Finite Group Databasebeta

← C2×#13080819 #15630572

Subgroups — C2×#13080819 #15630572

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×#10623096C211yesmaximal, characteristic, complemented
2C2×#10623081C211yesmaximal, characteristic, complemented
3#13080819C2116yesmaximal, direct product factor
4C2×#10622310C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622349C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622457C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622345C211yesmaximal, characteristic, complemented
13C2×C4×D88C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622744C211yesmaximal, characteristic, complemented
16C2×C11×#436C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992—21no—
23C2×#66990—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic, complemented
27C2×#66979C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C2×#66977C2211yescharacteristic
30C22×D88C2211yescharacteristic
31C22×D88C2211yescharacteristic
32C22×#4314C2211yescharacteristic, complemented
33#10623096—24no—
34#10623096C2218yescomplemented
35#10623081—24no—
36#10623081C2218yescomplemented
37C2×#66951—21no—
38C2×#66947—21no—
39C2×#66937—21no—
40C2×#66936—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66923C2211yescharacteristic, complemented
47C11×#436C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52#10622748C2218yescomplemented
53#10622747C2218yescomplemented
54#10622746C2218yescomplemented
55#10622744C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic, complemented
63C2×#66882C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66880C2211yescharacteristic, complemented
69#10622460C2218yescomplemented
70#10622457C2218yescomplemented
71#10622349C2218yescomplemented
72#10622347C2218yescomplemented
73#10622345C2218yescomplemented
74#10622336C2218yescomplemented
75#10622310C2218yescomplemented
76C4×D88C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11D411yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C2×#4339—22no—
87C2×#4339—24no—
88C2×#4339—42no—
89C2×#4339C2314yes—
90C22×D44—24no—
91C22×D44—21no—
92C22×D44—22no—
93C22×D44—42no—
94C22×D44C2311yescharacteristic
95C22×D44C2311yescharacteristic
96C22×D44C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×Dic22C2311yescharacteristic
102C2×C11×M16—42no—
103C2×C11×M16—42no—
104C2×C11×M16C2314yes—
105C2×C11×M16C2314yescomplemented
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C4×D4×C11D414yes—
111C4×D4×C11C2314yes—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118#66992—28no—
119#66990—28no—
120#66983—22no—
121#66983—22no—
122#66983—22no—
123#66983C2314yes—
124#66983C2314yes—
125#66983C2314yescomplemented
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
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—
133#66979—22no—
134#66979C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2314yescomplemented
142#66977—22no—
143#66977C2314yes—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C2×D88—24no—
149C2×D88—42no—
150C2×D88C2314yes—
151C2×D88C2314yes—
152C2×#4314—42no—
153C2×#4314C2314yescomplemented
154#66951—28no—
155#66947—28no—
156#66937—28no—
157#66936—28no—
158(C22⋊D11)⋊C4—28no—
159C22⋊C4×D11—28no—
160#66928—22no—
161#66928C2314yes—
162C4×D44—22no—
163C4×D44—22no—
164C4×D44C2314yes—
165C4×D44C2314yescomplemented
166#66923—22no—
167#66923C2314yescomplemented
168C11×C4⋊C8C2314yescomplemented
169C11×C22⋊C8C2314yes—
170C11×C22⋊C8C2314yescomplemented
171C4×C8×C11C2314yescomplemented
172#66885C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178#66885C2314yescomplemented
179#66882C2314yescomplemented
180#66882C2314yescomplemented
181#66881C2314yescomplemented
182#66880C2314yescomplemented
183#66880C2314yescomplemented
184#66880C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11—82no—
195C2×D4×C11—42no—
196C2×D4×C11C2×D414yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11—82no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—24no—
224C22×Dic11—82no—
225#4339—28no—
226#4339—44no—
227#4339—48no—
228C2×D44—28no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—24no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—22no—
238C2×D44—44no—
239C2×D44—44no—
240C2×D44—48no—
241C2×D44#4114yes—
242C2×D44C2412yes—
243C2×D44C2412yes—
244C2×D44C2412yes—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—44no—
249C2×C4×D11—82no—
250C2×C4×D11—82no—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22C2412yes—
255C11×M16—44no—
256C11×M16—44no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11C2412yes—
262C2×C8×C11C2412yes—
263C2×C8×C11C2412yes—
