Finite Group Databasebeta

← #14912708

Subgroups — #14912708

Order 2816.

2202 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623069C211yesmaximal, characteristic
2#13071430C212yesmaximal, complemented
3#13071421C212yesmaximal, complemented
4#13071411C212yesmaximal, complemented
5#13071407C212yesmaximal, complemented
6#13071396C212yesmaximal, complemented
7#13071392C212yesmaximal, complemented
8#13071382C212yesmaximal
9#13071373C212yesmaximal, complemented
10#13071112C211yesmaximal, characteristic, complemented
11#13071109C211yesmaximal, characteristic, complemented
12#13071090C211yesmaximal, characteristic, complemented
13#13071088C211yesmaximal, characteristic, complemented
14#13071081C211yesmaximal, characteristic, complemented
15#13071075C211yesmaximal, characteristic, complemented
16#13071062C211yesmaximal, characteristic, complemented
17#13071062C211yesmaximal, characteristic, complemented
18#13071059C211yesmaximal, characteristic, complemented
19#13071010C211yesmaximal, characteristic, complemented
20#117×Dic11C211yesmaximal, characteristic, complemented
21C4×#66979C211yesmaximal, characteristic, complemented
22#13070955C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C2×#66992C2211yescharacteristic
28C2×#66988C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35#10623069C4116yescomplemented
36C2×#66951C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66939C2211yescharacteristic
39C2×#66938C2211yescharacteristic
40C2×#66932C2211yescharacteristic
41C2×#66931C2211yescharacteristic
42C2×#66925C2211yescharacteristic
43C2×#66925C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#388C2212yes—
47C11×#387C2212yes—
48C11×#386C2212yes—
49C11×#385C2212yes—
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#376C2211yescharacteristic
54#10622834C2212yes—
55#10622826C2212yes—
56#10622823C2212yes—
57C4×C22⋊Dic11C2211yescharacteristic
58C4×C22⋊Dic11C2212yes—
59C4×C22⋊Dic11C2212yes—
60C4×C22⋊Dic11C2211yescharacteristic
61#10622603C2212yes—
62#10622603C2212yes—
63#10622598C2212yes—
64#10622591C2212yes—
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2212yes—
67#10622587C2212yes—
68#10622586C2212yes—
69#10622585C2212yes—
70#10622570C2212yes—
71#10622569C2212yes—
72#10622569C2212yes—
73#10622564C2212yes—
74#10622564C2212yes—
75#10622558C2212yes—
76#10622558C2212yes—
77#10622558C2212yes—
78#10622558C2212yes—
79#10622557C2212yes—
80#10622556C2212yes—
81#10622555C2212yes—
82C22⋊C4×Dic11C2212yes—
83C22⋊C4×Dic11C2212yes—
84#10622553C2212yes—
85C4×(C2×D11)⋊C4C2211yescharacteristic
86C4×(C2×D11)⋊C4C2211yescharacteristic
87C4×C4⋊Dic11C2211yescharacteristic
88C4×C4⋊Dic11C2212yes—
89C4×C4⋊Dic11C2212yes—
90#10622546C2212yes—
91#10622545C2211yescharacteristic
92#10622545C2211yescharacteristic
93#10622545C2211yescharacteristic
94#10622545C2211yescharacteristic
95#10622545C2211yescharacteristic
96C4×Dic11⋊C4C2211yescharacteristic
97C4×Dic11⋊C4C2211yescharacteristic
98C4×Dic11⋊C4C2211yescharacteristic
99C4×Dic11⋊C4C2211yescharacteristic
100C42×Dic11C2211yescharacteristic
101C42×Dic11C2211yescharacteristic
102C42×Dic11C2211yescharacteristic
103C42×Dic11C2211yescharacteristic
104#10622283C2212yes—
105#10622281C2212yes—
106#10622281C2212yes—
107#10622279C2212yes—
108#10622279C2212yes—
109#10622268C2212yes—
110#10622268C2212yes—
111#10622268C2212yes—
112#10622268C2212yes—
113#10622267C2212yes—
114#10622267C2212yes—
115#10622266C2212yes—
116#10622265C2212yes—
117#10622265C2212yes—
118#10622264C2212yes—
119#10622263C2212yes—
120#10622262C2212yes—
121#10622262C2212yes—
122#10622260C2212yes—
