Finite Group Databasebeta

← C2×D11×#548 #15660703

Subgroups — C2×D11×#548 #15660703

Order 2816.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D11C211yesmaximal, characteristic, complemented
2C23×Q8×D11C211yesmaximal, characteristic, complemented
3C2×#10623107C211yesmaximal, characteristic, complemented
4C2×#10623348C211yesmaximal, characteristic, complemented
5C2×#10623164C213yesmaximal, complemented
6C2×#10623083C213yesmaximal, complemented
7C2×#10623208C213yesmaximal, complemented
8C2×#10623362C211yesmaximal, characteristic, complemented
9C2×#10623129C213yesmaximal, complemented
10D11×#548C2132yesmaximal, direct product factor
11C2×D11×#124C213yesmaximal, complemented
12C2×D11×C22⋊Q8C213yesmaximal, complemented
13C2×D11×#121C213yesmaximal, complemented
14C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
15C2×C4×D4×D11C213yesmaximal, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×Q8×C11C2211yescharacteristic, complemented
19C2×#41×D11—216no—
20C2×#41×D11C22116yescomplemented
21C22×#4343C2211yescharacteristic, complemented
22C22×Q8×D11—216no—
23C22×Q8×D11C2213yes—
24C22×Q8×D11C2211yescharacteristic
25C22×Q8×D11C2211yescharacteristic, complemented
26C22×Q8×D11C2213yescomplemented
27C22×Q8×D11C22116yescomplemented
28C22×#4341C2213yescomplemented
29C22×D4×D11C2213yes—
30C22×D4×D11C2213yes—
31C22×#4339C2213yescomplemented
32C23×C4×D11C2213yes—
33C23×C4×D11C2213yes—
34C23×Dic22C2213yescomplemented
35C11×#548C22116yescomplemented
36C2×C11×#124C2213yescomplemented
37C2×C11×C22⋊Q8C2213yescomplemented
38C2×C11×#121C2213yescomplemented
39C2×C4×Q8×C11C2211yescharacteristic, complemented
40C2×C4×D4×C11C2213yescomplemented
41#10623362C22116yescomplemented
42#10623348C22116yescomplemented
43C2×#67000C2213yescomplemented
44C2×#66999C2213yescomplemented
45C2×Q8×Dic11C2211yescharacteristic, complemented
46C2×#66992C2216yescomplemented
47C2×#66991C2213yescomplemented
48C2×#66989C2213yescomplemented
49C2×D4×Dic11C2213yescomplemented
50C2×#66983C2213yescomplemented
51C2×C4×C22⋊D11C2213yescomplemented
52C2×C4×C22⋊D11C2213yescomplemented
53C2×#66977C2213yescomplemented
54#10623208C22148yescomplemented
55D11×#124C22148yescomplemented
56#10623164C22148yescomplemented
57D11×C22⋊Q8C22148yescomplemented
58D11×#121C22148yescomplemented
59#10623129C22148yescomplemented
60#10623107C22116yescomplemented
61C4×Q8×D11C22116yescomplemented
62#10623083C22148yescomplemented
63C4×D4×D11C22148yescomplemented
64C2×#66950C2213yescomplemented
65C2×#66949C2216yescomplemented
66C2×#66948C2213yescomplemented
67C2×#66946C2213yescomplemented
68C2×C4⋊C4×D11C2213yes—
69C2×C4⋊C4×D11C2213yes—
70C2×#66940C2213yescomplemented
71C2×#66938C2216yescomplemented
72C2×#66938C2216yescomplemented
73C2×#66937C2216yescomplemented
74C2×(C22⋊D11)⋊C4C2213yescomplemented
75C2×(C22⋊D11)⋊C4C2213yescomplemented
76C2×C22⋊C4×D11C2213yes—
77C2×C22⋊C4×D11C2216yes—
78C2×C22⋊C4×D11C2211yescharacteristic
79C2×#66931C2216yescomplemented
