Finite Group Databasebeta

← C2×#13080817 #15630570

Subgroups — C2×#13080817 #15630570

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2#13080817C2116yesmaximal, direct product factor
3C2×#10622669C211yesmaximal, characteristic, complemented
4C2×#10622658C211yesmaximal, characteristic, complemented
5C2×#10622646C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622830C211yesmaximal, characteristic, complemented
12C2×C4×#4323C211yesmaximal, characteristic, complemented
13C2×#10622625C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622828C211yesmaximal, characteristic, complemented
16C2×C11×#546C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C11×#546—24no—
20C11×#546C2218yescomplemented
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#120—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C22⋊C4—21no—
30C22×#4325C2211yescharacteristic, complemented
31C2×#66992—21no—
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×#4318C2211yescharacteristic
39C22×#4318C2211yescharacteristic, complemented
40#10623096—24no—
41#10623096C2218yescomplemented
42C2×#66951—21no—
43C2×#66936—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66923C2211yescharacteristic, complemented
47#10622851C2218yescomplemented
48#10622845C2218yescomplemented
49C2×#66899C2211yescharacteristic, complemented
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622830C2218yescomplemented
53#10622828C2218yescomplemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622670C2218yescomplemented
63#10622669C2218yescomplemented
64#10622662C2218yescomplemented
65#10622658C2218yescomplemented
66#10622652C2218yescomplemented
67#10622646C2218yescomplemented
68C4×#4323C2218yescomplemented
69#10622625C2218yescomplemented
70#10622622C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66871C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×C4×C11⋊C8C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—22no—
88C22×D4×C11—42no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2314yes—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C23×Dic11—21no—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C11×#124—22no—
103C11×#124C2314yes—
104C11×#123—28no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8C2314yes—
107C11×#121—22no—
108C11×#121—28no—
109C11×#121C2314yes—
110C11×#120—28no—
111C4×D4×C11—22no—
112C4×D4×C11D414yes—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—28no—
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×#4325—42no—
129C2×#4325C2314yescomplemented
130#66992—28no—
131C2×#4323—24no—
132C2×#4323—42no—
133C2×#4323C2314yes—
134C2×#4323C2314yes—
135#66983—22no—
136#66983—22no—
137#66983C2314yes—
138#66983C2314yescomplemented
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142#66979—22no—
143#66979C2314yes—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2314yescomplemented
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318—42no—
155C2×#4318C2314yes—
156C2×#4318C2314yescomplemented
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161#66951—28no—
162#66936—28no—
163(C22⋊D11)⋊C4—28no—
164C4×D44—22no—
165C4×D44C2314yescomplemented
166#66923—22no—
167#66923C2314yescomplemented
168#66899C2314yescomplemented
169#66899C2314yescomplemented
170#66899C2314yescomplemented
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yescomplemented
179#66873C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184C4×C11⋊C8C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—24no—
189C24×C11—44no—
190C24×C11—44no—
191C24×C11—82no—
192C24×C11C2×D411yescharacteristic
193C24×C11C2×D411yescharacteristic
194C23×D11—21no—
195C11×#41—28no—
196C11×#41—44no—
197C11×#41—48no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—28no—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—24no—
207C2×D4×C11—21no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—44no—
212C2×D4×C11—48no—
213C2×D4×C11—42no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—82no—
217C2×D4×C11C2×D414yes—
218C2×D4×C11#4114yes—
219C2×D4×C11C2412yes—
220C2×D4×C11C2412yes—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—24no—
228C22×C4×C11—24no—
229C22×C4×C11—44no—
230C22×C4×C11—82no—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2411yescharacteristic
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—82no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—24no—
248C22×Dic11—82no—
249C2×D44—21no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—82no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2×D414yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4C2×D414yes—
265C11×C22⋊C4C2×D414yes—
