Finite Group Databasebeta

← #14913827

Subgroups — #14913827

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2#13071492C212yesmaximal, complemented
3#13071490C214yesmaximal, complemented
4#13071489C212yesmaximal, complemented
5#13071487C211yesmaximal, characteristic, complemented
6#13071486C212yesmaximal, complemented
7#13071485C211yesmaximal, characteristic, complemented
8#13071483C211yesmaximal, characteristic, complemented
9#13071480C212yesmaximal, complemented
10#13071231C212yesmaximal, complemented
11#13071215C214yesmaximal, complemented
12#13070998C211yesmaximal, characteristic
13#13070997C211yesmaximal, characteristic
14#13070996C212yesmaximal
15#13070995C212yesmaximal
16#13070970C212yesmaximal, complemented
17C11×#2344C211yesmaximal, characteristic, complemented
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2212yes—
20C2×C11×#117C2212yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66979C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C2×#66945C2212yes—
26C2×C4⋊C4×D11C4116yescomplemented
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C4⋊C4×D11C2212yes—
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×#66930C2212yes—
34C2×#66930C2212yes—
35C2×#66925C2212yes—
36C11×#389C2212yescomplemented
37C11×#387C2214yescomplemented
38C11×#381C2212yes—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4C2212yescomplemented
41C4×C11×C22⋊C4C2211yescharacteristic
42#10622825C2211yescharacteristic
43#10622824C2212yes—
44C4×C22⋊Dic11C2211yescharacteristic
45#10622600C2214yes—
46#10622600C2212yes—
47#10622600C2214yes—
48#10622598C2212yescomplemented
49#10622594C2214yescomplemented
50#10622591C2214yescomplemented
51C4⋊C4×Dic11C2212yescomplemented
52C4⋊C4×Dic11C2212yescomplemented
53#10622586C2212yescomplemented
54#10622585C2214yescomplemented
55#10622568C2211yescharacteristic
56#10622568C2212yes—
57#10622568C2211yescharacteristic
58#10622556C2212yes—
59#10622556C2212yes—
60#10622555C2211yescharacteristic
61#10622555C2211yescharacteristic
62C22⋊C4×Dic11C2212yes—
63C4×(C2×D11)⋊C4C2214yes—
64C4×(C2×D11)⋊C4C2214yes—
65C4×(C2×D11)⋊C4C2212yes—
66C4×C4⋊Dic11C2212yescomplemented
67#10622546C2214yescomplemented
68C4×Dic11⋊C4C2214yescomplemented
69#10622541C2212yescomplemented
70#10622280C2214yes—
71#10622280C2214yes—
72#10622280C2212yes—
73#10622279C2214yes—
74#10622279C2212yes—
75#10622279C2214yes—
76#10622277C2212yes—
77#10622277C2212yes—
78#10622268C2214yescomplemented
79#10622267C2214yescomplemented
80#10622266C2214yescomplemented
81#10622265C2214yescomplemented
82#10622262C2214yescomplemented
83#10622260C2214yescomplemented
84C24×D11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×Dic11C2312yes—
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—28no—
90C22×C4×D11—44no—
91C22×C4×D11—44no—
92C22×C4×D11C2×C418yes—
93C22×C4×D11C2×C4116yes—
94C22×C4×D11C2311yescharacteristic
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C22×C4×D11C2311yescharacteristic
102C11×#117—44no—
103C2×C11×C4⋊C4C2×C418yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2311yescharacteristic
112C2×C42×C11C2312yes—
113C2×C42×C11C2314yes—
114C2×C22⋊Dic11C2311yescharacteristic
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2311yescharacteristic
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2312yes—
123#66979—44no—
124C2×C4⋊Dic11C2×C418yes—
125C2×C4⋊Dic11C2312yes—
126C2×C4⋊Dic11C2314yes—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4C2×C4116yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144#66945—28no—
145C4⋊C4×D11C2×C4116yes—
146C4⋊C4×D11C2×C418yes—
147C4⋊C4×D11C2×C4116yes—
148C4⋊C4×D11C2×C418yes—
149C4⋊C4×D11C2×C418yes—
150C4⋊C4×D11C2×C418yes—
151#66930—44no—
152#66930—44no—
153#66925—28no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11×#95C2312yes—
157C11×#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2312yes—
