Finite Group Databasebeta

← #14797513

Subgroups — #14797513

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×#10622830C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13072130C211yesmaximal, characteristic, complemented
4#13070144C211yesmaximal, characteristic, complemented
5#13070042C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic, complemented
7#13069798C211yesmaximal, characteristic, complemented
8#13069302C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068863C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66936—21no—
24C2×C4×D44C2211yescharacteristic, complemented
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#386—21no—
28C11×#386—21no—
29C11×#380C2211yescharacteristic
30C11×#379—21no—
31C4×C11×C22⋊C4C2211yescharacteristic
32#10622830—24no—
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C4×#4323—24no—
43C2×#66873C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622574—21no—
48#10622552C2211yescharacteristic, complemented
49#10622548C2211yescharacteristic, complemented
50#10622541C2211yescharacteristic, complemented
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×C4×C11⋊C8C2211yescharacteristic, complemented
53#10622287—21no—
54#10622281—21no—
55#10622167C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—41no—
80C4×D4×C11—41no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×#4323—22no—
97C2×#4323—22no—
98C2×#4323—22no—
99C2×#4323—22no—
100C2×#4323—41no—
101C2×#4323D414yes—
102#66983—22no—
103#66983—41no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×Dic11⋊C4—21no—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118#66936—44no—
119C4×D44—22no—
120C4×D44—41no—
121C11×#95—21no—
122C11×#95D411yescharacteristic
123C11×#95D411yescharacteristic
124#66896—22no—
125#66896—22no—
126#66896—22no—
127#66896—22no—
128#66896—22no—
129#66896—41no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—41no—
134#66873—22no—
135#66873—41no—
136#66871—22no—
137#66871—41no—
138C4⋊(C11⋊C8)—41no—
139C4×C11⋊C8—22no—
140#24893—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—24no—
143C24×C11—21no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—42no—
148C24×C11—81no—
149C24×C11—81no—
150C24×C11C2×D411yescharacteristic
151C23×D11—21no—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—42no—
162C2×D4×C11—42no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11C2×D412yes—
168C2×D4×C11#4112yes—
169C2×D4×C11#4112yes—
170C2×D4×C11#4112yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—81no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44C2×D412yes—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—81no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4D814yescomplemented
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C22⋊Dic11—42no—
224#4323—28no—
225#4323—44no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—42no—
237C4⋊Dic11—81no—
238Dic11⋊C4—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8C2×D412yes—
251C2×#447—111no—
252C2×C4×D8—111no—
253#2422—111no—
254D4×C22⋊C4D1111yescharacteristic, complemented
255#2093—111no—
256#2075—111no—
257#2054—111no—
258#2033—111no—
259#1934—111no—
260#1923—111no—
261#1879—111no—
262#1879—111no—
263#1862—111no—
264#1802—111no—
265#1786—111no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—21no—
270C23×C11—22no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—22no—
276C23×C11—48no—
277C23×C11—48no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11—84no—
293C23×C11C2×D812yes—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—48no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11#12314yescomplemented
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—84no—
335C2×C4×C11—84no—
336C2×C4×C11C2×D812yes—
337C2×C4×C11C2×D812yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C2×#4111yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C22⋊D11—84no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354D44—22no—
355D44—22no—
356D44—41no—
357D44—41no—
358C4×D11—84no—
359C11⋊C8—22no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C23×D4C2×D1111yescharacteristic
364C22×D8—111no—
365C22×D8—111no—
366C2×#123—221no—
367C2×#121—111no—
368C2×C4×D4—111no—
369C2×C4×D4C2×D1111yescharacteristic
370C2×C4×D4C2×D1111yescharacteristic
371C22×C22⋊C4—21no—
372#447—224no—
373C4×D8—224no—
374C2×#107—111no—
375C2×#107—111no—
376C2×C4⋊C8—111no—
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⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C4×C8—111no—
388#397—221no—
389#394—221no—
390#390—111no—
391#390C2×D1111yescharacteristic
392#390C2×D1111yescharacteristic
393#389—111no—
394#386—21no—
395#386—21no—
396#385—221no—
397#384—111no—
398#380—111no—
399#380C2×D1111yescharacteristic
400#379—21no—
401C4×C22⋊C4C2×D1111yescharacteristic
402#340—111no—
403#340—111no—
404#340—111no—
405#340—111no—
406#336—111no—
407#336—111no—
408C22×C11—22no—
409C22×C11—24no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—42no—
413C22×C11—41no—
414C22×C11—42no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—41no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—816no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11#52511yescharacteristic
431C22×C11D4211yescharacteristic
432C22×C11#54611yescharacteristic
433C22×C11C22×D811yescharacteristic
434C22×C11#57511yescharacteristic
435C22×C11#57611yescharacteristic
