Finite Group Databasebeta

← C2×#13077832 #15620108

Subgroups — C2×#13077832 #15620108

Order 2816.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C22×#67003C212yesmaximal, complemented
3#13077832C2116yesmaximal, direct product factor
4C2×#10622660C212yesmaximal, complemented
5C2×#10622650C212yesmaximal, complemented
6C2×#10622663C211yesmaximal, characteristic, complemented
7C2×#10622653C211yesmaximal, characteristic, complemented
8C2×#10622659C211yesmaximal, characteristic, complemented
9C2×#10622649C211yesmaximal, characteristic, complemented
10C2×#10622615C212yesmaximal, complemented
11C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
12C2×C11×#525C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic, complemented
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11—21no—
16C22×#4339—21no—
17C22×#4339—21no—
18C22×#4339—24no—
19C22×#4339—216no—
20C22×#4339C2212yes—
21C22×#4339C2212yes—
22C22×#4339C2218yescomplemented
23C23×D44C2211yescharacteristic
24C23×C4×D11—21no—
25C23×Dic22C2211yescharacteristic
26C11×#525—24no—
27C11×#525C2218yescomplemented
28C2×C11×#123—21no—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×C22⋊Q8C2211yescharacteristic, complemented
31C2×C11×#121C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic, complemented
33C2×C11×#120—21no—
34C2×C4×D4×C11—21no—
35C2×C4×D4×C11—21no—
36C2×C11×#117C2211yescharacteristic, complemented
37C2×#67003—216no—
38C2×#67003C22116yescomplemented
39C22×#4326C2212yescomplemented
40C22×#4325C2212yescomplemented
41C22×#4324C2212yescomplemented
42C22×#4323C2212yescomplemented
43C23×C11⋊C8C2212yescomplemented
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46C2×C22⋊(C11⋊C8)C2218yescomplemented
47C2×C22⋊(C11⋊C8)C2212yescomplemented
48#10622663C2218yescomplemented
49#10622660C22116yescomplemented
50#10622659C2218yescomplemented
51#10622653C2218yescomplemented
52#10622650C22116yescomplemented
53#10622649C2218yescomplemented
54#10622615C22116yescomplemented
55C2×#66874C2212yescomplemented
56C2×#66874C2212yescomplemented
57C2×#66873C2212yescomplemented
58C2×#66873C2212yescomplemented
59C25×C11D411yescharacteristic
60C24×D11—21no—
61C2×C11×#41—22no—
62C2×C11×#41—28no—
63C2×C11×#41C2314yescomplemented
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—28no—
70C23×C4×C11—21no—
71C23×C4×C11D411yescharacteristic
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D414yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—216no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—28no—
83C23×Dic11—21no—
84C2×#4339—216no—
85C2×#4339—264no—
86C2×#4339—216no—
87C2×#4339—28no—
88C2×#4339—24no—
89C2×#4339—24no—
90C2×#4339—28no—
91C2×#4339—28no—
92C2×#4339—264no—
93C2×#4339—28no—
94C2×#4339—28no—
95C2×#4339D4116yescomplemented
96C2×#4339C2318yes—
97C2×#4339C2318yes—
98C22×D44—21no—
99C22×D44—22no—
100C22×D44—28no—
101C22×D44C2314yes—
102C22×D44C2312yes—
103C22×C4×D11—216no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—28no—
107C22×Dic22—21no—
108C22×Dic22—22no—
109C22×Dic22—28no—
110C22×Dic22C2314yes—
111C22×Dic22C2312yes—
112C11×#123—28no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8C2314yes—
116C11×C22⋊Q8C2314yescomplemented
117C11×#121—22no—
118C11×#121—22no—
119C11×#121C2314yes—
120C11×#121C2314yescomplemented
121C11×#120—28no—
122C4×D4×C11—28no—
123C4×D4×C11—28no—
124C11×#117—22no—