166C11⋊#95C2312yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169#34178—111nomaximal, Sylow
170C24×C11C2411yescharacteristic
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—24no—
174C23×D11—24no—
175C23×D11C22×C414yes—
176C23×D11C2411yescharacteristic
177C23×D11C2411yescharacteristic
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11C22×C418yes—
182C22×C4×C11C22×C414yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2414yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—24no—
193C22×Dic11C22×C414yes—
194C22×Dic11C22×C418yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2414yes—
198C22×Dic11C2411yescharacteristic
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2411yescharacteristic
202C2×C4×D11—24no—
203C2×C4×D11—232no—
204C2×C4×D11—24no—
205C2×C4×D11—24no—
206C2×C4×D11—432no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11C22×C414yes—
216C2×C4×D11C22×C414yes—
217C2×C4×D11C22×C414yes—
218C2×C4×D11C22×C418yes—
219C2×C4×D11C22×C418yes—
220C2×C4×D11C22×C418yes—
221C2×C4×D11C22×C418yes—
222C2×C4×D11C22×C414yes—
223C2×C4×D11#4118yes—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—44no—
226C11×C4⋊C4C22×C418yes—
227C11×C4⋊C4C22×C414yes—
228C11×C4⋊C4C22×C414yes—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—22no—
232C42×C11—24no—
233C42×C11—44no—
234C22⋊Dic11—22no—
235C22⋊Dic11—24no—
236C22⋊Dic11—22no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—24no—
243C4⋊Dic11—24no—
244C4⋊Dic11—44no—
245C4⋊Dic11C22×C418yes—
246C4⋊Dic11C22×C414yes—
247C4⋊Dic11C22×C414yes—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—44no—
251Dic11⋊C4—44no—
252Dic11⋊C4C22×C418yes—
253Dic11⋊C4C22×C418yes—
254Dic11⋊C4C22×C418yes—
255Dic11⋊C4C22×C418yes—
256C4×Dic11—28no—
257C4×Dic11—24no—
258C4×Dic11—44no—
259C4×Dic11—44no—
260C4×Dic11—44no—
261C23×C4⋊C4—111no—
262#2345—112no—
263#2345—114no—
264#2345—112no—
265#2344—112no—
266#2344—111no—
267#2344—111no—
268#2344—112no—
269#2344—111no—
270#2344D1111yescharacteristic, complemented
271#2316—112no—
272#2313—114no—
273#2280—112no—
274#2280—111no—
275#2280—111no—
276#2280—112no—
277#2274—112no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11C23×C412yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C11H(5,𝔽2)12yes—
283C23×C11C2511yescharacteristic
284C22×D11—216no—
285C22×D11—216no—
286C22×D11—28no—
287C22×D11—22no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—22no—
293C22×D11—28no—
294C22×D11—28no—
295C22×D11C23×C412yes—
296C22×D11C23×C412yes—
297C22×D11C2×#4114yes—
298C22×D112−1+414yes—
299C2×C4×C11—216no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—28no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11C23×C414yes—
316C2×C4×C11C23×C414yes—
317C2×C4×C11C23×C412yes—
318C2×C4×C11C23×C412yes—
319C2×C4×C11C2×#4114yes—
320C2×Dic11—216no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—28no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11C23×C412yes—
337C2×Dic11C23×C414yes—
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C412yes—
340C2×Dic11C2×#4114yes—
341C4×D11—28no—
342C4×D11—28no—
343C4×D11—28no—
344C4×D11—48no—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—48no—
348C4×D11#117116yescomplemented
349C24×C4—111no—
350C24×C4—112no—
351C2×#117—112no—
352C2×#117—112no—
353C2×#117—112no—
354C2×#117—112no—
355C2×#117—112no—
356C2×#117C2×D1112yes—
357C22×C4⋊C4—112no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—112no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—112no—
362C22×C4⋊C4—111no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—1116no—
366C22×C4⋊C4C2×D1111yescharacteristic
367#389—114no—
368#389—112no—
369#389—112no—
370#389—112no—
371#389—114no—
372#389C2×D1112yescomplemented
373#387—114no—
374#387—114no—
375#387—114no—
376#387—114no—
377#387—114no—
378#387—114no—
379#387—114no—