123#10622259C2212yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2312yes—
134C22×Dic22C2311yescharacteristic
135C4×D4×C11C2×C418yescomplemented
136C11×#117—24no—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C42×C11—24no—
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2311yescharacteristic
157C2×C22⋊Dic11C2311yescharacteristic
158C2×C22⋊Dic11C2311yescharacteristic
159C2×C22⋊Dic11C2311yescharacteristic
160#66992C2×C418yes—
161#66988C2×C418yescomplemented
162C4×C22⋊D11C2×C418yes—
163C4×C22⋊D11C2×C418yescomplemented
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×(C2×D11)⋊C4C2311yescharacteristic
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×(C2×D11)⋊C4C2311yescharacteristic
171#66979—24no—
172#66979—24no—
173#66979C2×C418yescomplemented
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2311yescharacteristic
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2311yescharacteristic
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×Dic11⋊C4C2311yescharacteristic
191C2×C4×Dic11C2×C418yescomplemented
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210#66951C2×C418yescomplemented
211#66942C2×C418yescomplemented
212#66939C2×C418yescomplemented
213#66938C2×C418yes—
214#66932C2×C418yescomplemented
215#66931C2×C418yescomplemented
216#66925—24no—
217#66925C2×C418yescomplemented
218C42×D11—24no—
219C4×Dic22C2×C418yescomplemented
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#34081—111nomaximal, Sylow
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C23×D11C2411yescharacteristic
248C2×D4×C11—42no—
249C2×D4×C11C22×C414yes—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—24no—
255C22×C4×C11—42no—
256C22×C4×C11—42no—
257C22×C4×C11C22×C414yes—
258C22×C4×C11C22×C414yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2412yes—
267C22×C4×C11C2411yescharacteristic
268C2×C22⋊D11—42no—
269C2×C22⋊D11—42no—
270C2×C22⋊D11C22×C414yes—
271C2×C22⋊D11C22×C414yes—
272C22×Dic11—42no—
273C22×Dic11—42no—
274C22×Dic11C22×C414yes—
275C22×Dic11C22×C414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2411yescharacteristic
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2412yes—
287C2×C4×D11—24no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—42no—
291C2×C4×D11—42no—
292C2×C4×D11C22×C414yes—
293C2×Dic22—42no—
294C2×Dic22C22×C414yes—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—42no—
297C11×C4⋊C4C22×C414yes—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—42no—
300C11×C22⋊C4—42no—
301C11×C22⋊C4C22×C414yes—
302C11×C22⋊C4C22×C414yes—
303C42×C11—22no—
304C42×C11—24no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11C22×C414yes—
308C42×C11#4114yes—
309C22⋊Dic11—24no—
310C22⋊Dic11—24no—
311C22⋊Dic11—42no—
312C22⋊Dic11—42no—
313C22⋊Dic11C22×C414yes—
314C22⋊Dic11C22×C414yes—
315C22⋊Dic11C22×C414yes—
316C22⋊Dic11C22×C414yes—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—42no—
319(C2×D11)⋊C4—42no—
320(C2×D11)⋊C4C22×C414yes—
321(C2×D11)⋊C4C22×C414yes—
322(C2×D11)⋊C4C22×C414yes—
323(C2×D11)⋊C4C22×C414yes—
324C4⋊Dic11—24no—
325C4⋊Dic11—24no—
326C4⋊Dic11—42no—
327C4⋊Dic11C22×C414yes—
328C4⋊Dic11C22×C414yes—
329C4⋊Dic11C22×C414yes—
330Dic11⋊C4—24no—
331Dic11⋊C4—42no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335Dic11⋊C4C22×C414yes—
336Dic11⋊C4C22×C414yes—
337Dic11⋊C4C22×C414yes—
338Dic11⋊C4C22×C414yes—
339Dic11⋊C4C22×C414yes—
340Dic11⋊C4C22×C414yes—
341C4×Dic11—24no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—42no—
346C4×Dic11—42no—
347C4×Dic11—42no—
348C4×Dic11—42no—
349C4×Dic11—42no—
350C4×Dic11—42no—
351C4×Dic11—42no—
352C4×Dic11—42no—
353C4×Dic11C22×C414yes—
