Finite Group Databasebeta

← C2×#13080639 #15630317

Subgroups — C2×#13080639 #15630317

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic
3#13080639C2116yesmaximal, direct product factor
4C2×#10622326C211yesmaximal, characteristic, complemented
5C2×#10622350C211yesmaximal, characteristic, complemented
6C2×#10622349C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622727C211yesmaximal, characteristic, complemented
10C2×#10622461C211yesmaximal, characteristic, complemented
11C2×#10622344C211yesmaximal, characteristic, complemented
12C2×#10622344C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622744C211yesmaximal, characteristic, complemented
15C22×#66885C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66988—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66979C2211yescharacteristic, complemented
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C2×#66977C2211yescharacteristic, complemented
29C2×#66977C2211yescharacteristic, complemented
30C22×#4314C2211yescharacteristic
31C22×#4314C2211yescharacteristic, complemented
32C22×#4314C2211yescharacteristic, complemented
33D4×D44—24no—
34D4×D44C2218yes—
35#10623072—24no—
36#10623072C2218yescomplemented
37C2×#66948—21no—
38C2×#66942—21no—
39C2×#66935—21no—
40C2×#66935—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×#66927C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66923C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#435C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C11×#97C2211yescharacteristic, complemented
52#10622747C2218yescomplemented
53#10622744C2218yescomplemented
54#10622727C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2218yescomplemented
59C2×#66885C2211yescharacteristic, complemented
60C2×#66885C2211yescharacteristic, complemented
61C2×#66885C2211yescharacteristic, complemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66885C2211yescharacteristic, complemented
64C2×#66885C2211yescharacteristic, complemented
65C2×#66882C2211yescharacteristic, complemented
66C2×#66882C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68C2×#66880C2211yescharacteristic, complemented
69#10622461C2218yescomplemented
70#10622460C2218yescomplemented
71#10622350C2218yescomplemented
72#10622349C2218yescomplemented
73#10622344C2218yescomplemented
74#10622344C2218yescomplemented
75#10622326C2218yescomplemented
76#10622323C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C2×D4×D11—28no—
86C2×D4×D11—48no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—21no—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44—22no—
93C22×D44—22no—
94C22×D44—21no—
95C22×D44—42no—
96C22×D44—42no—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×D44C2314yes—
100C22×D44C2314yes—
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×Dic22C2311yescharacteristic
104C2×C11×M16—42no—
105C2×C11×M16C2314yescomplemented
106C22×C8×C11—42no—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2314yescomplemented
112C4×D4×C11D414yes—
113C4×D4×C11C2314yes—
114C2×C11×C4⋊C4D411yescharacteristic
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121#66988—28no—
122#66983—22no—
123#66983—22no—
124#66983C2314yes—
125#66983C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129#66979—22no—
130#66979C2314yescomplemented
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2314yescomplemented
138#66977—22no—
139#66977—22no—
140#66977C2314yescomplemented
141#66977C2314yescomplemented
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×#4314—24no—
150C2×#4314—42no—
151C2×#4314—42no—
152C2×#4314C2314yes—
153C2×#4314C2314yescomplemented
154C2×#4314C2314yescomplemented
155#66948—28no—
156#66942—28no—
157#66935—28no—
158#66935—28no—
159#66932—28no—
160#66930—28no—
161#66927—22no—
162#66927C2314yes—
163C4×D44—22no—
164C4×D44C2314yes—
165#66923—22no—
166#66923C2314yescomplemented
167C4×Dic22—22no—
168C4×Dic22C2314yescomplemented
169C11×C4⋊C8C2314yescomplemented
170C11×C22⋊C8C2314yescomplemented
171C11×C22⋊C8C2314yescomplemented
172C11×#97C2314yescomplemented
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yescomplemented
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179#66885C2314yescomplemented
180#66885C2314yescomplemented
181#66885C2314yescomplemented
