Finite Group Databasebeta

← #15620268

Subgroups — #15620268

Order 2816.

4726 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic, complemented
2C22×#66995C211yesmaximal, characteristic, complemented
3#13081945C211yesmaximal, characteristic, complemented
4#13077931C218yesmaximal, complemented
5#13077911C214yesmaximal, complemented
6#13077902C214yesmaximal, complemented
7#13077858C214yesmaximal, complemented
8#13077850C214yesmaximal, complemented
9#13077135C211yesmaximal, characteristic, complemented
10C2×#10622838C211yesmaximal, characteristic, complemented
11#13077061C211yesmaximal, characteristic, complemented
12C22×C11×2−1+4C211yesmaximal, characteristic, complemented
13C2×C11×2−1+4—22no—
14C2×C11×2−1+4—22no—
15C2×C11×2−1+4—28no—
16C2×C11×2−1+4—28no—
17C2×C11×2−1+4C2214yes—
18C2×C11×2−1+4C2214yescomplemented
19C22×C11×#41—22no—
20C22×C11×#41—21no—
21C22×C11×#41C2211yescharacteristic
22C22×C11×#41C2211yescharacteristic
23C22×C11×#41C2212yescomplemented
24C23×Q8×C11—21no—
25C23×Q8×C11C2211yescharacteristic
26C23×Q8×C11C2212yescomplemented
27C22×#4339C2211yescharacteristic
28#10623364C2214yescomplemented
29#10623363—22no—
30#10623361C2212yescomplemented
31#10623359—22no—
32#10623356C2212yescomplemented
33C2×#67004C2212yescomplemented
34#10623353—28no—
35C2×#67003C2214yescomplemented
36C2×#67002C2212yescomplemented
37#10623347—21no—
38C22×#4326C2212yescomplemented
39C2×#66995—28no—
40C2×#66995C2212yes—
41C2×#66995C2214yes—
42C2×#66995C2214yescomplemented
43C22×#4325C2212yescomplemented
44#10623336—21no—
45#10623335—22no—
46C2×#66985C2212yes—
47#10623322C2214yes—
48C2×#66979C2211yescharacteristic
49C22×#4318C2211yescharacteristic
50C22×#4318C2211yescharacteristic
51#10622852C22116yescomplemented
52#10622851C22116yescomplemented
53#10622847C2214yescomplemented
54#10622847C2214yescomplemented
55#10622846C2214yescomplemented
56#10622845C2214yescomplemented
57#10622841C22116yescomplemented
58#10622840C22116yescomplemented
59#10622838C2212yescomplemented
60#10622838C2214yescomplemented
61#10622838C2214yescomplemented
62C2×#66899C2214yescomplemented
63#10622828C2212yescomplemented
64#10622820C2214yescomplemented
65C11×2−1+4—232no—
66C11×2−1+4—232no—
67C11×2−1+4—216no—
68C11×2−1+4—216no—
69C11×2−1+4—216no—
70C11×2−1+4—216no—
71C2×C11×#41—232no—
72C2×C11×#41—216no—
73C2×C11×#41—28no—
74C2×C11×#41—28no—
75C2×C11×#41—24no—
76C2×C11×#41—24no—
77C2×C11×#41—28no—
78C2×C11×#41—28no—
79C2×C11×#41—24no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41—24no—
83C2×C11×#41—24no—
84C2×C11×#41—24no—
85C2×C11×#41D412yes—
86C2×C11×#41D412yes—
87C2×C11×#41D418yescomplemented
88C2×C11×#41C2318yes—
89C2×C11×#41C2312yes—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C2×C11×#41C2312yes—
93C22×Q8×C11—216no—
94C22×Q8×C11—24no—
95C22×Q8×C11—24no—
96C22×Q8×C11—28no—
97C22×Q8×C11—28no—
98C22×Q8×C11—21no—
99C22×Q8×C11—22no—
100C22×Q8×C11—24no—
101C22×Q8×C11—21no—
102C22×Q8×C11—21no—
103C22×Q8×C11—24no—
104C22×Q8×C11D411yescharacteristic
105C22×Q8×C11D418yescomplemented
106C22×Q8×C11C2318yes—
