Finite Group Databasebeta

← #13074885

Subgroups — #13074885

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×#66948C211yesmaximal, characteristic, complemented
2C2×#66948C211yesmaximal, characteristic, complemented
3C2×#66947C211yesmaximal, characteristic, complemented
4C2×#66927C211yesmaximal, characteristic, complemented
5C11×#387C211yesmaximal, characteristic, complemented
6#10622604C211yesmaximal, characteristic, complemented
7#10622553C211yesmaximal, characteristic, complemented
8#10622285C211yesmaximal, characteristic, complemented
9#10622284C211yesmaximal, characteristic, complemented
10#10622284C211yesmaximal, characteristic, complemented
11#10622284C211yesmaximal, characteristic, complemented
12#10622284C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C22×D44C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic
24C22×D44C2211yescharacteristic
25C22×D44C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic
27C22×C4×D11C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45#66948—24no—
46#66948—24no—
47#66947—24no—
48#66927—24no—
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
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
66C22×C4×C11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C2×D44—22no—
71C2×D44—22no—
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
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×C4⋊C4D414yescomplemented
108C42×C11—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—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—22no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122Dic11⋊C4—22no—
123#2673—111nomaximal, Sylow
124C23×C11C2411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
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×C11—21no—
176C2×C4×C11C2×D412yes—
177C2×C4×C11C2×D412yes—
178C2×C4×C11C2×D412yes—
179C2×C4×C11C2×D412yes—
180C2×C4×C11#4112yes—
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—
190D44—44no—
191D44—44no—
192D44—44no—
193D44—44no—
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#388—111no—
213#387D1111yescharacteristic, complemented
214#386—111no—
215#386—111no—
216#386—111no—
217C22×C11C22×D411yescharacteristic
218C22×C11C22×D411yescharacteristic
219C22×C11C2×#4111yescharacteristic
220C22×C11H(5,𝔽2)11yescharacteristic
221C22×C11H(5,𝔽2)11yescharacteristic
222C22×C11H(5,𝔽2)11yescharacteristic
223C22×C11H(5,𝔽2)11yescharacteristic
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
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—22no—
263C4×C11—22no—
264C4×C11—41no—
265C4×C11—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×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⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
300C2×C22⋊C4—111no—
301C2×C42C2×D1111yescharacteristic
302#95—111no—
303#95—111no—
304#95C2×D1111yescharacteristic
305#95C2×D1111yescharacteristic
306#95C2×D1111yescharacteristic
307#95C2×D1111yescharacteristic
308C2×C11#53411yescharacteristic
309C2×C11#53511yescharacteristic
310C2×C11#54011yescharacteristic
311C2×C11D4211yescharacteristic
312C2×C11#54611yescharacteristic
313C2×C11#55011yescharacteristic
314C2×C11#56011yescharacteristic
315D11—42no—
316D11—42no—
317D11—81no—
318D11—81no—
319D11—81no—
320C24—111no—
321C24—111no—
322C24—111no—
323C24—111no—
324C24—111no—
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—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4C22×D1111yescharacteristic
365C22×C4C22×D1111yescharacteristic
366C22×C4C22×D1111yescharacteristic
367C22×C4C22×D1111yescharacteristic
368C22×C4C22×D1111yescharacteristic
369C22×C4C22×D1111yescharacteristic
370C22×C4C22×D1111yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—222no—
373C4⋊C4D4414yescomplemented
374C22⋊C4—222no—
375C22⋊C4—222no—
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—22no—
388C11#267311yescharacteristic, complemented, Sylow
389C23—112no—
390C23—112no—
391C23—221no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23—221no—
397C23—221no—
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—21no—
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—444no—
461C2×C4—444no—
462C2×C4C2×D4412yes—
463C2×C4C2×D4412yes—
464C2×C4C2×D4412yes—
465C2×C4D4×D1112yes—
466C2×C4#434312yes—
467C22—222no—
468C22—222no—
469C22—222no—
470C22—222no—
471C22—222no—
472C22—222no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22—441no—
479C22—441no—
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—
502C22C22×D4411yescharacteristic
503C22C2×D4×D1111yescharacteristic
504C22C2×#434311yescharacteristic
505C22#6704211yescharacteristic
506C22#6704211yescharacteristic
507C22#6704211yescharacteristic
508C22#6704211yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—41no—
515C4—41no—
516C4—441no—
517C4—441no—
518C4—441no—
519C2—442no—
520C2—442no—
521C2—881no—
522C2—881no—
523C2—881no—
524C2#1062305611yescharacteristic
525C2D4×D4411yescharacteristic
526C2#1062310811yescharacteristic
527C2#1062316111yescharacteristic
528C2#1062318411yescharacteristic
529C2#1062322911yescharacteristic
530C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#387C2
hypercenter#387D11
hypocenterC11#2673
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66948C2semidirect
3. C2×#66947C2semidirect
4. C2×#66927C2semidirect
5. C11×#387C2semidirect
6. #10622604C2semidirect
7. #10622553C2semidirect
8. #10622285C2semidirect
9. #10622284C2semidirect
10. #10622284C2semidirect
11. #10622284C2semidirect
12. #10622284C2semidirect
13. #10622278C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
99. C2×D44D4semidirect
107. C11×C4⋊C4D4semidirect
213. #387D11semidirect
373. C4⋊C4D44semidirect
388. C11#2673semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669472
C2×#669272
C11×#3872
#106226042
#106225532
#106222852
#106222842
#106222782
#267311