Finite Group Databasebeta

← #14676552

Subgroups — #14676552

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066868C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066865C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066839C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×#66936—24no—
37C2×#66936—24no—
38C2×#66936C418yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622569—24no—
58#10622277—24no—
59D11×#95—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11D414yes—
81C22×C22⋊D11D414yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11C2×C414yescomplemented
109C22×C4×D11D414yes—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4C2×C414yescomplemented
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11C2×C414yescomplemented
125C4×C22⋊D11—232no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4C2×C414yescomplemented
134C2×(C2×D11)⋊C4D414yes—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11C2×C414yescomplemented
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4C2×C414yescomplemented
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147#66936—232no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—41no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166#13968—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11C22×C412yes—
180C24×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2411yescharacteristic
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11C22×C412yes—
192C23×D11C2×D412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11C2×D412yes—
196C23×D11#4112yes—
197C23×D11#4112yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—28no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11C22×C412yes—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
246C22×C4×C11#4112yes—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11C22⋊C4116yes—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11C22×C412yes—
296C22×Dic11C22×C412yes—
297C22×Dic11C22×C412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11#4112yes—
303C2×C4×D11—28no—
304C2×C4×D11—28no—
305C2×C4×D11—28no—
306C2×C4×D11—28no—
307C2×C4×D11—28no—
308C2×C4×D11—28no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C11×C22⋊C4—28no—
325C11×C22⋊C4—44no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—44no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—44no—
332C4⋊Dic11—28no—
333Dic11⋊C4—28no—
334Dic11⋊C4—28no—
335C4×Dic11—28no—
336C22×#123—111no—
337C22×C4×D4—111no—
338C2×#386—111no—
339C2×#381—111no—
340C22×#95—111no—
341#1441—111no—
342#1441—111no—
343#1440—111no—
344#1440—111no—
345#1436—111no—
346#1436—111no—
347C22⋊#95—111no—
348C22⋊#95—111no—
349C22⋊#95—111no—
350C22⋊#95D1111yescharacteristic, complemented
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11C2×C22⋊C414yes—
386C23×C11C23×C411yescharacteristic
387C23×C11C22×D411yescharacteristic
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C112−1+411yescharacteristic
400C23×C112−1+411yescharacteristic
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11C2×C22⋊C414yes—
430C22×D11C4×D414yes—
431C22×D11C4×D414yes—
432C22×D11#12014yes—
433C22×D11#12114yes—
434C22×D11#12114yes—
435C22×D11#12314yes—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—416no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11#12314yescomplemented
479C22⋊D11—232no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11C2×C22⋊C414yes—
529C4×D11—416no—
530C4×D11—416no—
531C4×D11—416no—
532C23×D4—111no—
533C24×C4—111no—
534C24×C4—111no—
535C24×C4—111no—
536C24×C4C2×D1111yescharacteristic
537C2×#123—118no—
538C2×#123—224no—
539C2×#123—224no—
540C2×C4×D4—224no—
541C2×C4×D4—224no—
542C2×C4×D4—224no—
543C22×C4⋊C4—111no—
544C22×C4⋊C4—111no—
545C22×C4⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4C2×D1111yescharacteristic
553C22×C22⋊C4C2×D1111yescharacteristic
554C22×C42—111no—
555#386—224no—
556#381—224no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—224no—
572C2×#95C2×D1111yescharacteristic
573C2×#95C2×D1111yescharacteristic
574C2×#95C2×D1111yescharacteristic
575C2×#95C2×D1111yescharacteristic
576C22×C11—24no—
577C22×C11—24no—
578C22×C11—24no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11C22×C22⋊C411yescharacteristic