182#66882C2314yescomplemented
183#66882C2314yescomplemented
184#66881C2314yescomplemented
185#66880C2314yescomplemented
186C2×#3310—111nomaximal, Sylow
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—82no—
199C23×D11—82no—
200C2×D4×C11—24no—
201C2×D4×C11C2×D414yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—44no—
226D4×D11—432no—
227C2×D44—28no—
228C2×D44—28no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—24no—
233C2×D44—24no—
234C2×D44—24no—
235C2×D44—24no—
236C2×D44—22no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—44no—
244C2×D44—44no—
245C2×D44—48no—
246C2×D44—48no—
247C2×D44—44no—
248C2×D44—82no—
249C2×D44#4114yes—
250C2×D44C2412yes—
251C2×D44C2412yes—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—44no—
255C2×Dic22—21no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22C2412yes—
259C11×M16—44no—
260C2×C8×C11—22no—
261C2×C8×C11—22no—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11—44no—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4C2×D414yes—
270C11×C22⋊C4C2×D414yes—
271C11×C22⋊C4C2×D414yes—
272C42×C11C2×D412yes—
273C42×C11C2412yes—
274C22⋊Dic11—24no—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—24no—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294C4×Dic11—24no—
295C4×Dic11—24no—
296#4314—28no—
297#4314—44no—
298#4314—44no—
299C2×#552—111no—
300C2×D42—111no—
301#3310—1116no—
302C2×#490—111no—
303C2×#482—111no—
304C2×#480—111no—
305C2×#478—111no—
306C2×#468—111no—
307C2×#465—111no—
308C2×#460—111no—
309C2×#450—111no—
310C2×#450—111no—
311C2×#440—111no—
312C2×#435D1111yescharacteristic, complemented
313C2×#418—111no—
314C22×#102—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11AGL(1,ℤ/8)14yes—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—48no—
329C22×D11—48no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—48no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—48no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—84no—
341C22×D11—84no—
342C22×D11—816no—
343C22×D11—816no—
344D4×C11—28no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—24no—
350C2×C4×C11—24no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4112yes—
361C2×C4×C11H(5,𝔽2)12yes—
362C2×C4×C11C2511yescharacteristic
363C22⋊D11—48no—
364C22⋊D11—48no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—48no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376D44—24no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—48no—
383D44—48no—
384D44—48no—
385D44—42no—
386D44—42no—
387D44—84no—
388D44C2×#4114yes—
389C4×D11—48no—
390Dic22—22no—
391Dic22—22no—
392Dic22—42no—
393C8×C11—22no—
394C8×C11—22no—
395C8×C11—22no—
396C8×C11—22no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4—221no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×M16C2×D1111yescharacteristic, complemented
404C23×C8C2×D1111yescharacteristic, complemented
405#552—118no—
406#552—224no—
407D42—118no—
408D42—224no—
409C2×#127—111no—
410C2×#126—221no—
411C2×#125—111no—
412C2×#125—221no—
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8—111no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—221no—
419C2×#120—221no—
420C2×#120—221no—
421C2×C4×Q8—111no—
422C2×C4×D4—111no—
423C2×C4×D4C2×D1111yescharacteristic
424C2×#117—111no—
425C2×#117—221no—
426C22×C4⋊C4—111no—
427#490—118no—
428#482—118no—
429#480—118no—
430#478—118no—
431#468—118no—
432#465—118no—
433#460—118no—
434#450—118no—
435#450—118no—
436#440—118no—
437#435C2×D1118yescomplemented
438C2×#107—111no—
439C2×#107—111no—
440C2×#106—111no—
441C2×C4⋊C8C2×D1111yescharacteristic, complemented
442#418—118no—
443C2×#103—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—118no—
454C2×C22⋊C8C2×D1111yescharacteristic, complemented
455C2×C22⋊C8C2×D1111yescharacteristic, complemented
456C2×#97C2×D1111yescharacteristic, complemented
457C22×C11—22no—
458C22×C11—28no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—44no—
464C22×C11#54612yes—
465C22×C11C2×AGL(1,ℤ/8)14yes—
466C22×C11C2×AGL(1,ℤ/8)12yes—
467C22×C11#57712yes—
468C22×C11C23×D411yescharacteristic
469C2×D11—24no—
470C2×D11—48no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—816no—
481C2×D11—84no—
482C2×D11—84no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11#54612yes—
