Finite Group Databasebeta

← #14765173

Subgroups — #14765173

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077830C211yesmaximal, characteristic
2#13077313C211yesmaximal, characteristic, complemented
3D11×#408C211yesmaximal, characteristic, complemented
4#13069503C211yesmaximal, characteristic, complemented
5#13069323C211yesmaximal, characteristic, complemented
6#13069320C211yesmaximal, characteristic, complemented
7#13069267C211yesmaximal, characteristic, complemented
8#13069263C211yesmaximal, characteristic, complemented
9#13068945C211yesmaximal, characteristic, complemented
10#13068941C211yesmaximal, characteristic, complemented
11#13068915C211yesmaximal, characteristic, complemented
12#13068819C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15C11×#1974C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18#10623359C2211yescharacteristic
19C2×#67003C2211yescharacteristic
20C2×#67001C2211yescharacteristic, complemented
21C2×M16×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic
25C2×C11×#104C2211yescharacteristic, complemented
26C11×#408C2211yescharacteristic
27C11×#408C2211yescharacteristic, complemented
28C2×C4×C8×C11C2211yescharacteristic, complemented
29C2×#66901C2211yescharacteristic
30C2×#66901C2211yescharacteristic, complemented
31#10622847C2211yescharacteristic
32#10622846C2211yescharacteristic
33#10622800C411yescharacteristic, complemented
34#10622799C411yescharacteristic, complemented
35#10622786C411yescharacteristic, complemented
36#10622785C411yescharacteristic, complemented
37#10622783C411yescharacteristic, complemented
38#10622782C411yescharacteristic, complemented
39#10622771C411yescharacteristic, complemented
40#10622769C411yescharacteristic, complemented
41C2×#66889C2211yescharacteristic
42#10622742C2211yescharacteristic
43#10622739C2211yescharacteristic
44C2×#66886C2211yescharacteristic, complemented
45#10622735C2211yescharacteristic, complemented
46#10622726C2211yescharacteristic
47#10622723C2211yescharacteristic
48C2×(C2×D11)⋊C8C2211yescharacteristic
49#10622715C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C2×#66869C2211yescharacteristic
53#10622341—21no—
54#10622341—21no—
55#10622340—21no—
56#10622340—21no—
57(C22⋊D11)⋊C8—21no—
58(C22⋊D11)⋊C8—21no—
59D11×C22⋊C8—21no—
60D11×C22⋊C8—21no—
61#10622196C2211yescharacteristic, complemented
62#10622193C2211yescharacteristic, complemented
63#10622190C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622162C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69#41×D11—41no—
70#41×D11—41no—
71#41×D11—41no—
72#41×D11—41no—
73C2×#4343C2×C411yescharacteristic
74C2×Q8×D11C2×C411yescharacteristic
75C2×#4341—21no—
76C2×#4341C2×C411yescharacteristic
77C2×D4×D11—21no—
78C2×D4×D11C2×C411yescharacteristic
79C2×#4339—21no—
80C2×#4339C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C11×#135—41no—
84C11×#135—41no—
85C2×C11×Q16C2×C411yescharacteristic
86C2×C11×SD16C2×C411yescharacteristic
87C2×C11×SD16C2×C411yescharacteristic
88C2×C11×D8C2×C411yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C2×C11×M16C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94#67003—41no—
95#67003—41no—
96#67001—41no—
97#67001—41no—
98#66999C2×C411yescharacteristic
99#66999C2×C411yescharacteristic
100C2×#4326C2×C411yescharacteristic
101C2×#4325C2×C411yescharacteristic
102#66991C2×C411yescharacteristic
103#66991C2×C411yescharacteristic
104#66990—21no—
105#66988—21no—
106C2×#4324C2×C411yescharacteristic
107C2×#4323C2×C411yescharacteristic
108C4×C22⋊D11—21no—
109C4×C22⋊D11—21no—
110C2×(C2×D11)⋊C4—21no—
111#66979C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×#4318—21no—
114C2×#4318C2311yescharacteristic
115C2×#4318C2311yescharacteristic
116C22×C11⋊C8—21no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119M16×D11—41no—
120M16×D11—41no—
121C2×#4313—21no—
122C2×C8×D11—21no—
123C2×C8×D11—41no—
124C2×C8×D11—41no—
125C2×C8×D11D411yescharacteristic
126C2×C8×D11D411yescharacteristic
127C2×C8×D11D411yescharacteristic
128C2×C8×D11D411yescharacteristic
129C11×#108—41no—
130C11×#104—41no—
131C11×#104—41no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C4×C8×C11—41no—
137#66901—41no—
138#66901—41no—
139#66899C2×C411yescharacteristic
140#66899C2×C411yescharacteristic
