Finite Group Databasebeta

← C2×#13080822 #15630575

Subgroups — C2×#13080822 #15630575

Order 2816.

2318 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×#10623089C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic, complemented
3#13080822C2116yesmaximal, direct product factor
4C2×#10622310C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622495C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622393C211yesmaximal, characteristic, complemented
10C2×#10622629C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×#10622769C211yesmaximal, characteristic, complemented
13C2×#10622301C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C4×C11×D8C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic, complemented
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic, complemented
24C22×#4324C2211yescharacteristic, complemented
25C22×#4323C2211yescharacteristic
26C2×#66983—21no—
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C22×(C2×D11)⋊C4—21no—
30C22×#4313C2211yescharacteristic
31C22×#4313C2211yescharacteristic, complemented
32#10623089—24no—
33#10623089C2218yescomplemented
34#10623085—24no—
35#10623085C2218yescomplemented
36C2×#66950C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic, complemented
40C2×#66939—21no—
41C2×#66937—21no—
42C2×#66935—21no—
43C2×#66932—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66923C2211yescharacteristic, complemented
47C4×C11×D8C2218yescomplemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622771C2218yescomplemented
55#10622769C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
60C2×#66880C2211yescharacteristic, complemented
61C2×#66880C2211yescharacteristic, complemented
62#10622629C2218yescomplemented
63#10622622C2218yescomplemented
64C2×#66874C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic, complemented
67C2×#66871C2211yescharacteristic, complemented
68C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
69#10622501C2218yescomplemented
70#10622495C2218yescomplemented
71#10622395C2218yescomplemented
72#10622393C2218yescomplemented
73#10622384C2218yescomplemented
74#10622383C2218yescomplemented
75#10622310C2218yescomplemented
76#10622301C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C2×#4341—24no—
88C2×#4341—22no—
89C2×#4341—42no—
90C2×#4341C2314yes—
91C2×D4×D11—24no—
92C2×D4×D11—22no—
93C2×D4×D11—42no—
94C2×D4×D11C2314yes—
95C22×D44—21no—
96C22×D44D411yescharacteristic
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C2×C11×D8—24no—
103C2×C11×D8C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11C2314yes—
109C4×D4×C11C2314yescomplemented
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66991—22no—
118#66991—22no—
119#66991C2314yes—
120#66991C2314yescomplemented
121C2×#4324—42no—
122C2×#4324C2314yescomplemented
123C2×#4323—42no—
124C2×#4323C2314yes—
125#66983—28no—
126#66982—28no—
127C4×C22⋊D11—28no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—28no—
134C2×(C2×D11)⋊C4D411yescharacteristic
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11D411yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×#4313—42no—
147C2×#4313—42no—
148C2×#4313C2314yes—
149C2×#4313C2314yescomplemented
150#66950—22no—
151#66950C2314yes—
152#66948—22no—
153#66948C2314yes—
154#66945—22no—
155#66945C2314yes—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yescomplemented
158#66939—28no—
159#66937—28no—
160#66935—28no—
161#66932—28no—
162#66928—22no—
163#66928C2314yes—
164C4×D44D414yes—
165C4×D44C2314yes—
166#66923—22no—
167#66923C2314yescomplemented
168C11×#107C2314yescomplemented
169C11×#102C2314yes—
170C11×#102C2314yescomplemented
171C4×C8×C11C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yescomplemented
178#66880C2314yescomplemented
179#66880C2314yescomplemented
180#66874C2314yescomplemented
181#66873C2314yes—
182#66872C2314yescomplemented
183#66871C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—82no—
193C23×D11C2×D411yescharacteristic
194C23×D11C2×D411yescharacteristic
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11#4114yes—
201C2×D4×C11C2412yes—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—82no—
208C22×C4×C11—82no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—82no—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—44no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227#4341—28no—
228#4341—44no—
229#4341—48no—
230D4×D11—28no—
231D4×D11—44no—
232D4×D11—48no—
233C2×D44—24no—
234C2×D44—21no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—42no—
238C2×D44—82no—
239C2×D44C2×D414yes—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—82no—
247C2×C4×D11C2×D412yes—
248C2×C4×D11C2×D412yes—