125C11×#117C2314yescomplemented
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C42×C11—21no—
136#67003—264no—
137C2×#4326—28no—
138C2×#4326C2318yescomplemented
139C2×#4325—28no—
140C2×#4325C2318yescomplemented
141C2×#4324—28no—
142C2×#4324C2318yescomplemented
143C2×#4323—28no—
144C2×#4323C2318yescomplemented
145C22×C11⋊C8—28no—
146C22×C11⋊C8C2312yes—
147C22×C11⋊C8C2312yes—
148C22×C11⋊C8C2318yescomplemented
149C22⋊(C11⋊C8)C2314yes—
150C22⋊(C11⋊C8)C2314yes—
151C22⋊(C11⋊C8)C2318yescomplemented
152#66874C2318yescomplemented
153#66874C2318yescomplemented
154#66873C2318yescomplemented
155#66873C2318yescomplemented
156C2×#3002—111nomaximal, Sylow
157C24×C11—24no—
158C24×C11—24no—
159C24×C11—21no—
160C24×C11—42no—
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D414yes—
163C24×C11C2×D411yescharacteristic
164C24×C11C2×D411yescharacteristic
165C23×D11—28no—
166C23×D11—24no—
167C23×D11—22no—
168C23×D11—44no—
169C23×D11—44no—
170C11×#41—216no—
171C11×#41—48no—
172C2×Q8×C11—21no—
173C2×Q8×C11—24no—
174C2×Q8×C11C2412yes—
175C2×D4×C11—24no—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—21no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—44no—
183C2×D4×C11C2412yes—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—216no—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—216no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—24no—
195C22×C4×C11—44no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2×D414yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D418yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2412yes—
210C2×C22⋊D11—264no—
211C2×C22⋊D11—216no—
212C2×C22⋊D11—216no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—28no—
215C22×Dic11—28no—
216C22×Dic11—24no—
217C22×Dic11—22no—
218#4339—264no—
219#4339—264no—
220#4339—232no—
221#4339—216no—
222#4339—216no—
223#4339—232no—
224#4339—216no—
225#4339C2×D4132yescomplemented
226C2×D44—28no—
227C2×D44—216no—
228C2×D44—216no—
229C2×D44—24no—
230C2×D44—24no—
231C2×D44—22no—
232C2×D44C2×D418yes—
233C2×D44C2414yes—
234C2×C4×D11—216no—
235C2×C4×D11—264no—
236C2×C4×D11—216no—
237C2×C4×D11—28no—
238C2×C4×D11—28no—
239C2×Dic22—28no—
240C2×Dic22—216no—
241C2×Dic22—216no—
242C2×Dic22—24no—
243C2×Dic22—24no—
244C2×Dic22—22no—
245C2×Dic22C2×D418yes—
246C2×Dic22C2414yes—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C42×C11—24no—
259#4326—216no—
260#4325—216no—
261#4324—216no—
262#4323—216no—
263C2×C11⋊C8—24no—
264C2×C11⋊C8—24no—
265C2×C11⋊C8—216no—
266C2×C11⋊C8C2414yes—
267C2×C11⋊C8C2414yes—
268C23×#41—111no—
269C22×#135—112no—
270C2×#525D1111yescharacteristic, complemented
271#3002—1116no—
272C2×#452—112no—
273C2×#449—112no—
274C2×#451—111no—
275C2×#448—111no—
276C2×#450—111no—
277C2×#447—111no—
278C2×#416—112no—
279C22×C22⋊C8—111no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—28no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—28no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—44no—
291C23×C11—416no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11#12014yes—
296C23×C11#13514yescomplemented
297C23×C11C22×D412yes—
298C23×C11C22×D412yes—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301C22×D11—216no—
302C22×D11—28no—
303C22×D11—24no—
304C22×D11—432no—
305C22×D11—48no—
306C22×D11—44no—
307C22×D11—48no—
308C22×D11—44no—
309Q8×C11—24no—
310Q8×C11—42no—
311D4×C11—24no—
312D4×C11—48no—
