Finite Group Databasebeta

← #14719964

Subgroups — #14719964

Order 2816.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623058C211yesmaximal, characteristic
2#13077274C211yesmaximal, characteristic, complemented
3#13066986C211yesmaximal, characteristic, complemented
4#13066983C211yesmaximal, characteristic, complemented
5#13066969C211yesmaximal, characteristic, complemented
6#13066967C211yesmaximal, characteristic, complemented
7#13066965C211yesmaximal, characteristic, complemented
8#13066962C211yesmaximal, characteristic, complemented
9#13066956C211yesmaximal, characteristic, complemented
10#13066948C211yesmaximal, characteristic, complemented
11#13066942C211yesmaximal, characteristic, complemented
12#13066936C211yesmaximal, characteristic, complemented
13#13066928C211yesmaximal, characteristic, complemented
14C2×#10622106C211yesmaximal, characteristic, complemented
15C11×#2924C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66982C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19#10623058—21no—
20#10623058—21no—
21#10623058—21no—
22#10623058—21no—
23#10623058—21no—
24#10623058—21no—
25#10623058—21no—
26#10623058—21no—
27C2×#66951C411yescharacteristic
28C2×#66949C411yescharacteristic
29C2×#66947C411yescharacteristic
30C2×#66947C411yescharacteristic
31C2×#66935C411yescharacteristic
32C2×(C22⋊D11)⋊C4C411yescharacteristic
33C2×C22⋊C4×D11C411yescharacteristic
34C2×#66931C411yescharacteristic
35C2×#66929C2211yescharacteristic
36C2×#66928C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×#66925C2211yescharacteristic
39C11×#433—21no—
40C11×#433—21no—
41C11×#432C2211yescharacteristic, complemented
42C11×#432C2211yescharacteristic, complemented
43C11×#431C2211yescharacteristic, complemented
44C11×#431C2211yescharacteristic, complemented
45C11×#424—21no—
46C11×#407C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C11×#405—21no—
49#10622820C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622613—21no—
52#10622613—21no—
53#10622612—21no—
54#10622610—21no—
55#10622539C2211yescharacteristic, complemented
56#10622539C2211yescharacteristic, complemented
57#10622538C2211yescharacteristic, complemented
58#10622538C2211yescharacteristic, complemented
59#10622107C2211yescharacteristic, complemented
60#10622107C2211yescharacteristic, complemented
61#10622107C2211yescharacteristic, complemented
62#10622107C2211yescharacteristic, complemented
63#10622106C2211yescharacteristic
64#10622106C2211yescharacteristic
65#10622106C2211yescharacteristic
66#10622106C2211yescharacteristic
67#10622106C2211yescharacteristic
68#10622106C2211yescharacteristic
69#10622106C2211yescharacteristic
70#10622106C2211yescharacteristic
71#10622106C2211yescharacteristic, complemented
72#10622106C2211yescharacteristic, complemented
73#10622106C2211yescharacteristic, complemented
74#10622106C2211yescharacteristic, complemented
75C24×D11C2×C411yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11C2×C411yescharacteristic
78C23×Dic11C2×C411yescharacteristic
79C22×D44C2×C411yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2×C411yescharacteristic
83C22×C4×D11C2×C411yescharacteristic
84C22×Dic22C2×C411yescharacteristic
85C2×C11×M16—21no—
86C22×C8×C11—21no—
87C11×#117D411yescharacteristic
88C11×#117D411yescharacteristic
89C11×#117D411yescharacteristic
90C11×#117D411yescharacteristic
91C11×#117D411yescharacteristic
