Finite Group Databasebeta

← C2×#13080971 #15632194

Subgroups — C2×#13080971 #15632194

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623042C211yesmaximal, characteristic, complemented
2C2×#10623142C211yesmaximal, characteristic
3#13080971C2116yesmaximal, direct product factor
4C2×#10622468C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622475C211yesmaximal, characteristic, complemented
7C2×#10622334C211yesmaximal, characteristic, complemented
8C2×#10622467C211yesmaximal, characteristic, complemented
9C2×#10622374C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622654C211yesmaximal, characteristic, complemented
12C2×#10622371C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
14C22×#66872C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#481C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C2×#66988—21no—
22C2×D4×Dic11C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C2×C4×C22⋊D11—21no—
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C2×#66977—21no—
28C2×#66977C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623142—24no—
32#10623142C2218yes—
33#10623042—24no—
34#10623042C2218yescomplemented
35C2×#66950C2211yescharacteristic
36C2×#66949—21no—
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66936—21no—
44C2×#66931—21no—
45C11×#481C2218yescomplemented
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×#66881C2211yescharacteristic
54C2×#66881C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622654C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66872C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2218yescomplemented
67#10622475C2218yescomplemented
68D11×#106C2218yescomplemented
69#10622468C2218yescomplemented
70#10622467C2218yescomplemented
71#10622391C2218yescomplemented
72#10622390C2218yescomplemented
73#10622374C2218yescomplemented
74#10622371C2218yescomplemented
75(C22⋊D11)⋊C8C2218yescomplemented
76#10622334C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×#4341—28no—
86C2×#4341—48no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22—21no—
91C22×Dic22—21no—
92C22×Dic22C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#121—22no—
96C11×#121C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C22⋊C4—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108#66991—22no—
109#66991C2314yes—
110#66988—28no—
111D4×Dic11—22no—
112D4×Dic11C2314yes—
113C2×#4324—24no—
114C2×#4324C2314yes—
115C4×C22⋊D11—28no—
116C4×C22⋊D11D414yes—
117C4×C22⋊D11C2314yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2314yes—
127#66977—22no—
128#66977—28no—
129#66977C2314yes—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C22×C11⋊C8—24no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2314yes—
142C22×C11⋊C8C2311yescharacteristic
143C2×C8×D11—24no—
144C2×C8×D11C2314yes—
145#66950—22no—
146#66950C2314yes—
147#66949—28no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11—22no—
150C4⋊C4×D11C2314yes—
151C4⋊C4×D11C2314yes—
152#66942—28no—
153#66941—22no—
154#66941—22no—
155#66941C2314yes—
156#66941C2314yes—
157#66940—22no—
158#66940C2314yes—
159#66936—28no—
160#66931—28no—
161C11×#106C2314yes—
162C11×#106C2314yes—
163C11×#102C2314yes—
164C11×#102C2314yes—
165C11×C22⋊C8C2314yes—
166#66896C2314yes—
167(C2×D11)⋊C8C2314yes—
168#66881C2314yes—
169#66881C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66874C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66872C2314yes—
179#66872C2314yes—
180C2×#3335—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D411yescharacteristic
183C23×D11C2×D411yescharacteristic
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—44no—
189C2×D4×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—82no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11SD1618yescomplemented
204C2×C22⋊D11C2×D414yes—
205C22×Dic11—24no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—24no—
211C22×Dic11—44no—
212C22×Dic11—44no—
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216#4341—432no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—44no—
222C2×C4×D11—82no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—24no—
227C2×Dic22—21no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—44no—
231C2×Dic22—82no—
232C2×Dic22C2412yes—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4C2412yes—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11C2×D414yes—
