Finite Group Databasebeta

← #15617221

Subgroups — #15617221

Order 2816.

5134 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D11C211yesmaximal, characteristic
2C2×#10623281C212yesmaximal, complemented
3#13077066C213yesmaximal, complemented
4#13077065C211yesmaximal, characteristic, complemented
5#13077064C216yesmaximal, complemented
6#13077063C212yesmaximal, complemented
7#13077062C213yesmaximal, complemented
8#13077058C216yesmaximal, complemented
9C2×#10622339C213yesmaximal, complemented
10D11×#407C213yesmaximal, complemented
11C11×#2880C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×#41×D11—216no—
14C2×#41×D11C411yescharacteristic
15C2×#41×D11C411yescharacteristic
16C2×#41×D11C413yes—
17C2×#41×D11C413yes—
18C2×#41×D11C2213yes—
19C2×#41×D11C2211yescharacteristic
20C2×#41×D11C2213yes—
21C2×#41×D11C2211yescharacteristic
22C22×#4343C411yescharacteristic
23C22×Q8×D11C411yescharacteristic
24C22×#4341C413yes—
25C22×D4×D11C413yes—
26C22×#4339C2213yes—
27C23×C4×D11C2213yes—
28C2×C11×#131C2212yescomplemented
29C2×#67001C2212yescomplemented
30#10623281—216no—
31C2×#66960C2216yescomplemented
32C2×M16×D11C2216yescomplemented
33C2×#66954C2216yescomplemented
34C22×#4313C2216yescomplemented
35C11×#408C2216yescomplemented
36C11×#407C2213yescomplemented
37C2×C11×C22⋊C8C2213yescomplemented
38#10622847C2216yescomplemented
39#10622820C2213yescomplemented
40C2×C22⋊(C11⋊C8)C2213yescomplemented
41#10622742C2216yescomplemented
42#10622739C2216yescomplemented
43#10622723C2216yescomplemented
44C2×(C2×D11)⋊C8C2216yescomplemented
45#10622340C22112yescomplemented
46#10622340C22112yescomplemented
47#10622339C2213yes—
48#10622339C2211yescharacteristic
49#10622339C2216yescomplemented
50#10622339C2213yescomplemented
51#10622339C2213yescomplemented
52#10622339C2216yescomplemented
53#10622339C2216yescomplemented
54D11×C22⋊C8C2216yescomplemented
55D11×C22⋊C8C2216yescomplemented
56C24×D11C2×C413yes—
57C2×C11×#41—28no—
58C2×C11×#41C2×C411yescharacteristic
59C2×C11×#41C2×C413yes—
60C2×C11×#41C2313yes—
61C2×C11×#41C2311yescharacteristic
62C22×Q8×C11C2×C411yescharacteristic
63C22×D4×C11C2×C413yes—
64C23×C4×C11C2313yes—
65C22×C22⋊D11C2×C416yes—
66C23×Dic11C2×C413yes—
67#41×D11—28no—
68#41×D11—28no—
69#41×D11—28no—
70#41×D11—224no—
71#41×D11—224no—
72#41×D11—224no—
73#41×D11—224no—
74#41×D11D4116yes—
75C2×#4343—28no—
76C2×#4343C2×C411yescharacteristic
77C2×#4343C2×C413yes—
78C2×#4343C2×C413yes—
79C2×#4343C2×C411yescharacteristic
80C2×Q8×D11—28no—
81C2×Q8×D11C2×C411yescharacteristic
82C2×Q8×D11C2×C413yes—
83C2×Q8×D11C2×C413yes—
84C2×Q8×D11C2×C411yescharacteristic
85C2×#4341—224no—
86C2×#4341C2×C416yes—
87C2×#4341C2×C416yes—