92C11×#117D411yescharacteristic
93C11×#117D411yescharacteristic
94C11×#117D411yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102#66982—21no—
103#66982—21no—
104#66982—21no—
105#66982—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4C2×C411yescharacteristic
111C2×(C2×D11)⋊C4C2×C411yescharacteristic
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×(C2×D11)⋊C4C2×C411yescharacteristic
114C2×(C2×D11)⋊C4C2×C411yescharacteristic
115C2×(C2×D11)⋊C4C2×C411yescharacteristic
116C2×(C2×D11)⋊C4C2×C411yescharacteristic
117C2×(C2×D11)⋊C4C2×C411yescharacteristic
118C2×(C2×D11)⋊C4C2311yescharacteristic
119C2×(C2×D11)⋊C4C2311yescharacteristic
120C2×(C2×D11)⋊C4C2311yescharacteristic
121C2×C4⋊Dic11C2×C411yescharacteristic
122C2×Dic11⋊C4C2×C411yescharacteristic
123C2×Dic11⋊C4C2×C411yescharacteristic
124C2×Dic11⋊C4C2×C411yescharacteristic
125C2×Dic11⋊C4C2×C411yescharacteristic
126C2×Dic11⋊C4C2311yescharacteristic
127C2×C4×Dic11C2×C411yescharacteristic
128C2×#4318—21no—
129C22×C11⋊C8—21no—
130#66951—21no—
131#66951—21no—
132#66951—21no—
133#66951—21no—
134#66949—21no—
135#66949—21no—
136#66949—21no—
137#66949—21no—
138#66947—21no—
139#66947—21no—
140#66947—21no—
141#66947—21no—
142#66947—21no—
143#66947—21no—
144#66947—21no—
145#66947—21no—
146#66935—21no—
147#66935—21no—
148#66935—21no—
149#66935—21no—
150(C22⋊D11)⋊C4—21no—
151(C22⋊D11)⋊C4—21no—
152(C22⋊D11)⋊C4—21no—
153(C22⋊D11)⋊C4—21no—
154C22⋊C4×D11—21no—
155C22⋊C4×D11—21no—
156C22⋊C4×D11—21no—
157C22⋊C4×D11—21no—
158#66931—21no—
159#66931—21no—
160#66931—21no—
161#66931—21no—
162#66929—21no—
163#66929—21no—
164#66929—21no—
165#66929—21no—
166#66928—21no—
167#66928—21no—
168#66928—21no—
169#66928—21no—
170C4×D44—21no—
171C4×D44—21no—
172C4×D44—21no—
173C4×D44—21no—
174#66925—21no—
175#66925—21no—
176#66925—21no—
177#66925—21no—
178C11×C4⋊C8—21no—
179C11×C4⋊C8—21no—
180C11×C4⋊C8—21no—
181C11×C4⋊C8—21no—
182C11×C22⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8C2311yescharacteristic
185C11×C22⋊C8C2311yescharacteristic
186C11×C22⋊C8C2311yescharacteristic
187C11×C22⋊C8C2311yescharacteristic
188C11×#97—21no—
189C11×#97—21no—
190C4×C8×C11—21no—
191C4×C8×C11—21no—
192C22⋊(C11⋊C8)—21no—
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)C2311yescharacteristic
195C22⋊(C11⋊C8)C2311yescharacteristic
196C22⋊(C11⋊C8)C2311yescharacteristic
197C22⋊(C11⋊C8)C2311yescharacteristic
198C4⋊(C11⋊C8)—21no—
199C4⋊(C11⋊C8)—21no—
200C4⋊(C11⋊C8)—21no—
201C4⋊(C11⋊C8)—21no—
202#66867—21no—
203#66867—21no—
204C4×C11⋊C8—21no—
205C4×C11⋊C8—21no—
206#17412—111nomaximal, Sylow
207C24×C11C22×C411yescharacteristic
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—22no—
211C23×D11—41no—
212C23×D11—42no—
213C23×D11—81no—
214C23×D11C22×C411yescharacteristic
215C23×D11C22×C411yescharacteristic
216C23×D11C22×C411yescharacteristic
217C22×C4×C11—42no—
218C22×C4×C11C22×C411yescharacteristic
219C22×C4×C11C22×C411yescharacteristic
220C22×C4×C11C22×C411yescharacteristic
221C22×C4×C11C22×C411yescharacteristic
222C22×C4×C11C22×C411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C2×C22⋊D11—21no—
229C2×C22⋊D11—21no—
230C2×C22⋊D11—42no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—81no—
234C22×Dic11C22×C411yescharacteristic
235C22×Dic11C22×C411yescharacteristic
236C22×Dic11C22×C411yescharacteristic
237C22×Dic11C22×C411yescharacteristic