266C42×C11C2×D412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269#4325—44no—
270#4323—28no—
271#4323—44no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—24no—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281C4⋊Dic11C2412yes—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284C4×Dic11—24no—
285#4318—44no—
286#4318—44no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×#553—111no—
296C2×#546D1111yescharacteristic, complemented
297#3322—1116no—
298C2×#488—111no—
299C2×#485—111no—
300C2×#480—111no—
301C2×#478—111no—
302C2×#469—111no—
303C2×#468—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×C4×D8—111no—
308C2×#436—111no—
309C2×#417—111no—
310C2×#418—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—24no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—48no—
321C23×C11—48no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—84no—
328C23×C11—816no—
329C23×C11C22×D412yes—
330C23×C11C22×D412yes—
331C23×C11C22×D411yescharacteristic
332C22×D11—22no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339D4×C11—24no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—44no—
344D4×C11—48no—
345D4×C11—48no—
346D4×C11—42no—
347D4×C11—84no—
348D4×C11C2×#4114yes—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—24no—
354C2×C4×C11—24no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—48no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—84no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4112yes—
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—48no—
374C22⋊D11—84no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—84no—
382D44—22no—
383D44—22no—
384D44—42no—
385C4×D11—84no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41C2×D1111yescharacteristic
391C23×D4C2×D1111yescharacteristic
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8—111no—
395C22×M16—111no—
396C22×M16—111no—
397#553—118no—
398#553—224no—
399#546—24no—
400#546C2×D1118yescomplemented
401C2×#126—221no—
402C2×#125—111no—
403C2×#124C2×D1111yescharacteristic
404C2×#123—21no—
405C2×#123—221no—
406C2×C22⋊Q8C2×D1111yescharacteristic
407C2×#121—21no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#121C2×D1111yescharacteristic
412C2×#120—21no—
413C2×C4×D4—111no—
414C2×C4×D4—221no—
415C2×C4×D4C2×D1111yescharacteristic
416C2×C4×D4C2×D1111yescharacteristic
417C2×#117—111no—
418C22×C4⋊C4—111no—
419C22×C22⋊C4—21no—
420#488—118no—
421#485—118no—
422#480—118no—
423#478—118no—
424#469—118no—
425#468—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429C4×D8—118no—
430#436—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#417—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×C4×C8—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—24no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11—48no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—816no—
466C22×C11—84no—
467C22×C11#54612yes—
468C22×C11#57512yes—
469C22×C11#57612yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11#54612yes—
482C4×C11C22×#4111yescharacteristic
483C4×C11C2×H(5,𝔽2)11yescharacteristic
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—21no—
488C2×#41—22no—
489C2×#41—24no—
490C2×#41—42no—
491C2×#41C22×D1114yes—
492C22×Q8C22×D1111yescharacteristic
493C22×D4—24no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—42no—
499C22×D4—111no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4C22⋊D1111yescharacteristic
503C22×D4C22×D1111yescharacteristic
504C22×D4C22×D1114yes—
505C22×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—114no—
520C2×M16—442no—
521C2×M16—442no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—111no—
526#126—228no—
527#125—114no—
528#125—222no—
529#124—22no—
530#124C22×D1114yes—
531#123—28no—
532#123—228no—
533C22⋊Q8—22no—
534C22⋊Q8C22×D1114yes—
535#121—22no—
536#121—28no—
537#121—114no—
538#121—114no—
539#121—228no—
540#121—222no—
541#121—222no—
542#121C22×D1114yes—
543#120—28no—
544C4×D4—22no—
545C4×D4—114no—
546C4×D4—228no—
547C4×D4—222no—
548C4×D4C22⋊D1114yes—
549C4×D4C22×D1114yes—
550C4×D4C22×D1114yes—
551#117—114no—
552#117—222no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4C22⋊D1111yescharacteristic
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—28no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4C22⋊D1111yescharacteristic
575C2×C22⋊C4C22⋊D1111yescharacteristic
576C2×C42—221no—
577C2×C42C22×D1111yescharacteristic
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102—114no—
591#102—114no—
592C22⋊C8—114no—
593C22⋊C8—114no—
594C4×C8—114no—
595C2×C11—42no—
596C2×C11—42no—
597C2×C11—44no—
598C2×C11—82no—
599C2×C11#332214yescomplemented
600C2×C11C2×#54611yescharacteristic
601C2×C11C2×#57511yescharacteristic