80C2×#66928C2213yescomplemented
81C2×C4×D44C2213yescomplemented
82C2×C42×D11C2213yes—
83C2×C4×Dic22C2213yescomplemented
84C24×D11C2313yes—
85C24×D11C2311yescharacteristic
86C2×C11×#41—28no—
87C2×C11×#41C2318yescomplemented
88C22×Q8×C11—28no—
89C22×Q8×C11C2313yes—
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2318yescomplemented
92C22×D4×C11C2313yes—
93C22×D4×C11C2313yes—
94C23×C4×C11C2313yes—
95C23×C4×C11C2313yes—
96C22×C22⋊D11C2313yes—
97C22×C22⋊D11C2313yes—
98C22×C22⋊D11C2316yes—
99C23×Dic11C2313yes—
100C23×Dic11C2313yes—
101#41×D11—2128no—
102C2×#4343—28no—
103C2×#4343C2318yescomplemented
104C2×Q8×D11—28no—
105C2×Q8×D11—2128no—
106C2×Q8×D11—224no—
107C2×Q8×D11—224no—
108C2×Q8×D11D4116yescomplemented
109C2×Q8×D11C23124yes—
110C2×Q8×D11C2318yes—
111C2×Q8×D11C2318yescomplemented
112C2×Q8×D11C23124yescomplemented
113C2×#4341—224no—
114C2×#4341C23124yescomplemented
115C2×D4×D11—224no—
116C2×D4×D11—224no—
117C2×D4×D11C23124yes—
118C2×D4×D11C23124yes—
119C2×#4339—224no—
120C2×#4339C23124yescomplemented
121C22×D44C2313yes—
122C22×D44C2313yes—
123C22×C4×D11—224no—
124C22×C4×D11—224no—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2313yes—
127C22×C4×D11C2313yes—
128C22×C4×D11C2313yes—
129C22×C4×D11C2313yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2313yes—
132C22×C4×D11C2313yes—
133C22×C4×D11C23124yes—
134C22×C4×D11C23124yes—
135C22×C4×D11C2313yes—
136C22×Dic22—224no—
137C22×Dic22C2313yes—
138C22×Dic22C2316yes—
139C22×Dic22C2313yes—
140C22×Dic22C23124yescomplemented
141C11×#124C23124yescomplemented
142C11×C22⋊Q8C23124yescomplemented
143C11×#121C23124yescomplemented
144C4×Q8×C11C2318yescomplemented
145C4×D4×C11C23124yescomplemented
146C2×C11×C4⋊C4C2313yes—
147C2×C11×C4⋊C4C2313yes—
148C2×C11×C22⋊C4C2316yes—
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2313yes—
151C2×C42×C11C2313yes—
152C2×C22⋊Dic11C2316yes—
153C2×C22⋊Dic11C2313yes—
154C2×C22⋊Dic11C2311yescharacteristic
155#67000C23124yescomplemented
156#66999C23124yescomplemented
157Q8×Dic11C2318yescomplemented
158#66992C23148yescomplemented
159#66991C23124yescomplemented
160#66989C23124yescomplemented
161D4×Dic11C23124yescomplemented
162#66983C23124yescomplemented
163C4×C22⋊D11C23124yescomplemented
164C4×C22⋊D11C23124yescomplemented
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2313yes—
167C2×(C2×D11)⋊C4C2316yes—
168C2×(C2×D11)⋊C4C2316yes—
169C2×(C2×D11)⋊C4C2313yes—
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×C4⋊Dic11C2313yes—
172C2×C4⋊Dic11C2313yes—
173#66977C23124yescomplemented
174C2×Dic11⋊C4C2316yes—
175C2×Dic11⋊C4C2313yes—
176C2×Dic11⋊C4C2313yes—
177C2×C4×Dic11C2313yes—
178C2×C4×Dic11C2313yes—
179C2×C4×Dic11C2313yes—
180#66950C23124yescomplemented
181#66949C23148yescomplemented
182#66948C23124yescomplemented
183#66946C23124yescomplemented
184C4⋊C4×D11C23124yes—
185C4⋊C4×D11C23124yes—
186#66940C23124yescomplemented
187#66938C23148yescomplemented
188#66938C23148yescomplemented
