Finite Group Databasebeta

← #14676895

Subgroups — #14676895

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C2×#10622569C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic, complemented
5C2×#10622277C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066885C211yesmaximal, characteristic, complemented
9#13066882C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066846C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66936—24no—
36C2×#66936—24no—
37C2×#66936C418yescomplemented
38C2×C11×#95C2211yescharacteristic
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
54#10622569—24no—
55#10622569—24no—
56C4×(C2×D11)⋊C4—24no—
57#10622281—24no—
58#10622277—24no—
59D11×#95—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
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—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C22×C4×D11C2×C414yes—
102C22×C4×D11D414yes—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4C2×C414yescomplemented
112C2×C42×C11—22no—
113C2×C42×C11—22no—
114C2×C42×C11—41no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11C2×C414yescomplemented
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4C2×C414yes—
130C2×(C2×D11)⋊C4D414yes—
131C2×(C2×D11)⋊C4D414yes—
132C2×(C2×D11)⋊C4D414yes—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—41no—
138C2×C4⋊Dic11C2×C414yescomplemented
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—41no—
144C2×Dic11⋊C4C2×C414yescomplemented
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—41no—
148#66936—232no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—22no—
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—22no—
164C11⋊#95—22no—
165#13996—111nomaximal, Sylow
166C24×C11—21no—
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×C11—21no—
180C24×C11C22×C412yes—
181C24×C11C2411yescharacteristic
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11C22×C412yes—
191C23×D11C2×D412yes—
192C23×D11C2×D412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11#4112yes—
196C23×D11#4112yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
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×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
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×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
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—
316C11×C22⋊C4—28no—
317C11×C22⋊C4—44no—
318C11×C22⋊C4—44no—
319C42×C11—44no—
320C22⋊Dic11—28no—
321C22⋊Dic11—44no—
322C22⋊Dic11—44no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—44no—
325(C2×D11)⋊C4C22⋊C4116yescomplemented
326C4⋊Dic11—28no—
327C4⋊Dic11—44no—
328Dic11⋊C4—28no—
329Dic11⋊C4—44no—
330C4×Dic11—44no—
331C22×#123—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#385—111no—
335C2×#381—111no—
336C2×C4×C22⋊C4—111no—
337C22×#95—111no—
338#1445—111no—
339#1445—111no—
340#1439—111no—
341#1439—111no—
342#1437—111no—
343#1437D1111yescharacteristic, complemented
344C4⋊#95—111no—
345C4⋊#95—111no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
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×C11C23×C411yescharacteristic
382C23×C11C22×D411yescharacteristic
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C112−1+411yescharacteristic
395C23×C112−1+411yescharacteristic
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
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×D11C2×C22⋊C414yes—
425C22×D11C4×D414yes—
426C22×D11C4×D414yes—
427C22×D11#12114yes—
428C22×D11#12114yes—
429C22×D11#12414yes—
430C22×D11#12714yes—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
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—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
472C2×C4×C11#12314yescomplemented
473C22⋊D11—416no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
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—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
523C4×D11—416no—
524C4×D11—416no—
525C4×D11—416no—
526C23×D4—111no—
527C24×C4—111no—
528C24×C4—111no—
529C24×C4—111no—
530C2×#123—118no—
531C2×#123—224no—
532C2×#123—224no—
533C22×C4⋊C4—111no—
534C22×C4⋊C4—111no—
535C22×C4⋊C4—111no—
536C22×C4⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4C2×D1111yescharacteristic
544C22×C22⋊C4C2×D1111yescharacteristic
545C22×C22⋊C4C2×D1111yescharacteristic
546C22×C42—111no—
547C22×C42C2×D1111yescharacteristic
548#386—224no—
549#386—224no—
550#385—224no—
551#381—224no—
