Finite Group Databasebeta

← #14769486

Subgroups — #14769486

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D11C211yesmaximal, characteristic
2C2×#10622777C211yesmaximal, characteristic, complemented
3Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13069497C211yesmaximal, characteristic, complemented
6#13069495C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic, complemented
8#13068969C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic, complemented
10#13068948C211yesmaximal, characteristic, complemented
11#13068642C211yesmaximal, characteristic, complemented
12#13068549C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic
14#13068393C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C22×#4325C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×(C2×D11)⋊C4—21no—
26C2×SD16×D11—24no—
27C2×SD16×D11—24no—
28C2×SD16×D11C418yescomplemented
29C22×#4314C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31C11×#440—24no—
32C2×C11×#107C2211yescharacteristic, complemented
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38#10622826—21no—
39#10622777—24no—
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66882C2211yescharacteristic, complemented
43C2×#66880C2211yescharacteristic, complemented
44C2×#66879C2211yescharacteristic, complemented
45#10622601C2211yescharacteristic
46#10622600—21no—
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic
49#10622587—21no—
50#10622587C2211yescharacteristic, complemented
51C2×#66874C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic
53#10622571—21no—
54#10622568—21no—
55#10622552C2211yescharacteristic
56C4×(C2×D11)⋊C4—21no—
57C4×(C2×D11)⋊C4C2211yescharacteristic
58#10622542—21no—
59#10622542C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—22no—
73C2×Q8×D11—41no—
74C2×Q8×D11—41no—
75C2×Q8×D11C2×C414yescomplemented
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11C2×C414yes—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22C2311yescharacteristic
87C2×C11×SD16C2×C414yes—
88C2×C11×SD16D414yes—
89C2×C11×SD16D414yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11—41no—
94C4×D4×C11—22no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103Q8×Dic11—22no—
104Q8×Dic11—41no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325C2×C414yescomplemented
108D4×Dic11—22no—
109D4×Dic11—41no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324C2×C414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—44no—
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129SD16×D11—232no—
130C2×#4314—22no—
131C2×#4314—22no—
132C2×#4314C2×C414yescomplemented
133C2×C8×D11—22no—
134C2×C8×D11—22no—
135C2×C8×D11C2×C414yescomplemented
136C11×#107—22no—
137C11×#103—22no—
138C11×#102—22no—
139C11×#97—22no—
140#66899—22no—
141#66896—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95D411yescharacteristic
149C11⋊#95D411yescharacteristic
150#66885—41no—
151(C2×D11)⋊C8—22no—
152#66882—22no—
153#66880—41no—
154#66879—22no—
155#66874—41no—
156#66873—41no—
157#22437—111nomaximal, Sylow
158C24×C11—21no—
159C23×D11—21no—
160C23×D11—24no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—81no—
166C23×D11—81no—
167C23×D11C2×D411yescharacteristic
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11C22×C412yes—
172C2×Q8×C11C2×D412yes—
173C2×Q8×C11C2×D412yes—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11C22×C412yes—
178C2×D4×C11C2×D412yes—
179C2×D4×C11C2×D412yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201Q8×D11—28no—
202Q8×D11—44no—
203Q8×D11—44no—
204Q8×D11—44no—
205D4×D11—28no—
206D4×D11—44no—
207D4×D11—44no—
208D4×D11—44no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44C22×C412yes—
215C2×C4×D11—24no—
216C2×C4×D11—21no—
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11C22×C412yes—