189#66937C23148yescomplemented
190(C22⋊D11)⋊C4C23124yescomplemented
191(C22⋊D11)⋊C4C23124yescomplemented
192C22⋊C4×D11C2318yes—
193C22⋊C4×D11C23124yes—
194C22⋊C4×D11C23148yes—
195#66931C23148yescomplemented
196#66928C23124yescomplemented
197C4×D44C23124yescomplemented
198C42×D11C23124yes—
199C4×Dic22C23124yescomplemented
200C22×#548—111nomaximal, Sylow
201C24×C11C2413yes—
202C24×C11C2411yescharacteristic
203C23×D11—24no—
204C23×D11—24no—
205C23×D11—212no—
206C23×D11—212no—
207C23×D11—212no—
208C23×D11#4118yescomplemented
209C23×D11C24112yes—
210C23×D11C2413yes—
211C23×D11C2414yes—
212C23×D11C2411yescharacteristic
213C23×D11C2411yescharacteristic
214C11×#41—232no—
215C2×Q8×C11—232no—
216C2×Q8×C11—212no—
217C2×Q8×C11C2×D418yescomplemented
218C2×Q8×C11C24112yes—
219C2×Q8×C11C2414yes—
220C2×D4×C11—212no—
221C2×D4×C11—212no—
222C2×D4×C11C24112yes—
223C2×D4×C11C24112yes—
224C22×C4×C11—212no—
225C22×C4×C11—212no—
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2413yes—
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2413yes—
230C22×C4×C11C24112yes—
231C22×C4×C11C24112yes—
232C22×C4×C11C2413yes—
233C2×C22⋊D11—224no—
234C2×C22⋊D11—212no—
235C2×C22⋊D11—212no—
236C2×C22⋊D11C24112yes—
237C2×C22⋊D11C24112yes—
238C2×C22⋊D11C24124yes—
239C22×Dic11—212no—
240C22×Dic11—212no—
241C22×Dic11C24112yes—
242C22×Dic11C24112yes—
243C22×Dic11C2411yescharacteristic
244C22×Dic11C2413yes—
245C22×Dic11C2411yescharacteristic
246C22×Dic11C2413yes—
247C22×Dic11C2413yes—
248#4343—232no—
249Q8×D11—296no—
250Q8×D11—296no—
251Q8×D11—232no—
252Q8×D11C2×D4164yescomplemented
253#4341—296no—
254D4×D11—296no—
255D4×D11—296no—
256#4339—296no—
257C2×D44—212no—
258C2×D44—212no—
259C2×D44C24112yes—
260C2×D44C24112yes—
261C2×C4×D11—212no—
262C2×C4×D11—212no—
263C2×C4×D11—296no—
264C2×C4×D11—296no—
265C2×C4×D11—24no—
266C2×C4×D11—212no—
267C2×C4×D11—212no—
268C2×C4×D11—24no—
269C2×C4×D11—212no—
270C2×C4×D11—212no—
271C2×C4×D11C2×D4124yes—
272C2×C4×D11C2414yes—
273C2×C4×D11C24112yes—
274C2×C4×D11C24112yes—
275C2×C4×D11C24112yes—
276C2×C4×D11C24112yes—
277C2×C4×D11C2414yes—
278C2×C4×D11C24112yes—
279C2×C4×D11C24112yes—
280C2×C4×D11C24112yes—
281C2×Dic22—224no—
282C2×Dic22—296no—
283C2×Dic22—212no—
284C2×Dic22C2×D4124yescomplemented
285C2×Dic22C24112yes—
286C2×Dic22C24124yes—
287C2×Dic22C24112yes—
288C11×C4⋊C4C24112yes—
289C11×C4⋊C4C24112yes—
290C11×C22⋊C4C24124yes—
291C11×C22⋊C4C2414yes—
292C11×C22⋊C4C24112yes—
293C42×C11C24112yes—
294C22⋊Dic11C24124yes—
295C22⋊Dic11C24112yes—
296C22⋊Dic11C2414yes—
297(C2×D11)⋊C4C2414yes—
298(C2×D11)⋊C4C24112yes—
299(C2×D11)⋊C4C24124yes—
300(C2×D11)⋊C4C24124yes—
301(C2×D11)⋊C4C24112yes—
302(C2×D11)⋊C4C2414yes—
303C4⋊Dic11C24112yes—
304C4⋊Dic11C24112yes—
305Dic11⋊C4C24124yes—
306Dic11⋊C4C24112yes—
307Dic11⋊C4C24112yes—
308C4×Dic11C24112yes—
309C4×Dic11C24112yes—
310C4×Dic11C24112yes—
311C23×#41—111no—
312C24×Q8—111no—
313C2×#548—111no—
314C2×#548—111no—
315C2×#548—1132no—
316C2×#548—113no—
