Finite Group Databasebeta

← C2×#13080185 #15628817

Subgroups — C2×#13080185 #15628817

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic, complemented
2C22×Q16×D11C211yesmaximal, characteristic, complemented
3C2×#10623258C211yesmaximal, characteristic, complemented
4C2×#10623208C211yesmaximal, characteristic
5#13080185C2116yesmaximal, direct product factor
6C2×#10622802C211yesmaximal, characteristic, complemented
7C2×#10622784C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622786C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622799C211yesmaximal, characteristic, complemented
13C2×#10622783C211yesmaximal, characteristic, complemented
14C2×#10622329C211yesmaximal, characteristic, complemented
15C2×#10622319C211yesmaximal, characteristic, complemented
16C2×C11×#497C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic
20C22×#4341C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic
22C22×C11×Q16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#124C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C2×Q16×D11—28no—
36C2×Q16×D11C2218yescomplemented
37C2×#66968—28no—
38C2×#66968C2218yescomplemented
39C22×Dic44C2211yescharacteristic
40C22×#4313C2211yescharacteristic
41C22×C8×D11C2211yescharacteristic
42#10623258—24no—
43#10623258C2218yescomplemented
44#10623208—24no—
45#10623208C2218yes—
46C2×#66949—21no—
47C2×#66949—21no—
48C2×#66946—21no—
49C2×#66941—21no—
50C2×#66938—21no—
51C2×#66937—21no—
52C2×(C22⋊D11)⋊C4—21no—
53C2×#66931—21no—
54C2×C4×D44C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57C11×#497C2218yescomplemented
58C2×C11×#97C2211yescharacteristic
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62C2×#66896C2211yescharacteristic
63#10622802C2218yescomplemented
64#10622799C2218yescomplemented
65#10622799C2218yescomplemented
66#10622786C2218yescomplemented
67#10622784C2218yescomplemented
68#10622783C2218yescomplemented
69C2×(C2×D11)⋊C8C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71C2×#66881C2211yescharacteristic
72C2×#66880C2211yescharacteristic
73C2×#66880C2211yescharacteristic
74#10622703C2218yescomplemented
75#10622667C2218yescomplemented
76C2×C4⋊(C11⋊C8)C2211yescharacteristic
77#10622329C2218yescomplemented
78#10622319C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C2×Q8×D11—22no—
87C2×Q8×D11—22no—
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—24no—
91C2×Q8×D11—24no—
92C2×Q8×D11—42no—
93C2×Q8×D11—42no—
94C2×Q8×D11—42no—
95C2×Q8×D11C2314yes—
96C2×Q8×D11C2314yes—
97C2×Q8×D11C2314yes—
98C2×#4341—22no—
99C2×#4341—24no—
100C2×#4341—42no—
101C2×#4341C2314yes—
102C22×D44D411yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11—21no—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×Dic22—21no—
109C22×Dic22—21no—
110C22×Dic22—21no—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2311yescharacteristic
113C2×C11×Q16—24no—
114C2×C11×Q16—42no—
115C2×C11×Q16C2314yes—
116C2×C11×Q16C2314yes—
117C2×C11×SD16—24no—
118C2×C11×SD16—42no—
119C2×C11×SD16C2314yes—
120C2×C11×SD16C2314yes—
121C22×C8×C11C2311yescharacteristic
122C22×C8×C11C2311yescharacteristic
123C11×C4⋊Q8—22no—
124C11×C4⋊Q8C2314yes—
125C11×#124—22no—
126C11×#124C2314yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C42×C11C2311yescharacteristic
132C2×C22⋊Dic11—21no—
133#66999—22no—
134#66999—22no—
135#66999—22no—
136#66999C2314yes—
137#66999C2314yes—
138#66999C2314yes—
139C2×#4326—24no—
140C2×#4326—24no—
141C2×#4326—24no—
142C2×#4326C2314yes—
143C2×#4326C2314yes—
144C2×#4326C2314yes—
145#66991—22no—
146#66991C2314yes—
147C2×#4324—24no—
148C2×#4324C2314yes—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4D411yescharacteristic
153C2×(C2×D11)⋊C4D411yescharacteristic
154C2×C4⋊Dic11D411yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×C4×Dic11—21no—
163C2×C4×Dic11—21no—
164C22×C11⋊C8C2311yescharacteristic
165C22×C11⋊C8C2311yescharacteristic
166Q16×D11—232no—
167#66968—232no—
168C2×Dic44D418yescomplemented
169C2×Dic44C2314yes—
170C2×#4313—24no—
171C2×#4313C2314yes—
172C2×C8×D11—24no—
173C2×C8×D11C2314yes—
174#66949—28no—
175#66949—28no—
176#66946—28no—
177#66941—28no—
178#66938—28no—