354C4×Dic11C22×C414yes—
355C4×Dic11C22×C414yes—
356C4×Dic11C22×C414yes—
357C4×Dic11C22×C414yes—
358C4×Dic11#4114yes—
359C2×#529—111no—
360#2337—112no—
361#2336—112no—
362#2335—112no—
363#2335—112no—
364#2334—112no—
365#2334—112no—
366#2333—112no—
367#2332—112no—
368#2298—111no—
369#2298—111no—
370#2295—111no—
371#2295—111no—
372#2293—111no—
373#2293—111no—
374#2290—111no—
375#2290—111no—
376#2290—111no—
377#2290D1111yescharacteristic, complemented
378#2283—111no—
379C4×#117—111no—
380C4×#117—111no—
381C4×#117—111no—
382C23×C11—21no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11C23×C412yes—
391C23×C11C23×C412yes—
392C23×C11C2511yescharacteristic
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11C23×C412yes—
398D4×C11—44no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—28no—
408C2×C4×C11—28no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—48no—
419C2×C4×C11C23×C412yes—
420C2×C4×C11C23×C412yes—
421C2×C4×C11C23×C412yes—
422C2×C4×C11C23×C412yes—
423C2×C4×C11C23×C412yes—
424C2×C4×C11C2×#4114yes—
425C2×C4×C11C2×#4112yes—
426C2×C4×C11C2×#4112yes—
427C22⋊D11—44no—
428C22⋊D11—44no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—44no—
449C2×Dic11—44no—
450C2×Dic11C23×C412yes—
451C2×Dic11C23×C412yes—
452C2×Dic11C23×C412yes—
453C2×Dic11C23×C412yes—
454C2×Dic11C23×C412yes—
455C2×Dic11C23×C412yes—
456C2×Dic11C23×C412yes—
457C2×Dic11C2×#4114yes—
458C4×D11—28no—
459C4×D11—48no—
460Dic22—44no—
461#529—1116no—
462C2×#126—111no—
463C2×#126—111no—
464C2×#125—111no—
465C2×#124—111no—
466C2×#123—111no—
467C2×#123—111no—
468C2×C22⋊Q8—111no—
469C2×#121—111no—
470C2×C4×Q8—111no—
471C2×C4×D4—111no—
472C2×C4×D4—111no—
473C2×C4×D4C2×D1111yescharacteristic
474C2×#117—111no—
475C2×#117—111no—
476C2×#117—111no—
477C2×#117—111no—
478C2×#117—111no—
479C2×#117C2×D1111yescharacteristic
480C22×C42—111no—
481C22×C42—111no—
482C22×C42C2×D1111yescharacteristic
483#391—112no—
484#391—112no—
485#390—112no—
486#390—112no—
487#389—112no—
488#389—112no—
489#389—112no—
490#389—112no—
491#388—112no—
492#388—112no—
493#388—112no—
494#388—112no—
495#388—112no—
496#388—112no—
497#388—112no—
498#388—112no—
499#388—112no—
500#388—112no—
501#388—112no—
502#388C2×D1112yes—
503#387—112no—
504#387—112no—
505#387—112no—
506#387—112no—
507#387—112no—
508#387—112no—
509#387—112no—
510#387—112no—
511#387—112no—
512#387—112no—
513#387—112no—
514#387C2×D1112yes—
515#386—112no—
516#386—112no—
517#386—112no—
518#386C2×D1112yes—
519#385—112no—
520#385—112no—
521#385—112no—
522#385C2×D1112yes—
523#383—112no—
524#382—112no—
525#381—112no—
526#380—112no—
527C4×C4⋊C4—112no—
528C4×C4⋊C4—112no—
529C4×C4⋊C4—112no—
530C4×C4⋊C4—112no—
531C4×C4⋊C4—111no—
532C4×C4⋊C4—111no—
533C4×C4⋊C4—111no—
534C4×C4⋊C4—111no—
535C4×C4⋊C4—111no—
536C4×C4⋊C4—112no—
537C4×C4⋊C4—112no—
538C4×C4⋊C4C2×D1111yescharacteristic
539C4×C22⋊C4—112no—
540C4×C22⋊C4—112no—
541C4×C22⋊C4—111no—
542C4×C22⋊C4—111no—
543C4×C22⋊C4—112no—
544C4×C22⋊C4—112no—
545C4×C22⋊C4—111no—
546C4×C22⋊C4—111no—
547C4×C22⋊C4—112no—
548C4×C22⋊C4—112no—
549C4×C22⋊C4C2×D1111yescharacteristic
550C4×C22⋊C4C2×D1111yescharacteristic
551#376—111no—
552#376—111no—
553#376—111no—
554#376—111no—
555#376—111no—
556#376C2×D1111yescharacteristic
557C43—111no—
558C43—111no—
559C43—111no—
560C43—111no—
561C22×C11—22no—
562C22×C11—22no—
563C22×C11—22no—
564C22×C11—22no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11C24×C411yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11#58512yes—
575C22×C11#58512yes—
576C2×D11—22no—
577C2×D11—22no—
578C2×D11—22no—
579C2×D11—42no—
580C2×D11—42no—
581C4×C11—22no—
