Finite Group Databasebeta

← #14660587

Subgroups — #14660587

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C211yesmaximal, characteristic
2C22×#66901C211yesmaximal, characteristic, complemented
3C22×#66889C211yesmaximal, characteristic, complemented
4C2×#10622723C211yesmaximal, characteristic, complemented
5C2×#10622196C211yesmaximal, characteristic, complemented
6C2×#10622188C211yesmaximal, characteristic, complemented
7C2×C11×#408C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×#67003—22no—
13C2×#67003—22no—
14C2×#67003—22no—
15C2×#67003—22no—
16C2×#67003—22no—
17C2×#67003—22no—
18C22×#4326C411yescharacteristic, complemented
19C22×#4325C411yescharacteristic, complemented
20C22×#4324C411yescharacteristic, complemented
21C22×#4323C411yescharacteristic, complemented
22C22×C4×Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#408—22no—
26C11×#408—22no—
27C2×C11×C22⋊C8—22no—
28C2×#66901—22no—
29C2×#66901—22no—
30C2×#66901—22no—
31C2×#66889—22no—
32C2×#66889—22no—
33C2×#66889—22no—
34#10622723—22no—
35#10622723—22no—
36C2×(C2×D11)⋊C8—22no—
37#10622196—22no—
38#10622188—22no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41D412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11C2×C411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2×C411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C23×Dic11—21no—
58C2×#4339—21no—
59C2×#4339—21no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339D412yes—
69C2×#4339D412yes—
70C22×D44C2×C411yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22C2×C411yescharacteristic
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16D412yes—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C22×C8×C11—21no—
85C22×C8×C11—21no—
86C22×C8×C11D412yes—
87#67003—28no—
88#67003—28no—
89#67003—28no—
90#67003—28no—
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326—22no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325—22no—
97C2×#4324—22no—
98C2×#4324—22no—
99C2×#4324—22no—
100C2×#4323—22no—
101C2×#4323—22no—
102C2×#4323—22no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11D412yes—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318D412yes—
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8—21no—
118C22×C11⋊C8—21no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8C2×C411yescharacteristic
121C22×C11⋊C8C2×C411yescharacteristic
122C22×C11⋊C8D412yes—
123C22×C11⋊C8D412yes—
124C11×C22⋊C8—28no—
125#66901—28no—
126#66889—28no—
127(C2×D11)⋊C8—28no—
128#11025—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11#4111yescharacteristic
131C23×D11—21no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22⋊C412yes—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11C22⋊C412yes—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C22×C4×C11#4111yescharacteristic
186C22×C4×C11#4111yescharacteristic
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—41no—
190C2×C22⋊D11—41no—
191C2×C22⋊D11—41no—
192C2×C22⋊D11—41no—
193C22×Dic11—24no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—42no—
197C22×Dic11—41no—
198C22×Dic11—41no—
199#4339—22no—
200#4339—22no—
201#4339—22no—
202#4339—22no—
203#4339—22no—
204#4339—22no—
205#4339—22no—
206#4339—22no—
207#4339—41no—
208#4339—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214#4339—41no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44C22⋊C412yes—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—41no—
224C2×C4×D11—41no—
225C2×C4×D11—41no—
226C2×C4×D11—41no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22C22⋊C412yes—
233C11×M16—22no—
234C11×M16—22no—
235C11×M16—41no—