313D4×C11—48no—
314D4×C11—48no—
315D4×C11—42no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—28no—
319C2×C4×C11—24no—
320C2×C4×C11—28no—
321C2×C4×C11—28no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—48no—
332C2×C4×C11#12014yes—
333C2×C4×C11#12018yes—
334C2×C4×C11C22×D414yes—
335C2×C4×C11C22×D418yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2511yescharacteristic
341C22⋊D11—232no—
342C22⋊D11—232no—
343C2×Dic11—216no—
344C2×Dic11—28no—
345C2×Dic11—24no—
346D44—216no—
347D44—28no—
348D44—24no—
349D44C22×D418yes—
350C4×D11—232no—
351C4×D11—232no—
352Dic22—216no—
353Dic22—28no—
354Dic22—24no—
355Dic22C22×D418yes—
356C11⋊C8—24no—
357C11⋊C8—24no—
358C22×#41—112no—
359C22×#41—112no—
360C22×#41—118no—
361C22×#41—2216no—
362C22×#41—221no—
363C22×#41—224no—
364C22×#41—221no—
365C22×#41C2×D1111yescharacteristic, complemented
366C23×Q8—111no—
367C23×D4—111no—
368C23×D4—221no—
369C24×C4—221no—
370C24×C4C2×D1111yescharacteristic
371C2×#135—1116no—
372C2×#135—2216no—
373C22×Q16—112no—
374C22×SD16—112no—
375C22×SD16—112no—
376C22×D8—112no—
377C23×C8—112no—
378#525—24no—
379#525C2×D1118yescomplemented
380C2×#123—21no—
381C2×C22⋊Q8C2×D1111yescharacteristic
382C2×C22⋊Q8C2×D1111yescharacteristic, complemented
383C2×#121C2×D1111yescharacteristic
384C2×#121C2×D1111yescharacteristic, complemented
385C2×#120—21no—
386C2×C4×D4—21no—
387C2×C4×D4—21no—
388C2×#117C2×D1111yescharacteristic, complemented
389#452—1116no—
390#451—118no—
391#450—118no—
392#449—1116no—
393#448—118no—
394#447—118no—
395#416—1116no—
396C2×#103—112no—
397C2×#103—112no—
398C2×#102—112no—
399C2×#102—112no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C22⋊C8—112no—
403C2×C22⋊C8—118no—
404C22×C11—22no—
405C22×C11—28no—
406C22×C11—28no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—416no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—84no—
419C22×C11C2×#12014yes—
420C22×C11C2×#12012yes—
421C22×C11C2×#13512yes—
422C22×C11C2×#13514yescomplemented
423C22×C11#57512yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—28no—
426C2×D11—432no—
427C2×D11—416no—
428C2×D11—44no—
429C2×D11—44no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11C2×#12014yes—
436C4×C11C2×#12012yes—
437C4×C11C23×D412yes—
438Dic11—28no—
439C25—221no—
440C25C22⋊D1111yescharacteristic
441C2×#41—22no—
442C2×#41—28no—
443C2×#41—1116no—
444C2×#41—118no—
445C2×#41—118no—
446C2×#41—228no—
447C2×#41—228no—
448C2×#41—2264no—
449C2×#41—2216no—
450C2×#41—2264no—
451C2×#41—2216no—
452C2×#41—228no—
453C2×#41—228no—
454C2×#41—224no—
455C2×#41—228no—
456C2×#41—224no—
457C2×#41C22×D1114yescomplemented
458C22×Q8—112no—
459C22×Q8—114no—
460C22×Q8—228no—
461C22×Q8—221no—
462C22×Q8—222no—
463C22×Q8C22×D1111yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—112no—
468C22×D4—114no—
469C22×D4—228no—
470C22×D4—2216no—
471C22×D4—222no—
472C22×D4—228no—
473C22×D4—222no—
474C22×D4—221no—
475C22×D4—222no—
476C22×D4C22×D1111yescharacteristic
477C23×C4—28no—
478C23×C4—21no—
479C23×C4—2216no—
480C23×C4—221no—
481C23×C4—222no—
482C23×C4—228no—
483C23×C4—222no—
484C23×C4C22⋊D1111yescharacteristic
485C23×C4C22⋊D1114yes—
486C23×C4C22⋊D1111yescharacteristic
487C23×C4C22⋊D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1114yes—
491C23×C4C22×D1111yescharacteristic
492#135—2264no—
493C2×Q16—118no—
494C2×Q16—228no—
495C2×SD16—118no—
496C2×SD16—118no—
