Finite Group Databasebeta

← #14685191

Subgroups — #14685191

Order 2816.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3C2×#10622269C211yesmaximal, characteristic, complemented
4C2×#10622592C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic
6C2×#10622602C211yesmaximal, characteristic
7#13066880C211yesmaximal, characteristic, complemented
8#13066879C211yesmaximal, characteristic, complemented
9#13066879C211yesmaximal, characteristic, complemented
10#13066868C211yesmaximal, characteristic, complemented
11#13066867C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1444C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C2×#66949—24no—
36C2×#66949—24no—
37C2×#66949—24no—
38C2×C4⋊C4×D11—24no—
39C2×C4⋊C4×D11—24no—
40C2×C4⋊C4×D11—24no—
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#10622602—24no—
58#10622592—24no—
59#10622281—24no—
60#10622269—24no—
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
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—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11D414yes—
96C22×C4×D11Q814yescomplemented
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22—41no—
103C22×Dic22—41no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—41no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4D414yes—
122C2×(C2×D11)⋊C4D414yes—
123C2×(C2×D11)⋊C4Q814yescomplemented
124C2×(C2×D11)⋊C4Q814yescomplemented
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—41no—
130C2×C4⋊Dic11D414yes—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—41no—
147C2×Dic11⋊C4—41no—
148C2×Dic11⋊C4D414yes—
149#66949—232no—
150C4⋊C4×D11—232no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—22no—
154C11×#95—41no—
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—
165C11⋊#95—22no—
166C11⋊#95—41no—
167#14720—111nomaximal, Sylow
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11C2×D412yes—
178C23×D11C2×D412yes—
179C23×D11C2×D412yes—
180C23×D11C2×Q812yes—
181C23×D11C2×Q812yes—
182C23×D11C2×Q812yes—
183C23×D11#4112yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
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×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×Q812yes—
230C22×C4×C11C2×Q812yes—
231C22×C4×C11C2×Q812yes—
232C22×C4×C11#4112yes—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
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×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×D412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11C2×Q812yes—
279C22×Dic11C2×Q812yes—
280C22×Dic11C2×Q812yes—
281C22×Dic11#4112yes—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—28no—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—28no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×Dic22—28no—
304C2×Dic22—44no—
305C2×Dic22—44no—
306C2×Dic22—44no—
307C2×Dic22—44no—
308C2×Dic22—44no—
309C2×Dic22—44no—
310C11×C4⋊C4—28no—
311C11×C4⋊C4—28no—
312C11×C4⋊C4—44no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317C4⋊Dic11—28no—
318C4⋊Dic11—44no—
319Dic11⋊C4—28no—
320Dic11⋊C4—28no—
321Dic11⋊C4—28no—
322Dic11⋊C4—28no—
323Dic11⋊C4—44no—
324Dic11⋊C4—44no—
325C22×C22⋊Q8—111no—
326C23×C4⋊C4—111no—
327C2×#395—111no—
328C2×#395—111no—
329C2×#385—111no—
330C2×#385—111no—
331#1444—111no—
332#1444—111no—
333#1444—111no—
334#1444D1111yescharacteristic, complemented
335#1441—111no—
336#1441—111no—
337C22⋊#95—111no—
338C22⋊#95—111no—
339C22⋊#95—111no—
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C23×C11C22×Q811yescharacteristic
