Finite Group Databasebeta

← #13074877

Subgroups — #13074877

Order 1408.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66991C211yesmaximal, characteristic, complemented
4C2×#66947C211yesmaximal, characteristic, complemented
5#10622836C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622835C211yesmaximal, characteristic, complemented
9#10622826C211yesmaximal, characteristic, complemented
10#10622826C211yesmaximal, characteristic, complemented
11#10622594C211yesmaximal, characteristic, complemented
12#10622574C211yesmaximal, characteristic, complemented
13#10622573C211yesmaximal, characteristic, complemented
14#10622569C211yesmaximal, characteristic, complemented
15#10622558C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C22×C22⋊D11C2211yescharacteristic
26C22×D44C2211yescharacteristic
27C22×C4×D11C2211yescharacteristic
28C11×#121—24no—
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38#66993—24no—
39#66991—24no—
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×C4⋊Dic11C2211yescharacteristic
46C2×Dic11⋊C4C2211yescharacteristic
47C2×C4×Dic11C2211yescharacteristic
48#66947—24no—
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—22no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11D414yescomplemented
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2311yescharacteristic
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—41no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—41no—
106C11×C4⋊C4D414yescomplemented
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—22no—
121Dic11⋊C4—22no—
122C4×Dic11—22no—
123#2673—111nomaximal, Sylow
124C23×C11—21no—
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×C11—21no—
144C23×C11C2×D412yes—
145C23×C11C2411yescharacteristic
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11C2×D412yes—
160D4×C11—44no—
161D4×C11—44no—
162D4×C11—44no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—44no—
173C2×C4×C11C2×D412yes—
174C2×C4×C11C2×D412yes—
175C2×C4×C11C2×D412yes—
176C22⋊D11—44no—
177C22⋊D11—44no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C22⋊D11—44no—
181C22⋊D11—44no—
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—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11C2×D412yes—
199C2×Dic11#4112yes—
200D44—44no—
201C4×D11—44no—
202C2×#127—111no—
203C2×#123—111no—
204C2×#121—111no—
205C2×#121D1111yescharacteristic, complemented
206#394—111no—
207#394—111no—
208#392—111no—
209#392—111no—
210#392—111no—
211#392—111no—
212#388—111no—
213#387—111no—
214#386—111no—
215#386—111no—
216#386—111no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—41no—
221C22×C11—41no—
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×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11C22×D411yescharacteristic
239C22×C11C22×D411yescharacteristic
240C22×C11C2×#4111yescharacteristic
241C22×C11H(5,𝔽2)11yescharacteristic
242C22×C11H(5,𝔽2)11yescharacteristic
243C22×C11H(5,𝔽2)11yescharacteristic
244C22×C11H(5,𝔽2)11yescharacteristic
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—41no—
263Dic11—22no—
264Dic11—22no—
265Dic11—41no—
266Dic11—41no—
267Dic11—41no—
268Dic11—41no—
269C22×D4—111no—
270C22×D4—111no—
271C22×D4—111no—
272C22×D4—111no—
273C22×D4—111no—
274C22×D4—111no—
275C22×D4—111no—
276C22×D4C2×D1111yescharacteristic
277C22×D4C2×D1111yescharacteristic
278C22×D4C2×D1111yescharacteristic
279C23×C4—111no—
280C23×C4C2×D1111yescharacteristic
281#127—224no—
282#123—224no—
283#121—24no—
284#121—224no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4C2×D1111yescharacteristic
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—111no—
291C2×C22⋊C4—111no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4—111no—
299C2×C22⋊C4C2×D1111yescharacteristic
300C2×C22⋊C4C2×D1111yescharacteristic
301C2×C42—111no—
302#95—111no—
303#95—111no—
304#95—111no—
305#95—111no—
306#95—111no—
307#95—111no—
308C2×C11—42no—
309C2×C11—81no—
310C2×C11—81no—
311C2×C11#53411yescharacteristic
312C2×C11#53511yescharacteristic
313C2×C11#54011yescharacteristic
314C2×C11D4211yescharacteristic
315C2×C11#54611yescharacteristic
316C2×C11#55011yescharacteristic
317C2×C11#56011yescharacteristic
318D11—42no—
319D11—81no—
320C24—111no—
321C24—111no—
322C24C22×D1111yescharacteristic
323C24C22×D1111yescharacteristic
324C24C22×D1111yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—114no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—441no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—441no—
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C22×C4C22×D1111yescharacteristic
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4C22⋊D1114yescomplemented
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—222no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C22⋊C4—222no—
380C22⋊C4—222no—
381C22⋊C4—222no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C42—222no—
388C11#267311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—112no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23—221no—
415C23—221no—
416C23—221no—
417C23—221no—
418C23—221no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23D4×D1112yes—
424C23C23×D1111yescharacteristic
425D4—44no—
426D4—44no—
427D4—44no—
428D4—444no—
429D4—444no—
430D4—444no—
431D4—444no—
432D4—444no—
433D4—444no—
434D4—444no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—44no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—444no—
464C2×C4C2×C22⋊D1112yes—
465C2×C4C2×C22⋊D1112yes—
466C2×C4C2×C22⋊D1112yes—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22—441no—
497C22—441no—
498C22—441no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22C2×D4×D1111yescharacteristic
503C22#6703711yescharacteristic
504C22#6703711yescharacteristic
505C22#6703711yescharacteristic
506C22#41×D1111yescharacteristic
507C22#6704211yescharacteristic
508C22C22×C22⋊D1111yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—41no—
513C4—222no—
514C4—222no—
515C4—441no—
516C4—441no—
517C4—441no—
518C4—441no—
519C2—42no—
520C2—81no—
521C2—81no—
522C2—442no—
523C2—881no—
524C2#1062313611yescharacteristic
525C2#1062314111yescharacteristic
526C2#1062314611yescharacteristic
527C2#1062315111yescharacteristic
528C2D4×C22⋊D1111yescharacteristic
529C2#1062333611yescharacteristic
530C2#1062336511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2673
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66993C2semidirect
3. C2×#66991C2semidirect
4. C2×#66947C2semidirect
5. #10622836C2semidirect
6. #10622836C2semidirect
7. #10622836C2semidirect
8. #10622835C2semidirect
9. #10622826C2semidirect
10. #10622826C2semidirect
11. #10622594C2semidirect
12. #10622574C2semidirect
13. #10622573C2semidirect
14. #10622569C2semidirect
15. #10622558C2semidirect
93. C2×C22⋊D11D4semidirect
106. C11×C4⋊C4D4semidirect
205. C2×#121D11semidirect
373. C4⋊C4C22⋊D11semidirect
388. C11#2673semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669932
C2×#669912
C2×#669472
#106228362
#106228352
#106228262
#106225942
#106225742
#106225732
#106225692
#106225582
#267311