Finite Group Databasebeta

← C2×#13079434 #15624377

Subgroups — C2×#13079434 #15624377

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079434C2116yesmaximal, direct product factor
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622475C211yesmaximal, characteristic, complemented
6C2×#10622495C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622499C211yesmaximal, characteristic, complemented
10C2×#10622393C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622650C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic, complemented
20C23×C4×D11C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic, complemented
23C2×#66992—21no—
24C2×#66991C2211yescharacteristic
25C22×#4324C2211yescharacteristic, complemented
26C22×#4323C2211yescharacteristic, complemented
27C2×#66983C2211yescharacteristic
28C22×D88C2211yescharacteristic, complemented
29C22×#4314C2211yescharacteristic, complemented
30C22×#4313C2211yescharacteristic, complemented
31C22×#4313C2211yescharacteristic, complemented
32D11×#121—24no—
33D11×#121C2218yescomplemented
34#10623055—24no—
35#10623055C2218yescomplemented
36C2×#66950C2211yescharacteristic
37C2×#66950C2211yescharacteristic, complemented
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66948C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66939—21no—
43C2×#66937—21no—
44C2×#66935—21no—
45C2×C22⋊C4×D11—21no—
46C2×C4×D44—21no—
47C2×C4×D44—21no—
48C11×#482C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#106C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×#102C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66885C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66880C2211yescharacteristic, complemented
59#10622650C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic, complemented
64C2×#66873C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622499C2218yescomplemented
68#10622495C2218yescomplemented
69#10622478C2218yescomplemented
70#10622475C2218yescomplemented
71#10622395C2218yescomplemented
72#10622393C2218yescomplemented
73#10622389C2218yescomplemented
74#10622386C2218yescomplemented
75#10622347C2218yescomplemented
76#10622339C2218yescomplemented
77C24×D11—21no—
78C24×D11D411yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11D411yescharacteristic
87C2×D4×D11—28no—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11—42no—
91C2×D4×D11—48no—
92C2×D4×D11C2314yes—
93C2×#4339—22no—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339C2314yescomplemented
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11D411yescharacteristic
107C22×C4×D11D411yescharacteristic
108C22×C4×D11D414yes—
109C22×C4×D11C2311yescharacteristic
110C22×C4×D11C2311yescharacteristic
111C22×C4×D11C2314yes—
112C22×Dic22C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C11×#121—22no—
116C11×#121C2314yes—
117C11×#117—22no—
118C11×#117C2314yescomplemented
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C42×C11—21no—
125C2×C22⋊Dic11—21no—
126#66992—28no—
127#66991—22no—
128#66991C2314yes—
129C2×#4324—42no—
130C2×#4324C2314yescomplemented
131C2×#4323—42no—
132C2×#4323C2314yescomplemented
133#66983—22no—
134#66983C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×Dic11⋊C4—21no—
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×D88—42no—
148C2×D88C2314yescomplemented
149C2×#4314—42no—
150C2×#4314C2314yescomplemented
151C2×#4313—42no—
152C2×#4313—42no—
153C2×#4313C2314yescomplemented
154C2×#4313C2314yescomplemented
155#66950—22no—
156#66950—22no—
157#66950C2314yes—
158#66950C2314yescomplemented
159#66948—22no—
160#66948—22no—
161#66948—22no—
162#66948C2314yes—
163#66948C2314yes—