317C2×#548—113no—
318C2×#548—113no—
319C2×#548—111no—
320C2×#548—113no—
321C2×#548D1111yescharacteristic, direct product factor
322C22×#124—113no—
323C22×C22⋊Q8—113no—
324C22×#121—113no—
325C22×C4×Q8—111no—
326C22×C4×D4—113no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—26no—
330C23×C11—26no—
331C23×C11—26no—
332C23×C11C2×#4114yescomplemented
333C23×C11C2516yes—
334C23×C11C2512yes—
335C23×C11C2511yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—232no—
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—26no—
342C22×D11—26no—
343C22×D11—26no—
344C22×D11—224no—
345C22×D11—224no—
346C22×D11—224no—
347C22×D11—448no—
348C22×D11C22×D414yes—
349C22×D11C2×#4114yes—
350C22×D11C2×#41116yescomplemented
351C22×D11C2×#4114yescomplemented
352C22×D112−1+414yes—
353C22×D11C2516yes—
354C22×D11C2512yes—
355C22×D11C2512yes—
356Q8×C11—224no—
357Q8×C11C22×D4116yescomplemented
358D4×C11—224no—
359D4×C11—224no—
360C2×C4×C11—26no—
361C2×C4×C11—22no—
362C2×C4×C11—26no—
363C2×C4×C11—22no—
364C2×C4×C11—224no—
365C2×C4×C11—224no—
366C2×C4×C11C22×D4112yes—
367C2×C4×C11C2512yes—
368C2×C4×C11C2516yes—
369C2×C4×C11C2512yes—
370C2×C4×C11C2516yes—
371C2×C4×C11C2516yes—
372C22⋊D11—224no—
373C22⋊D11—224no—
374C22⋊D11—248no—
375C2×Dic11—26no—
376C2×Dic11—22no—
377C2×Dic11—26no—
378C2×Dic11—22no—
379C2×Dic11—224no—
380C2×Dic11—224no—
381C2×Dic11C22×D4112yes—
382C2×Dic11C2512yes—
383C2×Dic11C2516yes—
384C2×Dic11C2512yes—
385C2×Dic11C2516yes—
386C2×Dic11C2516yes—
387D44—224no—
388D44—224no—
389C4×D11—28no—
390C4×D11—224no—
391C4×D11—224no—
392C4×D11—28no—
393C4×D11—224no—
394C4×D11—224no—
395C4×D11—224no—
396C4×D11—224no—
397C4×D11C22×D4148yes—
398Dic22—224no—
399Dic22—248no—
400Dic22C22×D4148yescomplemented
401C22×#41—1116no—
402C22×#41—111no—
403C22×#41—113no—
404C22×#41—113no—
405C22×#41—2216no—
406C22×#41C2×D1111yescharacteristic, complemented
407C23×Q8—111no—
408C23×Q8—113no—
409C23×Q8—113no—
410C23×Q8—111no—
411C23×Q8—1116no—
412C23×Q8—113no—
413C23×Q8—2216no—
414C23×Q8C2×D1111yescharacteristic, complemented
415C23×D4—113no—
416C23×D4—113no—
417C24×C4—113no—
418C24×C4—113no—
419#548—1116no—
420#548—1116no—
421#548—1148no—
422#548—1148no—
423#548—1148no—
424#548—1116no—
425#548—1148no—
426#548C2×D11116yesdirect product factor
427C2×#124—113no—
428C2×#124—113no—
429C2×#124—1148no—
430C2×#124—116no—
431C2×#124—116no—
432C2×#124—113no—
433C2×#124C2×D1113yescomplemented
434C2×C22⋊Q8—113no—
435C2×C22⋊Q8—113no—
436C2×C22⋊Q8—1148no—
437C2×C22⋊Q8—116no—
438C2×C22⋊Q8—113no—
439C2×C22⋊Q8—116no—
440C2×C22⋊Q8C2×D1113yescomplemented
441C2×#121—113no—
442C2×#121—116no—
443C2×#121—113no—
444C2×#121—1148no—
445C2×#121—113no—
446C2×#121—116no—
447C2×#121C2×D1113yescomplemented
448C2×C4×Q8—111no—
449C2×C4×Q8—1116no—
450C2×C4×Q8—113no—
451C2×C4×Q8—113no—
452C2×C4×Q8C2×D1111yescharacteristic, complemented
453C2×C4×D4—113no—
454C2×C4×D4—113no—
455C2×C4×D4—113no—
456C2×C4×D4—1148no—
457C2×C4×D4—113no—
458C2×C4×D4—113no—
