Finite Group Databasebeta

← #14914804

Subgroups — #14914804

Order 2816.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic, complemented
5#13071455C213yesmaximal, complemented
6#13071455C213yesmaximal, complemented
7C22⋊C4×Dic22C213yesmaximal, complemented
8Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10#13071448C213yesmaximal, complemented
11#13071206C213yesmaximal, complemented
12#13071205C213yesmaximal, complemented
13#13071103C213yesmaximal, complemented
14#13071102C213yesmaximal, complemented
15C11×#2341C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#67043—28no—
18C2×#67043—28no—
19C2×#67043C4116yescomplemented
20C22×Q8×D11C2211yescharacteristic
21C22×Q8×D11C2211yescharacteristic
22C22×#4341C2213yes—
23C22×#4341C2213yes—
24C22×#4339C2213yes—
25C23×Dic22C2213yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30#10623103—28no—
31C4×Q8×D11—28no—
32C2×#66945C2213yes—
33C2×C4⋊C4×D11C2213yes—
34C2×#66940C2213yes—
35C2×#66940C2213yes—
36C2×#66925C2213yes—
37C2×C42×D11C2213yes—
38C2×C4×Dic22C2213yes—
39C2×C4×Dic22C2213yes—
40C11×#390C2213yes—
41C11×#390C2213yes—
42C11×#380C2213yes—
43C4×C11×C22⋊C4C2213yes—
44#10622834C2213yes—
45#10622834C2213yes—
46#10622825C2213yes—
47C4×C22⋊Dic11C2213yes—
48#10622600C2213yes—
49#10622600C2213yes—
50#10622587C2213yes—
51#10622587C2213yes—
52#10622570C2216yes—
53#10622570C2213yes—
54#10622570C2213yes—
55#10622569C2216yes—
56#10622569C2213yes—
57#10622569C2213yes—
58#10622555C2216yes—
59#10622555C2216yes—
60C22⋊C4×Dic11C2216yes—
61C22⋊C4×Dic11C2216yes—
62C4×(C2×D11)⋊C4C2213yes—
63C4×(C2×D11)⋊C4C2213yes—
64#10622542C2213yes—
65#10622542C2213yes—
66#10622278C2213yes—
67#10622278C2211yescharacteristic
68#10622259C2213yes—
69#10622259C2216yes—
70#10622259C2213yes—
71C2×C11×#41—24no—
72C2×C11×#41—24no—
73C2×C11×#41C2×C418yescomplemented
74C22×Q8×C11C2311yescharacteristic
75C22×D4×C11C2313yes—
76C23×C4×C11C2313yes—
77C22×C22⋊D11C2313yes—
78C22×C22⋊D11C2313yes—
79C23×Dic11C2316yes—
80#67043—2128no—
81C2×Q8×D11—24no—
82C2×Q8×D11—24no—
83C2×Q8×D11C2×C418yes—
84C2×Q8×D11C2×C418yescomplemented
85C2×Q8×D11D418yes—
86C2×Q8×D11D418yes—
87C2×#4341—212no—
88C2×#4341—212no—
89C2×#4341—212no—
90C2×#4341—212no—
91C2×#4341C2×C4124yes—
92C2×#4341C2×C4124yescomplemented
93C2×#4339—212no—
94C2×#4339—212no—
95C2×#4339C2×C4124yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2313yes—
99C22×C4×D11C2313yes—
100C22×C4×D11C2313yes—
101C22×Dic22—212no—
102C22×Dic22—212no—
103C22×Dic22C2×C4124yescomplemented
104C22×Dic22C2313yes—
105C22×Dic22C2313yes—
106C22×Dic22C2313yes—
107C4×Q8×C11—24no—
108C4×Q8×C11—24no—
