Finite Group Databasebeta

← #13074883

Subgroups — #13074883

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×#66947C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C2×#66937C211yesmaximal, characteristic, complemented
4C2×#66927C211yesmaximal, characteristic, complemented
5C11×#388C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622573C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622546C211yesmaximal, characteristic, complemented
12#10622285C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic
24C22×D44C2211yescharacteristic
25C22×D44C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic
27C22×C4×D11C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45#66947—24no—
46#66937—24no—
47#66937—24no—
48#66927—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C23×D11C2311yescharacteristic
57C23×D11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C23×D11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—22no—
67C2×C22⋊D11—22no—
68C2×C22⋊D11—22no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C22×Dic11C2311yescharacteristic
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2311yescharacteristic
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44D414yescomplemented
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C11×C4⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—22no—
110C42×C11—22no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121Dic11⋊C4—22no—
122Dic11⋊C4D414yescomplemented
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×C11C2411yescharacteristic
132C22×D11—21no—
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×D11—21no—
145C22×D11—21no—
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×D11C2×D412yes—
159C22×D11C2×D412yes—
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×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11C2×D412yes—
176C2×C4×C11C2×D412yes—
177C2×C4×C11#4112yes—
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×Dic11C2×D412yes—
193C2×Dic11C2×D412yes—
194D44—44no—
195D44—44no—
196D44—44no—
197D44—44no—
198D44—44no—
199D44—44no—
200C4×D11—44no—
201C4×D11—44no—
202C2×#127—111no—
203C2×#123—111no—
204C2×#121—111no—
205C2×#121—111no—
206#394—111no—
207#394—111no—
208#392—111no—
209#392—111no—
210#392—111no—
211#392—111no—
212#388D1111yescharacteristic, complemented
213#387—111no—
214#386—111no—
215#386—111no—
216#386—111no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11C22×D411yescharacteristic
225C22×C11C22×D411yescharacteristic
226C22×C11C2×#4111yescharacteristic
227C22×C11H(5,𝔽2)11yescharacteristic
228C22×C11H(5,𝔽2)11yescharacteristic
229C22×C11H(5,𝔽2)11yescharacteristic
230C22×C11H(5,𝔽2)11yescharacteristic
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—41no—
243C2×D11—41no—
244C2×D11—41no—
245C2×D11—41no—
246C2×D11—41no—
247C2×D11—41no—
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—
263C4×C11—41no—
264C4×C11—41no—
265Dic11—22no—
266Dic11—22no—
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×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C23×C4—111no—
280C23×C4—111no—
281#127—224no—
282#123—224no—
283#121—224no—
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⋊C4C2×D1111yescharacteristic
299C2×C22⋊C4C2×D1111yescharacteristic
300C2×C22⋊C4C2×D1111yescharacteristic
301C2×C42C2×D1111yescharacteristic
302#95—111no—
303#95—111no—
304#95—111no—
305#95—111no—
306#95C2×D1111yescharacteristic
307#95C2×D1111yescharacteristic
308C2×C11—81no—
309C2×C11#53411yescharacteristic
310C2×C11#53511yescharacteristic
311C2×C11#54011yescharacteristic
312C2×C11D4211yescharacteristic
313C2×C11#54611yescharacteristic
314C2×C11#55011yescharacteristic
315C2×C11#56011yescharacteristic
316D11—42no—
317D11—42no—
318D11—81no—
319D11—81no—
320C24—111no—
321C24—111no—
322C24—111no—
323C24—111no—
324C24C22×D1111yescharacteristic
325C2×D4—114no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—222no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—222no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—441no—
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—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4C22×D1111yescharacteristic
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C22×C4C22×D1111yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—114no—
373C4⋊C4—222no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
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—22no—
388C11#267311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—112no—
397C23—112no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23—221no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23—221no—
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—
423C23—221no—
424C23C23×D1111yescharacteristic
425D4—444no—
426D4—444no—
427D4—444no—
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—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—112no—
451C2×C4—112no—
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—444no—
463C2×C4—444no—
464C2×C4#433912yes—
465C2×C4D4×D1112yes—
466C2×C4D4×D1112yes—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—222no—
478C22—222no—
479C22—222no—
480C22—441no—
481C22—441no—
482C22—441no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22—441no—
492C22—441no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22—441no—
497C22—441no—
498C22—441no—
499C22—441no—
500C22—441no—
501C22—441no—
502C22C2×#433911yescharacteristic
503C22C2×D4×D1111yescharacteristic
504C22C2×D4×D1111yescharacteristic
505C22#6704211yescharacteristic
506C22#6704211yescharacteristic
507C22#6704211yescharacteristic
508C22#6704211yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—222no—
516C4—222no—
517C4—441no—
518C4—441no—
519C2—81no—
520C2—442no—
521C2—442no—
522C2—881no—
523C2—881no—
524C2#1062306611yescharacteristic
525C2#1062308111yescharacteristic
526C2#1062308411yescharacteristic
527C2#1062314011yescharacteristic
528C2#1062318411yescharacteristic
529C2#1062320511yescharacteristic
530C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
hypercenter#388D11
hypocenterC11#2673
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66947C2semidirect
2. C2×#66937C2semidirect
3. C2×#66937C2semidirect
4. C2×#66927C2semidirect
5. C11×#388C2semidirect
6. #10622604C2semidirect
7. #10622573C2semidirect
8. #10622573C2semidirect
9. #10622573C2semidirect
10. #10622573C2semidirect
11. #10622546C2semidirect
12. #10622285C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
99. C2×D44D4semidirect
122. Dic11⋊C4D4semidirect
212. #388D11semidirect
388. C11#2673semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×#669372
C2×#669272
C11×#3882
#106226042
#106225732
#106225462
#106222852
#106222782
#267311