238C22×Dic11C22×C411yescharacteristic
239C2×D44—22no—
240C2×D44—21no—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44—41no—
245C2×D44—81no—
246C2×C4×D11—22no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—41no—
254C2×C4×D11—81no—
255C2×C4×D11—81no—
256C2×Dic22—21no—
257C2×Dic22—21no—
258C2×Dic22—81no—
259C11×M16—42no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—42no—
265C11×C4⋊C4C22⋊C411yescharacteristic
266C11×C4⋊C4C22⋊C411yescharacteristic
267C11×C4⋊C4C22⋊C411yescharacteristic
268C11×C4⋊C4C22⋊C411yescharacteristic
269C11×C4⋊C4C22⋊C411yescharacteristic
270C11×C4⋊C4C22⋊C411yescharacteristic
271C11×C4⋊C4C22⋊C411yescharacteristic
272C11×C4⋊C4C22⋊C411yescharacteristic
273C11×C22⋊C4C22⋊C411yescharacteristic
274C11×C22⋊C4C22⋊C411yescharacteristic
275C11×C22⋊C4C22⋊C411yescharacteristic
276C11×C22⋊C4C22⋊C411yescharacteristic
277C11×C22⋊C4C22⋊C411yescharacteristic
278C11×C22⋊C4C22⋊C411yescharacteristic
279C11×C22⋊C4C22⋊C411yescharacteristic
280C11×C22⋊C4C22⋊C411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—21no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—21no—
312(C2×D11)⋊C4—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327#4318—42no—
328C2×C11⋊C8—21no—
329C2×C11⋊C8—21no—
330C2×C11⋊C8—21no—
331C2×C11⋊C8—21no—
332C2×C11⋊C8—42no—
333C2×#551—111no—
334#2924—111no—
335#2924D1111yescharacteristic, complemented
336#1473—111no—
337#1473—111no—
338#1469—111no—
339#1469—111no—
340#1468—111no—
341#1468—111no—
342#1466—111no—
343#1464—111no—
344#1462—111no—
345#1460—111no—
346#1458—111no—
347C2×#323—111no—
348C23×C11—21no—
349C23×C11—21no—
350C23×C11—22no—
351C23×C11—41no—
352C23×C11C2×C22⋊C411yescharacteristic
353C23×C11C2×C22⋊C411yescharacteristic
354C23×C11C23×C411yescharacteristic
355C22×D11—21no—
356C22×D11—21no—
357C22×D11—21no—
358C22×D11—21no—
359C22×D11—21no—
360C22×D11—21no—
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—41no—
366C22×D11—41no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—81no—
374C22×D11—81no—
375C22×D11—84no—
376C22×D11—84no—
377C22×D11#13112yes—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11C2×C22⋊C411yescharacteristic
391C2×C4×C11C2×C22⋊C411yescharacteristic
392C2×C4×C11C2×C22⋊C411yescharacteristic
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C2×C22⋊C411yescharacteristic
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C2×C22⋊C411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C22⋊D11—42no—
403C22⋊D11—42no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—21no—
410C2×Dic11—21no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—81no—
416C2×Dic11—81no—
417D44—42no—
418D44—42no—
419D44—81no—
420D44—81no—
421C4×D11—42no—
422C4×D11—42no—
423C4×D11—81no—
424C4×D11—81no—
425C4×D11—81no—
426C4×D11—81no—
427Dic22—81no—
428Dic22—81no—
429C8×C11—41no—
430C8×C11—41no—
431C8×C11—41no—
432C8×C11—41no—
433C11⋊C8—41no—
434C11⋊C8—41no—
435C11⋊C8—41no—
436C11⋊C8—41no—
437#551—221no—
438#551—221no—
439#551—221no—
440#551—221no—
441#551—221no—
442#551—221no—
443#551—221no—
444#551—221no—
445C2×#126—111no—
446C2×#126—111no—
447C2×#124—111no—
448C2×#123—111no—
449C2×#123—111no—
450C2×#123—111no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—111no—
453C2×#120—111no—
454C2×C4×D4—111no—
455C2×C4×D4—111no—
456C2×#117—111no—
457C2×#117C2×D1111yescharacteristic
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460#433—21no—