109C2×C11×C4⋊C4C2313yes—
110C2×C11×C4⋊C4C2313yes—
111C2×C11×C22⋊C4C2313yes—
112C2×C11×C22⋊C4C2316yes—
113C2×C11×C22⋊C4C2313yes—
114C2×C42×C11C2313yes—
115C2×C42×C11C2313yes—
116C2×C22⋊Dic11C2313yes—
117C2×C22⋊Dic11C2316yes—
118C2×C22⋊Dic11C2313yes—
119Q8×Dic11—24no—
120Q8×Dic11—24no—
121C2×(C2×D11)⋊C4C2311yescharacteristic
122C2×(C2×D11)⋊C4C2313yes—
123C2×(C2×D11)⋊C4C2311yescharacteristic
124C2×(C2×D11)⋊C4C2311yescharacteristic
125C2×(C2×D11)⋊C4C2313yes—
126C2×(C2×D11)⋊C4C2313yes—
127C2×C4⋊Dic11C2313yes—
128C2×C4⋊Dic11C2313yes—
129C2×Dic11⋊C4C2313yes—
130C2×Dic11⋊C4C2316yes—
131C2×Dic11⋊C4C2313yes—
132C2×C4×Dic11C2313yes—
133C2×C4×Dic11C2316yes—
134C2×C4×Dic11C2313yes—
135C2×C4×Dic11C2313yes—
136C2×C4×Dic11C2313yes—
137#66945—212no—
138C4⋊C4×D11—212no—
139#66940—212no—
140#66940—212no—
141#66925—212no—
142C42×D11—212no—
143C4×Dic22—212no—
144C4×Dic22—212no—
145C11×#95C2311yescharacteristic
146C11×#95C2313yes—
147C11⋊#95C2311yescharacteristic
148C11⋊#95C2313yes—
149C11⋊#95C2313yes—
150C11⋊#95C2313yes—
151C11⋊#95C2316yes—
152C11⋊#95C2316yes—
153C11⋊#95C2313yes—
154C11⋊#95C2313yes—
155#34257—111nomaximal, Sylow
156C24×C11C2413yes—
157C23×D11C2411yescharacteristic
158C23×D11C2411yescharacteristic
159C11×#41—232no—
160C2×Q8×C11C22×C414yes—
161C2×Q8×C11C2×D414yes—
162C2×Q8×C11C2×D414yes—
163C2×D4×C11—26no—
164C2×D4×C11—26no—
165C2×D4×C11C22×C4112yes—
166C22×C4×C11—26no—
167C22×C4×C11—26no—
168C22×C4×C11C22×C4112yes—
169C22×C4×C11C2413yes—
170C22×C4×C11C2413yes—
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2413yes—
175C2×C22⋊D11—26no—
176C2×C22⋊D11—26no—
177C2×C22⋊D11—26no—
178C2×C22⋊D11—26no—
179C2×C22⋊D11C22×C4112yes—
180C2×C22⋊D11C22×C4112yes—
181C22×Dic11—212no—
182C22×Dic11—212no—
183C22×Dic11C22×C4124yes—
184C22×Dic11C2411yescharacteristic
185C22×Dic11C2413yes—
186C22×Dic11C2413yes—
187C22×Dic11C2413yes—
188C22×Dic11C2411yescharacteristic
189C22×Dic11C2413yes—
190Q8×D11—232no—
191Q8×D11C22⋊C4164yescomplemented
192#4341—296no—
193#4341—296no—
194#4339—296no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44C22×C414yes—
198C2×C4×D11—22no—
199C2×C4×D11—22no—
200C2×C4×D11—26no—
201C2×C4×D11—26no—
202C2×C4×D11—26no—
203C2×C4×D11—22no—
204C2×C4×D11—43no—
205C2×C4×D11—43no—
206C2×C4×D11C22×C4112yes—
207C2×C4×D11C22×C4112yes—
208C2×C4×D11C2×D4112yes—
209C2×C4×D11C2×D4112yes—
210C2×Dic22—26no—
211C2×Dic22—26no—
212C2×Dic22—296no—
213C2×Dic22—26no—
214C2×Dic22—26no—
215C2×Dic22C22×C4112yes—
216C2×Dic22C22×C4112yes—
217C2×Dic22C22×C4112yes—
218C2×Dic22C2×D4112yes—
219C2×Dic22C2×D4112yes—
220C11×C4⋊C4—26no—
221C11×C4⋊C4—26no—
222C11×C22⋊C4—26no—