88C2×#4341C2×C413yes—
89C2×#4341C2×C413yes—
90C2×#4341C2×C413yes—
91C2×#4341C2×C413yes—
92C2×D4×D11—224no—
93C2×D4×D11C2×C416yes—
94C2×D4×D11C2×C416yes—
95C2×D4×D11C2×C413yes—
96C2×D4×D11C2×C413yes—
97C2×D4×D11C2×C413yes—
98C2×D4×D11C2×C413yes—
99C2×#4339—224no—
100C2×#4339C2×C416yes—
101C2×#4339C2×C413yes—
102C2×#4339C2×C413yes—
103C2×#4339C2313yes—
104C2×#4339C2316yes—
105C2×#4339C2313yes—
106C22×D44C2×C413yes—
107C22×C4×D11—224no—
108C22×C4×D11C2×C413yes—
109C22×C4×D11C2×C413yes—
110C22×C4×D11C2×C413yes—
111C22×C4×D11C2×C413yes—
112C22×C4×D11C2×C413yes—
113C22×C4×D11C2×C413yes—
114C22×C4×D11C2313yes—
115C22×C4×D11C2313yes—
116C22×C4×D11C2313yes—
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2313yes—
119C22×C4×D11C2313yes—
120C22×Dic22C2×C413yes—
121C11×#131—28no—
122C2×C11×M16C2316yescomplemented
123C22×C8×C11C2316yescomplemented
124#67001—28no—
125C2×#4318C2316yescomplemented
126C22×C11⋊C8C2316yescomplemented
127#66960—224no—
128M16×D11—224no—
129#66954—224no—
130C2×#4313—224no—
131C2×#4313C2312yes—
132C2×#4313C2316yes—
133C2×#4313C2316yescomplemented
134C2×#4313C2316yescomplemented
135C2×C8×D11C23112yescomplemented
136C11×C22⋊C8C2313yes—
137C11×C22⋊C8C2311yescharacteristic
138C11×C22⋊C8C2316yescomplemented
139C11×C22⋊C8C2316yescomplemented
140C22⋊(C11⋊C8)C2311yescharacteristic
141C22⋊(C11⋊C8)C2313yes—
142C22⋊(C11⋊C8)C2316yescomplemented
143C22⋊(C11⋊C8)C2316yescomplemented
144(C2×D11)⋊C8C2312yes—
145(C2×D11)⋊C8C2316yes—
146(C2×D11)⋊C8C2316yescomplemented
147(C2×D11)⋊C8C2316yescomplemented
148(C2×D11)⋊C8C23112yescomplemented
149#60064—111nomaximal, Sylow
150C24×C11C22×C413yes—
151C23×D11—212no—
152C23×D11—46no—
153C23×D11—46no—
154C23×D11C22×C411yescharacteristic
155C23×D11C22×C413yes—
156C23×D11C22×C413yes—
157C23×D11C22×C413yes—
158C23×D11C22×C413yes—
159C23×D11C22×C413yes—
160C11×#41—24no—
161C11×#41—212no—
162C11×#41—212no—
163C11×#41C2×D418yes—
164C2×Q8×C11—24no—
165C2×Q8×C11C22×C413yes—
166C2×Q8×C11C22×C411yescharacteristic
167C2×D4×C11—212no—
168C2×D4×C11C22×C416yes—
169C2×D4×C11C22×C413yes—
170C2×D4×C11C22×C413yes—
171C22×C4×C11—212no—
172C22×C4×C11C22×C413yes—
173C22×C4×C11C22×C413yes—
174C22×C4×C11C22×C413yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2413yes—
177C22×C4×C11C2413yes—
178C2×C22⋊D11—224no—
179C2×C22⋊D11C22×C416yes—
180C2×C22⋊D11C22×C416yes—
181C2×C22⋊D11C22×C416yes—
182C2×C22⋊D11C22×C416yes—
183C22×Dic11—212no—
184C22×Dic11C22×C413yes—
185C22×Dic11C22×C411yescharacteristic
186C22×Dic11C22×C413yes—
187C22×Dic11C22×C413yes—
188C22×Dic11C22×C413yes—
189C22×Dic11C22×C413yes—
190#4343—212no—
191#4343—212no—
192#4343—24no—
193#4343C22⋊C418yes—