461#433—21no—
462#433—221no—
463#433—221no—
464#432—111no—
465#432—111no—
466#432C2×D1111yescharacteristic, complemented
467#432C2×D1111yescharacteristic, complemented
468#431—111no—
469#431—111no—
470#431C2×D1111yescharacteristic, complemented
471#431C2×D1111yescharacteristic, complemented
472#424—21no—
473#424—221no—
474#407—111no—
475#407C2×D1111yescharacteristic
476C2×C22⋊C8—111no—
477C2×C22⋊C8C2×D1111yescharacteristic
478#405—21no—
479#405—221no—
480#324—111no—
481#324—111no—
482#324—111no—
483#324—111no—
484#323—111no—
485#323—111no—
486#323—111no—
487#323—111no—
488#323—111no—
489#323—111no—
490#323—111no—
491#323—111no—
492#323—111no—
493#323—111no—
494#323—111no—
495#323—111no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11#41012yes—
506C22×C11C22×C22⋊C411yescharacteristic
507C22×C11C2×#13111yescharacteristic
508C22×C11#56811yescharacteristic
509C2×D11—22no—
510C2×D11—42no—
511C2×D11—41no—
512C2×D11—41no—
513C2×D11—42no—
514C2×D11—41no—
515C2×D11—41no—
516C2×D11—41no—
517C2×D11—41no—
518C2×D11—41no—
519C2×D11—41no—
520C2×D11—84no—
521C2×D11—84no—
522C2×D11—81no—
523C2×D11—81no—
524C2×D11—81no—
525C2×D11—81no—
526C4×C11—21no—
527C4×C11—21no—
528C4×C11—21no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—21no—
532C4×C11—21no—
533C4×C11—21no—
534C4×C11—21no—
535C4×C11—21no—
536C4×C11—21no—
537C4×C11—21no—
538Dic11—41no—
539Dic11—41no—
540Dic11—41no—
541Dic11—41no—
542Dic11—41no—
543C25—111no—
544C22×Q8—111no—
545C22×D4—111no—
546C22×D4—111no—
547C22×D4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4C22×D1111yescharacteristic
553C2×M16—21no—
554C2×M16—221no—
555C22×C8—21no—
556C22×C8—221no—
557#126—221no—
558#126—221no—
559#126—221no—
560#126—221no—
561#126—221no—
562#126—221no—
563#126—221no—
564#126—221no—
565#124—221no—
566#124—221no—
567#124—221no—
568#124—221no—
569#123—221no—
570#123—221no—
571#123—221no—
572#123—221no—
573#123—221no—
574#123—221no—
575#123—221no—
576#123—221no—
577#123—221no—
578#123—221no—
579#123—221no—
580#123—221no—
581C22⋊Q8—221no—
582C22⋊Q8—221no—
583C22⋊Q8—221no—
584C22⋊Q8—221no—
585C22⋊Q8—221no—
586C22⋊Q8—221no—
587C22⋊Q8—221no—
588C22⋊Q8—221no—
589#120—221no—
590#120—221no—
591#120—221no—
592#120—221no—
593C4×D4—221no—
594C4×D4—221no—
595C4×D4—221no—
596C4×D4—221no—
597C4×D4—221no—
598C4×D4—221no—
599C4×D4—221no—
600C4×D4—221no—
601#117—221no—
602#117—221no—
603#117—221no—
604#117—221no—
605#117D4411yescharacteristic
606#117D4411yescharacteristic
607#117D4411yescharacteristic
608#117D4411yescharacteristic
609#117C22⋊D1111yescharacteristic
610#117C22⋊D1111yescharacteristic
611#117C22⋊D1111yescharacteristic
612#117C22⋊D1111yescharacteristic
613C2×C4⋊C4—111no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4C4×D1111yescharacteristic
620C2×C4⋊C4C4×D1111yescharacteristic
621C2×C22⋊C4—111no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—111no—
626C2×C22⋊C4—111no—
627C2×C22⋊C4—111no—
628C2×C22⋊C4—111no—
629C2×C22⋊C4—111no—
630C2×C22⋊C4—111no—
631C2×C22⋊C4—111no—
632C2×C22⋊C4—111no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C22⋊C4—221no—
636C2×C22⋊C4—221no—
637C2×C22⋊C4—221no—
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4C4×D1111yescharacteristic
642C2×C22⋊C4C4×D1111yescharacteristic
643C2×C42—111no—
644C2×C42C22×D1111yescharacteristic
645C2×C42C22×D1111yescharacteristic
646C4⋊C8—21no—
647C4⋊C8—21no—