164#66948C2314yescomplemented
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2314yes—
167#66939—28no—
168#66937—28no—
169#66935—28no—
170C22⋊C4×D11—28no—
171C4×D44—28no—
172C4×D44—28no—
173C11×#107C2314yescomplemented
174C11×#106C2314yescomplemented
175C11×#102C2314yescomplemented
176C11×#102C2314yescomplemented
177C11×C22⋊C8C2314yescomplemented
178C22⋊(C11⋊C8)C2314yescomplemented
179#66885C2314yescomplemented
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66880C2314yescomplemented
183#66874C2314yescomplemented
184#66873C2314yescomplemented
185#66873C2314yescomplemented
186#66873C2314yescomplemented
187#66872C2314yescomplemented
188#66871C2314yescomplemented
189C2×#3194—111nomaximal, Sylow
190C24×C11—21no—
191C24×C11C2×D411yescharacteristic
192C23×D11—24no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—24no—
196C23×D11—42no—
197C23×D11—42no—
198C23×D11—44no—
199C23×D11—44no—
200C23×D11—44no—
201C23×D11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C23×D11C2×D414yes—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
209C2×D4×C11C2412yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—42no—
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D414yes—
233D4×D11—44no—
234D4×D11—44no—
235D4×D11—432no—
236D4×D11—48no—
237#4339—44no—
238#4339—44no—
239#4339—48no—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—24no—
243C2×D44—21no—
244C2×D44—21no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—44no—
250C2×D44—44no—
251C2×D44—44no—
252C2×D44C2412yes—
253C2×D44C2412yes—
254C2×C4×D11—24no—
255C2×C4×D11—24no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—42no—
261C2×C4×D11—42no—
262C2×C4×D11—48no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11C2×D412yes—
268C2×C4×D11C2×D412yes—
269C2×C4×D11C2×D414yes—
270C2×C4×D11C2×D414yes—
271C2×C4×D11C2412yes—
272C2×C4×D11C2412yes—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22—22no—
276C2×Dic22C2412yes—
277C2×C8×C11—22no—
278C2×C8×C11—22no—
279C2×C8×C11C2412yes—
280C2×C8×C11C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4C2412yes—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C42×C11—24no—
290C22⋊Dic11—24no—
291#4324—44no—
292#4323—44no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299C4⋊Dic11—24no—
300C4⋊Dic11—24no—
301C4⋊Dic11—21no—
302C4⋊Dic11C2412yes—
303Dic11⋊C4—24no—
304C2×C11⋊C8—22no—
305C2×C11⋊C8—22no—
306C2×C11⋊C8C2412yes—
307C2×C11⋊C8C2412yes—
308D88—44no—
309#4314—44no—
310#4313—44no—
311#4313—44no—
312C2×#525—111no—
313C22×#121—111no—
314#3194—1116no—
315C2×#482—111no—
316C2×#482D1111yescharacteristic, complemented
317C2×#483—111no—
318C2×#480—111no—
319C2×#469—111no—
320C2×#469—111no—
321C2×#468—111no—
322C2×#468—111no—
323C2×#449—111no—
324C2×#449—111no—
325C2×#450—111no—
326C2×#447—111no—
327C2×#407—111no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11C22×D412yes—
336C23×C11C22×D411yescharacteristic
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—416no—
348C22×D11—48no—
349C22×D11—48no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—48no—
357C22×D11—816no—
358C22×D11AGL(1,ℤ/8)14yes—
359C22×D11C22×D412yes—
360C22×D11C22×D412yes—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—48no—
364D4×C11—42no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11H(5,𝔽2)12yes—
378C2×C4×C11H(5,𝔽2)12yes—
379C2×C4×C11C2511yescharacteristic
380C22⋊D11—48no—
381C22⋊D11—48no—
382C22⋊D11—48no—
383C22⋊D11—48no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—44no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393D44—22no—
394D44—22no—
395D44—22no—
396D44—22no—
397D44—48no—
398D44—48no—
399D44—48no—
400D44—42no—
401D44—42no—