194Q8×D11—212no—
195Q8×D11—212no—
196Q8×D11—24no—
197Q8×D11C22⋊C418yes—
198#4341—224no—
199#4341—224no—
200#4341—212no—
201#4341—212no—
202#4341—212no—
203#4341C22⋊C4124yes—
204D4×D11—224no—
205D4×D11—212no—
206D4×D11—212no—
207D4×D11—224no—
208D4×D11—212no—
209D4×D11C22⋊C4124yes—
210#4339—224no—
211#4339—212no—
212#4339—224no—
213#4339—212no—
214#4339—212no—
215#4339C2×D4124yes—
216C2×D44—212no—
217C2×D44C22×C416yes—
218C2×D44C22×C413yes—
219C2×D44C22×C413yes—
220C2×C4×D11—212no—
221C2×C4×D11—212no—
222C2×C4×D11—212no—
223C2×C4×D11—212no—
224C2×C4×D11—212no—
225C2×C4×D11—24no—
226C2×C4×D11—212no—
227C2×C4×D11—212no—
228C2×C4×D11—212no—
229C2×C4×D11—212no—
230C2×C4×D11—212no—
231C2×C4×D11C22×C411yescharacteristic
232C2×C4×D11C22×C411yescharacteristic
233C2×C4×D11C22×C413yes—
234C2×C4×D11C22×C413yes—
235C2×C4×D11C22×C413yes—
236C2×C4×D11C22×C413yes—
237C2×C4×D11C22×C413yes—
238C2×C4×D11C22×C413yes—
239C2×C4×D11C22×C413yes—
240C2×C4×D11C22×C413yes—
241C2×C4×D11C22×C413yes—
242C2×C4×D11C22×C413yes—
243C2×C4×D11C2×D4124yes—
244C2×C4×D11C2411yescharacteristic
245C2×C4×D11C2413yes—
246C2×C4×D11C2413yes—
247C2×C4×D11C2411yescharacteristic
248C2×Dic22—212no—
249C2×Dic22C22×C416yes—
250C2×Dic22C22×C413yes—
251C2×Dic22C22×C413yes—
252C11×M16—212no—
253C2×C8×C11—212no—
254C2×C8×C11C2416yes—
255C2×C8×C11C2412yes—
256#4318—212no—
257C2×C11⋊C8—212no—
258C2×C11⋊C8C2416yes—
259C2×C11⋊C8C2412yes—
260#4313—24no—
261#4313—212no—
262#4313—212no—
263#4313—212no—
264C8×D11—224no—
265C23×#41—111no—
266C2×#568—112no—
267#2880—116no—
268#2880—113no—
269#2880—113no—
270#2880—111no—
271#2880—112no—
272#2880D1111yescharacteristic, complemented
273#2879—116no—
274C2×#407—113no—
275C2×#407—113no—
276C23×C11—26no—
277C23×C11—26no—
278C23×C11—43no—
279C23×C11C23×C413yes—
280C23×C11C23×C413yes—
281C23×C11C23×C411yescharacteristic
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—26no—
286C22×D11—26no—
287C22×D11—26no—
288C22×D11—26no—
289C22×D11—26no—
290C22×D11—26no—
291C22×D11—26no—
292C22×D11—43no—
293C22×D11—43no—
294C22×D11—43no—
295C22×D11—43no—
296C22×D11—43no—
297C22×D11—43no—
298C22×D11—43no—
299C22×D11—448no—
300C22×D11C2×C22⋊C4112yes—
301C22×D11C23×C413yes—
302C22×D11C23×C411yescharacteristic
303C22×D11C23×C413yes—
304C22×D11C23×C411yescharacteristic
305Q8×C11—26no—
306Q8×C11C2×C22⋊C414yes—
307D4×C11—212no—
308D4×C11—26no—
309D4×C11C2×C22⋊C4112yes—
310C2×C4×C11—26no—
311C2×C4×C11—26no—
312C2×C4×C11—26no—
313C2×C4×C11—22no—
314C2×C4×C11—26no—
315C2×C4×C11C23×C413yes—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C23×C413yes—
318C2×C4×C11C22×D4112yes—
319C2×C4×C11C2511yescharacteristic
320C22⋊D11—212no—
