Finite Group Databasebeta

← #14920192

Subgroups — #14920192

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623117C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074535C212yesmaximal, complemented
4#13074502C212yesmaximal, complemented
5#13074458C212yesmaximal, complemented
6#13074456C212yesmaximal, complemented
7#13074435C211yesmaximal, characteristic, complemented
8#13074427C211yesmaximal, characteristic, complemented
9#13074389C211yesmaximal, characteristic, complemented
10#13074364C211yesmaximal, characteristic, complemented
11#13074356C211yesmaximal, characteristic, complemented
12#13074331C211yesmaximal, characteristic, complemented
13#13074330C211yesmaximal, characteristic, complemented
14#13071874C212yesmaximal, complemented
15#13071859C212yesmaximal, complemented
16#13071853C212yesmaximal, complemented
17#13071830C212yesmaximal, complemented
18#13071141C211yesmaximal, characteristic, complemented
19#13071135C211yesmaximal, characteristic, complemented
20#13071121C211yesmaximal, characteristic, complemented
21#13071117C211yesmaximal, characteristic, complemented
22#13070994C211yesmaximal, characteristic, complemented
23C11×#2622C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4341C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C2×#67006C2211yescharacteristic
31C2×#66992C2211yescharacteristic
32C2×#66992C2211yescharacteristic, complemented
33C2×#66990C2211yescharacteristic
34C2×#66988C2211yescharacteristic
35C2×#66988C2211yescharacteristic, complemented
36C2×D4×Dic11C2211yescharacteristic
37C2×D4×Dic11C2211yescharacteristic, complemented
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41#10623117—28no—
42C2×#66946C2212yescomplemented
43C2×#66939C2211yescharacteristic
44C2×#66939C2211yescharacteristic, complemented
45C2×#66935C2211yescharacteristic
46C2×(C22⋊D11)⋊C4—28no—
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×#66931C2211yescharacteristic
55C2×#66931C2211yescharacteristic, complemented
56C2×#66930C2211yescharacteristic, complemented
57C2×#66930C2212yescomplemented
58C11×#397C2212yescomplemented
59C11×#397C2212yescomplemented
60C11×#394C2212yescomplemented
61C11×#394C2212yescomplemented
62C11×#386C2211yescharacteristic
63C11×#386C2211yescharacteristic
64C11×#385C2211yescharacteristic
65C11×#385C2211yescharacteristic
66C11×#379C2211yescharacteristic
67#10622860C2211yescharacteristic
68#10622836C2212yes—
69#10622836C2212yes—
70#10622826C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622823C2211yescharacteristic
73#10622823C2211yescharacteristic
74#10622607C2212yescomplemented
75#10622605C2212yescomplemented
76#10622603C2212yescomplemented
77#10622602C2212yescomplemented
78#10622593C2212yescomplemented
79#10622592C2212yescomplemented
80C4⋊C4×Dic11C2212yescomplemented
81#10622574C2212yes—
82#10622574C2212yes—
83#10622573C2212yes—
84#10622573C2212yes—
85#10622573C2212yescomplemented
86#10622572C2212yes—
87#10622572C2212yes—
88#10622572C2212yescomplemented
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622572C2212yescomplemented
92#10622569C2212yescomplemented
93#10622568C2211yescharacteristic
94#10622568C2211yescharacteristic
95#10622565C2212yescomplemented
96#10622565C2212yescomplemented
97#10622561C2212yescomplemented
98#10622558C2212yescomplemented
99#10622556C2211yescharacteristic
100#10622556C2211yescharacteristic
101#10622556C2212yescomplemented
102#10622555C2211yescharacteristic
103#10622555C2211yescharacteristic
104#10622555C2212yescomplemented
105C22⋊C4×Dic11C2211yescharacteristic
106C22⋊C4×Dic11C2211yescharacteristic
107C22⋊C4×Dic11C2212yescomplemented
108C22⋊C4×Dic11C2212yescomplemented
109#10622289C2212yescomplemented
110#10622289C2212yescomplemented
111#10622288C2212yescomplemented
112#10622286C2212yescomplemented
113#10622285C2212yescomplemented
114#10622281C2212yescomplemented
115#10622279C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622278C2212yescomplemented
119#10622271C2212yescomplemented
120#10622270C2212yescomplemented
121#10622270C2212yescomplemented
122#10622268C2212yescomplemented
123#10622267C2212yescomplemented
124#10622262C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11—24no—
133C22×C22⋊D11—24no—
134C22×C22⋊D11—24no—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C23×Dic11—44no—
143C23×Dic11D418yescomplemented
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C23×Dic11C2311yescharacteristic
151C23×Dic11C2311yescharacteristic
152C2×#4341—24no—
153C2×#4341—44no—
154C22×D44C2312yes—
155C22×C4×D11—24no—
156C22×C4×D11—44no—