223C2×C4×D11#4112yes—
224C2×Dic22—24no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—42no—
231C2×Dic22—42no—
232C2×Dic22C22×C412yes—
233C11×SD16C22⋊C4116yescomplemented
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11C22×C412yes—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—42no—
245C11×C22⋊C4—42no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—42no—
249C22⋊Dic11—42no—
250#4325—28no—
251#4324—28no—
252(C2×D11)⋊C4—22no—
253(C2×D11)⋊C4—22no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—81no—
259(C2×D11)⋊C4—81no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—42no—
265C4×Dic11—21no—
266C4×Dic11—21no—
267C4×Dic11—42no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8C22×C412yes—
274#4314—28no—
275C8×D11—28no—
276C23×SD16—111no—
277C2×#440—111no—
278C2×#440D1111yescharacteristic, complemented
279Q8×C22⋊C4—111no—
280D4×C22⋊C4—111no—
281#1973—111no—
282#1973—111no—
283#1880—111no—
284#1880—111no—
285#1877—111no—
286#1877—111no—
287#1808—111no—
288#1787—111no—
289#1786—111no—
290#1752—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11C22×D411yescharacteristic
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—22no—
304C22×D11—48no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—48no—
312C22×D11—84no—
313C22×D11—84no—
314C22×D11—84no—
315C22×D11—84no—
316C22×D11—84no—
317C22×D11C4×D412yes—
318C22×D11AGL(1,ℤ/8)12yes—
319C22×D11#13712yes—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11C2×C22⋊C414yescomplemented
324D4×C11—22no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11C2×C22⋊C414yes—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—84no—
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C22⋊D11—48no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—22no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—84no—
369C2×Dic11C4×D412yes—
370D44—22no—
371D44—22no—
372D44—41no—
373D44—41no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—48no—
379Dic22—22no—
380Dic22—22no—
381Dic22—48no—
382Dic22—41no—
383Dic22—41no—
384C8×C11—41no—
385C8×C11C2×C22⋊C414yescomplemented
386C11⋊C8—22no—
387C11⋊C8—41no—
388C23×Q8—111no—
389C23×D4—111no—
390C22×SD16—111no—
391C22×SD16—111no—
392C22×SD16—118no—
393C22×SD16—111no—
394C22×SD16—224no—
395C22×SD16—224no—
396C22×SD16C2×D1111yescharacteristic
397C23×C8—111no—
398C2×C4×Q8—111no—
399C2×C4×Q8C2×D1111yescharacteristic, complemented
400C2×C4×D4—111no—
401C2×C4×D4C2×D1111yescharacteristic
402C22×C22⋊C4—221no—
403#440—24no—
404#440—224no—
405C2×#107—111no—
406C2×#107C2×D1111yescharacteristic, complemented
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic, complemented
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×C22⋊C8—111no—
416C2×#97—111no—
417C2×#97C2×D1111yescharacteristic, complemented
418#391—111no—
419#391—111no—
420#391—221no—
421#391—221no—
422#390—111no—
423#390—111no—
424#386—221no—
425#386—221no—
426#380—111no—
427#380—111no—
428#380—221no—
429#379—221no—
430C4×C22⋊C4—111no—
431C4×C22⋊C4—221no—
432#340—111no—
433#340—111no—
434#336—111no—
435#336—111no—
436C22×C11—24no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11C2×C4×D411yescharacteristic
444C22×C11D4211yescharacteristic
445C22×C11D4211yescharacteristic
446C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
447C22×C11C2×#13711yescharacteristic
448C22×C11#57711yescharacteristic
449C22×C11#57711yescharacteristic
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—816no—
460C2×D11—81no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11#44014yescomplemented
465C4×C11—24no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—81no—
469C4×C11—81no—
470C4×C11C22×C22⋊C411yescharacteristic
471C4×C11#51811yescharacteristic
472C4×C11#54611yescharacteristic
473C4×C11#54611yescharacteristic