552C4×C22⋊C4—224no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
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—224no—
567C2×#95C2×D1111yescharacteristic
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—81no—
578C22×C11—81no—
579C22×C11—81no—
580C22×C11—81no—
581C22×C11—81no—
582C22×C11—81no—
583C22×C11—81no—
584C22×C11—81no—
585C22×C11C22×C22⋊C411yescharacteristic
586C22×C11C2×C4×D411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C4×#4111yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11#52011yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11C2×#12111yescharacteristic
593C22×C11C2×#12111yescharacteristic
594C22×C11C2×#12311yescharacteristic
595C22×C11#52511yescharacteristic
596C22×C11C2×#12411yescharacteristic
597C22×C11#52911yescharacteristic
598C22×C11#52911yescharacteristic
599C22×C11C2×#12711yescharacteristic
600C22×C11#53411yescharacteristic
601C22×C11#53611yescharacteristic
602C22×C11#53911yescharacteristic
603C22×C11#53911yescharacteristic
604C22×C11#54611yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54711yescharacteristic
611C22×C11#54711yescharacteristic
612C22×C11#54711yescharacteristic
613C22×C11#54711yescharacteristic
614C22×C11#54711yescharacteristic
615C22×C11#54711yescharacteristic
616C22×C11#55111yescharacteristic
617C22×C11#55111yescharacteristic
618C22×C11#55211yescharacteristic
619C22×C11#55211yescharacteristic
620C2×D11—24no—
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
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#39018yes—
635C4×C11—24no—
636C4×C11—24no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—81no—
641Dic11—24no—
642Dic11—42no—
643Dic11—42no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648C25—111no—
649C25C22×D1111yescharacteristic
650C22×D4—114no—
651C22×D4—222no—
652C22×D4—222no—
653C22×D4—222no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—114no—
664C23×C4—114no—
665C23×C4—111no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—441no—
682C23×C4—441no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4C22×D1111yescharacteristic
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691#123—2232no—
692C2×C4⋊C4—114no—
693C2×C4⋊C4—114no—
694C2×C4⋊C4—222no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C4⋊C4—222no—
701C2×C4⋊C4—222no—
702C2×C4⋊C4—441no—
703C2×C4⋊C4—441no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—114no—
713C2×C22⋊C4—114no—
714C2×C22⋊C4—114no—
715C2×C22⋊C4—114no—
716C2×C22⋊C4—114no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4C4×D1114yescomplemented
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—441no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—222no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—222no—
753C2×C11—82no—
754C2×C11C2×#39011yescharacteristic
755C2×C11C4×#12311yescharacteristic
756C2×C11#232211yescharacteristic
757C2×C11#233911yescharacteristic
758C2×C11#233911yescharacteristic
759C2×C11#235911yescharacteristic
760C2×C11#235911yescharacteristic
761C2×C11#241211yescharacteristic
762C2×C11#241311yescharacteristic
763C2×C11#242511yescharacteristic
764C2×C11#242511yescharacteristic
765C2×C11#248811yescharacteristic
766C2×C11#248811yescharacteristic
767C2×C11#250111yescharacteristic
768C2×C11#253911yescharacteristic
769D11—28no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—112no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24C2×C4×D1112yes—
800C24C23×D1111yescharacteristic
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C2×D4—444no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
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—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—228no—
850C22×C4—228no—
851C22×C4—228no—
852C22×C4—228no—
853C22×C4—228no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
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—228no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—444no—
897C22×C4—444no—
898C22×C4—444no—
899C22×C4—444no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4C2×C4×D1112yes—
912C22×C4C2×C4×D1112yes—
913C22×C4#433912yes—
914C22×C4#433912yes—
915C22×C4D4×D1112yes—
916C22×C4D4×D1112yes—
917C22×C4D4×D1112yes—
918C22×C4D4×D1112yes—
919C22×C4#434112yes—
920C4⋊C4—228no—
921C4⋊C4—228no—
922C4⋊C4—444no—
923C4⋊C4—444no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—1116no—
928C22⋊C4—228no—
929C22⋊C4—228no—
930C22⋊C4—444no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C42—44no—