321C22⋊D11—212no—
322C22⋊D11—212no—
323C22⋊D11C2×C22⋊C4124yes—
324C2×Dic11—26no—
325C2×Dic11—26no—
326C2×Dic11—22no—
327C2×Dic11—26no—
328C2×Dic11—26no—
329C2×Dic11C2×C22⋊C4112yes—
330C2×Dic11C23×C413yes—
331C2×Dic11C23×C411yescharacteristic
332C2×Dic11C23×C413yes—
333C2×Dic11C23×C411yescharacteristic
334D44—212no—
335D44—26no—
336D44C2×C22⋊C4112yes—
337C4×D11—22no—
338C4×D11—26no—
339C4×D11—26no—
340C4×D11—26no—
341C4×D11—26no—
342C4×D11—26no—
343C4×D11—22no—
344C4×D11—26no—
345C4×D11—22no—
346C4×D11—26no—
347C4×D11—26no—
348C4×D11—26no—
349C4×D11C2×C22⋊C4112yes—
350C4×D11C2×C22⋊C4112yes—
351C4×D11C22×D4112yes—
352C4×D11C22×D414yes—
353Dic22—26no—
354Dic22—212no—
355Dic22C2×C22⋊C4112yes—
356C8×C11—26no—
357C8×C11—22no—
358C11⋊C8—26no—
359C11⋊C8—22no—
360C22×#41—111no—
361C22×#41—113no—
362C22×#41—113no—
363C22×#41—111no—
364C22×#41—113no—
365C22×#41—111no—
366C22×#41—111no—
367C22×#41—113no—
368C22×#41—111no—
369C22×#41—113no—
370C22×#41—113no—
371C22×#41—2216no—
372C22×#41C2×D1111yescharacteristic
373C23×Q8—111no—
374C23×D4—113no—
375C24×C4—113no—
376#568—2216no—
377C2×#131—112no—
378C2×#131—116no—
379C2×#131—116no—
380C2×#131C2×D1112yescomplemented
381C22×M16—116no—
382C22×M16—116no—
383#408—116no—
384#408—116no—
385#408—116no—
386#408—1112no—
387#408—1112no—
388#408C2×D1116yescomplemented
389#407—113no—
390#407—116no—
391#407—113no—
392#407—111no—
393#407—113no—
394#407—113no—
395#407—116no—
396#407—116no—
397#407—116no—
398#407C2×D1113yescomplemented
399C2×C22⋊C8—113no—
400C2×C22⋊C8—116no—
401C2×C22⋊C8—116no—
402C2×C22⋊C8—116no—
403C2×C22⋊C8C2×D1113yescomplemented
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—23no—
407C22×C11—23no—
408C22×C11—23no—
409C22×C11—23no—
410C22×C11—23no—
411C22×C11—412no—
412C22×C11C22×C22⋊C416yes—
413C22×C11#56812yescomplemented
414C22×C11C24×C411yescharacteristic
415C2×D11—28no—
416C2×D11—21no—
417C2×D11—21no—
418C2×D11—21no—
419C2×D11—21no—
420C2×D11—23no—
421C2×D11—23no—
422C2×D11—23no—
423C2×D11—23no—
424C2×D11—23no—
425C2×D11—412no—
426C2×D11—412no—
427C2×D11—412no—
428C2×D11—412no—
429C2×D11—412no—
430C2×D11C22×C22⋊C412yes—
431C2×D11C22×C22⋊C416yes—
432C2×D11#56812yescomplemented
433C4×C11—21no—
434C4×C11—23no—
435C4×C11C22×C22⋊C416yes—
436C4×C11C23×D412yes—
437Dic11—23no—
438Dic11—21no—
439Dic11C22×C22⋊C416yes—
440Dic11C22×C22⋊C412yes—
441C25—113no—
442C2×#41—28no—
443C2×#41—1116no—
444C2×#41—111no—
445C2×#41—113no—
446C2×#41—113no—
447C2×#41—111no—
448C2×#41—113no—
449C2×#41—116no—
450C2×#41—113no—
451C2×#41—116no—
452C2×#41—113no—
453C2×#41—113no—
454C2×#41—116no—
455C2×#41—113no—
456C2×#41—113no—
457C2×#41—113no—
458C2×#41—116no—
