Finite Group Databasebeta

← C2×#13079279 #15623636

Subgroups — C2×#13079279 #15623636

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623134C211yesmaximal, characteristic
2C2×#10623156C211yesmaximal, characteristic, complemented
3#13079279C2116yesmaximal, direct product factor
4C2×#10622469C211yesmaximal, characteristic, complemented
5C2×#10622780C211yesmaximal, characteristic, complemented
6C2×#10622381C211yesmaximal, characteristic, complemented
7C2×#10622405C211yesmaximal, characteristic, complemented
8C2×#10622665C211yesmaximal, characteristic, complemented
9C2×#10622655C211yesmaximal, characteristic
10C2×#10622729C211yesmaximal, characteristic, complemented
11C2×#10622466C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×#10622371C211yesmaximal, characteristic, complemented
15C2×#10622714C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic
17C22×C11×SD16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×#66989—21no—
25C2×#66989C2211yescharacteristic
26C2×#66988—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×Dic44C2211yescharacteristic
34#10623156—24no—
35#10623156C2218yescomplemented
36#10623134—24no—
37#10623134C2218yes—
38C2×#66943—21no—
39C2×#66943C2211yescharacteristic
40C2×#66942—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66932—21no—
47C2×#66931—21no—
48C11×#465C2218yes—
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622780C2218yescomplemented
55#10622777C2218yescomplemented
56#10622729C2218yescomplemented
57C2×#66882C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60#10622714C2218yescomplemented
61C2×#66879C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622665C2218yescomplemented
66#10622655C2218yes—
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622469C2218yescomplemented
72#10622466C2218yescomplemented
73#10622405C2218yescomplemented
74#10622403C2218yescomplemented
75#10622381C2218yescomplemented
76#10622371C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×Dic11—21no—
82C22×Dic22—21no—
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×SD16—24no—
86C2×C11×SD16C2314yes—
87C22×C8×C11—24no—
88C22×C8×C11C2314yes—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8C2314yes—
93C11×#121—22no—
94C11×#121C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11D411yescharacteristic
106C2×C22⋊Dic11D411yescharacteristic
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109#66997—22no—
110#66997C2314yes—
111C2×#4326—24no—
112C2×#4326C2314yes—
113#66989—28no—
114#66989—22no—
115#66989C2314yes—
116#66988—28no—
117D4×Dic11—22no—
118D4×Dic11C2314yes—
119C2×#4324—24no—
120C2×#4324C2314yes—
121#66979D414yes—
122#66979C2314yes—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11D411yescharacteristic
126C2×C4⋊Dic11D411yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129#66977—22no—
130#66977—22no—
131#66977C2314yes—
132#66977C2314yes—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×C4×Dic11—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11C2311yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C2×#4318—24no—
147C2×#4318C2314yes—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×Dic44—24no—
151C2×Dic44C2314yes—
152#66943—28no—
153#66943—22no—
154#66943C2314yes—
155#66942—28no—
156#66941—22no—
157#66941C2314yes—
158#66940—22no—
159#66940—22no—
160#66940C2314yes—
161#66940C2314yes—
162#66932—28no—
163#66932—28no—
164#66932—28no—
165#66931—28no—
166C11×#106C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66882C2314yes—
172#66880C2314yes—
173#66880C2314yes—
174#66879C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177C8×Dic11C2314yes—
178#66874C2314yes—
179#66874C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3178—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C2×D4×C11—24no—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—82no—
194C2×D4×C11C2412yes—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—24no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—82no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C2×Dic22—24no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—22no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—22no—
221C2×Dic22—82no—
222C2×Dic22C2412yes—