249#4324—28no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4C2×D414yes—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4C2×D414yes—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—28no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8#4114yescomplemented
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275C8×D11—28no—
276C2×#554—111no—
277C2×#547—111no—
278#3335—1116no—
279C2×#498—111no—
280C2×#481—111no—
281C2×#481D1111yescharacteristic, complemented
282C2×#483—111no—
283C2×#483—111no—
284C2×#475—111no—
285C2×#476—111no—
286C2×#465—111no—
287C2×#465—111no—
288C2×C4×SD16—111no—
289C2×C8×D4—111no—
290C22×#106—111no—
291C22×#106—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C2×SD1614yes—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301C22×D11—22no—
302C22×D11—22no—
303C22×D11C2×SD1614yes—
304C22×D11C22×D412yes—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—48no—
308D4×C11—42no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—84no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4112yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—48no—
326C22⋊D11C2×SD16116yescomplemented
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—42no—
336C2×Dic11—48no—
337C2×Dic11—42no—
338C2×Dic11—48no—
339C2×Dic11C2×SD1614yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C4×D11—24no—
344C4×D11—22no—
345C4×D11—22no—
346C4×D11—48no—
347C4×D11—84no—
348Dic22—22no—
349Dic22—22no—
350Dic22—42no—
351Dic22—48no—
352Dic22—84no—
353C8×C11—22no—
354C8×C11—22no—
355C11⋊C8—22no—
356C11⋊C8C2×#4114yescomplemented
357C22×#41—221no—
358C22×SD16—111no—
359C23×C8—111no—
360C23×C8—111no—
361#554—118no—
362#554—224no—
363#547—118no—
364#547—224no—
365C2×C4⋊Q8—111no—
366C2×C4⋊Q8—111no—
367C2×#125—221no—
368C2×#123—221no—
369C2×#123—221no—
370C2×C22⋊Q8—111no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—221no—
373C2×C22⋊Q8—221no—
374C2×C22⋊Q8—221no—
375C2×#121—111no—
376C2×#121C2×D1111yescharacteristic
377C2×C4×Q8—111no—
378C2×C4×D4—111no—
379C2×C4×D4—111no—
380C2×C4×D4—221no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—111no—
384C22×C4⋊C4C2×D1111yescharacteristic
385#498—118no—
386#483—118no—
387#483—118no—
388#481—118no—
389#481C2×D1118yescomplemented
390#476—118no—
391#475—118no—
392#465—118no—
393#465—118no—
394C4×SD16—118no—
395C8×D4—118no—
396C2×#106—111no—
397C2×#106—111no—
398C2×#106—111no—
399C2×#106—118no—
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×#106—111no—
404C2×#106—118no—
405C2×#106C2×D1111yescharacteristic
406C2×#106C2×D1111yescharacteristic
407C2×C4⋊C8—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#102—111no—
412C2×#102C2×D1111yescharacteristic
413C2×#102C2×D1111yescharacteristic
414C2×C22⋊C8—111no—
415C2×C22⋊C8C2×D1111yescharacteristic
416C2×C4×C8—111no—
417C22×C11—28no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—84no—
424C22×C11#54712yes—
425C22×C11C22×SD1614yes—
426C22×C11C22×SD1612yes—
427C22×C11#57712yes—
428C22×C11C23×D411yescharacteristic
429C2×D11—28no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11C22×SD1614yes—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11#54712yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C2×2−1+411yescharacteristic
440Dic11—22no—
441Dic11—22no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C22×SD1614yes—
447C2×#41—228no—
448C2×#41—448no—
449C22×Q8—111no—
450C22×Q8—221no—
451C22×Q8—221no—
452C22×D4—21no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—21no—
457C23×C4—111no—
458C23×C4—221no—
459C23×C4—221no—
460C23×C4—221no—
461C23×C4—221no—
462C23×C4C22×D1111yescharacteristic
463C2×SD16—114no—
464C2×SD16—224no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—114no—
468C22×C8—114no—
469C22×C8—224no—
470C22×C8—224no—
471C22×C8C22×D1111yescharacteristic
472C22×C8C22×D1111yescharacteristic
473C4⋊Q8—114no—
474C4⋊Q8—114no—
475C4⋊Q8—222no—
476C4⋊Q8—222no—
477#125—228no—
478#123—228no—
479#123—228no—
480C22⋊Q8—114no—
481C22⋊Q8—114no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C22⋊Q8—228no—
485C22⋊Q8—222no—
486C22⋊Q8—222no—
487#121—22no—
488#121—114no—
489#121—222no—
490#121C22×D1114yes—
491C4×Q8—114no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—114no—
496C4×D4—222no—
497C4×D4—228no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1114yes—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—221no—
531#106—114no—
532#106—114no—
533#106—114no—
534#106—114no—
535#106—114no—
536#106—114no—
537#106—114no—