249C2×C4×D11C2412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22C2412yes—
255C11×D8—28no—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
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(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278(C2×D11)⋊C4C2×D414yes—
279C4⋊Dic11—24no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2×D414yes—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288C4×Dic11—24no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293#4313—44no—
294#4313—44no—
295C2×#553—111no—
296C2×#546—111no—
297#3322—1116no—
298C2×#488—111no—
299C2×#485—111no—
300C2×#480—111no—
301C2×#478—111no—
302C2×#469—111no—
303C2×#468—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×C4×D8D1111yescharacteristic, complemented
308C2×#436—111no—
309C2×#417—111no—
310C2×#418—111no—
311C23×C11—24no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—48no—
328C22×D11—48no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—84no—
333C22×D11—816no—
334C22×D11C22×D412yes—
335C22×D11C22×D412yes—
336D4×C11—24no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—42no—
341D4×C11C2×#4114yes—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—84no—
349C2×C4×C11—84no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—48no—
357C22⋊D11—48no—
358C22⋊D11—48no—
359C22⋊D11—84no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—48no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—22no—
372D44—22no—
373D44—44no—
374D44—42no—
375D44—84no—
376C4×D11—24no—
377C4×D11—24no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8C2×D1111yescharacteristic
395C22×M16—111no—
396C22×M16—111no—
397#553—118no—
398#553—224no—
399#546—118no—
400#546—224no—
401C2×#126—221no—
402C2×#125—111no—
403C2×#124—111no—
404C2×#123—221no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#121—221no—
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—221no—
415C2×C4×D4C2×D1111yescharacteristic
416C2×C4×D4C2×D1111yescharacteristic, complemented
417C2×#117—111no—
418C22×C4⋊C4—111no—
419C22×C22⋊C4—221no—
420#488—118no—
421#485—118no—
422#480—118no—
423#478—118no—
424#469—118no—
425#468—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429C4×D8C2×D1118yescomplemented
430#436—118no—
431C2×#107—111no—
432C2×#107C2×D1111yescharacteristic, complemented
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#417—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102C2×D1111yescharacteristic
446C2×#102C2×D1111yescharacteristic, complemented
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×C4×C8C2×D1111yescharacteristic, complemented
450C22×C11—24no—
451C22×C11—48no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—84no—
458C22×C11#54612yes—
459C22×C11#57512yes—
460C22×C11#57612yes—
461C22×C11C23×D411yescharacteristic
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—44no—
469C2×D11—44no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—816no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—224no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×D4—114no—
494C22×D4—111no—
495C22×D4—111no—
496C22×D4—221no—
497C22×D4—222no—
498C22×D4—221no—
499C22×D4—224no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—442no—
504C22×D4C22×D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—221no—
511C23×C4—221no—
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—24no—
515C2×D8—114no—
516C2×D8—442no—
517C2×D8C22×D1114yes—
518C2×M16—114no—
519C2×M16—114no—
520C2×M16—442no—
521C2×M16—442no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#126—228no—
527#125—114no—
528#125—222no—
529#124—114no—
530#124—222no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—114no—
536#121—114no—
537#121—114no—
538#121—228no—
539#121—228no—
540#121—222no—
541#121—222no—
542#121—222no—
543#120—228no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—228no—
549C4×D4C22×D1114yes—
550C4×D4C22×D1114yescomplemented
551#117—114no—
552#117—222no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4—111no—
568C2×C22⋊C4—228no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C42—221no—
577C2×C42C22×D1111yescharacteristic
578#107—114no—
579#107C22×D1114yescomplemented
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102C22×D1114yes—
591#102C22×D1114yescomplemented
592C22⋊C8—114no—
593C22⋊C8—114no—
594C4×C8C22×D1114yescomplemented
595C2×C11—44no—
596C2×C11—82no—
597C2×C11#332214yescomplemented
598C2×C11C2×#54611yescharacteristic
599C2×C11C2×#57511yescharacteristic
600C2×C11C2×#57611yescharacteristic
601D11—42no—
602D11—42no—
603D11—82no—
604C24—21no—
605C24—21no—
606C24—111no—
607C24—111no—
608C24—224no—
609C24—221no—
610C24—444no—
611C24—444no—
612C24—882no—
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—112no—