582C4×C11—22no—
583C4×C11—22no—
584C4×C11—22no—
585C4×C11—24no—
586C4×C11—42no—
587C4×C11—42no—
588C4×C11—42no—
589C4×C11C4×#4114yes—
590Dic11—22no—
591Dic11—22no—
592Dic11—22no—
593Dic11—22no—
594Dic11—22no—
595Dic11—22no—
596Dic11—22no—
597Dic11—24no—
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601C22×Q8—111no—
602C22×D4—111no—
603C22×D4—111no—
604C22×D4C22×D1111yescharacteristic
605C23×C4—111no—
606C23×C4—111no—
607C23×C4—111no—
608C23×C4—112no—
609C23×C4C22×D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1112yes—
612#126—118no—
613#126—118no—
614#125—118no—
615#124—118no—
616#123—118no—
617#123—118no—
618C22⋊Q8—118no—
619#121—118no—
620C4×Q8—118no—
621C4×D4—118no—
622C4×D4—118no—
623C4×D4C4×D1118yescomplemented
624#117—24no—
625#117—118no—
626#117—118no—
627#117—224no—
628#117—224no—
629#117—224no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4C22×D1112yes—
648C2×C4⋊C4C22×D1112yes—
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C22⋊C4—111no—
651C2×C22⋊C4—111no—
652C2×C22⋊C4—111no—
653C2×C22⋊C4—111no—
654C2×C22⋊C4—111no—
655C2×C22⋊C4—111no—
656C2×C22⋊C4—111no—
657C2×C22⋊C4—111no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C22⋊C4C22×D1111yescharacteristic
669C2×C22⋊C4C22×D1111yescharacteristic
670C2×C42—24no—
671C2×C42—118no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—111no—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—112no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—112no—
683C2×C42—112no—
684C2×C42—112no—
685C2×C42—112no—
686C2×C42—112no—
687C2×C42—112no—
688C2×C42—112no—
689C2×C42—112no—
690C2×C42—224no—
691C2×C42C22×D1112yes—
692C2×C42C22×D1111yescharacteristic
693C2×C42C22×D1111yescharacteristic
694C2×C42C22×D1111yescharacteristic
695C2×C42C22×D1111yescharacteristic
696C2×C42C22×D1111yescharacteristic
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95C22×D1112yes—
717#95C22×D1112yes—
718#95C22×D1112yes—
719#95C22×D1112yes—
720#95C22×D1112yes—
721C2×C11—42no—
722C2×C11—42no—
723C2×C11C2×C4×#4111yescharacteristic
724C2×C11#342811yescharacteristic
725C2×C11#342811yescharacteristic
726C2×C11#345512yes—
727C2×C11#345512yes—
728D11—42no—
729C24—111no—
730C24C23×D1111yescharacteristic
731C24C23×D1111yescharacteristic
732C2×Q8—114no—
733C2×Q8—442no—
734C2×D4—42no—
735C2×D4—114no—
736C2×D4—114no—
737C2×D4—442no—
738C2×D4—442no—
739C2×D4C2×C4×D1114yes—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—24no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—111no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—112no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—114no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—224no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—442no—
765C22×C4—442no—
766C22×C4—442no—
767C22×C4—442no—
768C22×C4C2×C4×D1114yes—
769C22×C4C2×C4×D1114yes—
770C22×C4C23×D1112yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1111yescharacteristic
775C22×C4C23×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C22×C4C23×D1112yes—
778C22×C4C23×D1111yescharacteristic
779C4⋊C4—24no—
780C4⋊C4—42no—
781C4⋊C4—114no—
782C4⋊C4—114no—
783C4⋊C4—114no—
784C4⋊C4—114no—
785C4⋊C4—114no—
786C4⋊C4—114no—
787C4⋊C4—114no—
788C4⋊C4—114no—
789C4⋊C4—114no—
790C4⋊C4—224no—
791C4⋊C4—224no—
792C4⋊C4—224no—
793C4⋊C4—442no—
794C4⋊C4—442no—
795C4⋊C4—442no—
796C4⋊C4—442no—
797C4⋊C4—442no—
798C4⋊C4C2×C4×D1114yes—
799C22⋊C4—24no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—114no—
803C22⋊C4—114no—
804C22⋊C4—114no—
805C22⋊C4—114no—
806C22⋊C4—114no—
807C22⋊C4—114no—
808C22⋊C4—114no—
809C22⋊C4—114no—
810C22⋊C4—224no—