402C4×D11—24no—
403C4×D11—24no—
404C4×D11—22no—
405C4×D11—22no—
406C4×D11—22no—
407C4×D11—22no—
408C4×D11—44no—
409C4×D11—44no—
410C4×D11—48no—
411C4×D11—48no—
412Dic22—22no—
413Dic22—22no—
414Dic22—42no—
415C8×C11—22no—
416C8×C11—22no—
417C11⋊C8—22no—
418C11⋊C8—22no—
419C22×#41—111no—
420C23×D4—111no—
421C23×D4—221no—
422C24×C4—111no—
423C22×SD16—111no—
424C22×SD16—111no—
425C22×D8—111no—
426C22×D8—111no—
427C22×M16—111no—
428C22×M16—111no—
429#525—118no—
430#525—224no—
431C2×#123—221no—
432C2×C22⋊Q8—111no—
433C2×C22⋊Q8—111no—
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—118no—
437C2×#121—111no—
438C2×#121—111no—
439C2×#121—111no—
440C2×#121—221no—
441C2×#121—224no—
442C2×#121—221no—
443C2×#121C2×D1111yescharacteristic
444C2×#120—221no—
445C2×C4×D4—221no—
446C2×C4×D4—221no—
447C2×#117C2×D1111yescharacteristic, complemented
448C22×C4⋊C4—111no—
449C22×C22⋊C4—221no—
450#483—118no—
451#482—118no—
452#482C2×D1118yescomplemented
453#480—118no—
454#469—118no—
455#469—118no—
456#468—118no—
457#468—118no—
458#450—118no—
459#449—118no—
460#449—118no—
461#447—118no—
462C2×#107—111no—
463C2×#107C2×D1111yescharacteristic, complemented
464C2×#106—111no—
465C2×#106C2×D1111yescharacteristic, complemented
466C2×#103—111no—
467C2×#103—111no—
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102—111no—
472C2×#102C2×D1111yescharacteristic, complemented
473C2×#102C2×D1111yescharacteristic, complemented
474#407—118no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8—111no—
477C2×C22⋊C8—111no—
478C2×C22⋊C8C2×D1111yescharacteristic, complemented
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—44no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—84no—
487C22×C11#53412yes—
488C22×C11C2×AGL(1,ℤ/8)12yes—
489C22×C11#57512yes—
490C22×C11C23×D411yescharacteristic
491C2×D11—22no—
492C2×D11—28no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—416no—
498C2×D11—44no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—816no—
506C2×D11—84no—
507C2×D11—84no—
508C2×D11C2×AGL(1,ℤ/8)14yes—
509C4×C11—22no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11#53412yes—
514C4×C11C2×H(5,𝔽2)11yescharacteristic
515C4×C11C2×H(5,𝔽2)11yescharacteristic
516Dic11—22no—
517Dic11—22no—
518Dic11—42no—
519Dic11—42no—
520C25—111no—
521C25—221no—
522C2×#41—114no—
523C2×#41—222no—
524C2×#41—442no—
525C2×#41—442no—
526C22×Q8—111no—
527C22×D4—21no—
528C22×D4—114no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—222no—
535C22×D4—221no—
536C22×D4—228no—
537C22×D4—221no—
538C22×D4—221no—
539C22×D4—221no—
540C22×D4—442no—
541C22×D4—442no—
542C22×D4—448no—
543C22×D4C22×D1111yescharacteristic
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—114no—
550C23×C4—114no—
551C23×C4—221no—
552C23×C4—221no—
553C23×C4—442no—
554C23×C4—442no—
555C23×C4C22×D1111yescharacteristic
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—442no—
559C2×SD16—442no—
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—442no—
563C2×D8—442no—
564C2×M16—114no—
565C2×M16—114no—
566C2×M16—442no—
567C2×M16—442no—
568C22×C8—111no—
569C22×C8—111no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#123—228no—
573C22⋊Q8—114no—
574C22⋊Q8—114no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577#121—22no—
578#121—114no—
579#121—114no—
580#121—114no—
581#121—114no—
582#121—114no—
583#121—228no—
584#121—222no—
585#121—222no—
586#121—222no—
587#121—222no—
588#121—228no—
589#121—222no—
590#121C22×D1114yes—
591#120—228no—
592C4×D4—228no—
593C4×D4—228no—
594#117—22no—
595#117C22×D1114yescomplemented
596C2×C4⋊C4—111no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4C22×D1111yescharacteristic
