Finite Group Databasebeta

← #14797518

Subgroups — #14797518

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622345C211yesmaximal, characteristic
2C2×C4×D88C211yesmaximal, characteristic, complemented
3#13072130C211yesmaximal, characteristic, complemented
4C22⋊C4×D44C211yesmaximal, characteristic, complemented
5#13070143C211yesmaximal, characteristic, complemented
6#13070039C211yesmaximal, characteristic, complemented
7#13069927C211yesmaximal, characteristic, complemented
8#13069799C211yesmaximal, characteristic, complemented
9#13069299C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068866C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×D88C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C2×#66936—21no—
21C2×C22⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic, complemented
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic, complemented
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic, complemented
39C2×#66885C2211yescharacteristic, complemented
40C2×#66882C2211yescharacteristic, complemented
41C2×#66882C2211yescharacteristic, complemented
42#10622574—21no—
43#10622568—21no—
44#10622552C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic, complemented
47#10622548C2211yescharacteristic, complemented
48#10622541C2211yescharacteristic, complemented
49#10622345—24no—
50C4×D88—24no—
51#10622287—21no—
52#10622281—21no—
53#10622278—21no—
54#10622278—21no—
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61C24×D11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87#66983—22no—
88#66983—41no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×D88—22no—
108C2×D88—22no—
109C2×D88—22no—
110C2×D88—22no—
111C2×D88—41no—
112C2×D88D414yes—
113#66936—44no—
114C22⋊C4×D11—44no—
115C4×D44—22no—
116C4×D44—22no—
117C4×D44—22no—
118C4×D44—41no—
119C4×D44—41no—
120C4×D44—41no—
121C11×C4⋊C8—41no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
124C4×C8×C11—22no—
125C11×#95D411yescharacteristic
126C11×#95D411yescharacteristic
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66885—22no—
131#66885—22no—
132#66885—22no—
133#66885—22no—
134#66885—22no—
135#66885—22no—
136#66885—41no—
137#66885—41no—
138#66882—22no—
139#66882—41no—
140#24893—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—24no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—81no—
151C23×D11—81no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—42no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—81no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C2×D44—24no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—42no—
187C2×D44—42no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—44no—
192C2×D44C2×D412yes—
193C2×D44C2×D412yes—
194C2×D44#4112yes—
195C2×D44#4112yes—
196C2×D44#4112yes—
197C2×C4×D11—42no—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×C4×D11—81no—
204C2×C4×D11—81no—
205C2×C4×D11—81no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11C2×D412yes—
218C11×C22⋊C4—41no—
219C11×C22⋊C4D814yescomplemented
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C22⋊Dic11—42no—
225C22⋊Dic11—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—81no—
235(C2×D11)⋊C4—81no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—42no—
247C4⋊Dic11—81no—
248Dic11⋊C4—42no—
249D88—28no—
250D88—44no—
251C2×#447—111no—
252C2×C4×D8—111no—
253#2422—111no—
254D4×C22⋊C4—111no—
255#2093—111no—
256#2075—111no—
257#2054—111no—
258#2033—111no—
259#1934—111no—
260#1923D1111yescharacteristic, complemented
261#1879—111no—
262#1879—111no—
263#1862—111no—
264#1802—111no—
265#1786—111no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11C2×D812yes—
273C23×C11C22×D411yescharacteristic
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—48no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—48no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—84no—
298C22×D11—84no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11—84no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11C2×D812yes—
