Finite Group Databasebeta

← #14914572

Subgroups — #14914572

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2#13071719C212yesmaximal, complemented
3#13071718C212yesmaximal, complemented
4#13071715C212yesmaximal, complemented
5#13071709C212yesmaximal, complemented
6#13071494C211yesmaximal, characteristic
7#13071488C211yesmaximal, characteristic
8#13071486C211yesmaximal, characteristic
9#13071486C211yesmaximal, characteristic
10#13071485C211yesmaximal, characteristic
11#13071480C211yesmaximal, characteristic
12#13071480C211yesmaximal, characteristic
13#13071421C212yesmaximal, complemented
14#13071414C212yesmaximal, complemented
15#13071218C211yesmaximal, characteristic
16#13071217C211yesmaximal, characteristic
17#13071173C212yesmaximal, complemented
18C4×#66942C212yesmaximal, complemented
19#13071007C211yesmaximal, characteristic
20#13070972C211yesmaximal, characteristic
21#13070971C211yesmaximal, characteristic
22#117×Dic11C211yesmaximal, characteristic
23C11×#2344C211yesmaximal, characteristic
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66942C4116yescomplemented
36C2×#66942C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66942C2211yescharacteristic
39C2×#66942C2211yescharacteristic
40C2×#66942C2211yescharacteristic
41C2×#66942C2211yescharacteristic
42C2×#66942C2211yescharacteristic
43C2×#66942C2211yescharacteristic
44C2×#66930C2211yescharacteristic
45C2×#66930C2211yescharacteristic
46C11×#389C2212yes—
47C11×#387C2212yes—
48C11×#387C2212yes—
49C11×#381C2211yescharacteristic
50C11×#381C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2212yes—
53C4×C11×C22⋊C4C2211yescharacteristic
54#10622825C2211yescharacteristic
55#10622824C2211yescharacteristic
56#10622824C2211yescharacteristic
57C4×C22⋊Dic11C2211yescharacteristic
58#10622598C2212yes—
59#10622594C2212yes—
60#10622594C2212yes—
61#10622591C2212yes—
62#10622591C2212yes—
63#10622591C2212yes—
64#10622591C2212yes—
65#10622591C2212yes—
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2212yes—
70C4⋊C4×Dic11C2212yes—
71#10622585C2212yes—
72#10622585C2212yes—
73#10622585C2212yes—
74#10622556C2211yescharacteristic
75#10622556C2211yescharacteristic
76#10622555C2211yescharacteristic
77#10622555C2211yescharacteristic
78#10622555C2211yescharacteristic
79#10622555C2211yescharacteristic
80C22⋊C4×Dic11C2211yescharacteristic
81C22⋊C4×Dic11C2211yescharacteristic
82C22⋊C4×Dic11C2211yescharacteristic
83C22⋊C4×Dic11C2211yescharacteristic
84C22⋊C4×Dic11C2211yescharacteristic
85C22⋊C4×Dic11C2211yescharacteristic
86C22⋊C4×Dic11C2211yescharacteristic
87C22⋊C4×Dic11C2211yescharacteristic
88C4×C4⋊Dic11C2212yes—
89C4×C4⋊Dic11C2212yes—
90#10622546C2212yes—
91#10622546C2212yes—
92#10622546C2212yes—
93#10622545C2212yes—
94C4×Dic11⋊C4C2212yes—
95C4×Dic11⋊C4C2212yes—
96C4×Dic11⋊C4C2212yes—
97C4×Dic11⋊C4C2212yes—
98C4×Dic11⋊C4C2212yes—
99C42×Dic11C2212yes—
100#10622268C2212yes—
101#10622268C2212yes—
102#10622268C2212yes—
103#10622268C2212yes—
104#10622268C2212yes—
105#10622267C2212yes—
106#10622267C2212yes—
107#10622266C2212yes—
108#10622266C2212yes—
109#10622265C2212yes—
110#10622265C2212yes—
111#10622265C2212yes—
112#10622264C2212yes—
113#10622263C2212yes—
114#10622262C2212yes—
115#10622262C2212yes—
116#10622262C2212yes—