488C4×C11C22×#4111yescharacteristic
489C4×C11C2×H(5,𝔽2)11yescharacteristic
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—221no—
496C25—221no—
497C22×Q8—111no—
498C22×D4—111no—
499C22×D4—111no—
500C22×D4—111no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—221no—
506C22×D4—221no—
507C22×D4—228no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—442no—
515C22×D4—442no—
516C22×D4—448no—
517C22×D4D4411yescharacteristic
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—114no—
525C2×SD16—224no—
526C2×SD16—442no—
527C2×SD16—442no—
528C2×M16—42no—
529C2×M16C22×D1114yescomplemented
530C22×C8—42no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1114yescomplemented
536#127—114no—
537#127—222no—
538#126—228no—
539#125—114no—
540#125—228no—
541#125—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—114no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547#121—114no—
548#121—114no—
549#121—222no—
550#121—222no—
551#121—228no—
552#120—228no—
553#120—228no—
554C4×Q8—114no—
555C4×Q8—222no—
556C4×D4—114no—
557C4×D4—222no—
558C4×D4D4414yes—
559C4×D4C22×D1114yes—
560#117—114no—
561#117—222no—
562#117—228no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—111no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C4⋊C4—221no—
574C2×C4⋊C4—221no—
575C2×C4⋊C4D4411yescharacteristic
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4D4411yescharacteristic
583C2×C22⋊C4D4411yescharacteristic
584C2×C42—221no—
585C2×C42—221no—
586C2×C42C22×D1111yescharacteristic
587#107—114no—
588#107—114no—
589#106—114no—
590C4⋊C8C22×D1114yescomplemented
591#103—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102—114no—
599#102—114no—
600#102—114no—
601C22⋊C8C22×D1114yescomplemented
602C22⋊C8C22×D1114yescomplemented
603#97C22×D1114yescomplemented
604C2×C11—24no—
605C2×C11—42no—
606C2×C11#331014yescomplemented
607C2×C11C2×#54611yescharacteristic
608C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
609C2×C11C2×#57711yescharacteristic
610D11—44no—
611D11—82no—
612D11—82no—
613C24—221no—
614C24—221no—
615C24—221no—
616C24—224no—
617C24—224no—
618C24—444no—
619C24—444no—
620C24—444no—
621C24—444no—
622C24—882no—
623C24—882no—
624C24C2×D4411yescharacteristic
625C24C2×D4411yescharacteristic
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×D4—24no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—228no—
636C2×D4—228no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—221no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—224no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—222no—
650C2×D4—222no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—448no—
654C2×D4—448no—
655C2×D4—444no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—4432no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—882no—
662C2×D4C2×D4414yes—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—224no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—224no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4C2×D4412yes—
677C22×C4C2×D4412yes—
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×D4411yescharacteristic
680C22×C4C2×D4411yescharacteristic
681C22×C4C2×D4411yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—228no—
686SD16—444no—
687SD16—444no—
688M16—44no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—44no—
694C2×C8C23×D1112yes—
695C2×C8C23×D1112yes—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—112no—
699C4⋊C4—112no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—224no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—224no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4C2×D4414yes—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4C2×D4414yes—
720C22⋊C4C2×D4414yes—
721C42—224no—
722C42—224no—
723C42C2×D4412yes—
724C42C23×D1112yes—
725C11C2×#331011yescharacteristic, complemented, Sylow
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—224no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—448no—
736C23—448no—
737C23—448no—
738C23—442no—
739C23—442no—
740C23—448no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—442no—
746C23—442no—
747C23—884no—
748C23—884no—
749C23—8816no—
750C23—8816no—
751C23#6696114yes—
752C23C22×D4412yes—
753C23C22×D4412yes—
754C23C22×D4411yescharacteristic
755Q8—222no—