459C2×C4×D4—113no—
460C2×C4×D4—113no—
461C2×C4×D4C2×D1113yescomplemented
462C22×C4⋊C4—113no—
463C22×C4⋊C4—113no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—113no—
466C22×C22⋊C4—116no—
467C22×C42—113no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—28no—
471C22×C11—26no—
472C22×C11—26no—
473C22×C11—26no—
474C22×C11—412no—
475C22×C11C23×D412yes—
476C22×C11C22×#4112yes—
477C22×C11C22×#4114yescomplemented
478C22×C11C2×2−1+412yes—
479C22×C11C2611yescharacteristic
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—28no—
483C2×D11—232no—
484C2×D11—26no—
485C2×D11—26no—
486C2×D11—26no—
487C2×D11—412no—
488C2×D11—448no—
489C2×D11#548116yesdirect product factor
490C2×D11C23×D414yes—
491C2×D11C22×#4114yes—
492C2×D11C22×#4114yescomplemented
493C2×D11C2×2−1+414yes—
494C4×C11—22no—
495C4×C11—26no—
496C4×C11—26no—
497C4×C11—22no—
498C4×C11C23×D4112yes—
499Dic11—26no—
500Dic11—22no—
501Dic11—26no—
502Dic11—22no—
503Dic11C23×D4112yes—
504C25—111no—
505C25—113no—
506C2×#41—28no—
507C2×#41—118no—
508C2×#41—1124no—
509C2×#41—1124no—
510C2×#41—2224no—
511C2×#41—2224no—
512C2×#41—22128no—
513C2×#41—228no—
514C2×#41C22×D1118yescomplemented
515C22×Q8—28no—
516C22×Q8—1116no—
517C22×Q8—118no—
518C22×Q8—1124no—
519C22×Q8—1124no—
520C22×Q8—118no—
521C22×Q8—113no—
522C22×Q8—116no—
523C22×Q8—113no—
524C22×Q8—1124no—
525C22×Q8—2224no—
526C22×Q8—2224no—
527C22×Q8—22128no—
528C22×Q8—2224no—
529C22×Q8—228no—
530C22×Q8C22×D1113yes—
531C22×Q8C22×D1111yescharacteristic
532C22×Q8C22×D1118yescomplemented
533C22×D4—113no—
534C22×D4—113no—
535C22×D4—116no—
536C22×D4—1124no—
537C22×D4—1124no—
538C22×D4—113no—
539C22×D4—113no—
540C22×D4—2224no—
541C22×D4—2224no—
542C22×D4C22×D1113yes—
543C22×D4C22×D1113yes—
544C23×C4—113no—
545C23×C4—113no—
546C23×C4—113no—
547C23×C4—111no—
548C23×C4—113no—
549C23×C4—113no—
550C23×C4—111no—
551C23×C4—113no—
552C23×C4—1124no—
553C23×C4—113no—
554C23×C4—113no—
555C23×C4—1124no—
556C23×C4—113no—
557C23×C4—2224no—
558C23×C4—2224no—
559C23×C4C22×D1113yes—
560C23×C4C22×D1113yes—
561#124—1124no—
562#124—1124no—
563#124—1148no—
564#124—1148no—
565#124—1124no—
566#124C22×D11124yescomplemented
567C22⋊Q8—1124no—
568C22⋊Q8—1124no—
569C22⋊Q8—1148no—
570C22⋊Q8—1124no—
571C22⋊Q8—1148no—
572C22⋊Q8C22×D11124yescomplemented
573#121—1124no—
574#121—1148no—
575#121—1124no—
576#121—1124no—
577#121—1148no—
578#121C22×D11124yescomplemented
579C4×Q8—118no—
580C4×Q8—1124no—
581C4×Q8—1124no—
582C4×Q8C22×D1118yescomplemented
583C4×D4—1124no—
584C4×D4—1124no—
585C4×D4—1124no—
586C4×D4—1124no—
587C4×D4—1124no—
588C4×D4—1124no—
589C4×D4—1124no—
590C4×D4C22×D11124yescomplemented
591C2×C4⋊C4—113no—
592C2×C4⋊C4—113no—
593C2×C4⋊C4—113no—
594C2×C4⋊C4—116no—
595C2×C4⋊C4—113no—
596C2×C4⋊C4—1124no—
597C2×C4⋊C4—1124no—
598C2×C4⋊C4C22×D1113yes—
599C2×C4⋊C4C22×D1113yes—
600C2×C22⋊C4—111no—
601C2×C22⋊C4—113no—
602C2×C22⋊C4—116no—
603C2×C22⋊C4—111no—
604C2×C22⋊C4—111no—
605C2×C22⋊C4—113no—
606C2×C22⋊C4—113no—
