Finite Group Databasebeta

← C2×#13080353 #15629034

Subgroups — C2×#13080353 #15629034

Order 2816.

2794 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic, complemented
2C23×#4326C211yesmaximal, characteristic, complemented
3C2×#10623083C211yesmaximal, characteristic, complemented
4#13080353C2116yesmaximal, direct product factor
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622664C211yesmaximal, characteristic, complemented
7C2×#10622651C211yesmaximal, characteristic, complemented
8C2×#10622641C211yesmaximal, characteristic, complemented
9C2×#10622667C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622660C211yesmaximal, characteristic, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14C2×C4×#4326C211yesmaximal, characteristic, complemented
15C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C11×#548—24no—
22C11×#548C2218yescomplemented
23C2×C11×#124—21no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×#67003—28no—
33C2×#67003C2218yescomplemented
34C22×#4326—28no—
35C22×#4326C2211yescharacteristic
36C22×#4326C2211yescharacteristic
37C22×#4326C2211yescharacteristic
38C22×#4326C2211yescharacteristic
39C22×#4326C2218yescomplemented
40C22×#4325C2211yescharacteristic
41C22×#4325C2211yescharacteristic
42C2×#66992—21no—
43C22×#4324C2211yescharacteristic
44C22×#4324C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983C2211yescharacteristic
47C2×#66977C2211yescharacteristic
48C23×C11⋊C8C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic
50#10623083—24no—
51#10623083C2218yescomplemented
52C2×#66949—21no—
53C2×#66938—21no—
54C2×(C22⋊D11)⋊C4—21no—
55C2×#66928C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622672C2218yescomplemented
65#10622667C2218yescomplemented
66#10622664C2218yescomplemented
67#10622660C2218yescomplemented
68#10622653C2218yescomplemented
69#10622651C2218yescomplemented
70C4×#4326C2218yescomplemented
71#10622641C2218yescomplemented
72D4×C11⋊C8C2218yescomplemented
73C2×#66874C2211yescharacteristic
74C2×#66874C2211yescharacteristic
75C2×#66873C2211yescharacteristic
76C2×#66871C2211yescharacteristic
77C2×C4⋊(C11⋊C8)C2211yescharacteristic
78C2×C4×C11⋊C8C2211yescharacteristic
79C2×C11×#41—22no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41C2314yes—
83C22×Q8×C11—21no—
84C22×Q8×C11—22no—
85C22×Q8×C11—24no—
86C22×Q8×C11—42no—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2314yes—
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11D411yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C23×Dic11—21no—
101C2×#4339—22no—
102C2×#4339—24no—
103C2×#4339—42no—
104C2×#4339C2314yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×Dic22—24no—
108C22×Dic22—21no—
109C22×Dic22—22no—
110C22×Dic22—42no—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2314yes—
113C22×Dic22C2311yescharacteristic
114C11×#124—28no—
115C11×#124—22no—
116C11×#124C2314yes—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—28no—
119C11×C22⋊Q8C2314yes—
120C11×#121—28no—
121C11×#121—22no—
122C11×#121C2314yes—
123C4×Q8×C11—22no—
124C4×Q8×C11C2314yes—
125C4×D4×C11—28no—
126C4×D4×C11D414yes—
127C4×D4×C11C2314yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C4⋊C4D411yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4D411yescharacteristic
137C2×C11×C22⋊C4D411yescharacteristic
138C2×C42×C11—21no—
139C2×C42×C11C2311yescharacteristic
140C2×C22⋊Dic11—21no—
141#67003—232no—
142C2×#4326—24no—
143C2×#4326—24no—
144C2×#4326—232no—
145C2×#4326—24no—
146C2×#4326D418yescomplemented
