Finite Group Databasebeta

← #14914591

Subgroups — #14914591

Order 2816.

2682 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×#67000C211yesmaximal, characteristic
2#13071727C214yesmaximal, complemented
3#13071692C212yesmaximal, complemented
4#13071683C212yesmaximal, complemented
5#13071468C212yesmaximal, complemented
6#13071462C212yesmaximal, complemented
7Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
8C22⋊C4×D44C211yesmaximal, characteristic
9#13071436C211yesmaximal, characteristic
10#13071428C214yesmaximal, complemented
11#13071213C212yesmaximal, complemented
12C4×#67000C212yesmaximal, complemented
13#13071159C212yesmaximal, complemented
14#13071011C211yesmaximal, characteristic, complemented
15#13070968C212yesmaximal, complemented
16C4×#66930C211yesmaximal, characteristic, complemented
17Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
18C23×Q8×C11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C4×Q8×C11C2212yescomplemented
21C2×#67000C4116yescomplemented
22C2×#67000C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×#67000C2211yescharacteristic
25C2×#67000C2212yes—
26C2×#67000C2211yescharacteristic
27C2×#67000C2212yes—
28C2×Q8×Dic11C2212yescomplemented
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32C2×#66946C2212yes—
33C2×C22⋊C4×D11C2212yes—
34C2×C22⋊C4×D11C2212yes—
35C2×#66930C2211yescharacteristic
36C2×#66930C2211yescharacteristic
37C2×C4×D44C2212yes—
38C11×#391C2212yescomplemented
39C11×#391C2214yescomplemented
40C11×#380C2211yescharacteristic
41C11×#380C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4C2212yes—
44#10622843C2212yescomplemented
45#10622843C2214yescomplemented
46#10622825C2211yescharacteristic
47#10622825C2212yes—
48C4×C22⋊Dic11C2211yescharacteristic
49C4×C22⋊Dic11C2212yes—
50#10622603C2214yescomplemented
51#10622603C2214yescomplemented
52#10622603C2214yescomplemented
53#10622602C2214yescomplemented
54#10622601C2212yes—
55#10622590C2212yescomplemented
56C4⋊C4×Dic11C2212yescomplemented
57#10622568C2212yes—
58#10622568C2212yes—
59#10622556C2212yes—
60C22⋊C4×Dic11C2211yescharacteristic
61C22⋊C4×Dic11C2211yescharacteristic
62C22⋊C4×Dic11C2212yes—
63#10622553C2214yescomplemented
64#10622552C2212yes—
65C4×(C2×D11)⋊C4C2214yescomplemented
66C4×(C2×D11)⋊C4C2214yescomplemented
67C4×(C2×D11)⋊C4C2214yescomplemented
68C4×Dic11⋊C4C2212yescomplemented
69C42×Dic11C2212yescomplemented
70#10622283C2214yescomplemented
71#10622283C2214yescomplemented
72#10622283C2214yescomplemented
73#10622282C2214yescomplemented
74#10622281C2214yescomplemented
75#10622279C2214yescomplemented
76#10622279C2214yescomplemented
77#10622279C2214yescomplemented
78#10622278C2214yes—
79#10622278C2214yes—
80#10622264C2212yescomplemented
81#10622262C2212yescomplemented
82#10622261C2212yescomplemented
83#10622261C2212yescomplemented
84C24×D11C2312yes—
85C22×Q8×C11—44no—
86C22×Q8×C11C2×C418yescomplemented
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2311yescharacteristic
89C22×Q8×C11C2312yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2312yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—44no—
95C22×D44C2×C418yes—
96C22×D44C2311yescharacteristic
97C22×D44C2311yescharacteristic