607C2×C22⋊C4—116no—
608C2×C22⋊C4—116no—
609C2×C22⋊C4—118no—
610C2×C22⋊C4—1124no—
611C2×C22⋊C4—1148no—
612C2×C22⋊C4C22×D1111yescharacteristic
613C2×C22⋊C4C22×D1113yes—
614C2×C22⋊C4C22×D1116yes—
615C2×C42—113no—
616C2×C42—113no—
617C2×C42—113no—
618C2×C42—1124no—
619C2×C42C22×D1113yes—
620C2×C11—24no—
621C2×C11—46no—
622C2×C11C2×#54814yescomplemented
623C2×C11C24×D411yescharacteristic
624C2×C11C23×#4111yescharacteristic
625C2×C11C22×2−1+411yescharacteristic
626D11—24no—
627D11—46no—
628D11C2×#54818yesdirect product factor
629C24—111no—
630C24—118no—
631C24—114no—
632C24—111no—
633C24—1112no—
634C24—113no—
635C24—224no—
636C24—224no—
637C24—2212no—
638C24—2212no—
639C24—2212no—
640C24C23×D1113yes—
641C24C23×D1111yescharacteristic
642#41—232no—
643#41—2296no—
644#41—2296no—
645#41—2232no—
646C2×Q8—232no—
647C2×Q8—212no—
648C2×Q8—1164no—
649C2×Q8—1124no—
650C2×Q8—1112no—
651C2×Q8—1124no—
652C2×Q8—1112no—
653C2×Q8—2224no—
654C2×Q8—2296no—
655C2×Q8—2296no—
656C2×Q8—2296no—
657C2×Q8—2232no—
658C2×Q8—2212no—
659C2×Q8D4×D1118yescomplemented
660C2×Q8C23×D11112yes—
661C2×Q8C23×D1114yes—
662C2×D4—212no—
663C2×D4—212no—
664C2×D4—1112no—
665C2×D4—1112no—
666C2×D4—1124no—
667C2×D4—1112no—
668C2×D4—1112no—
669C2×D4—2212no—
670C2×D4—2296no—
671C2×D4—2224no—
672C2×D4—2296no—
673C2×D4—2212no—
674C2×D4—2212no—
675C2×D4—2212no—
676C2×D4C23×D11112yes—
677C2×D4C23×D11112yes—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—113no—
681C22×C4—1124no—
682C22×C4—1112no—
683C22×C4—1112no—
684C22×C4—1112no—
685C22×C4—111no—
686C22×C4—113no—
687C22×C4—113no—
688C22×C4—111no—
689C22×C4—114no—
690C22×C4—1112no—
691C22×C4—1112no—
692C22×C4—114no—
693C22×C4—1112no—
694C22×C4—1112no—
695C22×C4—1112no—
696C22×C4—1112no—
697C22×C4—2212no—
698C22×C4—2296no—
699C22×C4—2212no—
700C22×C4—2296no—
701C22×C4—224no—
702C22×C4—2212no—
703C22×C4—2212no—
704C22×C4—224no—
705C22×C4—2212no—
706C22×C4—2212no—
707C22×C4—2212no—
708C22×C4—2212no—
709C22×C4C23×D11112yes—
710C22×C4C23×D11112yes—
711C22×C4C23×D1111yescharacteristic
712C22×C4C23×D1113yes—
713C22×C4C23×D1113yes—
714C22×C4C23×D1111yescharacteristic
715C22×C4C23×D1113yes—
716C4⋊C4—1112no—
717C4⋊C4—1112no—
718C4⋊C4—1112no—
719C4⋊C4—1124no—
720C4⋊C4—1112no—
721C4⋊C4C23×D11112yes—
722C4⋊C4C23×D11112yes—
723C22⋊C4—114no—
724C22⋊C4—1112no—
725C22⋊C4—1124no—
726C22⋊C4—114no—
727C22⋊C4—114no—
728C22⋊C4—1112no—
729C22⋊C4—1112no—
730C22⋊C4—1124no—
731C22⋊C4—1124no—
732C22⋊C4C23×D1114yes—
733C22⋊C4C23×D11112yes—
734C22⋊C4C23×D11124yes—
735C42—1112no—
736C42—1112no—
737C42—1112no—
738C42C23×D11112yes—
739C11C22×#54811yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—114no—
746C23—114no—
747C23—114no—
748C23—112no—
749C23—114no—
750C23—1116no—
751C23—112no—
752C23—116no—
753C23—228no—
754C23—228no—
755C23—2232no—
756C23—2224no—
757C23—2224no—
758C23—2224no—
759C23—222no—
760C23—222no—
761C23—226no—
762C23—226no—
763C23—226no—
764C23—4448no—
765C23#41×D1114yescomplemented