236C11×M16—41no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11—41no—
242C2×C8×C11—41no—
243C2×C8×C11—41no—
244C2×C8×C11—41no—
245C2×C8×C11—41no—
246C2×C8×C11—41no—
247#4326—28no—
248#4325—28no—
249#4324—28no—
250#4323—28no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—41no—
254C4×Dic11—41no—
255#4318—22no—
256#4318—22no—
257#4318—41no—
258#4318—41no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—41no—
269C2×C11⋊C8—41no—
270C2×C11⋊C8C22⋊C412yes—
271C2×C11⋊C8C22⋊C412yes—
272C22×#135—111no—
273C22×#104—111no—
274C22×#104—111no—
275C2×#408—111no—
276C2×#408D1111yescharacteristic, complemented
277C2×#341—111no—
278C2×#336—111no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11C4×D411yescharacteristic
287C23×C11#12111yescharacteristic
288C23×C11#12111yescharacteristic
289C23×C11#12111yescharacteristic
290C23×C11#12311yescharacteristic
291C23×C11#12311yescharacteristic
292C23×C11#12411yescharacteristic
293C22×D11—22no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—42no—
297C22×D11—42no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—41no—
301Q8×C11—41no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—41no—
309D4×C11—41no—
310C2×C4×C11—22no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C2×C22⋊C411yescharacteristic
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C2×C22⋊C411yescharacteristic
320C2×C4×C11C4×D411yescharacteristic
321C2×C4×C11C4×D411yescharacteristic
322C2×C4×C11C4×D411yescharacteristic
323C2×C4×C11#12011yescharacteristic
324C2×C4×C11#12011yescharacteristic
325C2×C4×C11#12011yescharacteristic
326C2×C4×C11#12011yescharacteristic
327C2×C4×C11#12011yescharacteristic
328C2×C4×C11#12011yescharacteristic
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12111yescharacteristic
332C2×C4×C11#12111yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12311yescharacteristic
341C2×C4×C11#12311yescharacteristic
342C2×C4×C11#12411yescharacteristic
343C2×C4×C11#12711yescharacteristic
344C2×C4×C11#12711yescharacteristic
345C22⋊D11—42no—
346C22⋊D11—42no—
347C22⋊D11—42no—
348C22⋊D11—42no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—44no—
352C2×Dic11—44no—
353C2×Dic11—42no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—42no—
357D44—22no—
358D44—22no—
359D44—41no—
360D44—41no—
361C4×D11—42no—
362C4×D11—42no—
363C4×D11—42no—
364C4×D11—42no—
365Dic22—22no—
366Dic22—22no—
367Dic22—41no—
368Dic22—41no—
369C8×C11—42no—
370C8×C11—42no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C11⋊C8—42no—
374C22×#41—111no—
375C22×#41C2×D1111yescharacteristic
376C2×#135—222no—
377C2×#135—222no—
378C2×#135—222no—
379C2×#135—222no—
380C2×#135—222no—
381C2×#135—222no—
382C22×Q16—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C22×M16C2×D1111yescharacteristic
388C23×C8—111no—
389C23×C8C2×D1111yescharacteristic
390C22×C42—111no—
391C2×#104—222no—
392C2×#104—222no—
393C2×#104—222no—
394C2×#104—222no—
395C2×#104—222no—
396C2×#104—222no—
397#408—22no—
398#408—22no—
399#408—222no—
400#408—222no—
401C2×C22⋊C8—22no—
402C2×C22⋊C8—222no—
403#341—222no—
404#336—222no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—21no—
413C22×C11—44no—
414C22×C11—42no—
415C22×C11—82no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11#38611yescharacteristic
419C22×C11#38611yescharacteristic
420C22×C11#39011yescharacteristic
421C22×C11#39211yescharacteristic
422C22×C11#39411yescharacteristic
423C22×C11#39411yescharacteristic
424C22×C11#39411yescharacteristic
425C22×C11#44312yes—
426C22×C11#44412yes—
427C2×D11—44no—
428C2×D11—42no—
429C2×D11—82no—
430C2×D11—81no—
