Finite Group Databasebeta

← C2×#13078555 #15621569

Subgroups — C2×#13078555 #15621569

Order 2816.

2670 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13078555C2116yesmaximal, direct product factor
4C2×#10622476C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622616C211yesmaximal, characteristic, complemented
8C2×#10622648C211yesmaximal, characteristic, complemented
9C2×#10622495C211yesmaximal, characteristic, complemented
10C2×#10622387C211yesmaximal, characteristic, complemented
11C2×#10622494C211yesmaximal, characteristic, complemented
12C2×#10622474C211yesmaximal, characteristic, complemented
13C2×#10622383C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic, complemented
22C2×#66992—21no—
23C2×#66991C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66979C2211yescharacteristic, complemented
26C22×#4313C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28D11×#121—24no—
29D11×#121C2218yes—
30D11×#117—24no—
31D11×#117C2218yescomplemented
32C2×#66948C2211yescharacteristic
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic, complemented
38C2×#66937—21no—
39C2×C22⋊C4×D11—21no—
40C2×C22⋊C4×D11—21no—
41C2×#66930—21no—
42C2×#66925—21no—
43C2×C42×D11—21no—
44C11×#482C2218yescomplemented
45C2×C11×#107C2211yescharacteristic, complemented
46C2×C11×#106C2211yescharacteristic, complemented
47C2×C11×#102C2211yescharacteristic, complemented
48C2×C11×#102C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C2×#66896C2211yescharacteristic, complemented
51C2×#66896C2211yescharacteristic, complemented
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53C2×#66885C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic, complemented
55C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×#66882C2211yescharacteristic, complemented
58C2×#66881C2211yescharacteristic, complemented
59#10622648C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66873C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic, complemented
63C2×#66872C2211yescharacteristic, complemented
64C2×#66872C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622495C2218yescomplemented
68#10622494C2218yescomplemented
69#10622476C2218yescomplemented
70#10622474C2218yescomplemented
71#10622390C2218yescomplemented
72#10622387C2218yescomplemented
73#10622383C2218yescomplemented
74#10622383C2218yescomplemented
75#10622350C2218yescomplemented
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—
85C23×Dic11D411yescharacteristic
86C2×D4×D11—28no—
87C2×D4×D11—22no—
88C2×D4×D11—24no—
89C2×D4×D11—24no—
90C2×D4×D11—48no—
91C2×D4×D11C2314yes—
92C22×D44—21no—
93C22×D44C2311yescharacteristic
94C22×C4×D11—24no—
95C22×C4×D11—24no—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×C4×D11D411yescharacteristic
100C22×C4×D11D411yescharacteristic
101C22×C4×D11D414yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2314yes—
104C22×C4×D11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×#121—22no—
108C11×#121C2314yes—
109C11×#117—22no—
110C11×#117C2314yescomplemented
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C42×C11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119#66992—28no—
120#66991—22no—
121#66991C2314yes—
122#66983—22no—
123#66983C2314yes—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128#66979—22no—
129#66979C2314yescomplemented
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C2×#4313—24no—
142C2×#4313—24no—
143C2×#4313C2314yes—
144C2×#4313C2314yes—
145#66948—22no—
146#66948C2314yes—
147#66945—22no—
148#66945—22no—
149#66945C2314yes—
150#66945C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11—22no—
153C4⋊C4×D11—22no—
154C4⋊C4×D11C2314yes—
155C4⋊C4×D11C2314yescomplemented
156C4⋊C4×D11C2314yescomplemented
157#66937—28no—
158C22⋊C4×D11—28no—
159C22⋊C4×D11—28no—
160#66930—28no—
161#66925—28no—
162C42×D11—28no—
163C11×#107C2314yescomplemented
164C11×#106C2314yescomplemented
165C11×#102C2314yescomplemented
166C11×#102C2314yescomplemented
167C11×C22⋊C8C2314yescomplemented
168#66896C2314yescomplemented
169#66896C2314yescomplemented
170C22⋊(C11⋊C8)C2314yescomplemented
171#66885C2314yescomplemented
172#66885C2314yescomplemented
173(C2×D11)⋊C8C2314yescomplemented
174(C2×D11)⋊C8C2314yescomplemented
