Finite Group Databasebeta

← #14765194

Subgroups — #14765194

Order 2816.

900 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#13077838C211yesmaximal, characteristic
2#13077315C211yesmaximal, characteristic, complemented
3#13077060C211yesmaximal, characteristic, complemented
4#13069507C211yesmaximal, characteristic, complemented
5#13069502C211yesmaximal, characteristic, complemented
6#13069325C211yesmaximal, characteristic, complemented
7#13069318C211yesmaximal, characteristic, complemented
8#13069263C211yesmaximal, characteristic, complemented
9#13069263C211yesmaximal, characteristic, complemented
10#13068944C211yesmaximal, characteristic, complemented
11#13068944C211yesmaximal, characteristic, complemented
12#13068918C211yesmaximal, characteristic, complemented
13#13068559C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1855C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18#10623322C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66960C2211yescharacteristic, complemented
21C2×#66957C2211yescharacteristic
22C2×#66957C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic, complemented
24C2×C11×#108C2211yescharacteristic, complemented
25C11×#407C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C2×#66889C2211yescharacteristic
29C2×#66889C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32C2×#66889C2211yescharacteristic, complemented
33C2×#66889C2211yescharacteristic, complemented
34#10622742C2211yescharacteristic
35#10622742C2211yescharacteristic
36#10622742C2211yescharacteristic
37#10622742C2211yescharacteristic
38#10622742C2211yescharacteristic, complemented
39#10622739—21no—
40#10622739—21no—
41#10622735C2211yescharacteristic, complemented
42#10622732C2211yescharacteristic, complemented
43#10622726C2211yescharacteristic
44#10622726C2211yescharacteristic
45#10622723—21no—
46#10622723—21no—
47C2×#66879C2211yescharacteristic, complemented
48C2×C8×Dic11C2211yescharacteristic, complemented
49#10622352C411yescharacteristic, complemented
50#10622351C411yescharacteristic, complemented
51#10622347C411yescharacteristic, complemented
52#10622347C411yescharacteristic, complemented
53#10622346C411yescharacteristic, complemented
54#10622346C411yescharacteristic, complemented
55#10622345C411yescharacteristic, complemented
56#10622344C411yescharacteristic, complemented
57#10622342—21no—
58#10622342—21no—
59#10622341—21no—
60#10622341—21no—
61C11×#341C2211yescharacteristic, complemented
62C11×#341C2211yescharacteristic, complemented
63#10622193C2211yescharacteristic, complemented
64#10622193C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622188C2211yescharacteristic, complemented
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—41no—
72C2×#4339—41no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339C2×C411yescharacteristic
76C2×#4339C2×C411yescharacteristic
77C2×#4339C2311yescharacteristic
78C2×#4339C2311yescharacteristic
79C2×#4339C2311yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22C2×C411yescharacteristic
83C2×C11×M16—21no—
84C2×C11×M16—41no—
85C2×C11×M16—41no—
86C2×C11×M16C2311yescharacteristic
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C2×C11×M16C2311yescharacteristic
90C22×C8×C11—21no—
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93#67006—21no—
94C2×C22⋊Dic11—21no—
95#66983C2×C411yescharacteristic
96#66983C2×C411yescharacteristic
97#66982—21no—
98C4×C22⋊D11—21no—
99C4×C22⋊D11—21no—
100#66979C2311yescharacteristic
101#66977C2×C411yescharacteristic
102#66977C2×C411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×#4318—41no—
106C2×#4318—41no—
107C2×#4318D411yescharacteristic
108C2×#4318D411yescharacteristic
109C2×#4318D411yescharacteristic
110C2×#4318D411yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113#66960—41no—
114#66960—41no—
115C2×Dic44C2×C411yescharacteristic
116C2×Dic44C2×C411yescharacteristic
117#66957—41no—
118#66957—41no—
119#66957—41no—
120#66957—41no—
121C2×D88C2×C411yescharacteristic
122C2×D88C2×C411yescharacteristic
123C2×#4314C2×C411yescharacteristic