179#66937—28no—
180(C22⋊D11)⋊C4—28no—
181#66931—28no—
182C4×D44D414yes—
183C4×D44C2314yes—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22C2314yes—
187C4×Dic22C2314yes—
188C11×#97C2314yes—
189#66899C2314yes—
190#66899C2314yes—
191#66899C2314yes—
192#66896C2314yes—
193(C2×D11)⋊C8C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66881C2314yes—
196#66880C2314yes—
197#66880C2314yes—
198C4⋊(C11⋊C8)C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11—21no—
201C23×D11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C2×Q8×C11—21no—
204C2×Q8×C11—21no—
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×Q8×C11C2412yes—
214C2×Q8×C11C2412yes—
215C2×D4×C11—22no—
216C2×D4×C11—21no—
217C2×D4×C11—22no—
218C2×D4×C11C2412yes—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—44no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237Q8×D11—28no—
238Q8×D11—28no—
239Q8×D11—28no—
240Q8×D11—44no—
241Q8×D11—44no—
242Q8×D11—44no—
243Q8×D11—48no—
244Q8×D11—48no—
245Q8×D11—48no—
246#4341—28no—
247#4341—44no—
248#4341—48no—
249C2×D44—24no—
250C2×D44C2×D414yes—
251C2×C4×D11—24no—
252C2×C4×D11—24no—
253C2×C4×D11—24no—
254C2×C4×D11—22no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2412yes—
264C2×C4×D11C2412yes—
265C2×Dic22—24no—
266C2×Dic22—24no—
267C2×Dic22—24no—
268C2×Dic22—21no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22—44no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22C2×D414yes—
276C2×Dic22C2×D414yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×Q16—28no—
280C11×Q16—44no—
281C11×SD16—28no—
282C11×SD16—44no—
283C2×C8×C11—22no—
284C2×C8×C11C2×D414yes—
285C2×C8×C11C2412yes—
286C2×C8×C11C2412yes—
287C11×C4⋊C4—24no—
288C11×C4⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C42×C11C2×D412yes—
292C42×C11C2412yes—
293C22⋊Dic11—24no—
294#4326—28no—
295#4326—28no—
296#4326—28no—
297#4324—28no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4C2×D414yes—
302(C2×D11)⋊C4C2×D414yes—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11C2×D414yes—
306C4⋊Dic11C2412yes—
307C4⋊Dic11C2412yes—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313C4×Dic11—24no—
314C4×Dic11—24no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8—22no—
317C2×C11⋊C8C2412yes—
318C2×C11⋊C8C2412yes—
319Dic44C2×D4116yescomplemented
320#4313—28no—
321C8×D11—28no—
322C22×#137—111no—
323C23×Q16—111no—
324C2×D4×Q8—111no—
325C2×#548—111no—
326#3270—1116no—
327C2×#497D1111yescharacteristic, complemented
328C2×#470—111no—
329C2×#465—111no—
330C2×#464—111no—
331C2×#462—111no—
332C2×#452—111no—
333C2×#451—111no—
334C2×#451—111no—
335C2×#448—111no—
336C2×#441—111no—
337C2×#435—111no—
338C23×C11—22no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11C22×D411yescharacteristic
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11#13714yescomplemented
349C22×D11C22×D412yes—
350C22×D11C22×D412yes—
351Q8×C11—22no—
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—22no—
357Q8×C11—42no—
358Q8×C11—42no—
359Q8×C11—42no—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—42no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D412yes—
375C2×C4×C11H(5,𝔽2)12yes—
376C2×C4×C11C2511yescharacteristic
377C22⋊D11—48no—
378C22⋊D11—48no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—48no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392D44—28no—
393C4×D11—24no—
394C4×D11—24no—
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400C4×D11—48no—
401C4×D11—48no—
402Dic22—24no—
403Dic22—24no—
404Dic22—22no—
405Dic22—22no—
406Dic22—48no—
407Dic22—48no—
408Dic22—48no—
409Dic22C22×D414yes—
410Dic22C22×D414yes—
411C8×C11—22no—
412C8×C11C22×D414yes—
413C11⋊C8—22no—
414C11⋊C8—22no—
415C22×#41—111no—
416C23×Q8—111no—
417C23×Q8—111no—
418C23×Q8—111no—
419C2×#137—118no—
420C2×#137—228no—
421C22×Q16—111no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16—118no—
425C22×Q16—111no—
426C22×Q16—228no—
427C22×Q16C2×D1111yescharacteristic
428C22×Q16C2×D1111yescharacteristic
429C22×SD16—111no—
430C22×SD16C2×D1111yescharacteristic
431C22×SD16C2×D1111yescharacteristic
432C22×M16—111no—
433C23×C8—111no—
434D4×Q8—118no—
435D4×Q8—224no—
436#548—118no—