431C2×D11—81no—
432C4×C11—42no—
433C4×C11#37911yescharacteristic
434C4×C11#38611yescharacteristic
435C4×C11#38611yescharacteristic
436C4×C11#39011yescharacteristic
437C4×C11#39211yescharacteristic
438C4×C11#39211yescharacteristic
439C4×C11#39211yescharacteristic
440C4×C11#39411yescharacteristic
441Dic11—44no—
442Dic11—42no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—112no—
454C2×#41—112no—
455C2×#41—221no—
456C2×#41—221no—
457C2×#41—221no—
458C2×#41—221no—
459C2×#41—221no—
460C2×#41—221no—
461C2×#41—221no—
462C2×#41—221no—
463C2×#41—221no—
464C2×#41—221no—
465C2×#41D4412yes—
466C2×#41C22⋊D1112yes—
467C22×Q8—111no—
468C22×Q8C4×D1111yescharacteristic
469C22×D4—21no—
470C22×D4—111no—
471C22×D4—221no—
472C22×D4C4×D1111yescharacteristic
473C23×C4—21no—
474C23×C4—221no—
475C23×C4—221no—
476C23×C4C22×D1111yescharacteristic
477#135—228no—
478#135—228no—
479#135—228no—
480#135—228no—
481C2×Q16—222no—
482C2×Q16—222no—
483C2×Q16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×SD16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×SD16—222no—
490C2×D8—222no—
491C2×D8—222no—
492C2×D8—222no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—112no—
499C2×M16—221no—
500C2×M16—221no—
501C2×M16—221no—
502C2×M16—221no—
503C2×M16—221no—
504C2×M16C22⋊D1112yes—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—21no—
508C22×C8—21no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—112no—
515C22×C8—112no—
516C22×C8—221no—
517C22×C8—221no—
518C22×C8—221no—
519C22×C8—221no—
520C22×C8—221no—
521C22×C8C22⋊D1112yes—
522C2×C42—112no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527C2×C42—221no—
528#104—228no—
529#104—228no—
530C22⋊C8—28no—
531C22⋊C8—228no—
532C2×C11—21no—
533C2×C11—21no—
534C2×C11—21no—
535C2×C11—21no—
536C2×C11—82no—
537C2×C11#143811yescharacteristic
538C2×C11#187612yes—
539C2×C11#187612yes—
540C2×C11#197411yescharacteristic
541C2×C11#197511yescharacteristic
542D11—82no—
543C24—21no—
544C24—221no—
545C24#433911yescharacteristic
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
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—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—112no—
584C2×Q8—221no—
585C2×Q8—221no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8(C2×D11)⋊C412yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—112no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—441no—
610C2×D4—441no—
611C2×D4—441no—
612C2×D4—441no—
613C2×D4(C2×D11)⋊C412yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—224no—
622C22×C4—222no—
623C22×C4—221no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—442no—
627C22×C4—441no—
628C22×C4—441no—
629C22×C4—441no—
630C22×C4—441no—
631C22×C4—441no—
632C22×C4—441no—
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×D4411yescharacteristic
635C22×C4#433911yescharacteristic
636C22×C4D4×D1111yescharacteristic
637C22×C4D4×D1111yescharacteristic
638C22×C4D4×D1111yescharacteristic
639C22×C4D4×D1111yescharacteristic
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4#434111yescharacteristic
643C22×C4#434111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647Q16—228no—
648SD16—228no—
649SD16—228no—
650D8—228no—
651M16—22no—
652M16—22no—
653M16—41no—
654M16—41no—
655M16—222no—
656M16—222no—
657M16—441no—
658M16—441no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—41no—
668C2×C8—41no—
669C2×C8—112no—
670C2×C8—112no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—222no—
674C2×C8—222no—
675C2×C8—221no—
676C2×C8—221no—
677C2×C8—222no—
678C2×C8—222no—
679C2×C8—222no—
680C2×C8—441no—
681C2×C8—441no—
682C42—222no—