497C2×SD16—228no—
498C2×SD16—228no—
499C2×D8—118no—
500C2×D8—228no—
501C22×C8—112no—
502C22×C8—112no—
503C22×C8—118no—
504C22×C8—228no—
505#123—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8C22×D1114yes—
509C22⋊Q8C22×D1114yescomplemented
510#121—22no—
511#121—22no—
512#121C22×D1114yes—
513#121C22×D1114yescomplemented
514#120—28no—
515C4×D4—28no—
516C4×D4—28no—
517#117—22no—
518#117C22×D1114yescomplemented
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C42—21no—
529#103—118no—
530#103—118no—
531#102—118no—
532#102—118no—
533C22⋊C8—114no—
534C22⋊C8—114no—
535C22⋊C8—118no—
536C2×C11—24no—
537C2×C11—24no—
538C2×C11—42no—
539C2×C11—82no—
540C2×C11#300214yescomplemented
541C2×C11C22×#12011yescharacteristic
542C2×C11C22×#13511yescharacteristic
543C2×C11C2×#57511yescharacteristic
544D11—48no—
545C24—24no—
546C24—24no—
547C24—21no—
548C24—42no—
549C24—228no—
550C24—224no—
551C24—222no—
552C24—444no—
553C24—444no—
554C24C2×C22⋊D1111yescharacteristic
555C24C2×C22⋊D1114yes—
556C24C2×C22⋊D1111yescharacteristic
557C24C2×C22⋊D1111yescharacteristic
558#41—216no—
559#41—48no—
560#41—1132no—
561#41—2216no—
562#41—2216no—
563#41—2264no—
564#41—2232no—
565#41—2264no—
566#41—2232no—
567#41—2216no—
568C2×Q8—21no—
569C2×Q8—24no—
570C2×Q8—118no—
571C2×Q8—114no—
572C2×Q8—2216no—
573C2×Q8—228no—
574C2×Q8—2216no—
575C2×Q8—224no—
576C2×Q8—224no—
577C2×Q8—222no—
578C2×Q8C23×D1112yes—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—118no—
588C2×D4—114no—
589C2×D4—2216no—
590C2×D4—228no—
591C2×D4—2216no—
592C2×D4—2264no—
593C2×D4—2216no—
594C2×D4—2216no—
595C2×D4—228no—
596C2×D4—228no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—222no—
600C2×D4C23×D1112yes—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—216no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—216no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—2216no—
614C22×C4—2264no—
615C22×C4—228no—
616C22×C4—224no—
617C22×C4—222no—
618C22×C4—2216no—
619C22×C4—228no—
620C22×C4—228no—
621C22×C4D4×D1118yes—
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1114yes—
625C22×C4C2×C22⋊D1114yes—
626C22×C4C2×C22⋊D1112yes—
627C22×C4C2×C22⋊D1112yes—
628C22×C4C2×C22⋊D1114yes—
629C22×C4C2×C22⋊D1112yes—
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C23×D1112yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1111yescharacteristic
634C22×C4C23×D1112yes—
635Q16—2216no—
636SD16—2216no—
637SD16—2216no—
638D8—2216no—
639C2×C8—114no—
640C2×C8—114no—
641C2×C8—224no—
642C2×C8—224no—
643C2×C8—2216no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4C23×D1112yes—
649C4⋊C4C23×D1112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C42—24no—
656C11C2×#300211yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—28no—
665C23—22no—
666C23—22no—
667C23—44no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—2216no—
673C23—228no—
674C23—224no—
675C23—4432no—
676C23—448no—
677C23—444no—
678C23—448no—
679C23—444no—
680C23#6699014yes—
681C23#6700314yescomplemented
682C23C22×C22⋊D1112yes—
683C23C22×C22⋊D1112yes—
684C23C22×C22⋊D1112yes—
685C23C22×C22⋊D1111yescharacteristic
686Q8—24no—
687Q8—42no—
688Q8—118no—
689Q8—2216no—
690Q8—228no—
691Q8—224no—
692D4—24no—
693D4—48no—
694D4—48no—
695D4—48no—
696D4—42no—
697D4—118no—
698D4—2216no—
699D4—2232no—
700D4—2232no—
701D4—228no—