437#548—224no—
438C2×C4⋊Q8—221no—
439C2×C4⋊Q8C2×D1111yescharacteristic
440C2×#124—221no—
441C2×#124C2×D1111yescharacteristic
442C2×C22⋊Q8—111no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—221no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8—221no—
448C2×#121—111no—
449C2×#121—221no—
450C2×C4×Q8—111no—
451C2×C4×Q8—111no—
452C2×C4×D4—111no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455#497C2×D1118yescomplemented
456#470—118no—
457#465—118no—
458#464—118no—
459#462—118no—
460#452—118no—
461#451—118no—
462#451—118no—
463#448—118no—
464#441—118no—
465#435—118no—
466C2×#106—111no—
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#102—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×#97C2×D1111yescharacteristic
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—84no—
481C22×C11D4212yes—
482C22×C11C2×#13712yes—
483C22×C11#57812yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—22no—
486C2×D11—28no—
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—44no—
492C2×D11C2×#13714yescomplemented
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11D4212yes—
499C4×C11C23×D411yescharacteristic
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501Dic11—24no—
502Dic11—24no—
503Dic11—22no—
504Dic11—22no—
505Dic11—42no—
506Dic11—42no—
507C2×#41—114no—
508C2×#41—222no—
509C2×#41—224no—
510C2×#41—442no—
511C22×Q8—114no—
512C22×Q8—114no—
513C22×Q8—114no—
514C22×Q8—111no—
515C22×Q8—111no—
516C22×Q8—221no—
517C22×Q8—221no—
518C22×Q8—221no—
519C22×Q8—222no—
520C22×Q8—222no—
521C22×Q8—222no—
522C22×Q8—224no—
523C22×Q8—224no—
524C22×Q8—224no—
525C22×Q8—442no—
526C22×Q8—442no—
527C22×Q8—442no—
528C22×Q8C22×D1111yescharacteristic
529C22×Q8C22×D1111yescharacteristic
530C22×Q8C22×D1111yescharacteristic
531C22×D4—111no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4C22×D1111yescharacteristic
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4—221no—
540C23×C4—221no—
541#137—2232no—
542C2×Q16—24no—
543C2×Q16—42no—
544C2×Q16—114no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—118no—
548C2×Q16—114no—
549C2×Q16—2232no—
550C2×Q16—224no—
551C2×Q16—224no—
552C2×Q16—224no—
553C2×Q16C22×D1114yes—
554C2×Q16C22×D1114yes—
555C2×SD16—24no—
556C2×SD16—42no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16C22×D1114yes—
560C2×SD16C22×D1114yes—
561C2×M16—114no—
562C2×M16—224no—
563C22×C8—111no—
564C22×C8—111no—
565C22×C8—114no—
566C22×C8—224no—
567C22×C8C22×D1111yescharacteristic
568C22×C8C22×D1111yescharacteristic
569C4⋊Q8—22no—
570C4⋊Q8—228no—
571C4⋊Q8C22×D1114yes—
572#124—22no—
573#124—228no—
574#124C22×D1114yes—
575C22⋊Q8—114no—
576C22⋊Q8—114no—
577C22⋊Q8—114no—
578C22⋊Q8—228no—
579C22⋊Q8—228no—
580C22⋊Q8—228no—
581C22⋊Q8—222no—
582C22⋊Q8—222no—
583C22⋊Q8—222no—
584#121—114no—
585#121—228no—
586#121—222no—
587C4×Q8—114no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×D4—114no—
592C4×D4—114no—
593C4×D4—228no—
594C4×D4—228no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—111no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—111no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C42—221no—
614C2×C42—221no—
615C2×C42C22×D1111yescharacteristic
616#106—114no—
617C4⋊C8—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103—114no—
623#102—114no—
624C22⋊C8—114no—
625C22⋊C8—114no—
626#97C22×D1114yes—
627C2×C11—82no—
628C2×C11#327014yescomplemented
629C2×C11C2×D4211yescharacteristic
630C2×C11C22×#13711yescharacteristic
631C2×C11C2×#57811yescharacteristic
632D11—24no—
633D11—42no—
634C24—21no—
635C24—111no—
636C24—111no—
637#41—228no—
638#41—444no—
639#41—448no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—114no—
650C2×Q8—114no—
651C2×Q8—112no—
652C2×Q8—112no—
653C2×Q8—224no—
654C2×Q8—224no—
655C2×Q8—224no—
656C2×Q8—221no—
657C2×Q8—221no—
658C2×Q8—222no—
659C2×Q8—222no—
660C2×Q8—228no—
661C2×Q8—228no—
662C2×Q8—228no—
663C2×Q8—444no—
664C2×Q8—444no—
665C2×Q8—444no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—444no—
669C2×Q8—448no—
670C2×Q8—448no—
671C2×Q8—448no—
672C2×Q8C23×D1112yes—
673C2×Q8C23×D1112yes—
674C2×Q8C23×D1112yes—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—114no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—224no—
