Finite Group Databasebeta

← C2×#13081659 #15634754

Subgroups — C2×#13081659 #15634754

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623090C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081659C2116yesmaximal, direct product factor
4C2×#10622325C211yesmaximal, characteristic, complemented
5C2×#10622767C211yesmaximal, characteristic, complemented
6C2×#10622764C211yesmaximal, characteristic, complemented
7C2×#10622375C211yesmaximal, characteristic, complemented
8C2×#10622629C211yesmaximal, characteristic, complemented
9C2×#10622400C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622399C211yesmaximal, characteristic, complemented
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622482C211yesmaximal, characteristic, complemented
15C2×#10622465C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66993C2211yescharacteristic
24C2×#66989C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4323C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983—21no—
30C2×#66982—21no—
31C2×C4×C22⋊D11—21no—
32C22×D88C2211yescharacteristic
33C22×D88C2211yescharacteristic
34C22×#4314C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36#10623090—24no—
37#10623090C2218yescomplemented
38#10623084—24no—
39#10623084C2218yescomplemented
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×#66937—21no—
46C2×#66937—21no—
47C2×#66936—21no—
48C2×#66928C2211yescharacteristic
49C2×#66927C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#442C2218yescomplemented
52C2×C11×#106C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56#10622767C2218yescomplemented
57#10622764C2218yescomplemented
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622629C2218yescomplemented
63#10622628C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622482C2218yescomplemented
70#10622465C2218yescomplemented
71#10622400C2218yescomplemented
72#10622399C2218yescomplemented
73#10622399C2218yescomplemented
74#10622375C2218yescomplemented
75#10622325C2218yescomplemented
76#10622314C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C2×#4339—28no—
88C2×#4339—48no—
89C22×D44—21no—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×Dic22D411yescharacteristic
98C22×Dic22C2311yescharacteristic
99C2×C11×D8—24no—
100C2×C11×D8C2314yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11C2314yes—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66993—22no—
115#66993—22no—
116#66993—22no—
117#66993C2314yes—
118#66993C2314yes—
119#66993C2314yes—
120#66989—22no—
121#66989C2314yes—
122C2×#4324—42no—
123C2×#4324C2314yes—
124C2×#4323—42no—
125C2×#4323—42no—
126C2×#4323—42no—
127C2×#4323C2314yes—
128C2×#4323C2314yes—
129C2×#4323C2314yes—
130#66983—28no—
131#66982—28no—
132C4×C22⋊D11—28no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11D411yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×D88—24no—
148C2×D88—42no—
149C2×D88C2314yes—
150C2×D88C2314yes—
151C2×#4314—24no—
152C2×#4314—42no—
153C2×#4314C2314yes—
154C2×#4314C2314yes—
155#66946—22no—
156#66946—22no—
157#66946—22no—
158#66946C2314yes—
159#66946C2314yes—
160#66946C2314yes—
161#66940—22no—
162#66940C2314yes—
163#66938—28no—
164#66937—28no—
165#66937—28no—
166#66936—28no—
167#66928—22no—
168#66928C2314yes—
169#66927—22no—
170#66927C2314yes—
171C4×Dic22D414yes—
172C4×Dic22C2314yes—
173C11×#106C2314yes—
174C11×#102C2314yes—
175C11×#102C2314yes—
176C11×#97C2314yes—
177#66879C2314yes—
178Dic11⋊C8C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66873C2314yes—
183#66873C2314yes—
184#66873C2314yes—
185C4⋊(C11⋊C8)C2314yes—
186C2×#3399—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—44no—
205C22×C4×C11—82no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
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—82no—
219C2×C22⋊D11—82no—
220C2×C22⋊D11—82no—
221C22×Dic11—21no—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4339—432no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—24no—
230C2×D44—21no—
231C2×D44—24no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—22no—
238C2×D44—44no—
239C2×D44—82no—
240C2×D44C2412yes—
241C2×D44C2412yes—
242C2×D44C2412yes—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—82no—
249C2×Dic22—24no—
250C2×Dic22—21no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22C2×D414yes—
254C2×Dic22C2412yes—
255C11×D8—28no—
256C2×C8×C11—22no—
257C2×C8×C11#4114yescomplemented
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4C2412yes—
263C11×C4⋊C4C2412yes—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C42×C11C2×D412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270#4324—44no—
271#4323—44no—
272#4323—44no—