756Q8—222no—
757Q8—442no—
758D4—28no—
759D4—114no—
760D4—224no—
761D4—222no—
762D4—222no—
763D4—222no—
764D4—222no—
765D4—222no—
766D4—448no—
767D4—448no—
768D4—448no—
769D4—448no—
770D4—448no—
771D4—442no—
772D4—442no—
773D4—884no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—448no—
790C2×C4—442no—
791C2×C4—448no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—442no—
796C2×C4C22×D4412yes—
797C2×C4C22×D4412yes—
798C2×C4C22×D4412yes—
799C2×C4C22×D4412yes—
800C2×C4C22×D4411yescharacteristic
801C2×C4#6703712yes—
802C2×C4#41×D1112yes—
803C2×C4C24×D1111yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—22no—
808C22—28no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—44no—
815C22—224no—
816C22—448no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—8816no—
826C22—8816no—
827C22—884no—
828C22—884no—
829C22#1062308512yes—
830C22C2×#6696114yes—
831C22C2×#6696112yes—
832C22#1062328212yes—
833C22C23×D4411yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—442no—
839C4—442no—
840C4—442no—
841C4—442no—
842C4—442no—
843C4#1062308512yes—
844C4C2×#6703711yescharacteristic
845C4C2×#41×D1111yescharacteristic
846C2—24no—
847C2—42no—
848C2—444no—
849C2—882no—
850C2—882no—
851C2#1308063914yesdirect product factor
852C2C2×#1062308511yescharacteristic
853C2C22×#6696111yescharacteristic
854C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenterC2×#435D11
hypocenterC11C2×#3310
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
3. #13080639C2direct (N × H)
4. C2×#10622326C2semidirect
5. C2×#10622350C2semidirect
6. C2×#10622349C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622727C2semidirect
10. C2×#10622461C2semidirect
11. C2×#10622344C2semidirect
12. C2×#10622344C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622744C2semidirect
15. C22×#66885C2semidirect
16. C2×C11×#435C2semidirect
20. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
26. C2×#66979C22semidirect
27. C22×C4⋊Dic11C22semidirect
28. C2×#66977C22semidirect
29. C2×#66977C22semidirect
31. C22×#4314C22semidirect
32. C22×#4314C22semidirect
36. #10623072C22semidirect
45. C2×#66923C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#435C22semidirect
48. C2×C11×C4⋊C8C22semidirect
49. C2×C11×C22⋊C8C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C11×#97C22semidirect
52. #10622747C22semidirect
53. #10622744C22semidirect
54. #10622727C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
60. C2×#66885C22semidirect
61. C2×#66885C22semidirect
62. C2×#66885C22semidirect
63. C2×#66885C22semidirect
64. C2×#66885C22semidirect
65. C2×#66882C22semidirect
66. C2×#66882C22semidirect
67. C2×#66881C22semidirect
68. C2×#66880C22semidirect
69. #10622461C22semidirect
70. #10622460C22semidirect
71. #10622350C22semidirect
72. #10622349C22semidirect
73. #10622344C22semidirect
74. #10622344C22semidirect
75. #10622326C22semidirect
76. #10622323C22semidirect
105. C2×C11×M16C23semidirect
111. C22×C8×C11C23semidirect
130. #66979C23semidirect
137. C2×C4⋊Dic11C23semidirect
140. #66977C23semidirect
141. #66977C23semidirect
153. C2×#4314C23semidirect
154. C2×#4314C23semidirect
166. #66923C23semidirect
168. C4×Dic22C23semidirect
169. C11×C4⋊C8C23semidirect
170. C11×C22⋊C8C23semidirect
171. C11×C22⋊C8C23semidirect
172. C11×#97C23semidirect
176. #66885C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. #66885C23semidirect
180. #66885C23semidirect
181. #66885C23semidirect
182. #66882C23semidirect
183. #66882C23semidirect
184. #66881C23semidirect
185. #66880C23semidirect
312. C2×#435D11semidirect
403. C22×M16C2×D11semidirect
404. C23×C8C2×D11semidirect
437. #435C2×D11semidirect
441. C2×C4⋊C8C2×D11semidirect
454. C2×C22⋊C8C2×D11semidirect
455. C2×C22⋊C8C2×D11semidirect
456. C2×#97C2×D11semidirect
529. C2×M16C22×D11semidirect
535. C22×C8C22×D11semidirect
590. C4⋊C8C22×D11semidirect
601. C22⋊C8C22×D11semidirect
602. C22⋊C8C22×D11semidirect
603. #97C22×D11semidirect
606. C2×C11#3310semidirect
725. C11C2×#3310semidirect
851. C2#13080639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×D4×D442
#130806392
C2×#106223262
C2×#106223502
C2×#106223492
C2×#106224602
C2×#106227472
C2×#106227272
C2×#106224612
C2×#106223442
C2×#106223232
C2×#106227442
C22×#668852
C2×C11×#4352
C2×#331011