Finite Group Databasebeta

← C2×#13080941 #15630704

Subgroups — C2×#13080941 #15630704

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623130C211yesmaximal, characteristic, complemented
2C2×#10623038C211yesmaximal, characteristic, complemented
3#13080941C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622467C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622399C211yesmaximal, characteristic, complemented
10C2×#10622347C211yesmaximal, characteristic, complemented
11C2×#10622394C211yesmaximal, characteristic, complemented
12C2×#10622465C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C2×#10622384C211yesmaximal, characteristic, complemented
16C2×C11×#481C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4339—21no—
19C22×#4339C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66993—21no—
23C2×#66993C2211yescharacteristic
24C2×#66992—21no—
25C22×#4323C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11C2211yescharacteristic
29C22×#4318C2211yescharacteristic
30C22×D88C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623130—24no—
34#10623130C2218yescomplemented
35C2×#66949—21no—
36#10623038—24no—
37#10623038C2218yescomplemented
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66941C2211yescharacteristic
44C2×#66940C2211yescharacteristic
45C2×#66937—21no—
46C2×(C22⋊D11)⋊C4—21no—
47C11×#481C2218yescomplemented
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622652C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62#10622579C2218yescomplemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67#10622478C2218yescomplemented
68#10622476C2218yescomplemented
69#10622467C2218yescomplemented
70#10622465C2218yescomplemented
71#10622399C2218yescomplemented
72#10622394C2218yescomplemented
73#10622384C2218yescomplemented
74#10622373C2218yescomplemented
75#10622347C2218yescomplemented
76#10622342C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C23×Dic11—21no—
88C2×#4341—22no—
89C2×#4341—24no—
90C2×#4341—42no—
91C2×#4341C2314yes—
92C2×#4339—22no—
93C2×#4339—28no—
94C2×#4339—24no—
95C2×#4339—42no—
96C2×#4339—48no—
97C2×#4339C2314yes—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×Dic22C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×#121—22no—
111C11×#121C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—21no—
119C2×C22⋊Dic11D411yescharacteristic
120#66993—28no—
121#66993—22no—
122#66993C2314yes—
123#66992—28no—
124C2×#4323—42no—
125C2×#4323C2314yes—
126#66983—22no—
127#66983C2314yes—
128#66982—28no—
129C4×C22⋊D11D414yes—
130C4×C22⋊D11C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×C4×Dic11—21no—
142C2×C4×Dic11C2311yescharacteristic
143C2×#4318—42no—
144C2×#4318C2314yes—
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×D88—42no—
148C2×D88C2314yes—
149C2×#4314—24no—
150C2×#4314C2314yes—
151C2×#4313—42no—
152C2×#4313C2314yes—
153#66949—28no—
154#66948—22no—
155#66948—22no—
156#66948C2314yes—
157#66948C2314yes—
158#66947—28no—
159#66946—22no—
160#66946C2314yes—
161C4⋊C4×D11—22no—
162C4⋊C4×D11C2314yes—
163#66941—22no—
164#66941C2314yes—
165#66940—22no—
166#66940C2314yes—
167#66937—28no—
168(C22⋊D11)⋊C4—28no—
169C11×#106C2314yes—
170C11×#106C2314yes—
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×C22⋊C8C2314yes—
174#66896C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66880C2314yes—
178Dic11⋊C8C2314yes—
179C8×Dic11C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66873C2314yes—
185#66872C2314yes—
186C2×#3332—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11C2×D411yescharacteristic
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—82no—
197C2×D4×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—44no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—82no—
220C2×C22⋊D11C2×D414yes—
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228#4341—28no—
229#4341—44no—
230#4341—48no—
231#4339—28no—
232#4339—44no—
233#4339—48no—
234#4339—432no—
235C2×D44—24no—
236C2×D44—24no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—44no—
244C2×D44—82no—
245C2×D44C2412yes—
246C2×D44C2412yes—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2412yes—
257C2×Dic22—24no—
258C2×Dic22—21no—
259C2×Dic22—22no—
260C2×Dic22—44no—
261C2×Dic22#4114yescomplemented
262C2×Dic22C2412yes—
263C2×C8×C11—22no—
264C2×C8×C11—22no—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4C2412yes—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C22⋊Dic11C2×D414yes—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4C2×D414yes—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4C2×D414yes—
288C4×Dic11—24no—