175#66882C2314yescomplemented
176#66881C2314yescomplemented
177#66873C2314yescomplemented
178#66873C2314yescomplemented
179#66872C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182#66871C2314yescomplemented
183C2×#3094—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—24no—
187C23×D11—24no—
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—42no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11C2×D414yes—
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D411yescharacteristic
197C2×D4×C11—24no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—44no—
202C2×D4×C11C2412yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C22×Dic11—24no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225D4×D11—28no—
226D4×D11—28no—
227D4×D11—432no—
228D4×D11—48no—
229C2×D44—24no—
230C2×D44—21no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—44no—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—216no—
237C2×C4×D11—28no—
238C2×C4×D11—28no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11C2×D414yes—
249C2×C4×D11C2×D414yes—
250C2×C4×D11C2×D412yes—
251C2×C4×D11C2×D412yes—
252C2×C4×D11#4114yes—
253C2×C4×D11#4114yes—
254C2×C4×D11C2412yes—
255C2×C4×D11C2412yes—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C42×C11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291#4313—28no—
292#4313—28no—
293C22×#121—111no—
294C22×#117—111no—
295#3094—1116no—
296C2×#481—111no—
297C2×#481—111no—
298C2×#482—111no—
299C2×#482—111no—
300C2×#482—111no—
301C2×#482D1111yescharacteristic, complemented
302C2×#480—111no—
303C2×#480—111no—
304C2×#428—111no—
305C2×#428—111no—
306C2×#418—111no—
307C2×#418—111no—
308C2×#407—111no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11C22×D412yes—
317C23×C11C22×D411yescharacteristic
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—28no—
323C22×D11—28no—
324C22×D11—22no—
325C22×D11—44no—
326C22×D11—416no—
327C22×D11—48no—
328C22×D11—48no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—48no—
333C22×D11—816no—
334C22×D11#12314yes—
335C22×D11AGL(1,ℤ/8)14yes—
336C22×D11C22×D412yes—
337C22×D11C22×D412yes—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11—42no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11C2×#4112yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—48no—
358C22⋊D11—48no—
359C22⋊D11—48no—
360C2×Dic11—22no—
361C2×Dic11—28no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11#12314yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—22no—
372D44—22no—
373D44—48no—
374D44—42no—
375C4×D11—28no—
376C4×D11—24no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—28no—
380C4×D11—48no—
381C4×D11—48no—
382C4×D11—48no—
383C4×D11#12318yes—
384C4×D11C2×#4114yes—
385C4×D11C2×#4114yes—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C23×D4—111no—
391C23×D4—221no—
392C24×C4—111no—
393C22×M16—111no—
394C22×M16—111no—
395C2×#121—111no—
396C2×#121—111no—
397C2×#121—118no—
398C2×#121—111no—
399C2×#121—221no—
400C2×#121—224no—
401C2×#121—221no—
402C2×#121C2×D1111yescharacteristic
403C2×#117—111no—
404C2×#117—118no—
405C2×#117—111no—
406C2×#117—111no—
407C2×#117—221no—
408C2×#117—221no—
409C2×#117—224no—
410C2×#117C2×D1111yescharacteristic, complemented
411C22×C4⋊C4—111no—
412C22×C4⋊C4—111no—
413C22×C4⋊C4—111no—
414C22×C22⋊C4—221no—
415C22×C22⋊C4—221no—
416C22×C42—221no—
417#482—118no—
418#482—118no—
419#482—118no—
420#482C2×D1118yescomplemented
421#481—118no—
422#481—118no—
423#480—118no—
424#480—118no—
425#428—118no—
426#428—118no—
427C2×#107—111no—
428C2×#107—111no—
429C2×#107—111no—
430C2×#107C2×D1111yescharacteristic, complemented
431C2×#106—111no—
432C2×#106—111no—
433C2×#106—111no—
434C2×#106C2×D1111yescharacteristic, complemented
435#418—118no—
436#418—118no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102C2×D1111yescharacteristic, complemented
444C2×#102C2×D1111yescharacteristic, complemented
445#407—118no—
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×C22⋊C8C2×D1111yescharacteristic, complemented
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—44no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—84no—
458C22×C11C2×#12312yes—
459C22×C11C2×AGL(1,ℤ/8)12yes—
460C22×C11#57512yes—
461C22×C11C23×D411yescharacteristic
