Finite Group Databasebeta

← C2×#13081431 #15633509

Subgroups — C2×#13081431 #15633509

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623090C211yesmaximal, characteristic
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3#13081431C2116yesmaximal, direct product factor
4C2×#10622327C211yesmaximal, characteristic, complemented
5C2×#10622378C211yesmaximal, characteristic, complemented
6C2×#10622373C211yesmaximal, characteristic
7C2×#10622488C211yesmaximal, characteristic, complemented
8C2×#10622620C211yesmaximal, characteristic, complemented
9C2×#10622503C211yesmaximal, characteristic, complemented
10C2×#10622641C211yesmaximal, characteristic, complemented
11C2×#10622779C211yesmaximal, characteristic, complemented
12C2×#10622776C211yesmaximal, characteristic
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622430C211yesmaximal, characteristic, complemented
15C2×#10622403C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66989C2211yescharacteristic
26C2×#66982—21no—
27C2×C4×C22⋊D11—21no—
28Q8×Dic22—24no—
29Q8×Dic22C2218yescomplemented
30#10623090—24no—
31#10623090C2218yes—
32C2×#66946C2211yescharacteristic
33C2×#66941—21no—
34C2×#66941—21no—
35C2×#66941C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66938—21no—
39C2×#66936—21no—
40C2×#66928C2211yescharacteristic
41C2×#66922—21no—
42C2×#66922C2211yescharacteristic
43C2×C4×Dic22—21no—
44C2×C4×Dic22C2211yescharacteristic
45C11×#440C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622779C2218yescomplemented
53#10622776C2218yes—
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622641C2218yescomplemented
63#10622620C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622503C2218yescomplemented
70#10622488C2218yescomplemented
71#10622430C2218yescomplemented
72#10622403C2218yescomplemented
73#10622378C2218yescomplemented
74#10622373C2218yes—
75#10622327C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22—21no—
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×Dic22D411yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×SD16—24no—
90C2×C11×SD16C2314yes—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C4×Q8×C11—22no—
94C4×Q8×C11C2314yes—
95C4×D4×C11—22no—
96C4×D4×C11C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105Q8×Dic11—22no—
106Q8×Dic11—22no—
107Q8×Dic11C2314yes—
108Q8×Dic11C2314yes—
109C2×#4326—24no—
110C2×#4326C2314yes—
111C2×#4325—24no—
112C2×#4325C2314yes—
113#66993—22no—
114#66993C2314yes—
115#66989—22no—
116#66989C2314yes—
117#66982—28no—
118C4×C22⋊D11—28no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11D411yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140#66946—22no—
141#66946C2314yes—
142#66941—28no—
143#66941—28no—
144#66941—22no—
145#66941—22no—
146#66941C2314yes—
147#66941C2314yes—
148#66940—22no—
149#66940C2314yes—
150#66938—28no—
151#66936—28no—
152#66928—22no—
153#66928C2314yes—
154#66922—22no—
155#66922—28no—
156#66922C2314yes—
157C4×Dic22—28no—
158C4×Dic22D414yes—
159C4×Dic22C2314yes—
160C11×#107C2314yes—
161C11×#103C2314yes—
162C11×#102C2314yes—
163C11×#97C2314yes—
164#66896C2314yes—
165#66896C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168#66880C2314yes—
169#66880C2314yes—
170#66879C2314yes—
171Dic11⋊C8C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66874C2314yes—
175#66873C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3375—111nomaximal, Sylow
180C24×C11—21no—
181C23×D11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—22no—
184C2×Q8×C11#4114yes—
185C2×Q8×C11C2412yes—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11C2412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—82no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—82no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C2×D44—21no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44C2412yes—
213C2×C4×D11—24no—
214C2×C4×D11—82no—
215C2×Dic22—24no—
216C2×Dic22—24no—
217C2×Dic22—24no—
218C2×Dic22—21no—
219C2×Dic22—24no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—82no—
223C2×Dic22—82no—
224C2×Dic22—82no—
225C2×Dic22C2×D414yes—
226C2×Dic22C2412yes—
227C11×SD16—28no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4C2412yes—
236C11×C4⋊C4C2412yes—
237C11×C22⋊C4—24no—
238C42×C11—24no—
239C42×C11C2×D412yes—
240C42×C11C2412yes—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243#4326—28no—
244#4325—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248C4⋊Dic11—24no—
249C4⋊Dic11—24no—