346C23×C11C22×Q811yescharacteristic
347C23×C11C22×Q811yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C112−1+411yescharacteristic
354C23×C112−1+411yescharacteristic
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11#12014yes—
384C22×D11C22⋊Q814yes—
385C22×D11C22⋊Q814yes—
386C22×D11C22⋊Q814yes—
387C22×D11C4⋊Q814yes—
388C22×D11C4⋊Q814yes—
389C22×D11C4⋊Q814yes—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11C22⋊Q814yescomplemented
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11#12014yes—
487C2×Dic11C22⋊Q814yescomplemented
488C4×D11—232no—
489C4×D11—416no—
490C4×D11—416no—
491Dic22—416no—
492C23×Q8—111no—
493C24×C4—111no—
494C24×C4—111no—
495C24×C4—111no—
496C2×C22⋊Q8—224no—
497C2×C22⋊Q8—224no—
498C2×C22⋊Q8—224no—
499C22×C4⋊C4—111no—
500C22×C4⋊C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—111no—
505C22×C4⋊C4—111no—
506C22×C4⋊C4—111no—
507C22×C4⋊C4—224no—
508C22×C4⋊C4—224no—
509C22×C4⋊C4—224no—
510C22×C4⋊C4C2×D1111yescharacteristic
511C22×C4⋊C4C2×D1111yescharacteristic
512C22×C4⋊C4C2×D1111yescharacteristic
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517#395—224no—
518#395—224no—
519#385—224no—
520#385—224no—
521C2×#95—111no—
522C2×#95—111no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95C2×D1111yescharacteristic
534C2×#95C2×D1111yescharacteristic
535C2×#95C2×D1111yescharacteristic
536C2×#95C2×D1111yescharacteristic
537C22×C11C2×#12011yescharacteristic
538C22×C11C2×#12011yescharacteristic
539C22×C11C2×C22⋊Q811yescharacteristic
540C22×C11C2×C22⋊Q811yescharacteristic
541C22×C11C2×C22⋊Q811yescharacteristic
542C22×C11C2×C22⋊Q811yescharacteristic
543C22×C11C2×C22⋊Q811yescharacteristic
544C22×C11#52511yescharacteristic
545C22×C11#52511yescharacteristic
546C22×C11#52511yescharacteristic
547C22×C11C2×C4⋊Q811yescharacteristic
548C22×C11C2×C4⋊Q811yescharacteristic
549C22×C11C2×C4⋊Q811yescharacteristic
550C22×C11#53411yescharacteristic
551C22×C11#53611yescharacteristic
552C22×C11#53911yescharacteristic
553C22×C11#53911yescharacteristic
554C22×C11#54411yescharacteristic
555C22×C11#54411yescharacteristic
556C22×C11D4211yescharacteristic
557C22×C11D4211yescharacteristic
558C22×C11D4211yescharacteristic
559C22×C11D4211yescharacteristic
560C22×C11#54711yescharacteristic
561C22×C11#54711yescharacteristic
562C22×C11#54711yescharacteristic
563C22×C11#54711yescharacteristic
564C22×C11D4×Q811yescharacteristic
565C22×C11D4×Q811yescharacteristic
566C22×C11D4×Q811yescharacteristic
567C22×C11D4×Q811yescharacteristic
568C22×C11#55411yescharacteristic
569C22×C11#55411yescharacteristic
570C22×C11#55411yescharacteristic
571C22×C11#55411yescharacteristic
572C2×D11—24no—
573C2×D11—24no—
574C2×D11—24no—
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—24no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—24no—
586C2×D11#39518yescomplemented
587C4×C11—24no—
588C4×C11—42no—
589C4×C11—42no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—42no—
594Dic11—24no—
595Dic11—24no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601C25—111no—
602C22×Q8—222no—
603C22×Q8—222no—
604C22×Q8—222no—
605C22×Q8—222no—
606C22×Q8—222no—
607C22×Q8—441no—
608C22×Q8—441no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—114no—
617C23×C4—114no—
618C23×C4—222no—
619C23×C4—222no—
620C23×C4—222no—
621C23×C4—222no—
622C23×C4—222no—
623C23×C4—222no—
624C23×C4—222no—
625C23×C4—222no—
626C23×C4—222no—
627C23×C4—222no—
628C23×C4—222no—
629C23×C4—222no—
630C23×C4—222no—