459C2×#41—113no—
460C2×#41—2224no—
461C2×#41—2224no—
462C2×#41—2224no—
463C2×#41—2224no—
464C2×#41—228no—
465C2×#41—228no—
466C2×#41—228no—
467C2×#41—2224no—
468C2×#41—2224no—
469C2×#41—228no—
470C2×#41C4×D1111yescharacteristic
471C2×#41C4×D1113yes—
472C2×#41C22×D1113yes—
473C2×#41C22×D1111yescharacteristic
474C22×Q8—111no—
475C22×Q8—113no—
476C22×Q8—113no—
477C22×Q8—111no—
478C22×Q8—113no—
479C22×Q8—228no—
480C22×Q8C4×D1111yescharacteristic
481C22×D4—113no—
482C22×D4—116no—
483C22×D4—113no—
484C22×D4—116no—
485C22×D4—113no—
486C22×D4—116no—
487C22×D4—113no—
488C22×D4—113no—
489C22×D4—2224no—
490C22×D4C4×D1113yes—
491C23×C4—113no—
492C23×C4—113no—
493C23×C4—113no—
494C23×C4—113no—
495C23×C4—113no—
496C23×C4—113no—
497C23×C4—113no—
498C23×C4—113no—
499C23×C4—111no—
500C23×C4—113no—
501C23×C4—113no—
502C23×C4—113no—
503C23×C4—113no—
504C23×C4—2224no—
505C23×C4C22×D1113yes—
506#131—28no—
507#131—2224no—
508#131—2224no—
509#131—228no—
510C2×M16—116no—
511C2×M16—116no—
512C2×M16—112no—
513C2×M16—116no—
514C2×M16—116no—
515C2×M16—2224no—
516C2×M16—2224no—
517C2×M16C22×D1116yescomplemented
518C22×C8—116no—
519C22×C8—1112no—
520C22×C8C22×D1116yescomplemented
521C22⋊C8—111no—
522C22⋊C8—113no—
523C22⋊C8—116no—
524C22⋊C8—116no—
525C22⋊C8—116no—
526C22⋊C8—112no—
527C22⋊C8—116no—
528C22⋊C8—1112no—
529C22⋊C8—116no—
530C22⋊C8C22×D1113yes—
531C22⋊C8C22×D1111yescharacteristic
532C22⋊C8C22×D1116yescomplemented
533C22⋊C8C22×D1116yescomplemented
534C2×C11—22no—
535C2×C11—26no—
536C2×C11—43no—
537C2×C11C23×C22⋊C411yescharacteristic
538C2×C11C2×#56811yescharacteristic
539C2×C11C2×#56811yescharacteristic
540D11—22no—
541D11—22no—
542D11—26no—
543D11—43no—
544C24—113no—
545C24—111no—
546C24—113no—
547C24—113no—
548C24—113no—
549C24—113no—
550C24—2212no—
551C24—446no—
552C24—446no—
553C24C2×C4×D1113yes—
554#41—24no—
555#41—212no—
556#41—212no—
557#41—118no—
558#41—1124no—
559#41—1124no—
560#41—2224no—
561#41—2224no—
562#41—2212no—
563#41—2212no—
564#41—2224no—
565#41—2212no—
566#41—2212no—
567#41—2224no—
568#41—2212no—
569#41—2212no—
570#41—224no—
571#41—2212no—
572#41—2212no—
573#41D4×D1118yes—
574C2×Q8—24no—
575C2×Q8—118no—
576C2×Q8—113no—
577C2×Q8—116no—
578C2×Q8—113no—
579C2×Q8—2212no—
580C2×Q8—2212no—
581C2×Q8—2212no—
582C2×Q8—224no—
583C2×Q8C2×C4×D1113yes—
584C2×Q8C2×C4×D1111yescharacteristic
585C2×D4—212no—
586C2×D4—116no—
587C2×D4—1124no—
588C2×D4—116no—
589C2×D4—116no—
590C2×D4—116no—
591C2×D4—113no—
592C2×D4—116no—
593C2×D4—113no—
594C2×D4—2212no—
595C2×D4—2212no—
596C2×D4—2224no—
597C2×D4—2212no—
598C2×D4—2224no—
599C2×D4—2224no—
600C2×D4—2212no—
601C2×D4C2×C4×D1116yes—
602C2×D4C2×C4×D1113yes—
603C2×D4C2×C4×D1113yes—