124C2×#4314C2×C411yescharacteristic
125C2×#4314C2×C411yescharacteristic
126C2×#4314C2×C411yescharacteristic
127C2×#4313—21no—
128C2×C8×D11—21no—
129C11×#108—41no—
130C11×#108—41no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8C2×C411yescharacteristic
134C11×C22⋊C8C2×C411yescharacteristic
135C11×C22⋊C8C2×C411yescharacteristic
136C11×C22⋊C8C2×C411yescharacteristic
137C11⋊#95—21no—
138#66889—41no—
139#66889—41no—
140#66889—41no—
141#66889—41no—
142#66889—41no—
143#66889—41no—
144#66885C2×C411yescharacteristic
145#66885C2×C411yescharacteristic
146#66885C2×C411yescharacteristic
147#66885C2×C411yescharacteristic
148(C2×D11)⋊C8—21no—
149(C2×D11)⋊C8—21no—
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)⋊C8—21no—
157(C2×D11)⋊C8—21no—
158#66880C2×C411yescharacteristic
159#66880C2×C411yescharacteristic
160#66880C2×C411yescharacteristic
161#66880C2×C411yescharacteristic
162#66879—21no—
163#66879—41no—
164Dic11⋊C8—21no—
165Dic11⋊C8—21no—
166C8×Dic11—21no—
167C8×Dic11—41no—
168#22062—111nomaximal, Sylow
169C24×C11#4111yescharacteristic
170C23×D11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—21no—
182C2×C22⋊D11—21no—
183C2×C22⋊D11—21no—
184C2×C22⋊D11—21no—
185C2×C22⋊D11—21no—
186C2×C22⋊D11—21no—
187C2×C22⋊D11—21no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193#4339—21no—
194#4339—21no—
195#4339—21no—
196#4339—21no—
197#4339—21no—
198#4339—21no—
199#4339—21no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—21no—
204#4339—21no—
205#4339—41no—
206#4339—41no—
207#4339—41no—
208#4339—41no—
209#4339—42no—
210#4339—42no—
211#4339—42no—
212#4339—42no—
213C2×D44—21no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44C22×C411yescharacteristic
217C2×D44C22×C411yescharacteristic
218C2×D44C22×C411yescharacteristic
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×Dic22—21no—
227C2×Dic22—41no—
228C2×Dic22—41no—
229C2×Dic22C22×C411yescharacteristic
230C2×Dic22C22×C411yescharacteristic
231C2×Dic22C22×C411yescharacteristic
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—21no—
236C11×M16—21no—
237C11×M16—21no—
238C11×M16—21no—
239C11×M16—21no—
240C11×M16—42no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—42no—
250C2×C8×C11C22×C411yescharacteristic
251C2×C8×C11C22×C411yescharacteristic
252C2×C8×C11C22×C411yescharacteristic
253C2×C8×C11C22×C411yescharacteristic
254C22⋊Dic11—21no—
255C22⋊Dic11—21no—
256C22⋊Dic11—21no—
257C22⋊Dic11—42no—
258(C2×D11)⋊C4—21no—
259(C2×D11)⋊C4—21no—
260C4⋊Dic11C22×C411yescharacteristic
261C4⋊Dic11C22×C411yescharacteristic
262Dic11⋊C4—21no—
263Dic11⋊C4—21no—
264C4×Dic11—21no—
265C4×Dic11—21no—
266C4×Dic11—21no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269#4318—41no—
270#4318—41no—
271#4318—41no—
272#4318—41no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8C2×D411yescharacteristic
278C2×C11⋊C8C2×D411yescharacteristic
279C2×C11⋊C8C2×D411yescharacteristic
280C2×C11⋊C8C2×D411yescharacteristic
281Dic44—41no—
282Dic44—41no—
283D88—41no—
284D88—41no—
285#4314—41no—
286#4314—41no—
287#4314—41no—
288#4314—41no—
289#4313—42no—
290C8×D11—42no—
291#3002—111no—
292#2930—111no—
293#2879—111no—
294#1975—111no—
295#1974—111no—
296#1938—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855D1111yescharacteristic, complemented
304#1789—111no—
305#1753—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C4×D411yescharacteristic
311C23×C11C4×D411yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—42no—
317C22×D11—81no—
318C22×D11—81no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11C4×D411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C22⋊D11—42no—
338C22⋊D11—42no—
339C22⋊D11—41no—
340C22⋊D11—41no—
341C22⋊D11—41no—
342C22⋊D11—41no—
343C22⋊D11—41no—
344C22⋊D11—41no—
345C22⋊D11—81no—
346C22⋊D11—81no—
347C2×Dic11—22no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—42no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359D44—21no—
360D44—21no—
361D44—21no—
362D44—21no—
363D44—21no—
364D44—21no—
365D44—42no—
366C4×D11—42no—