117#10622262C2212yes—
118#10622262C2212yes—
119#10622262C2212yes—
120#10622261C2212yes—
121#10622260C2212yes—
122#10622260C2212yes—
123#10622260C2212yes—
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C11×#117—24no—
132C11×#117—24no—
133C2×C11×C4⋊C4C2×C418yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C42×C11C2312yes—
147C2×C42×C11C2312yes—
148C2×C22⋊Dic11C2311yescharacteristic
149C2×C22⋊Dic11C2311yescharacteristic
150C2×C22⋊Dic11C2311yescharacteristic
151C2×C22⋊Dic11C2311yescharacteristic
152#66979—24no—
153#66979—24no—
154C2×C4⋊Dic11C2×C418yes—
155C2×C4⋊Dic11C2312yes—
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2311yescharacteristic
162C2×Dic11⋊C4C2×C418yes—
163C2×Dic11⋊C4C2×C418yes—
164C2×Dic11⋊C4C2×C418yes—
165C2×Dic11⋊C4C2×C418yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2311yescharacteristic
173C2×Dic11⋊C4C2311yescharacteristic
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2311yescharacteristic
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2311yescharacteristic
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2311yescharacteristic
188C2×C4×Dic11C2×C418yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206#66942C2×C418yes—
207#66942C2×C418yes—
208#66942C2×C418yes—
209#66942C2×C418yes—
210#66942C2×C418yes—
211#66942C2×C418yes—
212#66942C2×C418yes—
213#66942C2×C418yes—
214#66930—24no—
215#66930—24no—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244#34239—111nomaximal, Sylow
245C24×C11C2411yescharacteristic
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—42no—
251C22×C4×C11C22×C414yes—
252C22×C4×C11C22×C414yes—
253C22×C4×C11C22×C414yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2412yes—
264C22×Dic11—24no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—42no—
268C22×Dic11—42no—
269C22×Dic11C22×C414yes—
270C22×Dic11C22×C414yes—
271C22×Dic11C22×C414yes—
272C22×Dic11C22×C414yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2411yescharacteristic
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285C11×C4⋊C4—24no—
286C11×C4⋊C4—24no—
287C11×C4⋊C4—42no—
288C11×C4⋊C4C22×C414yes—
289C11×C4⋊C4C22×C414yes—
290C11×C4⋊C4C22×C414yes—
291C11×C4⋊C4C22×C414yes—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4#4114yes—
296C42×C11—24no—
297C42×C11—24no—
298C42×C11—42no—
299C22⋊Dic11—22no—
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302C22⋊Dic11#4114yes—
303C4⋊Dic11—24no—
304C4⋊Dic11—24no—
305C4⋊Dic11—42no—
306C4⋊Dic11C22×C414yes—
307C4⋊Dic11C22×C414yes—
308C4⋊Dic11C22×C414yes—
309C4⋊Dic11C22×C414yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4—42no—
315Dic11⋊C4—42no—
316Dic11⋊C4C22×C414yes—
317Dic11⋊C4C22×C414yes—
318Dic11⋊C4C22×C414yes—
319Dic11⋊C4C22×C414yes—
320Dic11⋊C4C22×C414yes—
321Dic11⋊C4C22×C414yes—
322Dic11⋊C4C22×C414yes—
323Dic11⋊C4C22×C414yes—
324Dic11⋊C4C22×C414yes—
325Dic11⋊C4C22×C414yes—
326Dic11⋊C4C22×C414yes—
327Dic11⋊C4C22×C414yes—
328Dic11⋊C4C22×C414yes—
329Dic11⋊C4C22×C414yes—
330Dic11⋊C4C22×C414yes—
331Dic11⋊C4C22×C414yes—
332C4×Dic11—24no—
333C4×Dic11—24no—
334C4×Dic11—24no—
335C4×Dic11—24no—
336C4×Dic11—24no—
337C4×Dic11—24no—
338C4×Dic11—42no—
339C4×Dic11—42no—
340C4×Dic11—42no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343C4×Dic11—42no—
344C4×Dic11—42no—