702D4—224no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—28no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—48no—
719C2×C4—2232no—
720C2×C4—2216no—
721C2×C4—228no—
722C2×C4—224no—
723C2×C4—2232no—
724C2×C4#6699014yes—
725C2×C4#6699018yes—
726C2×C4C2×D4×D1114yes—
727C2×C4C2×D4×D1118yes—
728C2×C4C22×C22⋊D1112yes—
729C2×C4C22×C22⋊D1112yes—
730C2×C4C22×C22⋊D1112yes—
731C2×C4C22×C22⋊D1111yescharacteristic
732C2×C4C24×D1111yescharacteristic
733C8—224no—
734C8—224no—
735C22—28no—
736C22—28no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—416no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—228no—
751C22—4432no—
752C22—4416no—
753C22—444no—
754C22—444no—
755C22C2×#6699014yes—
756C22C2×#6699012yes—
757C22C2×#6700312yes—
758C22C2×#6700314yescomplemented
759C22#1062335312yes—
760C22C23×C22⋊D1111yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—228no—
767C4C2×#6699014yes—
768C4C2×#6699012yes—
769C4C22×D4×D1112yes—
770C2—24no—
771C2—24no—
772C2—42no—
773C2—82no—
774C2—448no—
775C2#1307783214yesdirect product factor
776C2C22×#6699011yescharacteristic
777C2C22×#6700311yescharacteristic
778C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC23×C11C22×D4
hypercenterC2×#525D11
hypocenterC11C2×#3002
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#67003C2semidirect
3. #13077832C2direct (N × H)
4. C2×#10622660C2semidirect
5. C2×#10622650C2semidirect
6. C2×#10622663C2semidirect
7. C2×#10622653C2semidirect
8. C2×#10622659C2semidirect
9. C2×#10622649C2semidirect
10. C2×#10622615C2semidirect
11. C22×C22⋊(C11⋊C8)C2semidirect
12. C2×C11×#525C2semidirect
13. C22×C11×#41C22semidirect
22. C22×#4339C22semidirect
27. C11×#525C22semidirect
30. C2×C11×C22⋊Q8C22semidirect
32. C2×C11×#121C22semidirect
36. C2×C11×#117C22semidirect
38. C2×#67003C22semidirect
39. C22×#4326C22semidirect
40. C22×#4325C22semidirect
41. C22×#4324C22semidirect
42. C22×#4323C22semidirect
43. C23×C11⋊C8C22semidirect
46. C2×C22⋊(C11⋊C8)C22semidirect
47. C2×C22⋊(C11⋊C8)C22semidirect
48. #10622663C22semidirect
49. #10622660C22semidirect
50. #10622659C22semidirect
51. #10622653C22semidirect
52. #10622650C22semidirect
53. #10622649C22semidirect
54. #10622615C22semidirect
55. C2×#66874C22semidirect
56. C2×#66874C22semidirect
57. C2×#66873C22semidirect
58. C2×#66873C22semidirect
63. C2×C11×#41C23semidirect
95. C2×#4339D4semidirect
116. C11×C22⋊Q8C23semidirect
120. C11×#121C23semidirect
125. C11×#117C23semidirect
138. C2×#4326C23semidirect
140. C2×#4325C23semidirect
142. C2×#4324C23semidirect
144. C2×#4323C23semidirect
148. C22×C11⋊C8C23semidirect
151. C22⋊(C11⋊C8)C23semidirect
152. #66874C23semidirect
153. #66874C23semidirect
154. #66873C23semidirect
155. #66873C23semidirect
225. #4339C2×D4semidirect
270. C2×#525D11semidirect
296. C23×C11#135semidirect
365. C22×#41C2×D11semidirect
379. #525C2×D11semidirect
382. C2×C22⋊Q8C2×D11semidirect
384. C2×#121C2×D11semidirect
388. C2×#117C2×D11semidirect
422. C22×C11C2×#135semidirect
457. C2×#41C22×D11semidirect
509. C22⋊Q8C22×D11semidirect
513. #121C22×D11semidirect
518. #117C22×D11semidirect
540. C2×C11#3002semidirect
656. C11C2×#3002semidirect
681. C23#67003semidirect
758. C22C2×#67003semidirect
775. C2#13077832direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#670032
#130778322
C2×#106226602
C2×#106226502
C2×#106226632
C2×#106226532
C2×#106226592
C2×#106226492
C2×#106226152
C22×C22⋊(C11⋊C8)2
C2×C11×#5252
C2×#300211