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2312yes—
160C22×Dic22C2311yescharacteristic
161C11×#120—24no—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C22⋊C4—24no—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176#67006—24no—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187#66992—24no—
188#66992—24no—
189#66990—24no—
190#66988—24no—
191#66988—24no—
192D4×Dic11—24no—
193D4×Dic11—24no—
194C2×(C2×D11)⋊C4—24no—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×Dic11⋊C4—24no—
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×C4×Dic11—24no—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230#66946—44no—
231#66939—24no—
232#66939—24no—
233#66935—24no—
234(C22⋊D11)⋊C4—28no—
235(C22⋊D11)⋊C4—28no—
236(C22⋊D11)⋊C4—28no—
237(C22⋊D11)⋊C4—28no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4—24no—
240(C22⋊D11)⋊C4—44no—
241#66931—24no—
242#66931—24no—
243#66930—24no—
244#66930—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34562—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11C2×D414yes—
267C24×C11C2411yescharacteristic
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C24×C11C2411yescharacteristic
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11#4114yescomplemented
276C23×D11C2411yescharacteristic
277C23×D11C2412yes—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C2×C22⋊D11—232no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C22×Dic11—24no—
316C22×Dic11—24no—
317C22×Dic11—24no—
318C22×Dic11—22no—
319C22×Dic11—24no—
320C22×Dic11—22no—
321C22×Dic11—22no—
322C22×Dic11—42no—
323C22×Dic11—42no—
324C22×Dic11—42no—
325C22×Dic11—416no—
326C22×Dic11C2×D414yes—
327C22×Dic11C2×D414yes—
328C22×Dic11C2×D414yes—
329C22×Dic11C2×D414yes—
330C22×Dic11C2×D414yes—
331C22×Dic11C2×D414yes—
332C22×Dic11#4114yescomplemented
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2412yes—
342C22×Dic11C2411yescharacteristic
343#4341—416no—
344C2×D44—24no—
345C2×D44—42no—
346C2×D44—42no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—416no—
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—42no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4—42no—
371C22⋊Dic11—22no—
372C22⋊Dic11—22no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—24no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C2×#525—111no—
415C22×C4×D4—111no—
416#2638—112no—
417#2635—112no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—111no—
423#2622D1111yescharacteristic, complemented
424#2618—111no—
425#2617—111no—
426#2613—111no—
427#2613—111no—
428#2395—112no—
429#2392—112no—
430#2392—112no—
431#2388—112no—
432C4×#123—111no—
433C4×#123—111no—
434C4×#120—111no—
435C4×#120—111no—
436#2280—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—28no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—44no—
454C23×C11—44no—
455C23×C11—48no—
456C23×C11—48no—
457C23×C11C22×D412yes—
458C23×C11C22×D412yes—
459C23×C11C22×D412yes—
460C23×C11C2×#4112yes—
461C23×C11C2×#4112yes—
462C23×C11C2511yescharacteristic
463C22×D11—28no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—48no—
476C22×D11—44no—
477C22×D11—44no—
478C22×D11—48no—
479C22×D11C2×#4114yes—
480D4×C11—44no—
481D4×C11—44no—
482D4×C11—44no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—44no—
503C2×C4×C11—44no—
504C22⋊D11—216no—
505C22⋊D11—216no—
506C22⋊D11—44no—
507C22⋊D11—48no—
508C22⋊D11—44no—
509C22⋊D11—44no—
510C22⋊D11—44no—
511C2×Dic11—28no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—28no—
518C2×Dic11—28no—
519C2×Dic11—28no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—44no—
534C2×Dic11—44no—
535C2×Dic11—44no—
536C2×Dic11—44no—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C2×#4114yes—
542C2×Dic11H(5,𝔽2)14yes—
543D44—48no—
544C4×D11—48no—
545C4×D11—48no—
546C4×D11—44no—
547Dic22—44no—
548C22×#41—111no—
549C23×D4—111no—
550C24×C4—111no—
551C24×C4—111no—
552#525—228no—
553C2×#123—111no—
554C2×#123—111no—
555C2×#123—111no—
556C2×#123—111no—
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×#121—111no—
560C2×#121—111no—
561C2×#120—111no—
562C2×#120—111no—
563C2×#120—111no—
564C2×#120C2×D1111yescharacteristic
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—228no—
576C2×#117—111no—
577C2×#117—112no—
578C22×C4⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4C2×D1111yescharacteristic
581C22×C42—111no—
582#400—112no—
583#399—112no—
584#398—112no—
585#398—112no—
586#398—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397C2×D1112yescomplemented
591#397C2×D1112yescomplemented
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394C2×D1112yescomplemented