147C2×#4326C2314yes—
148C2×#4326C2314yes—
149C2×#4326C2314yes—
150C2×#4326C2314yes—
151C2×#4325—24no—
152C2×#4325—42no—
153C2×#4325C2314yes—
154C2×#4325C2314yes—
155#66992—28no—
156C2×#4324—24no—
157C2×#4324—42no—
158C2×#4324C2314yes—
159C2×#4324C2314yes—
160C2×#4323—24no—
161C2×#4323C2314yes—
162#66983—22no—
163#66983C2314yes—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×C4⋊Dic11C2311yescharacteristic
168#66977—22no—
169#66977C2314yes—
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×C4×Dic11—21no—
173C22×C11⋊C8—24no—
174C22×C11⋊C8—24no—
175C22×C11⋊C8C2311yescharacteristic
176C22×C11⋊C8C2311yescharacteristic
177C22×C11⋊C8C2311yescharacteristic
178C22×C11⋊C8C2314yes—
179C22×C11⋊C8C2314yes—
180C22×C11⋊C8C2311yescharacteristic
181#66949—28no—
182#66938—28no—
183(C22⋊D11)⋊C4—28no—
184#66928—22no—
185#66928C2314yes—
186C4×Dic22—22no—
187C4×Dic22C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66896C2314yes—
191C22⋊(C11⋊C8)C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66874C2314yes—
194#66874C2314yes—
195#66873C2314yes—
196#66871C2314yes—
197C4⋊(C11⋊C8)C2314yes—
198C4×C11⋊C8C2314yes—
199C2×#3285—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C24×C11C2×D411yescharacteristic
203C23×D11—21no—
204C11×#41—28no—
205C11×#41—44no—
206C11×#41—48no—
207C2×Q8×C11—21no—
208C2×Q8×C11—24no—
209C2×Q8×C11—21no—
210C2×Q8×C11—22no—
211C2×Q8×C11—28no—
212C2×Q8×C11—22no—
213C2×Q8×C11—22no—
214C2×Q8×C11—44no—
215C2×Q8×C11—44no—
216C2×Q8×C11—48no—
217C2×Q8×C11C2×D414yes—
218C2×Q8×C11C2412yes—
219C2×Q8×C11C2412yes—
220C2×D4×C11—24no—
221C2×D4×C11—24no—
222C2×D4×C11—24no—
223C2×D4×C11—22no—
224C2×D4×C11—21no—
225C2×D4×C11—22no—
226C2×D4×C11—44no—
227C2×D4×C11—44no—
228C2×D4×C11C2×D414yes—
229C2×D4×C11C2412yes—
230C22×C4×C11—21no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—24no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C22×Dic11—21no—
255C22×Dic11—24no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—44no—
259#4339—28no—
260#4339—44no—
261#4339—48no—
262C2×D44—21no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44C2412yes—
266C2×C4×D11—24no—
267C2×C4×D11—44no—
268C2×Dic22—28no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—21no—
272C2×Dic22—24no—
273C2×Dic22—22no—
274C2×Dic22—22no—
275C2×Dic22—44no—
276C2×Dic22—48no—
277C2×Dic22—44no—
278C2×Dic22C2×D414yes—
279C2×Dic22C2412yes—
280C2×Dic22C2412yes—
281C11×C4⋊C4—24no—
282C11×C4⋊C4—24no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2×D414yes—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4C2×D414yes—
291C11×C22⋊C4C2×D414yes—
292C42×C11—24no—
293C42×C11C2×D412yes—
294C42×C11C2412yes—
295C22⋊Dic11—24no—
296#4326—28no—
297#4326—28no—
298#4326—28no—
299#4326C2×D4116yescomplemented
300#4325—28no—
301#4325—44no—
302#4324—28no—
303#4324—44no—
304#4323—28no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308C4⋊Dic11—21no—
309C4⋊Dic11C2412yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312C4×Dic11—24no—
313C2×C11⋊C8—28no—
314C2×C11⋊C8—28no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8—22no—
317C2×C11⋊C8—22no—
318C2×C11⋊C8C2×D414yes—
319C2×C11⋊C8C2412yes—
320C2×C11⋊C8C2412yes—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323C22×#135—111no—
324C23×Q16—111no—
325C2×#548—111no—
326C2×#548D1111yescharacteristic, complemented
327#3285—1116no—
328C2×#495—111no—
329C2×#467—111no—
330C2×#466—111no—
331C2×#464—111no—
332C2×#464—111no—
333C2×#452—111no—
334C2×#452—111no—
335C2×#448—111no—