320C2×C4×C11C2×D812yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C22⋊D11—84no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343D44—22no—
344D44—22no—
345D44—22no—
346D44—22no—
347D44—22no—
348D44—22no—
349D44—22no—
350D44—48no—
351D44—41no—
352D44—41no—
353D44—41no—
354D44—41no—
355D44#12314yescomplemented
356C4×D11—84no—
357C4×D11—84no—
358C4×D11—84no—
359C8×C11—22no—
360C8×C11—41no—
361C8×C11—41no—
362C8×C11—41no—
363C23×D4—111no—
364C22×D8—111no—
365C22×D8—111no—
366C2×#123—221no—
367C2×#121—111no—
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C22×C22⋊C4—221no—
372#447—224no—
373C4×D8—224no—
374C2×#107—111no—
375C2×#107—111no—
376C2×C4⋊C8C2×D1111yescharacteristic, complemented
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×C22⋊C8C2×D1111yescharacteristic
386C2×C22⋊C8C2×D1111yescharacteristic
387C2×C4×C8C2×D1111yescharacteristic, complemented
388#397—221no—
389#394—221no—
390#390—111no—
391#390—111no—
392#390—111no—
393#389—111no—
394#386—221no—
395#386—221no—
396#385—221no—
397#384—111no—
398#380—111no—
399#380—111no—
400#379—221no—
401C4×C22⋊C4C2×D1111yescharacteristic
402#340—111no—
403#340—111no—
404#340—111no—
405#340—111no—
406#336C2×D1111yescharacteristic, complemented
407#336C2×D1111yescharacteristic, complemented
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11#52511yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11#54611yescharacteristic
418C22×C11C22×D811yescharacteristic
419C22×C11#57511yescharacteristic
420C22×C11#57611yescharacteristic
421C22×C11#57711yescharacteristic
422C2×D11—24no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—816no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C4×C11—22no—
445C4×C11—22no—
446C4×C11—41no—
447C4×C11—41no—
448C4×C11—41no—
449C4×C11C2×#12311yescharacteristic
450C4×C11#53811yescharacteristic
451C4×C11#54611yescharacteristic
452C4×C11#55111yescharacteristic
453Dic11—81no—
454Dic11—81no—
455Dic11—81no—
456Dic11—81no—
457Dic11—81no—
458C25—221no—
459C22×D4—111no—
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C22×D4—222no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—441no—
469C22×D4—441no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C23×C4C22×D1111yescharacteristic
474C2×D8—114no—
475C2×D8—222no—
476C2×D8—222no—
477C2×D8—222no—
478C2×D8—222no—
479C2×D8—441no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484#123—444no—
485#121—222no—
486#121—441no—
487C4×D4—222no—
488C4×D4—222no—
489C4×D4—222no—
490C4×D4—441no—
491C4×D4—441no—
492C4×D4—441no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—444no—
514C2×C22⋊C4D4411yescharacteristic
515C2×C22⋊C4D4411yescharacteristic
516C2×C42C22×D1111yescharacteristic
517C2×C42C22×D1111yescharacteristic
518#107—222no—
519#107—441no—
520C4⋊C8—41no—
521#102—222no—
522#102—222no—
523#102—222no—
524#102—222no—
525#102—222no—
526#102—222no—
527#102—441no—
528#102—441no—
529C22⋊C8—22no—
530C22⋊C8—41no—
531C4×C8—22no—
532#95—221no—
533#95—221no—
534#95—221no—
535#95D4411yescharacteristic
536#95D4411yescharacteristic
537C2×C11—42no—
538C2×C11#241811yescharacteristic
539C2×C11#310011yescharacteristic
540C2×C11#311811yescharacteristic
541C2×C11#326711yescharacteristic
542C2×C11D4×D811yescharacteristic
543C2×C11#329411yescharacteristic
544C2×C11#332211yescharacteristic
545D11—44no—
546D11—82no—
547D11—82no—
548C24—224no—
549C24—221no—
550C24—221no—
551C24—221no—
552C24—442no—
553C24—442no—
554C24—442no—
555C24—442no—
556C24—881no—
557C24—881no—
558C24C2×D4411yescharacteristic
559C2×D4—112no—
560C2×D4—112no—
561C2×D4—112no—
562C2×D4—112no—
563C2×D4—112no—
564C2×D4—224no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—442no—
579C2×D4—442no—
580C2×D4—444no—
581C2×D4—444no—
582C2×D4—444no—
583C2×D4—444no—
584C2×D4—442no—
585C2×D4—442no—
586C2×D4—881no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4—442no—
601C22×C4—442no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4—881no—