264C2×C8×C11C2412yes—
265C11×C4⋊C4C2×D414yes—
266C11×C22⋊C4C2×D414yes—
267C11×C22⋊C4C2×D414yes—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
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)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—24no—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291C4×Dic11—24no—
292D88—28no—
293D88—44no—
294#4314—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×D8—111no—
308C2×#436D1111yescharacteristic, complemented
309C2×#417—111no—
310C2×#418—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11C22×D412yes—
318C23×C11C22×D412yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—24no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—48no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—48no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—84no—
335C22×D11—816no—
336D4×C11—44no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4112yes—
353C2×C4×C11H(5,𝔽2)12yes—
354C2×C4×C11C2511yescharacteristic
355C22⋊D11—48no—
356C22⋊D11—48no—
357C22⋊D11—84no—
358C22⋊D11—84no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—84no—
370D44—24no—
371D44—22no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—42no—
378D44—42no—
379D44C2×#4114yes—
380C4×D11—48no—
381C4×D11—84no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386C8×C11—22no—
387C8×C11—22no—
388C8×C11—22no—
389C8×C11—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8—111no—
395C22×M16C2×D1111yescharacteristic
396C22×M16C2×D1111yescharacteristic, complemented
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—111no—
415C2×C4×D4—221no—
416C2×C4×D4C2×D1111yescharacteristic
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×D8—118no—
430#436C2×D1118yescomplemented
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8C2×D1111yescharacteristic, complemented
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×#102—111no—
446C2×#102—111no—
447C2×C22⋊C8C2×D1111yescharacteristic
448C2×C22⋊C8C2×D1111yescharacteristic, complemented
449C2×C4×C8C2×D1111yescharacteristic, complemented
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—44no—
457C22×C11—44no—
458C22×C11#54612yes—
459C22×C11#57512yes—
460C22×C11#57612yes—
461C22×C11C23×D411yescharacteristic
462C2×D11—24no—
463C2×D11—48no—
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—816no—
473C2×D11—84no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—42no—
483Dic11—42no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—224no—
490C2×#41—222no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×D4—111no—
494C22×D4—111no—
495C22×D4—111no—
496C22×D4—114no—
497C22×D4—224no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—222no—
504C22×D4—442no—
505C22×D4D4411yescharacteristic
506C23×C4—221no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—42no—
519C2×M16—42no—
520C2×M16C22×D1114yes—
521C2×M16C22×D1114yescomplemented
522C22×C8C22×D1111yescharacteristic
523C22×C8C22×D1111yescharacteristic
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—222no—
540#121—222no—
541#121—222no—
542#121—228no—
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—228no—
547C4×D4—222no—
548C4×D4—222no—
549C4×D4D4414yes—
550C4×D4C22×D1114yes—
551#117—114no—
552#117—222no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4D4411yescharacteristic
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—228no—
574C2×C22⋊C4D4411yescharacteristic
575C2×C22⋊C4D4411yescharacteristic
576C2×C42—221no—
577C2×C42C22×D1111yescharacteristic
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8C22×D1114yescomplemented
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#102—114no—
591#102—114no—
592C22⋊C8C22×D1114yes—
593C22⋊C8C22×D1114yescomplemented
594C4×C8C22×D1114yescomplemented
595C2×C11—42no—
596C2×C11—42no—
597C2×C11#332214yescomplemented
598C2×C11C2×#54611yescharacteristic
599C2×C11C2×#57511yescharacteristic
600C2×C11C2×#57611yescharacteristic
601D11—44no—
602D11—82no—
603D11—82no—
604C24—221no—
605C24—221no—
606C24—221no—
607C24—224no—
608C24—444no—
609C24—444no—
610C24—882no—
611C24C2×D4411yescharacteristic
612C24C2×D4411yescharacteristic
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—112no—
617C2×Q8—221no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×D4—42no—
621C2×D4—114no—
622C2×D4—112no—
623C2×D4—112no—
624C2×D4—112no—
625C2×D4—228no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—222no—
639C2×D4—444no—
640C2×D4—448no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—882no—
645C2×D4—882no—
646C2×D4C2×D4414yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—444no—