250C4⋊Dic11—24no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11C2×D414yes—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4C2×D414yes—
260Dic11⋊C4C2×D414yes—
261C4×Dic11—24no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C4×Dic11C2×D412yes—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C4×Dic11C2412yes—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C2×#559—111no—
273C2×Q82—111no—
274#3375—1116no—
275C2×#489—111no—
276C2×#489—111no—
277C2×#486—111no—
278C2×#477—111no—
279C2×#474—111no—
280C2×#474—111no—
281C2×#464—111no—
282C2×#464—111no—
283C2×#460—111no—
284C2×#446—111no—
285C2×#440—111no—
286C2×#440D1111yescharacteristic, complemented
287C2×C4×Q16—111no—
288C23×C11—22no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11C22×D411yescharacteristic
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297Q8×C11—24no—
298Q8×C11—22no—
299Q8×C11C2×#4114yes—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—42no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—84no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4112yes—
316C2×C4×C112−1+412yes—
317C2×C4×C11C2511yescharacteristic
318C22⋊D11—48no—
319C22⋊D11—84no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11#13714yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334D44—22no—
335D44—22no—
336D44—42no—
337C4×D11—84no—
338Dic22—28no—
339Dic22—22no—
340Dic22—22no—
341Dic22—42no—
342Dic22—84no—
343Dic22—84no—
344Dic22—84no—
345C8×C11—22no—
346C8×C11—22no—
347C11⋊C8—22no—
348C11⋊C8—22no—
349C22×Q16—111no—
350C22×SD16—111no—
351C22×SD16C2×D1111yescharacteristic
352#559—118no—
353#559—224no—
354Q82—118no—
355Q82—224no—
356C2×C4⋊Q8—111no—
357C2×C4⋊Q8—111no—
358C2×C4⋊Q8—111no—
359C2×C4⋊Q8—221no—
360C2×C4⋊Q8—221no—
361C2×C4⋊Q8—221no—
362C2×#127—111no—
363C2×#124—111no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#123—221no—
367C2×#123—221no—
368C2×C4×Q8—111no—
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×Q8—111no—
372C2×C4×Q8—221no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4—221no—
376C2×C4×D4C2×D1111yescharacteristic
377#489—118no—
378#489—118no—
379#486—118no—
380#477—118no—
381#474—118no—
382#474—118no—
383#464—118no—
384#464—118no—
385#460—118no—
386#446—118no—
387#440—118no—
388#440C2×D1118yescomplemented
389C4×Q16—118no—
390C2×#107—111no—
391C2×#107—111no—
392C2×#107C2×D1111yescharacteristic
393C2×C4⋊C8—111no—
394C2×C4⋊C8—111no—
395C2×C4⋊C8—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103C2×D1111yescharacteristic
400C2×#102—111no—
401C2×#102—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102C2×D1111yescharacteristic
406C2×#97—111no—
407C2×#97C2×D1111yescharacteristic
408C2×C4×C8—111no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—84no—
413C22×C11#54812yes—
414C22×C11C2×#13712yes—
415C22×C11#57612yes—
416C22×C11C23×D411yescharacteristic
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—84no—
421C4×C11—24no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11#54812yes—
427C4×C11C22×#4111yescharacteristic
428C4×C11C2×2−1+411yescharacteristic
429Dic11—22no—
430Dic11—22no—
431Dic11—22no—
432Dic11—42no—
433Dic11—42no—
434Dic11—42no—
435Dic11C2×#13714yes—
436C22×Q8—111no—
437C22×Q8—111no—
438C22×Q8—221no—
439C22×Q8—221no—
440C22×Q8—221no—
441C22×Q8C22×D1111yescharacteristic
442C22×D4—111no—
443C22×D4—221no—
444C22×D4—221no—
445C22×D4C22×D1111yescharacteristic
446C23×C4—21no—
447C23×C4—221no—
448C2×Q16—114no—
449C2×Q16—224no—
450C2×SD16—24no—
451C2×SD16—114no—
452C2×SD16—224no—
453C2×SD16C22×D1114yes—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C4⋊Q8—114no—
459C4⋊Q8—114no—
460C4⋊Q8—114no—
461C4⋊Q8—228no—
462C4⋊Q8—222no—
463C4⋊Q8—222no—
464C4⋊Q8—228no—
465C4⋊Q8—228no—
466C4⋊Q8—222no—
467#127—114no—
468#127—222no—
469#124—114no—
470#124—114no—
471#124—222no—
472#124—228no—
473#124—222no—
474#123—228no—
475#123—228no—
476C4×Q8—22no—
477C4×Q8—114no—
478C4×Q8—114no—
479C4×Q8—114no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—228no—
483C4×Q8—222no—
484C4×Q8—222no—
485C4×Q8—222no—
486C4×Q8C22×D1114yes—
487C4×D4—22no—
488C4×D4—114no—
489C4×D4—222no—
490C4×D4—228no—
491C4×D4C22×D1114yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C42—21no—
513C2×C42—111no—
514C2×C42—111no—
515C2×C42—221no—
516C2×C42—221no—
517C2×C42—221no—
518C2×C42C22×D1111yescharacteristic
519#107—114no—
520#107—114no—
521#107C22×D1114yes—
522C4⋊C8—114no—
523C4⋊C8—114no—
524C4⋊C8—114no—
525#103—114no—