223C11×C22⋊C4—46no—
224C11×C22⋊C4—43no—
225C42×C11—26no—
226C42×C11—26no—
227C22⋊Dic11—26no—
228C22⋊Dic11—46no—
229C22⋊Dic11—43no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—26no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—43no—
235(C2×D11)⋊C4—43no—
236C4⋊Dic11—26no—
237C4⋊Dic11—26no—
238Dic11⋊C4—26no—
239Dic11⋊C4—212no—
240Dic11⋊C4—26no—
241C4×Dic11—26no—
242C4×Dic11—212no—
243C4×Dic11—26no—
244C4×Dic11—26no—
245C4×Dic11—26no—
246C22×2−1+4—111no—
247C2×#519—111no—
248C22×C4×Q8—111no—
249#2341—113no—
250#2341—113no—
251#2341—111no—
252#2341D1111yescharacteristic, complemented
253Q8×C22⋊C4—113no—
254Q8×C22⋊C4—113no—
255Q8×C22⋊C4—111no—
256Q8×C22⋊C4—111no—
257#2311—113no—
258#2311—113no—
259#2297—113no—
260#2297—113no—
261C23×C11—23no—
262C23×C11—23no—
263C23×C11—23no—
264C23×C11—23no—
265C23×C11—23no—
266C23×C11—23no—
267C23×C11C23×C416yes—
268C23×C11C2511yescharacteristic
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11C23×C412yes—
280C22×D11C23×C412yes—
281C22×D11C22×D412yes—
282C22×D11C22×D412yes—
283Q8×C11C2×C22⋊C4116yes—
284D4×C11—224no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—224no—
290C2×C4×C11—23no—
291C2×C4×C11—23no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—23no—
295C2×C4×C11—23no—
296C2×C4×C11—23no—
297C2×C4×C11—21no—
298C2×C4×C11—23no—
299C2×C4×C11C23×C412yes—
300C2×C4×C11C23×C416yes—
301C2×C4×C11C22×D416yes—
302C2×C4×C11C22×D416yes—
303C2×C4×C112−1+412yescomplemented
304C22⋊D11—224no—
305C22⋊D11—224no—
306C2×Dic11—21no—
307C2×Dic11—23no—
308C2×Dic11—23no—
309C2×Dic11—21no—
310C2×Dic11—248no—
311C2×Dic11—21no—
312C2×Dic11—23no—
313C2×Dic11—23no—
314C2×Dic11—21no—
315C2×Dic11—23no—
316C2×Dic11—23no—
317C2×Dic11—23no—
318C2×Dic11—21no—
319C2×Dic11—23no—
320C2×Dic11C23×C416yes—
321C2×Dic11C23×C416yes—
322C2×Dic11C22×D416yes—
323C2×Dic11C22×D416yes—
324C2×Dic112−1+412yescomplemented
325D44—28no—
326C4×D11—28no—
327C4×D11—224no—
328C4×D11—412no—
329C4×D11C2×C22⋊C4148yes—
330Dic22—224no—
331Dic22—224no—
332Dic22C2×C22⋊C4148yes—
333C2×2−1+4—1116no—
334C2×2−1+4—228no—
335C2×2−1+4—228no—
336C22×#41—113no—
337C22×#41—113no—
338C22×#41—113no—
339C22×#41C2×D1111yescharacteristic
340C23×Q8—111no—
341C23×Q8—111no—
342C23×Q8—113no—
343#519—228no—
344C2×C4×Q8—111no—
345C2×C4×Q8—111no—
346C2×C4×Q8—113no—
347C2×C4×Q8—113no—
348C2×C4×Q8—113no—
349C2×C4×Q8—113no—
350C2×C4×Q8—228no—
351C2×C4×Q8C2×D1111yescharacteristic
352C2×C4×Q8C2×D1111yescharacteristic
353C2×#117—113no—
354C2×#117—113no—
355C22×C4⋊C4—113no—
356C22×C42—113no—
357#391—113no—
358#391—113no—
359#391—113no—
360#391—113no—
361#391—116no—
