Finite Group Databasebeta

← C2×#13080350 #15629031

Subgroups — C2×#13080350 #15629031

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×#66969C211yesmaximal, characteristic, complemented
2C23×#4326C211yesmaximal, characteristic, complemented
3C2×#10623348C211yesmaximal, characteristic, complemented
4C2×#10623129C211yesmaximal, characteristic, complemented
5#13080350C2116yesmaximal, direct product factor
6C2×#10622781C211yesmaximal, characteristic, complemented
7C2×#10622426C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622411C211yesmaximal, characteristic, complemented
10C2×#10622779C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622786C211yesmaximal, characteristic, complemented
13C2×#10622351C211yesmaximal, characteristic, complemented
14C2×#10622403C211yesmaximal, characteristic, complemented
15C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#448C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24#10623348—24no—
25#10623348C2218yescomplemented
26C2×#67000—21no—
27C2×#67000C2211yescharacteristic
28C2×#66999—21no—
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic
31C22×#4326—28no—
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C22×#4326C2211yescharacteristic
35C22×#4326C2211yescharacteristic
36C22×#4326C2218yescomplemented
37C2×#66992—21no—
38C2×#66989C2211yescharacteristic
39C2×D4×Dic11—21no—
40C22×#4323C2211yescharacteristic
41C2×#66983—21no—
42C2×#66983C2211yescharacteristic
43C2×C4×C22⋊D11—21no—
44C2×C4×C22⋊D11C2211yescharacteristic
45C23×C11⋊C8C2211yescharacteristic
46C2×#66969—28no—
47C2×#66969C2218yescomplemented
48C22×#4314C2211yescharacteristic
49C22×#4314C2211yescharacteristic
50C22×C8×D11C2211yescharacteristic
51#10623129—24no—
52#10623129C2218yescomplemented
53C2×#66950C2211yescharacteristic
54C2×#66940C2211yescharacteristic
55C2×#66938—21no—
56C2×#66931—21no—
57C11×#448C2218yescomplemented
58C2×C11×#103C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62#10622786C2218yescomplemented
63#10622781C2218yescomplemented
64#10622779C2218yescomplemented
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×Dic11⋊C8C2211yescharacteristic
69C2×C8×Dic11C2211yescharacteristic
70#10622651C2218yescomplemented
71C2×#66873C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73#10622426C2218yescomplemented
74#10622423C2218yescomplemented
75#10622411C2218yescomplemented
76#10622403C2218yescomplemented
77#10622351C2218yescomplemented
78(C22⋊D11)⋊C8C2218yescomplemented
79C22×Q8×C11—21no—
80C22×Q8×C11—22no—
81C22×Q8×C11—24no—
82C22×Q8×C11—42no—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2314yes—
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C23×Dic11—21no—
94C23×Dic11—21no—
95C2×#4343—22no—
96C2×#4343—24no—
97C2×#4343—42no—
98C2×#4343C2314yes—
99C2×#4341—22no—
100C2×#4341—24no—
101C2×#4341—42no—
102C2×#4341C2314yes—
103C22×D44—21no—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×Dic22—24no—
108C22×Dic22—21no—
109C22×Dic22—22no—
110C22×Dic22—42no—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2314yes—
113C22×Dic22C2311yescharacteristic
114C2×C11×SD16—24no—
115C2×C11×SD16—42no—
116C2×C11×SD16C2314yes—
117C2×C11×SD16C2314yes—
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2311yescharacteristic
120C11×#121—22no—
121C11×#121C2314yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#67000—28no—
128#67000—22no—