592C22×C11C2×C4×D411yescharacteristic
593C22×C11C2×C4×D411yescharacteristic
594C22×C11C4×#4111yescharacteristic
595C22×C11C4×#4111yescharacteristic
596C22×C11#52011yescharacteristic
597C22×C11#52011yescharacteristic
598C22×C11C2×#12011yescharacteristic
599C22×C11C2×#12111yescharacteristic
600C22×C11C2×#12111yescharacteristic
601C22×C11C2×#12311yescharacteristic
602C22×C11C2×#12311yescharacteristic
603C22×C11#52511yescharacteristic
604C22×C11#52911yescharacteristic
605C22×C11#52911yescharacteristic
606C22×C11#53411yescharacteristic
607C22×C11#53611yescharacteristic
608C22×C11#53911yescharacteristic
609C22×C11#53911yescharacteristic
610C22×C11#54611yescharacteristic
611C22×C11#54611yescharacteristic
612C22×C11#54611yescharacteristic
613C22×C11#54611yescharacteristic
614C22×C11#54611yescharacteristic
615C22×C11#54611yescharacteristic
616C22×C11#54711yescharacteristic
617C22×C11#54711yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54711yescharacteristic
620C22×C11#54711yescharacteristic
621C22×C11#54711yescharacteristic
622C22×C11#55111yescharacteristic
623C22×C11#55111yescharacteristic
624C22×C11#55211yescharacteristic
625C22×C11#55211yescharacteristic
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
634C2×D11—24no—
635C2×D11—24no—
636C2×D11—24no—
637C2×D11—24no—
638C2×D11—24no—
639C2×D11—24no—
640C2×D11#38618yes—
641C4×C11—24no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11—42no—
645C4×C11—42no—
646C4×C11—81no—
647Dic11—24no—
648Dic11—42no—
649Dic11—42no—
650Dic11—42no—
651Dic11—42no—
652Dic11—42no—
653Dic11—81no—
654C25—111no—
655C25C22×D1111yescharacteristic
656C22×D4—114no—
657C22×D4—114no—
658C22×D4—114no—
659C22×D4—222no—
660C22×D4—222no—
661C22×D4—222no—
662C22×D4—222no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—41no—
669C23×C4—41no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—114no—
677C23×C4—114no—
678C23×C4—111no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—222no—
692C23×C4—222no—
693C23×C4—222no—
694C23×C4—441no—
695C23×C4—441no—
696C23×C4—441no—
697C23×C4—441no—
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C23×C4C22×D1111yescharacteristic
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704#123—2232no—
705C4×D4—2232no—
706C2×C4⋊C4—114no—
707C2×C4⋊C4—114no—
708C2×C4⋊C4—222no—
709C2×C4⋊C4—222no—
710C2×C4⋊C4—222no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—114no—
721C2×C22⋊C4—114no—
722C2×C22⋊C4—114no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—222no—
730C2×C22⋊C4—222no—
731C2×C22⋊C4—222no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—441no—
738C2×C22⋊C4C4×D1114yescomplemented
739C2×C42—222no—
740C2×C42—222no—
741C2×C42—222no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—222no—
753#95—222no—
754#95—222no—
755#95—222no—
756#95—222no—
757#95—441no—
758#95—441no—
759#95—441no—
760C2×C11—44no—
761C2×C11C2×#38611yescharacteristic
762C2×C11C4×#12311yescharacteristic
763C2×C11#232211yescharacteristic
764C2×C11#233911yescharacteristic
765C2×C11#233911yescharacteristic
766C2×C11#235911yescharacteristic
767C2×C11#235911yescharacteristic
768C2×C11#240511yescharacteristic
769C2×C11#240611yescharacteristic
770C2×C11#241911yescharacteristic
771C2×C11#241911yescharacteristic
772C2×C11#242511yescharacteristic
773C2×C11#242511yescharacteristic
774C2×C11#248611yescharacteristic
775C2×C11#253411yescharacteristic
776D11—28no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—112no—
790C24—112no—
791C24—112no—
792C24—112no—
793C24—112no—
794C24—112no—
795C24—112no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24C2×C4×D1112yes—
805C24D4×D1112yes—
806C24D4×D1112yes—
807C24C23×D1111yescharacteristic
808C2×D4—1116no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—228no—
866C22×C4—228no—
867C22×C4—228no—
868C22×C4—228no—
869C22×C4—228no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—228no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4C2×C4×D1112yes—
928C22×C4C2×C4×D1112yes—
929C22×C4#433912yes—
930C22×C4#433912yes—
931C22×C4D4×D1112yes—
932C22×C4D4×D1112yes—
933C22×C4#434112yes—
934C4⋊C4—228no—
935C4⋊C4—228no—
936C4⋊C4—228no—
937C22⋊C4—28no—
938C22⋊C4—44no—
939C22⋊C4—228no—
940C22⋊C4—228no—
941C22⋊C4—228no—
942C22⋊C4—228no—
943C22⋊C4—444no—