607#394C2×D1112yescomplemented
608#393—112no—
609#392—112no—
610#392—112no—
611#392—112no—
612#392—112no—
613#392—112no—
614#388—112no—
615#388—112no—
616#387—112no—
617#387—112no—
618#386—111no—
619#386—111no—
620#386—112no—
621#386—112no—
622#386C2×D1111yescharacteristic
623#386C2×D1111yescharacteristic
624#385—111no—
625#385—111no—
626#385—112no—
627#385—112no—
628#385C2×D1111yescharacteristic
629#385C2×D1111yescharacteristic
630#381—111no—
631#381—111no—
632#381—112no—
633#380—111no—
634#380—111no—
635#380—112no—
636#379—111no—
637#379—111no—
638#379—111no—
639#379C2×D1111yescharacteristic
640C4×C4⋊C4—112no—
641C4×C4⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—416no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11#52514yes—
670C22×C11C23×D411yescharacteristic
671C22×C11C22×#4111yescharacteristic
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×H(5,𝔽2)12yes—
674C22×C11#58512yes—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—24no—
678C2×D11—416no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—42no—
687C2×D11—42no—
688C4×C11—41no—
689C4×C11—42no—
690C4×C11—41no—
691C4×C11—42no—
692C4×C11—41no—
693C4×C11—42no—
694C4×C11—42no—
695Dic11—24no—
696Dic11—22no—
697Dic11—22no—
698Dic11—22no—
699Dic11—41no—
700Dic11—41no—
701Dic11—41no—
702Dic11—42no—
703Dic11—42no—
704Dic11#53414yes—
705C25—111no—
706C25C22×D1111yescharacteristic
707C2×#41—224no—
708C2×#41—444no—
709C22×Q8—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—112no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—112no—
718C22×D4—224no—
719C22×D4—224no—
720C22×D4—224no—
721C22×D4C22×D1111yescharacteristic
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1111yescharacteristic
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—118no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—112no—
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—224no—
737C23×C4—444no—
738C23×C4—444no—
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741#123—224no—
742#123—224no—
743#123—224no—
744#123—224no—
745C22⋊Q8—224no—
746C22⋊Q8—224no—
747#121—224no—
748#121—224no—
749#120—24no—
750#120—224no—
751#120—224no—
752#120—224no—
753C4×D4—228no—
754C4×D4—228no—
755C4×D4—228no—
756C4×D4—228no—
757C4×D4—224no—
758C4×D4—224no—
759C4×D4—224no—
760C4×D4—224no—
761C4×D4—444no—
762C4×D4—444no—
763#117—224no—
764#117—444no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—224no—
780C2×C4⋊C4C22×D1112yes—
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—24no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—224no—
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1111yescharacteristic
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1112yes—
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—112no—
823C2×C42—112no—
824C2×C42—224no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95C22×D1112yes—
838#95C22×D1112yes—
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—24no—
842C2×C11—42no—
843C2×C11—42no—
844C2×C11—81no—
845C2×C11C2×#52511yescharacteristic
846C2×C11C2×#53411yescharacteristic
847C2×C11#344911yescharacteristic
848C2×C11#345912yes—
849C2×C11#346012yes—
850D11—44no—
851D11—81no—
852C24—22no—
853C24—22no—
854C24—42no—
855C24—42no—
856C24—112no—
857C24—114no—
858C24—111no—
859C24—222no—
860C24—222no—
861C24—442no—
862C24—442no—
863C24D4×D1114yes—
864C24C23×D1111yescharacteristic
865C24C23×D1111yescharacteristic
866C24C23×D1111yescharacteristic
867C24C23×D1111yescharacteristic
868#41—4416no—
869C2×Q8—222no—
870C2×Q8—442no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—222no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—2232no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—111no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—114no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—111no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—224no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—4416no—
937C22×C4—4416no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4C23×D1112yes—
942C22×C4C23×D1112yes—
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1112yes—
947C22×C4C23×D1111yescharacteristic
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—224no—
951C4⋊C4—224no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—224no—
959C4⋊C4—224no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—224no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C42—224no—
999C42—224no—
1000C42—222no—
1001C42—222no—
1002C42—224no—
1003C42—224no—
1004C11#3456211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—22no—