273#4323—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279C4⋊Dic11C2×D414yes—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282Dic11⋊C4C2×D414yes—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2×D412yes—
286C4×Dic11C2412yes—
287C4×Dic11C2412yes—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292D88—28no—
293D88—44no—
294#4314—28no—
295#4314—44no—
296C2×#559—111no—
297C2×#550—111no—
298#3399—1116no—
299C2×#496—111no—
300C2×#496—111no—
301C2×#493—111no—
302C2×#460—111no—
303C2×#463—111no—
304C2×#463—111no—
305C2×#459—111no—
306C2×#459—111no—
307C2×#459—111no—
308C2×#446—111no—
309C2×#442—111no—
310C2×#442D1111yescharacteristic, complemented
311C2×C4×SD16—111no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—42no—
338D4×C11—42no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—48no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—84no—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4112yes—
351C2×C4×C11H(5,𝔽2)12yes—
352C2×C4×C11C2511yescharacteristic
353C22⋊D11—48no—
354C22⋊D11—48no—
355C22⋊D11—48no—
356C22⋊D11—84no—
357C22⋊D11—84no—
358C22⋊D11—84no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—42no—
364C2×Dic11AGL(1,ℤ/8)14yes—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369D44—22no—
370D44—22no—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—42no—
377D44—42no—
378D44—42no—
379D44—84no—
380C4×D11—48no—
381C4×D11—48no—
382C4×D11—84no—
383Dic22—28no—
384Dic22—22no—
385Dic22—22no—
386Dic22—42no—
387C8×C11—22no—
388C8×C11C2×#4114yescomplemented
389C11⋊C8—22no—
390C11⋊C8—22no—
391C22×#41—221no—
392C22×SD16—111no—
393C22×SD16—111no—
394C22×SD16—111no—
395C22×D8—111no—
396C22×D8—111no—
397C22×D8—111no—
398C22×D8—111no—
399C22×D8—111no—
400C22×D8C2×D1111yescharacteristic
401#559—118no—
402#559—224no—
403#550—118no—
404#550—224no—
405C2×#127—111no—
406C2×#127—111no—
407C2×#127—111no—
408C2×#127—111no—
409C2×#124—111no—
410C2×#124—111no—
411C2×#124—221no—
412C2×#123—221no—
413C2×#123—221no—
414C2×#121—221no—
415C2×#121—221no—
416C2×#121—221no—
417C2×C4×Q8—111no—
418C2×C4×Q8—111no—
419C2×C4×D4—111no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—221no—
423C2×C4×D4C2×D1111yescharacteristic
424C2×C4×D4C2×D1111yescharacteristic
425#496—118no—
426#496—118no—
427#493—118no—
428#463—118no—
429#463—118no—
430#460—118no—
431#459—118no—
432#459—118no—
433#459—118no—
434#446—118no—
435#442—118no—
436#442C2×D1118yescomplemented
437C4×SD16—118no—
438C2×#106C2×D1111yescharacteristic
439C2×C4⋊C8—111no—
440C2×C4⋊C8—111no—
441C2×C4⋊C8—111no—
442C2×#103—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102C2×D1111yescharacteristic
447C2×#102C2×D1111yescharacteristic
448C2×#97—111no—
449C2×#97C2×D1111yescharacteristic
450C2×C4×C8—111no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—84no—
458C22×C11—84no—
459C22×C11#55012yes—
460C22×C11C2×AGL(1,ℤ/8)12yes—
461C22×C11#57612yes—
462C22×C11C23×D411yescharacteristic
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—84no—
473C2×D11—84no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#55012yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11C2×AGL(1,ℤ/8)14yes—
487C2×#41—228no—
488C2×#41—448no—
489C22×Q8—111no—
490C22×Q8—111no—
491C22×D4—111no—
492C22×D4—111no—
493C22×D4—111no—
494C22×D4—221no—
495C22×D4—221no—
496C22×D4—221no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4C22×D1111yescharacteristic
503C22×D4C22×D1111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—221no—
507C23×C4—221no—
508C23×C4—221no—
509C2×SD16—114no—
510C2×SD16—114no—
511C2×SD16—114no—
512C2×SD16—224no—
513C2×SD16—442no—
514C2×SD16—442no—
515C2×D8—24no—
516C2×D8—114no—
517C2×D8—114no—
518C2×D8—114no—
519C2×D8—114no—
520C2×D8—114no—
521C2×D8—224no—
522C2×D8—442no—
523C2×D8—442no—
524C2×D8—442no—
525C2×D8—442no—
526C2×D8C22×D1114yes—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531#127—114no—
532#127—114no—
533#127—114no—
534#127—114no—
535#127—222no—
536#127—222no—
537#127—222no—
538#127—222no—
539#124—114no—
540#124—114no—
541#124—222no—
542#124—228no—
543#124—222no—
544#123—228no—
545#123—228no—
546#121—228no—
547#121—228no—
548#121—228no—
549C4×Q8—114no—
550C4×Q8—114no—
551C4×Q8—114no—
552C4×Q8—222no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—114no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—222no—
559C4×D4—222no—
560C4×D4—222no—
561C4×D4—228no—
562C4×D4C22×D1114yes—
563C4×D4C22×D1114yes—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C4⋊C4C22×D1111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C42—111no—
580C2×C42—111no—
581C2×C42—221no—
582C2×C42C22×D1111yescharacteristic
583#106C22×D1114yes—
584C4⋊C8—114no—
585C4⋊C8—114no—
586C4⋊C8—114no—
587#103—114no—
588#102—114no—
589#102—114no—
590#102—114no—
591#102C22×D1114yes—