107C22×Q8×C11C2312yes—
108C22×Q8×C11C2312yes—
109C22×Q8×C11C2311yescharacteristic
110C22×Q8×C11C2312yes—
111C22×D4×C11—21no—
112C22×D4×C11—22no—
113C22×D4×C11D412yes—
114C22×D4×C11D411yescharacteristic
115C22×D4×C11C2311yescharacteristic
116C23×C4×C11—21no—
117C23×C4×C11—22no—
118C23×C4×C11—21no—
119C23×C4×C11—22no—
120C23×C4×C11C2312yes—
121C23×C4×C11C2311yescharacteristic
122C22×C22⋊D11—21no—
123C2×#4339—21no—
124C2×#4339—21no—
125C2×#4339—24no—
126C2×#4339—24no—
127C2×#4339C2312yes—
128C2×#4339C2312yes—
129C22×D44C2311yescharacteristic
130C22×C4×D11—21no—
131C22×Dic22C2311yescharacteristic
132#67006—24no—
133C2×C22⋊Dic11—21no—
134#67004—28no—
135#67003—216no—
136#67002—28no—
137#67000—22no—
138#66999—24no—
139#66997—22no—
140C2×#4326—28no—
141C2×#4326C2318yes—
142C2×#4326C2314yes—
143#66995—216no—
144#66995—216no—
145#66995—28no—
146C2×#4325—28no—
147C2×#4325C2318yes—
148C2×#4325C2314yes—
149#66993—22no—
150#66992—28no—
151#66991—24no—
152#66990—24no—
153#66989—22no—
154#66988—24no—
155C2×#4324C2314yes—
156#66985—28no—
157C2×#4323C2314yes—
158#66983C2318yes—
159#66982—24no—
160C4×C22⋊D11—28no—
161#66979—21no—
162#66979—21no—
163#66979C2312yes—
164#66979C2312yes—
165C2×C4⋊Dic11C2312yes—
166#66977C2318yes—
167C2×C4×Dic11—21no—
168C2×#4318—24no—
169C2×#4318—24no—
170C2×#4318C2312yes—
171C2×#4318C2312yes—
172C2×#4318C2312yes—
173C2×#4318C2312yes—
174C22×C11⋊C8C2312yes—
175C22×C11⋊C8C2312yes—
176#66899C23116yes—
177#66899C2318yes—
178#66896C2318yes—
179C22⋊(C11⋊C8)C23116yes—
180#60368—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11C2×D412yes—
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C11×#41—264no—
186C11×#41—264no—
187C11×#41—232no—
188C11×#41—232no—
189C11×#41—232no—
190C11×#41—216no—
191C11×#41—216no—
192C11×#41—28no—
193C11×#41—28no—
194C11×#41—28no—
195C11×#41—28no—
196C11×#41—24no—
197C11×#41—24no—
198C11×#41—24no—
199C11×#41—24no—
200C11×#41—24no—
201C11×#41—24no—
202C11×#41C2×D418yes—
203C11×#41C2×D418yes—
204C2×Q8×C11—216no—
205C2×Q8×C11—232no—
206C2×Q8×C11—232no—
207C2×Q8×C11—232no—
208C2×Q8×C11—216no—
209C2×Q8×C11—216no—
210C2×Q8×C11—24no—
211C2×Q8×C11—28no—
212C2×Q8×C11—28no—
213C2×Q8×C11—28no—
214C2×Q8×C11—22no—
215C2×Q8×C11—24no—
216C2×Q8×C11—28no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11—21no—
220C2×Q8×C11—22no—
221C2×Q8×C11—24no—
222C2×Q8×C11—24no—
223C2×Q8×C11C2×D418yes—
224C2×Q8×C11C2×D414yes—
225C2×Q8×C11C2×D418yes—
226C2×Q8×C11C2×D418yes—
227C2×Q8×C11C2×D412yes—
228C2×Q8×C11C2×D412yes—
229C2×Q8×C11C2412yes—
230C2×Q8×C11C2414yes—
231C2×D4×C11—216no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—24no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11C2×D414yes—
241C2×D4×C11C2×D412yes—
242C2×D4×C11C2×D412yes—
243C2×D4×C11C2×D414yes—
244C2×D4×C11C2×D414yes—
245C2×D4×C11C2412yes—
246C22×C4×C11—216no—
247C22×C4×C11—216no—
248C22×C4×C11—28no—
249C22×C4×C11—22no—
250C22×C4×C11—21no—
251C22×C4×C11—28no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—28no—
255C22×C4×C11—28no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—24no—
