Finite Group Databasebeta

← #14770170

Subgroups — #14770170

Order 2816.

1186 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
1C2×#10623061C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3#13071560C211yesmaximal, characteristic, complemented
4#13069583C211yesmaximal, characteristic, complemented
5#13069570C211yesmaximal, characteristic, complemented
6#13069053C211yesmaximal, characteristic, complemented
7#13069042C211yesmaximal, characteristic, complemented
8#13068937C211yesmaximal, characteristic, complemented
9#13068936C211yesmaximal, characteristic, complemented
10#13068701C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068440C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22#10623061—24no—
23#10623061C418yescomplemented
24C2×#66948C2211yescharacteristic
25C2×#66946C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic
28C2×#66943C2211yescharacteristic
29C2×#66937—21no—
30C2×#66936—21no—
31C2×#66929—21no—
32C2×C4×D44—21no—
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45#10622570—21no—
46#10622558—21no—
47#10622343—24no—
48#10622282—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11D411yescharacteristic
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117—22no—
73C11×#117C2×C414yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83#66983—22no—
84#66983C2×C414yes—
85C4×C22⋊D11C2×C414yes—
86C4×C22⋊D11D414yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93#66979—22no—
94#66979—41no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8—22no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—41no—
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×#4313—22no—
114C2×#4313—22no—
115C2×#4313—41no—
116#66948—22no—
117#66948C2×C414yes—
118#66946—22no—
119#66946C2×C414yes—
120#66945—22no—
121#66945—41no—
122C4⋊C4×D11—22no—
123C4⋊C4×D11C2×C414yes—
124#66943—22no—
125#66943C2×C414yes—
126#66937—28no—
127#66936—28no—
128#66929—28no—
129C4×D44—28no—
130C11×C22⋊C8—22no—
131C11×#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66885—22no—
135#66885—41no—
136(C2×D11)⋊C8—22no—
137#66879—22no—
138Dic11⋊C8—22no—
139#66873—22no—
140#66873—41no—
141#22498—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C23×D11C2×D411yescharacteristic
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—81no—
161C2×C22⋊D11—81no—
162C2×C22⋊D11C22⋊C414yes—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×D44—24no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—42no—
176C2×D44—42no—
177C2×D44C22×C412yes—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—81no—
185C2×C4×D11—81no—
186C2×C4×D11—81no—
187C2×C4×D11—81no—
188C2×C4×D11C22×C412yes—
189C2×C4×D11C2×D412yes—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4C22×C412yes—
203C11×C4⋊C4C22×C412yes—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—81no—
206C42×C11—24no—
207C22⋊Dic11—42no—
208C22⋊Dic11C22⋊C414yes—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—42no—
213(C2×D11)⋊C4—81no—
214(C2×D11)⋊C4C22⋊C414yes—
215C4⋊Dic11—24no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11C22×C412yes—
221C4⋊Dic11#4112yes—
222Dic11⋊C4—24no—
223Dic11⋊C4—24no—
224Dic11⋊C4—42no—
225Dic11⋊C4—81no—
226Dic11⋊C4C22⋊C414yes—
227C4×Dic11—42no—
228C4×Dic11—42no—
229C4×Dic11—42no—
230C4×Dic11C22×C412yes—
231C4×Dic11C2×D412yes—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—44no—
238C2×C11⋊C8#4112yes—
239#4313—44no—
240C2×#553—111no—
241C2×#435—111no—
242#2354—111no—
243#1992—111no—
244#1989—111no—
245#1895—111no—
246#1893—111no—
247#1875—111no—
248#1875—111no—
249#1825D1111yescharacteristic, complemented
250#1823—111no—
251#1802—111no—
252#1762—111no—
253#1736—111no—
254#1735—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11C2×C22⋊C412yes—
