Finite Group Databasebeta

← #14769069

Subgroups — #14769069

Order 2816.

1908 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C212yesmaximal, complemented
2C2×#10622820C212yesmaximal, complemented
3#13069411C212yesmaximal, complemented
4#13068914C214yesmaximal, complemented
5#13068596C211yesmaximal, characteristic, complemented
6#13068526C212yesmaximal, complemented
7C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C22×C4×D4×C11C211yesmaximal, characteristic
9C23×D4×C11C411yescharacteristic
10C24×C4×C11C2212yes—
11C2×C4×D4×C11—28no—
12C2×C4×D4×C11C411yescharacteristic
13C2×C4×D4×C11C411yescharacteristic
14C2×C4×D4×C11C412yes—
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2212yes—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C411yescharacteristic
19C22×C11×C22⋊C4C412yes—
20C22×C42×C11C2211yescharacteristic
21C22×#4318C2214yescomplemented
22#10622820—28no—
23C2×C22⋊(C11⋊C8)C2212yes—
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2214yescomplemented
27C2×C22⋊(C11⋊C8)C2214yescomplemented
28C2×C22⋊(C11⋊C8)C2214yescomplemented
29#10622625—28no—
30C2×C4⋊(C11⋊C8)C2212yescomplemented
31C2×C4×C11⋊C8C2212yescomplemented
32#10622162C2212yescomplemented
33#10622162C2212yescomplemented
34C25×C11C2×C412yes—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11—24no—
42C23×C4×C11—28no—
43C23×C4×C11—24no—
44C23×C4×C11—44no—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C412yes—
47C23×C4×C11C2×C412yes—
48C23×C4×C11C2×C412yes—
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C4×D4×C11—24no—
54C4×D4×C11—28no—
55C4×D4×C11—24no—
56C4×D4×C11—28no—
57C4×D4×C11—24no—
58C4×D4×C11D418yes—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C412yes—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4—28no—
64C2×C11×C22⋊C4C2×C412yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2×C412yes—
68C2×C42×C11—24no—
69C2×C42×C11C2×C411yescharacteristic
70C2×C42×C11C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×#4318—28no—
74C2×#4318—28no—
75C2×#4318—44no—
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2314yes—
78C22×C11⋊C8C2312yes—
79C22⋊(C11⋊C8)—24no—
80C22⋊(C11⋊C8)—28no—
81C22⋊(C11⋊C8)—22no—
82C22⋊(C11⋊C8)—28no—
83C22⋊(C11⋊C8)—44no—
84C22⋊(C11⋊C8)D414yescomplemented
85C4⋊(C11⋊C8)—24no—
86C4×C11⋊C8—24no—
87#22401—111nomaximal, Sylow
88C24×C11—24no—
89C24×C11—24no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11C22×C412yes—
96C24×C11C22×C412yes—
97C24×C11C22×C411yescharacteristic
98C2×D4×C11—232no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C22⋊C414yes—
107C2×D4×C11M1614yescomplemented
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—41no—
131C22×C4×C11—416no—
132C22×C4×C11—416no—
133C22×C4×C11M1614yescomplemented
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D418yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C22⋊C414yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4C22⋊C418yes—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11C2×D414yes—
156#4318—416no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—24no—
160C2×C11⋊C8—24no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8C2×D414yescomplemented
166C22×C4×D4D1111yescharacteristic
167C2×#436—112no—
168C2×#407—112no—
169#1954—112no—
170#1870—114no—
171#1797—111no—
172#1779—112no—
173C4×C22⋊C8—111no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—216no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—48no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—48no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11C2×C22⋊C414yes—
198C23×C11C4×D412yes—
199C23×C11C2×M1614yes—
