Finite Group Databasebeta

← #14801521

Subgroups — #14801521

Order 2816.

1046 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622644C211yesmaximal, characteristic, complemented
2C2×#10622841C211yesmaximal, characteristic
3C2×#10622841C211yesmaximal, characteristic
4C2×#10622643C211yesmaximal, characteristic, complemented
5#13072215C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic
8#13069812C211yesmaximal, characteristic
9#13069715C211yesmaximal, characteristic, complemented
10#13069486C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic
12#13068960C211yesmaximal, characteristic, complemented
13#13068957C211yesmaximal, characteristic, complemented
14#13068884C211yesmaximal, characteristic, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#391—21no—
28C11×#391—21no—
29C11×#391C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622841—24no—
36#10622841—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622644—24no—
44#10622643—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51#10622564—21no—
52#10622561—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622270—21no—
58#10622260—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—21no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×Dic22C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—41no—
79C4×Q8×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—22no—
98C2×#4326—22no—
99C2×#4326—22no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—41no—
103C2×#4326—41no—
104C2×#4326D414yes—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109#66977—22no—
110#66977—22no—
111#66977—41no—
112#66977—41no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66922—22no—
123#66922—41no—
124C4×Dic22—22no—
125C4×Dic22—41no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95D411yescharacteristic
132C11×#95D411yescharacteristic
133#66899—22no—
134#66899—22no—
135#66899—22no—
136#66899D414yes—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66874—41no—
146#66872—22no—
147#66872—41no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25173—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C2×Q8×C11—24no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—42no—
162C2×Q8×C11—42no—
163C2×Q8×C11—44no—
164C2×Q8×C11—44no—
165C2×Q8×C11—44no—
166C2×Q8×C11—44no—
167C2×Q8×C11C2×D412yes—
168C2×Q8×C11C2×D412yes—
169C2×Q8×C11#4112yes—
170C2×Q8×C11#4112yes—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22C2×D412yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—42no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—42no—
220C42×C11—42no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223#4326—28no—
224#4326—44no—
225#4326—44no—
226#4326—44no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—42no—
231C4⋊Dic11—42no—
232C4⋊Dic11C2×D412yes—
233Dic11⋊C4—42no—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237C4×Dic11—42no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
249C2×C11⋊C8C2×D412yes—
250C2×#462—111no—
251C2×#451—111no—
252C2×#451—111no—
253C2×#441—111no—
254#2429—111no—
255Q8×C22⋊C4D1111yescharacteristic
256#2066—111no—
257#2035—111no—
258#2035—111no—
259#2016—111no—
260#1971—111no—
261#1924—111no—
262#1878—111no—
263#1878—111no—
264#1865—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11#13712yes—
272C23×C11C22×D411yescharacteristic
273Q8×C11—22no—
274Q8×C11—22no—
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—48no—
279Q8×C11—41no—
280Q8×C11—41no—
281Q8×C11#12114yes—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—48no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11#13712yes—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332Dic22—22no—
333Dic22—22no—
334Dic22—41no—
335Dic22—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339Dic22—41no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C23×Q8C2×D1111yescharacteristic
345C22×Q16—111no—
346C22×Q16—111no—
347C22×Q16—111no—
348C22×Q16—111no—
349C2×C4⋊Q8—111no—
350C2×C22⋊Q8—111no—
351C2×C22⋊Q8—111no—
352C2×C4×Q8—111no—
353C2×C4×Q8C2×D1111yescharacteristic
354C2×C4×Q8C2×D1111yescharacteristic
355#462—224no—
356#451—224no—
357#451—224no—
358#441—224no—
359C2×#106—111no—
360C2×#106—111no—
361C2×C4⋊C8—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×#97—111no—
373#398—221no—
374#396—221no—
375#391—21no—
376#391—21no—
377#391—111no—
378#391C2×D1111yescharacteristic
379#391C2×D1111yescharacteristic
380#389—111no—
381#389—221no—
382#388—221no—
383#380—21no—
384#380C2×D1111yescharacteristic
385C4×C22⋊C4—21no—
386C4×C22⋊C4C2×D1111yescharacteristic
387#340—111no—
388#340—111no—
389#336—111no—
390#336—111no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11#52511yescharacteristic
399C22×C11D4211yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11C2×#13711yescharacteristic
