Finite Group Databasebeta

← #14806861

Subgroups — #14806861

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622646C211yesmaximal, characteristic, complemented
3C2×#10622655C211yesmaximal, characteristic, complemented
4#13069944C211yesmaximal, characteristic, complemented
5#13069819C211yesmaximal, characteristic, complemented
6#13069752C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic, complemented
8#13068974C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068928C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic, complemented
12#13068869C211yesmaximal, characteristic, complemented
13#13068803C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2414C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×D4×Dic11—21no—
21C22×#4324C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27#10623074—24no—
28#10623074—24no—
29C2×#66943—21no—
30C2×#66931—21no—
31C2×#66931—21no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#394—21no—
35C11×#392—21no—
36C11×#390—21no—
37C11×#390C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#388—21no—
40C11×#380C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2211yescharacteristic
47#10622655—24no—
48#10622646—24no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11D411yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11—21no—
70C23×Dic11—21no—
71C22×Dic22—21no—
72C22×Dic22C2311yescharacteristic
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—41no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C11×#117—22no—
80C11×#117—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98D4×Dic11—28no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324—41no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11D414yescomplemented
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112#66977—22no—
113#66977—22no—
114#66977—22no—
115#66977D414yescomplemented
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127#66943—28no—
128#66931—28no—
129#66931—28no—
130#66922—22no—
131#66922—22no—
132C4×Dic22—22no—
133C4×Dic22—22no—
134C11×#95—21no—
135C11×#95—21no—
136#66896—22no—
137#66896—22no—
138#66896—22no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66874—41no—
145#66871—22no—
146#66871—22no—
147#66871—22no—
148#25559—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C24×C11C2×D411yescharacteristic
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
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—42no—
164C2×D4×C11—81no—
165C2×D4×C11—81no—
166C2×D4×C11—81no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
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—21no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×Dic11—24no—
188C22×Dic11—24no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—81no—
194C22×Dic11—81no—
195C22×Dic11—81no—
196C22×Dic11—81no—
197C2×Dic22—24no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—81no—
204C2×Dic22—81no—
205C2×Dic22C2×D412yes—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—81no—
213C11×C4⋊C4#4112yes—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—81no—
221C11×C22⋊C4—81no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—42no—
225C22⋊Dic11—24no—
226C22⋊Dic11—24no—
227#4324—44no—
228C4⋊Dic11—24no—
229C4⋊Dic11—24no—
230C4⋊Dic11—24no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11C2×D412yes—
235C4⋊Dic11C2×D412yes—
236C4⋊Dic11C2×D412yes—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240C4×Dic11—24no—
241#4318—44no—
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⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8#4112yes—
254C2×#554—111no—
255C2×#480—111no—
256C2×#468—111no—
257#2414D1111yescharacteristic
258#2057—111no—
259#2036—111no—
260#2023—111no—
261#2000—111no—
262#1880—111no—
263#1874—111no—
264#1873—111no—
265#1870—111no—
266#1863—111no—
267#1852—111no—
268#1736—111no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11#12012yes—
289C23×C11#13712yes—
290C23×C11C22×D411yescharacteristic
291D4×C11—28no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—84no—
297D4×C11—84no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11#12012yes—
326C2×C4×C11#13712yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—84no—
346C2×Dic11—84no—
347Dic22—22no—
348Dic22—22no—
349Dic22—41no—
350Dic22—41no—
351Dic22—84no—
352C11⋊C8—22no—
353C11⋊C8—41no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C22×SD16—111no—
357C22×M16—111no—
358#554—224no—
359#554—224no—
360C2×C4⋊Q8—111no—
361C2×#125—221no—
362C2×C22⋊Q8—111no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—221no—
365C2×C22⋊Q8—221no—
366C2×#121C2×D1111yescharacteristic
367C2×#121C2×D1111yescharacteristic
368C2×C4×Q8—111no—
369C2×C4×D4—221no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117C2×D1111yescharacteristic
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374#480—224no—
375#468—224no—
376C2×#107—111no—
377C2×#107—111no—
378C2×#107—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C22⋊C8—111no—
388#394—21no—
389#392—21no—
390#390—21no—
391#390C2×D1111yescharacteristic
392#389C2×D1111yescharacteristic
393#388—21no—
394#380C2×D1111yescharacteristic
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399#340—111no—