631C23×C4—222no—
632C23×C4—222no—
633C23×C4—441no—
634C23×C4—441no—
635C23×C4—441no—
636C23×C4—441no—
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639C23×C4C22×D1111yescharacteristic
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C22⋊Q8—2232no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—114no—
655C2×C4⋊C4—114no—
656C2×C4⋊C4—2232no—
657C2×C4⋊C4—222no—
658C2×C4⋊C4—222no—
659C2×C4⋊C4—222no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—222no—
667C2×C4⋊C4—222no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—441no—
677C2×C4⋊C4—441no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691#95—22no—
692#95—22no—
693#95—22no—
694#95—41no—
695#95—222no—
696#95—222no—
697#95—222no—
698#95—222no—
699#95—222no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—441no—
707C2×C11C2×#39511yescharacteristic
708C2×C11#240311yescharacteristic
709C2×C11#240611yescharacteristic
710C2×C11#243411yescharacteristic
711C2×C11#244011yescharacteristic
712C2×C11#244011yescharacteristic
713C2×C11#244011yescharacteristic
714C2×C11#244011yescharacteristic
715C2×C11#244911yescharacteristic
716C2×C11#244911yescharacteristic
717C2×C11#244911yescharacteristic
718C2×C11#244911yescharacteristic
719C2×C11#258311yescharacteristic
720C2×C11#262711yescharacteristic
721C2×C11#284811yescharacteristic
722D11—28no—
723C24—112no—
724C24—112no—
725C24—112no—
726C24—112no—
727C24—112no—
728C24—112no—
729C24—112no—
730C24—221no—
731C24—221no—
732C24—221no—
733C24—221no—
734C24—221no—
735C24—221no—
736C24—221no—
737C24—221no—
738C24C23×D1111yescharacteristic
739C2×Q8—228no—
740C2×Q8—444no—
741C2×Q8—444no—
742C2×Q8—444no—
743C2×Q8—444no—
744C2×Q8—444no—
745C2×Q8—444no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—112no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—228no—
798C22×C4—228no—
799C22×C4—228no—
800C22×C4—228no—
801C22×C4—228no—
802C22×C4—228no—
803C22×C4—228no—
804C22×C4—228no—
805C22×C4—228no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—228no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—444no—
846C22×C4—444no—
847C22×C4—444no—
848C22×C4—444no—
849C22×C4—444no—
850C22×C4—444no—
851C22×C4—444no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4#433912yes—
857C22×C4D4×D1112yes—
858C22×C4D4×D1112yes—
859C22×C4D4×D1112yes—
860C22×C4D4×D1112yes—
861C22×C4D4×D1112yes—
862C22×C4Q8×D1112yes—
863C22×C4Q8×D1112yes—
864C22×C4Q8×D1112yes—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—44no—
868C4⋊C4—228no—
869C4⋊C4—228no—
870C4⋊C4—228no—
871C4⋊C4—228no—
872C4⋊C4—228no—
873C4⋊C4—444no—
874C4⋊C4—444no—
875C4⋊C4—444no—
876C22⋊C4—228no—
877C22⋊C4—228no—
878C22⋊C4—228no—
879C22⋊C4—228no—
880C11#1472011yescharacteristic, complemented, Sylow
881C23—114no—
882C23—114no—
883C23—114no—
884C23—114no—
885C23—114no—
886C23—114no—
887C23—114no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23—222no—
894C23—222no—
895C23—222no—
896C23—222no—
897C23—222no—
898C23—222no—
899C23—222no—
900C23—222no—
901C23—222no—
902C23—222no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23C2×#433911yescharacteristic
917C23C2×D4×D1111yescharacteristic
918C23C2×D4×D1111yescharacteristic
919C23C2×D4×D1111yescharacteristic
920C23C2×D4×D1111yescharacteristic
921C23C2×D4×D1111yescharacteristic
922C23#6703711yescharacteristic
923C23C2×Q8×D1111yescharacteristic
924C23C2×Q8×D1111yescharacteristic
925C23C2×Q8×D1111yescharacteristic
926C23#6704011yescharacteristic
927C23#41×D1111yescharacteristic
