Finite Group Databasebeta

← #14914801

Subgroups — #14914801

Order 2816.

5898 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67042C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4#13071445C214yesmaximal, complemented
5#13071444C214yesmaximal, complemented
6#13071437C214yesmaximal, complemented
7#13071436C214yesmaximal, complemented
8#13071209C211yesmaximal, characteristic, complemented
9#13071190C214yesmaximal, complemented
10#13071107C211yesmaximal, characteristic, complemented
11#13071104C211yesmaximal, characteristic, complemented
12D11×#386C214yesmaximal, complemented
13C11×#2311C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C2×#67042—28no—
16C2×#67042—28no—
17C2×#67042C4116yescomplemented
18C22×#4343C2212yes—
19C22×D4×D11C2212yes—
20C22×D4×D11C2214yes—
21C22×#4339C2211yescharacteristic
22C22×#4339C2212yes—
23C23×D44C2212yes—
24C23×D44C2211yescharacteristic
25C23×C4×D11C2212yescomplemented
26C2×C11×#117C2211yescharacteristic, complemented
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×(C2×D11)⋊C4C2212yescomplemented
29C2×#66979C2211yescharacteristic, complemented
30C22×C4×Dic11C2211yescharacteristic, complemented
31#10623052—28no—
32C2×#66946—28no—
33C2×#66946C2214yescomplemented
34C2×#66946C2214yescomplemented
35C2×#66946C2214yescomplemented
36C2×C22⋊C4×D11C2214yescomplemented
37C2×C22⋊C4×D11C2218yescomplemented
38C2×C4×D44C2214yescomplemented
39C11×#391C2212yescomplemented
40C11×#390C2212yescomplemented
41C11×#386C2214yescomplemented
42C11×#380C2214yescomplemented
43#10622843C2212yescomplemented
44#10622834C2212yescomplemented
45#10622833C2212yescomplemented
46#10622833C2212yescomplemented
47#10622826C2214yescomplemented
48C4×C22⋊Dic11C2214yescomplemented
49#10622601C2212yescomplemented
50#10622601C2212yescomplemented
51#10622600C2214yescomplemented
52#10622587C2212yescomplemented
53#10622587C2212yescomplemented
54#10622571C2212yescomplemented
55#10622571C2212yescomplemented
56#10622569C2218yescomplemented
57#10622569C2218yescomplemented
58#10622568C2218yescomplemented
59C4×(C2×D11)⋊C4C2214yescomplemented
60#10622278C2218yescomplemented
61#10622278C2218yescomplemented
62#10622277C2218yescomplemented
63D11×#95C2218yescomplemented
64C24×D11C2314yes—
65C24×D11C2312yes—
66C2×C11×#41—24no—
67C2×C11×#41—24no—
68C2×C11×#41C2×C418yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11C2312yes—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2312yes—
76C22×C22⋊D11C2314yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79#67042—2128no—
80C2×#4343—28no—
81C2×#4343—28no—
82C2×#4343C2×C4116yescomplemented
83C2×D4×D11—216no—
84C2×D4×D11—216no—
85C2×D4×D11—28no—
86C2×D4×D11—28no—
87C2×D4×D11C2×C4116yescomplemented
88C2×D4×D11C2×C4132yescomplemented
89C2×#4339—24no—
90C2×#4339—24no—
91C2×#4339—28no—
92C2×#4339—28no—
93C2×#4339C2×C4116yescomplemented
94C2×#4339C2×C418yescomplemented
95C22×D44—28no—
96C22×D44—28no—
97C22×D44C2×C418yes—
98C22×D44C2×C4116yescomplemented
99C22×D44D418yes—
100C22×D44D418yes—
101C22×D44C2314yes—
102C22×D44C2311yescharacteristic
103C22×D44C2312yes—
104C22×D44C2312yes—
105C22×C4×D11—28no—
106C22×C4×D11—48no—
107C22×C4×D11C2318yes—
108C22×C4×D11C2314yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2318yes—
111C22×Dic22C2311yescharacteristic
112C11×#117—24no—
113C2×C11×C4⋊C4—24no—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2318yes—
119C2×C42×C11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×(C2×D11)⋊C4—28no—
124C2×(C2×D11)⋊C4C2318yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2318yes—
127C2×(C2×D11)⋊C4C2318yes—