345C4×Dic11C22×C414yes—
346C4×Dic11C22×C414yes—
347C4×Dic11C22×C414yes—
348C4×Dic11C22×C414yes—
349C22×#125—111no—
350#2371—112no—
351#2371—112no—
352#2370—112no—
353#2370—112no—
354#2345—111no—
355#2345—111no—
356#2344—111no—
357#2344—111no—
358#2344—111no—
359#2344—111no—
360#2344—111no—
361#2344D1111yescharacteristic
362#2336—112no—
363#2336—112no—
364#2313—111no—
365#2313—111no—
366C4×#125—112no—
367C4×#125—112no—
368#2283—111no—
369#2274—111no—
370#2274—111no—
371C4×#117—111no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11C23×C412yes—
375C23×C11C2×#4112yes—
376C23×C11C2×#4112yes—
377C23×C11C2511yescharacteristic
378C2×C4×C11—28no—
379C2×C4×C11—28no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—44no—
402C2×C4×C11C23×C412yes—
403C2×C4×C11C23×C412yes—
404C2×C4×C11C23×C412yes—
405C2×C4×C11C23×C412yes—
406C2×C4×C11C23×C412yes—
407C2×C4×C11C23×C412yes—
408C2×C4×C11C2×#4114yes—
409C2×Dic11—28no—
410C2×Dic11—21no—
411C2×Dic11—21no—
412C2×Dic11—21no—
413C2×Dic11—21no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—28no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C23×C412yes—
434C2×Dic11C23×C412yes—
435C2×Dic11C23×C412yes—
436C2×Dic11C23×C412yes—
437C2×Dic11C23×C412yes—
438C2×Dic11C23×C412yes—
439C2×Dic11C23×C412yes—
440C2×Dic11C23×C412yes—
441C2×Dic11C2×#4114yes—
442C2×Dic112−1+414yes—
443C2×#125—111no—
444C2×#125—111no—
445C2×#125—111no—
446C2×#125—111no—
447C2×#125—111no—
448C2×#125—111no—
449C2×#125—111no—
450C2×#125—111no—
451C2×#125—1116no—
452C2×#117—111no—
453C2×#117—111no—
454C2×#117—111no—
455C2×#117—111no—
456C2×#117C2×D1111yescharacteristic
457C2×#117C2×D1111yescharacteristic
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4C2×D1111yescharacteristic
464C22×C42—111no—
465#389—112no—
466#389—112no—
467#389—112no—
468#389—112no—
469#389—112no—
470#389—112no—
471#389—112no—
472#389C2×D1112yes—
473#387—112no—
474#387—112no—
475#387—112no—
476#387—112no—
477#387—112no—
478#387—112no—
479#387—112no—
480#387—112no—
481#387—112no—
482#387—112no—
483#387—112no—
484#387—112no—
485#387—112no—
486#387—112no—
487#387—112no—
488#387—112no—
489#387—112no—
490#387—112no—
491#387—112no—
492#387—112no—
493#387—112no—
494#387—112no—
495#387C2×D1112yes—
496#387C2×D1112yes—
497#383—112no—
498#382—112no—
499#381—111no—
500#381—111no—
501#381—111no—
502#381—111no—
503#381C2×D1111yescharacteristic
504#381C2×D1111yescharacteristic
505#380—111no—
506#380—111no—
507#380—111no—
508#380—111no—
509#380—111no—
510#380C2×D1111yescharacteristic
511C4×C4⋊C4—112no—
512C4×C4⋊C4—112no—
513C4×C4⋊C4—112no—
514C4×C4⋊C4—112no—
515C4×C4⋊C4—112no—
516C4×C4⋊C4—112no—
517C4×C4⋊C4—112no—
518C4×C4⋊C4—112no—
519C4×C4⋊C4—112no—
520C4×C4⋊C4—112no—
521C4×C4⋊C4—112no—
522C4×C4⋊C4—112no—
523C4×C4⋊C4—112no—
524C4×C4⋊C4—112no—
525C4×C4⋊C4—112no—
526C4×C4⋊C4—112no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—112no—
529C4×C4⋊C4C2×D1112yes—
530C4×C22⋊C4—111no—
531C4×C22⋊C4—111no—
532C4×C22⋊C4—111no—
533C4×C22⋊C4—111no—
534C4×C22⋊C4—111no—
535C4×C22⋊C4—111no—
536C4×C22⋊C4—111no—
537C4×C22⋊C4—111no—
538C4×C22⋊C4—111no—
539C4×C22⋊C4C2×D1111yescharacteristic
540#376—112no—
541#376—112no—
542C43—112no—
543C22×C11—22no—
544C22×C11—22no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11C4×#4114yes—