603C2×C4⋊C4C22×D1111yescharacteristic
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—228no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C42—21no—
616#107—114no—
617#107C22×D1114yescomplemented
618#106—114no—
619#106C22×D1114yescomplemented
620#103—114no—
621#103—114no—
622#102—114no—
623#102—114no—
624#102—114no—
625#102—114no—
626#102C22×D1114yescomplemented
627#102C22×D1114yescomplemented
628C22⋊C8—114no—
629C22⋊C8—114no—
630C22⋊C8—114no—
631C22⋊C8C22×D1114yescomplemented
632C2×C11—42no—
633C2×C11—82no—
634C2×C11#319414yescomplemented
635C2×C11C2×#53411yescharacteristic
636C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
637C2×C11C2×#57511yescharacteristic
638D11—24no—
639D11—42no—
640D11—82no—
641D11—82no—
642C24—21no—
643C24—111no—
644C24—111no—
645C24—114no—
646C24—224no—
647C24—224no—
648C24—221no—
649C24—221no—
650C24—442no—
651C24—442no—
652C24—444no—
653C24—444no—
654C24—444no—
655C24D4×D1111yescharacteristic
656#41—444no—
657#41—444no—
658#41—448no—
659C2×Q8—112no—
660C2×Q8—221no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—44no—
668C2×D4—112no—
669C2×D4—112no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—221no—
678C2×D4—221no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—448no—
689C2×D4—444no—
690C2×D4—4432no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4C23×D1112yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—111no—
701C22×C4—111no—
702C22×C4—114no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—224no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—224no—
717C22×C4—448no—
718C22×C4—444no—
719C22×C4—444no—
720C22×C4—442no—
721C22×C4—442no—
722C22×C4—444no—
723C22×C4—444no—
724C22×C4—442no—
725C22×C4D4×D1112yes—
726C22×C4D4×D1111yescharacteristic
727C22×C4C23×D1112yes—
728C22×C4C23×D1111yescharacteristic
729SD16—444no—
730SD16—444no—
731D8—444no—
732D8—444no—
733M16—444no—
734M16—444no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—112no—
738C2×C8—112no—
739C2×C8—222no—
740C2×C8—222no—
741C2×C8C23×D1112yes—
742C2×C8C23×D1112yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—112no—
747C4⋊C4—224no—
748C4⋊C4—224no—
749C4⋊C4—224no—
750C4⋊C4—221no—
751C4⋊C4C23×D1112yes—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1112yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C42—24no—
764C11C2×#319411yescharacteristic, complemented, Sylow
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—114no—
773C23—112no—
774C23—112no—
775C23—228no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—444no—
784C23—444no—
785C23—448no—
786C23—4416no—
787C23—448no—
788C23—448no—
789C23—442no—
790C23—442no—
791C23—442no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—8816no—
796C23C2×D4×D1112yes—
797C23C2×D4×D1111yescharacteristic
798Q8—222no—
799Q8—222no—
800Q8—442no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—222no—
806D4—222no—
807D4—222no—
808D4—222no—
809D4—448no—
810D4—448no—
811D4—448no—
812D4—448no—
813D4—448no—
814D4—448no—
815D4—448no—
816D4—442no—
817D4—442no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—112no—
829C2×C4—112no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—224no—
833C2×C4—224no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—448no—
843C2×C4—448no—
844C2×C4—444no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4C2×D4×D1112yes—
848C2×C4C2×D4×D1111yescharacteristic
849C2×C4#6704212yes—
850C2×C4#6704212yes—
851C2×C4C24×D1111yescharacteristic
852C8—22no—
853C8—22no—
854C8—222no—
855C8—222no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—114no—
865C22—222no—
866C22—228no—
867C22—222no—
868C22—222no—
869C22—222no—
