Finite Group Databasebeta

← #14755255

Subgroups — #14755255

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10622752C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4#13077060C211yesmaximal, characteristic, complemented
5#13068978C218yesmaximal, complemented
6C2×#10622194C211yesmaximal, characteristic, complemented
7#13068342C211yesmaximal, characteristic, complemented
8C2×C11×#568C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C11×#568—22no—
12C11×#568—22no—
13C11×#568—22no—
14C11×#568C2214yescomplemented
15C2×C11×#131—22no—
16C2×C11×#131—22no—
17C22×C11×M16—22no—
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×#67004C412yescomplemented
21#10623353—22no—
22#10623353—22no—
23#10623353C414yescomplemented
24#10623353C2214yes—
25C2×#67003—22no—
26C2×#67002C412yescomplemented
27C2×#66995—21no—
28C2×#66985—21no—
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622846C2214yescomplemented
33#10622845—22no—
34#10622838—21no—
35#10622828—21no—
36#10622752—22no—
37#10622752C2214yescomplemented
38C2×#66889—22no—
39#10622742C2214yescomplemented
40#10622739—22no—
41#10622723—22no—
42#10622196C2214yescomplemented
43#10622194C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41C2×C412yes—
51C2×C11×#41C2×C412yes—
52C2×C11×#41D412yes—
53C2×C11×#41D412yes—
54C2×C11×#41D412yes—
55C2×C11×#41C2312yes—
56C22×Q8×C11D411yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339C2×C412yes—
73C2×#4339C2312yes—
74C22×D44C2×C411yescharacteristic
75C22×C4×D11—21no—
76C22×Dic22C2×C411yescharacteristic
77C11×#131—28no—
78C11×#131—28no—
79C11×#131—28no—
80C11×#131—28no—
81C2×C11×M16—24no—
82C2×C11×M16—28no—
83C2×C11×M16—21no—
84C2×C11×M16—21no—
85C2×C11×M16—21no—
86C2×C11×M16—21no—
87C2×C11×M16—21no—
88C2×C11×M16—21no—
89C2×C11×M16—21no—
90C2×C11×M16—28no—
91C2×C11×M16D412yes—
92C2×C11×M16D412yes—
93C2×C11×M16D412yes—
94C2×C11×M16C2312yes—
95C2×C11×M16C2312yes—
96C22×C8×C11—24no—
97C22×C8×C11—21no—
98C22×C8×C11D412yes—
99C2×C22⋊Dic11—21no—
100#67004—24no—
101#67004C2×C418yescomplemented
102#67003—28no—
103#67003—28no—
104#67002—24no—
105#67002C2×C418yescomplemented
106C2×#4326—22no—
107#66995—24no—
108#66995—24no—
109C2×#4325—22no—
110C2×#4324—22no—
111#66985—24no—
112#66985—24no—
113C2×#4323—22no—
114#66979—21no—
115#66979—21no—
116#66979—21no—
117#66979C2312yes—
118C2×C4⋊Dic11—21no—
119C2×C4×Dic11—21no—
120C2×#4318—21no—
121C2×#4318—21no—
122C2×#4318—21no—
123C2×#4318—21no—
124C2×#4318—21no—
125C2×#4318—21no—
126C2×#4318—21no—
127C2×#4318—21no—
128C2×#4318—21no—
129C2×#4318C2×C412yes—
130C2×#4318C2×C412yes—
131C2×#4318C2312yes—
132C22×C11⋊C8—21no—
133C22×C11⋊C8C2312yes—
134#66899—24no—
135#66896—24no—
136#66889—28no—
137(C2×D11)⋊C8—28no—
138#20939—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11#4111yescharacteristic
141C23×D11—21no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41C22⋊C414yes—
155C11×#41C22⋊C414yes—
156C11×#41C22×C414yes—
157C11×#41C2×D414yes—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C22⋊C412yes—
162C2×Q8×C11C22⋊C412yes—
163C2×Q8×C11C2×D412yes—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11C22⋊C412yes—
174C2×D4×C11C22⋊C412yes—
175C2×D4×C11C2×D412yes—
176C22×C4×C11—21no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C2×C22⋊D11—41no—
202C2×C22⋊D11—41no—
203C22×Dic11—21no—
204C22×Dic11—41no—
205#4339—22no—
206#4339—22no—
207#4339—22no—
208#4339—22no—
209#4339—22no—
210#4339—22no—
211#4339—22no—
212#4339—22no—
213#4339—41no—
214#4339—41no—
215#4339—41no—
216#4339—41no—
217#4339—41no—
218#4339—41no—
219#4339—41no—
220#4339—41no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44C22×C412yes—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—41no—
230C2×C4×D11—41no—
231C2×C4×D11—41no—