129#67000C2314yes—
130#66999—22no—
131#66999—28no—
132#66999C2314yes—
133Q8×Dic11—22no—
134Q8×Dic11C2314yes—
135C2×#4326—24no—
136C2×#4326—24no—
137C2×#4326—232no—
138C2×#4326—24no—
139C2×#4326D418yescomplemented
140C2×#4326C2314yes—
141C2×#4326C2314yes—
142C2×#4326C2314yes—
143C2×#4326C2314yes—
144#66992—28no—
145#66989—22no—
146#66989C2314yes—
147D4×Dic11—28no—
148C2×#4323—24no—
149C2×#4323C2314yes—
150#66983—22no—
151#66983—28no—
152#66983C2314yes—
153C4×C22⋊D11—28no—
154C4×C22⋊D11D414yes—
155C4×C22⋊D11C2314yes—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4D411yescharacteristic
162C2×C4⋊Dic11—21no—
163C2×C4⋊Dic11—21no—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4—21no—
167C2×Dic11⋊C4D411yescharacteristic
168C2×C4×Dic11—21no—
169C2×C4×Dic11—21no—
170C2×C4×Dic11C2311yescharacteristic
171C22×C11⋊C8—24no—
172C22×C11⋊C8C2311yescharacteristic
173C22×C11⋊C8C2314yes—
174C22×C11⋊C8C2311yescharacteristic
175#66969—232no—
176C2×#4314—24no—
177C2×#4314—42no—
178C2×#4314C2314yes—
179C2×#4314C2314yes—
180C2×C8×D11—24no—
181C2×C8×D11C2314yes—
182#66950—22no—
183#66950C2314yes—
184#66940—22no—
185#66940C2314yes—
186#66938—28no—
187#66931—28no—
188C11×#103C2314yes—
189C11×#103C2314yes—
190C11×C22⋊C8C2314yes—
191#66896C2314yes—
192(C2×D11)⋊C8C2314yes—
193#66880C2314yes—
194#66880C2314yes—
195Dic11⋊C8C2314yes—
196C8×Dic11C2314yes—
197#66873C2314yes—
198#66871C2314yes—
199C2×#3285—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11C2×D411yescharacteristic
204C2×Q8×C11—21no—
205C2×Q8×C11—24no—
206C2×Q8×C11—21no—
207C2×Q8×C11—22no—
208C2×Q8×C11—28no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—44no—
212C2×Q8×C11—44no—
213C2×Q8×C11—48no—
214C2×Q8×C11C2×D414yes—
215C2×Q8×C11C2412yes—
216C2×Q8×C11C2412yes—
217C2×D4×C11—24no—
218C2×D4×C11—22no—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—44no—
222C2×D4×C11C2412yes—
223C22×C4×C11—21no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—24no—
229C22×C4×C11—44no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2411yescharacteristic
234C2×C22⋊D11—24no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11C2×D414yes—
240C22×Dic11—24no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—24no—
245C22×Dic11—44no—
246C22×Dic11—44no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249C22×Dic11C2×D411yescharacteristic
250#4343—28no—
251#4343—44no—
252#4343—48no—
253#4341—28no—
254#4341—44no—
255#4341—48no—
256C2×D44—24no—
257C2×D44—21no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—44no—
261C2×D44C2412yes—
262C2×C4×D11—24no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—44no—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2412yes—
268C2×Dic22—28no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—24no—
272C2×Dic22—21no—
273C2×Dic22—22no—
274C2×Dic22—22no—
275C2×Dic22—44no—
276C2×Dic22—48no—
277C2×Dic22—44no—
278C2×Dic22C2×D414yes—
279C2×Dic22C2412yes—
280C2×Dic22C2412yes—
281C11×SD16—28no—
282C11×SD16—44no—
283C2×C8×C11—22no—
284C2×C8×C11—22no—
285C2×C8×C11C2412yes—
286C2×C8×C11C2412yes—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C22⋊C4—24no—
290C22⋊Dic11—24no—
291C22⋊Dic11—24no—
292C22⋊Dic11C2×D414yes—
293#4326—28no—
294#4326—28no—
295#4326—28no—
296#4326C2×D4116yescomplemented
297#4323—28no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4C2×D414yes—
304C4⋊Dic11—24no—
305C4⋊Dic11—24no—