462C2×D11—28no—
463C2×D11—28no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—416no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—816no—
473C2×D11—84no—
474C2×D11C2×#12314yes—
475C2×D11C2×AGL(1,ℤ/8)14yes—
476C4×C11—22no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11C2×#12312yes—
481C4×C11C22×#4111yescharacteristic
482C4×C11C22×#4111yescharacteristic
483Dic11—22no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487Dic11C2×#12314yes—
488C25—111no—
489C25—221no—
490C22×D4—21no—
491C22×D4—114no—
492C22×D4—111no—
493C22×D4—221no—
494C22×D4—224no—
495C22×D4—224no—
496C22×D4—222no—
497C22×D4—221no—
498C22×D4—228no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—448no—
502C22×D4C22×D1111yescharacteristic
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—114no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4—114no—
510C23×C4—224no—
511C23×C4—224no—
512C23×C4—221no—
513C23×C4—221no—
514C23×C4—221no—
515C23×C4C22×D1111yescharacteristic
516C2×M16—114no—
517C2×M16—114no—
518C2×M16—224no—
519C2×M16—224no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8C22×D1111yescharacteristic
523C22×C8C22×D1111yescharacteristic
524#121—22no—
525#121—114no—
526#121—114no—
527#121—114no—
528#121—228no—
529#121—222no—
530#121—222no—
531#121—228no—
532#121—222no—
533#121C22×D1114yes—
534#117—22no—
535#117—114no—
536#117—114no—
537#117—114no—
538#117—228no—
539#117—228no—
540#117—222no—
541#117—222no—
542#117—222no—
543#117C22×D1114yescomplemented
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4—228no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—21no—
570C2×C42—228no—
571C2×C42—221no—
572C2×C42—221no—
573C2×C42—221no—
574#107—114no—
575#107—114no—
576#107—114no—
577#107C22×D1114yescomplemented
578#106—114no—
579#106—114no—
580#106—114no—
581#106C22×D1114yescomplemented
582#102—114no—
583#102—114no—
584#102—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102C22×D1114yescomplemented
589#102C22×D1114yescomplemented
590C22⋊C8—114no—
591C22⋊C8—114no—
592C22⋊C8—114no—
593C22⋊C8C22×D1114yescomplemented
594C2×C11—42no—
595C2×C11—82no—
596C2×C11#309414yescomplemented
597C2×C11C22×#12311yescharacteristic
598C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
599C2×C11C2×#57511yescharacteristic
600D11—24no—
601D11—24no—
602D11—82no—
603C24—21no—
604C24—111no—
605C24—111no—
606C24—114no—
607C24—224no—
608C24—224no—
609C24—224no—
610C24—221no—
611C24—442no—
612C24—444no—
613C24—444no—
614C24—444no—
615C24D4×D1111yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—112no—
622C2×D4—224no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—221no—
629C2×D4—222no—
630C2×D4—222no—
631C2×D4—444no—
632C2×D4—448no—
633C2×D4—444no—
634C2×D4—4432no—
635C2×D4—444no—
636C2×D4—444no—
637C2×D4C23×D1112yes—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—111no—
644C22×C4—112no—
645C22×C4—114no—
646C22×C4—114no—
647C22×C4—112no—
648C22×C4—114no—
649C22×C4—111no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—224no—
655C22×C4—2216no—
656C22×C4—228no—
657C22×C4—228no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—444no—
669C22×C4—444no—
670C22×C4—444no—
671C22×C4D4×D1112yes—
672C22×C4D4×D1111yescharacteristic
673C22×C4C23×D1112yes—
674C22×C4C23×D1111yescharacteristic
675M16—228no—
676M16—228no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8C23×D1112yes—
684C2×C8C23×D1112yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—112no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C4⋊C4C23×D1112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C42—24no—
709C42—224no—
710C42—224no—
711C42—224no—
712C11C2×#309411yescharacteristic, complemented, Sylow
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—114no—
721C23—114no—
722C23—112no—
723C23—112no—
724C23—228no—
725C23—228no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—444no—
732C23—448no—
733C23—4416no—
734C23—448no—
735C23—448no—
736C23—442no—
737C23—442no—
738C23—442no—
739C23—8816no—
740C23C2×D4×D1112yes—
741C23C2×D4×D1111yescharacteristic
742D4—22no—
743D4—22no—
744D4—48no—
745D4—42no—
746D4—222no—
747D4—222no—
748D4—448no—
749D4—448no—
750D4—448no—
751D4—448no—