232C2×C4×D11—41no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22C22×C412yes—
239C11×M16—216no—
240C11×M16—22no—
241C11×M16—22no—
242C11×M16—22no—
243C11×M16—22no—
244C11×M16—22no—
245C11×M16—22no—
246C11×M16—22no—
247C11×M16C2×D414yes—
248C2×C8×C11—216no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11C2×D414yes—
255C22⋊Dic11—22no—
256C22⋊Dic11—41no—
257#4326—28no—
258#4325—28no—
259#4324—28no—
260#4323—28no—
261C4⋊Dic11—22no—
262C4⋊Dic11—41no—
263C4×Dic11—22no—
264C4×Dic11—41no—
265#4318—22no—
266#4318—22no—
267#4318—22no—
268#4318—41no—
269#4318—41no—
270#4318—41no—
271#4318—41no—
272#4318C22×C414yes—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×#575—111no—
280C2×#568D1111yescharacteristic, complemented
281C2×#421—111no—
282#2896—111no—
283#2879—111no—
284#1881—118no—
285C2×#344—111no—
286#1738—111no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—81no—
291C23×C11—82no—
292C23×C11C4×D411yescharacteristic
293C23×C11C4×D411yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12311yescharacteristic
297C23×C11#12311yescharacteristic
298C23×C11C2×#4111yescharacteristic
299C22×D11—22no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—82no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11C2×C22⋊C414yes—
307D4×C11—24no—
308D4×C11—24no—
309D4×C11—24no—
310D4×C11—24no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11C2×C22⋊C414yes—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11C2×C22⋊C411yescharacteristic
323C2×C4×C11C2×C22⋊C411yescharacteristic
324C2×C4×C11C2×C22⋊C411yescharacteristic
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C4×D411yescharacteristic
327C2×C4×C11C4×D411yescharacteristic
328C2×C4×C11C4×D411yescharacteristic
329C2×C4×C11C4×D411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11#12011yescharacteristic
333C2×C4×C11#12011yescharacteristic
334C2×C4×C11#12011yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12311yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C22⋊D11—42no—
351C22⋊D11—42no—
352C22⋊D11—42no—
353C22⋊D11—42no—
354C2×Dic11—22no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—42no—
358C2×Dic11—82no—
359D44—22no—
360D44—22no—
361D44—41no—
362D44—41no—
363C4×D11—42no—
364C4×D11—42no—
365C4×D11—42no—
366C4×D11—42no—
367Dic22—22no—
368Dic22—22no—
369Dic22—41no—
370Dic22—41no—
371C8×C11—24no—
372C8×C11—24no—
373C11⋊C8—24no—
374C11⋊C8—42no—
375C22×#41—111no—
376C22×#41C2×D1111yescharacteristic
377#575—114no—
378#575—114no—
379#575—222no—
380#575—222no—
381C2×#137—112no—
382C2×#137—221no—
383C2×AGL(1,ℤ/8)—112no—
384C2×AGL(1,ℤ/8)—221no—
385C2×#135—222no—
386#568—22no—
387#568—22no—
388#568—22no—
389#568C2×D1114yescomplemented
390C2×#131—22no—
391C2×#131—22no—
392C22×M16—22no—
393C22×M16—111no—
394C22×M16—111no—
395C22×M16C2×D1111yescharacteristic
396C22×M16C2×D1111yescharacteristic
397C2×#117—111no—
398#421—114no—
399#421—222no—
400C2×#104—222no—
401#419—221no—
402#418—221no—
403#417—222no—
404#416—114no—
405#408—114no—
406#408—222no—
407#407—222no—
408#344—114no—
409#341—114no—
410C22×C11—24no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—44no—
419C22×C11—82no—
420C22×C11—82no—
421C22×C11#38611yescharacteristic
422C22×C11#38611yescharacteristic
423C22×C11#38611yescharacteristic
424C22×C11#38611yescharacteristic
425C22×C11C2×C4×D411yescharacteristic
426C22×C11C2×#12111yescharacteristic
427C22×C11C2×#12311yescharacteristic
428C2×D11—44no—
429C2×D11—42no—
430C2×D11—82no—
431C2×D11—82no—
432C4×C11—24no—
433C4×C11#38611yescharacteristic
434C4×C11#38611yescharacteristic
435C4×C11#38611yescharacteristic
436C4×C11#38611yescharacteristic
437C4×C11C22×C22⋊C411yescharacteristic
438C4×C11C2×C4×D411yescharacteristic
439C4×C11C2×#12011yescharacteristic