538#106C22×D1114yes—
539#106C22×D1114yes—
540C4⋊C8—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#102—114no—
545#102C22×D1114yes—
546#102C22×D1114yes—
547C22⋊C8—114no—
548C22⋊C8C22×D1114yes—
549C4×C8—114no—
550C2×C11—24no—
551C2×C11—82no—
552C2×C11#333514yescomplemented
553C2×C11C2×#54711yescharacteristic
554C2×C11C23×SD1611yescharacteristic
555C2×C11C2×#57711yescharacteristic
556D11—24no—
557C24—21no—
558C24—111no—
559C24D4×D1111yescharacteristic
560#41—4432no—
561C2×Q8—112no—
562C2×Q8—224no—
563C2×Q8—224no—
564C2×Q8—221no—
565C2×Q8—222no—
566C2×Q8—222no—
567C2×Q8—444no—
568C2×Q8—882no—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4—118no—
575C2×D4—114no—
576C2×D4—224no—
577C2×D4—444no—
578C2×D4C23×D1112yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—224no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4—882no—
605C22×C4D4×D1112yes—
606C22×C4D4×D1111yescharacteristic
607C22×C4C23×D1112yes—
608C22×C4C23×D1111yescharacteristic
609SD16—228no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—114no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—228no—
616C2×C8—228no—
617C2×C8—222no—
618C2×C8C23×D1112yes—
619C2×C8C23×D1112yes—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—114no—
625C4⋊C4—112no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—224no—
637C4⋊C4—221no—
638C4⋊C4—224no—
639C4⋊C4C23×D1112yes—
640C4⋊C4C23×D1112yes—
641C4⋊C4C23×D1112yes—
642C22⋊C4—24no—
643C22⋊C4—114no—
644C22⋊C4—114no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—224no—
652C11C2×#333511yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—114no—
660C23—112no—
661C23—222no—
662C23—222no—
663C23SD16×D1114yes—
664C23C2×D4×D1112yes—
665C23C2×D4×D1111yescharacteristic
666Q8—222no—
667Q8—222no—
668Q8—448no—
669Q8—442no—
670Q8—884no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—1116no—
676D4—448no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—114no—
689C2×C4—112no—
690C2×C4—112no—
691C2×C4—112no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—448no—
702C2×C4—448no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—448no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—884no—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4#41×D1112yes—
712C2×C4#6704312yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—22no—
716C8—114no—
717C8—222no—
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—114no—
726C22—228no—
727C22—222no—
728C22—222no—
729C22#1062318612yes—
730C22C2×SD16×D1114yes—
731C22C2×SD16×D1112yes—
732C22#1062330612yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—114no—
739C4—222no—
740C4—222no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4—442no—
745C4#1062318612yes—
746C4C2×#41×D1111yescharacteristic
747C4C2×#6704311yescharacteristic
748C2—24no—
749C2—82no—
750C2—224no—
751C2#1308097114yesdirect product factor
752C2C2×#1062318611yescharacteristic
753C2C22×SD16×D1111yescharacteristic
754C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
prime radicalC2×#10623142C2
hypercenterC2×#481D11
hypocenterC11C2×#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#10623042C2semidirect
3. #13080971C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622475C2semidirect
7. C2×#10622334C2semidirect
8. C2×#10622467C2semidirect
9. C2×#10622374C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622654C2semidirect
12. C2×#10622371C2semidirect
13. C2×(C22⋊D11)⋊C8C2semidirect
14. C22×#66872C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#481C2semidirect
34. #10623042C22semidirect
45. C11×#481C22semidirect
59. #10622654C22semidirect
66. C2×#66872C22semidirect
67. #10622475C22semidirect
68. D11×#106C22semidirect
69. #10622468C22semidirect
70. #10622467C22semidirect
71. #10622391C22semidirect
72. #10622390C22semidirect
73. #10622374C22semidirect
74. #10622371C22semidirect
75. (C22⋊D11)⋊C8C22semidirect
76. #10622334C22semidirect
203. C2×C22⋊D11SD16semidirect
272. C2×C11⋊C8#41semidirect
281. C2×#481D11semidirect
326. C22⋊D11C2×SD16semidirect
356. C11⋊C8C2×#41semidirect
389. #481C2×D11semidirect
552. C2×C11#3335semidirect
652. C11C2×#3335semidirect
751. C2#13080971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230422
C2×#106231422
#130809712
C2×#106224682
C2×#106223902
C2×#106224752
C2×#106223342
C2×#106224672
C2×#106223742
C2×#106223912
C2×#106226542
C2×#106223712
C2×(C22⋊D11)⋊C82
C22×#668722
C2×D11×#1062
C2×C11×#4812
C2×#333511