944C22⋊C4—444no—
945C42—228no—
946C11#1396811yescharacteristic, complemented, Sylow
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—114no—
982C23—114no—
983C23—114no—
984C23—114no—
985C23—114no—
986C23—114no—
987C23—114no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23C22⋊C4×D1114yes—
1017C23C22×C4×D1111yescharacteristic
1018C23C2×#433911yescharacteristic
1019C23C2×#433911yescharacteristic
1020C23C2×D4×D1111yescharacteristic
1021C23C2×D4×D1111yescharacteristic
1022C23C2×D4×D1111yescharacteristic
1023C23C2×D4×D1111yescharacteristic
1024C23C2×#434111yescharacteristic
1025C23#6703711yescharacteristic
1026C23#6703711yescharacteristic
1027C23#6704011yescharacteristic
1028C23#41×D1111yescharacteristic
1029C23#41×D1111yescharacteristic
1030C23#41×D1111yescharacteristic
1031C23#6704311yescharacteristic
1032D4—2232no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—416no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—114no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—4416no—
1098C2×C4—4416no—
1099C2×C4—4416no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4#6693614yescomplemented
1128C22—24no—
1129C22—24no—
1130C22—24no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—118no—
1144C22—224no—
1145C22—224no—
1146C22—224no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—224no—
1157C22—224no—
1158C22C4×#433911yescharacteristic
1159C22C2×C22⋊C4×D1111yescharacteristic
1160C22C2×#6693611yescharacteristic
1161C22#1062302111yescharacteristic
1162C22#1062302111yescharacteristic
1163C22#1062302111yescharacteristic
1164C22#1062303511yescharacteristic
1165C22#1062303811yescharacteristic
1166C22#1062303811yescharacteristic
1167C22#1062305911yescharacteristic
1168C22#1062306011yescharacteristic
1169C22C4×#434111yescharacteristic
1170C22C4×D4×D1111yescharacteristic
1171C22C4×D4×D1111yescharacteristic
1172C22#1062307711yescharacteristic
1173C22#1062307811yescharacteristic
1174C22#1062308211yescharacteristic
1175C22#1062308711yescharacteristic
1176C22#1062308811yescharacteristic
1177C22D11×#12011yescharacteristic
1178C22#1062312011yescharacteristic
1179C22#1062312211yescharacteristic
1180C22#1062312211yescharacteristic
1181C22D11×#12111yescharacteristic
1182C22D11×#12111yescharacteristic
1183C22#1062314111yescharacteristic
1184C22#1062314211yescharacteristic
1185C22#1062315911yescharacteristic
1186C22#1062316211yescharacteristic
1187C22#1062316911yescharacteristic
1188C22#1062317011yescharacteristic
1189C22D11×#12311yescharacteristic
1190C22#1062318611yescharacteristic
1191C22#1062319011yescharacteristic
1192C22#1062319111yescharacteristic
1193C4—24no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—81no—
1199C4—224no—
1200C4—442no—
1201C4—442no—
1202C4—442no—
1203C4—442no—
1204C4—442no—
1205C4—881no—
1206C2—44no—
1207C2—228no—
1208C2D11×#38611yescharacteristic
1209C2C4×#6693611yescharacteristic
1210C2#1307128311yescharacteristic
1211C2#1307144211yescharacteristic
1212C2#1307144311yescharacteristic
1213C2#1307160911yescharacteristic
1214C2#1307161111yescharacteristic
1215C2#1307194111yescharacteristic
1216C2#1307194911yescharacteristic
1217C2#1307209011yescharacteristic
1218C2#1307209211yescharacteristic
1219C2#1307216411yescharacteristic
1220C2#1307216611yescharacteristic
1221C2#1307292011yescharacteristic
1222C2#1307350411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622277C2semidirect
5. C2×D11×#95C2semidirect
6. #13066868C2semidirect
7. #13066867C2semidirect
8. #13066865C2semidirect
9. #13066863C2semidirect
10. #13066850C2semidirect
11. #13066847C2semidirect
12. #13066839C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
38. C2×#66936C4semidirect
108. C22×C4×D11C2×C4semidirect
115. C2×C11×C22⋊C4C2×C4semidirect
124. C2×C22⋊Dic11C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
137. C2×C4⋊Dic11C2×C4semidirect
143. C2×Dic11⋊C4C2×C4semidirect
350. C22⋊#95D11semidirect
478. C2×C4×C11#123semidirect
738. C2×C22⋊C4C4×D11semidirect
946. C11#13968semidirect
1127. C2×C4#66936semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
C22×C4×C22⋊D112
C2×#106225692
C2×#106222772
C2×D11×#952
#130668682
#130668672
#130668652
#130668632
#130668502
#130668472
#130668392
(C2×D11)⋊#952
C11×C22⋊#952
#1396811