Finite Group Databasebeta

← #14788592

Subgroups — #14788592

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622670C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic, complemented
4#13069852C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic, complemented
6#13069693C211yesmaximal, characteristic, complemented
7#13069687C211yesmaximal, characteristic
8#13069553C211yesmaximal, characteristic, complemented
9#13069428C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068870C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068626C211yesmaximal, characteristic, complemented
15C2×C11×#559C211yesmaximal, characteristic, complemented
16C11×#559—24no—
17C11×#559—24no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124—21no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#123—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33#10622844—21no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622670—24no—
44C4×#4323—24no—
45#10622605—21no—
46#10622602—21no—
47#10622602—21no—
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622549C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C11×#127—22no—
74C11×#127—22no—
75C11×#124—28no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—22no—
79C11×#124D414yes—
80C11×#123—28no—
81C11×#123—28no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—28no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11D414yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—41no—
109C2×#4323—22no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×#4323—22no—
114C2×#4323—41no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C4×D44—22no—
130C4×D44—22no—
131#66899—22no—
132#66899—22no—
133#66899—41no—
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896—41no—
138#66896—41no—
139#66896—41no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66873—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24192—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C23×D11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—41no—
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—24no—
162C2×D4×C11—24no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11C2×D412yes—
178C2×D4×C11C2×D412yes—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11—81no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
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×D44#4112yes—
203C2×C4×D11—42no—
204C2×C4×D11—81no—
205C2×C4×D11—81no—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C42×C11—24no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11C2×D412yes—
224C42×C11C2×D412yes—
225#4325—44no—
226#4323—28no—
227#4323—44no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—81no—
232(C2×D11)⋊C4—81no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239Dic11⋊C4—81no—
240Dic11⋊C4—81no—
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⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8#4112yes—
253C2×#559D1111yescharacteristic, complemented
254C2×#463—111no—
255C2×C4×D8—111no—
256#2580—111no—
257#2042—111no—
258#2041—111no—
259#2012—111no—
260#2011—111no—
261#1984—111no—
262#1958—111no—
263#1880—111no—
264#1879—111no—
265#1863—111no—
266#1862—111no—
267#1804—111no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11C22×D411yescharacteristic
283C22×D11—22no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—44no—
293Q8×C11—41no—
294Q8×C11—41no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—48no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—84no—
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—22no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
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—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—84no—
327C2×C4×C11—84no—
328C2×C4×C11#12012yes—
329C2×C4×C11#12012yes—
330C2×C4×C11#13512yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C112−1+411yescharacteristic
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—41no—
346D44—22no—
347D44—22no—
348D44—41no—
349D44—41no—
350C4×D11—84no—
351C11⋊C8—22no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C11⋊C8—41no—
355C22×SD16—111no—
356C22×D8—111no—
357C22×D8—111no—
358#559—24no—
359#559—24no—
360C2×#127C2×D1111yescharacteristic
361C2×#124—21no—
362C2×#124C2×D1111yescharacteristic
363C2×#124C2×D1111yescharacteristic
364C2×#123—21no—
365C2×#123—21no—
366C2×C4×Q8C2×D1111yescharacteristic
367C2×C4×Q8C2×D1111yescharacteristic
368C2×C4×D4—21no—
369C2×C4×D4—111no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×C4×D4C2×D1111yescharacteristic
372#463—224no—
373C4×D8—224no—
374C2×#107—111no—
375C2×C4⋊C8—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×C4×C8—111no—
387#399—221no—
388#393—221no—
389#390—111no—
390#390—111no—
391#389—111no—
392#389—111no—
393#385—221no—
394#385—221no—
395#382—111no—
396#340—111no—
397#340—111no—
398#336—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11C2×#12011yescharacteristic
417C22×C11#54811yescharacteristic
418C22×C11#55011yescharacteristic
419C22×C11C2×#13511yescharacteristic
420C22×C11#57511yescharacteristic
421C22×C11#57611yescharacteristic
422C22×C11#57611yescharacteristic
