Finite Group Databasebeta

← C2×#13078840 #15622047

Subgroups — C2×#13078840 #15622047

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623134C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3#13078840C2116yesmaximal, direct product factor
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622488C211yesmaximal, characteristic, complemented
6C2×#10622467C211yesmaximal, characteristic, complemented
7C2×#10622380C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622352C211yesmaximal, characteristic, complemented
10C2×#10622653C211yesmaximal, characteristic
11C2×#10622466C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622486C211yesmaximal, characteristic, complemented
14C2×#10622371C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66989—21no—
21C2×#66989C2211yescharacteristic
22C2×#66988—21no—
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C22×Dic44C2211yescharacteristic
29C22×Dic44C2211yescharacteristic
30#10623134—24no—
31#10623134C2218yes—
32#10623047—24no—
33#10623047C2218yescomplemented
34C2×#66941C2211yescharacteristic
35C2×#66940C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66932—21no—
41C2×#66931—21no—
42C2×#66930—21no—
43C2×#66930—21no—
44C2×C4×Dic22—21no—
45C2×C4×Dic22—21no—
46C11×#482C2218yes—
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622653C2218yes—
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622488C2218yescomplemented
68#10622486C2218yescomplemented
69#10622467C2218yescomplemented
70#10622466C2218yescomplemented
71#10622380C2218yescomplemented
72#10622380C2218yescomplemented
73#10622371C2218yescomplemented
74#10622370C2218yescomplemented
75#10622352C2218yescomplemented
76#10622333C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11—21no—
81C23×Dic11—21no—
82C22×Dic22—21no—
83C22×Dic22—22no—
84C22×Dic22—24no—
85C22×Dic22—24no—
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2314yes—
89C22×Dic22C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×#121—22no—
94C11×#121C2314yes—
95C11×#117—22no—
96C11×#117C2314yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108C2×C22⋊Dic11D411yescharacteristic
109#66989—28no—
110#66989—22no—
111#66989C2314yes—
112#66988—28no—
113D4×Dic11—22no—
114D4×Dic11C2314yes—
115C2×#4324—24no—
116C2×#4324—24no—
117C2×#4324C2314yes—
118C2×#4324C2314yes—
119#66979D414yes—
120#66979C2314yes—
121C2×C4⋊Dic11D411yescharacteristic
122C2×C4⋊Dic11D411yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124#66977—22no—
125#66977C2314yes—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×Dic44—24no—
143C2×Dic44—24no—
144C2×Dic44C2314yes—
145C2×Dic44C2314yes—
146#66941—22no—
147#66941C2314yes—
148#66940—22no—
149#66940—22no—
150#66940—22no—
151#66940—22no—
152#66940—22no—
153#66940C2314yes—
154#66940C2314yes—
155#66940C2314yes—
156#66940C2314yes—
157#66940C2314yes—
158#66932—28no—
159#66931—28no—
160#66930—28no—
161#66930—28no—
162C4×Dic22—28no—
163C4×Dic22—28no—
164C11×#107C2314yes—
165C11×#106C2314yes—
166C11×#102C2314yes—
167C11×#102C2314yes—
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66874C2314yes—
179#66874C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3121—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C2×D4×C11—24no—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—82no—
190C2×D4×C11C2412yes—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C22×Dic11—28no—
201C22×Dic11—24no—
202C22×Dic11—24no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—82no—
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C2×Dic22—28no—
213C2×Dic22—216no—
214C2×Dic22—28no—
215C2×Dic22—28no—
216C2×Dic22—24no—
217C2×Dic22—24no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—22no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—82no—
226C2×Dic22#4114yes—
227C2×Dic22#4114yes—
228C2×Dic22C2412yes—
229C2×Dic22C2412yes—
230C2×Dic22C2412yes—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C42×C11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11C2×D414yes—
249C22⋊Dic11C2×D414yes—
250#4324—28no—
251#4324—28no—
252C4⋊Dic11—21no—
253C4⋊Dic11C2×D414yes—
254C4⋊Dic11C2×D414yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276Dic44—28no—
277Dic44—28no—
278C2×#542—111no—
279C2×#519—111no—
280#3121—1116no—
281C2×#485—111no—
282C2×#482D1111yescharacteristic
283C2×#477—111no—
284C2×#475—111no—
285C2×#464—111no—
286C2×#464—111no—
287C2×#451—111no—
288C2×#448—111no—
289C2×#441—111no—
290C2×#440—111no—
291C2×C4×Q16—111no—
292C2×C4×SD16—111no—
293C2×#433—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
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—216no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—84no—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340Dic22—216no—
341Dic22—24no—
342Dic22—24no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22—22no—
347Dic22—42no—
348Dic22—84no—
349Dic22C2×#4114yes—
350Dic22C2×#4114yes—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×SD16—111no—
359C22×SD16—111no—
360#542—118no—
361#542—224no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#123—221no—
367C2×C22⋊Q8—111no—
368C2×C22⋊Q8—221no—
369C2×#121C2×D1111yescharacteristic
370#519—118no—
371#519—224no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—221no—
378C2×C4×Q8—221no—
379C2×C4×D4—111no—
380C2×#117—111no—
381C2×#117—221no—
382C2×#117—221no—
383C2×#117C2×D1111yescharacteristic
384#485—118no—
385#482C2×D1118yes—
386#477—118no—
387#475—118no—
388#464—118no—
389#464—118no—
390#451—118no—
391#448—118no—
392#441—118no—
393#440—118no—
394C4×Q16—118no—
395C4×SD16—118no—
396#433—118no—
397C2×#107—111no—
398C2×#107C2×D1111yescharacteristic
399C2×#106—111no—
400C2×#106C2×D1111yescharacteristic