128C2×(C2×D11)⋊C4C2314yes—
129#66979—24no—
130C2×C4⋊Dic11C2312yes—
131C2×C4×Dic11—24no—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135#66946—216no—
136#66946—216no—
137#66946—216no—
138C22⋊C4×D11—216no—
139C22⋊C4×D11—416no—
140C4×D44—216no—
141C11×#95C2318yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2318yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147#34256—111nomaximal, Sylow
148C24×C11C2412yes—
149C24×C11C2411yescharacteristic
150C23×D11—28no—
151C23×D11—28no—
152C23×D11—44no—
153C23×D11—44no—
154C23×D11—48no—
155C23×D11—48no—
156C23×D11C22×C418yes—
157C23×D11C22×C4116yescomplemented
158C23×D11C2×D418yes—
159C23×D11C2×D418yes—
160C23×D11C2412yes—
161C23×D11C2414yes—
162C11×#41—232no—
163C2×Q8×C11—22no—
164C2×Q8×C11—22no—
165C2×Q8×C11C22×C414yescomplemented
166C2×D4×C11—24no—
167C2×D4×C11—24no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11C22×C418yes—
171C2×D4×C11C22×C414yescomplemented
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—44no—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C22×C418yescomplemented
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2414yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—24no—
186C2×C22⋊D11—24no—
187C2×C22⋊D11—28no—
188C2×C22⋊D11—28no—
189C2×C22⋊D11C22×C418yes—
190C2×C22⋊D11C22×C4116yescomplemented
191C22×Dic11—24no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—42no—
195C22×Dic11C2412yes—
196C22×Dic11C2414yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199#4343—264no—
200D4×D11—264no—
201D4×D11—2128no—
202#4339—264no—
203#4339—232no—
204C2×D44—264no—
205C2×D44—28no—
206C2×D44—28no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44C22⋊C4164yescomplemented
210C2×D44C22×C418yes—
211C2×D44C22×C418yes—
212C2×D44C22×C414yescomplemented
213C2×D44C22×C4116yescomplemented
214C2×D44C2×D418yes—
215C2×D44C2×D418yes—
216C2×D44C2×D418yes—
217C2×D44C2×D418yes—
218C2×C4×D11—216no—
219C2×C4×D11—28no—
220C2×C4×D11—28no—
221C2×C4×D11—216no—
222C2×C4×D11—216no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—48no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—432no—
229C2×C4×D11C22×C4116yescomplemented
230C2×C4×D11C22×C418yescomplemented
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22C22×C414yescomplemented
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—48no—
239C42×C11—24no—
240C22⋊Dic11—28no—
241C22⋊Dic11—24no—
242C22⋊Dic11—44no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—216no—
245(C2×D11)⋊C4—216no—
246(C2×D11)⋊C4—48no—
247(C2×D11)⋊C4—44no—
248C4⋊Dic11—24no—
249C4×Dic11—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C22×H(5,𝔽2)—111no—
253C2×#518—111no—
254C22×C4×D4—111no—
255#2339—114no—
256#2339—114no—
257D4×C22⋊C4—114no—
258D4×C22⋊C4—114no—
259#2311—111no—
260#2311D1111yescharacteristic, complemented
261#2308—114no—
262#2297—111no—
263#2297—111no—
264C2×#386—114no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11C23×C414yes—
272C23×C11C23×C412yes—
273C23×C11C22×D412yes—
274C23×C11C22×D412yes—
275C23×C11C2511yescharacteristic
276C22×D11—28no—
277C22×D11—28no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—232no—
283C22×D11—48no—
284C22×D11—416no—
285C22×D11—48no—
286C22×D11—416no—
287C22×D11—432no—
288C22×D11—88no—
289C22×D11—88no—
290C22×D11—816no—
291C22×D11C2×C22⋊C4132yescomplemented
292C22×D11C23×C414yes—
293C22×D11C23×C418yes—
294C22×D11C22×D418yes—
295C22×D11C22×D418yes—
296Q8×C11—28no—
297D4×C11—216no—
298D4×C11—28no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—216no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—28no—