367C4×D11—42no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C4×D11—41no—
372C4×D11—41no—
373C4×D11—41no—
374Dic22—21no—
375Dic22—21no—
376Dic22—21no—
377Dic22—21no—
378Dic22—21no—
379Dic22—21no—
380Dic22—42no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C8×C11—41no—
386C8×C11—41no—
387C8×C11—41no—
388C8×C11—41no—
389C11⋊C8—21no—
390C11⋊C8—21no—
391C11⋊C8—21no—
392C11⋊C8—21no—
393C22×#41—111no—
394C2×#135—111no—
395C2×#135—111no—
396C2×#131—111no—
397C22×M16—111no—
398C22×M16C2×D1111yescharacteristic
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#436—221no—
409#436—221no—
410#435—221no—
411#435—221no—
412C2×#108C2×D1111yescharacteristic, complemented
413C2×#108C2×D1111yescharacteristic, complemented
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104—111no—
420C2×#104—111no—
421#416—111no—
422#416—111no—
423#408—111no—
424#408—111no—
425#408—111no—
426#408—111no—
427#408—111no—
428#408—221no—
429#408—221no—
430#407—221no—
431#407—221no—
432#407C2×D1111yescharacteristic
433C2×C22⋊C8C2×D1111yescharacteristic
434#405—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341C2×D1111yescharacteristic, complemented
439#341C2×D1111yescharacteristic, complemented
440#339—111no—
441#339—111no—
442#336—111no—
443#336—111no—
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11C2×C4×D411yescharacteristic
455C22×C11#53811yescharacteristic
456C22×C11#53811yescharacteristic
457C2×D11—41no—
458C2×D11—41no—
459C2×D11—41no—
460C2×D11—41no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—84no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11#51811yescharacteristic
470C4×C11#51811yescharacteristic
471C4×C11#53411yescharacteristic
472C4×C11#53511yescharacteristic
473Dic11—42no—
474Dic11—41no—
475Dic11—41no—
476Dic11—41no—
477Dic11—41no—
478Dic11—41no—
479Dic11—81no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—111no—
484C2×#41—111no—
485C2×#41—221no—
486C2×#41—221no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41—441no—
490C2×#41—441no—
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—221no—
494C23×C4—221no—
495C23×C4C22×D1111yescharacteristic
496#135—441no—
497#135—441no—
498#135—441no—
499#135—441no—
500C2×Q16—111no—
501C2×Q16—111no—
502C2×SD16—111no—
503C2×SD16—111no—
504C2×SD16—111no—
505C2×SD16—111no—
506C2×D8—111no—
507C2×D8—111no—
508#131—441no—
509#131—441no—
510C2×M16—21no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—111no—
514C2×M16—111no—
515C2×M16—111no—
516C2×M16—111no—
517C2×M16—221no—
518C2×M16—441no—
519C2×M16—441no—
520C2×M16C22×D1111yescharacteristic
521C2×M16C22×D1111yescharacteristic
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C22×C8—21no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—221no—
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×C42—111no—
542#108—41no—
543#108—41no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—441no—
547#104—441no—
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—221no—
563C22⋊C8—221no—
564C22⋊C8—221no—
565C22⋊C8—221no—
566C22⋊C8—221no—
567C22⋊C8—221no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8C4×D1111yescharacteristic
573C22⋊C8C4×D1111yescharacteristic
574C22⋊C8C4×D1111yescharacteristic
575C22⋊C8C4×D1111yescharacteristic
576#97—221no—
577#97—441no—
578C4×C8—221no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—41no—
584C2×C11—41no—
585C2×C11#232111yescharacteristic
586C2×C11#295611yescharacteristic
587C2×C11#295711yescharacteristic
588D11—81no—
589D11—81no—
590D11—81no—
591C24—221no—
592C24#434311yescharacteristic
593#41—221no—
594#41—221no—
595#41—221no—
596#41—221no—
597#41—221no—
598#41—221no—
599#41—221no—
600#41—221no—
601#41—221no—
602#41—221no—
603#41—221no—
604#41—221no—
605#41—441no—
606#41—441no—
607#41—441no—
608#41—441no—
609#41—442no—
610#41—442no—
611#41—442no—
612#41—442no—
613C2×Q8—111no—
614C2×Q8—111no—
615C2×Q8—111no—
616C2×Q8—221no—
617C2×Q8—441no—
618C2×Q8—441no—
619C2×D4—111no—
620C2×D4—111no—
621C2×D4—111no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—441no—
631C2×D4—441no—