362#391—113no—
363#391—113no—
364#390—113no—
365#390—113no—
366#390—116no—
367#390—113no—
368#390—113no—
369#390C2×D1113yes—
370#390C2×D1113yes—
371#386—116no—
372#386—113no—
373#386—113no—
374#386—113no—
375#386—111no—
376#380—113no—
377#380—113no—
378#380—113no—
379#380—116no—
380#380—116no—
381#380C2×D1113yes—
382C4×C22⋊C4—113no—
383C4×C22⋊C4—116no—
384C4×C22⋊C4—116no—
385C4×C22⋊C4—113no—
386C4×C22⋊C4—113no—
387C4×C22⋊C4C2×D1113yes—
388C22×C11—26no—
389C22×C11—26no—
390C22×C11—26no—
391C22×C11—43no—
392C22×C11—43no—
393C22×C11—43no—
394C22×C11—43no—
395C22×C11C24×C411yescharacteristic
396C22×C11C23×D411yescharacteristic
397C22×C11C23×D411yescharacteristic
398C22×C11C2×2−1+411yescharacteristic
399C22×C11C2×2−1+411yescharacteristic
400C22×C11#58511yescharacteristic
401C22×C11#58511yescharacteristic
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11C22×C22⋊C414yes—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—43no—
419C4×C11—43no—
420C4×C11—41no—
421C4×C11C22×C22⋊C4112yes—
422Dic11—26no—
423Dic11—22no—
424Dic11—43no—
425Dic11—41no—
426Dic11—43no—
427Dic11C22×C22⋊C4112yes—
4282−1+4—22128no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—1124no—
432C2×#41—1124no—
433C2×#41—1124no—
434C2×#41—2212no—
435C2×#41—2212no—
436C2×#41—2212no—
437C2×#41—2212no—
438C2×#41—2212no—
439C2×#41—2212no—
440C2×#41C4×D1118yescomplemented
441C22×Q8—118no—
442C22×Q8—118no—
443C22×Q8—118no—
444C22×Q8—118no—
445C22×Q8—1124no—
446C22×Q8—113no—
447C22×Q8—113no—
448C22×Q8—113no—
449C22×Q8—2212no—
450C22×Q8—2212no—
451C22×Q8—224no—
452C22×Q8—224no—
453C22×Q8C22×D1111yescharacteristic
454C22×D4—113no—
455C22×D4—113no—
456C22×D4—111no—
457C22×D4C22×D1113yes—
458C23×C4—113no—
459C23×C4—116no—
460C23×C4—113no—
461C23×C4—111no—
462C23×C4—113no—
463C23×C4C22×D1113yes—
464C4×Q8—24no—
465C4×Q8—24no—
466C4×Q8—2212no—
467C4×Q8—2212no—
468C4×Q8—2212no—
469C4×Q8—2212no—
470C4×Q8—224no—
471C4×Q8—224no—
472#117—2212no—
473#117—2212no—
474C2×C4⋊C4—116no—
475C2×C4⋊C4—113no—
476C2×C4⋊C4—113no—
477C2×C4⋊C4—113no—
478C2×C4⋊C4—113no—
479C2×C4⋊C4—2212no—
480C2×C4⋊C4C22×D1113yes—
481C2×C4⋊C4C22×D1113yes—
482C2×C22⋊C4—113no—
483C2×C22⋊C4—113no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—111no—
486C2×C22⋊C4—111no—
487C2×C22⋊C4—113no—
488C2×C22⋊C4—116no—
489C2×C22⋊C4—113no—
490C2×C22⋊C4—113no—
491C2×C22⋊C4C22×D1113yes—
492C2×C22⋊C4C22×D1116yes—
493C2×C22⋊C4C22×D1113yes—
494C2×C42—116no—
495C2×C42—113no—
496C2×C42—113no—
497C2×C42—113no—
498C2×C42—113no—
499C2×C42—2212no—
500C2×C42C22×D1113yes—
501C2×C42C22×D1113yes—
502#95—113no—
503#95—113no—
504#95—111no—
505#95—116no—