548C22×C11C24×C411yescharacteristic
549C22×C11C22×#4111yescharacteristic
550C22×C11C22×#4111yescharacteristic
551C22×C11C2×2−1+412yes—
552C22×C11#58512yes—
553C4×C11—22no—
554C4×C11—22no—
555C4×C11—22no—
556C4×C11—22no—
557C4×C11—22no—
558C4×C11—22no—
559C4×C11—24no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—42no—
563Dic11—22no—
564Dic11—22no—
565Dic11—22no—
566Dic11—22no—
567Dic11—22no—
568Dic11—22no—
569Dic11—22no—
570Dic11—24no—
571Dic11—42no—
572Dic11—42no—
573Dic11—42no—
574Dic11#51914yes—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582#125—118no—
583#125—118no—
584#125—118no—
585#125—118no—
586#125—118no—
587#125—118no—
588#125—118no—
589#125—118no—
590#117—24no—
591#117—24no—
592#117—224no—
593#117—224no—
594#117—224no—
595#117—224no—
596C2×C4⋊C4—118no—
597C2×C4⋊C4—118no—
598C2×C4⋊C4—118no—
599C2×C4⋊C4—118no—
600C2×C4⋊C4—118no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—111no—
604C2×C4⋊C4—111no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—111no—
608C2×C4⋊C4—111no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—111no—
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⋊C4—111no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4C4×D1118yes—
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1112yes—
633C2×C4⋊C4C22×D1112yes—
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4—111no—
641C2×C22⋊C4—111no—
642C2×C22⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4C22×D1111yescharacteristic
644C2×C22⋊C4C22×D1111yescharacteristic
645C2×C22⋊C4C22×D1111yescharacteristic
646C2×C42—118no—
647C2×C42—111no—
648C2×C42—111no—
649C2×C42—111no—
650C2×C42—111no—
651C2×C42—112no—
652C2×C42—112no—
653C2×C42—112no—
654C2×C42—112no—
655C2×C42—112no—
656C2×C42—112no—
657C2×C42—112no—
658C2×C42—112no—
659C2×C42—112no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42—112no—
663C2×C42—112no—
664C2×C42C22×D1112yes—
665C2×C42C22×D1112yes—
666C2×C42C22×D1112yes—
667#95—112no—
668#95—112no—
669#95—112no—
670#95—112no—
671#95—112no—
672#95—112no—
673#95—112no—
674#95—112no—
675#95—112no—
676#95—112no—
677#95—112no—
678#95—112no—
679#95—112no—
680#95—112no—
681#95—112no—
682#95—112no—
683#95—112no—
684#95—112no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—112no—
689#95C22×D1112yes—
690#95C22×D1112yes—
691#95C22×D1112yes—
692#95C22×D1112yes—
693#95C22×D1112yes—
694#95C22×D1112yes—
695C2×C11—24no—
696C2×C11C2×C4×#4111yescharacteristic
697C2×C11C2×#51911yescharacteristic
698C2×C11#342811yescharacteristic
699C2×C11#351512yes—
700C2×C11#351512yes—
701C24C23×D1111yescharacteristic
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—42no—
707C22×C4—111no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—111no—
711C22×C4—112no—
712C22×C4—111no—
713C22×C4—111no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—111no—
717C22×C4—111no—
718C22×C4—114no—
719C22×C4—114no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—224no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—442no—
727C22×C4—442no—
728C22×C4C2×C4×D1114yes—
729C22×C4C2×C4×D1114yes—
730C22×C4C2×C4×D1114yes—
731C22×C4C23×D1112yes—
732C22×C4C23×D1112yes—
733C22×C4C23×D1112yes—
734C22×C4C23×D1111yescharacteristic
735C22×C4C23×D1111yescharacteristic