259C22×C4×C11—24no—
260C22×C4×C11C2×D414yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D414yes—
266C22×C4×C11C2×D414yes—
267C22×C4×C11C2414yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C2×C22⋊D11—22no—
272C2×C22⋊D11—22no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—44no—
275C22×Dic11—21no—
276C22×Dic11—22no—
277#4339—24no—
278#4339—24no—
279#4339—24no—
280#4339—24no—
281#4339—44no—
282#4339—44no—
283C2×D44—21no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44C2412yes—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—44no—
290C2×Dic22—22no—
291C2×Dic22—22no—
292C2×Dic22—21no—
293C2×Dic22C2412yes—
294C22⋊Dic11—28no—
295C22⋊Dic11—22no—
296C22⋊Dic11—22no—
297#4326—216no—
298#4326—28no—
299#4325—216no—
300#4325—28no—
301#4324—28no—
302#4323—28no—
303(C2×D11)⋊C4—28no—
304C4⋊Dic11—22no—
305C4⋊Dic11C2414yes—
306Dic11⋊C4—28no—
307C4×Dic11—22no—
308C4×Dic11—22no—
309#4318—24no—
310#4318—24no—
311#4318—24no—
312#4318—24no—
313C2×C11⋊C8—24no—
314C2×C11⋊C8—24no—
315C2×C11⋊C8C2414yes—
316C2×C11⋊C8C2414yes—
317C22×2−1+4D1111yescharacteristic, complemented
318C2×#575—111no—
319C22×#137—111no—
320#3449—111no—
321#3013—118no—
322#3011—114no—
323#3010—114no—
324#3005—114no—
325#3004—114no—
326#2896—111no—
327C2×#419—111no—
328#2879—111no—
329C23×C11—24no—
330C23×C11—24no—
331C23×C11—22no—
332C23×C11—42no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11#12014yes—
336C23×C11C22×D414yes—
337C23×C11C22×D411yescharacteristic
338C23×C11C22×D411yescharacteristic
339C23×C11C22×D411yescharacteristic
340C22×D11—22no—
341C22×D11—42no—
342C22×D11—82no—
343Q8×C11—232no—
344Q8×C11—28no—
345Q8×C11—24no—
346Q8×C11—28no—
347Q8×C11—28no—
348Q8×C11—24no—
349Q8×C11—24no—
350Q8×C11—22no—
351Q8×C11—24no—
352Q8×C11C22×D414yes—
353Q8×C11C22×D418yes—
354D4×C11—232no—
355D4×C11—28no—
356D4×C11—28no—
357D4×C11—28no—
358D4×C11—28no—
359D4×C11—24no—
360D4×C11—24no—
361D4×C11—24no—
362D4×C11—22no—
363D4×C11C22×D414yes—
364C2×C4×C11—232no—
365C2×C4×C11—232no—
366C2×C4×C11—28no—
367C2×C4×C11—24no—
368C2×C4×C11—24no—
369C2×C4×C11—28no—
370C2×C4×C11—28no—
371C2×C4×C11—24no—
372C2×C4×C11—22no—
373C2×C4×C11—28no—
374C2×C4×C11—28no—
375C2×C4×C11—28no—
376C2×C4×C11—24no—
377C2×C4×C11—24no—
378C2×C4×C11#12014yes—
379C2×C4×C11#12014yes—
380C2×C4×C11#12014yes—
381C2×C4×C11C22×D414yes—
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C2511yescharacteristic
392C22⋊D11—44no—
393C22⋊D11—44no—
394C22⋊D11—88no—
395C2×Dic11—24no—
396C2×Dic11—22no—
397C2×Dic11—42no—
398C2×Dic11—82no—
399D44—22no—
400D44—22no—
401D44—42no—
402C4×D11—44no—
403C4×D11—44no—
404Dic22—22no—
405Dic22—22no—
406Dic22—42no—
407C11⋊C8—24no—
408C11⋊C8—24no—
409C2×2−1+4—22no—
410C2×2−1+4—22no—
411C2×2−1+4—28no—
412C2×2−1+4—28no—
413C2×2−1+4C2×D1114yes—
414C2×2−1+4C2×D1114yescomplemented
415C22×#41—22no—
416C22×#41—21no—
417C22×#41—111no—
418C22×#41C2×D1111yescharacteristic
419C22×#41C2×D1111yescharacteristic
420C22×#41C2×D1112yescomplemented
421C23×Q8—21no—
422C23×Q8C2×D1111yescharacteristic
423C23×Q8C2×D1112yescomplemented
424#575—228no—