306C4⋊Dic11—21no—
307C4⋊Dic11C2412yes—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4C2×D414yes—
311C4×Dic11—24no—
312C4×Dic11—24no—
313C4×Dic11C2×D412yes—
314C4×Dic11C2412yes—
315C2×C11⋊C8—28no—
316C2×C11⋊C8—22no—
317C2×C11⋊C8C2×D414yes—
318C2×C11⋊C8C2412yes—
319C2×C11⋊C8C2412yes—
320#4314—28no—
321#4314—44no—
322C8×D11—28no—
323C22×#135—111no—
324C23×Q16—111no—
325C2×#548—111no—
326C2×#548—111no—
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×#448D1111yescharacteristic, complemented
337C2×C4×Q16—111no—
338C2×C8×D4—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11#13514yescomplemented
346C23×C11C22×D412yes—
347C23×C11C22×D411yescharacteristic
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11C22×D412yes—
356Q8×C11—24no—
357Q8×C11—22no—
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—48no—
361Q8×C11—42no—
362Q8×C11C22×D414yes—
363D4×C11—22no—
364D4×C11—22no—
365D4×C11—48no—
366D4×C11—42no—
367C2×C4×C11—22no—
368C2×C4×C11—24no—
369C2×C4×C11—22no—
370C2×C4×C11—24no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—48no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D412yes—
381C2×C4×C11H(5,𝔽2)12yes—
382C2×C4×C11C2511yescharacteristic
383C22⋊D11—28no—
384C22⋊D11—48no—
385C22⋊D11—48no—
386C2×Dic11—24no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—48no—
394C2×Dic11—48no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11C22×D412yes—
398C2×Dic11C22×D412yes—
399C2×Dic11C22×D412yes—
400D44—22no—
401D44—22no—
402D44—48no—
403D44—42no—
404C4×D11—24no—
405C4×D11—22no—
406C4×D11—22no—
407C4×D11—48no—
408Dic22—24no—
409Dic22—22no—
410Dic22—22no—
411Dic22—22no—
412Dic22—48no—
413Dic22—42no—
414Dic22C22×D414yes—
415C8×C11—22no—
416C8×C11—22no—
417C11⋊C8—22no—
418C11⋊C8C22×D414yes—
419C22×#41—111no—
420C22×#41—111no—
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×SD16C2×D1111yescharacteristic
434C22×SD16C2×D1111yescharacteristic
435C22×D8—111no—
436C23×C8—111no—
437C23×C8—111no—
438#548—118no—
439#548—118no—
440#548—224no—
441#548—224no—
442C2×#124—111no—
443C2×#124—111no—
444C2×#124—221no—
445C2×#124—221no—
446C2×C22⋊Q8—111no—
447C2×C22⋊Q8—111no—
448C2×C22⋊Q8—221no—
449C2×C22⋊Q8—221no—
450C2×#121—111no—
451C2×#121—221no—
452C2×#121—221no—
453C2×#121C2×D1111yescharacteristic
454C2×C4×Q8—111no—
455C2×C4×Q8—111no—
456C2×C4×D4—111no—
457C2×C4×D4—221no—
458C2×C4×D4—221no—
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#448C2×D1118yescomplemented
468C4×Q16—118no—
469C8×D4—118no—
470C2×#107—111no—
471C2×C4⋊C8—111no—
472C2×#103—111no—
473C2×#103—111no—
474C2×#103C2×D1111yescharacteristic
475C2×#103C2×D1111yescharacteristic
476C2×#102—111no—
477C2×#102—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8C2×D1111yescharacteristic
480C2×C4×C8—111no—
481C22×C11—22no—
482C22×C11—28no—
483C22×C11—22no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—84no—
488C22×C11D4212yes—
489C22×C11C2×#13512yes—
490C22×C11C2×#13514yescomplemented
491C22×C11#57812yes—
492C22×C11C23×D411yescharacteristic
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—44no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11D4212yes—
506C4×C11C23×D411yescharacteristic
507C4×C11C2×H(5,𝔽2)11yescharacteristic
508Dic11—24no—
509Dic11—22no—
510Dic11—22no—
511Dic11—22no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—222no—
518C2×#41—224no—
519C2×#41—224no—