928C23#41×D1111yescharacteristic
929C23#6704211yescharacteristic
930C23#6704311yescharacteristic
931Q8—4416no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—114no—
981C2×C4—114no—
982C2×C4—2232no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—4416no—
1011C2×C4—4416no—
1012C2×C4—441no—
1013C2×C4—441no—
1014C2×C4—441no—
1015C2×C4—441no—
1016C2×C4—441no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4#6694914yescomplemented
1033C22—118no—
1034C22—224no—
1035C22—224no—
1036C22—224no—
1037C22—224no—
1038C22—224no—
1039C22—224no—
1040C22—224no—
1041C22—224no—
1042C22—224no—
1043C22—224no—
1044C22—224no—
1045C22—224no—
1046C22—224no—
1047C22—224no—
1048C22#1062303811yescharacteristic
1049C22C2×#6694911yescharacteristic
1050C22#1062304211yescharacteristic
1051C22#1062307811yescharacteristic
1052C22#1062307811yescharacteristic
1053C22#1062308211yescharacteristic
1054C22#1062311011yescharacteristic
1055C22D11×#12011yescharacteristic
1056C22D11×#12011yescharacteristic
1057C22#1062312111yescharacteristic
1058C22#1062313611yescharacteristic
1059C22#1062314011yescharacteristic
1060C22#1062314011yescharacteristic
1061C22D11×C22⋊Q811yescharacteristic
1062C22D11×C22⋊Q811yescharacteristic
1063C22D11×C22⋊Q811yescharacteristic
1064C22D11×C22⋊Q811yescharacteristic
1065C22#1062315911yescharacteristic
1066C22#1062316211yescharacteristic
1067C22#1062316311yescharacteristic
1068C22#1062316311yescharacteristic
1069C22#1062316711yescharacteristic
1070C22#1062318611yescharacteristic
1071C22#1062318711yescharacteristic
1072C22#1062319111yescharacteristic
1073C22#1062322011yescharacteristic
1074C22#1062322111yescharacteristic
1075C22#1062322311yescharacteristic
1076C22#1062324811yescharacteristic
1077C22D11×C4⋊Q811yescharacteristic
1078C22D11×C4⋊Q811yescharacteristic
1079C22D11×C4⋊Q811yescharacteristic
1080C22#1062325811yescharacteristic
1081C22#1062325811yescharacteristic
1082C22#1062326011yescharacteristic
1083C4—24no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—42no—
1090C4—224no—
1091C4—224no—
1092C4—442no—
1093C4—442no—
1094C4—442no—
1095C4—442no—
1096C4—442no—
1097C2—228no—
1098C2D11×#39511yescharacteristic
1099C2#1307192511yescharacteristic
1100C2#1307194911yescharacteristic
1101C2#1307225511yescharacteristic
1102C2#1307231111yescharacteristic
1103C2#1307231311yescharacteristic
1104C2#1307232011yescharacteristic
1105C2#1307232111yescharacteristic
1106C2#1307242011yescharacteristic
1107C2#1307242411yescharacteristic
1108C2#1307242811yescharacteristic
1109C2#1307243211yescharacteristic
1110C2#1307399411yescharacteristic
1111C2#1307443411yescharacteristic
1112C2#1307690211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1444C2
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11#14720
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. C2×#10622269C2semidirect
4. C2×#10622592C2semidirect
7. #13066880C2semidirect
8. #13066879C2semidirect
9. #13066879C2semidirect
10. #13066868C2semidirect
11. #13066867C2semidirect
15. C11×#1444C2semidirect
96. C22×C4×D11Q8semidirect
123. C2×(C2×D11)⋊C4Q8semidirect
124. C2×(C2×D11)⋊C4Q8semidirect
334. #1444D11semidirect
438. C2×C4×C11C22⋊Q8semidirect
487. C2×Dic11C22⋊Q8semidirect
586. C2×D11#395semidirect
880. C11#14720semidirect
1032. C2×C4#66949semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C4⋊C4×D112
C2×#106222692
C2×#106225922
C2×#106222812
C2×#106226022
#130668802
#130668792
#130668682
#130668672
(C2×D11)⋊#952
C11×#14442
#1472011