289C4×Dic11C2×D412yes—
290C4×Dic11C2412yes—
291#4318—44no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296D88—44no—
297#4314—28no—
298#4313—44no—
299C2×#550—111no—
300C2×#547—111no—
301#3332—1116no—
302C2×#486—111no—
303C2×#481—111no—
304C2×#481D1111yescharacteristic, complemented
305C2×#475—111no—
306C2×#469—111no—
307C2×#469—111no—
308C2×#459—111no—
309C2×#449—111no—
310C2×#449—111no—
311C2×C4×SD16—111no—
312C2×#436—111no—
313C2×#417—111no—
314C2×#417—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11C22×D412yes—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—42no—
339D4×C11—84no—
340C2×C4×C11—22no—
341C2×C4×C11—24no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—48no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—28no—
357C22⋊D11—48no—
358C22⋊D11—48no—
359C22⋊D11—48no—
360C22⋊D11—48no—
361C22⋊D11—84no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—48no—
368C2×Dic11—42no—
369C2×Dic11AGL(1,ℤ/8)14yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—22no—
377D44—48no—
378D44—42no—
379D44—42no—
380D44—84no—
381C4×D11—24no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—48no—
385C4×D11—48no—
386C4×D11—48no—
387Dic22—24no—
388Dic22—22no—
389Dic22—48no—
390Dic22C2×#4114yescomplemented
391C8×C11—22no—
392C8×C11—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41—111no—
397C22×#41—221no—
398C22×SD16—111no—
399C22×D8—111no—
400C22×D8—111no—
401C22×M16—111no—
402C22×M16—111no—
403#550—118no—
404#550—224no—
405#547—118no—
406#547—224no—
407C2×C4⋊Q8—111no—
408C2×#127—111no—
409C2×#127—221no—
410C2×#123—221no—
411C2×#123—221no—
412C2×C22⋊Q8—221no—
413C2×#121—111no—
414C2×#121—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#121—221no—
418C2×#121C2×D1111yescharacteristic
419C2×C4×Q8—111no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—221no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4C2×D1111yescharacteristic
425#486—118no—
426#481—118no—
427#481C2×D1118yescomplemented
428#475—118no—
429#469—118no—
430#469—118no—
431#459—118no—
432#449—118no—
433#449—118no—
434C4×SD16—118no—
435#436—118no—
436C2×#106—111no—
437C2×#106C2×D1111yescharacteristic
438C2×#106C2×D1111yescharacteristic
439C2×C4⋊C8—111no—
440#417—118no—
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102C2×D1111yescharacteristic
451C2×#102C2×D1111yescharacteristic
452C2×C22⋊C8—111no—
453C2×C22⋊C8C2×D1111yescharacteristic
454C2×C4×C8—111no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—44no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—84no—
463C22×C11#54612yes—
464C22×C11C2×AGL(1,ℤ/8)12yes—
465C22×C11#57712yes—
466C22×C11C23×D411yescharacteristic
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—44no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—84no—
478C2×D11—84no—
479C4×C11—22no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11#54612yes—
484C4×C11C22×#4111yescharacteristic
485C4×C11C2×H(5,𝔽2)11yescharacteristic
486Dic11—24no—
487Dic11—22no—
488Dic11—22no—
489Dic11—42no—
490Dic11C2×AGL(1,ℤ/8)14yes—
491C2×#41—114no—
492C2×#41—114no—
493C2×#41—228no—
494C2×#41—224no—
495C2×#41—222no—
496C2×#41—222no—
497C2×#41—224no—
498C2×#41—442no—
499C2×#41—448no—
500C2×#41—442no—
501C22×Q8—111no—
502C22×Q8—221no—
503C22×D4—21no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—111no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—224no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—442no—
527C2×D8—442no—
528C2×M16—114no—
529C2×M16—114no—
530C2×M16—442no—
531C2×M16—442no—
532C22×C8—111no—
533C22×C8—111no—
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#127—114no—
539#127—222no—
540#127—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—228no—
544#121—22no—
545#121—114no—
546#121—114no—
547#121—114no—
548#121—228no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121—222no—
553#121C22×D1114yes—
554C4×Q8—114no—
555C4×Q8—222no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—114no—
559C4×D4—222no—
560C4×D4—228no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4C22×D1111yescharacteristic
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1114yes—
573C2×C4⋊C4C22×D1111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C42—111no—
582C2×C42—221no—
583#106—114no—
584#106C22×D1114yes—
585#106C22×D1114yes—
586C4⋊C8—114no—
587#103—114no—
588#103—114no—
589#103—114no—
590#102—114no—
591#102—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102C22×D1114yes—
596#102C22×D1114yes—
597C22⋊C8—114no—
598C22⋊C8C22×D1114yes—
599C4×C8—114no—
600C2×C11—42no—
601C2×C11—82no—
602C2×C11#333214yescomplemented