934C42—444no—
935C11#1399611yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—114no—
972C23—114no—
973C23—114no—
974C23—114no—
975C23—114no—
976C23—114no—
977C23—114no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
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—
1006C23C22×C4×D1111yescharacteristic
1007C23C2×#433911yescharacteristic
1008C23C2×#433911yescharacteristic
1009C23C2×D4×D1111yescharacteristic
1010C23C2×D4×D1111yescharacteristic
1011C23C2×D4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×#434111yescharacteristic
1014C23#6703711yescharacteristic
1015C23#41×D1111yescharacteristic
1016C23#41×D1111yescharacteristic
1017C23#41×D1111yescharacteristic
1018C23#6704211yescharacteristic
1019C23#6704311yescharacteristic
1020C23#6704311yescharacteristic
1021D4—4416no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
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—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
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—114no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
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—4416no—
1085C2×C4—4416no—
1086C2×C4—4416no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
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×C4C22⋊C4×D1114yes—
1115C2×C4#6693614yescomplemented
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—118no—
1132C22—224no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—224no—
1145C22—224no—
1146C22C4×#433911yescharacteristic
1147C22C2×C22⋊C4×D1111yescharacteristic
1148C22C2×#6693611yescharacteristic
1149C22#1062302111yescharacteristic
1150C22#1062305411yescharacteristic
1151C22#1062305911yescharacteristic
1152C22#1062306011yescharacteristic
1153C22C4×#434111yescharacteristic
1154C22C4×D4×D1111yescharacteristic
1155C22C4×D4×D1111yescharacteristic
1156C22#1062307711yescharacteristic
1157C22#1062307811yescharacteristic
1158C22#1062308111yescharacteristic
1159C22#1062308111yescharacteristic
1160C22#1062308211yescharacteristic
1161C22#1062308211yescharacteristic
1162C22#1062308211yescharacteristic
1163C22#1062308711yescharacteristic
1164C22#1062308811yescharacteristic
1165C22#1062312211yescharacteristic
1166C22D11×#12111yescharacteristic
1167C22D11×#12111yescharacteristic
1168C22#1062313611yescharacteristic
1169C22#1062314111yescharacteristic
1170C22#1062314211yescharacteristic
1171C22#1062314211yescharacteristic
1172C22#1062318611yescharacteristic
1173C22#1062318911yescharacteristic
1174C22#1062319111yescharacteristic
1175C22D11×#12411yescharacteristic
1176C22#1062320611yescharacteristic
1177C22#1062320711yescharacteristic
1178C22#1062323811yescharacteristic
1179C22#1062323911yescharacteristic
1180C22D11×#12711yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—224no—
1188C4—442no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—442no—
1193C4—881no—
1194C2—82no—
1195C2—228no—
1196C2D11×#39011yescharacteristic
1197C2C4×#6693611yescharacteristic
1198C2#1307128611yescharacteristic
1199C2#1307144211yescharacteristic
1200C2#1307144711yescharacteristic
1201C2#1307160711yescharacteristic
1202C2#1307160911yescharacteristic
1203C2#1307201111yescharacteristic
1204C2#1307202211yescharacteristic
1205C2#1307216611yescharacteristic
1206C2#1307217211yescharacteristic
1207C2#1307294111yescharacteristic
1208C2#1307294711yescharacteristic
1209C2#1307308611yescharacteristic
1210C2#1307354511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#13996
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
4. C2×#10622281C2semidirect
5. C2×#10622277C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. C2×D11×#95C2semidirect
8. #13066885C2semidirect
9. #13066882C2semidirect
10. #13066861C2semidirect
11. #13066859C2semidirect
12. #13066853C2semidirect
13. #13066846C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1437C2semidirect
37. C2×#66936C4semidirect
111. C2×C11×C22⋊C4C2×C4semidirect
123. C2×C22⋊Dic11C2×C4semidirect
138. C2×C4⋊Dic11C2×C4semidirect
144. C2×Dic11⋊C4C2×C4semidirect
325. (C2×D11)⋊C4C22⋊C4semidirect
343. #1437D11semidirect
472. C2×C4×C11#123semidirect
730. C2×C22⋊C4C4×D11semidirect
935. C11#13996semidirect
1115. 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
C2×#106225692
C2×#106222812
C2×#106222772
C2×C4×(C2×D11)⋊C42
C2×D11×#952
#130668852
#130668822
#130668612
#130668592
#130668532
#130668462
Dic11⋊#952
C11×#14372
#1399611