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#102C2×D1111yescharacteristic
410C2×#102C2×D1111yescharacteristic
411C2×C22⋊C8—111no—
412C2×C22⋊C8C2×D1111yescharacteristic
413C2×#97—111no—
414C2×C4×C8—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—44no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—84no—
423C22×C11#52512yes—
424C22×C11#57712yes—
425C22×C11#57812yes—
426C22×C11C23×D411yescharacteristic
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11#52512yes—
432C4×C11C22×#4111yescharacteristic
433C4×C11C22×#4111yescharacteristic
434Dic11—24no—
435Dic11—24no—
436Dic11—22no—
437Dic11—22no—
438Dic11—22no—
439Dic11—22no—
440Dic11—42no—
441Dic11—42no—
442C22×Q8—111no—
443C22×Q8—111no—
444C22×Q8—111no—
445C22×Q8—114no—
446C22×Q8—221no—
447C22×Q8—224no—
448C22×Q8—224no—
449C22×Q8—221no—
450C22×Q8—222no—
451C22×D4—21no—
452C22×D4C22×D1111yescharacteristic
453C23×C4—221no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C2×Q16—114no—
457C2×Q16—114no—
458C2×Q16—224no—
459C2×Q16—224no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—224no—
463C2×SD16—224no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470#126—228no—
471#124—114no—
472#124—222no—
473#124—228no—
474#123—228no—
475C22⋊Q8—114no—
476C22⋊Q8—228no—
477C22⋊Q8—222no—
478#121—22no—
479#121C22×D1114yes—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—114no—
485C4×Q8—228no—
486C4×Q8—228no—
487C4×Q8—222no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×Q8—222no—
492C4×D4—114no—
493C4×D4—222no—
494#117—22no—
495#117—114no—
496#117—114no—
497#117—228no—
498#117—228no—
499#117C22×D1114yes—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
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×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527C2×C42—221no—
528C2×C42—221no—
529#107—114no—
530#107C22×D1114yes—
531#106—114no—
532#106C22×D1114yes—
533C4⋊C8—114no—
534C4⋊C8—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#103—114no—
541#102C22×D1114yes—
542#102C22×D1114yes—
543C22⋊C8—114no—
544C22⋊C8C22×D1114yes—
545#97—114no—
546C4×C8—114no—
547C2×C11—42no—
548C2×C11—82no—
549C2×C11#312114yescomplemented
550C2×C11C2×#52511yescharacteristic
551C2×C11C2×#57711yescharacteristic
552C2×C11C2×#57811yescharacteristic
553C24—21no—
554C24D4×D1111yescharacteristic
555C2×Q8—114no—
556C2×Q8—114no—
557C2×Q8—112no—
558C2×Q8—112no—
559C2×Q8—112no—
560C2×Q8—224no—
561C2×Q8—228no—
562C2×Q8—228no—
563C2×Q8—228no—
564C2×Q8—2216no—
565C2×Q8—224no—
566C2×Q8—221no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8—222no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—882no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—82no—
579C2×D4C23×D1112yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—224no—
590C22×C4—228no—
591C22×C4—224no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—882no—
597C22×C4D4×D1112yes—
598C22×C4D4×D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601Q16—228no—
602Q16—228no—
603SD16—228no—
604SD16—228no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8C23×D1112yes—
612C2×C8C23×D1112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—114no—
617C4⋊C4—114no—
618C4⋊C4—112no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—224no—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—114no—
633C22⋊C4—114no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—24no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42—224no—
645C42—224no—
646C42—224no—
647C42—224no—
648C11C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×D4×D1112yes—
657C23C2×D4×D1111yescharacteristic
658Q8—114no—
659Q8—114no—
660Q8—2216no—
661Q8—224no—
662Q8—224no—
663Q8—222no—
664Q8—222no—
665Q8—222no—
666Q8—222no—
667Q8—442no—
668Q8—884no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—112no—
684C2×C4—112no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—2216no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—884no—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#41×D1112yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—222no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1062318712yes—
719C22#1062330212yes—
720C22#1062330612yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—222no—
727C4—222no—
728C4—222no—
729C4—222no—
730C4—224no—
731C4—224no—
732C4—442no—
733C4—442no—
734C4#1062318712yes—
735C4C2×#41×D1111yescharacteristic
736C4C2×#41×D1111yescharacteristic
737C2—42no—
738C2—82no—
739C2#1307884014yesdirect product factor
740C2C2×#1062318711yescharacteristic
741C2C2×#1062330611yescharacteristic
742C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#482D11
hypocenterC11C2×#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
3. #13078840C2direct (N × H)
4. C2×#10622609C2semidirect
5. C2×#10622488C2semidirect
6. C2×#10622467C2semidirect
7. C2×#10622380C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622352C2semidirect
11. C2×#10622466C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622486C2semidirect
14. C2×#10622371C2semidirect
15. C2×#10622333C2semidirect
33. #10623047C22semidirect
60. #10622609C22semidirect
67. #10622488C22semidirect
68. #10622486C22semidirect
69. #10622467C22semidirect
70. #10622466C22semidirect
71. #10622380C22semidirect
72. #10622380C22semidirect
73. #10622371C22semidirect
74. #10622370C22semidirect
75. #10622352C22semidirect
76. #10622333C22semidirect
549. C2×C11#3121semidirect
648. C11C2×#3121semidirect
739. C2#13078840direct (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×#106230472
#130788402
C2×#106226092
C2×#106224882
C2×#106224672
C2×#106223802
C2×#106223522
C2×#106226532
C2×#106224662
C2×#106223702
C2×#106224862
C2×#106223712
C2×#106223332
C2×C11×#4822
C2×#312111