682C2×D4—444no—
683C2×D4—444no—
684C2×D4C23×D1112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—111no—
689C22×C4—111no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—224no—
695C22×C4—224no—
696C22×C4—224no—
697C22×C4—224no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4—444no—
710C22×C4D4×D1111yescharacteristic
711C22×C4D4×D1111yescharacteristic
712C22×C4C23×D1111yescharacteristic
713Q16—28no—
714Q16—44no—
715Q16—1116no—
716Q16—228no—
717Q16—228no—
718Q16—228no—
719SD16—28no—
720SD16—44no—
721SD16—228no—
722M16—228no—
723C2×C8—22no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—222no—
727C2×C8—222no—
728C2×C8—228no—
729C2×C8D4×D1114yes—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—114no—
735C4⋊C4—112no—
736C4⋊C4—112no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—221no—
741C4⋊C4—221no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—114no—
747C22⋊C4—114no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C42—224no—
753C42—224no—
754C42D4×D1112yes—
755C42C23×D1112yes—
756C11C2×#327011yescharacteristic, complemented, Sylow
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—114no—
762C23—112no—
763C23—112no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23C2×D4×D1111yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8—114no—
780Q8—114no—
781Q8—224no—
782Q8—224no—
783Q8—222no—
784Q8—222no—
785Q8—448no—
786Q8—448no—
787Q8—448no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—228no—
792D4—448no—
793D4—448no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—112no—
803C2×C4—112no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—224no—
807C2×C4—224no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—448no—
819C2×C4—448no—
820C2×C4—448no—
821C2×C4—448no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4C2×D4×D1112yes—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1111yescharacteristic
827C2×C4C2×D4×D1112yes—
828C2×C4#6703712yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—222no—
832C8—222no—
833C8C2×D4×D1114yes—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—84no—
838C22—114no—
839C22—228no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—222no—
845C22—444no—
846C22#1062324812yes—
847C22D11×#13712yes—
848C22#1062331012yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—222no—
856C4—222no—
857C4—224no—
858C4—224no—
859C4—442no—
860C4—442no—
861C4#1062324812yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6703711yescharacteristic
864C2—82no—
865C2—224no—
866C2—442no—
867C2#1308018514yesdirect product factor
868C2C2×#1062324811yescharacteristic
869C2C2×D11×#13711yescharacteristic
870C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC2×#10623208C2
hypercenterC2×#497D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C22×Q16×D11C2semidirect
3. C2×#10623258C2semidirect
5. #13080185C2direct (N × H)
6. C2×#10622802C2semidirect
7. C2×#10622784C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622703C2semidirect
10. C2×#10622786C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622799C2semidirect
13. C2×#10622783C2semidirect
14. C2×#10622329C2semidirect
15. C2×#10622319C2semidirect
16. C2×C11×#497C2semidirect
36. C2×Q16×D11C22semidirect
38. C2×#66968C22semidirect
43. #10623258C22semidirect
57. C11×#497C22semidirect
63. #10622802C22semidirect
64. #10622799C22semidirect
65. #10622799C22semidirect
66. #10622786C22semidirect
67. #10622784C22semidirect
68. #10622783C22semidirect
74. #10622703C22semidirect
75. #10622667C22semidirect
77. #10622329C22semidirect
78. #10622319C22semidirect
168. C2×Dic44D4semidirect
319. Dic44C2×D4semidirect
327. C2×#497D11semidirect
348. C22×D11#137semidirect
455. #497C2×D11semidirect
492. C2×D11C2×#137semidirect
628. C2×C11#3270semidirect
756. C11C2×#3270semidirect
867. C2#13080185direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C22×Q16×D112
C2×#106232582
C2×#106232082
#130801852
C2×#106228022
C2×#106227842
C2×#106226672
C2×#106227032
C2×#106227862
C2×#106227992
C2×#106227832
C2×#106223292
C2×#106223192
C2×C11×#4972
C2×#327011