440C4×C11C2×#12111yescharacteristic
441Dic11—42no—
442Dic11—82no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—112no—
450C2×#41—112no—
451C2×#41—221no—
452C2×#41—221no—
453C2×#41—221no—
454C2×#41—221no—
455C2×#41—221no—
456C2×#41—221no—
457C2×#41—221no—
458C2×#41—221no—
459C2×#41—221no—
460C2×#41—221no—
461C2×#41C4×D1112yes—
462C2×#41C4×D1112yes—
463C2×#41D4412yes—
464C2×#41C22⋊D1112yes—
465C2×#41C22⋊D1112yes—
466C2×#41C22×D1112yes—
467C22×Q8—111no—
468C22×Q8D4411yescharacteristic
469C22×D4—21no—
470C22×D4—111no—
471C22×D4—221no—
472C22×D4D4411yescharacteristic
473C23×C4—21no—
474C23×C4—221no—
475C23×C4C22×D1111yescharacteristic
476#137—118no—
477#137—224no—
478#137—224no—
479#137—224no—
480AGL(1,ℤ/8)—118no—
481AGL(1,ℤ/8)—224no—
482AGL(1,ℤ/8)—224no—
483AGL(1,ℤ/8)—224no—
484#135—228no—
485#135—228no—
486C2×Q16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×D8—222no—
490#131—28no—
491#131—28no—
492#131—28no—
493#131—28no—
494C2×M16—24no—
495C2×M16—28no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—28no—
504C2×M16—112no—
505C2×M16—112no—
506C2×M16—112no—
507C2×M16—221no—
508C2×M16—221no—
509C2×M16—221no—
510C2×M16—221no—
511C2×M16—221no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—221no—
515C2×M16—221no—
516C2×M16C22⋊D1112yes—
517C2×M16C22⋊D1112yes—
518C2×M16C22⋊D1112yes—
519C2×M16C22×D1112yes—
520C2×M16C22×D1112yes—
521C22×C8—24no—
522C22×C8—21no—
523C22×C8—112no—
524C22×C8—221no—
525C22×C8C22⋊D1112yes—
526#117—112no—
527#117—221no—
528#117—221no—
529#117—221no—
530C2×C4⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C42—221no—
533#104—228no—
534#103—224no—
535#102—224no—
536C22⋊C8—228no—
537C2×C11—21no—
538C2×C11—21no—
539C2×C11—21no—
540C2×C11—21no—
541C2×C11—21no—
542C2×C11—21no—
543C2×C11—21no—
544C2×C11—44no—
545C2×C11C2×#38611yescharacteristic
546D11—82no—
547C24—21no—
548C24—221no—
549C24#433911yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—222no—
563#41—222no—
564#41—222no—
565#41—222no—
566#41—222no—
567#41—222no—
568#41—222no—
569#41—222no—
570#41—441no—
571#41—441no—
572#41—441no—
573#41—441no—
574#41—441no—
575#41—441no—
576#41—441no—
577#41—441no—
578#41(C2×D11)⋊C414yes—
579#41(C2×D11)⋊C414yes—
580#41C2×C4×D1114yes—
581#41C2×C22⋊D1114yes—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—112no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8—221no—
590C2×Q8—221no—
591C2×Q8(C2×D11)⋊C412yes—
592C2×Q8(C2×D11)⋊C412yes—
593C2×Q8C2×D4412yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—112no—
604C2×D4—222no—
605C2×D4—222no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—441no—
612C2×D4—441no—
613C2×D4—441no—
614C2×D4—441no—
615C2×D4(C2×D11)⋊C412yes—
616C2×D4(C2×D11)⋊C412yes—
617C2×D4C2×D4412yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—221no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—441no—
629C22×C4—441no—
630C22×C4—441no—
631C22×C4—441no—
632C22×C4—441no—
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4C2×D4411yescharacteristic
636C22×C4C2×D4411yescharacteristic
637C22×C4#433911yescharacteristic
638C22×C4#433911yescharacteristic
639C22×C4#433911yescharacteristic
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C2×C22⋊D1111yescharacteristic
642C22×C4C2×C22⋊D1111yescharacteristic
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C23×D1111yescharacteristic
647Q16—228no—
648SD16—228no—
649SD16—228no—
650D8—228no—
651M16—216no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—114no—
660M16—222no—
661M16—222no—
662M16—222no—
663M16—441no—
664M16—441no—
665M16—441no—
666M16—441no—
667M16C2×C22⋊D1114yes—
668C2×C8—216no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—222no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8—222no—
678C2×C8—222no—
679C2×C8—222no—