811C22⋊C4—224no—
812C22⋊C4—224no—
813C22⋊C4—442no—
814C22⋊C4—442no—
815C22⋊C4—442no—
816C22⋊C4—442no—
817C22⋊C4C2×C4×D1114yes—
818C22⋊C4C2×C4×D1114yes—
819C42—24no—
820C42—22no—
821C42—22no—
822C42—22no—
823C42—114no—
824C42—114no—
825C42—114no—
826C42—114no—
827C42—114no—
828C42—114no—
829C42—224no—
830C42—222no—
831C42—222no—
832C42—222no—
833C42—442no—
834C42—442no—
835C42—442no—
836C42—442no—
837C42—442no—
838C42—442no—
839C42—442no—
840C42—442no—
841C42C2×C4×D1114yes—
842C42#434114yes—
843C11#3408111yescharacteristic, complemented, Sylow
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—112no—
853C23—221no—
854C23—221no—
855C23—222no—
856C23—222no—
857C23C22×C4×D1112yes—
858C23C22×C4×D1112yes—
859C23C24×D1111yescharacteristic
860Q8—444no—
861D4—44no—
862D4—444no—
863D4—444no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—48no—
884C2×C4—112no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—112no—
888C2×C4—112no—
889C2×C4—112no—
890C2×C4—112no—
891C2×C4—114no—
892C2×C4—221no—
893C2×C4—221no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—228no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—448no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4C22×C4×D1112yes—
916C2×C4C22×C4×D1112yes—
917C2×C4C22×C4×D1112yes—
918C2×C4C22×C4×D1112yes—
919C2×C4C22×C4×D1112yes—
920C2×C4C2×#434114yes—
921C2×C4C2×#434112yes—
922C2×C4#41×D1112yes—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—222no—
934C22—222no—
935C22—222no—
936C22—442no—
937C22—442no—
938C22C23×C4×D1111yescharacteristic
939C22C22×#434111yescharacteristic
940C22C2×#41×D1111yescharacteristic
941C22#1062345312yes—
942C22#1062345312yes—
943C4—24no—
944C4—22no—
945C4—22no—
946C4—22no—
947C4—22no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—224no—
952C4—222no—
953C4—222no—
954C4—222no—
955C4—222no—
956C4—222no—
957C4—222no—
958C4—222no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4C4×#434114yes—
963C2—42no—
964C2—42no—
965C2—442no—
966C2C2×C4×#434111yescharacteristic
967C2#1308181511yescharacteristic
968C2#1308181711yescharacteristic
969C2#1308199912yes—
970C2#1308200412yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2290C2
socle, cosocleC23×C11C25
prime radicalC2×#66992C22
hypercenter#2290D11
hypocenterC11#34081
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. #13071430C2semidirect
3. #13071421C2semidirect
4. #13071411C2semidirect
5. #13071407C2semidirect
6. #13071396C2semidirect
7. #13071392C2semidirect
9. #13071373C2semidirect
10. #13071112C2semidirect
11. #13071109C2semidirect
12. #13071090C2semidirect
13. #13071088C2semidirect
14. #13071081C2semidirect
15. #13071075C2semidirect
16. #13071062C2semidirect
17. #13071062C2semidirect
18. #13071059C2semidirect
19. #13071010C2semidirect
20. #117×Dic11C2semidirect
21. C4×#66979C2semidirect
22. #13070955C2semidirect
23. C11×#2290C2semidirect
35. #10623069C4semidirect
135. C4×D4×C11C2×C4semidirect
161. #66988C2×C4semidirect
163. C4×C22⋊D11C2×C4semidirect
173. #66979C2×C4semidirect
191. C2×C4×Dic11C2×C4semidirect
210. #66951C2×C4semidirect
211. #66942C2×C4semidirect
212. #66939C2×C4semidirect
214. #66932C2×C4semidirect
215. #66931C2×C4semidirect
217. #66925C2×C4semidirect
219. C4×Dic22C2×C4semidirect
377. #2290D11semidirect
623. C4×D4C4×D11semidirect
843. C11#34081semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
#130714302
#130714212
#130714112
#130714072
#130713962
#130713922
#130713822
#130713732
#130711122
#130711092
#130710902
#130710882
#130710812
#130710752
#130710622
#130710592
#130710102
#117×Dic112
C4×#669792
#130709552
C11×#22902
#3408111