336C2×#448—111no—
337C2×C4×Q16—111no—
338C2×C8×D4—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—42no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11#13514yescomplemented
349C23×C11C22×D412yes—
350C23×C11C22×D412yes—
351C23×C11C22×D411yescharacteristic
352C22×D11—22no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356Q8×C11—24no—
357Q8×C11—22no—
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—48no—
361Q8×C11—42no—
362Q8×C11C22×D414yes—
363D4×C11—28no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—48no—
367D4×C11—48no—
368D4×C11—42no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—24no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—48no—
384C2×C4×C11—48no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11H(5,𝔽2)12yes—
394C2×C4×C11C2511yescharacteristic
395C22⋊D11—48no—
396C22⋊D11—48no—
397C2×Dic11—24no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—48no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404D44—22no—
405D44—22no—
406D44—42no—
407C4×D11—48no—
408Dic22—24no—
409Dic22—22no—
410Dic22—22no—
411Dic22—22no—
412Dic22—48no—
413Dic22—42no—
414Dic22C22×D414yes—
415C11⋊C8—22no—
416C11⋊C8—22no—
417C11⋊C8—22no—
418C11⋊C8C22×D414yes—
419C22×#41—111no—
420C22×#41C2×D1111yescharacteristic
421C23×Q8—111no—
422C23×Q8C2×D1111yescharacteristic
423C2×#135—118no—
424C2×#135—228no—
425C22×Q16—111no—
426C22×Q16—111no—
427C22×Q16—111no—
428C22×Q16—111no—
429C22×Q16—118no—
430C22×Q16—228no—
431C22×SD16—111no—
432C22×SD16—111no—
433C22×SD16—111no—
434C22×SD16—111no—
435C22×D8—111no—
436C23×C8—111no—
437C23×C8—111no—
438#548—24no—
439#548—118no—
440#548—224no—
441#548C2×D1118yescomplemented
442C2×#124—21no—
443C2×#124—111no—
444C2×#124—221no—
445C2×#124C2×D1111yescharacteristic
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—111no—
448C2×C22⋊Q8—221no—
449C2×C22⋊Q8C2×D1111yescharacteristic
450C2×#121—21no—
451C2×#121—111no—
452C2×#121—221no—
453C2×#121C2×D1111yescharacteristic
454C2×C4×Q8—111no—
455C2×C4×Q8C2×D1111yescharacteristic
456C2×C4×D4—21no—
457C2×C4×D4—221no—
458C2×C4×D4C2×D1111yescharacteristic
459#495—118no—
460#467—118no—
461#466—118no—
462#464—118no—
463#464—118no—
464#452—118no—
465#452—118no—
466#448—118no—
467#448—118no—
468C4×Q16—118no—
469C8×D4—118no—
470C2×#107—111no—
471C2×C4⋊C8—111no—
472C2×#103—111no—
473C2×#103—111no—
474C2×#103—111no—
475C2×#103—111no—
476C2×#102—111no—
477C2×#102—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C4×C8—111no—
481C22×C11—22no—
482C22×C11—28no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—44no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—84no—
492C22×C11D4212yes—
493C22×C11C2×#13512yes—
494C22×C11C2×#13514yescomplemented
495C22×C11#57812yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—24no—
504C4×C11—22no—
505C4×C11—22no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11D4212yes—
509C4×C11C23×D411yescharacteristic
510C4×C11C2×H(5,𝔽2)11yescharacteristic
511Dic11—24no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—22no—
515C2×#41—24no—
516C2×#41—42no—
517C2×#41—114no—
518C2×#41—224no—
519C2×#41—222no—
520C2×#41—442no—
521C2×#41C22×D1114yes—
522C22×Q8—21no—
523C22×Q8—22no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—111no—
527C22×Q8—111no—
528C22×Q8—114no—
529C22×Q8—224no—
530C22×Q8—221no—
531C22×Q8—222no—
532C22×Q8—442no—
533C22×Q8C22×D1111yescharacteristic
534C22×Q8C22×D1114yes—
535C22×Q8C22×D1111yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—111no—
539C22×D4—221no—