425C2×#137—112no—
426C2×#137—112no—
427C2×#137—114no—
428C2×#137—114no—
429C2×#137—228no—
430C2×AGL(1,ℤ/8)—112no—
431C2×AGL(1,ℤ/8)—112no—
432C2×#135—114no—
433C22×Q16—112no—
434C22×SD16—112no—
435C22×M16—111no—
436C22×M16—111no—
437#537—114no—
438#536—112no—
439#536—221no—
440#535—112no—
441#535—221no—
442#534—222no—
443#532—222no—
444#525—114no—
445#525—222no—
446C2×#117—111no—
447#452—1116no—
448#451—1116no—
449#449—1116no—
450#448—1116no—
451#419—114no—
452#419—114no—
453#419—112no—
454#418—112no—
455#417—114no—
456#416—114no—
457C2×#103—114no—
458#408—114no—
459#408—114no—
460#407—114no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—28no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—44no—
468C22×C11—48no—
469C22×C11—48no—
470C22×C11—44no—
471C22×C11C2×#12012yes—
472C22×C11C2×#12012yes—
473C22×C11C2×#12012yes—
474C22×C11C23×D411yescharacteristic
475C2×D11—44no—
476C2×D11—42no—
477C2×D11—84no—
478C4×C11—28no—
479C4×C11—24no—
480C4×C11—24no—
481C4×C11C2×#12012yes—
482C4×C11C2×#12012yes—
483C4×C11C2×#12012yes—
484C4×C11C23×D411yescharacteristic
485C4×C11C23×D411yescharacteristic
486Dic11—44no—
487Dic11—42no—
4882−1+4—232no—
4892−1+4—232no—
4902−1+4—216no—
4912−1+4—216no—
4922−1+4—216no—
4932−1+4—216no—
494C2×#41—232no—
495C2×#41—216no—
496C2×#41—28no—
497C2×#41—28no—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—28no—
501C2×#41—28no—
502C2×#41—24no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—112no—
509C2×#41—112no—
510C2×#41—221no—
511C2×#41—221no—
512C2×#41—224no—
513C2×#41—224no—
514C2×#41C22⋊D1112yes—
515C2×#41C22⋊D1112yes—
516C2×#41C22⋊D1118yescomplemented
517C2×#41C22×D1118yes—
518C2×#41C22×D1112yes—
519C2×#41C22×D1112yes—
520C2×#41C22×D1112yes—
521C2×#41C22×D1112yes—
522C22×Q8—216no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—28no—
526C22×Q8—28no—
527C22×Q8—21no—
528C22×Q8—22no—
529C22×Q8—24no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—24no—
533C22×Q8—111no—
534C22×Q8C22⋊D1111yescharacteristic
535C22×Q8C22⋊D1118yescomplemented
536C22×Q8C22×D1118yes—
537C22×Q8C22×D1112yes—
538C22×Q8C22×D1112yes—
539C22×Q8C22×D1112yes—
540C22×Q8C22×D1111yescharacteristic
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—111no—
544C22×D4—221no—
545C22×D4C22⋊D1112yes—
546C22×D4C22⋊D1111yescharacteristic
547C22×D4C22×D1111yescharacteristic
548C23×C4—21no—
549C23×C4—22no—
550C23×C4—21no—
551C23×C4—22no—
552C23×C4—221no—
553C23×C4C22×D1112yes—
554C23×C4C22×D1111yescharacteristic
555#137—228no—
556#137—2216no—
557#137—2216no—
558#137—228no—
559AGL(1,ℤ/8)—228no—
560AGL(1,ℤ/8)—228no—
561#135—2216no—
562C2×Q16—118no—
563C2×Q16—114no—
564C2×Q16—228no—
565C2×SD16—118no—
566C2×SD16—114no—
567C2×SD16—114no—
568C2×SD16—228no—
569C2×D8—114no—
570C2×M16—112no—
571C2×M16—112no—
572C2×M16—112no—
573C2×M16—112no—
574C2×M16—224no—
575C2×M16—224no—
576C22×C8—112no—
577C22×C8—112no—
578C4⋊Q8—222no—
579#127—222no—
580#124—222no—
581#124—222no—
582#123—224no—
583#123—224no—
584C22⋊Q8—118no—
585C22⋊Q8—224no—
586#121—118no—
587#121—224no—
588#121—228no—
589#120—224no—