1020C23—22no—
1021C23—44no—
1022C23—44no—
1023C23—48no—
1024C23—48no—
1025C23—114no—
1026C23—228no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—222no—
1037C23—222no—
1038C23—448no—
1039C23—444no—
1040C23—444no—
1041C23—448no—
1042C23C2×D4×D1112yes—
1043C23C2×D4×D1112yes—
1044C23C2×D4×D1112yes—
1045C23#41×D1112yes—
1046C23#41×D1112yes—
1047C23C24×D1111yescharacteristic
1048Q8—444no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—2216no—
1053D4—2216no—
1054D4—448no—
1055D4—444no—
1056D4—444no—
1057D4—444no—
1058D4—448no—
1059D4—444no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—112no—
1082C2×C4—114no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—114no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—448no—
1110C2×C4—444no—
1111C2×C4—448no—
1112C2×C4—444no—
1113C2×C4—444no—
1114C2×C4—444no—
1115C2×C4—444no—
1116C22—22no—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—41no—
1132C22—41no—
1133C22—42no—
1134C22—42no—
1135C22—41no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—4416no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—441no—
1145C22—441no—
1146C22—442no—
1147C22—442no—
1148C22—441no—
1149C22#1062318714yes—
1150C22C22×D4×D1111yescharacteristic
1151C22C2×#41×D1111yescharacteristic
1152C22C2×#41×D1111yescharacteristic
1153C22D11×H(5,𝔽2)12yes—
1154C22#1062345512yes—
1155C4—42no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—42no—
1161C4—41no—
1162C4—114no—
1163C4—222no—
1164C4—222no—
1165C4—222no—
1166C4—224no—
1167C4—441no—
1168C4—441no—
1169C4—442no—
1170C4—442no—
1171C4—441no—
1172C2—24no—
1173C2—42no—
1174C2—42no—
1175C2—81no—
1176C2—444no—
1177C2—881no—
1178C2C2×#1062318711yescharacteristic
1179C2D11×#53411yescharacteristic
1180C2#1308194211yescharacteristic
1181C2#1308202712yes—
1182C2#1308203512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2622C2
hypercenter#2622D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2622

Complements

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

NH ≅ G/Ntype
1. C2×#10623117C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074535C2semidirect
4. #13074502C2semidirect
5. #13074458C2semidirect
6. #13074456C2semidirect
7. #13074435C2semidirect
8. #13074427C2semidirect
9. #13074389C2semidirect
10. #13074364C2semidirect
11. #13074356C2semidirect
12. #13074331C2semidirect
13. #13074330C2semidirect
14. #13071874C2semidirect
15. #13071859C2semidirect
16. #13071853C2semidirect
17. #13071830C2semidirect
18. #13071141C2semidirect
19. #13071135C2semidirect
20. #13071121C2semidirect
21. #13071117C2semidirect
22. #13070994C2semidirect
23. C11×#2622C2semidirect
26. C22×#4341C22semidirect
32. C2×#66992C22semidirect
35. C2×#66988C22semidirect
37. C2×D4×Dic11C22semidirect
42. C2×#66946C22semidirect
44. C2×#66939C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×#66931C22semidirect
56. C2×#66930C22semidirect
57. C2×#66930C22semidirect
58. C11×#397C22semidirect
59. C11×#397C22semidirect
60. C11×#394C22semidirect
61. C11×#394C22semidirect
74. #10622607C22semidirect
75. #10622605C22semidirect
76. #10622603C22semidirect
77. #10622602C22semidirect
78. #10622593C22semidirect
79. #10622592C22semidirect
80. C4⋊C4×Dic11C22semidirect
85. #10622573C22semidirect
88. #10622572C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
91. #10622572C22semidirect
92. #10622569C22semidirect
95. #10622565C22semidirect
96. #10622565C22semidirect
97. #10622561C22semidirect
98. #10622558C22semidirect
101. #10622556C22semidirect
104. #10622555C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C22⋊C4×Dic11C22semidirect
109. #10622289C22semidirect
110. #10622289C22semidirect
111. #10622288C22semidirect
112. #10622286C22semidirect
113. #10622285C22semidirect
114. #10622281C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622278C22semidirect
119. #10622271C22semidirect
120. #10622270C22semidirect
121. #10622270C22semidirect
122. #10622268C22semidirect
123. #10622267C22semidirect
124. #10622262C22semidirect
143. C23×Dic11D4semidirect
275. C23×D11#41semidirect
332. C22×Dic11#41semidirect
423. #2622D11semidirect
590. #397C2×D11semidirect
591. #397C2×D11semidirect
606. #394C2×D11semidirect
607. #394C2×D11semidirect
1004. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106231172
C22×(C22⋊D11)⋊C42
#130745352
#130745022
#130744582
#130744562
#130744352
#130744272
#130743892
#130743642
#130743562
#130743312
#130743302
#130718742
#130718592
#130718532
#130718302
#130711412
#130711352
#130711212
#130711172
#130709942
C11×#26222
#3456211