200C23×C11C2×M1612yes—
201C23×C11#13112yes—
202C23×C11C23×C411yescharacteristic
203D4×C11—216no—
204D4×C11—28no—
205D4×C11—28no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—28no—
218C2×C4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—48no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11—48no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11C2×M1612yes—
236C2×C4×C11C2×M1612yes—
237C2×C4×C11C2×M1612yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)12yes—
242C11⋊C8—24no—
243C11⋊C8—44no—
244C11⋊C8—42no—
245C23×D4Dic1111yescharacteristic
246C24×C4C2×D1112yes—
247C22×M16—114no—
248C2×C4×D4—28no—
249C2×C4×D4Dic1111yescharacteristic
250C2×C4×D4Dic1111yescharacteristic
251C2×C4×D4Dic1112yes—
252C2×C4×D4C2×D1112yes—
253C2×C4×D4C2×D1111yescharacteristic
254C2×C4×D4C2×D1111yescharacteristic
255C22×C4⋊C4Dic1111yescharacteristic
256C22×C22⋊C4Dic1112yes—
257C22×C42C2×D1111yescharacteristic
258#436—228no—
259C2×C4⋊C8—112no—
260#407—228no—
261C2×C22⋊C8—111no—
262C2×C22⋊C8—112no—
263C2×C22⋊C8—114no—
264C2×C22⋊C8—114no—
265C2×C22⋊C8—111no—
266C2×C22⋊C8—114no—
267C2×C4×C8—112no—
268#336—112no—
269#336—112no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—432no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11#43614yescomplemented
292C22×C11C22×C22⋊C411yescharacteristic
293C22×C11C2×C4×D411yescharacteristic
294C22×C11#51811yescharacteristic
295C22×C11C22×M1611yescharacteristic
296C22×C11C22×M1611yescharacteristic
297C22×C11C2×#13111yescharacteristic
298C22×C11#56811yescharacteristic
299C4×C11—22no—
300C4×C11—24no—
301C4×C11—22no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11#40714yescomplemented
306C4×C11D4212yes—
307C4×C11#54612yes—
308C25C2×Dic1112yes—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4C2×Dic1112yes—
313C22×D4C2×Dic1111yescharacteristic
314C22×D4C2×Dic1111yescharacteristic
315C23×C4—24no—
316C23×C4—24no—
317C23×C4—28no—
318C23×C4—44no—
319C23×C4C2×Dic1111yescharacteristic
320C23×C4C2×Dic1112yes—
321C23×C4C2×Dic1112yes—
322C23×C4C2×Dic1112yes—
323C23×C4C2×Dic1111yescharacteristic
324C23×C4C22×D1112yes—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1112yes—
327C2×M16—228no—
328C2×M16—228no—
329C2×M16—444no—
330C22×C8—112no—
331C22×C8—114no—
332C22×C8—112no—
333C4×D4—24no—
334C4×D4—28no—
335C4×D4—24no—
336C4×D4—28no—
337C4×D4—24no—
338C4×D4C22⋊D1118yes—
339C2×C4⋊C4—24no—
340C2×C4⋊C4C2×Dic1111yescharacteristic
341C2×C4⋊C4C2×Dic1112yes—
342C2×C4⋊C4C2×Dic1111yescharacteristic
343C2×C22⋊C4—28no—
344C2×C22⋊C4C2×Dic1112yes—
345C2×C22⋊C4C2×Dic1112yes—
346C2×C22⋊C4C2×Dic1112yes—
347C2×C22⋊C4C2×Dic1112yes—
348C2×C42—24no—
349C2×C42C2×Dic1111yescharacteristic
350C2×C42C2×Dic1111yescharacteristic
351C2×C42C22×D1111yescharacteristic
352C2×C42C22×D1111yescharacteristic
353C4⋊C8—224no—
354C22⋊C8—114no—
355C22⋊C8—228no—
356C22⋊C8—224no—
357C22⋊C8—222no—
358C22⋊C8—228no—
359C22⋊C8—444no—
360C4×C8—224no—
361C2×C11—24no—
362C2×C11—44no—
363C2×C11—44no—
364C2×C11D4×C22⋊C411yescharacteristic
365C2×C11C2×#40711yescharacteristic
366C2×C11#288011yescharacteristic
367C2×C11C2×#43611yescharacteristic
368C2×C11D4×M1611yescharacteristic
369C2×C11#297411yescharacteristic
370C2×C11#297511yescharacteristic
371C24—24no—
372C24—24no—
373C24—24no—
374C24—24no—
375C24—24no—
376C24—42no—
377C24—42no—
378C24C22×Dic1112yes—
379C24C22×Dic1112yes—
380C24C22×Dic1111yescharacteristic
381C2×D4—232no—
382C2×D4—24no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4#431814yescomplemented
390C2×D4C22⋊Dic1114yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—41no—
414C22×C4—416no—
415C22×C4—416no—