402C22×C11C2×#13711yescharacteristic
403C22×C11#57811yescharacteristic
404C22×C11#57811yescharacteristic
405C4×C11—24no—
406C4×C11—22no—
407C4×C11—41no—
408C4×C11—42no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11C2×#12111yescharacteristic
415C4×C11#53811yescharacteristic
416C4×C11#54611yescharacteristic
417C4×C11#54611yescharacteristic
418Dic11—42no—
419Dic11—42no—
420Dic11—81no—
421Dic11—81no—
422C22×Q8—22no—
423C22×Q8—22no—
424C22×Q8—21no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8—111no—
430C22×Q8—111no—
431C22×Q8C22×D1111yescharacteristic
432C22×Q8C22×D1111yescharacteristic
433C23×C4—21no—
434C23×C4C22×D1111yescharacteristic
435C2×Q16—114no—
436C2×Q16—222no—
437C2×Q16—222no—
438C2×Q16—222no—
439C2×Q16—222no—
440C2×Q16—222no—
441C2×Q16—222no—
442C2×Q16—222no—
443C2×Q16—222no—
444C2×Q16—222no—
445C2×Q16—441no—
446C2×Q16—441no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C4⋊Q8—222no—
452C4⋊Q8—441no—
453C22⋊Q8—222no—
454C22⋊Q8—222no—
455C22⋊Q8—441no—
456C22⋊Q8—441no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—41no—
460C4×Q8—41no—
461C4×Q8—222no—
462C4×Q8—441no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4C22⋊D1111yescharacteristic
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—221no—
483C2×C42C22×D1111yescharacteristic
484C2×C42C22×D1111yescharacteristic
485#106—222no—
486#106—441no—
487C4⋊C8—222no—
488#103—114no—
489#103—222no—
490#103—222no—
491#103—222no—
492#103—222no—
493#103—222no—
494#103—222no—
495#103—441no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498#97—222no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95C22⋊D1111yescharacteristic
508#95C22⋊D1111yescharacteristic
509C2×C11—42no—
510C2×C11#242411yescharacteristic
511C2×C11#311311yescharacteristic
512C2×C11#312711yescharacteristic
513C2×C11#327011yescharacteristic
514C2×C11#327011yescharacteristic
515C2×C11#327011yescharacteristic
516C2×C11#327611yescharacteristic
517C24C2×C22⋊D1111yescharacteristic
518C2×Q8—24no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—112no—
534C2×Q8—221no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—221no—
538C2×Q8—221no—
539C2×Q8—221no—
540C2×Q8—221no—
541C2×Q8—221no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8#433912yes—
546C2×Q8#433912yes—
547C2×Q8D4×D1112yes—
548C2×Q8D4×D1112yes—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572Q16—228no—
573Q16—444no—
574Q16—444no—
575Q16—444no—
576C2×C8—112no—
577C2×C8—112no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—112no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—442no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—42no—
614C42—42no—
615C42—442no—
616C11#2517311yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#6700412yes—
624C23C22×C22⋊D1111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—48no—
631Q8—41no—
632Q8—41no—
633Q8—222no—
634Q8—222no—
635Q8—441no—
636Q8—441no—
637Q8—441no—
638Q8—441no—
639Q8—441no—
640Q8—441no—
641Q8#6693714yes—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—48no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4#6699512yes—
686C2×C4C2×#433911yescharacteristic
687C2×C4C2×#433911yescharacteristic
688C2×C4C2×D4×D1111yescharacteristic
689C2×C4C2×D4×D1111yescharacteristic
690C2×C4#6703711yescharacteristic
691C2×C4#6703711yescharacteristic
692C8—222no—
693C8—222no—
694C8—441no—
695C8—441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22#1062332211yescharacteristic
704C22D4×C22⋊D1111yescharacteristic
705C22D4×C22⋊D1111yescharacteristic
706C22C2×#6699511yescharacteristic
707C22C2×#6700411yescharacteristic
708C22#1062336911yescharacteristic
709C22#1062336911yescharacteristic
710C4—24no—
711C4—22no—
712C4—41no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—442no—
720C4—442no—
721C4—881no—
722C4—881no—
723C4C2×#6693711yescharacteristic
724C4#1062302111yescharacteristic
725C4#1062302111yescharacteristic
726C4#1062302511yescharacteristic
727C2—42no—
728C2#1307215211yescharacteristic
729C2#1307874611yescharacteristic
730C2#1307891611yescharacteristic
731C2#1308018211yescharacteristic
732C2#1308018211yescharacteristic
733C2#1308018711yescharacteristic
734C2#1308026211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterQ8×C22⋊C4D11
hypocenterC11#25173
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622644C2semidirect
4. C2×#10622643C2semidirect
6. #13069997C2semidirect
9. #13069715C2semidirect
10. #13069486C2semidirect
12. #13068960C2semidirect
13. #13068957C2semidirect
14. #13068884C2semidirect
616. C11#25173semidirect

Maximal subgroups

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

subgroupindex
C2×#106226442
C2×#106228412
C2×#106226432
#130722152
#130699972
#130698122
#130697152
#130694862
#130692312
#130689602
#130689572
#130688842
Q8×C11×C22⋊C42
#2517311