141#66896C2×C411yescharacteristic
142#66896C2×C411yescharacteristic
143C11⋊#95—21no—
144C22⋊(C11⋊C8)—21no—
145C22⋊(C11⋊C8)—21no—
146#66889—41no—
147#66886—41no—
148#66885C2×C411yescharacteristic
149#66885C2×C411yescharacteristic
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152(C2×D11)⋊C8—21no—
153(C2×D11)⋊C8—21no—
154(C2×D11)⋊C8—21no—
155(C2×D11)⋊C8—21no—
156(C2×D11)⋊C8C2×C411yescharacteristic
157(C2×D11)⋊C8C2×C411yescharacteristic
158(C2×D11)⋊C8C2×C411yescharacteristic
159(C2×D11)⋊C8C2×C411yescharacteristic
160#66880C2×C411yescharacteristic
161#66880C2×C411yescharacteristic
162#66879—21no—
163Dic11⋊C8—21no—
164Dic11⋊C8—21no—
165C8×Dic11—21no—
166C8×Dic11—41no—
167#66869—41no—
168#22060—111nomaximal, Sylow
169C23×D11—21no—
170C23×D11#4111yescharacteristic
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C11×#41—21no—
176C11×#41—21no—
177C11×#41—21no—
178C11×#41—21no—
179C2×Q8×C11C22×C411yescharacteristic
180C2×Q8×C11C22×C411yescharacteristic
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11C22×C411yescharacteristic
184C2×D4×C11C22×C411yescharacteristic
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—21no—
190C2×C22⋊D11—21no—
191C2×C22⋊D11—21no—
192C2×C22⋊D11—21no—
193C2×C22⋊D11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11#4111yescharacteristic
197#4343—41no—
198#4343—41no—
199Q8×D11—41no—
200Q8×D11—41no—
201#4341—41no—
202#4341—41no—
203#4341—42no—
204#4341—42no—
205D4×D11—41no—
206D4×D11—41no—
207D4×D11—42no—
208D4×D11—42no—
209#4339—21no—
210#4339—21no—
211#4339—21no—
212#4339—21no—
213#4339—42no—
214#4339—42no—
215C2×D44—21no—
216C2×D44C22×C411yescharacteristic
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11C22×C411yescharacteristic
227C2×C4×D11C22×C411yescharacteristic
228C2×C4×D11C2×D411yescharacteristic
229C2×C4×D11C2×D411yescharacteristic
230C2×Dic22—21no—
231C2×Dic22C22×C411yescharacteristic
232C11×Q16—41no—
233C11×SD16—41no—
234C11×SD16—41no—
235C11×D8—41no—
236C11×M16—21no—
237C11×M16—21no—
238C11×M16—21no—
239C11×M16—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11C22×C411yescharacteristic
247C2×C8×C11C22×C411yescharacteristic
248C2×C8×C11C2×D411yescharacteristic
249C2×C8×C11C2×D411yescharacteristic
250C42×C11—21no—
251C42×C11—21no—
252C22⋊Dic11—21no—
253C22⋊Dic11—21no—
254C22⋊Dic11—21no—
255#4326—41no—
256#4325—41no—
257#4324—41no—
258#4323—41no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—21no—
261(C2×D11)⋊C4—21no—
262C4⋊Dic11C22×C411yescharacteristic
263C4⋊Dic11C22×C411yescharacteristic
264Dic11⋊C4—21no—
265Dic11⋊C4—21no—
266C4×Dic11—21no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269#4318—21no—
270#4318—21no—
271#4318—21no—
272#4318—21no—
273#4318—42no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—42no—
281C2×C11⋊C8C22×C411yescharacteristic
282C2×C11⋊C8C22×C411yescharacteristic
283C2×C11⋊C8C2×D411yescharacteristic
284C2×C11⋊C8C2×D411yescharacteristic
285#4313—42no—
286C8×D11—41no—
287C8×D11—41no—
288C8×D11—41no—
289C8×D11—41no—
290C8×D11—42no—
291#3002—111no—
292#2929—111no—
293C2×#408—111no—
294#1974—111no—
295#1974D1111yescharacteristic, complemented
296#1937—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855—111no—
304#1789—111no—
305C8×C22⋊C4—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11C2×#4111yescharacteristic
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—22no—
312C22×D11—21no—
313C22×D11—41no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11C4×D411yescharacteristic
318C22×D11C4×D411yescharacteristic
319Q8×C11—21no—
320Q8×C11—21no—
321Q8×C11—21no—
322Q8×C11—21no—
323D4×C11—21no—
324D4×C11—21no—
325D4×C11—21no—
326D4×C11—21no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—41no—
330D4×C11—41no—
331C2×C4×C11—22no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11C23×C411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C22⋊D11—42no—
347C22⋊D11—42no—
348C22⋊D11—42no—
349C22⋊D11—41no—
350C22⋊D11—41no—
351C22⋊D11—42no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—22no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—42no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11C4×D411yescharacteristic
362C2×Dic11C4×D411yescharacteristic
363D44—21no—
364D44—21no—
365D44—42no—
366C4×D11—21no—
367C4×D11—21no—
368C4×D11—21no—