540C22×D4—221no—
541C22×D4C22⋊D1111yescharacteristic
542C22×D4C22×D1111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—221no—
546C23×C4—221no—
547C23×C4C22×D1111yescharacteristic
548C23×C4C22×D1111yescharacteristic
549#135—2232no—
550C2×Q16—118no—
551C2×Q16—114no—
552C2×Q16—114no—
553C2×Q16—114no—
554C2×Q16—114no—
555C2×Q16—224no—
556C2×Q16—2232no—
557C2×Q16—224no—
558C2×Q16—224no—
559C2×SD16—114no—
560C2×SD16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—224no—
564C2×SD16—224no—
565C2×SD16—442no—
566C2×SD16—442no—
567C2×D8—114no—
568C2×D8—224no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—111no—
572C22×C8—114no—
573C22×C8—114no—
574C22×C8—111no—
575C22×C8—224no—
576C22×C8—224no—
577#124—28no—
578#124—22no—
579#124—114no—
580#124—228no—
581#124—222no—
582#124C22×D1114yes—
583C22⋊Q8—22no—
584C22⋊Q8—28no—
585C22⋊Q8—114no—
586C22⋊Q8—222no—
587C22⋊Q8—228no—
588C22⋊Q8C22×D1114yes—
589#121—28no—
590#121—22no—
591#121—114no—
592#121—228no—
593#121—222no—
594#121C22×D1114yes—
595C4×Q8—22no—
596C4×Q8—114no—
597C4×Q8—222no—
598C4×Q8C22×D1114yes—
599C4×D4—28no—
600C4×D4—228no—
601C4×D4C22⋊D1114yes—
602C4×D4C22×D1114yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4C22⋊D1111yescharacteristic
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C22⋊C4C22⋊D1111yescharacteristic
619C2×C22⋊C4C22⋊D1111yescharacteristic
620C2×C42—21no—
621C2×C42—221no—
622C2×C42C22×D1111yescharacteristic
623#107—114no—
624C4⋊C8—114no—
625#103—114no—
626#103—114no—
627#103—114no—
628#103—114no—
629#102—114no—
630#102—114no—
631C22⋊C8—114no—
632C22⋊C8—114no—
633C4×C8—114no—
634C2×C11—24no—
635C2×C11—42no—
636C2×C11—82no—
637C2×C11#328514yescomplemented
638C2×C11C2×D4211yescharacteristic
639C2×C11C22×#13511yescharacteristic
640C2×C11C2×#57811yescharacteristic
641D11—82no—
642C24—21no—
643C24—221no—
644C24C2×C22⋊D1111yescharacteristic
645C24C2×C22⋊D1111yescharacteristic
646#41—28no—
647#41—44no—
648#41—48no—
649#41—228no—
650#41—444no—
651#41—448no—
652C2×Q8—22no—
653C2×Q8—21no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—28no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—48no—
662C2×Q8—114no—
663C2×Q8—112no—
664C2×Q8—112no—
665C2×Q8—228no—
666C2×Q8—222no—
667C2×Q8—221no—
668C2×Q8—224no—
669C2×Q8—221no—
670C2×Q8—222no—
671C2×Q8—222no—
672C2×Q8—444no—
673C2×Q8—444no—
674C2×Q8—448no—
675C2×Q8D4×D1114yes—
676C2×Q8C23×D1112yes—
677C2×Q8C23×D1112yes—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—21no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—112no—
687C2×D4—224no—
688C2×D4—224no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—221no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4C2×C22⋊D1114yes—
695C2×D4C23×D1112yes—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—24no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—221no—
708C22×C4—224no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—224no—
712C22×C4—444no—
713C22×C4—444no—
714C22×C4C2×C22⋊D1112yes—
715C22×C4C2×C22⋊D1112yes—
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1111yescharacteristic
720C22×C4C23×D1112yes—
721C22×C4C23×D1112yes—
722C22×C4C23×D1111yescharacteristic
723Q16—1116no—
724Q16—228no—
725Q16—228no—
726Q16—228no—
727SD16—228no—
728SD16—228no—
729SD16—444no—
730SD16—444no—
731D8—228no—
732C2×C8—114no—
733C2×C8—112no—
734C2×C8—112no—
735C2×C8—112no—
736C2×C8—112no—
737C2×C8—228no—
738C2×C8—228no—
739C2×C8—222no—
740C2×C8—222no—
741C2×C8—222no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—112no—