262C23×C11C22×D411yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11C2×C22⋊C412yes—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11C2×C22⋊C412yes—
296C2×C4×C11C23×C411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11H(5,𝔽2)11yescharacteristic
301C2×C4×C112−1+411yescharacteristic
302C22⋊D11—44no—
303C22⋊D11—84no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11C2×C22⋊C412yes—
320C2×Dic11C2×C22⋊C412yes—
321C2×Dic11C2×C22⋊C412yes—
322D44—22no—
323D44—22no—
324D44—48no—
325D44—41no—
326D44—41no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—22no—
330C4×D11—22no—
331C4×D11—84no—
332C4×D11—84no—
333C8×C11—41no—
334C8×C11—41no—
335C11⋊C8—22no—
336C11⋊C8—41no—
337C22×M16—111no—
338C23×C8—111no—
339#553—118no—
340#553—224no—
341C2×#126—221no—
342C2×#125—111no—
343C2×#123—221no—
344C2×#121—111no—
345C2×#121—111no—
346C2×#121—221no—
347C2×C4×D4—111no—
348C2×C4×D4—111no—
349C2×C4×D4—221no—
350C2×#117—111no—
351C2×#117—111no—
352C2×#117C2×D1111yescharacteristic
353C22×C4⋊C4—111no—
354#435—224no—
355C2×C4⋊C8—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8C2×D1111yescharacteristic
362C2×#97—111no—
363#390—221no—
364#388—221no—
365#388—221no—
366#384—111no—
367#380—111no—
368#380C2×D1111yescharacteristic
369C4×C4⋊C4—111no—
370C4×C4⋊C4—221no—
371#340—111no—
372#340—111no—
373#340—111no—
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
378#340—111no—
379#340C2×D1111yescharacteristic
380#340C2×D1111yescharacteristic
381#340C2×D1111yescharacteristic
382#340C2×D1111yescharacteristic
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11C22×C22⋊C411yescharacteristic
391C22×C11#54611yescharacteristic
392C22×C11#54711yescharacteristic
393C22×C11#57511yescharacteristic
394C22×C11#57511yescharacteristic
395C22×C11#57611yescharacteristic
396C22×C11#57711yescharacteristic
397C2×D11—22no—
398C2×D11—22no—
399C2×D11—22no—
400C2×D11—41no—
401C2×D11—41no—
402C2×D11—41no—
403C2×D11—41no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C2×D11—81no—
411C4×C11—22no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—81no—
415C4×C11—81no—
416C4×C11C4×#4111yescharacteristic
417C4×C11#52011yescharacteristic
418C4×C11#54611yescharacteristic
419C4×C11#54711yescharacteristic
420Dic11—22no—
421Dic11—22no—
422Dic11—22no—
423Dic11—42no—
424Dic11—42no—
425Dic11—81no—
426C22×D4—111no—
427C22×D4—111no—
428C22×D4—221no—
429C22×D4—221no—
430C23×C4—111no—
431C23×C4—221no—
432C23×C4—221no—
433C23×C4C22×D1111yescharacteristic
434C2×M16—222no—
435C2×M16—222no—
436C2×M16—441no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—222no—
440C22×C8—222no—
441C22×C8—441no—
442C22×C8C22×D1111yescharacteristic
443C22×C8C22×D1111yescharacteristic
444#126—228no—
445#125—114no—
446#125—222no—
447#123—228no—
448#121—114no—
449#121—114no—
450#121—228no—
451#121—222no—
452#121—222no—
453C4×D4—114no—
454C4×D4—114no—
455C4×D4—114no—
456C4×D4—228no—
457C4×D4—222no—
458#117—22no—
459#117—222no—
460#117—222no—
461#117—441no—
462#117—441no—
463#117C4×D1114yes—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C42—21no—
490C2×C42—111no—
491C2×C42—221no—
492C2×C42—221no—
493C2×C42—221no—
494C4⋊C8—222no—
495#102—222no—
496#102—222no—
497#102—441no—
498#102—441no—
499C22⋊C8—22no—
500C22⋊C8—222no—
501#97—222no—
502#95—21no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11#233911yescharacteristic
507C2×C11#289611yescharacteristic
508C2×C11#289711yescharacteristic
509C2×C11#330711yescharacteristic
510C2×C11#330911yescharacteristic
511C2×C11#334711yescharacteristic
512C2×C11#335011yescharacteristic
513D11—42no—
514D11—82no—
515C24—111no—
516C24—221no—
517C24D4×D1111yescharacteristic
518C2×D4—114no—
519C2×D4—112no—
520C2×D4—224no—
521C2×D4—224no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4—442no—
528C2×D4—442no—
529C2×D4—441no—
530C2×D4—441no—