766C23C24×D1116yes—
767C23C24×D1112yes—
768C23C24×D1111yescharacteristic
769Q8—224no—
770Q8—1148no—
771Q8—2248no—
772Q8—2224no—
773Q8C2×D4×D11116yescomplemented
774D4—224no—
775D4—224no—
776D4—2224no—
777D4—2248no—
778D4—2224no—
779D4—2224no—
780D4—2224no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—1112no—
788C2×C4—116no—
789C2×C4—1148no—
790C2×C4—112no—
791C2×C4—116no—
792C2×C4—116no—
793C2×C4—112no—
794C2×C4—2224no—
795C2×C4—2224no—
796C2×C4—228no—
797C2×C4—2224no—
798C2×C4—2224no—
799C2×C4—228no—
800C2×C4—2224no—
801C2×C4—2224no—
802C2×C4—222no—
803C2×C4—226no—
804C2×C4—226no—
805C2×C4—222no—
806C2×C4—2224no—
807C2×C4—2224no—
808C2×C4C2×D4×D11112yes—
809C2×C4C24×D1112yes—
810C2×C4C24×D1116yes—
811C2×C4C24×D1116yes—
812C2×C4C24×D1112yes—
813C2×C4C24×D1116yes—
814C22—22no—
815C22—22no—
816C22—28no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—114no—
822C22—114no—
823C22—114no—
824C22—1116no—
825C22—114no—
826C22—2232no—
827C22—222no—
828C22—222no—
829C22—228no—
830C22—226no—
831C22—226no—
832C22—226no—
833C22—4448no—
834C22—4412no—
835C22C22×D4×D1112yes—
836C22C2×#41×D1112yes—
837C22C2×#41×D1114yescomplemented
838C22D11×2−1+412yes—
839C22C25×D1111yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—1112no—
845C4—222no—
846C4—226no—
847C4—226no—
848C4—222no—
849C4C22×D4×D11112yes—
850C2—24no—
851C2—46no—
852C2—118no—
853C2—224no—
854C2—446no—
855C2D11×#54814yesdirect product factor
856C2C23×D4×D1111yescharacteristic
857C2C22×#41×D1111yescharacteristic
858C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C22×#548
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D11C2semidirect
2. C23×Q8×D11C2semidirect
3. C2×#10623107C2semidirect
4. C2×#10623348C2semidirect
5. C2×#10623164C2semidirect
6. C2×#10623083C2semidirect
7. C2×#10623208C2semidirect
8. C2×#10623362C2semidirect
9. C2×#10623129C2semidirect
10. D11×#548C2direct (N × H)
11. C2×D11×#124C2semidirect
12. C2×D11×C22⋊Q8C2semidirect
13. C2×D11×#121C2semidirect
14. C2×C4×Q8×D11C2semidirect
15. C2×C4×D4×D11C2semidirect
16. C2×C11×#548C2semidirect
17. C22×C11×#41C22semidirect
18. C23×Q8×C11C22semidirect
20. C2×#41×D11C22semidirect
21. C22×#4343C22semidirect
25. C22×Q8×D11C22semidirect
26. C22×Q8×D11C22semidirect
27. C22×Q8×D11C22semidirect
28. C22×#4341C22semidirect
31. C22×#4339C22semidirect
34. C23×Dic22C22semidirect
35. C11×#548C22semidirect
36. C2×C11×#124C22semidirect
37. C2×C11×C22⋊Q8C22semidirect
38. C2×C11×#121C22semidirect
39. C2×C4×Q8×C11C22semidirect
40. C2×C4×D4×C11C22semidirect
41. #10623362C22semidirect
42. #10623348C22semidirect
43. C2×#67000C22semidirect
44. C2×#66999C22semidirect
45. C2×Q8×Dic11C22semidirect
46. C2×#66992C22semidirect
47. C2×#66991C22semidirect
48. C2×#66989C22semidirect
49. C2×D4×Dic11C22semidirect
50. C2×#66983C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×C4×C22⋊D11C22semidirect
53. C2×#66977C22semidirect
54. #10623208C22semidirect
55. D11×#124C22semidirect