98C22×D44C2312yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2314yes—
101C4×Q8×C11—44no—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2311yescharacteristic
107C2×C42×C11C2312yes—
108C2×C42×C11C2314yes—
109C2×C22⋊Dic11C2311yescharacteristic
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2311yescharacteristic
112#67000C2×C418yescomplemented
113#67000C2×C418yescomplemented
114#67000C2×C418yescomplemented
115#67000C2×C418yescomplemented
116#67000C2×C4116yescomplemented
117#67000C2×C4116yescomplemented
118Q8×Dic11—44no—
119C2×(C2×D11)⋊C4C2×C4116yescomplemented
120C2×(C2×D11)⋊C4C2×C4116yescomplemented
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2314yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×C4×Dic11C2×C418yescomplemented
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151#66946—44no—
152C22⋊C4×D11—28no—
153C22⋊C4×D11—28no—
154#66930—24no—
155#66930—24no—
156C4×D44—44no—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2312yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170#34240—111nomaximal, Sylow
171C24×C11C2411yescharacteristic
172C23×D11—24no—
173C23×D11—24no—
174C23×D11—44no—
175C23×D11—44no—
176C23×D11C22×C418yes—
177C23×D11C2412yes—
178C23×D11C2412yes—
179C2×Q8×C11—24no—
180C2×Q8×C11—24no—
181C2×Q8×C11—44no—
182C2×Q8×C11—416no—
183C2×Q8×C11C22×C414yes—
184C2×Q8×C11C22×C414yes—
185C2×Q8×C11C22×C418yes—
186C22×C4×C11—24no—
187C22×C4×C11—44no—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C22×C418yes—
190C22×C4×C11C2414yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—42no—
200C22×Dic11C22×C414yes—
201C22×Dic11C22×C414yes—
202C22×Dic11C2414yes—
203C22×Dic11C2412yes—
204C22×Dic11C2411yescharacteristic
205C22×Dic11C2411yescharacteristic
206C22×Dic11C2411yescharacteristic
207C22×Dic11C2411yescharacteristic
208C22×Dic11C2412yes—
209C2×D44—24no—
210C2×D44—24no—
211C2×D44—44no—
212C2×D44—416no—
213C2×D44C22×C414yes—
214C2×D44C22×C414yes—
215C2×D44C22×C418yes—
216C2×C4×D11—28no—
217C2×C4×D11—28no—
218C2×C4×D11—44no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—44no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4#4114yes—
227C42×C11—24no—
228C42×C11—44no—
229C22⋊Dic11—22no—
230C22⋊Dic11—24no—
231C22⋊Dic11#4114yes—
232(C2×D11)⋊C4—28no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—44no—
235(C2×D11)⋊C4—44no—
236(C2×D11)⋊C4—44no—
237(C2×D11)⋊C4—44no—
238(C2×D11)⋊C4C22×C418yes—
239(C2×D11)⋊C4C22×C418yes—
240(C2×D11)⋊C4C22×C418yes—
241(C2×D11)⋊C4C22×C418yes—
242(C2×D11)⋊C4C22×C418yes—
243(C2×D11)⋊C4C22×C418yes—
244(C2×D11)⋊C4C22×C418yes—
245(C2×D11)⋊C4C22×C418yes—
246C4⋊Dic11—24no—
247C4⋊Dic11—44no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—42no—
254C4×Dic11—42no—
255C4×Dic11—44no—
256C4×Dic11—44no—
257C4×Dic11C22×C414yes—
258C4×Dic11C22×C414yes—
259C4×Dic11C22×C414yes—
260C4×Dic11C22×C414yes—
261C22×#124—111no—
262#2372—114no—
263#2367—112no—
264#2367—112no—
265#2342—112no—
266#2342—112no—
267Q8×C22⋊C4—111no—
268Q8×C22⋊C4D1111yescharacteristic, complemented
269D4×C22⋊C4—111no—
270D4×C22⋊C4—111no—
271#2337—114no—
272#2312—112no—
273C4×#124—112no—
274C4×#124—112no—
275#2283—111no—
276#2273—112no—
277C4×#117—111no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11C23×C412yes—