306C2×C4×C11—24no—
307C2×C4×C11—48no—
308C2×C4×C11C2×C22⋊C4116yescomplemented
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C22⋊D11—216no—
317C22⋊D11—232no—
318C2×Dic11—28no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—24no—
329C2×Dic11—44no—
330C2×Dic11C23×C414yes—
331C2×Dic11H(5,𝔽2)14yescomplemented
332D44—232no—
333D44—28no—
334D44C2×C22⋊C4132yescomplemented
335D44C2×C22⋊C4132yescomplemented
336C4×D11—232no—
337C4×D11—216no—
338C4×D11—432no—
339C4×D11—816no—
340Dic22—28no—
341C2×H(5,𝔽2)—1116no—
342C2×H(5,𝔽2)—228no—
343C2×H(5,𝔽2)—228no—
344C22×#41—112no—
345C22×#41—111no—
346C22×#41—112no—
347C22×#41C2×D1111yescharacteristic
348C23×D4—114no—
349C23×D4—112no—
350C23×D4—111no—
351C23×D4—112no—
352C24×C4—112no—
353#518—228no—
354C2×C4×D4—114no—
355C2×C4×D4—114no—
356C2×C4×D4—114no—
357C2×C4×D4—114no—
358C2×C4×D4—228no—
359C2×#117—111no—
360C2×#117C2×D1111yescharacteristic, complemented
361C22×C4⋊C4C2×D1111yescharacteristic, complemented
362C22×C22⋊C4—112no—
363C22×C22⋊C4—114no—
364C22×C22⋊C4—118no—
365C22×C42—111no—
366#391—112no—
367#391—112no—
368#391—112no—
369#391C2×D1112yescomplemented
370#390—112no—
371#390—112no—
372#390—112no—
373#390C2×D1112yescomplemented
374#386—112no—
375#386—112no—
376#386—114no—
377#386—112no—
378#386—118no—
379#386—118no—
380#386—112no—
381#386—118no—
382#386—118no—
383#386C2×D1114yescomplemented
384#381—118no—
385#380—114no—
386#380C2×D1114yescomplemented
387#379—118no—
388C4×C22⋊C4—114no—
389C4×C22⋊C4—114no—
390C2×#95—118no—
391C22×C11—24no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—28no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—44no—
400C22×C11C22×C22⋊C414yes—
401C22×C11C24×C411yescharacteristic
402C22×C11C23×D411yescharacteristic
403C22×C11C23×D411yescharacteristic
404C22×C11C2×H(5,𝔽2)12yes—
405C22×C11#58512yes—
406C2×D11—216no—
407C2×D11—28no—
408C2×D11—28no—
409C2×D11—216no—
410C2×D11—24no—
411C2×D11—28no—
412C2×D11—432no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—44no—
416C2×D11—832no—
417C2×D11C22×C22⋊C4116yes—
418C4×C11—24no—
419C4×C11—44no—
420C4×C11—44no—
421C4×C11C22×C22⋊C414yes—
422C4×C11C22×C22⋊C414yes—
423Dic11—24no—
424Dic11—24no—
425Dic11—42no—
426Dic11—44no—
427C25—112no—
428C25—114no—
429H(5,𝔽2)—22128no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—1116no—
433C2×#41—118no—
434C2×#41—1116no—
435C2×#41—228no—
436C2×#41—228no—
437C2×#41—228no—
438C2×#41—228no—
439C2×#41—224no—
440C2×#41—224no—
441C2×#41C4×D1118yescomplemented
442C22×Q8—111no—
443C22×Q8C22×D1111yescharacteristic
444C22×D4—112no—
445C22×D4—114no—
446C22×D4—1132no—
447C22×D4—1116no—
448C22×D4—118no—
449C22×D4—1116no—
450C22×D4—118no—
451C22×D4—118no—
452C22×D4—112no—
453C22×D4—112no—
454C22×D4—114no—
455C22×D4—111no—
456C22×D4—228no—
457C22×D4—228no—
458C22×D4—228no—
459C22×D4—228no—
460C22×D4—2216no—
461C22×D4—2216no—
462C22×D4C22×D1112yes—
463C22×D4C22×D1111yescharacteristic
464C23×C4—114no—
465C23×C4—112no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—118no—
469C23×C4—118no—
470C23×C4—228no—
471C23×C4—448no—
472C23×C4C22×D1112yes—
473C23×C4C22×D1112yes—
474C23×C4C22×D1111yescharacteristic
475C4×D4—2216no—
476C4×D4—2216no—
477C4×D4—2216no—
478C4×D4—2216no—
479#117—24no—
480#117—224no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—112no—
483C2×C4⋊C4C22×D1112yes—
484C2×C4⋊C4C22×D1112yes—
485C2×C4⋊C4C22×D1112yes—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—118no—
490C2×C22⋊C4—118no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—118no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—2216no—