56. #10623164C22semidirect
57. D11×C22⋊Q8C22semidirect
58. D11×#121C22semidirect
59. #10623129C22semidirect
60. #10623107C22semidirect
61. C4×Q8×D11C22semidirect
62. #10623083C22semidirect
63. C4×D4×D11C22semidirect
64. C2×#66950C22semidirect
65. C2×#66949C22semidirect
66. C2×#66948C22semidirect
67. C2×#66946C22semidirect
70. C2×#66940C22semidirect
71. C2×#66938C22semidirect
72. C2×#66938C22semidirect
73. C2×#66937C22semidirect
74. C2×(C22⋊D11)⋊C4C22semidirect
75. C2×(C22⋊D11)⋊C4C22semidirect
79. C2×#66931C22semidirect
80. C2×#66928C22semidirect
81. C2×C4×D44C22semidirect
83. C2×C4×Dic22C22semidirect
87. C2×C11×#41C23semidirect
91. C22×Q8×C11C23semidirect
103. C2×#4343C23semidirect
108. C2×Q8×D11D4semidirect
111. C2×Q8×D11C23semidirect
112. C2×Q8×D11C23semidirect
114. C2×#4341C23semidirect
120. C2×#4339C23semidirect
140. C22×Dic22C23semidirect
141. C11×#124C23semidirect
142. C11×C22⋊Q8C23semidirect
143. C11×#121C23semidirect
144. C4×Q8×C11C23semidirect
145. C4×D4×C11C23semidirect
155. #67000C23semidirect
156. #66999C23semidirect
157. Q8×Dic11C23semidirect
158. #66992C23semidirect
159. #66991C23semidirect
160. #66989C23semidirect
161. D4×Dic11C23semidirect
162. #66983C23semidirect
163. C4×C22⋊D11C23semidirect
164. C4×C22⋊D11C23semidirect
173. #66977C23semidirect
180. #66950C23semidirect
181. #66949C23semidirect
182. #66948C23semidirect
183. #66946C23semidirect
186. #66940C23semidirect
187. #66938C23semidirect
188. #66938C23semidirect
189. #66937C23semidirect
190. (C22⋊D11)⋊C4C23semidirect
191. (C22⋊D11)⋊C4C23semidirect
195. #66931C23semidirect
196. #66928C23semidirect
197. C4×D44C23semidirect
199. C4×Dic22C23semidirect
208. C23×D11#41semidirect
217. C2×Q8×C11C2×D4semidirect
252. Q8×D11C2×D4semidirect
284. C2×Dic22C2×D4semidirect
321. C2×#548D11direct (N × H)
332. C23×C11C2×#41semidirect
350. C22×D11C2×#41semidirect
351. C22×D11C2×#41semidirect
357. Q8×C11C22×D4semidirect
400. Dic22C22×D4semidirect
406. C22×#41C2×D11semidirect
414. C23×Q8C2×D11semidirect
426. #548C2×D11direct (N × H)
433. C2×#124C2×D11semidirect
440. C2×C22⋊Q8C2×D11semidirect
447. C2×#121C2×D11semidirect
452. C2×C4×Q8C2×D11semidirect
461. C2×C4×D4C2×D11semidirect
477. C22×C11C22×#41semidirect
489. C2×D11#548direct (N × H)
492. C2×D11C22×#41semidirect
514. C2×#41C22×D11semidirect
532. C22×Q8C22×D11semidirect
566. #124C22×D11semidirect
572. C22⋊Q8C22×D11semidirect
578. #121C22×D11semidirect
582. C4×Q8C22×D11semidirect
590. C4×D4C22×D11semidirect
622. C2×C11C2×#548semidirect
628. D11C2×#548direct (N × H)
659. C2×Q8D4×D11semidirect
739. C11C22×#548semidirect
765. C23#41×D11semidirect
773. Q8C2×D4×D11semidirect
837. C22C2×#41×D11semidirect
855. C2D11×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D112
C23×Q8×D112
C2×#106231072
C2×#106233482
C2×#106231642
C2×#106230832
C2×#106232082
C2×#106233622
C2×#106231292
D11×#5482
C2×D11×#1242
C2×D11×C22⋊Q82
C2×D11×#1212
C2×C4×Q8×D112
C2×C4×D4×D112
C2×C11×#5482
C22×#54811