746C4⋊C4—221no—
747C4⋊C4—224no—
748C4⋊C4—224no—
749C4⋊C4C2×C22⋊D1114yes—
750C4⋊C4C23×D1112yes—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4C2×C22⋊D1114yes—
760C22⋊C4C2×C22⋊D1114yes—
761C42—24no—
762C42—224no—
763C42C2×C22⋊D1112yes—
764C42C23×D1112yes—
765C11C2×#328511yescharacteristic, complemented, Sylow
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—222no—
776C23—442no—
777C23—442no—
778C23—442no—
779C23#6700314yescomplemented
780C23C22×C22⋊D1112yes—
781C23C22×C22⋊D1112yes—
782C23C22×C22⋊D1111yescharacteristic
783Q8—24no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—42no—
789Q8—114no—
790Q8—224no—
791Q8—222no—
792Q8—222no—
793Q8—222no—
794Q8—448no—
795Q8—442no—
796Q8C2×D4×D1114yes—
797D4—28no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—42no—
803D4—222no—
804D4—222no—
805D4—448no—
806D4—448no—
807D4—442no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—48no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—224no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—448no—
831C2×C4—448no—
832C2×C4—442no—
833C2×C4—442no—
834C2×C4C2×D4×D1112yes—
835C2×C4#6703712yes—
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1112yes—
838C2×C4C22×C22⋊D1112yes—
839C2×C4C22×C22⋊D1112yes—
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C24×D1111yescharacteristic
842C8—114no—
843C8—222no—
844C8—222no—
845C8—222no—
846C22—28no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—884no—
861C22D4×C22⋊D1112yes—
862C22C2×#6700312yes—
863C22C2×#6700314yescomplemented
864C22#1062336912yes—
865C22C23×C22⋊D1111yescharacteristic
866C4—22no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—22no—
871C4—42no—
872C4—42no—
873C4—224no—
874C4—442no—
875C4—442no—
876C4D4×C22⋊D1112yes—
877C4C22×D4×D1111yescharacteristic
878C4C2×#6703711yescharacteristic
879C2—24no—
880C2—42no—
881C2—82no—
882C2—882no—
883C2#1308035314yesdirect product factor
884C2C2×D4×C22⋊D1111yescharacteristic
885C2C22×#6700311yescharacteristic
886C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11C2×#3285
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C23×#4326C2semidirect
3. C2×#10623083C2semidirect
4. #13080353C2direct (N × H)
5. C2×#10622672C2semidirect
6. C2×#10622664C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622667C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622660C2semidirect
12. C2×#10622840C2semidirect
13. C2×#10622653C2semidirect
14. C2×C4×#4326C2semidirect
15. C2×D4×C11⋊C8C2semidirect
16. C2×C11×#548C2semidirect
22. C11×#548C22semidirect
33. C2×#67003C22semidirect
39. C22×#4326C22semidirect
51. #10623083C22semidirect
57. #10622852C22semidirect
58. #10622840C22semidirect
64. #10622672C22semidirect
65. #10622667C22semidirect
66. #10622664C22semidirect
67. #10622660C22semidirect
68. #10622653C22semidirect
69. #10622651C22semidirect
70. C4×#4326C22semidirect
71. #10622641C22semidirect
72. D4×C11⋊C8C22semidirect
146. C2×#4326D4semidirect
299. #4326C2×D4semidirect
326. C2×#548D11semidirect
348. C23×C11#135semidirect
441. #548C2×D11semidirect
494. C22×C11C2×#135semidirect
637. C2×C11#3285semidirect
765. C11C2×#3285semidirect
779. C23#67003semidirect
863. C22C2×#67003semidirect
883. C2#13080353direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670032
C23×#43262
C2×#106230832
#130803532
C2×#106226722
C2×#106226642
C2×#106226512
C2×#106226412
C2×#106226672
C2×#106228522
C2×#106226602
C2×#106228402
C2×#106226532
C2×C4×#43262
C2×D4×C11⋊C82
C2×C11×#5482
C2×#328511