752D4—442no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—114no—
764C2×C4—112no—
765C2×C4—118no—
766C2×C4—114no—
767C2×C4—114no—
768C2×C4—112no—
769C2×C4—228no—
770C2×C4—228no—
771C2×C4—228no—
772C2×C4—222no—
773C2×C4—224no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—448no—
780C2×C4—448no—
781C2×C4—448no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4#41×D1112yes—
788C2×C4#41×D1112yes—
789C2×C4C24×D1111yescharacteristic
790C8—22no—
791C8—22no—
792C8—222no—
793C8—222no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—114no—
803C22—114no—
804C22—228no—
805C22—228no—
806C22—222no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—4416no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—8816no—
815C22—884no—
816C22D11×#12312yes—
817C22#1062329912yes—
818C22D11×AGL(1,ℤ/8)12yes—
819C22C22×D4×D1111yescharacteristic
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—114no—
825C4—222no—
826C4—442no—
827C4—442no—
828C4—442no—
829C4D11×#12312yes—
830C4C2×#41×D1111yescharacteristic
831C4C2×#41×D1111yescharacteristic
832C2—42no—
833C2—82no—
834C2—224no—
835C2—224no—
836C2—882no—
837C2#1307855514yesdirect product factor
838C2C2×D11×#12311yescharacteristic
839C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
840C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×D11×#121C2
hypercenterC2×#482D11
hypocenterC11C2×#3094
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
2. C2×D11×#117C2semidirect
3. #13078555C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622616C2semidirect
8. C2×#10622648C2semidirect
9. C2×#10622495C2semidirect
10. C2×#10622387C2semidirect
11. C2×#10622494C2semidirect
12. C2×#10622474C2semidirect
13. C2×#10622383C2semidirect
14. C2×#10622383C2semidirect
15. C2×#10622339C2semidirect
16. C2×C11×#482C2semidirect
21. C2×C11×#117C22semidirect
25. C2×#66979C22semidirect
31. D11×#117C22semidirect
36. C2×C4⋊C4×D11C22semidirect
37. C2×C4⋊C4×D11C22semidirect
44. C11×#482C22semidirect
45. C2×C11×#107C22semidirect
46. C2×C11×#106C22semidirect
47. C2×C11×#102C22semidirect
48. C2×C11×#102C22semidirect
49. C2×C11×C22⋊C8C22semidirect
50. C2×#66896C22semidirect
51. C2×#66896C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
53. C2×#66885C22semidirect
54. C2×#66885C22semidirect
55. C2×(C2×D11)⋊C8C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×#66882C22semidirect
58. C2×#66881C22semidirect
59. #10622648C22semidirect
60. #10622616C22semidirect
61. C2×#66873C22semidirect
62. C2×#66873C22semidirect
63. C2×#66872C22semidirect
64. C2×#66872C22semidirect
65. C2×#66871C22semidirect
66. C2×#66871C22semidirect
67. #10622495C22semidirect
68. #10622494C22semidirect
69. #10622476C22semidirect
70. #10622474C22semidirect
71. #10622390C22semidirect
72. #10622387C22semidirect
73. #10622383C22semidirect
74. #10622383C22semidirect
75. #10622350C22semidirect
76. #10622339C22semidirect
110. C11×#117C23semidirect
129. #66979C23semidirect
155. C4⋊C4×D11C23semidirect
156. C4⋊C4×D11C23semidirect
163. C11×#107C23semidirect
164. C11×#106C23semidirect
165. C11×#102C23semidirect
166. C11×#102C23semidirect
167. C11×C22⋊C8C23semidirect
168. #66896C23semidirect
169. #66896C23semidirect
170. C22⋊(C11⋊C8)C23semidirect
171. #66885C23semidirect
172. #66885C23semidirect
173. (C2×D11)⋊C8C23semidirect
174. (C2×D11)⋊C8C23semidirect
175. #66882C23semidirect
176. #66881C23semidirect
177. #66873C23semidirect
178. #66873C23semidirect
179. #66872C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
182. #66871C23semidirect
301. C2×#482D11semidirect
410. C2×#117C2×D11semidirect
420. #482C2×D11semidirect
430. C2×#107C2×D11semidirect
434. C2×#106C2×D11semidirect
443. C2×#102C2×D11semidirect
444. C2×#102C2×D11semidirect
449. C2×C22⋊C8C2×D11semidirect
543. #117C22×D11semidirect
577. #107C22×D11semidirect
581. #106C22×D11semidirect
588. #102C22×D11semidirect
589. #102C22×D11semidirect
593. C22⋊C8C22×D11semidirect
596. C2×C11#3094semidirect
712. C11C2×#3094semidirect
837. C2#13078555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×D11×#1172
#130785552
C2×#106224762
C2×#106223902
C2×#106223502
C2×#106226162
C2×#106226482
C2×#106224952
C2×#106223872
C2×#106224942
C2×#106224742
C2×#106223832
C2×#106223392
C2×C11×#4822
C2×#309411