680C2×C8C2×C22⋊D1114yes—
681C4⋊C4—222no—
682C4⋊C4—441no—
683C22⋊C4—222no—
684C22⋊C4—441no—
685C42—222no—
686C42—441no—
687C11#2093911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—81no—
692C23—82no—
693C23—222no—
694C23—441no—
695C23—441no—
696C23—882no—
697C23C4×C22⋊D1111yescharacteristic
698C23C4×C22⋊D1111yescharacteristic
699C23#6698211yescharacteristic
700C23#6698211yescharacteristic
701C23#6698311yescharacteristic
702C23#6698311yescharacteristic
703C23C2×#433911yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—222no—
708Q8—222no—
709Q8—441no—
710Q8—441no—
711Q8C2×(C2×D11)⋊C414yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—222no—
720D4—222no—
721D4—442no—
722D4—442no—
723D4—442no—
724D4—442no—
725D4—441no—
726D4—441no—
727D4C2×(C2×D11)⋊C414yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—222no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—882no—
744C2×C4C2×(C2×D11)⋊C411yescharacteristic
745C2×C4C2×(C2×D11)⋊C411yescharacteristic
746C2×C4C2×(C2×D11)⋊C411yescharacteristic
747C2×C4C2×(C2×D11)⋊C411yescharacteristic
748C2×C4C4×C22⋊D1111yescharacteristic
749C2×C4C4×C22⋊D1111yescharacteristic
750C2×C4C4×C22⋊D1111yescharacteristic
751C2×C4C4×C22⋊D1111yescharacteristic
752C2×C4C4×C22⋊D1111yescharacteristic
753C2×C4C4×C22⋊D1111yescharacteristic
754C2×C4#6698211yescharacteristic
755C2×C4#6698211yescharacteristic
756C2×C4#6698311yescharacteristic
757C2×C4#6698311yescharacteristic
758C2×C4#6698311yescharacteristic
759C2×C4#6698311yescharacteristic
760C2×C4#6698311yescharacteristic
761C2×C4#6698311yescharacteristic
762C2×C4#6700611yescharacteristic
763C2×C4#6700611yescharacteristic
764C2×C4#6700611yescharacteristic
765C2×C4#6700611yescharacteristic
766C2×C4C22×C4×D1111yescharacteristic
767C2×C4C22×D4411yescharacteristic
768C2×C4C2×#433911yescharacteristic
769C2×C4C22×C22⋊D1111yescharacteristic
770C2×C4C22×C22⋊D1111yescharacteristic
771C2×C4C22×C22⋊D1111yescharacteristic
772C8—24no—
773C8—24no—
774C8—224no—
775C8—442no—
776C22—24no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—82no—
786C22—82no—
787C22—444no—
788C22—442no—
789C22—882no—
790C22—882no—
791C22#1062282611yescharacteristic
792C22#1062282611yescharacteristic
793C22#1062282611yescharacteristic
794C22#1062282611yescharacteristic
795C22C2×C4×C22⋊D1111yescharacteristic
796C22C2×#6698211yescharacteristic
797C22C2×#6698311yescharacteristic
798C4—24no—
799C4—442no—
800C4—882no—
801C4#1062282611yescharacteristic
802C4#1062282611yescharacteristic
803C4#1062282611yescharacteristic
804C4#1062282611yescharacteristic
805C4C22×(C2×D11)⋊C411yescharacteristic
806C4C2×C4×C22⋊D1111yescharacteristic
807C4C2×#6698311yescharacteristic
808C4C2×#6700611yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—44no—
817C2—882no—
818C2C2×#1062282611yescharacteristic
subgroupG/H
centerC4C2×#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#568C2
socleC2×C11C2×#386
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenterC2×#568D11
hypocenterC11#20939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#10622752C2semidirect
3. #13077135C2semidirect
4. #13077060C2semidirect
5. #13068978C2semidirect
6. C2×#10622194C2semidirect
7. #13068342C2semidirect
8. C2×C11×#568C2semidirect
14. C11×#568C22semidirect
20. C2×#67004C4semidirect
23. #10623353C4semidirect
26. C2×#67002C4semidirect
32. #10622846C22semidirect
37. #10622752C22semidirect
39. #10622742C22semidirect
42. #10622196C22semidirect
43. #10622194C22semidirect
101. #67004C2×C4semidirect
105. #67002C2×C4semidirect
280. C2×#568D11semidirect
389. #568C2×D11semidirect
687. C11#20939semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106227522
#130771352
#130770602
#130689782
C2×#106221942
#130683422
C2×C11×#5682
#2093911