604C22×C4—212no—
605C22×C4—113no—
606C22×C4—113no—
607C22×C4—113no—
608C22×C4—1124no—
609C22×C4—113no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—113no—
613C22×C4—113no—
614C22×C4—113no—
615C22×C4—113no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—113no—
619C22×C4—113no—
620C22×C4—113no—
621C22×C4—113no—
622C22×C4—113no—
623C22×C4—113no—
624C22×C4—113no—
625C22×C4—113no—
626C22×C4—111no—
627C22×C4—113no—
628C22×C4—224no—
629C22×C4—2212no—
630C22×C4—2212no—
631C22×C4—2212no—
632C22×C4—2212no—
633C22×C4—2212no—
634C22×C4—2212no—
635C22×C4—2212no—
636C22×C4—2212no—
637C22×C4—2212no—
638C22×C4—2212no—
639C22×C4—2212no—
640C22×C4C2×C4×D1113yes—
641C22×C4C2×C4×D1113yes—
642C22×C4C2×C4×D1113yes—
643C22×C4C23×D1111yescharacteristic
644C22×C4C23×D1113yes—
645C22×C4C23×D1113yes—
646M16—212no—
647M16—224no—
648M16—2212no—
649M16—2212no—
650M16—2212no—
651M16—2212no—
652C2×C8—212no—
653C2×C8—112no—
654C2×C8—116no—
655C2×C8—2224no—
656C2×C8—2212no—
657C2×C8C23×D1116yes—
658C2×C8C23×D1112yes—
659C11#6006411yescharacteristic, complemented, Sylow
660C23—26no—
661C23—26no—
662C23—43no—
663C23—111no—
664C23—111no—
665C23—113no—
666C23—1112no—
667C23—113no—
668C23—222no—
669C23—222no—
670C23—226no—
671C23—226no—
672C23—226no—
673C23—226no—
674C23—226no—
675C23—222no—
676C23—226no—
677C23—226no—
678C23—443no—
679C23—443no—
680C23—443no—
681C23—443no—
682C23—443no—
683C23—443no—
684C23—443no—
685C23—4448no—
686C23C22×C4×D1113yes—
687C23C22×C4×D1113yes—
688C23C22×C4×D1111yescharacteristic
689Q8—26no—
690Q8—1112no—
691Q8—2212no—
692Q8—226no—
693Q8C22⋊C4×D1114yes—
694D4—212no—
695D4—26no—
696D4—1124no—
697D4—1112no—
698D4—2212no—
699D4—2212no—
700D4—2212no—
701D4—2212no—
702D4—226no—
703D4C22⋊C4×D11112yes—
704C2×C4—26no—
705C2×C4—26no—
706C2×C4—26no—
707C2×C4—22no—
708C2×C4—26no—
709C2×C4—1112no—
710C2×C4—111no—
711C2×C4—113no—
712C2×C4—1112no—
713C2×C4—1112no—
714C2×C4—1112no—
715C2×C4—114no—
716C2×C4—111no—
717C2×C4—113no—
718C2×C4—222no—
719C2×C4—226no—
720C2×C4—226no—
721C2×C4—226no—
722C2×C4—222no—
723C2×C4—226no—
724C2×C4—226no—
725C2×C4—226no—
726C2×C4—222no—
727C2×C4—226no—
728C2×C4—226no—
729C2×C4—226no—
730C2×C4—226no—
731C2×C4—226no—
732C2×C4—226no—
733C2×C4—222no—
734C2×C4—226no—
735C2×C4C22×C4×D1111yescharacteristic
736C2×C4C22×C4×D1113yes—
737C2×C4C22×C4×D1113yes—
738C2×C4C2×D4×D11112yes—
739C2×C4C24×D1111yescharacteristic
740C8—22no—
741C8—26no—
742C8—226no—
743C8—222no—
744C22—21no—
745C22—21no—
746C22—23no—
747C22—23no—
748C22—23no—
749C22—23no—
750C22—23no—
751C22—412no—
752C22—112no—
753C22—116no—
754C22—112no—
755C22—228no—
756C22—221no—
757C22—221no—
758C22—223no—