870C22—222no—
871C22—4416no—
872C22—444no—
873C22—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—8816no—
880C22—884no—
881C22—884no—
882C22#1062318412yes—
883C22#1062329912yes—
884C22D11×AGL(1,ℤ/8)12yes—
885C22C22×D4×D1111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—222no—
891C4—222no—
892C4—442no—
893C4—442no—
894C4#1062318412yes—
895C4C2×#6704211yescharacteristic
896C4C2×#6704211yescharacteristic
897C2—42no—
898C2—82no—
899C2—224no—
900C2—442no—
901C2—882no—
902C2—882no—
903C2#1307943414yesdirect product factor
904C2C2×#1062318411yescharacteristic
905C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
906C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
hypercenterC2×#482D11
hypocenterC11C2×#3194
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623055C2semidirect
2. C2×D11×#121C2semidirect
3. #13079434C2direct (N × H)
4. C2×#10622616C2semidirect
5. C2×#10622475C2semidirect
6. C2×#10622495C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622499C2semidirect
10. C2×#10622393C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622650C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622339C2semidirect
16. C2×C11×#482C2semidirect
19. C22×#4339C22semidirect
22. C2×C11×#117C22semidirect
25. C22×#4324C22semidirect
26. C22×#4323C22semidirect
28. C22×D88C22semidirect
29. C22×#4314C22semidirect
30. C22×#4313C22semidirect
31. C22×#4313C22semidirect
33. D11×#121C22semidirect
35. #10623055C22semidirect
37. C2×#66950C22semidirect
40. C2×#66948C22semidirect
48. C11×#482C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#106C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×#102C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C22⋊(C11⋊C8)C22semidirect
55. C2×#66885C22semidirect
58. C2×#66880C22semidirect
59. #10622650C22semidirect
60. #10622616C22semidirect
61. C2×#66874C22semidirect
62. C2×#66873C22semidirect
63. C2×#66873C22semidirect
64. C2×#66873C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622499C22semidirect
68. #10622495C22semidirect
69. #10622478C22semidirect
70. #10622475C22semidirect
71. #10622395C22semidirect
72. #10622393C22semidirect
73. #10622389C22semidirect
74. #10622386C22semidirect
75. #10622347C22semidirect
76. #10622339C22semidirect
96. C2×#4339C23semidirect
118. C11×#117C23semidirect
130. C2×#4324C23semidirect
132. C2×#4323C23semidirect
148. C2×D88C23semidirect
150. C2×#4314C23semidirect
153. C2×#4313C23semidirect
154. C2×#4313C23semidirect
158. #66950C23semidirect
164. #66948C23semidirect
173. C11×#107C23semidirect
174. C11×#106C23semidirect
175. C11×#102C23semidirect
176. C11×#102C23semidirect
177. C11×C22⋊C8C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. #66885C23semidirect
182. #66880C23semidirect
183. #66874C23semidirect
184. #66873C23semidirect
185. #66873C23semidirect
186. #66873C23semidirect
187. #66872C23semidirect
188. #66871C23semidirect
316. C2×#482D11semidirect
447. C2×#117C2×D11semidirect
452. #482C2×D11semidirect
463. C2×#107C2×D11semidirect
465. C2×#106C2×D11semidirect
472. C2×#102C2×D11semidirect
473. C2×#102C2×D11semidirect
478. C2×C22⋊C8C2×D11semidirect
595. #117C22×D11semidirect
617. #107C22×D11semidirect
619. #106C22×D11semidirect
626. #102C22×D11semidirect
627. #102C22×D11semidirect
631. C22⋊C8C22×D11semidirect
634. C2×C11#3194semidirect
764. C11C2×#3194semidirect
903. C2#13079434direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×D11×#1212
#130794342
C2×#106226162
C2×#106224752
C2×#106224952
C2×#106224782
C2×#106223952
C2×#106224992
C2×#106223932
C2×#106223472
C2×#106226502
C2×#106223892
C2×#106223862
C2×#106223392
C2×C11×#4822
C2×#319411