590#120—224no—
591C4×D4—228no—
592#117—112no—
593#117—112no—
594#117—221no—
595#117—221no—
596C2×C4⋊C4—112no—
597C2×C22⋊C4—221no—
598C2×C42—221no—
599#103—1116no—
600#103—118no—
601#102—118no—
602C22⋊C8—1116no—
603C2×C11—22no—
604C2×C11—22no—
605C2×C11—22no—
606C2×C11—44no—
607C2×C11—44no—
608C2×C11C22×#12011yescharacteristic
609C2×C11#358612yes—
610D11—82no—
611C24—21no—
612C24—221no—
613C24C2×C22⋊D1112yes—
614C24C2×C22⋊D1111yescharacteristic
615#41—264no—
616#41—264no—
617#41—232no—
618#41—232no—
619#41—232no—
620#41—216no—
621#41—216no—
622#41—28no—
623#41—28no—
624#41—28no—
625#41—28no—
626#41—24no—
627#41—24no—
628#41—24no—
629#41—24no—
630#41—24no—
631#41—24no—
632#41—224no—
633#41—224no—
634#41—224no—
635#41—224no—
636#41—444no—
637#41—444no—
638#41C2×C22⋊D1118yes—
639#41C2×C22⋊D1118yes—
640C2×Q8—216no—
641C2×Q8—232no—
642C2×Q8—232no—
643C2×Q8—232no—
644C2×Q8—216no—
645C2×Q8—216no—
646C2×Q8—24no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—28no—
650C2×Q8—22no—
651C2×Q8—24no—
652C2×Q8—28no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—112no—
660C2×Q8—221no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×Q8C2×C22⋊D1118yes—
664C2×Q8C2×C22⋊D1114yes—
665C2×Q8C2×C22⋊D1118yes—
666C2×Q8C2×C22⋊D1118yes—
667C2×Q8C2×C22⋊D1112yes—
668C2×Q8C2×C22⋊D1112yes—
669C2×Q8C23×D1112yes—
670C2×Q8C23×D1114yes—
671C2×D4—216no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—112no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—228no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—221no—
687C2×D4—444no—
688C2×D4C2×C22⋊D1114yes—
689C2×D4C2×C22⋊D1114yes—
690C2×D4C2×C22⋊D1112yes—
691C2×D4C2×C22⋊D1112yes—
692C2×D4C2×C22⋊D1114yes—
693C2×D4C23×D1112yes—
694C22×C4—216no—
695C22×C4—216no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—28no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—221no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—444no—
713C22×C4C2×C22⋊D1114yes—
714C22×C4C2×C22⋊D1112yes—
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1114yes—
719C22×C4C2×C22⋊D1114yes—
720C22×C4C23×D1114yes—
721C22×C4C23×D1111yescharacteristic
722C22×C4C23×D1111yescharacteristic
723C22×C4C23×D1111yescharacteristic
724Q16—2216no—
725Q16—228no—
726SD16—2216no—
727SD16—228no—
728SD16—228no—
729D8—228no—
730M16—224no—
731M16—224no—
732M16—224no—
733M16—224no—
734C2×C8—114no—
735C2×C8—114no—
736C2×C8—224no—
737C2×C8—224no—
738C4⋊C4—114no—
739C4⋊C4—222no—
740C4⋊C4—228no—
741C22⋊C4—222no—
742C22⋊C4—222no—
743C22⋊C4—228no—
744C22⋊C4—228no—
745C42—222no—
746C42—222no—
747C11#6036811yescharacteristic, complemented, Sylow
748C23—24no—
749C23—24no—
750C23—22no—
751C23—42no—
752C23—44no—
753C23—44no—
754C23—222no—
755C23—442no—
756C23—882no—
757C23#6700614yes—
758C23C22×C22⋊D1114yes—
759C23C22×C22⋊D1111yescharacteristic
760C23C22×C22⋊D1111yescharacteristic
761C23C22×C22⋊D1111yescharacteristic
762Q8—232no—
763Q8—24no—
764Q8—28no—
765Q8—28no—
766Q8—28no—
767Q8—24no—
768Q8—24no—
769Q8—22no—
770Q8—24no—
771Q8—222no—
772Q8—222no—
773Q8—442no—
774Q8C22×C22⋊D1114yes—
775Q8C22×C22⋊D1118yes—