436C22×C11#57711yescharacteristic
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
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×C11—81no—
450C4×C11—81no—
451C4×C11C2×#12311yescharacteristic
452C4×C11#53811yescharacteristic
453C4×C11#54611yescharacteristic
454C4×C11#55111yescharacteristic
455Dic11—81no—
456Dic11—81no—
457Dic11—81no—
458C25—21no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—41no—
465C22×D4—41no—
466C22×D4—111no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
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×C8—111no—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8—111no—
484#123—444no—
485#121—222no—
486#121—441no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491C4×D4—222no—
492C4×D4—441no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4C22⋊D1111yescharacteristic
515C2×C22⋊C4C22⋊D1111yescharacteristic
516C2×C42C22×D1111yescharacteristic
517C2×C42C22×D1111yescharacteristic
518#107—222no—
519#107—441no—
520C4⋊C8—441no—
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—222no—
530C22⋊C8—441no—
531C4×C8—222no—
532#95—21no—
533#95—221no—
534#95—221no—
535#95C22⋊D1111yescharacteristic
536#95C22⋊D1111yescharacteristic
537C2×C11—42no—
538C2×C11—44no—
539C2×C11—82no—
540C2×C11#241811yescharacteristic
541C2×C11#310011yescharacteristic
542C2×C11#311811yescharacteristic
543C2×C11#326711yescharacteristic
544C2×C11D4×D811yescharacteristic
545C2×C11#329411yescharacteristic
546C2×C11#332211yescharacteristic
547D11—82no—
548C24—21no—
549C24—24no—
550C24—21no—
551C24—42no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—81no—
556C24—81no—
557C24—221no—
558C24C2×C22⋊D1111yescharacteristic
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—112no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—442no—
581C2×D4—442no—
582C2×D4—881no—
583C2×D4#433912yes—
584C2×D4#433912yes—
585C2×D4D4×D1112yes—
586C2×D4#434112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—881no—
607C22×C4C2×C22⋊D1111yescharacteristic
608C22×C4C2×C22⋊D1111yescharacteristic
609C22×C4C2×C22⋊D1111yescharacteristic
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613D8—228no—
614D8—444no—
615C2×C8—112no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
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—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—442no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—442no—
653C22⋊C4#432314yescomplemented
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C11#2489311yescharacteristic, complemented, Sylow
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—48no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—222no—
687C23—441no—
688C23—441no—
689C23—441no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23C2×#432312yes—
694C23C22×C22⋊D1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—222no—
704D4—222no—
705D4—441no—
706D4—441no—
707D4—884no—
708D4#6693614yescomplemented
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—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—884no—
744C2×C4C2×#432312yes—
745C2×C4C2×#432312yes—
746C2×C4C2×#433911yescharacteristic
747C2×C4C2×#433911yescharacteristic
748C2×C4C2×D4×D1111yescharacteristic
749C2×C4C2×#434111yescharacteristic
750C2×C4#6703711yescharacteristic
751C2×C4#6703711yescharacteristic
752C8—222no—
753C8—441no—
754C8—441no—
755C8—441no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—881no—
782C22—881no—
783C22—881no—
784C22—881no—
785C22#1062332211yescharacteristic
786C22C22×#432311yescharacteristic
787C22D4×C22⋊D1111yescharacteristic
788C22#1062333711yescharacteristic
789C22#1062335311yescharacteristic
790C22#1062336611yescharacteristic
791C22#1062336711yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—881no—
800C4—881no—
801C4—881no—
802C4C2×#6693611yescharacteristic
803C4#1062302111yescharacteristic
804C4#1062302511yescharacteristic
805C4#1062302611yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—882no—
810C2#1307207811yescharacteristic
811C2#1307861611yescharacteristic
812C2#1307880011yescharacteristic
813C2#1308013711yescharacteristic
814C2D4×#432311yescharacteristic
815C2#1308042911yescharacteristic
816C2#1308081711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterD4×C22⋊C4D11
hypocenterC11#24893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4323C2semidirect
3. #13072130C2semidirect
4. #13070144C2semidirect
5. #13070042C2semidirect
6. #13069926C2semidirect
7. #13069798C2semidirect
8. #13069302C2semidirect
9. #13069224C2semidirect
10. #13068967C2semidirect
11. #13068964C2semidirect
12. #13068863C2semidirect
13. #13068616C2semidirect
14. #13068547C2semidirect
15. D4×C11×C22⋊C4C2semidirect
24. C2×C4×D44C22semidirect
43. C2×#66873C22semidirect
44. C2×#66873C22semidirect
45. C2×#66871C22semidirect
46. C2×#66871C22semidirect
48. #10622552C22semidirect
49. #10622548C22semidirect
50. #10622541C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×C4×C11⋊C8C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
218. C11×C22⋊C4D8semidirect
254. D4×C22⋊C4D11semidirect
310. D4×C11#123semidirect
653. C22⋊C4#4323semidirect
658. C11#24893semidirect
708. D4#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
C2×C4×#43232
#130721302
#130701442
#130700422
#130699262
#130697982
#130693022
#130692242
#130689672
#130689642
#130688632
#130686162
#130685472
D4×C11×C22⋊C42
#2489311