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739C22×C4C23×D1111yescharacteristic
740C22×C4C23×D1112yes—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—42no—
744C4⋊C4—114no—
745C4⋊C4—114no—
746C4⋊C4—114no—
747C4⋊C4—114no—
748C4⋊C4—114no—
749C4⋊C4—114no—
750C4⋊C4—114no—
751C4⋊C4—114no—
752C4⋊C4—114no—
753C4⋊C4—114no—
754C4⋊C4—114no—
755C4⋊C4—114no—
756C4⋊C4—114no—
757C4⋊C4—114no—
758C4⋊C4—114no—
759C4⋊C4—114no—
760C4⋊C4—114no—
761C4⋊C4—114no—
762C4⋊C4—114no—
763C4⋊C4—114no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4—224no—
768C4⋊C4—224no—
769C4⋊C4—224no—
770C4⋊C4—442no—
771C4⋊C4—442no—
772C4⋊C4—442no—
773C4⋊C4C2×C4×D1114yes—
774C4⋊C4C2×C4×D1114yes—
775C4⋊C4C2×C4×D1114yes—
776C4⋊C4C2×C4×D1114yes—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—114no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4#434114yes—
785C42—24no—
786C42—24no—
787C42—42no—
788C42—114no—
789C42—114no—
790C42—114no—
791C42—114no—
792C42—224no—
793C42—224no—
794C42—224no—
795C42—224no—
796C42—224no—
797C42—224no—
798C42—442no—
799C42—442no—
800C42—442no—
801C42—442no—
802C42—442no—
803C42—442no—
804C42—442no—
805C11#3423911yescharacteristic, complemented, Sylow
806C23—22no—
807C23—22no—
808C23C22×C4×D1112yes—
809C23C2×#434112yes—
810C23#41×D1112yes—
811C23C24×D1111yescharacteristic
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—44no—
836C2×C4—112no—
837C2×C4—114no—
838C2×C4—112no—
839C2×C4—112no—
840C2×C4—112no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—112no—
844C2×C4—112no—
845C2×C4—114no—
846C2×C4—228no—
847C2×C4—228no—
848C2×C4—221no—
849C2×C4—221no—
850C2×C4—221no—
851C2×C4—221no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—444no—
869C2×C4—444no—
870C2×C4C22×C4×D1112yes—
871C2×C4C22×C4×D1112yes—
872C2×C4C22×C4×D1112yes—
873C2×C4C22×C4×D1112yes—
874C2×C4C22×C4×D1112yes—
875C2×C4C22×C4×D1112yes—
876C2×C4C2×#434114yes—
877C22—22no—
878C22—24no—
879C22—24no—
880C22—22no—
881C22C4×#434114yes—
882C22C23×C4×D1111yescharacteristic
883C22C22×#434111yescharacteristic
884C22C2×#41×D1111yescharacteristic
885C22#1062345312yes—
886C22D11×2−1+412yes—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—24no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—114no—
898C4—222no—
899C4—222no—
900C4—222no—
901C4—224no—
902C4—222no—
903C4—222no—
904C4—222no—
905C4—222no—
906C4—442no—
907C4—442no—
908C4—442no—
909C2—24no—
910C2C2×C4×#434111yescharacteristic
911C2D11×#51911yescharacteristic
912C2#1308181711yescharacteristic
913C2#1308258112yes—
914C2#1308258312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2344C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2344D11
hypocenterC11#34239
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #13071719C2semidirect
3. #13071718C2semidirect
4. #13071715C2semidirect
5. #13071709C2semidirect
13. #13071421C2semidirect
14. #13071414C2semidirect
17. #13071173C2semidirect
18. C4×#66942C2semidirect
35. C2×#66942C4semidirect
805. C11#34239semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
#130717192
#130717182
#130717152
#130717092
#130714942
#130714882
#130714862
#130714852
#130714802
#130714212
#130714142
#130712182
#130712172
#130711732
C4×#669422
#130710072
#130709722
#130709712
#117×Dic112
C11×#23442
#3423911