380#387C2×D1114yescomplemented
381#381—112no—
382#381—112no—
383#381—112no—
384#381—112no—
385#381—112no—
386#381C2×D1112yes—
387#380—111no—
388#380—114no—
389#380—114no—
390#380—112no—
391#380—111no—
392#380—111no—
393#380—114no—
394#380—114no—
395#380—112no—
396#380C2×D1111yescharacteristic
397#379—111no—
398#379—112no—
399#379—111no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—112no—
402C4×C4⋊C4—114no—
403C4×C4⋊C4—112no—
404C4×C4⋊C4—114no—
405C4×C4⋊C4C2×D1112yescomplemented
406C4×C22⋊C4—111no—
407C4×C22⋊C4—112no—
408C4×C22⋊C4—114no—
409C4×C22⋊C4—112no—
410C4×C22⋊C4—114no—
411C4×C22⋊C4—114no—
412C4×C22⋊C4—112no—
413C4×C22⋊C4—114no—
414C4×C22⋊C4C2×D1111yescharacteristic
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—24no—
418C22×C11—24no—
419C22×C11#51814yes—
420C22×C11C24×C411yescharacteristic
421C22×C11C22×#4112yes—
422C22×C11C2×H(5,𝔽2)11yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×2−1+412yes—
425C2×D11—232no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—24no—
431C2×D11—24no—
432C2×D11—24no—
433C2×D11—24no—
434C2×D11C2×#11714yes—
435C2×D11#51914yes—
436C4×C11—22no—
437C4×C11—24no—
438C4×C11—24no—
439C4×C11—42no—
440C4×C11—44no—
441C4×C11—42no—
442C4×C11C2×#11714yes—
443Dic11—22no—
444Dic11—24no—
445Dic11—24no—
446Dic11—42no—
447Dic11—44no—
448Dic11—42no—
449Dic11C2×#11714yes—
450C25—111no—
451C23×C4—111no—
452C23×C4—112no—
453C23×C4—111no—
454C23×C4—118no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—1116no—
459C23×C4—112no—
460C23×C4—112no—
461C23×C4—112no—
462C23×C4—112no—
463C23×C4—228no—
464C23×C4—444no—
465C23×C4—444no—
466C23×C4C22×D1112yes—
467C23×C4C22×D1111yescharacteristic
468#117—44no—
469#117—228no—
470#117—228no—
471#117—444no—
472#117—444no—
473#117—444no—
474C2×C4⋊C4—1116no—
475C2×C4⋊C4—118no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—118no—
484C2×C4⋊C4—118no—
485C2×C4⋊C4—1116no—
486C2×C4⋊C4—1116no—
487C2×C4⋊C4—118no—
488C2×C4⋊C4—118no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4C4×D1118yes—
496C2×C4⋊C4C22×D1112yes—
497C2×C4⋊C4C22×D1114yes—
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1112yes—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—111no—
502C2×C22⋊C4—111no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4C22×D1111yescharacteristic
511C2×C22⋊C4C22×D1112yes—
512C2×C22⋊C4C22×D1111yescharacteristic
513C2×C42—114no—
514C2×C42—112no—
515C2×C42—114no—
516C2×C42—114no—
517C2×C42—114no—
518C2×C42C22×D1112yes—
519C2×C42C22×D1114yes—
520#95—114no—
521#95—114no—
522#95—114no—
523#95—112no—
524#95—114no—
525#95—112no—
526#95—112no—
527#95—112no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95C22×D1114yes—
532#95C22×D1114yes—
533#95C22×D1112yes—
534#95C22×D1112yes—
535C2×C11—24no—
536C2×C11C22×#11711yescharacteristic
537C2×C11C2×#51811yescharacteristic
538C2×C11C2×#51911yescharacteristic
539C2×C11#349212yes—
540C2×C11#349212yes—
541D11—24no—
542D11—24no—
543C24—111no—
544C24—111no—
545C24—114no—
546C24—224no—
547C24—224no—
548C24—222no—
549C24—222no—
550C24C23×D1111yescharacteristic
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—111no—
555C22×C4—114no—
556C22×C4—118no—
557C22×C4—114no—
558C22×C4—118no—
559C22×C4—111no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—114no—
565C22×C4—118no—
566C22×C4—118no—
567C22×C4—118no—
568C22×C4—118no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—114no—
572C22×C4—224no—
573C22×C4—2232no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—224no—
578C22×C4—224no—
579C22×C4—4432no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4—442no—
583C22×C4—442no—
584C22×C4—442no—
585C22×C4—442no—
586C22×C4—442no—
587C22×C4—442no—
588C22×C4C2×C4×D1118yes—
589C22×C4C2×C4×D1114yes—
590C22×C4C23×D1112yes—
591C22×C4C23×D1114yes—
592C22×C4C23×D1112yes—
593C22×C4C23×D1111yescharacteristic