632C2×D4—442no—
633C2×D4—442no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4D4×D1111yescharacteristic
651C22×C4D4×D1111yescharacteristic
652C22×C4#434311yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—441no—
655Q16—441no—
656SD16—441no—
657SD16—441no—
658SD16—441no—
659SD16—441no—
660D8—441no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—42no—
671M16—442no—
672M16—441no—
673M16—441no—
674M16—441no—
675M16—441no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—42no—
685C2×C8—111no—
686C2×C8—111no—
687C2×C8—111no—
688C2×C8—111no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—442no—
694C2×C8C2×C4×D1111yescharacteristic
695C2×C8C2×C4×D1111yescharacteristic
696C2×C8C2×C4×D1111yescharacteristic
697C2×C8C2×C4×D1111yescharacteristic
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—221no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—442no—
708C42—221no—
709C42—221no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—41no—
717C23—41no—
718C23—221no—
719C23—221no—
720C23—221no—
721C23—442no—
722C23—881no—
723C23—881no—
724C23#6694611yescharacteristic
725C23#6694611yescharacteristic
726C23C2×#434311yescharacteristic
727Q8—221no—
728Q8—221no—
729Q8—221no—
730Q8—221no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—221no—
735D4—221no—
736D4—221no—
737D4—221no—
738D4—221no—
739D4—221no—
740D4—442no—
741D4—442no—
742D4—442no—
743D4—441no—
744D4—441no—
745D4—441no—
746D4—441no—
747D4—441no—
748D4—441no—
749D4—881no—
750D4—881no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—222no—
762C2×C4—221no—
763C2×C4—221no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—221no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4#6694611yescharacteristic
782C2×C4#6694611yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6704211yescharacteristic
788C2×C4#6704211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C8—221no—
798C8—221no—
799C8—221no—
800C8—221no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—81no—
810C22—81no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C2×#6694611yescharacteristic
822C22#1062317511yescharacteristic
823C22#1062317511yescharacteristic
824C4—21no—
825C4—21no—
826C4—442no—
827C4—441no—
828C4—441no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—881no—
833C4#1062307611yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062312311yescharacteristic
836C4#1062318411yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—881no—
842C2—881no—
843C2—881no—
844C2#1307127311yescharacteristic
845C2#1307752511yescharacteristic
846C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C2×C4×D4
prime radical#13077838C2
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
2. #13077315C2semidirect
3. #13077060C2semidirect
4. #13069507C2semidirect
5. #13069502C2semidirect
6. #13069325C2semidirect
7. #13069318C2semidirect
8. #13069263C2semidirect
9. #13069263C2semidirect
10. #13068944C2semidirect
11. #13068944C2semidirect
12. #13068918C2semidirect
13. #13068559C2semidirect
14. #13068402C2semidirect
15. C11×#1855C2semidirect
20. C2×#66960C22semidirect
23. C2×C11×#108C22semidirect
24. C2×C11×#108C22semidirect
32. C2×#66889C22semidirect
33. C2×#66889C22semidirect
38. #10622742C22semidirect
41. #10622735C22semidirect
42. #10622732C22semidirect
47. C2×#66879C22semidirect
48. C2×C8×Dic11C22semidirect
49. #10622352C4semidirect
50. #10622351C4semidirect
51. #10622347C4semidirect
52. #10622347C4semidirect
53. #10622346C4semidirect
54. #10622346C4semidirect
55. #10622345C4semidirect
56. #10622344C4semidirect
61. C11×#341C22semidirect
62. C11×#341C22semidirect
63. #10622193C22semidirect
64. #10622193C22semidirect
65. #10622188C22semidirect
66. #10622188C22semidirect
303. #1855D11semidirect
412. C2×#108C2×D11semidirect
413. C2×#108C2×D11semidirect
438. #341C2×D11semidirect
439. #341C2×D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778382
#130773152
#130770602
#130695072
#130695022
#130693252
#130693182
#130692632
#130689442
#130689182
#130685592
#130684022
C11×#18552
#2206211