400#340—111no—
401#336—111no—
402#336—111no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11C2×#12011yescharacteristic
425C22×C11#54611yescharacteristic
426C22×C11#54711yescharacteristic
427C22×C11C2×#13711yescharacteristic
428C22×C11C2×#13711yescharacteristic
429C22×C11#57611yescharacteristic
430C22×C11#57611yescharacteristic
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—42no—
436C4×C11—81no—
437C4×C11—81no—
438C4×C11#53211yescharacteristic
439C4×C11#53711yescharacteristic
440C4×C11#54611yescharacteristic
441C4×C11#54711yescharacteristic
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446C22×Q8—111no—
447C22×Q8—221no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C22⋊D1111yescharacteristic
451C22×D4C22×D1111yescharacteristic
452C23×C4—221no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C2×SD16—222no—
457C2×SD16—222no—
458C2×SD16—441no—
459C2×M16—222no—
460C2×M16—222no—
461C2×M16—441no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—111no—
466C4⋊Q8—222no—
467C4⋊Q8—222no—
468#125—228no—
469C22⋊Q8—114no—
470C22⋊Q8—228no—
471C22⋊Q8—228no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474C22⋊Q8—222no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—41no—
479C4×Q8—222no—
480C4×Q8—222no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—228no—
484#117—22no—
485#117—41no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—222no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4C22⋊D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4C22⋊D1111yescharacteristic
513C2×C22⋊C4C22⋊D1111yescharacteristic
514C2×C42—21no—
515C2×C42—221no—
516C2×C42C22×D1111yescharacteristic
517#107—222no—
518#107—222no—
519#107—222no—
520#103—222no—
521#103—222no—
522#103—441no—
523#102—222no—
524#102—222no—
525#102—222no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8—441no—
529#95—21no—
530#95—21no—
531C2×C11—42no—
532C2×C11—42no—
533C2×C11—161no—
534C2×C11#243011yescharacteristic
535C2×C11#300411yescharacteristic
536C2×C11#300811yescharacteristic
537C2×C11#331411yescharacteristic
538C2×C11#333311yescharacteristic
539C2×C11#334611yescharacteristic
540C2×C11#335711yescharacteristic
541C24—21no—
542C24C2×C22⋊D1111yescharacteristic
543C24C2×C22⋊D1111yescharacteristic
544C2×Q8—112no—
545C2×Q8—224no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×Q8—881no—
552C2×Q8—881no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—881no—
588C22×C4—881no—
589C22×C4—881no—
590C22×C4—881no—
591C22×C4D4×D1112yes—
592C22×C4D4×D1112yes—
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C23×D1111yescharacteristic
598SD16—444no—
599M16—444no—
600C2×C8—112no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—81no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—112no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4#434112yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42—224no—
646C11#2555911yescharacteristic, complemented, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#6699012yes—
667C23#6700412yes—
668C23C22×C22⋊D1111yescharacteristic
669Q8—222no—
670Q8—222no—
671Q8—441no—
672Q8—441no—
673Q8—884no—
674D4—28no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—84no—
680D4—84no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—884no—
721C2×C4—884no—
722C2×C4#6699012yes—
723C2×C4#6700412yes—
724C2×C4C2×D4×D1111yescharacteristic
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4C2×#434111yescharacteristic
727C2×C4#6703711yescharacteristic
728C2×C4#41×D1111yescharacteristic
729C2×C4#6704311yescharacteristic
730C8—222no—
731C8—441no—
732C8—441no—
733C8—441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#6699011yescharacteristic
756C22#1062333711yescharacteristic
757C22C2×#6700411yescharacteristic
758C22C2×#6700411yescharacteristic
759C22#1062335511yescharacteristic
760C22#1062336611yescharacteristic
761C22#1062336611yescharacteristic
762C4—22no—
763C4—22no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—442no—
770C4—442no—
771C4—442no—
772C4—442no—
773C4#1062312711yescharacteristic
774C4#1062312811yescharacteristic
775C4#1062314111yescharacteristic
776C4#1062314211yescharacteristic
777C2—42no—
778C2—42no—
779C2—161no—
780C2#1307222211yescharacteristic
781C2#1307784911yescharacteristic
782C2#1307788211yescharacteristic
783C2#1308069711yescharacteristic
784C2#1308095411yescharacteristic
785C2#1308110111yescharacteristic
786C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2414C2
socleC23×C11C22×D4
hypercenter#2414D11
hypocenterC11#25559
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622646C2semidirect
3. C2×#10622655C2semidirect
4. #13069944C2semidirect
5. #13069819C2semidirect
6. #13069752C2semidirect
7. #13069619C2semidirect
8. #13068974C2semidirect
9. #13068934C2semidirect
10. #13068928C2semidirect
11. #13068914C2semidirect
12. #13068869C2semidirect
13. #13068803C2semidirect
14. #13068337C2semidirect
108. C2×C4⋊Dic11D4semidirect
115. #66977D4semidirect
646. C11#25559semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226462
C2×#106226552
#130699442
#130698192
#130697522
#130696192
#130689742
#130689342
#130689282
#130689142
#130688692
#130688032
#130683372
C11×#24142
#2555911