Finite Group Databasebeta

← #13073575

Subgroups — #13073575

Order 1408.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66937C211yesmaximal, characteristic, complemented
5C11×#386C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622826C211yesmaximal, characteristic, complemented
8#10622572C211yesmaximal, characteristic, complemented
9#10622569C211yesmaximal, characteristic, complemented
10#10622565C211yesmaximal, characteristic, complemented
11#10622557C211yesmaximal, characteristic, complemented
12#10622283C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14D11×#95C211yesmaximal, characteristic, complemented
15#10622270C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33#66991—24no—
34C4×C22⋊D11—24no—
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
45#66937—24no—
46#66937—24no—
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11D414yescomplemented
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11D414yescomplemented
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—41no—
103C22⋊Dic11—22no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116C4×Dic11—22no—
117#2543—111nomaximal, Sylow
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11C2×D412yes—
132C23×C11C2411yescharacteristic
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—21no—
144C22×D11C2×D412yes—
145C22×D11C2×D412yes—
146C22×D11#4112yes—
147D4×C11—44no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—44no—
162C2×C4×C11C2×D412yes—
163C2×C4×C11#4112yes—
164C22⋊D11—28no—
165C22⋊D11—44no—
166C22⋊D11—44no—
167C22⋊D11—44no—
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—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11C2×D412yes—
184C2×Dic11C2×D412yes—
185C2×Dic11#4112yes—
186D44—44no—
187C4×D11—44no—
188C4×D11—44no—
189C4×D11—44no—
190C2×#121—111no—
191C2×#121—111no—
192C2×#121—111no—
193C2×C4×D4—111no—
194#398—111no—
195#397—111no—
196#394—111no—
197#392—111no—
198#388—111no—
199#388—111no—
200#386—111no—
201#386—111no—
202#386—111no—
203#386D1111yescharacteristic, complemented
204C2×#95—111no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11C22×D411yescharacteristic
220C22×C11C22×D411yescharacteristic
221C22×C11C2×#4111yescharacteristic
222C22×C11C2×#4111yescharacteristic
223C22×C11C2×#4111yescharacteristic
224C22×C11H(5,𝔽2)11yescharacteristic
225C22×C11H(5,𝔽2)11yescharacteristic
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11#12114yes—
240C4×C11—22no—
241C4×C11—22no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11—41no—
245Dic11—22no—
246Dic11—22no—
247Dic11—22no—
248Dic11—41no—
249Dic11—41no—
250Dic11—41no—
251C22×D4—111no—
252C22×D4—111no—
253C22×D4—111no—
254C22×D4—111no—
255C22×D4—111no—
256C22×D4C2×D1111yescharacteristic
257C23×C4—111no—
258C23×C4—111no—
259C23×C4—111no—
260C23×C4C2×D1111yescharacteristic
261#121—224no—
262#121—224no—
263#121—224no—
264C4×D4—224no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4C2×D1111yescharacteristic
279C2×C22⋊C4C2×D1111yescharacteristic
280C2×C22⋊C4C2×D1111yescharacteristic
281C2×C42—111no—
282#95—111no—
283#95—111no—
284#95—111no—
285#95—111no—
286#95—111no—
287#95—111no—
288#95C2×D1111yescharacteristic
289#95C2×D1111yescharacteristic
290C2×C11—42no—
291C2×C11—81no—
292C2×C11C2×#12111yescharacteristic
293C2×C11#53211yescharacteristic
294C2×C11#53411yescharacteristic
295C2×C11#54611yescharacteristic
296C2×C11#54611yescharacteristic
297C2×C11#55311yescharacteristic
298C2×C11#55311yescharacteristic
299D11—24no—
300D11—81no—
301C24—111no—
302C24—111no—
303C24C22×D1111yescharacteristic
304C24C22×D1111yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—114no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—222no—
312C2×D4—222no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—441no—
323C22×C4—22no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—114no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4C22×D1111yescharacteristic
342C22×C4C22×D1111yescharacteristic
343C22×C4C22×D1111yescharacteristic
344C22×C4C22×D1111yescharacteristic
345C22×C4C22×D1111yescharacteristic
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—222no—
357C22⋊C4—222no—
358C22⋊C4—222no—
359C22⋊C4—222no—
360C22⋊C4—222no—
361C22⋊C4—441no—
362C42—222no—
363C11#254311yescharacteristic, complemented, Sylow
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—112no—
378C23—112no—
379C23—112no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23D4×D1112yes—
392C23C23×D1111yescharacteristic
393D4—44no—
394D4—228no—
395D4—444no—
396D4—444no—
397D4—444no—
398D4—444no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—44no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—112no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—444no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4#433912yes—
435C2×C4D4×D1112yes—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—114no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—222no—
456C22—222no—
457C22—441no—
458C22—441no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22—441no—
463C22—441no—
464C22C2×#433911yescharacteristic
465C22C2×D4×D1111yescharacteristic
466C22C2×D4×D1111yescharacteristic
467C22#6703711yescharacteristic
468C22#6703711yescharacteristic
469C22#41×D1111yescharacteristic
470C22#41×D1111yescharacteristic
471C4—22no—
472C4—22no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—222no—
477C4—222no—
478C4—222no—
479C4—441no—
480C4—441no—
481C4—441no—
482C2—42no—
483C2—81no—
484C2—224no—
485C2—881no—
486C2#1062302111yescharacteristic
487C2#1062307911yescharacteristic
488C2#1062308911yescharacteristic
489C2#1062312011yescharacteristic
490C2D11×#12111yescharacteristic
491C2#1062314111yescharacteristic
492C2#1062319211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#66991C2semidirect
2. C2×C4×C22⋊D11C2semidirect
3. C2×#66937C2semidirect
4. C2×#66937C2semidirect
5. C11×#386C2semidirect
6. #10622836C2semidirect
7. #10622826C2semidirect
8. #10622572C2semidirect
9. #10622569C2semidirect
10. #10622565C2semidirect
11. #10622557C2semidirect
12. #10622283C2semidirect
13. #10622278C2semidirect
14. D11×#95C2semidirect
15. #10622270C2semidirect
81. C2×C22⋊D11D4semidirect
99. C2×C4×D11D4semidirect
203. #386D11semidirect
363. C11#2543semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×C4×C22⋊D112
C2×#669372
C11×#3862
#106228362
#106228262
#106225722
#106225692
#106225652
#106225572
#106222832
#106222782
D11×#952
#106222702
#254311