661C22×C4—882no—
662C22×C4—882no—
663C22×C4—882no—
664C22×C4C2×D4412yes—
665C22×C4C2×D4412yes—
666C22×C4C2×D4411yescharacteristic
667C22×C4C2×D4411yescharacteristic
668C22×C4C2×D4411yescharacteristic
669C22×C4C2×D4411yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—228no—
675D8—444no—
676M16—44no—
677M16—44no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8C23×D1112yes—
683C2×C8C23×D1112yes—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—112no—
687C4⋊C4—112no—
688C4⋊C4—112no—
689C4⋊C4—112no—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—224no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4—224no—
698C4⋊C4C2×D4414yes—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4C2×D4414yes—
709C22⋊C4C2×D4414yes—
710C42—224no—
711C42C2×D4412yes—
712C42C23×D1112yes—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—224no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—448no—
725C23—448no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—884no—
735C23—8816no—
736C23C22×D4412yes—
737C23C22×D4412yes—
738C23C22×D4411yescharacteristic
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—44no—
743D4—114no—
744D4—224no—
745D4—222no—
746D4—222no—
747D4—222no—
748D4—222no—
749D4—222no—
750D4—448no—
751D4—448no—
752D4—448no—
753D4—442no—
754D4—442no—
755D4—884no—
756D4—884no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—448no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—884no—
779C2×C4—884no—
780C2×C4—884no—
781C2×C4C22×D4412yes—
782C2×C4C22×D4412yes—
783C2×C4C22×D4412yes—
784C2×C4C22×D4412yes—
785C2×C4C22×D4411yescharacteristic
786C2×C4#6703712yes—
787C2×C4#41×D1112yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—224no—
802C22—442no—
803C22—442no—
804C22—448no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—8816no—
812C22—884no—
813C22—884no—
814C22#1062308512yes—
815C22#1062327912yes—
816C22#1062328312yes—
817C22C23×D4411yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—442no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4#1062308512yes—
828C4C2×#6703711yescharacteristic
829C4C2×#41×D1111yescharacteristic
830C2—42no—
831C2—42no—
832C2—444no—
833C2—882no—
834C2—882no—
835C2#1308081914yesdirect product factor
836C2C2×#1062308511yescharacteristic
837C2C2×#1062327911yescharacteristic
838C2C2×#1062328311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
hypercenterC2×#436D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. C2×#10623081C2semidirect
3. #13080819C2direct (N × H)
4. C2×#10622310C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622349C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622457C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622345C2semidirect
13. C2×C4×D88C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622744C2semidirect
16. C2×C11×#436C2semidirect
20. C22×C11×M16C22semidirect
26. C2×#66983C22semidirect
28. C22×C4⋊Dic11C22semidirect
32. C22×#4314C22semidirect
34. #10623096C22semidirect
36. #10623081C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66923C22semidirect
47. C11×#436C22semidirect
48. C2×C11×C4⋊C8C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C4×C8×C11C22semidirect
52. #10622748C22semidirect
53. #10622747C22semidirect
54. #10622746C22semidirect
55. #10622744C22semidirect
62. C2×#66885C22semidirect
63. C2×#66882C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. C2×#66880C22semidirect
69. #10622460C22semidirect
70. #10622457C22semidirect
71. #10622349C22semidirect
72. #10622347C22semidirect
73. #10622345C22semidirect
74. #10622336C22semidirect
75. #10622310C22semidirect
76. C4×D88C22semidirect
105. C2×C11×M16C23semidirect
125. #66983C23semidirect
141. C2×C4⋊Dic11C23semidirect
153. C2×#4314C23semidirect
165. C4×D44C23semidirect
167. #66923C23semidirect
168. C11×C4⋊C8C23semidirect
170. C11×C22⋊C8C23semidirect
171. C4×C8×C11C23semidirect
178. #66885C23semidirect
179. #66882C23semidirect
180. #66882C23semidirect
181. #66881C23semidirect
182. #66880C23semidirect
183. #66880C23semidirect
184. #66880C23semidirect
308. C2×#436D11semidirect
396. C22×M16C2×D11semidirect
430. #436C2×D11semidirect
434. C2×C4⋊C8C2×D11semidirect
448. C2×C22⋊C8C2×D11semidirect
449. C2×C4×C8C2×D11semidirect
521. C2×M16C22×D11semidirect
581. C4⋊C8C22×D11semidirect
593. C22⋊C8C22×D11semidirect
594. C4×C8C22×D11semidirect
597. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106230812
#130808192
C2×#106223102
C2×#106223362
C2×#106223492
C2×#106224602
C2×#106227482
C2×#106227472
C2×#106224572
C2×#106223472
C2×#106223452
C2×C4×D882
C2×#106227462
C2×#106227442
C2×C11×#4362
C2×#332211