281C23×C11C2×#4112yes—
282C23×C11C2×#4112yes—
283C23×C11C2511yescharacteristic
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—24no—
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—216no—
293C22×D11—48no—
294C22×D11—48no—
295C22×D11—88no—
296C22×D11—88no—
297C22×D11C23×C414yes—
298C22×D11C23×C414yes—
299Q8×C11—28no—
300Q8×C11—28no—
301Q8×C11—48no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—28no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—48no—
315C2×C4×C11C23×C412yes—
316C2×C4×C11C23×C414yes—
317C2×C4×C11C23×C414yes—
318C2×C4×C11C23×C412yes—
319C2×C4×C11C2×#4114yes—
320C2×C4×C11H(5,𝔽2)14yes—
321C2×Dic11—28no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—44no—
337C2×Dic11C23×C412yes—
338C2×Dic11C23×C412yes—
339C2×Dic11C23×C412yes—
340C2×Dic11C23×C412yes—
341C2×Dic11C2×#4114yes—
342D44—28no—
343D44—28no—
344D44—48no—
345C4×D11—88no—
346C4×D11—88no—
347C23×Q8C2×D1111yescharacteristic
348C23×D4—111no—
349C2×#124—112no—
350C2×#124—111no—
351C2×#124—111no—
352C2×#124—112no—
353C2×#124—111no—
354C2×#124—111no—
355C2×#124—1116no—
356C2×C4×Q8—112no—
357C2×C4×Q8C2×D1112yescomplemented
358C2×C4×D4—112no—
359C2×C4×D4—112no—
360C2×#117—111no—
361C2×#117—111no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C42—111no—
367#391—114no—
368#391—112no—
369#391C2×D1114yescomplemented
370#391C2×D1112yescomplemented
371#390—112no—
372#390—112no—
373#388—114no—
374#388—114no—
375#388—114no—
376#388—114no—
377#388—114no—
378#388—114no—
379#388—114no—
380#388—114no—
381#386—114no—
382#386—114no—
383#385—114no—
384#385—114no—
385#383—112no—
386#382—112no—
387#381—112no—
388#380—112no—
389#380—111no—
390#380C2×D1112yes—
391#380C2×D1111yescharacteristic
392#379—112no—
393#379—112no—
394C4×C4⋊C4—112no—
395C4×C4⋊C4—112no—
396C4×C4⋊C4—112no—
397C4×C22⋊C4—111no—
398C4×C22⋊C4—112no—
399C4×C22⋊C4—111no—
400C4×C22⋊C4—112no—
401C4×C22⋊C4—111no—
402C4×C22⋊C4—114no—
403C4×C22⋊C4—114no—
404C4×C22⋊C4—114no—
405C4×C22⋊C4—114no—
406C4×C22⋊C4—114no—
407C4×C22⋊C4—114no—
408C4×C22⋊C4C2×D1111yescharacteristic
409C4×C22⋊C4C2×D1112yes—
410#376—112no—
411#376—112no—
412C43—112no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11C4×#4114yes—
418C22×C11C24×C411yescharacteristic
419C22×C11C22×#4111yescharacteristic
420C22×C11C22×#4111yescharacteristic
421C22×C11C2×H(5,𝔽2)12yes—
422C22×C11#58512yes—
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—24no—
426C2×D11—24no—
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—44no—
430C2×D11—44no—
431C2×D11—44no—
432C2×D11—44no—
433C2×D11—816no—
434C4×C11—22no—
435C4×C11—24no—
436C4×C11—24no—
437C4×C11—24no—
438C4×C11—42no—
439C4×C11—44no—
440C4×C11#51814yes—
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—24no—
446Dic11—44no—
447Dic11—42no—
448C25—112no—
449C22×Q8—44no—
450C22×Q8C4×D1118yescomplemented
451C22×Q8C22×D1111yescharacteristic
452C22×Q8C22×D1111yescharacteristic
453C22×Q8C22×D1112yes—
454C22×D4—118no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4—112no—
458C22×D4—444no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—114no—
462C23×C4—114no—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1112yes—
465#124—118no—
466#124—118no—
467#124—118no—
468#124—118no—