648C4⋊C8—21no—
649C4⋊C8—21no—
650C4⋊C8—221no—
651C4⋊C8—221no—
652C4⋊C8—221no—
653C4⋊C8—221no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—111no—
657C22⋊C8—111no—
658C22⋊C8—111no—
659C22⋊C8—111no—
660C22⋊C8—221no—
661C22⋊C8—221no—
662C22⋊C8C22×D1111yescharacteristic
663C22⋊C8C22×D1111yescharacteristic
664C22⋊C8C22×D1111yescharacteristic
665C22⋊C8C22×D1111yescharacteristic
666#97—21no—
667#97—21no—
668#97—221no—
669#97—221no—
670C4×C8—21no—
671C4×C8—21no—
672C4×C8—221no—
673C4×C8—221no—
674C2×C11—21no—
675C2×C11—21no—
676C2×C11—22no—
677C2×C11—41no—
678C2×C11#288011yescharacteristic
679C2×C11C2×#41011yescharacteristic
680C2×C11#288811yescharacteristic
681D11—42no—
682D11—81no—
683D11—81no—
684C24—111no—
685C24—111no—
686C24—111no—
687C24—222no—
688C24—221no—
689C24—221no—
690C24—441no—
691C24—442no—
692C24—881no—
693C24C2×C4×D1111yescharacteristic
694C2×Q8—221no—
695C2×Q8—221no—
696C2×Q8—881no—
697C2×D4—222no—
698C2×D4—221no—
699C2×D4—221no—
700C2×D4—221no—
701C2×D4—221no—
702C2×D4—221no—
703C2×D4—221no—
704C2×D4—441no—
705C2×D4—442no—
706C2×D4—881no—
707C22×C4—42no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—111no—
711C22×C4—111no—
712C22×C4—111no—
713C22×C4—222no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—441no—
723C22×C4—881no—
724C22×C4—881no—
725C22×C4—881no—
726C22×C4C2×C4×D1111yescharacteristic
727C22×C4C2×C4×D1111yescharacteristic
728C22×C4C2×C4×D1111yescharacteristic
729C22×C4C2×C4×D1111yescharacteristic
730C22×C4C2×C4×D1111yescharacteristic
731C22×C4C2×D4411yescharacteristic
732C22×C4C2×D4411yescharacteristic
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C23×D1111yescharacteristic
736M16—42no—
737M16—442no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—42no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—442no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4(C2×D11)⋊C411yescharacteristic
761C4⋊C4(C2×D11)⋊C411yescharacteristic
762C4⋊C4(C2×D11)⋊C411yescharacteristic
763C4⋊C4(C2×D11)⋊C411yescharacteristic
764C4⋊C4(C2×D11)⋊C411yescharacteristic
765C4⋊C4(C2×D11)⋊C411yescharacteristic
766C4⋊C4(C2×D11)⋊C411yescharacteristic
767C4⋊C4(C2×D11)⋊C411yescharacteristic
768C22⋊C4—221no—
769C22⋊C4—221no—
770C22⋊C4—221no—
771C22⋊C4—221no—
772C22⋊C4—221no—
773C22⋊C4—221no—
774C22⋊C4—221no—
775C22⋊C4—221no—
776C22⋊C4—221no—
777C22⋊C4—221no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—221no—
781C22⋊C4—221no—
782C22⋊C4—221no—
783C22⋊C4—221no—
784C22⋊C4—221no—
785C22⋊C4—221no—
786C22⋊C4—221no—
787C22⋊C4—221no—
788C22⋊C4—221no—
789C22⋊C4—221no—
790C22⋊C4—221no—
791C22⋊C4—221no—
792C22⋊C4(C2×D11)⋊C411yescharacteristic
793C22⋊C4(C2×D11)⋊C411yescharacteristic
794C22⋊C4(C2×D11)⋊C411yescharacteristic
795C22⋊C4(C2×D11)⋊C411yescharacteristic
796C22⋊C4(C2×D11)⋊C411yescharacteristic
797C22⋊C4(C2×D11)⋊C411yescharacteristic
798C22⋊C4(C2×D11)⋊C411yescharacteristic
799C22⋊C4(C2×D11)⋊C411yescharacteristic
800C42—221no—
801C42—221no—
802C42C2×D4411yescharacteristic
803C42C2×D4411yescharacteristic
804C42C2×D4411yescharacteristic
805C42C2×D4411yescharacteristic
806C42C2×C22⋊D1111yescharacteristic
807C42C2×C22⋊D1111yescharacteristic
808C42C2×C22⋊D1111yescharacteristic
809C42C2×C22⋊D1111yescharacteristic
810C11#1741211yescharacteristic, complemented, Sylow
811C23—21no—
812C23—21no—
813C23—22no—
814C23—41no—
815C23—112no—
816C23—221no—
817C23—221no—
818C23—221no—