506#95—113no—
507#95—116no—
508#95—113no—
509#95—113no—
510#95C22×D1111yescharacteristic
511#95C22×D1113yes—
512C2×C11—46no—
513C2×C11C23×C22⋊C411yescharacteristic
514C2×C11C4×2−1+411yescharacteristic
515C2×C11C4×2−1+411yescharacteristic
516C2×C11#348611yescharacteristic
517C2×C11#348711yescharacteristic
518C2×C11#349711yescharacteristic
519C2×C11#349711yescharacteristic
520D11—24no—
521D11—42no—
522C24—111no—
523C24—111no—
524C24C23×D1113yes—
525#41—232no—
526#41—2296no—
527#41—2296no—
528#41—2296no—
529C2×Q8—1164no—
530C2×Q8—1112no—
531C2×Q8—1112no—
532C2×Q8—1112no—
533C2×Q8—1112no—
534C2×Q8—1112no—
535C2×Q8—226no—
536C2×Q8—226no—
537C2×Q8—2296no—
538C2×Q8—2232no—
539C2×Q8—226no—
540C2×Q8—226no—
541C2×Q8C2×C4×D1114yes—
542C2×Q8D4×D1114yes—
543C2×Q8D4×D1114yes—
544C2×D4—26no—
545C2×D4—26no—
546C2×D4—1112no—
547C2×D4—1112no—
548C2×D4—114no—
549C2×D4—222no—
550C2×D4—222no—
551C2×D4—226no—
552C2×D4—226no—
553C2×D4—226no—
554C2×D4—226no—
555C2×D4C2×C4×D11112yes—
556C22×C4—26no—
557C22×C4—26no—
558C22×C4—113no—
559C22×C4—1112no—
560C22×C4—1112no—
561C22×C4—1112no—
562C22×C4—1124no—
563C22×C4—113no—
564C22×C4—111no—
565C22×C4—1112no—
566C22×C4—111no—
567C22×C4—113no—
568C22×C4—113no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—226no—
572C22×C4—2212no—
573C22×C4—2212no—
574C22×C4—226no—
575C22×C4—226no—
576C22×C4—222no—
577C22×C4—443no—
578C22×C4—443no—
579C22×C4C2×C4×D11112yes—
580C22×C4C23×D1113yes—
581C22×C4C23×D1113yes—
582C22×C4C23×D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1113yes—
586C4⋊C4—26no—
587C4⋊C4—26no—
588C4⋊C4—2212no—
589C4⋊C4—226no—
590C4⋊C4—226no—
591C4⋊C4—226no—
592C4⋊C4—226no—
593C22⋊C4—26no—
594C22⋊C4—43no—
595C22⋊C4—46no—
596C22⋊C4—222no—
597C22⋊C4—222no—
598C22⋊C4—226no—
599C22⋊C4—226no—
600C22⋊C4—222no—
601C22⋊C4—443no—
602C22⋊C4—443no—
603C22⋊C4—446no—
604C22⋊C4—443no—
605C42—26no—
606C42—26no—
607C42—226no—
608C42—226no—
609C42—2212no—
610C42—226no—
611C42—226no—
612C11#3425711yescharacteristic, complemented, Sylow
613C23—23no—
614C23—23no—
615C23—23no—
616C23—23no—
617C23—23no—
618C23—23no—
619C23—112no—
620C23—112no—
621C23—112no—
622C23—112no—
623C23—221no—
624C23—221no—
625C23—221no—
626C23—221no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23C22×C4×D1116yes—
634C23C24×D1111yescharacteristic
635Q8—1148no—
636Q8—2224no—
637Q8—2224no—
638Q8C22⋊C4×D11116yes—
639D4—224no—
640D4—228no—
641D4—2224no—
642D4—2224no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—224no—
648C2×C4—21no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—23no—
656C2×C4—21no—
657C2×C4—116no—
658C2×C4—116no—