759C22—221no—
760C22—221no—
761C22—223no—
762C22—223no—
763C22—223no—
764C22—223no—
765C22—4412no—
766C22—4412no—
767C22—4412no—
768C22—4412no—
769C22—4412no—
770C22C2×C22⋊C4×D1116yes—
771C22#1062328112yescomplemented
772C22C23×C4×D1111yescharacteristic
773C4—21no—
774C4—23no—
775C4—112no—
776C4—116no—
777C4—221no—
778C4—223no—
779C4C2×C22⋊C4×D1116yes—
780C4C22×D4×D1112yes—
781C2—22no—
782C2—26no—
783C2—43no—
784C2—222no—
785C2—222no—
786C2—226no—
787C2—443no—
788C2C22×C22⋊C4×D1111yescharacteristic
789C2D11×#56811yescharacteristic
790C2C2×#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2880C2
prime radicalC22×#41×D11C2
cosocleC2×C4×C11C25
hypercenter#2880D11
hypocenterC11#60064
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#10623281C2semidirect
3. #13077066C2semidirect
4. #13077065C2semidirect
5. #13077064C2semidirect
6. #13077063C2semidirect
7. #13077062C2semidirect
8. #13077058C2semidirect
9. C2×#10622339C2semidirect
10. D11×#407C2semidirect
11. C11×#2880C2semidirect
28. C2×C11×#131C22semidirect
29. C2×#67001C22semidirect
31. C2×#66960C22semidirect
32. C2×M16×D11C22semidirect
33. C2×#66954C22semidirect
34. C22×#4313C22semidirect
35. C11×#408C22semidirect
36. C11×#407C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. #10622847C22semidirect
39. #10622820C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. #10622742C22semidirect
42. #10622739C22semidirect
43. #10622723C22semidirect
44. C2×(C2×D11)⋊C8C22semidirect
45. #10622340C22semidirect
46. #10622340C22semidirect
49. #10622339C22semidirect
50. #10622339C22semidirect
51. #10622339C22semidirect
52. #10622339C22semidirect
53. #10622339C22semidirect
54. D11×C22⋊C8C22semidirect
55. D11×C22⋊C8C22semidirect
122. C2×C11×M16C23semidirect
123. C22×C8×C11C23semidirect
125. C2×#4318C23semidirect
126. C22×C11⋊C8C23semidirect
133. C2×#4313C23semidirect
134. C2×#4313C23semidirect
135. C2×C8×D11C23semidirect
138. C11×C22⋊C8C23semidirect
139. C11×C22⋊C8C23semidirect
142. C22⋊(C11⋊C8)C23semidirect
143. C22⋊(C11⋊C8)C23semidirect
146. (C2×D11)⋊C8C23semidirect
147. (C2×D11)⋊C8C23semidirect
148. (C2×D11)⋊C8C23semidirect
272. #2880D11semidirect
380. C2×#131C2×D11semidirect
388. #408C2×D11semidirect
398. #407C2×D11semidirect
403. C2×C22⋊C8C2×D11semidirect
413. C22×C11#568semidirect
432. C2×D11#568semidirect
517. C2×M16C22×D11semidirect
520. C22×C8C22×D11semidirect
532. C22⋊C8C22×D11semidirect
533. C22⋊C8C22×D11semidirect
659. C11#60064semidirect
771. C22#10623281semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D112
C2×#106232812
#130770662
#130770652
#130770642
#130770632
#130770622
#130770582
C2×#106223392
D11×#4072
C11×#28802
#6006411