683C42—222no—
684C42—441no—
685C42—441no—
686C11#1102511yescharacteristic, complemented, Sylow
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—222no—
695C23—442no—
696C23—442no—
697C23—441no—
698C23—441no—
699C23#6693611yescharacteristic
700C23#6693711yescharacteristic
701C23#6693711yescharacteristic
702C23#6693811yescharacteristic
703C23C4×C22⋊D1111yescharacteristic
704C23#6698211yescharacteristic
705C23#6698311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—222no—
711Q8—222no—
712Q8—441no—
713Q8—441no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—42no—
720D4—41no—
721D4—41no—
722D4—222no—
723D4—222no—
724D4—442no—
725D4—442no—
726D4—442no—
727D4—442no—
728D4—441no—
729D4—441no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—224no—
738C2×C4—222no—
739C2×C4—444no—
740C2×C4—444no—
741C2×C4—442no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4C22⋊C4×D1111yescharacteristic
750C2×C4C22⋊C4×D1111yescharacteristic
751C2×C4(C22⋊D11)⋊C411yescharacteristic
752C2×C4(C22⋊D11)⋊C411yescharacteristic
753C2×C4#6693511yescharacteristic
754C2×C4#6693511yescharacteristic
755C2×C4#6693511yescharacteristic
756C2×C4#6693611yescharacteristic
757C2×C4#6693711yescharacteristic
758C2×C4#6693711yescharacteristic
759C2×C4#6693811yescharacteristic
760C2×C4#6693911yescharacteristic
761C2×C4C2×(C2×D11)⋊C411yescharacteristic
762C2×C4C4×C22⋊D1111yescharacteristic
763C2×C4#6698311yescharacteristic
764C2×C4#6699011yescharacteristic
765C2×C4#6699011yescharacteristic
766C2×C4#6699011yescharacteristic
767C2×C4#6699011yescharacteristic
768C2×C4#6699111yescharacteristic
769C2×C4#6699111yescharacteristic
770C2×C4#6699211yescharacteristic
771C2×C4#6699211yescharacteristic
772C2×C4#6699211yescharacteristic
773C2×C4#6699211yescharacteristic
774C2×C4#6699311yescharacteristic
775C2×C4#6699311yescharacteristic
776C2×C4#6700611yescharacteristic
777C8—42no—
778C8—42no—
779C8—222no—
780C8—222no—
781C8—442no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—42no—
791C22—44no—
792C22—82no—
793C22—81no—
794C22—81no—
795C22—442no—
796C22—444no—
797C22—882no—
798C22—881no—
799C22—881no—
800C22#1062256911yescharacteristic
801C22#1062257011yescharacteristic
802C22#1062257211yescharacteristic
803C22#1062257211yescharacteristic
804C22#1062257311yescharacteristic
805C22#1062257411yescharacteristic
806C22#1062275712yes—
807C22#1062275812yes—
808C22#1062282611yescharacteristic
809C4—42no—
810C4—444no—
811C4—442no—
812C4#1062256811yescharacteristic
813C4#1062256911yescharacteristic
814C4#1062257011yescharacteristic
815C4#1062257111yescharacteristic
816C4#1062257311yescharacteristic
817C4#1062257411yescharacteristic
818C4#1062283611yescharacteristic
819C4#1062283611yescharacteristic
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—82no—
825C2—882no—
826C2#1306685511yescharacteristic
827C2#1306894312yes—
828C2#1306894612yes—
829C2#1306950311yescharacteristic
830C2#1306950811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#408C2
socleC23×C11C4×D4
prime radicalC22×#67003C2
cosocleC23×C4×C11C23
hypercenterC2×#408D11
hypocenterC11#11025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C22×#66901C2semidirect
3. C22×#66889C2semidirect
4. C2×#10622723C2semidirect
5. C2×#10622196C2semidirect
6. C2×#10622188C2semidirect
7. C2×C11×#408C2semidirect
18. C22×#4326C4semidirect
19. C22×#4325C4semidirect
20. C22×#4324C4semidirect
21. C22×#4323C4semidirect
276. C2×#408D11semidirect
686. C11#11025semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C22×#669012
C22×#668892
C2×#106227232
C2×#106221962
C2×#106221882
C2×C11×#4082
#1102511