474Dic11—22no—
475Dic11—42no—
476Dic11—41no—
477Dic11—41no—
478Dic11—81no—
479Dic11—81no—
480C25—221no—
481C22×Q8—114no—
482C22×Q8—111no—
483C22×Q8—221no—
484C22×Q8—222no—
485C22×Q8—222no—
486C22×Q8—222no—
487C22×Q8—441no—
488C22×Q8—441no—
489C22×Q8C22×D1111yescharacteristic
490C22×D4—114no—
491C22×D4—111no—
492C22×D4—222no—
493C22×D4—221no—
494C22×D4—222no—
495C22×D4—222no—
496C22×D4—441no—
497C22×D4—441no—
498C22×D4C22×D1111yescharacteristic
499C23×C4—21no—
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C2×SD16—114no—
504C2×SD16—114no—
505C2×SD16—114no—
506C2×SD16—222no—
507C2×SD16—222no—
508C2×SD16—222no—
509C2×SD16—222no—
510C2×SD16—2232no—
511C2×SD16—222no—
512C2×SD16—222no—
513C2×SD16C4×D1114yes—
514C2×SD16D4414yes—
515C2×SD16C22⋊D1114yes—
516C22×C8—111no—
517C22×C8—114no—
518C22×C8—111no—
519C22×C8—222no—
520C22×C8—222no—
521C22×C8C22×D1111yescharacteristic
522C22×C8C22×D1111yescharacteristic
523C4×Q8—22no—
524C4×Q8—41no—
525C4×Q8—222no—
526C4×Q8—441no—
527C4×D4—22no—
528C4×D4—41no—
529C4×D4—222no—
530C4×D4—441no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—111no—
539C2×C22⋊C4—111no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—444no—
548C2×C42—21no—
549C2×C42—111no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552#107—22no—
553#107—222no—
554#103—22no—
555#103—222no—
556#103—441no—
557#103—441no—
558#102—22no—
559#102—222no—
560#102—441no—
561#102—441no—
562C22⋊C8—222no—
563#97—22no—
564#97—222no—
565#95—111no—
566#95—111no—
567#95—221no—
568#95—221no—
569#95—221no—
570#95—221no—
571#95—221no—
572#95—221no—
573C2×C11—44no—
574C2×C11D4×C22⋊C411yescharacteristic
575C2×C11C2×#44011yescharacteristic
576C2×C11#294911yescharacteristic
577C2×C11#326511yescharacteristic
578C2×C11#326511yescharacteristic
579C2×C11#326611yescharacteristic
580C2×C11#326611yescharacteristic
581D11—24no—
582D11—82no—
583C24—21no—
584C24—111no—
585C24—224no—
586C24—221no—
587C24—442no—
588C24—442no—
589C24—442no—
590C24—442no—
591C24—881no—
592C24—881no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—112no—
597C2×Q8—224no—
598C2×Q8—221no—
599C2×Q8—228no—
600C2×Q8—221no—
601C2×Q8—221no—
602C2×Q8—221no—
603C2×Q8—221no—
604C2×Q8—442no—
605C2×Q8—442no—
606C2×Q8—444no—
607C2×Q8—444no—
608C2×Q8—444no—
609C2×Q8C2×C4×D1112yes—
610C2×Q8C2×D4412yes—
611C2×Q8C2×C22⋊D1112yes—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—112no—
616C2×D4—224no—
617C2×D4—228no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—221no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—442no—
627C2×D4—442no—
628C2×D4C2×C4×D1112yes—
629C2×D4C2×D4412yes—
630C2×D4C2×C22⋊D1112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—111no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—224no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—881no—
655C22×C4D4×D1111yescharacteristic
656C22×C4D4×D1111yescharacteristic
657C22×C4C23×D1111yescharacteristic
658SD16—228no—
659SD16—228no—
660SD16—228no—
661SD16(C2×D11)⋊C4116yescomplemented
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—112no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—228no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8C2×C4×D1112yes—
673C2×C8C2×D4412yes—
674C2×C8C2×C22⋊D1112yes—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—42no—
680C4⋊C4—221no—
681C4⋊C4—221no—
682C4⋊C4—221no—
683C4⋊C4—221no—
684C4⋊C4—442no—
685C22⋊C4—42no—
686C22⋊C4—222no—
687C22⋊C4—222no—
688C22⋊C4—442no—
689C22⋊C4—442no—
690C22⋊C4—442no—
691C22⋊C4—442no—
692C22⋊C4—442no—
693C22⋊C4—881no—
694C22⋊C4—881no—
695C42—21no—
696C42—21no—
697C42—42no—
698C42—221no—
699C42—221no—
700C42—442no—
701C11#2243711yescharacteristic, complemented, Sylow
702C23—22no—
703C23—22no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—112no—
710C23—112no—