617C2×Q8—221no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—114no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—228no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—222no—
634C2×D4—221no—
635C2×D4—222no—
636C2×D4—442no—
637C2×D4—444no—
638C2×D4—448no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4—882no—
644C2×D4#433914yes—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—82no—
652C22×C4—82no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—444no—
669C22×C4—882no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—28no—
675D8—444no—
676M16—444no—
677M16—444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—114no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—114no—
702C22⋊C4—114no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—224no—
711C42D4×D1112yes—
712C42C23×D1112yes—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—24no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—112no—
723C23—112no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—448no—
732C23—448no—
733C23—442no—
734C23—442no—
735C23—442no—
736C23—884no—
737C23—8816no—
738C23C2×D4×D1111yescharacteristic
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—24no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—42no—
747D4—222no—
748D4—222no—
749D4—444no—
750D4—448no—
751D4—448no—
752D4—448no—
753D4—442no—
754D4—884no—
755D4—884no—
756D4C2×#433914yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—112no—
766C2×C4—112no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—448no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4—884no—
783C2×C4C2×#433912yes—
784C2×C4C2×D4×D1112yes—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4#6704212yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—48no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—444no—
808C22—444no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—8816no—
813C22—884no—
814C22#1062308112yes—
815C22#1062328812yes—
816C22#1062329912yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4#1062308112yes—
828C4C22×#433911yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—44no—
831C2—82no—
832C2—442no—
833C2—442no—
834C2—882no—
835C2#1308082214yesdirect product factor
836C2C2×#1062308111yescharacteristic
837C2C2×#1062329911yescharacteristic
838C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623089C2semidirect
2. C2×#10623085C2semidirect
3. #13080822C2direct (N × H)
4. C2×#10622310C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622495C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622393C2semidirect
10. C2×#10622629C2semidirect
11. C2×#10622771C2semidirect
12. C2×#10622769C2semidirect
13. C2×#10622301C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622383C2semidirect
16. C2×C4×C11×D8C2semidirect
21. C2×C4×D4×C11C22semidirect
23. C2×#66991C22semidirect
24. C22×#4324C22semidirect
31. C22×#4313C22semidirect
33. #10623089C22semidirect
35. #10623085C22semidirect
39. C2×C4⋊C4×D11C22semidirect
46. C2×#66923C22semidirect
47. C4×C11×D8C22semidirect
48. C2×C11×#107C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C4×C8×C11C22semidirect
54. #10622771C22semidirect
55. #10622769C22semidirect
59. C2×(C2×D11)⋊C8C22semidirect
60. C2×#66880C22semidirect
61. C2×#66880C22semidirect
62. #10622629C22semidirect
63. #10622622C22semidirect
64. C2×#66874C22semidirect
66. C2×#66872C22semidirect
67. C2×#66871C22semidirect
68. C2×C4⋊(C11⋊C8)C22semidirect
69. #10622501C22semidirect
70. #10622495C22semidirect
71. #10622395C22semidirect
72. #10622393C22semidirect
73. #10622384C22semidirect
74. #10622383C22semidirect
75. #10622310C22semidirect
76. #10622301C22semidirect
109. C4×D4×C11C23semidirect
120. #66991C23semidirect
122. C2×#4324C23semidirect
149. C2×#4313C23semidirect
157. C4⋊C4×D11C23semidirect
167. #66923C23semidirect
168. C11×#107C23semidirect
170. C11×#102C23semidirect
171. C4×C8×C11C23semidirect
177. (C2×D11)⋊C8C23semidirect
178. #66880C23semidirect
179. #66880C23semidirect
180. #66874C23semidirect
182. #66872C23semidirect
183. #66871C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
307. C2×C4×D8D11semidirect
416. C2×C4×D4C2×D11semidirect
429. C4×D8C2×D11semidirect
432. C2×#107C2×D11semidirect
446. C2×#102C2×D11semidirect
449. C2×C4×C8C2×D11semidirect
550. C4×D4C22×D11semidirect
579. #107C22×D11semidirect
591. #102C22×D11semidirect
594. C4×C8C22×D11semidirect
597. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230892
C2×#106230852
#130808222
C2×#106223102
C2×#106225012
C2×#106224952
C2×#106226222
C2×#106223952
C2×#106223932
C2×#106226292
C2×#106227712
C2×#106227692
C2×#106223012
C2×#106223842
C2×#106223832
C2×C4×C11×D82
C2×#332211