369C4×D11—21no—
370C4×D11—21no—
371C4×D11—21no—
372C4×D11—21no—
373C4×D11—21no—
374C4×D11—42no—
375C4×D11—42no—
376C4×D11—41no—
377C4×D11—41no—
378Dic22—21no—
379Dic22—21no—
380Dic22—42no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C8×C11—41no—
386C8×C11—41no—
387C11⋊C8—21no—
388C11⋊C8—21no—
389C11⋊C8—21no—
390C11⋊C8—21no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C22×#41—111no—
394C2×#135—111no—
395C2×#135C2×D1111yescharacteristic
396C2×#131—111no—
397C22×M16—111no—
398C23×C8—111no—
399#525—111no—
400#452—111no—
401#452—111no—
402#451—111no—
403#450—111no—
404#449—111no—
405#449—111no—
406#448—111no—
407#447—111no—
408#435—221no—
409#435—221no—
410C8×D4—221no—
411C8×D4—221no—
412C2×#108—111no—
413C2×#108C2×D1111yescharacteristic, complemented
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104C2×D1111yescharacteristic
420C2×#104C2×D1111yescharacteristic, complemented
421#416—111no—
422#416—111no—
423#408—111no—
424#408—111no—
425#408—111no—
426#408—221no—
427#408—221no—
428#408C2×D1111yescharacteristic
429#408C2×D1111yescharacteristic, complemented
430#407—111no—
431C2×C22⋊C8—111no—
432C2×C22⋊C8—221no—
433C2×C22⋊C8—221no—
434#405—111no—
435C2×C4×C8—111no—
436C2×C4×C8C2×D1111yescharacteristic, complemented
437C4×C22⋊C4—111no—
438#341—111no—
439#341—111no—
440#339—111no—
441#339—111no—
442#336—111no—
443#336—111no—
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11C2×C4×D411yescharacteristic
453C22×C11#53811yescharacteristic
454C22×C11#53811yescharacteristic
455C2×D11—21no—
456C2×D11—21no—
457C2×D11—21no—
458C2×D11—21no—
459C2×D11—21no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—84no—
466C2×D11#44312yes—
467C4×C11—42no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11#51811yescharacteristic
471C4×C11#51811yescharacteristic
472C4×C11#53411yescharacteristic
473C4×C11#53511yescharacteristic
474Dic11—21no—
475Dic11—21no—
476Dic11—42no—
477Dic11—41no—
478Dic11—41no—
479Dic11—41no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—221no—
484C2×#41—221no—
485C2×#41—441no—
486C2×#41—441no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41C22×D1111yescharacteristic
490C2×#41C22×D1111yescharacteristic
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—221no—
494C23×C4—111no—
495C23×C4—221no—
496#135—41no—
497#135—41no—
498#135—441no—
499#135—441no—
500C2×Q16—111no—
501C2×Q16C4×D1111yescharacteristic
502C2×SD16—111no—
503C2×SD16—111no—
504C2×SD16C4×D1111yescharacteristic
505C2×SD16C4×D1111yescharacteristic
506C2×D8—111no—
507C2×D8C4×D1111yescharacteristic
508#131—441no—
509#131—441no—
510C2×M16—111no—
511C2×M16—111no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—441no—
515C2×M16—441no—
516C2×M16C22×D1111yescharacteristic
517C2×M16C22×D1111yescharacteristic
518C22×C8—111no—
519C22×C8—111no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—221no—
525C22×C8—221no—
526C22×C8—441no—
527C22×C8—441no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#123—221no—
531C22⋊Q8—111no—
532C22⋊Q8—111no—
533#121—111no—
534#121—111no—
535#120—221no—
536C4×D4—221no—
537C4×D4—221no—
538#117—111no—
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42C22×D1111yescharacteristic
542#108—41no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—41no—
547#104—41no—
548#104—441no—
549#104—441no—
550#104—441no—
551#104—441no—
552#103—111no—
553#103—111no—
554#103—111no—
555#103—111no—
556#102—111no—
557#102—111no—
558#102—111no—
559#102—111no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—21no—
564C22⋊C8—111no—
565C22⋊C8—111no—
566C22⋊C8—111no—
567C22⋊C8—111no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8—221no—
573C22⋊C8—221no—
574C22⋊C8—221no—
575C22⋊C8—221no—
576#97—221no—
577C4×C8—41no—
578C4×C8—221no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—81no—
584C2×C11—81no—
585C2×C11#232111yescharacteristic
586C2×C11C2×#44311yescharacteristic
587C2×C11#295511yescharacteristic
588D11—22no—
589D11—41no—
590D11—81no—
591C24—111no—
592C24—221no—
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—221no—
602#41—221no—
603#41—221no—
604#41—221no—
605#41—442no—
606#41—442no—
607#41—441no—
608#41—441no—
609#41—442no—
610#41—442no—
611#41—441no—
612#41—441no—
613C2×Q8—111no—
614C2×Q8—221no—
615C2×Q8—441no—
