6704011yescharacteristic
429C22#41×D1111yescharacteristic
430C22#41×D1111yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—114no—
438C4—222no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—441no—
443C2—42no—
444C2—442no—
445C2—442no—
446C2#1062302111yescharacteristic
447C2#1062303811yescharacteristic
448C2#1062305911yescharacteristic
449C2D11×#12111yescharacteristic
450C2#1062314111yescharacteristic
451C2#1062316411yescharacteristic
452C2#1062317111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC2×#66937C2
hypercenter#380D11
hypocenterC11#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊D11C2semidirect
2. C2×#66949C2semidirect
3. C2×#66938C2semidirect
5. C11×#380C2semidirect
6. #10622826C2semidirect
7. #10622606C2semidirect
8. #10622604C2semidirect
9. #10622585C2semidirect
10. #10622572C2semidirect
11. #10622565C2semidirect
12. #10622280C2semidirect
13. #10622279C2semidirect
14. #10622278C2semidirect
15. #10622259C2semidirect
108. Dic11⋊C4D4semidirect
190. #380D11semidirect
337. C11#2427semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D112
C2×#669492
C2×#669382
C2×#669372
C11×#3802
#106228262
#106226062
#106226042
#106225852
#106225722
#106225652
#106222802
#106222792
#106222782
#106222592
#242711