223C2×Dic22C2412yes—
224C11×SD16—28no—
225C2×C8×C11—28no—
226C2×C8×C11—22no—
227C2×C8×C11#4114yes—
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4C2412yes—
234C11×C4⋊C4C2412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11C2×D414yes—
243C22⋊Dic11C2×D414yes—
244#4326—28no—
245#4324—28no—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11C2×D414yes—
251C4⋊Dic11C2×D414yes—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D412yes—
266C4×Dic11C2×D412yes—
267C4×Dic11C2412yes—
268C4×Dic11C2412yes—
269#4318—28no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8#4114yes—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274Dic44—28no—
275C2×#542—111no—
276C2×#541—111no—
277#3178—1116no—
278C2×#501—111no—
279C2×#497—111no—
280C2×#488—111no—
281C2×#487—111no—
282C2×#470—111no—
283C2×#468—111no—
284C2×#467—111no—
285C2×#465D1111yescharacteristic
286C2×#441—111no—
287C2×#440—111no—
288C2×C4×Q16—111no—
289C2×C4×SD16—111no—
290C2×#405—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C22×D412yes—
299C23×C11C22×D411yescharacteristic
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—42no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—42no—
306D4×C11—84no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C11C2×#4112yes—
321C2×C4×C11C2511yescharacteristic
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—84no—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339Dic22—22no—
340Dic22—22no—
341Dic22—22no—
342Dic22—22no—
343Dic22—42no—
344Dic22—42no—
345Dic22—84no—
346C8×C11—22no—
347C8×C11C2×#4114yes—
348C11⋊C8—22no—
349C11⋊C8C2×#4114yes—
350C22×Q16—111no—
351C22×Q16—111no—
352C22×SD16—111no—
353C22×SD16C2×D1111yescharacteristic
354C22×M16—111no—
355C23×C8C2×D1111yescharacteristic
356#542—118no—
357#542—224no—
358#541—118no—
359#541—224no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8—111no—
362C2×#126—221no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#125—111no—
366C2×#125—221no—
367C2×#125—221no—
368C2×#124—111no—
369C2×#124—221no—
370C2×#123—221no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—111no—
373C2×C22⋊Q8—221no—
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121C2×D1111yescharacteristic
376C2×C4×Q8—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×D4—111no—
380C2×#117—111no—
381#501—118no—
382#497—118no—
383#488—118no—
384#487—118no—
385#470—118no—
386#468—118no—
387#467—118no—
388#465C2×D1118yes—
389#441—118no—
390#440—118no—
391C4×Q16—118no—
392C4×SD16—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#106—111no—
396C2×#106C2×D1111yescharacteristic
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103C2×D1111yescharacteristic
403C2×#102—111no—
404C2×#102C2×D1111yescharacteristic
405#405—118no—
406C2×#97—111no—
407C2×#97—111no—
408C2×C4×C8—111no—
409C2×C4×C8—111no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—84no—
418C22×C11#53212yes—
419C22×C11#57712yes—
420C22×C11#57812yes—
421C22×C11C23×D411yescharacteristic
422C4×C11—22no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11#53212yes—
427C4×C11C22×#4111yescharacteristic
428C4×C11C22×#4111yescharacteristic
429Dic11—22no—
430Dic11—22no—
431Dic11—22no—
432Dic11—22no—
433Dic11—42no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—111no—
438C22×Q8—111no—
439C22×Q8—221no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—21no—
442C22×D4C22×D1111yescharacteristic
443C23×C4—221no—
444C23×C4C22×D1111yescharacteristic
445C2×Q16—114no—
446C2×Q16—114no—
447C2×Q16—224no—
448C2×Q16—224no—
449C2×SD16—24no—
450C2×SD16—114no—
451C2×SD16—224no—
452C2×SD16C22×D1114yes—
453C2×M16—114no—
454C2×M16—224no—
455C22×C8—24no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8C22×D1111yescharacteristic
459C22×C8C22×D1114yes—
460C22×C8C22×D1111yescharacteristic
461C4⋊Q8—114no—
462C4⋊Q8—114no—
463C4⋊Q8—222no—
464C4⋊Q8—222no—
465#126—228no—
466#126—228no—
467#126—228no—
468#125—114no—
469#125—222no—
470#125—228no—
471#125—228no—
472#124—114no—
473#124—222no—
474#124—228no—
475#123—228no—
476C22⋊Q8—22no—
477C22⋊Q8—114no—
478C22⋊Q8—114no—
479C22⋊Q8—228no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482C22⋊Q8C22×D1114yes—
483#121—22no—
484#121C22×D1114yes—