526#103—114no—
527#103—114no—
528#103C22×D1114yes—
529#102—114no—
530#102—114no—
531#102—114no—
532#102—114no—
533#102—114no—
534#102C22×D1114yes—
535#97—114no—
536#97C22×D1114yes—
537C4×C8—114no—
538C2×C11—82no—
539C2×C11#337514yescomplemented
540C2×C11C2×#54811yescharacteristic
541C2×C11C22×#13711yescharacteristic
542C2×C11C2×#57611yescharacteristic
543D11—82no—
544C24—21no—
545C24—221no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—114no—
549C2×Q8—112no—
550C2×Q8—224no—
551C2×Q8—224no—
552C2×Q8—224no—
553C2×Q8—221no—
554C2×Q8—224no—
555C2×Q8—222no—
556C2×Q8—222no—
557C2×Q8—882no—
558C2×Q8—882no—
559C2×Q8—882no—
560C2×Q8#433914yes—
561C2×Q8C23×D1112yes—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—112no—
566C2×D4—224no—
567C2×D4—224no—
568C2×D4—222no—
569C2×D4—221no—
570C2×D4—222no—
571C2×D4—444no—
572C2×D4—882no—
573C2×D4C23×D1112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—224no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—882no—
588C22×C4D4×D1111yescharacteristic
589C22×C4D4×D1111yescharacteristic
590C22×C4C23×D1111yescharacteristic
591Q16—228no—
592SD16—28no—
593SD16—228no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—112no—
597C2×C8—112no—
598C2×C8—222no—
599C2×C8—222no—
600C2×C8C23×D1112yes—
601C2×C8C23×D1112yes—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—114no—
606C4⋊C4—114no—
607C4⋊C4—114no—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—224no—
618C4⋊C4C23×D1112yes—
619C4⋊C4C23×D1112yes—
620C22⋊C4—24no—
621C22⋊C4—224no—
622C22⋊C4—224no—
623C22⋊C4—224no—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C42—24no—
627C42—112no—
628C42—112no—
629C42—112no—
630C42—112no—
631C42—224no—
632C42—224no—
633C42—224no—
634C42D4×D1112yes—
635C42C23×D1112yes—
636C11C2×#337511yescharacteristic, complemented, Sylow
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—222no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23C2×D4×D1111yescharacteristic
646Q8—24no—
647Q8—22no—
648Q8—228no—
649Q8—222no—
650Q8—222no—
651Q8—442no—
652Q8—884no—
653Q8—884no—
654Q8—884no—
655Q8C2×#433914yes—
656D4—22no—
657D4—22no—
658D4—42no—
659D4—222no—
660D4—222no—
661D4—448no—
662D4—442no—
663D4—884no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—114no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—112no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4—884no—
688C2×C4C2×#433912yes—
689C2×C4C2×D4×D1112yes—
690C2×C4C2×D4×D1112yes—
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4#6704312yes—
693C2×C4C24×D1111yescharacteristic
694C8—22no—
695C8—22no—
696C8—222no—
697C8—222no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—442no—
703C22—442no—
704C22—442no—
705C22—884no—
706C22#1062308312yes—
707C22#1062330512yes—
708C22D11×#13712yes—
709C22C22×D4×D1111yescharacteristic
710C4—22no—
711C4—24no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—114no—
716C4—222no—
717C4—222no—
718C4—222no—
719C4—442no—
720C4—442no—
721C4—442no—
722C4#1062308312yes—
723C4C22×#433911yescharacteristic
724C4C2×#6704311yescharacteristic
725C2—82no—
726C2—882no—
727C2#1308143114yesdirect product factor
728C2C2×#1062308311yescharacteristic
729C2C2×D11×#13711yescharacteristic
730C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenterC2×#440D11
hypocenterC11C2×#3375
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic22C2semidirect
3. #13081431C2direct (N × H)
4. C2×#10622327C2semidirect
5. C2×#10622378C2semidirect
7. C2×#10622488C2semidirect
8. C2×#10622620C2semidirect
9. C2×#10622503C2semidirect
10. C2×#10622641C2semidirect
11. C2×#10622779C2semidirect
13. C2×#10622314C2semidirect
14. C2×#10622430C2semidirect
15. C2×#10622403C2semidirect
16. C2×C11×#440C2semidirect
29. Q8×Dic22C22semidirect
45. C11×#440C22semidirect
52. #10622779C22semidirect
62. #10622641C22semidirect
63. #10622620C22semidirect
69. #10622503C22semidirect
70. #10622488C22semidirect
71. #10622430C22semidirect
72. #10622403C22semidirect
73. #10622378C22semidirect
75. #10622327C22semidirect
76. #10622314C22semidirect
286. C2×#440D11semidirect
388. #440C2×D11semidirect
539. C2×C11#3375semidirect
636. C11C2×#3375semidirect
727. C2#13081431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230902
C2×Q8×Dic222
#130814312
C2×#106223272
C2×#106223782
C2×#106223732
C2×#106224882
C2×#106226202
C2×#106225032
C2×#106226412
C2×#106227792
C2×#106227762
C2×#106223142
C2×#106224302
C2×#106224032
C2×C11×#4402
C2×#337511