531C2×D4—881no—
532C2×D4—881no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—111no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—224no—
547C22×C4—224no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—881no—
556C22×C4—881no—
557C22×C4—881no—
558C22×C4—881no—
559C22×C4C2×C4×D1112yes—
560C22×C4D4×D1111yescharacteristic
561C22×C4D4×D1112yes—
562C22×C4C23×D1111yescharacteristic
563M16—444no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—112no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—444no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—114no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4—224no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—442no—
594C4⋊C4—881no—
595C4⋊C4C2×C4×D1112yes—
596C4⋊C4C2×C4×D1112yes—
597C22⋊C4—24no—
598C22⋊C4—81no—
599C22⋊C4—114no—
600C22⋊C4—114no—
601C22⋊C4—224no—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C22⋊C4—442no—
605C22⋊C4—442no—
606C22⋊C4—881no—
607C42—24no—
608C42—112no—
609C42—112no—
610C42—442no—
611C42—442no—
612C42—442no—
613C11#2249811yescharacteristic, complemented, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—112no—
621C23—221no—
622C23—221no—
623C23—221no—
624C23—221no—
625C23—221no—
626C23—221no—
627C23—222no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23C22⋊C4×D1112yes—
635C23C2×D4×D1111yescharacteristic
636D4—222no—
637D4—222no—
638D4—448no—
639D4—444no—
640D4—441no—
641D4—441no—
642D4—884no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—112no—
662C2×C4—112no—
663C2×C4—112no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—884no—
684C2×C4—884no—
685C2×C4C22⋊C4×D1112yes—
686C2×C4C22×C4×D1111yescharacteristic
687C2×C4C2×D4×D1111yescharacteristic
688C2×C4#41×D1111yescharacteristic
689C2×C4#41×D1111yescharacteristic
690C2×C4#6704211yescharacteristic
691C2×C4#6704311yescharacteristic
692C8—41no—
693C8—41no—
694C8—222no—
695C8—441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—222no—
704C22—222no—
705C22—222no—
706C22—441no—
707C22—441no—
708C22—441no—
709C22—441no—
710C22—442no—
711C22—442no—
712C22—442no—
713C22—881no—
714C22—881no—
715C22—881no—
716C22—881no—
717C22C2×C22⋊C4×D1111yescharacteristic
718C22#1062318511yescharacteristic
719C22#1062318611yescharacteristic
720C22#1062329911yescharacteristic
721C22#1062329911yescharacteristic
722C22#1062330511yescharacteristic
723C22#1062330911yescharacteristic
724C4—22no—
725C4—42no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—222no—
730C4—222no—
731C4—222no—
732C4—442no—
733C4—442no—
734C4—881no—
735C4#1062305311yescharacteristic
736C4#1062305411yescharacteristic
737C4#1062318511yescharacteristic
738C4#1062318611yescharacteristic
739C2—42no—
740C2—442no—
741C2—882no—
742C2#1307144011yescharacteristic
743C2#1307713111yescharacteristic
744C2#1307714011yescharacteristic
745C2#1308059011yescharacteristic
746C2#1308062011yescharacteristic
747C2#1308111411yescharacteristic
748C2#1308115911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC2×#10623061C2
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#22498
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
2. C2×#10622343C2semidirect
3. #13071560C2semidirect
4. #13069583C2semidirect
5. #13069570C2semidirect
6. #13069053C2semidirect
7. #13069042C2semidirect
8. #13068937C2semidirect
9. #13068936C2semidirect
10. #13068701C2semidirect
11. #13068615C2semidirect
12. #13068440C2semidirect
13. #13068334C2semidirect
14. #13068332C2semidirect
15. C11×#1825C2semidirect
23. #10623061C4semidirect
249. #1825D11semidirect
613. C11#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#106230612
C2×#106223432
#130715602
#130695832
#130695702
#130690532
#130690422
#130689372
#130689362
#130687012
#130686152
#130684402
#130683342
#130683322
C11×#18252
#2249811