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—81no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—42no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—41no—
437C4×C11—42no—
438C4×C11#52511yescharacteristic
439C4×C11#53711yescharacteristic
440C4×C11#54611yescharacteristic
441C4×C11#54711yescharacteristic
442Dic11—81no—
443Dic11—81no—
444Dic11—81no—
445C22×Q8C22⋊D1111yescharacteristic
446C22×Q8C22×D1111yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—111no—
450C22×D4C22×D1111yescharacteristic
451C22×D4C22×D1111yescharacteristic
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—221no—
455C2×SD16—222no—
456C2×SD16—222no—
457C2×SD16—441no—
458C2×D8—222no—
459C2×D8—222no—
460C2×D8—222no—
461C2×D8—222no—
462C2×D8—222no—
463C2×D8—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468#127—22no—
469#127—22no—
470#124—28no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124C22⋊D1114yes—
475#123—28no—
476#123—28no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×D4—28no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—222no—
486C4×D4—222no—
487C4×D4C22⋊D1114yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4C22⋊D1111yescharacteristic
495C2×C4⋊C4C22⋊D1111yescharacteristic
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C42—21no—
510C2×C42C22×D1111yescharacteristic
511C2×C42C22×D1111yescharacteristic
512C2×C42C22×D1111yescharacteristic
513#107—222no—
514C4⋊C8—222no—
515#103—222no—
516#103—222no—
517#103—441no—
518#102—222no—
519#102—222no—
520#102—222no—
521#102—222no—
522#102—441no—
523#102—441no—
524#102—441no—
525C4×C8—222no—
526#95—221no—
527#95—221no—
528#95—221no—
529#95—221no—
530C2×C11—82no—
531C2×C11—82no—
532C2×C11#240711yescharacteristic
533C2×C11#300211yescharacteristic
534C2×C11#300811yescharacteristic
535C2×C11#336111yescharacteristic
536C2×C11#337011yescharacteristic
537C2×C11#339611yescharacteristic
538C2×C11#340311yescharacteristic
539D11—82no—
540C24—21no—
541C24—21no—
542C24—221no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—41no—
551C2×Q8C2×C22⋊D1112yes—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—112no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4C2×C22⋊D1112yes—
575C2×D4C2×C22⋊D1112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—442no—
588C22×C4—881no—
589C22×C4—881no—
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597SD16—444no—
598D8—228no—
599D8—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—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—881no—
624C4⋊C4—881no—
625C4⋊C4C2×C22⋊D1112yes—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—442no—
633C22⋊C4—442no—
634C22⋊C4—442no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C42—24no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42C2×C22⋊D1112yes—
643C42C2×C22⋊D1112yes—
644C11#2419211yescharacteristic, complemented, Sylow
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—222no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23C22×C22⋊D1111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—44no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—48no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—222no—
683D4—222no—
684D4—441no—
685D4—441no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—884no—
719C2×C4#6700312yes—
720C2×C4#6700612yes—
721C2×C4#6700612yes—
722C2×C4#41×D1111yescharacteristic
723C2×C4#41×D1111yescharacteristic
724C2×C4#6704211yescharacteristic
725C2×C4#6704311yescharacteristic
726C2×C4C22×C22⋊D1111yescharacteristic
727C2×C4C22×C22⋊D1111yescharacteristic
728C8—222no—
729C8—441no—
730C8—441no—
731C8—441no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—881no—
750C22—881no—
751C22—881no—
752C22—881no—
753C22C2×#6700311yescharacteristic
754C22#1062335311yescharacteristic
755C22#1062336211yescharacteristic
756C22#1062336511yescharacteristic
757C22#1062336611yescharacteristic
758C22#1062336611yescharacteristic
759C22C2×#6700611yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—881no—
769C4—881no—
770C4—881no—
771C4#1062335511yescharacteristic
772C4#1062335911yescharacteristic
773C4#1062336011yescharacteristic
774C4#1062336411yescharacteristic
775C2—82no—
776C2—82no—
777C2—882no—
778C2#1307195511yescharacteristic
779C2#1307783411yescharacteristic
780C2#1307788411yescharacteristic
781C2#1308127211yescharacteristic
782C2#1308136311yescharacteristic
783C2#1308162411yescharacteristic
784C2#1308170011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radical#13069687C2
hypercenterC2×#559D11
hypocenterC11#24192
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×C4×#4323C2semidirect
3. #13073974C2semidirect
4. #13069852C2semidirect
5. #13069847C2semidirect
6. #13069693C2semidirect
8. #13069553C2semidirect
9. #13069428C2semidirect
10. #13068971C2semidirect
11. #13068964C2semidirect
12. #13068870C2semidirect
13. #13068863C2semidirect
14. #13068626C2semidirect
15. C2×C11×#559C2semidirect
253. C2×#559D11semidirect
644. C11#24192semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×C4×#43232
#130739742
#130698522
#130698472
#130696932
#130696872
#130695532
#130694282
#130689712
#130689642
#130688702
#130688632
#130686262
C2×C11×#5592
#2419211