485C4×Q8—114no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×D4—114no—
492C4×D4—222no—
493#117—114no—
494#117—114no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—111no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42—221no—
526#107—114no—
527#107—114no—
528#106—114no—
529#106C22×D1114yes—
530#103—114no—
531#103—114no—
532#103—114no—
533#103—114no—
534#103—114no—
535#103C22×D1114yes—
536#102—114no—
537#102C22×D1114yes—
538#97—114no—
539#97—114no—
540C4×C8—114no—
541C4×C8—114no—
542C2×C11—42no—
543C2×C11—82no—
544C2×C11#317814yescomplemented
545C2×C11C2×#53211yescharacteristic
546C2×C11C2×#57711yescharacteristic
547C2×C11C2×#57811yescharacteristic
548C24—21no—
549C24D4×D1111yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—112no—
554C2×Q8—112no—
555C2×Q8—224no—
556C2×Q8—221no—
557C2×Q8—221no—
558C2×Q8—222no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—882no—
563C2×Q8C23×D1112yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—82no—
569C2×D4C23×D1112yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—224no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—882no—
585C22×C4D4×D1112yes—
586C22×C4D4×D1111yescharacteristic
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589Q16—228no—
590Q16—228no—
591SD16—28no—
592SD16—228no—
593M16—228no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8—114no—
597C2×C8—112no—
598C2×C8—112no—
599C2×C8—222no—
600C2×C8#434114yes—
601C2×C8C23×D1112yes—
602C2×C8C23×D1112yes—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
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—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—114no—
627C22⋊C4—114no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C42—112no—
634C42—112no—
635C42—112no—
636C42—112no—
637C42—224no—
638C42—224no—
639C42—224no—
640C11C2×#317811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23C2×D4×D1112yes—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—222no—
654Q8—222no—
655Q8—222no—
656Q8—222no—
657Q8—442no—
658Q8—442no—
659Q8—884no—
660D4—22no—
661D4—22no—
662D4—42no—
663D4—84no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
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—222no—
685C2×C4—222no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—884no—
691C2×C4C2×D4×D1112yes—
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×#434112yes—
694C2×C4#41×D1112yes—
695C2×C4C24×D1111yescharacteristic
696C8—22no—
697C8—114no—
698C8—222no—
699C8C2×#434114yes—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22#1062312712yes—
709C22#1062329312yes—
710C22#1062330212yes—
711C22C22×D4×D1111yescharacteristic
712C4—22no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—222no—
717C4—222no—
718C4—222no—
719C4—222no—
720C4—442no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062312712yes—
725C4C22×#434111yescharacteristic
726C4C2×#41×D1111yescharacteristic
727C2—42no—
728C2—82no—
729C2#1307927914yesdirect product factor
730C2C2×#1062312711yescharacteristic
731C2C2×#1062329311yescharacteristic
732C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#465D11
hypocenterC11C2×#3178
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. C2×#10623156C2semidirect
3. #13079279C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622780C2semidirect
6. C2×#10622381C2semidirect
7. C2×#10622405C2semidirect
8. C2×#10622665C2semidirect
10. C2×#10622729C2semidirect
11. C2×#10622466C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622403C2semidirect
14. C2×#10622371C2semidirect
15. C2×#10622714C2semidirect
35. #10623156C22semidirect
54. #10622780C22semidirect
55. #10622777C22semidirect
56. #10622729C22semidirect
60. #10622714C22semidirect
65. #10622665C22semidirect
71. #10622469C22semidirect
72. #10622466C22semidirect
73. #10622405C22semidirect
74. #10622403C22semidirect
75. #10622381C22semidirect
76. #10622371C22semidirect
544. C2×C11#3178semidirect
640. C11C2×#3178semidirect
729. C2#13079279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231342
C2×#106231562
#130792792
C2×#106224692
C2×#106227802
C2×#106223812
C2×#106224052
C2×#106226652
C2×#106226552
C2×#106227292
C2×#106224662
C2×#106227772
C2×#106224032
C2×#106223712
C2×#106227142
C2×C11×#4652
C2×#317811