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597C4⋊C4—24no—
598C4⋊C4—44no—
599C4⋊C4—118no—
600C4⋊C4—118no—
601C4⋊C4—118no—
602C4⋊C4—118no—
603C4⋊C4—118no—
604C4⋊C4—114no—
605C4⋊C4—114no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—444no—
610C4⋊C4—444no—
611C4⋊C4—444no—
612C4⋊C4C2×C4×D1118yes—
613C4⋊C4C2×C4×D1114yes—
614C4⋊C4C2×C4×D1114yes—
615C22⋊C4—22no—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—228no—
621C22⋊C4—224no—
622C22⋊C4—224no—
623C22⋊C4—228no—
624C22⋊C4—222no—
625C22⋊C4—224no—
626C22⋊C4—222no—
627C42—24no—
628C42—44no—
629C42—228no—
630C42—224no—
631C42—444no—
632C42—444no—
633C42—444no—
634C11#3417811yescharacteristic, complemented, Sylow
635C23—22no—
636C23—22no—
637C23—112no—
638C23—112no—
639C23—114no—
640C23—114no—
641C23—228no—
642C23—228no—
643C23—2216no—
644C23—2216no—
645C23—228no—
646C23—221no—
647C23—221no—
648C23—222no—
649C23—221no—
650C23—221no—
651C23—222no—
652C23C22×C4×D1112yes—
653C23#6703712yes—
654C23#6704212yes—
655C23C24×D1111yescharacteristic
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—112no—
673C2×C4—114no—
674C2×C4—1116no—
675C2×C4—112no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—228no—
679C2×C4—228no—
680C2×C4—228no—
681C2×C4—2216no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—228no—
688C2×C4—222no—
689C2×C4—224no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—224no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—222no—
697C2×C4—448no—
698C2×C4—448no—
699C2×C4—448no—
700C2×C4—448no—
701C2×C4C22×C4×D1112yes—
702C2×C4C22×C4×D1114yes—
703C2×C4C22×C4×D1114yes—
704C2×C4C22×C4×D1112yes—
705C2×C4#41×D1114yes—
706C22—22no—
707C22—22no—
708C22—24no—
709C22—24no—
710C22—114no—
711C22—114no—
712C22—2232no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22—224no—
718C22—224no—
719C22—224no—
720C22—224no—
721C22#1062307614yes—
722C22C23×C4×D1111yescharacteristic
723C22C2×#6703711yescharacteristic
724C22C2×#41×D1112yes—
725C22C2×#6704211yescharacteristic
726C22D11×2−1+412yes—
727C4—22no—
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—44no—
733C4—114no—
734C4—222no—
735C4—224no—
736C4—224no—
737C4—444no—
738C4—442no—
739C4—442no—
740C4D11×#11714yes—
741C2—24no—
742C2—224no—
743C2—224no—
744C2C2×D11×#11711yescharacteristic
745C2C2×#1062307611yescharacteristic
746C2D11×#51911yescharacteristic
747C2#1308231612yes—
748C2#1308231812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2344C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2344D11
hypocenterC11#34178
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #13071492C2semidirect
3. #13071490C2semidirect
4. #13071489C2semidirect
5. #13071487C2semidirect
6. #13071486C2semidirect
7. #13071485C2semidirect
8. #13071483C2semidirect
9. #13071480C2semidirect
10. #13071231C2semidirect
11. #13071215C2semidirect
16. #13070970C2semidirect
17. C11×#2344C2semidirect
26. C2×C4⋊C4×D11C4semidirect
36. C11×#389C22semidirect
37. C11×#387C22semidirect
40. C4×C11×C4⋊C4C22semidirect
48. #10622598C22semidirect
49. #10622594C22semidirect
50. #10622591C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C4⋊C4×Dic11C22semidirect
53. #10622586C22semidirect
54. #10622585C22semidirect
66. C4×C4⋊Dic11C22semidirect
67. #10622546C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. #10622541C22semidirect
78. #10622268C22semidirect
79. #10622267C22semidirect
80. #10622266C22semidirect
81. #10622265C22semidirect
82. #10622262C22semidirect
83. #10622260C22semidirect
270. #2344D11semidirect
348. C4×D11#117semidirect
372. #389C2×D11semidirect
380. #387C2×D11semidirect
405. C4×C4⋊C4C2×D11semidirect
634. C11#34178semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
#130714922
#130714902
#130714892
#130714872
#130714862
#130714852
#130714832
#130714802
#130712312
#130712152
#130709982
#130709972
#130709962
#130709952
#130709702
C11×#23442
#3417811