469#124—1116no—
470#124—1116no—
471C4×Q8—44no—
472C4×Q8—444no—
473C4×D4—444no—
474C4×D4—444no—
475#117—224no—
476#117—224no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4C22×D1112yes—
482C2×C4⋊C4C22×D1114yes—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—1116no—
485C2×C22⋊C4—1116no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—114no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—228no—
503C2×C22⋊C4—228no—
504C2×C22⋊C4C22×D1112yes—
505C2×C22⋊C4C22×D1111yescharacteristic
506C2×C22⋊C4C22×D1111yescharacteristic
507C2×C42—118no—
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—112no—
513C2×C42—112no—
514C2×C42—112no—
515C2×C42—114no—
516C2×C42—112no—
517C2×C42—112no—
518C2×C42—114no—
519C2×C42C22×D1112yes—
520C2×C42C22×D1114yes—
521#95—112no—
522#95—114no—
523#95—112no—
524#95—112no—
525#95—112no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95C22×D1112yes—
531#95C22×D1112yes—
532#95C22×D1114yes—
533#95C22×D1114yes—
534C2×C11—24no—
535C2×C11C2×C4×#4111yescharacteristic
536C2×C11C2×#51811yescharacteristic
537C2×C11#342811yescharacteristic
538C2×C11#351412yes—
539C2×C11#351412yes—
540D11—44no—
541D11—44no—
542C24—112no—
543C24—112no—
544C24—118no—
545C24—224no—
546C24—224no—
547C24—444no—
548C24—444no—
549C24C23×D1111yescharacteristic
550C2×Q8—24no—
551C2×Q8—24no—
552C2×Q8—44no—
553C2×Q8—416no—
554C2×Q8C2×C4×D1114yes—
555C2×Q8C2×C4×D1114yes—
556C2×Q8C2×C4×D1118yes—
557C2×D4—114no—
558C2×D4—114no—
559C2×D4—118no—
560C2×D4—224no—
561C2×D4—224no—
562C2×D4—4416no—
563C2×D4—444no—
564C22×C4—24no—
565C22×C4—44no—
566C22×C4—114no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—112no—
571C22×C4—111no—
572C22×C4—114no—
573C22×C4—114no—
574C22×C4—112no—
575C22×C4—228no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—228no—
579C22×C4—444no—
580C22×C4—444no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—442no—
584C22×C4C2×C4×D1114yes—
585C22×C4C2×C4×D1118yes—
586C22×C4C23×D1114yes—
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589C22×C4C23×D1112yes—
590C22×C4C23×D1112yes—
591C22×C4C23×D1112yes—
592C22×C4C23×D1111yescharacteristic
593C4⋊C4—24no—
594C4⋊C4—44no—
595C4⋊C4—224no—
596C4⋊C4—224no—
597C4⋊C4—224no—
598C4⋊C4—444no—
599C22⋊C4—24no—
600C22⋊C4—22no—
601C22⋊C4—114no—
602C22⋊C4—118no—
603C22⋊C4—118no—
604C22⋊C4—118no—
605C22⋊C4—118no—
606C22⋊C4—118no—
607C22⋊C4—118no—
608C22⋊C4—118no—
609C22⋊C4—118no—
610C22⋊C4—228no—
611C22⋊C4—224no—
612C22⋊C4—222no—
613C22⋊C4—228no—
614C22⋊C4—444no—
615C22⋊C4—444no—
616C22⋊C4—444no—
617C22⋊C4—444no—
618C22⋊C4#434314yes—
619C42—24no—
620C42—44no—
621C42—114no—
622C42—114no—
623C42—114no—
624C42—114no—
625C42—224no—
626C42—224no—
627C42—224no—
628C42—444no—
629C42—442no—
630C42—442no—
631C42—444no—
632C11#3424011yescharacteristic, complemented, Sylow
633C23—22no—
634C23—22no—
635C23—114no—
636C23—114no—
637C23—224no—
638C23—224no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—224no—
644C23—224no—
645C23—2216no—
646C23—448no—
647C23—448no—
648C23—888no—
649C23—888no—
650C23C22×C4×D1112yes—
651C23C2×#434312yes—
652C23#41×D1112yes—
653C23C24×D1111yescharacteristic
654Q8—28no—
655Q8—28no—
656Q8—48no—
657D4—228no—
658D4—228no—
659D4—448no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—48no—