416C22×C4#431814yescomplemented
417C22×C4D4×D1112yes—
418C22×C4#434112yes—
419C22×C4C22×Dic1111yescharacteristic
420C22×C4C22×Dic1112yes—
421C22×C4C22×Dic1111yescharacteristic
422C22×C4C22×Dic1111yescharacteristic
423C22×C4C22×Dic1111yescharacteristic
424C22×C4C22×Dic1112yes—
425C22×C4C22×Dic1111yescharacteristic
426C22×C4C2×C22⋊D1118yes—
427C22×C4C23×D1111yescharacteristic
428M16—4416no—
429C2×C8—114no—
430C2×C8—222no—
431C2×C8—222no—
432C2×C8—224no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—224no—
436C2×C8—222no—
437C2×C8—224no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4C22⋊Dic1114yes—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4C22⋊Dic1118yes—
445C42—22no—
446C42—22no—
447C42—22no—
448C42C2×C22⋊D1114yes—
449C11#2240111yescharacteristic, complemented, Sylow
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—216no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—48no—
468C23—48no—
469C23—48no—
470C23—48no—
471C23—48no—
472C23—48no—
473C23C2×#431814yes—
474C23C2×#431812yes—
475C23D4×Dic1112yes—
476C23#6700112yes—
477C23C2×C22⋊Dic1114yes—
478C23C23×Dic1111yescharacteristic
479D4—216no—
480D4—28no—
481D4—28no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—28no—
491C2×C4—28no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—48no—
504C2×C4—48no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4C2×#431812yes—
508C2×C4C2×#431812yes—
509C2×C4C2×#431812yes—
510C2×C4D4×Dic1112yes—
511C2×C4C2×C22⋊Dic1112yes—
512C2×C4C2×C22⋊Dic1114yes—
513C2×C4C2×C22⋊Dic1112yes—
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4#6703712yes—
517C2×C4C22×C22⋊D1112yes—
518C8—224no—
519C8—444no—
520C8—442no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—24no—
528C22—24no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—432no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22#1062262514yescomplemented
543C22C22×#431811yescharacteristic
544C22C22×#431811yescharacteristic
545C22C2×D4×Dic1111yescharacteristic
546C22#1062332911yescharacteristic
547C22C2×#6700111yescharacteristic
548C22#1062335011yescharacteristic
549C22C22×C22⋊Dic1111yescharacteristic
550C4—22no—
551C4—22no—
552C4—22no—
553C4—24no—
554C4—41no—
555C4—42no—
556C4#1062282014yescomplemented
557C4D4×C22⋊D1112yes—
558C4#1062333712yes—
559C2—24no—
560C2—44no—
561C2—44no—
562C2D4×C22⋊Dic1111yescharacteristic
563C2C2×#1062282011yescharacteristic
564C2#1307706511yescharacteristic
565C2C2×#1062262511yescharacteristic
566C2D4×#431811yescharacteristic
567C2#1307765111yescharacteristic
568C2#1307765711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC22×C4×D4×C11C2
prime radicalC23×D4×C11C4
cosocleC22×C4×C11C24
hypercenterC22×C4×D4D11
hypocenterC11#22401
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622820C2semidirect
3. #13069411C2semidirect
4. #13068914C2semidirect
5. #13068596C2semidirect
6. #13068526C2semidirect
7. C4×C22⋊(C11⋊C8)C2semidirect
21. C22×#4318C22semidirect
26. C2×C22⋊(C11⋊C8)C22semidirect
27. C2×C22⋊(C11⋊C8)C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
30. C2×C4⋊(C11⋊C8)C22semidirect
31. C2×C4×C11⋊C8C22semidirect
32. #10622162C22semidirect
33. #10622162C22semidirect
84. C22⋊(C11⋊C8)D4semidirect
107. C2×D4×C11M16semidirect
133. C22×C4×C11M16semidirect
165. C2×C11⋊C8C2×D4semidirect
291. C22×C11#436semidirect
305. C4×C11#407semidirect
389. C2×D4#4318semidirect
416. C22×C4#4318semidirect
449. C11#22401semidirect
542. C22#10622625semidirect
556. C4#10622820semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228202
#130694112
#130689142
#130685962
#130685262
C4×C22⋊(C11⋊C8)2
C22×C4×D4×C112
#2240111