659C2×C4—116no—
660C2×C4—1148no—
661C2×C4—116no—
662C2×C4—112no—
663C2×C4—228no—
664C2×C4—2248no—
665C2×C4—221no—
666C2×C4—223no—
667C2×C4—223no—
668C2×C4—221no—
669C2×C4—2224no—
670C2×C4—221no—
671C2×C4—223no—
672C2×C4—223no—
673C2×C4—221no—
674C2×C4—223no—
675C2×C4—223no—
676C2×C4—221no—
677C2×C4—223no—
678C2×C4—223no—
679C2×C4—4412no—
680C2×C4C22×C4×D1112yes—
681C2×C4C22×C4×D1116yes—
682C2×C4C2×D4×D1116yes—
683C2×C4C2×D4×D1116yes—
684C2×C4#6704312yescomplemented
685C22—26no—
686C22—26no—
687C22—26no—
688C22—43no—
689C22—43no—
690C22—43no—
691C22—43no—
692C22—114no—
693C22—222no—
694C22—222no—
695C22—222no—
696C22—222no—
697C22—222no—
698C22—222no—
699C22—222no—
700C22—222no—
701C22—222no—
702C22—441no—
703C22—441no—
704C22—441no—
705C22—441no—
706C22C23×C4×D1111yescharacteristic
707C22C22×D4×D1111yescharacteristic
708C22C22×D4×D1111yescharacteristic
709C22C2×#6704311yescharacteristic
710C22#1062345311yescharacteristic
711C22#1062345511yescharacteristic
712C22D11×2−1+411yescharacteristic
713C4—22no—
714C4—22no—
715C4—43no—
716C4—41no—
717C4—43no—
718C4—1112no—
719C4—222no—
720C4—226no—
721C4—441no—
722C4—443no—
723C4—443no—
724C4C2×C22⋊C4×D11112yes—
725C2—46no—
726C2—224no—
727C2—442no—
728C2C22×C22⋊C4×D1111yescharacteristic
729C2C4×#6704311yescharacteristic
730C2#1308182711yescharacteristic
731C2#1308226211yescharacteristic
732C2#1308226911yescharacteristic
733C2#1308238111yescharacteristic
734C2#1308238411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2341C2
socle, cosocleC23×C11C25
prime radicalC22×#67043C2
hypercenter#2341D11
hypocenterC11#34257
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#10623103C2semidirect
3. C2×C4×Q8×D11C2semidirect
4. #13071457C2semidirect
5. #13071455C2semidirect
6. #13071455C2semidirect
7. C22⋊C4×Dic22C2semidirect
8. Q8×(C2×D11)⋊C4C2semidirect
9. Q8×(C2×D11)⋊C4C2semidirect
10. #13071448C2semidirect
11. #13071206C2semidirect
12. #13071205C2semidirect
13. #13071103C2semidirect
14. #13071102C2semidirect
15. C11×#2341C2semidirect
19. C2×#67043C4semidirect
73. C2×C11×#41C2×C4semidirect
84. C2×Q8×D11C2×C4semidirect
92. C2×#4341C2×C4semidirect
103. C22×Dic22C2×C4semidirect
191. Q8×D11C22⋊C4semidirect
252. #2341D11semidirect
303. C2×C4×C112−1+4semidirect
324. C2×Dic112−1+4semidirect
440. C2×#41C4×D11semidirect
612. C11#34257semidirect
684. C2×C4#67043semidirect

Maximal subgroups

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

subgroupindex
C22×#670432
C2×#106231032
C2×C4×Q8×D112
#130714572
#130714552
C22⋊C4×Dic222
Q8×(C2×D11)⋊C42
#130714482
#130712062
#130712052
#130711032
#130711022
C11×#23412
#3425711