819C23—221no—
820C23—221no—
821C23—221no—
822C23—221no—
823C23—221no—
824C23—442no—
825C23—442no—
826C23—441no—
827C23—441no—
828C23—442no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—442no—
834C23—881no—
835C23—881no—
836C23—884no—
837C23—884no—
838C23C2×(C2×D11)⋊C411yescharacteristic
839C23C2×(C2×D11)⋊C411yescharacteristic
840C23C22×C4×D1111yescharacteristic
841Q8—881no—
842Q8—881no—
843D4—442no—
844D4—442no—
845D4—442no—
846D4—442no—
847D4—881no—
848D4—881no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—221no—
864C2×C4—221no—
865C2×C4—221no—
866C2×C4—221no—
867C2×C4—221no—
868C2×C4—442no—
869C2×C4—442no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—881no—
875C2×C4—881no—
876C2×C4—881no—
877C2×C4—881no—
878C2×C4—881no—
879C2×C4—881no—
880C2×C4C2×(C2×D11)⋊C411yescharacteristic
881C2×C4C2×(C2×D11)⋊C411yescharacteristic
882C2×C4C2×(C2×D11)⋊C411yescharacteristic
883C2×C4C2×(C2×D11)⋊C411yescharacteristic
884C2×C4C2×(C2×D11)⋊C411yescharacteristic
885C2×C4C2×(C2×D11)⋊C411yescharacteristic
886C2×C4C2×(C2×D11)⋊C411yescharacteristic
887C2×C4C2×(C2×D11)⋊C411yescharacteristic
888C2×C4C2×(C2×D11)⋊C411yescharacteristic
889C2×C4C2×(C2×D11)⋊C411yescharacteristic
890C2×C4C22×D4411yescharacteristic
891C2×C4C22×C22⋊D1111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—441no—
897C8—441no—
898C8—441no—
899C8—441no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—222no—
910C22—442no—
911C22—442no—
912C22—441no—
913C22—441no—
914C22—441no—
915C22—441no—
916C22—441no—
917C22—441no—
918C22—441no—
919C22—441no—
920C22—884no—
921C22—881no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—884no—
926C22#1062261912yes—
927C22D11×#13111yescharacteristic
928C22#1062328111yescharacteristic
929C22C22×(C2×D11)⋊C411yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—441no—
943C4—441no—
944C4—441no—
945C4—441no—
946C4—441no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—442no—
952C2—881no—
953C2—881no—
954C2#1307706311yescharacteristic
955C2C2×#1062261911yescharacteristic
956C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66935C4
cosocleC22×C4×C11C24
hypercenter#2924D11
hypocenterC11#17412
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13077274C2semidirect
3. #13066986C2semidirect
4. #13066983C2semidirect
5. #13066969C2semidirect
6. #13066967C2semidirect
7. #13066965C2semidirect
8. #13066962C2semidirect
9. #13066956C2semidirect
10. #13066948C2semidirect
11. #13066942C2semidirect
12. #13066936C2semidirect
13. #13066928C2semidirect
14. C2×#10622106C2semidirect
15. C11×#2924C2semidirect
41. C11×#432C22semidirect
42. C11×#432C22semidirect
43. C11×#431C22semidirect
44. C11×#431C22semidirect
55. #10622539C22semidirect
56. #10622539C22semidirect
57. #10622538C22semidirect
58. #10622538C22semidirect
59. #10622107C22semidirect
60. #10622107C22semidirect
61. #10622107C22semidirect
62. #10622107C22semidirect
71. #10622106C22semidirect
72. #10622106C22semidirect
73. #10622106C22semidirect
74. #10622106C22semidirect
335. #2924D11semidirect
466. #432C2×D11semidirect
467. #432C2×D11semidirect
470. #431C2×D11semidirect
471. #431C2×D11semidirect
810. C11#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#106230582
#130772742
#130669862
#130669832
#130669692
#130669672
#130669652
#130669622
#130669562
#130669482
#130669422
#130669362
#130669282
C2×#106221062
C11×#29242
#1741211