776D4—232no—
777D4—28no—
778D4—28no—
779D4—28no—
780D4—28no—
781D4—24no—
782D4—24no—
783D4—24no—
784D4—22no—
785D4—222no—
786D4—222no—
787D4—444no—
788D4—444no—
789D4—442no—
790D4—888no—
791D4C22×C22⋊D1114yes—
792C2×C4—232no—
793C2×C4—232no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—224no—
807C2×C4—222no—
808C2×C4—442no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—882no—
812C2×C4#6700614yes—
813C2×C4#6700614yes—
814C2×C4#6700614yes—
815C2×C4C22×C22⋊D1114yes—
816C2×C4C22×C22⋊D1111yescharacteristic
817C2×C4C22×C22⋊D1111yescharacteristic
818C2×C4C22×C22⋊D1111yescharacteristic
819C2×C4C22×C22⋊D1112yes—
820C2×C4C22×C22⋊D1112yes—
821C2×C4C22×C22⋊D1112yes—
822C2×C4C22×C22⋊D1112yes—
823C2×C4C22×C22⋊D1112yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C24×D1111yescharacteristic
826C8—224no—
827C8—224no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—28no—
832C22—24no—
833C22—24no—
834C22—44no—
835C22—48no—
836C22—48no—
837C22—44no—
838C22—444no—
839C22—442no—
840C22—884no—
841C22C2×#6700612yes—
842C22C2×#6700612yes—
843C22C2×#6700612yes—
844C22C23×C22⋊D1111yescharacteristic
845C4—28no—
846C4—24no—
847C4—24no—
848C4—444no—
849C4—442no—
850C4C2×#6700612yes—
851C4C2×#6700612yes—
852C4C2×#6700612yes—
853C4C23×C22⋊D1111yescharacteristic
854C4C23×C22⋊D1111yescharacteristic
855C2—22no—
856C2—22no—
857C2—22no—
858C2—44no—
859C2—44no—
860C2—882no—
861C2C22×#6700611yescharacteristic
862C2#1308340312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×2−1+4C2
socleC22×C11C23×D4
hypercenterC22×2−1+4D11
hypocenterC11#60368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C22×#66995C2semidirect
3. #13081945C2semidirect
4. #13077931C2semidirect
5. #13077911C2semidirect
6. #13077902C2semidirect
7. #13077858C2semidirect
8. #13077850C2semidirect
9. #13077135C2semidirect
10. C2×#10622838C2semidirect
11. #13077061C2semidirect
12. C22×C11×2−1+4C2semidirect
18. C2×C11×2−1+4C22semidirect
23. C22×C11×#41C22semidirect
26. C23×Q8×C11C22semidirect
28. #10623364C22semidirect
30. #10623361C22semidirect
32. #10623356C22semidirect
33. C2×#67004C22semidirect
35. C2×#67003C22semidirect
36. C2×#67002C22semidirect
38. C22×#4326C22semidirect
42. C2×#66995C22semidirect
43. C22×#4325C22semidirect
51. #10622852C22semidirect
52. #10622851C22semidirect
53. #10622847C22semidirect
54. #10622847C22semidirect
55. #10622846C22semidirect
56. #10622845C22semidirect
57. #10622841C22semidirect
58. #10622840C22semidirect
59. #10622838C22semidirect
60. #10622838C22semidirect
61. #10622838C22semidirect
62. C2×#66899C22semidirect
63. #10622828C22semidirect
64. #10622820C22semidirect
87. C2×C11×#41D4semidirect
105. C22×Q8×C11D4semidirect
317. C22×2−1+4D11semidirect
414. C2×2−1+4C2×D11semidirect
420. C22×#41C2×D11semidirect
423. C23×Q8C2×D11semidirect
516. C2×#41C22⋊D11semidirect
535. C22×Q8C22⋊D11semidirect
747. C11#60368semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×#669952
#130819452
#130779312
#130779112
#130779022
#130778582
#130778502
#130771352
C2×#106228382
#130770612
C22×C11×2−1+42
#6036811