605C22×C4—881no—
606C22×C4—881no—
607C22×C4C2×D4411yescharacteristic
608C22×C4C2×D4411yescharacteristic
609C22×C4C2×D4411yescharacteristic
610C22×C4C2×D4411yescharacteristic
611C22×C4C2×D4411yescharacteristic
612C22×C4C23×D1111yescharacteristic
613D8—228no—
614D8—444no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8D4×D1112yes—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—442no—
638C4⋊C4—442no—
639C4⋊C4—881no—
640C22⋊C4—41no—
641C22⋊C4—442no—
642C22⋊C4—442no—
643C22⋊C4—442no—
644C22⋊C4—442no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—881no—
652C22⋊C4—881no—
653C22⋊C4D8814yescomplemented
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C11#2489311yescharacteristic, complemented, Sylow
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—448no—
671C23—448no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—884no—
689C23—884no—
690C23—884no—
691C23—884no—
692C23—884no—
693C23C2×D8812yes—
694C23C22×D4411yescharacteristic
695D4—114no—
696D4—222no—
697D4—222no—
698D4—222no—
699D4—222no—
700D4—222no—
701D4—222no—
702D4—222no—
703D4—448no—
704D4—441no—
705D4—441no—
706D4—441no—
707D4—441no—
708D4—884no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4—884no—
744C2×C4C2×D8812yes—
745C2×C4C2×D8812yes—
746C2×C4C2×D4×D1111yescharacteristic
747C2×C4#6703711yescharacteristic
748C2×C4#41×D1111yescharacteristic
749C2×C4#41×D1111yescharacteristic
750C2×C4#41×D1111yescharacteristic
751C2×C4#6704211yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—224no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—442no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—8816no—
777C22—881no—
778C22—881no—
779C22—881no—
780C22—881no—
781C22—881no—
782C22—881no—
783C22—881no—
784C22—881no—
785C22#1062305511yescharacteristic
786C22D4×D4411yescharacteristic
787C22#1062308511yescharacteristic
788C22C22×D8811yescharacteristic
789C22#1062327911yescharacteristic
790C22#1062328211yescharacteristic
791C22#1062328311yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—881no—
798C4—881no—
799C4—881no—
800C4—881no—
801C4—881no—
802C4#1062314311yescharacteristic
803C4D11×#12311yescharacteristic
804C4#1062320911yescharacteristic
805C4#1062323611yescharacteristic
806C2—42no—
807C2—444no—
808C2—882no—
809C2—882no—
810C2#1307208311yescharacteristic
811C2#1307861711yescharacteristic
812C2#1307880211yescharacteristic
813C2#1308014611yescharacteristic
814C2D4×D8811yescharacteristic
815C2#1308043011yescharacteristic
816C2#1308081911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1923C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
hypercenter#1923D11
hypocenterC11#24893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. C2×C4×D88C2semidirect
3. #13072130C2semidirect
4. C22⋊C4×D44C2semidirect
5. #13070143C2semidirect
6. #13070039C2semidirect
7. #13069927C2semidirect
8. #13069799C2semidirect
9. #13069299C2semidirect
10. #13068963C2semidirect
11. #13068963C2semidirect
12. #13068866C2semidirect
13. #13068617C2semidirect
14. #13068548C2semidirect
15. C11×#1923C2semidirect
24. C2×C4×D44C22semidirect
25. C2×C11×C4⋊C8C22semidirect
28. C2×C4×C8×C11C22semidirect
38. C2×#66885C22semidirect
39. C2×#66885C22semidirect
40. C2×#66882C22semidirect
41. C2×#66882C22semidirect
46. #10622552C22semidirect
47. #10622548C22semidirect
48. #10622541C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. #10622189C22semidirect
58. #10622189C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
219. C11×C22⋊C4D8semidirect
260. #1923D11semidirect
355. D44#123semidirect
376. C2×C4⋊C8C2×D11semidirect
387. C2×C4×C8C2×D11semidirect
406. #336C2×D11semidirect
407. #336C2×D11semidirect
653. C22⋊C4D88semidirect
658. C11#24893semidirect

Maximal subgroups

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

subgroupindex
C2×#106223452
C2×C4×D882
#130721302
C22⋊C4×D442
#130701432
#130700392
#130699272
#130697992
#130692992
#130689632
#130688662
#130686172
#130685482
C11×#19232
#2489311