520C2×#41—442no—
521C2×#41—442no—
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—111no—
538C22×D4—111no—
539C22×D4—221no—
540C22×D4—221no—
541C22×D4—221no—
542C22×D4C22×D1111yescharacteristic
543C23×C4—21no—
544C23×C4—111no—
545C23×C4—221no—
546C23×C4—221no—
547C23×C4—221no—
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—24no—
560C2×SD16—42no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—224no—
564C2×SD16—442no—
565C2×SD16C22×D1114yes—
566C2×SD16C22×D1114yes—
567C2×D8—114no—
568C2×D8—224no—
569C22×C8—111no—
570C22×C8—111no—
571C22×C8—114no—
572C22×C8—114no—
573C22×C8—224no—
574C22×C8—224no—
575C22×C8C22×D1111yescharacteristic
576C22×C8C22×D1111yescharacteristic
577#124—114no—
578#124—114no—
579#124—222no—
580#124—222no—
581#124—228no—
582#124—228no—
583C22⋊Q8—114no—
584C22⋊Q8—114no—
585C22⋊Q8—228no—
586C22⋊Q8—222no—
587C22⋊Q8—228no—
588C22⋊Q8—222no—
589#121—22no—
590#121—114no—
591#121—228no—
592#121—228no—
593#121—222no—
594#121C22×D1114yes—
595C4×Q8—114no—
596C4×Q8—114no—
597C4×Q8—222no—
598C4×Q8—222no—
599C4×D4—114no—
600C4×D4—114no—
601C4×D4—228no—
602C4×D4—228no—
603C2×C4⋊C4—111no—
604C2×C4⋊C4—111no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—111no—
612C2×C22⋊C4—111no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C22⋊C4—221no—
619C2×C22⋊C4—221no—
620C2×C42—111no—
621C2×C42—221no—
622C2×C42—221no—
623#107—114no—
624C4⋊C8—114no—
625#103—114no—
626#103—114no—
627#103C22×D1114yes—
628#103C22×D1114yes—
629#102—114no—
630#102—114no—
631C22⋊C8—114no—
632C22⋊C8C22×D1114yes—
633C4×C8—114no—
634C2×C11—24no—
635C2×C11—82no—
636C2×C11#328514yescomplemented
637C2×C11C2×D4211yescharacteristic
638C2×C11C22×#13511yescharacteristic
639C2×C11C2×#57811yescharacteristic
640D11—42no—
641D11—82no—
642C24—21no—
643C24—111no—
644C24—221no—
645C24D4×D1111yescharacteristic
646#41—228no—
647#41—228no—
648#41—444no—
649#41—448no—
650#41—444no—
651#41—448no—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—21no—
655C2×Q8—22no—
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—221no—
667C2×Q8—224no—
668C2×Q8—221no—
669C2×Q8—222no—
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—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—44no—
683C2×D4—114no—
684C2×D4—112no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—224no—
689C2×D4—222no—
690C2×D4—221no—
691C2×D4—222no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4C23×D1112yes—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—44no—
703C22×C4—111no—
704C22×C4—111no—
705C22×C4—111no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—224no—
709C22×C4—224no—
710C22×C4—221no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—224no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—444no—
717C22×C4—444no—
718C22×C4—444no—
719C22×C4D4×D1112yes—
720C22×C4D4×D1111yescharacteristic
721C22×C4C23×D1112yes—
722C22×C4C23×D1111yescharacteristic
723Q16—1116no—
724Q16—228no—
725Q16—228no—
726Q16—228no—
727SD16—28no—
728SD16—44no—
729SD16—228no—
730SD16—444no—
731D8—228no—
732C2×C8—22no—
733C2×C8—22no—
734C2×C8—114no—
735C2×C8—112no—
736C2×C8—112no—
737C2×C8—228no—
738C2×C8—228no—
739C2×C8—222no—
740C2×C8C23×D1112yes—
741C2×C8C23×D1112yes—
742C4⋊C4—21no—
743C4⋊C4—114no—
744C4⋊C4—112no—
745C4⋊C4—224no—
746C4⋊C4—224no—
747C4⋊C4—224no—
748C4⋊C4—224no—
749C4⋊C4—221no—
750C4⋊C4C23×D1112yes—
751C22⋊C4—24no—
752C22⋊C4—114no—