495C2×C22⋊C4—228no—
496C2×C22⋊C4—4416no—
497C2×C22⋊C4C22×D1112yes—
498C2×C22⋊C4C22×D1118yes—
499C2×C42—112no—
500C2×C42—112no—
501C2×C42—112no—
502C2×C42—224no—
503C2×C42C22×D1112yes—
504#95—114no—
505#95—114no—
506#95—118no—
507#95—114no—
508#95—114no—
509#95C22×D1118yes—
510C2×C11—24no—
511C2×C11—44no—
512C2×C11C23×C22⋊C411yescharacteristic
513C2×C11C4×H(5,𝔽2)12yes—
514C2×C11#348411yescharacteristic
515C2×C11#348511yescharacteristic
516C2×C11#349612yes—
517D11—216no—
518D11—44no—
519C24—114no—
520C24—118no—
521C24—118no—
522C24—118no—
523C24—112no—
524C24—1116no—
525C24—228no—
526C24—228no—
527C24—444no—
528C24—444no—
529C24—448no—
530C24—448no—
531C24C23×D1112yes—
532C24C23×D1111yescharacteristic
533#41—232no—
534#41—2264no—
535#41—2264no—
536#41—2232no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—114no—
540C2×Q8—222no—
541C2×Q8—222no—
542C2×Q8C2×C4×D1114yescomplemented
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—118no—
548C2×D4—1116no—
549C2×D4—1164no—
550C2×D4—118no—
551C2×D4—118no—
552C2×D4—1116no—
553C2×D4—114no—
554C2×D4—118no—
555C2×D4—118no—
556C2×D4—118no—
557C2×D4—118no—
558C2×D4—2264no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—2264no—
562C2×D4—22128no—
563C2×D4—228no—
564C2×D4—228no—
565C2×D4—224no—
566C2×D4—224no—
567C2×D4—222no—
568C2×D4—222no—
569C2×D4C2×C4×D1118yes—
570C2×D4C2×C4×D1114yescomplemented
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—44no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—1116no—
578C22×C4—118no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—2216no—
582C22×C4—228no—
583C22×C4—228no—
584C22×C4—2216no—
585C22×C4—2216no—
586C22×C4—224no—
587C22×C4—222no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—222no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—448no—
594C22×C4—4432no—
595C22×C4—442no—
596C22×C4C2×C4×D1114yes—
597C22×C4C2×C4×D1118yescomplemented
598C22×C4D4×D1114yes—
599C22×C4D4×D1114yes—
600C22×C4C23×D1114yes—
601C22×C4C23×D1114yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1111yescharacteristic
604C22×C4C23×D1111yescharacteristic
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—224no—
609C22⋊C4—24no—
610C22⋊C4—48no—
611C22⋊C4—228no—
612C22⋊C4—2216no—
613C22⋊C4—2216no—
614C22⋊C4—228no—
615C22⋊C4—224no—
616C22⋊C4—448no—
617C22⋊C4—444no—
618C22⋊C4—444no—
619C42—24no—
620C42—224no—
621C42—224no—
622C42—224no—
623C11#3425611yescharacteristic, complemented, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—118no—
631C23—118no—
632C23—118no—
633C23—1132no—
634C23—114no—
635C23—2232no—
636C23—228no—
637C23—228no—
638C23—222no—
639C23—222no—
640C23—224no—
641C23—224no—
642C23—448no—
643C23—4416no—
644C23—448no—
645C23—4416no—
646C23—4432no—
647C23—8816no—
648C23—888no—
649C23—888no—
650C23C22×C4×D1114yes—
651C23C22×C4×D1112yes—
652C23C2×D4×D1112yes—
653C23C2×D4×D1112yes—
654C23C24×D1111yescharacteristic
655Q8—28no—
656Q8—228no—
657D4—216no—
658D4—28no—
659D4—1132no—
660D4—1132no—
661D4—2232no—
662D4—2232no—
663D4—2216no—
664D4—228no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—216no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—48no—
674C2×C4—114no—
675C2×C4—114no—
676C2×C4—2232no—
677C2×C4—228no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—2216no—
683C2×C4—222no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—224no—
689C2×C4—4432no—
690C2×C4—444no—
691C2×C4—8816no—
692C2×C4C22⋊C4×D11116yescomplemented
693C2×C4C22×C4×D1114yes—
694C2×C4C22×C4×D1112yes—
695C2×C4C22×C4×D1112yes—
696C2×C4C2×D4×D1112yes—
697C2×C4C2×D4×D1112yes—
698C2×C4C2×D4×D1112yes—