616C2×Q8—441no—
617C2×Q8C2×C4×D1111yescharacteristic
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—111no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—441no—
629C2×D4—441no—
630C2×D4—442no—
631C2×D4—442no—
632C2×D4C2×C4×D1111yescharacteristic
633C2×D4C2×C4×D1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4C23×D1111yescharacteristic
654Q16—41no—
655Q16—441no—
656SD16—41no—
657SD16—41no—
658SD16—441no—
659SD16—441no—
660D8—41no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—221no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—442no—
671M16—442no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—111no—
679C2×C8—111no—
680C2×C8—111no—
681C2×C8—111no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—441no—
689C2×C8—441no—
690C2×C8—441no—
691C2×C8—441no—
692C2×C8—442no—
693C2×C8—442no—
694C2×C8C2×C4×D1111yescharacteristic
695C2×C8C2×C4×D1111yescharacteristic
696C2×C8D4×D1111yescharacteristic
697C2×C8D4×D1111yescharacteristic
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—221no—
703C22⋊C4—221no—
704C22⋊C4—224no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—221no—
708C42—21no—
709C42—21no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206011yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—111no—
717C23—111no—
718C23—222no—
719C23—221no—
720C23—221no—
721C23—221no—
722C23—441no—
723C23—442no—
724C23—442no—
725C23—442no—
726C23#41×D1111yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—221no—
743D4—221no—
744D4—442no—
745D4—442no—
746D4—442no—
747D4—442no—
748D4—442no—
749D4—441no—
750D4—441no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—111no—
761C2×C4—111no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—222no—
773C2×C4—221no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6703711yescharacteristic
788C2×C4#6704211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—221no—
796C8—221no—
797C8—221no—
798C8—221no—
799C8—441no—
800C8—441no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—112no—
810C22—221no—
811C22—221no—
812C22—221no—
813C22—221no—
814C22—221no—
815C22—442no—
816C22—442no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C4×D4×D1111yescharacteristic
822C22#1062314411yescharacteristic
823C22#1062320911yescharacteristic
824C4—42no—
825C4—41no—
826C4—41no—
827C4—221no—
828C4—221no—
829C4—442no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4#1062301711yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062313611yescharacteristic
836C4#1062324611yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—222no—
842C2—441no—
843C2—881no—
844C2#1307127511yescharacteristic
845C2D11×#44311yescharacteristic
846C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1974C2
socleC22×C11C2×C4×D4
prime radical#13077830C2
cosocleC22×C4×C11C24
hypercenter#1974D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. #13077313C2semidirect
3. D11×#408C2semidirect
4. #13069503C2semidirect
5. #13069323C2semidirect
6. #13069320C2semidirect
7. #13069267C2semidirect
8. #13069263C2semidirect
9. #13068945C2semidirect
10. #13068941C2semidirect
11. #13068915C2semidirect
12. #13068819C2semidirect
13. #13068558C2semidirect
14. C8×(C2×D11)⋊C4C2semidirect
15. C11×#1974C2semidirect
20. C2×#67001C22semidirect
23. C2×C11×#108C22semidirect
25. C2×C11×#104C22semidirect
27. C11×#408C22semidirect
28. C2×C4×C8×C11C22semidirect
30. C2×#66901C22semidirect
33. #10622800C4semidirect
34. #10622799C4semidirect
35. #10622786C4semidirect
36. #10622785C4semidirect
37. #10622783C4semidirect
38. #10622782C4semidirect
39. #10622771C4semidirect
40. #10622769C4semidirect
44. C2×#66886C22semidirect
45. #10622735C22semidirect
49. #10622715C22semidirect
50. C2×C8×Dic11C22semidirect
61. #10622196C22semidirect
62. #10622193C22semidirect
63. #10622190C22semidirect
64. #10622188C22semidirect
65. #10622162C22semidirect
66. #10622161C22semidirect
295. #1974D11semidirect
413. C2×#108C2×D11semidirect
420. C2×#104C2×D11semidirect
429. #408C2×D11semidirect
436. C2×C4×C8C2×D11semidirect
713. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778302
#130773132
D11×#4082
#130695032
#130693232
#130693202
#130692672
#130692632
#130689452
#130689412
#130689152
#130688192
#130685582
C8×(C2×D11)⋊C42
C11×#19742
#2206011