753C22⋊C4—114no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C42—112no—
762C42—112no—
763C42—224no—
764C42—224no—
765C11C2×#328511yescharacteristic, complemented, Sylow
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—112no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—442no—
778C23—442no—
779C23—442no—
780C23#6696914yescomplemented
781C23C2×D4×D1112yes—
782C23C2×D4×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—22no—
798D4—22no—
799D4—48no—
800D4—42no—
801D4—228no—
802D4—222no—
803D4—222no—
804D4—448no—
805D4—448no—
806D4—448no—
807D4—442no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—48no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—112no—
820C2×C4—112no—
821C2×C4—112no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—224no—
826C2×C4—222no—
827C2×C4—224no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—448no—
833C2×C4—448no—
834C2×C4—448no—
835C2×C4—442no—
836C2×C4—442no—
837C2×C4C2×D4×D1112yes—
838C2×C4C2×D4×D1111yescharacteristic
839C2×C4C2×D4×D1112yes—
840C2×C4#6703712yes—
841C2×C4C24×D1111yescharacteristic
842C8—22no—
843C8—22no—
844C8—114no—
845C8—222no—
846C22—28no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—444no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—884no—
861C22#1062312112yes—
862C22C2×#6696912yes—
863C22C2×#6696914yescomplemented
864C22#1062331012yes—
865C22C22×D4×D1111yescharacteristic
866C4—22no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—222no—
871C4—224no—
872C4—222no—
873C4—222no—
874C4—442no—
875C4—442no—
876C4#1062312112yes—
877C4C22×D4×D1111yescharacteristic
878C4C2×#6703711yescharacteristic
879C2—24no—
880C2—82no—
881C2—442no—
882C2—882no—
883C2#1308035014yesdirect product factor
884C2C2×#1062312111yescharacteristic
885C2C22×#6696911yescharacteristic
886C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
hypercenterC2×#448D11
hypocenterC11C2×#3285
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C23×#4326C2semidirect
3. C2×#10623348C2semidirect
4. C2×#10623129C2semidirect
5. #13080350C2direct (N × H)
6. C2×#10622781C2semidirect
7. C2×#10622426C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622411C2semidirect
10. C2×#10622779C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622786C2semidirect
13. C2×#10622351C2semidirect
14. C2×#10622403C2semidirect
15. C2×(C22⋊D11)⋊C8C2semidirect
16. C2×C11×#448C2semidirect
25. #10623348C22semidirect
36. C22×#4326C22semidirect
47. C2×#66969C22semidirect
52. #10623129C22semidirect
57. C11×#448C22semidirect
62. #10622786C22semidirect
63. #10622781C22semidirect
64. #10622779C22semidirect
70. #10622651C22semidirect
73. #10622426C22semidirect
74. #10622423C22semidirect
75. #10622411C22semidirect
76. #10622403C22semidirect
77. #10622351C22semidirect
78. (C22⋊D11)⋊C8C22semidirect
139. C2×#4326D4semidirect
296. #4326C2×D4semidirect
336. C2×#448D11semidirect
345. C23×C11#135semidirect
467. #448C2×D11semidirect
490. C22×C11C2×#135semidirect
636. C2×C11#3285semidirect
765. C11C2×#3285semidirect
780. C23#66969semidirect
863. C22C2×#66969semidirect
883. C2#13080350direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C23×#43262
C2×#106233482
C2×#106231292
#130803502
C2×#106227812
C2×#106224262
C2×#106226512
C2×#106224112
C2×#106227792
C2×#106224232
C2×#106227862
C2×#106223512
C2×#106224032
C2×(C22⋊D11)⋊C82
C2×C11×#4482
C2×#328511