699C2×C4C2×D4×D1112yes—
700C22—24no—
701C22—22no—
702C22—22no—
703C22—24no—
704C22—24no—
705C22—28no—
706C22—44no—
707C22—42no—
708C22—42no—
709C22—1116no—
710C22—2216no—
711C22—228no—
712C22—228no—
713C22—2216no—
714C22—224no—
715C22—228no—
716C22—4432no—
717C22—444no—
718C22—442no—
719C22—442no—
720C22—8832no—
721C22C2×C22⋊C4×D1114yes—
722C22C23×C4×D1111yescharacteristic
723C22C22×D4×D1111yescharacteristic
724C22C22×D4×D1111yescharacteristic
725C22D11×H(5,𝔽2)12yes—
726C22#1062345712yes—
727C4—24no—
728C4—44no—
729C4—44no—
730C4—224no—
731C4—224no—
732C4—444no—
733C4—442no—
734C4C2×C22⋊C4×D1114yes—
735C4C2×C22⋊C4×D1114yes—
736C2—24no—
737C2—44no—
738C2—2216no—
739C2—444no—
740C2C22×C22⋊C4×D1111yescharacteristic
741C2#1308182212yes—
742C2#1308225011yescharacteristic
743C2#1308225911yescharacteristic
744C2#1308237912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC22×#67042C2
hypercenter#2311D11
hypocenterC11#34256
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C22×#66946C2semidirect
4. #13071445C2semidirect
5. #13071444C2semidirect
6. #13071437C2semidirect
7. #13071436C2semidirect
8. #13071209C2semidirect
9. #13071190C2semidirect
10. #13071107C2semidirect
11. #13071104C2semidirect
12. D11×#386C2semidirect
13. C11×#2311C2semidirect
17. C2×#67042C4semidirect
25. C23×C4×D11C22semidirect
26. C2×C11×#117C22semidirect
27. C22×C11×C4⋊C4C22semidirect
28. C22×(C2×D11)⋊C4C22semidirect
29. C2×#66979C22semidirect
30. C22×C4×Dic11C22semidirect
33. C2×#66946C22semidirect
34. C2×#66946C22semidirect
35. C2×#66946C22semidirect
36. C2×C22⋊C4×D11C22semidirect
37. C2×C22⋊C4×D11C22semidirect
38. C2×C4×D44C22semidirect
39. C11×#391C22semidirect
40. C11×#390C22semidirect
41. C11×#386C22semidirect
42. C11×#380C22semidirect
43. #10622843C22semidirect
44. #10622834C22semidirect
45. #10622833C22semidirect
46. #10622833C22semidirect
47. #10622826C22semidirect
48. C4×C22⋊Dic11C22semidirect
49. #10622601C22semidirect
50. #10622601C22semidirect
51. #10622600C22semidirect
52. #10622587C22semidirect
53. #10622587C22semidirect
54. #10622571C22semidirect
55. #10622571C22semidirect
56. #10622569C22semidirect
57. #10622569C22semidirect
58. #10622568C22semidirect
59. C4×(C2×D11)⋊C4C22semidirect
60. #10622278C22semidirect
61. #10622278C22semidirect
62. #10622277C22semidirect
63. D11×#95C22semidirect
68. C2×C11×#41C2×C4semidirect
82. C2×#4343C2×C4semidirect
87. C2×D4×D11C2×C4semidirect
88. C2×D4×D11C2×C4semidirect
93. C2×#4339C2×C4semidirect
94. C2×#4339C2×C4semidirect
98. C22×D44C2×C4semidirect
157. C23×D11C22×C4semidirect
165. C2×Q8×C11C22×C4semidirect
171. C2×D4×C11C22×C4semidirect
177. C22×C4×C11C22×C4semidirect
190. C2×C22⋊D11C22×C4semidirect
209. C2×D44C22⋊C4semidirect
212. C2×D44C22×C4semidirect
213. C2×D44C22×C4semidirect
229. C2×C4×D11C22×C4semidirect
230. C2×C4×D11C22×C4semidirect
233. C2×Dic22C22×C4semidirect
260. #2311D11semidirect
291. C22×D11C2×C22⋊C4semidirect
308. C2×C4×C11C2×C22⋊C4semidirect
331. C2×Dic11H(5,𝔽2)semidirect
334. D44C2×C22⋊C4semidirect
335. D44C2×C22⋊C4semidirect
360. C2×#117C2×D11semidirect
361. C22×C4⋊C4C2×D11semidirect
369. #391C2×D11semidirect
373. #390C2×D11semidirect
383. #386C2×D11semidirect
386. #380C2×D11semidirect
441. C2×#41C4×D11semidirect
542. C2×Q8C2×C4×D11semidirect
570. C2×D4C2×C4×D11semidirect
597. C22×C4C2×C4×D11semidirect
623. C11#34256semidirect
692. C2×C4C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#670422
C2×#106230522
C22×#669462
#130714452
#130714442
#130714372
#130714362
#130712092
#130711902
#130711072
#130711042
D11×#3862
C11×#23112
#3425611