Finite Group Databasebeta

← #13071954

Subgroups — #13071954

Order 1408.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4341C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×D4×Dic11C211yesmaximal, characteristic, complemented
4C2×#66931C211yesmaximal, characteristic, complemented
5C11×#392C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622835C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622569C211yesmaximal, characteristic, complemented
12#10622563C211yesmaximal, characteristic, complemented
13#10622555C211yesmaximal, characteristic, complemented
14#10622281C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C23×Dic11C2211yescharacteristic
24C23×Dic11C2211yescharacteristic
25C2×#4341—24no—
26C2×#4341—24no—
27C2×#4341—24no—
28C22×C4×D11C2211yescharacteristic
29C22×Dic22C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39#66992—24no—
40D4×Dic11—24no—
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊Dic11C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×Dic11⋊C4C2211yescharacteristic
49C2×C4×Dic11C2211yescharacteristic
50#66931—24no—
51C11×#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C24×C11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—22no—
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11D414yescomplemented
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11D414yescomplemented
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99#4341—232no—
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×Dic22—22no—
104C2×Dic22—22no—
105C2×Dic22D414yescomplemented
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123C4×Dic11—22no—
124#2407—111nomaximal, Sylow
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11C2×D412yes—
144C23×C11C2×D412yes—
145C23×C11#4112yescomplemented
146C23×C11C2411yescharacteristic
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11C2×D412yes—
154D4×C11—28no—
155D4×C11—28no—
156D4×C11—44no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11C2×D412yes—
168C2×C4×C11#4112yescomplemented
169C22⋊D11—28no—
170C22⋊D11—28no—
171C22⋊D11—44no—
172C2×Dic11—28no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—28no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—44no—
191C2×Dic11C2×D412yes—
192C2×Dic11C2×D412yes—
193C2×Dic11C2×D412yes—
194C2×Dic11C2×D412yes—
195C2×Dic11C2×D412yes—
196C4×D11—28no—
197Dic22—28no—
198C22×#41—111no—
199C2×C22⋊Q8—111no—
200C2×#121—111no—
201C2×C4×D4—111no—
202#394—111no—
203#394—111no—
204#392—111no—
205#392D1111yescharacteristic, complemented
206#391—111no—
207#390—111no—
208#386—111no—
209#386—111no—
210#385—111no—
211#385—111no—
212#380—111no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11C22×D411yescharacteristic
235C22×C11C22×D411yescharacteristic
236C22×C11C22×D411yescharacteristic
237C22×C11C2×#4111yescharacteristic
238C22×C11C2×#4111yescharacteristic
239C22×C11H(5,𝔽2)11yescharacteristic
240C22×C112−1+411yescharacteristic
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—41no—
251C4×C11—41no—
252Dic11—22no—
253Dic11—22no—
254Dic11—41no—
255Dic11—41no—
256Dic11—41no—
257Dic11—41no—
258Dic11#12014yes—
259C2×#41—224no—
260C2×#41—224no—
261C2×#41—224no—
262C22×Q8—111no—
263C22×D4—111no—
264C22×D4—111no—
265C22×D4—111no—
266C22×D4C2×D1111yescharacteristic
267C22×D4C2×D1111yescharacteristic
268C22×D4C2×D1111yescharacteristic
269C23×C4—111no—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C22⋊Q8—224no—
274#121—224no—
275C4×D4—224no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—111no—
283C2×C22⋊C4—111no—
284C2×C22⋊C4—111no—
285C2×C22⋊C4—111no—
286C2×C22⋊C4—111no—
287C2×C22⋊C4—111no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4C2×D1111yescharacteristic
291C2×C22⋊C4C2×D1111yescharacteristic
292C2×C22⋊C4C2×D1111yescharacteristic
293C2×C42—111no—
294#95—111no—
295#95—111no—
296#95—111no—
297#95—111no—
298#95—111no—
299#95C2×D1111yescharacteristic
300C2×C11—42no—
301C2×C11—42no—
302C2×C11—42no—
303C2×C11C2×#12011yescharacteristic
304C2×C11#52511yescharacteristic
305C2×C11#53711yescharacteristic
306C2×C11#54611yescharacteristic
307C2×C11#54711yescharacteristic
308C2×C11#54811yescharacteristic
309C2×C11#55011yescharacteristic
310D11—42no—
311C24—111no—
312C24C22×D1111yescharacteristic
313C24C22×D1111yescharacteristic
314C24C22×D1111yescharacteristic
315#41—2232no—
316C2×Q8—114no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—41no—
328C2×D4—114no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—441no—
337C22×C4—111no—
338C22×C4—114no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4C22×D1111yescharacteristic
357C22×C4C22×D1111yescharacteristic
358C22×C4C22×D1111yescharacteristic
359C22×C4C22×D1111yescharacteristic
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—41no—
368C22⋊C4—222no—
369C22⋊C4—222no—
370C22⋊C4—222no—
371C22⋊C4—222no—
372C22⋊C4—222no—
373C22⋊C4—222no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C42—222no—
378C11#240711yescharacteristic, complemented, Sylow
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—112no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23D4×D1112yes—
405C23D4×D1112yes—
406C23#434112yescomplemented
407C23C23×D1111yescharacteristic
408Q8—228no—
409D4—28no—
410D4—28no—
411D4—44no—
412D4—228no—
413D4—228no—
414D4—444no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—228no—
431C2×C4—228no—
432C2×C4—228no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—444no—
450C2×C4D4×D1112yes—
451C2×C4#434112yescomplemented
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—441no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22C2×D4×D1111yescharacteristic
481C22C2×D4×D1111yescharacteristic
482C22C2×D4×D1111yescharacteristic
483C22C2×#434111yescharacteristic
484C22C2×#434111yescharacteristic
485C22#6703711yescharacteristic
486C22#6704311yescharacteristic
487C4—22no—
488C4—22no—
489C4—41no—
490C4—41no—
491C4—114no—
492C4—222no—
493C4—222no—
494C4—441no—
495C4—441no—
496C4—441no—
497C4—441no—
498C2—42no—
499C2—42no—
500C2—42no—
501C2—442no—
502C2#1062311711yescharacteristic
503C2D11×#12011yescharacteristic
504C2#1062312211yescharacteristic
505C2#1062312811yescharacteristic
506C2#1062312911yescharacteristic
507C2#1062314211yescharacteristic
508C2#1062324911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#4341C2semidirect
2. C2×#66992C2semidirect
3. C2×D4×Dic11C2semidirect
4. C2×#66931C2semidirect
5. C11×#392C2semidirect
6. #10622836C2semidirect
7. #10622835C2semidirect
8. #10622833C2semidirect
9. #10622574C2semidirect
10. #10622570C2semidirect
11. #10622569C2semidirect
12. #10622563C2semidirect
13. #10622555C2semidirect
14. #10622281C2semidirect
15. #10622259C2semidirect
82. C2×C22⋊D11D4semidirect
91. C22×Dic11D4semidirect
105. C2×Dic22D4semidirect
145. C23×C11#41semidirect
168. C2×C4×C11#41semidirect
205. #392D11semidirect
378. C11#2407semidirect
406. C23#4341semidirect
451. C2×C4#4341semidirect

Maximal subgroups

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

subgroupindex
C22×#43412
C2×#669922
C2×D4×Dic112
C2×#669312
C11×#3922
#106228362
#106228352
#106228332
#106225742
#106225702
#106225692
#106225632
#106225552
#106222812
#106222592
#240711