602C2×C11C2×#57611yescharacteristic
603D11—82no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—44no—
608C24—44no—
609C24—82no—
610C24—221no—
611C24C2×C22⋊D1111yescharacteristic
612C24C2×C22⋊D1111yescharacteristic
613#41—28no—
614#41—44no—
615#41—48no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8C23×D1112yes—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—44no—
630C2×D4—48no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—82no—
635C2×D4—112no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—222no—
639C2×D4—222no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4#434114yes—
644C2×D4C2×C22⋊D1114yes—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—882no—
663C22×C4—882no—
664C22×C4C2×C22⋊D1112yes—
665C22×C4C2×C22⋊D1112yes—
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—228no—
675D8—444no—
676M16—444no—
677M16—444no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—222no—
685C2×C8—222no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—112no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4C2×C22⋊D1114yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4C2×C22⋊D1114yes—
709C22⋊C4C2×C22⋊D1114yes—
710C42—224no—
711C42C2×C22⋊D1112yes—
712C42C23×D1112yes—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—48no—
724C23—48no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—84no—
731C23—816no—
732C23—222no—
733C23—442no—
734C23—442no—
735C23—442no—
736C23C22×C22⋊D1112yes—
737C23C22×C22⋊D1112yes—
738C23C22×C22⋊D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—24no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—48no—
748D4—48no—
749D4—42no—
750D4—84no—
751D4—222no—
752D4—222no—
753D4—448no—
754D4—442no—
755D4—884no—
756D4C2×#434114yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—84no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—884no—
780C2×C4—884no—
781C2×C4C2×#434112yes—
782C2×C4#6703712yes—
783C2×C4C22×C22⋊D1112yes—
784C2×C4C22×C22⋊D1112yes—
785C2×C4C22×C22⋊D1112yes—
786C2×C4C22×C22⋊D1112yes—
787C2×C4C22×C22⋊D1111yescharacteristic
788C2×C4C24×D1111yescharacteristic
789C8—222no—
790C8—222no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—48no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—816no—
809C22—84no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—884no—
814C22#1062333712yes—
815C22#1062335312yes—
816C22#1062336612yes—
817C22C23×C22⋊D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4#1062333712yes—
828C4C22×#434111yescharacteristic
829C4C2×#6703711yescharacteristic
830C2—42no—
831C2—42no—
832C2—44no—
833C2—82no—
834C2—882no—
835C2#1308081714yesdirect product factor
836C2C2×#1062333711yescharacteristic
837C2C2×#1062335311yescharacteristic
838C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. #13080817C2direct (N × H)
3. C2×#10622669C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622646C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622830C2semidirect
12. C2×C4×#4323C2semidirect
13. C2×#10622625C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622828C2semidirect
16. C2×C11×#546C2semidirect
20. C11×#546C22semidirect
30. C22×#4325C22semidirect
35. C2×#66983C22semidirect
37. C22×C4⋊Dic11C22semidirect
39. C22×#4318C22semidirect
41. #10623096C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66923C22semidirect
47. #10622851C22semidirect
48. #10622845C22semidirect
49. C2×#66899C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
52. #10622830C22semidirect
53. #10622828C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622670C22semidirect
63. #10622669C22semidirect
64. #10622662C22semidirect
65. #10622658C22semidirect
66. #10622652C22semidirect
67. #10622646C22semidirect
68. C4×#4323C22semidirect
69. #10622625C22semidirect
70. #10622622C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. C2×#66871C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×C4×C11⋊C8C22semidirect
129. C2×#4325C23semidirect
138. #66983C23semidirect
149. C2×C4⋊Dic11C23semidirect
156. C2×#4318C23semidirect
165. C4×D44C23semidirect
167. #66923C23semidirect
168. #66899C23semidirect
169. #66899C23semidirect
170. #66899C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. #66873C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. C4×C11⋊C8C23semidirect
296. C2×#546D11semidirect
400. #546C2×D11semidirect
599. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080817direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
#130808172
C2×#106226692
C2×#106226582
C2×#106226462
C2×#106226222
C2×#106226522
C2×#106226622
C2×#106226702
C2×#106228512
C2×#106228302
C2×C4×#43232
C2×#106226252
C2×#106228452
C2×#106228282
C2×C11×#5462
C2×#332211