711C23—112no—
712C23—221no—
713C23—221no—
714C23—221no—
715C23—221no—
716C23—222no—
717C23—448no—
718C23—448no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23—441no—
725C23—884no—
726C23—884no—
727C23—884no—
728C23—884no—
729C23—884no—
730C23C2×D4×D1111yescharacteristic
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—222no—
735Q8—222no—
736Q8—448no—
737Q8—441no—
738Q8—441no—
739Q8C2×(C2×D11)⋊C414yescomplemented
740D4—22no—
741D4—22no—
742D4—22no—
743D4—222no—
744D4—222no—
745D4—448no—
746D4—441no—
747D4—441no—
748D4C2×(C2×D11)⋊C414yes—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—84no—
765C2×C4—112no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—222no—
777C2×C4—221no—
778C2×C4—221no—
779C2×C4—448no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—441no—
787C2×C4—441no—
788C2×C4—884no—
789C2×C4C22×C4×D1111yescharacteristic
790C2×C4C22×D4411yescharacteristic
791C2×C4#6703711yescharacteristic
792C2×C4#41×D1111yescharacteristic
793C2×C4#6704211yescharacteristic
794C2×C4C22×C22⋊D1111yescharacteristic
795C8—41no—
796C8—222no—
797C8—441no—
798C8C2×(C2×D11)⋊C414yescomplemented
799C22—24no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—114no—
807C22—222no—
808C22—222no—
809C22—222no—
810C22—222no—
811C22—222no—
812C22—222no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—8816no—
817C22—881no—
818C22—881no—
819C22—881no—
820C22—881no—
821C22C4×D4×D1111yescharacteristic
822C22D4×D4411yescharacteristic
823C22D11×AGL(1,ℤ/8)11yescharacteristic
824C22#1062330611yescharacteristic
825C22D11×#13711yescharacteristic
826C22#1062330911yescharacteristic
827C22D4×C22⋊D1111yescharacteristic
828C4—24no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—222no—
834C4—441no—
835C4—441no—
836C4—442no—
837C4—881no—
838C4—881no—
839C4#1062307611yescharacteristic
840C4#1062308511yescharacteristic
841C4C22×(C2×D11)⋊C411yescharacteristic
842C4#1062336011yescharacteristic
843C2—44no—
844C2—224no—
845C2—882no—
846C2D4×(C2×D11)⋊C411yescharacteristic
847C2D11×#44011yescharacteristic
848C2#1307747211yescharacteristic
849C2#1308010511yescharacteristic
850C2#1308011311yescharacteristic
851C2#1308012011yescharacteristic
852C2#1308012811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenterC2×#440D11
hypocenterC11#22437
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#10622777C2semidirect
3. Q8×(C2×D11)⋊C4C2semidirect
5. #13069497C2semidirect
6. #13069495C2semidirect
7. #13068971C2semidirect
8. #13068969C2semidirect
9. #13068950C2semidirect
10. #13068948C2semidirect
11. #13068642C2semidirect
12. #13068549C2semidirect
14. #13068393C2semidirect
15. C2×C11×#440C2semidirect
19. C2×C4×Q8×C11C22semidirect
21. C2×Q8×Dic11C22semidirect
28. C2×SD16×D11C4semidirect
32. C2×C11×#107C22semidirect
33. C2×C11×#103C22semidirect
35. C2×C11×#97C22semidirect
36. C2×#66899C22semidirect
42. C2×#66882C22semidirect
43. C2×#66880C22semidirect
44. C2×#66879C22semidirect
50. #10622587C22semidirect
51. C2×#66874C22semidirect
59. #10622542C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
75. C2×Q8×D11C2×C4semidirect
107. C2×#4325C2×C4semidirect
132. C2×#4314C2×C4semidirect
135. C2×C8×D11C2×C4semidirect
233. C11×SD16C22⋊C4semidirect
278. C2×#440D11semidirect
323. Q8×C11C2×C22⋊C4semidirect
385. C8×C11C2×C22⋊C4semidirect
399. C2×C4×Q8C2×D11semidirect
406. C2×#107C2×D11semidirect
410. C2×#103C2×D11semidirect
417. C2×#97C2×D11semidirect
464. C2×D11#440semidirect
661. SD16(C2×D11)⋊C4semidirect
701. C11#22437semidirect
739. Q8C2×(C2×D11)⋊C4semidirect
798. C8C2×(C2×D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D112
C2×#106227772
Q8×(C2×D11)⋊C42
D4×(C2×D11)⋊C42
#130694972
#130694952
#130689712
#130689692
#130689502
#130689482
#130686422
#130685492
#130685452
#130683932
C2×C11×#4402
#2243711