603C2×C11C2×#54611yescharacteristic
604C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
605C2×C11C2×#57711yescharacteristic
606D11—42no—
607D11—82no—
608D11—82no—
609C24—21no—
610C24—111no—
611C24—221no—
612C24—221no—
613C24D4×D1111yescharacteristic
614#41—228no—
615#41—228no—
616#41—444no—
617#41—448no—
618#41—4432no—
619#41—444no—
620#41—448no—
621C2×Q8—114no—
622C2×Q8—112no—
623C2×Q8—224no—
624C2×Q8—221no—
625C2×Q8—222no—
626C2×Q8—444no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—82no—
632C2×D4—114no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—222no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—882no—
655C2×D4—882no—
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—44no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—111no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—224no—
672C22×C4—221no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—221no—
676C22×C4—224no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—228no—
686D8—444no—
687D8—444no—
688M16—444no—
689M16—444no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—112no—
693C2×C8—112no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—114no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4C23×D1112yes—
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—114no—
713C22⋊C4—114no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C42—112no—
719C42—112no—
720C42—224no—
721C11C2×#333211yescharacteristic, complemented, Sylow
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—112no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—442no—
736C23—442no—
737C23—442no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23C2×D4×D1112yes—
742C23C2×D4×D1111yescharacteristic
743Q8—114no—
744Q8—224no—
745Q8—222no—
746Q8—448no—
747D4—22no—
748D4—22no—
749D4—42no—
750D4—84no—
751D4—228no—
752D4—222no—
753D4—222no—
754D4—222no—
755D4—222no—
756D4—448no—
757D4—448no—
758D4—448no—
759D4—448no—
760D4—448no—
761D4—442no—
762D4—442no—
763D4—884no—
764D4—884no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—114no—
777C2×C4—112no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—224no—
783C2×C4—222no—
784C2×C4—224no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—448no—
791C2×C4—448no—
792C2×C4—442no—
793C2×C4C2×D4×D1112yes—
794C2×C4C2×D4×D1111yescharacteristic
795C2×C4#41×D1112yes—
796C2×C4#6704212yes—
797C2×C4C24×D1111yescharacteristic
798C8—22no—
799C8—22no—
800C8—222no—
801C8—222no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—84no—
810C22—222no—
811C22—222no—
812C22—222no—
813C22—444no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—884no—
821C22—884no—
822C22#1062318512yes—
823C22#1062329312yes—
824C22D11×AGL(1,ℤ/8)12yes—
825C22C22×D4×D1111yescharacteristic
826C4—22no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—114no—
831C4—222no—
832C4—224no—
833C4—222no—
834C4—442no—
835C4#1062318512yes—
836C4C2×#41×D1111yescharacteristic
837C4C2×#6704211yescharacteristic
838C2—42no—
839C2—82no—
840C2—442no—
841C2—882no—
842C2—882no—
843C2#1308094114yesdirect product factor
844C2C2×#1062318511yescharacteristic
845C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
846C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#481C2
socleC23×C11C22×D4
hypercenterC2×#481D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#10623130C2semidirect
2. C2×#10623038C2semidirect
3. #13080941C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622467C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622347C2semidirect
11. C2×#10622394C2semidirect
12. C2×#10622465C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622579C2semidirect
15. C2×#10622384C2semidirect
16. C2×C11×#481C2semidirect
34. #10623130C22semidirect
37. #10623038C22semidirect
47. C11×#481C22semidirect
59. #10622652C22semidirect
62. #10622579C22semidirect
67. #10622478C22semidirect
68. #10622476C22semidirect
69. #10622467C22semidirect
70. #10622465C22semidirect
71. #10622399C22semidirect
72. #10622394C22semidirect
73. #10622384C22semidirect
74. #10622373C22semidirect
75. #10622347C22semidirect
76. #10622342C22semidirect
261. C2×Dic22#41semidirect
304. C2×#481D11semidirect
390. Dic22C2×#41semidirect
427. #481C2×D11semidirect
602. C2×C11#3332semidirect
721. C11C2×#3332semidirect
843. C2#13080941direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231302
C2×#106230382
#130809412
C2×#106223732
C2×#106224762
C2×#106224672
C2×#106224782
C2×#106226522
C2×#106223992
C2×#106223472
C2×#106223942
C2×#106224652
C2×#106223422
C2×#106225792
C2×#106223842
C2×C11×#4812
C2×#333211