592#102C22×D1114yes—
593#97—114no—
594#97C22×D1114yes—
595C4×C8—114no—
596C2×C11—82no—
597C2×C11—82no—
598C2×C11#339914yescomplemented
599C2×C11C2×#55011yescharacteristic
600C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
601C2×C11C2×#57611yescharacteristic
602D11—82no—
603D11—82no—
604D11—82no—
605C24—21no—
606C24—21no—
607C24—221no—
608C24—221no—
609C24—221no—
610#41—4432no—
611C2×Q8—114no—
612C2×Q8—112no—
613C2×Q8—224no—
614C2×Q8—221no—
615C2×Q8—222no—
616C2×Q8—222no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—112no—
624C2×D4—112no—
625C2×D4—112no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—222no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4—882no—
648C2×D4—882no—
649C2×D4—882no—
650C2×D4—882no—
651C2×D4C23×D1112yes—
652C2×D4C23×D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—44no—
658C22×C4—82no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—224no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—444no—
668C22×C4—444no—
669C22×C4—882no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674SD16—444no—
675SD16—444no—
676D8—28no—
677D8—228no—
678D8—444no—
679D8—444no—
680D8—444no—
681D8—444no—
682C2×C8—22no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—222no—
686C2×C8—222no—
687C2×C8#433914yescomplemented
688C2×C8C23×D1112yes—
689C2×C8C23×D1112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—114no—
693C4⋊C4—114no—
694C4⋊C4—114no—
695C4⋊C4—224no—
696C4⋊C4C23×D1112yes—
697C4⋊C4C23×D1112yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C42—112no—
708C42—112no—
709C42—112no—
710C42—112no—
711C42—224no—
712C42D4×D1112yes—
713C42C23×D1112yes—
714C11C2×#339911yescharacteristic, complemented, Sylow
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23C2×D4×D1111yescharacteristic
736Q8—228no—
737Q8—222no—
738Q8—222no—
739Q8—442no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—222no—
747D4—222no—
748D4—222no—
749D4—222no—
750D4—222no—
751D4—222no—
752D4—448no—
753D4—448no—
754D4—448no—
755D4—448no—
756D4—442no—
757D4—442no—
758D4—442no—
759D4—884no—
760D4—884no—
761D4—884no—
762D4—884no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—48no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—84no—
771C2×C4—114no—
772C2×C4—112no—
773C2×C4—112no—
774C2×C4—112no—
775C2×C4—112no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—448no—
781C2×C4—448no—
782C2×C4—442no—
783C2×C4—884no—
784C2×C4C2×#433912yes—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6704212yes—
789C2×C4C24×D1111yescharacteristic
790C8—22no—
791C8—222no—
792C8—222no—
793C8C2×#433914yescomplemented
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—84no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—884no—
812C22—884no—
813C22—884no—
814C22#1062308412yes—
815C22D11×AGL(1,ℤ/8)12yes—
816C22#1062330512yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—114no—
823C4—222no—
824C4—222no—
825C4—222no—
826C4—442no—
827C4#1062308412yes—
828C4C22×#433911yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—82no—
831C2—82no—
832C2—882no—
833C2—882no—
834C2—882no—
835C2#1308165914yesdirect product factor
836C2C2×#1062308411yescharacteristic
837C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
838C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
hypercenterC2×#442D11
hypocenterC11C2×#3399
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623090C2semidirect
2. C2×#10623084C2semidirect
3. #13081659C2direct (N × H)
4. C2×#10622325C2semidirect
5. C2×#10622767C2semidirect
6. C2×#10622764C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622629C2semidirect
9. C2×#10622400C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622399C2semidirect
13. C2×#10622314C2semidirect
14. C2×#10622482C2semidirect
15. C2×#10622465C2semidirect
16. C2×C11×#442C2semidirect
37. #10623090C22semidirect
39. #10623084C22semidirect
51. C11×#442C22semidirect
56. #10622767C22semidirect
57. #10622764C22semidirect
62. #10622629C22semidirect
63. #10622628C22semidirect
69. #10622482C22semidirect
70. #10622465C22semidirect
71. #10622400C22semidirect
72. #10622399C22semidirect
73. #10622399C22semidirect
74. #10622375C22semidirect
75. #10622325C22semidirect
76. #10622314C22semidirect
257. C2×C8×C11#41semidirect
310. C2×#442D11semidirect
388. C8×C11C2×#41semidirect
436. #442C2×D11semidirect
598. C2×C11#3399semidirect
687. C2×C8#4339semidirect
714. C11C2×#3399semidirect
793. C8C2×#4339semidirect
835. C2#13081659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230902
C2×#106230842
#130816592
C2×#106223252
C2×#106227672
C2×#106227642
C2×#106223752
C2×#106226292
C2×#106224002
C2×#106226282
C2×#106223992
C2×#106223142
C2×#106224822
C2×#106224652
C2×C11×#4422
C2×#339911