673C2×C4—112no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—114no—
678C2×C4—228no—
679C2×C4—222no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—224no—
689C2×C4—222no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—444no—
694C2×C4—888no—
695C2×C4—888no—
696C2×C4C22×C4×D1112yes—
697C2×C4C22×C4×D1114yes—
698C2×C4C22×C4×D1114yes—
699C2×C4C22×C4×D1112yes—
700C2×C4#6703714yes—
701C2×C4C2×#434314yes—
702C22—22no—
703C22—24no—
704C22—24no—
705C22—22no—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—224no—
710C22—224no—
711C22—224no—
712C22—444no—
713C22—444no—
714C22—444no—
715C22—444no—
716C22—8816no—
717C22C4×#434314yes—
718C22C23×C4×D1111yescharacteristic
719C22C2×#6703712yes—
720C22C22×#434311yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22#1062345712yes—
723C4—22no—
724C4—24no—
725C4—24no—
726C4—24no—
727C4—44no—
728C4—42no—
729C4—222no—
730C4—222no—
731C4—224no—
732C4—222no—
733C4—222no—
734C4—444no—
735C4—442no—
736C4#1062301714yes—
737C2—24no—
738C2—444no—
739C2—444no—
740C2C2×C4×#434311yescharacteristic
741C2C2×#1062301711yescharacteristic
742C2#1308181811yescharacteristic
743C2#1308257012yes—
744C2#1308257812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D44C22
hypercenterQ8×C22⋊C4D11
hypocenterC11#34240
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071727C2semidirect
3. #13071692C2semidirect
4. #13071683C2semidirect
5. #13071468C2semidirect
6. #13071462C2semidirect
7. Q8×C22⋊Dic11C2semidirect
10. #13071428C2semidirect
11. #13071213C2semidirect
12. C4×#67000C2semidirect
13. #13071159C2semidirect
14. #13071011C2semidirect
15. #13070968C2semidirect
16. C4×#66930C2semidirect
17. Q8×C11×C22⋊C4C2semidirect
20. C2×C4×Q8×C11C22semidirect
21. C2×#67000C4semidirect
28. C2×Q8×Dic11C22semidirect
38. C11×#391C22semidirect
39. C11×#391C22semidirect
44. #10622843C22semidirect
45. #10622843C22semidirect
50. #10622603C22semidirect
51. #10622603C22semidirect
52. #10622603C22semidirect
53. #10622602C22semidirect
55. #10622590C22semidirect
56. C4⋊C4×Dic11C22semidirect
63. #10622553C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. C42×Dic11C22semidirect
70. #10622283C22semidirect
71. #10622283C22semidirect
72. #10622283C22semidirect
73. #10622282C22semidirect
74. #10622281C22semidirect
75. #10622279C22semidirect
76. #10622279C22semidirect
77. #10622279C22semidirect
80. #10622264C22semidirect
81. #10622262C22semidirect
82. #10622261C22semidirect
83. #10622261C22semidirect
86. C22×Q8×C11C2×C4semidirect
112. #67000C2×C4semidirect
113. #67000C2×C4semidirect
114. #67000C2×C4semidirect
115. #67000C2×C4semidirect
116. #67000C2×C4semidirect
117. #67000C2×C4semidirect
119. C2×(C2×D11)⋊C4C2×C4semidirect
120. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×C4×Dic11C2×C4semidirect
268. Q8×C22⋊C4D11semidirect
357. C2×C4×Q8C2×D11semidirect
369. #391C2×D11semidirect
370. #391C2×D11semidirect
450. C22×Q8C4×D11semidirect
632. C11#34240semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
#130717272
#130716922
#130716832
#130714682
#130714622
Q8×C22⋊Dic112
C22⋊C4×D442
#130714362
#130714282
#130712132
C4×#670002
#130711592
#130710112
#130709682
C4×#669302
Q8×C11×C22⋊C42
#3424011