Finite Group Databasebeta

← #14677474

Subgroups — #14677474

Order 2816.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic
5C2×#10622602C211yesmaximal, characteristic
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066880C211yesmaximal, characteristic, complemented
8#13066879C211yesmaximal, characteristic, complemented
9#13066869C211yesmaximal, characteristic, complemented
10#13066867C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C2×C11×#389C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C4⋊C4×D11—24no—
36C2×C4⋊C4×D11—24no—
37C2×C4⋊C4×D11—24no—
38C11×#389—24no—
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
55#10622602—24no—
56#10622602—24no—
57#10622602C418yescomplemented
58#10622585—24no—
59C4×(C2×D11)⋊C4—24no—
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—22no—
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—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11C2×C414yes—
95C22×C4×D11D414yes—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—41no—
106C2×C11×C4⋊C4C2×C414yescomplemented
107C2×C11×C4⋊C4D414yes—
108C2×C42×C11—22no—
109C2×C42×C11—22no—
110C2×C42×C11—41no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yes—
119C2×(C2×D11)⋊C4C2×C414yes—
120C2×(C2×D11)⋊C4D414yes—
121C2×(C2×D11)⋊C4Q814yes—
122C2×(C2×D11)⋊C4Q814yes—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×Dic11⋊C4—41no—
139C2×Dic11⋊C4C2×C414yescomplemented
140C2×Dic11⋊C4D414yes—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—41no—
144C4⋊C4×D11—232no—
145C11×#95—22no—
146C11×#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
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—41no—
158C11⋊#95—41no—
159C11⋊#95C2×C414yescomplemented
160C11⋊#95C2×C414yescomplemented
161#14043—111nomaximal, Sylow
162C24×C11C2411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11C22×C412yes—
172C23×D11C2×D412yes—
173C23×D11C2×D412yes—
174C23×D11C2×Q812yes—
175C23×D11C2×Q812yes—
176C23×D11#4112yes—
177C23×D11#4112yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
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×C11C22×C412yes—
216C22×C4×C11C22×C412yes—
217C22×C4×C11C22×C412yes—
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×Q812yes—
225C22×C4×C11C2×Q812yes—
226C22×C4×C11#4112yes—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
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×Dic11C22×C412yes—
267C22×Dic11C22×C412yes—
268C22×Dic11C22×C412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11C2×D412yes—
273C22×Dic11C2×Q812yes—
274C22×Dic11C2×Q812yes—
275C22×Dic11#4112yes—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—44no—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C2×C4×D11—44no—
297C11×C4⋊C4—28no—
298C11×C4⋊C4—28no—
299C11×C4⋊C4—44no—
300C11×C4⋊C4—44no—
301C42×C11—44no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4C4⋊C4116yescomplemented
306C4⋊Dic11—28no—
307Dic11⋊C4—28no—
308Dic11⋊C4—28no—
309Dic11⋊C4—28no—
310Dic11⋊C4—44no—
311Dic11⋊C4—44no—
312C4×Dic11—44no—
313C23×C4⋊C4—111no—
314C2×#389—111no—
315C2×#389D1111yescharacteristic, complemented
316C2×#385—111no—
317C2×#385—111no—
318C2×#385—111no—
319C2×C4×C22⋊C4—111no—
320#1444—111no—
321#1444—111no—
322#1441—111no—
323#1441—111no—
324#1436—111no—
325#1436—111no—
326C22⋊#95—111no—
327C22⋊#95—111no—
328C23×C11C23×C411yescharacteristic
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C22×Q811yescharacteristic
334C23×C11C22×Q811yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C112−1+411yescharacteristic
342C23×C112−1+411yescharacteristic
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
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×D11C2×C4⋊C414yes—
372C22×D11C4×D414yes—
373C22×D11C4×Q814yes—
374C22×D11#12114yes—
375C22×D11C22⋊Q814yes—
376C22×D11#12514yes—
377C22×D11C4⋊Q814yes—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
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—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
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×C11C2×C4⋊C414yescomplemented
425C2×C4×C11C4×D414yes—
426C2×C4×C11#12014yes—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
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—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
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×Dic11C2×C4⋊C414yescomplemented
475C2×Dic11C4×D414yes—
476C4×D11—232no—
477C4×D11—416no—
478C4×D11—416no—
479C24×C4—111no—
480C24×C4—111no—
481C24×C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4—111no—
485C22×C4⋊C4—111no—
486C22×C4⋊C4—111no—
487C22×C4⋊C4—111no—
488C22×C4⋊C4—224no—
489C22×C4⋊C4—224no—
490C22×C4⋊C4—224no—
491C22×C4⋊C4C2×D1111yescharacteristic
492C22×C4⋊C4C2×D1111yescharacteristic
493C22×C4⋊C4C2×D1111yescharacteristic
494C22×C4⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4—111no—
496C22×C22⋊C4—111no—
497C22×C22⋊C4—111no—
498C22×C22⋊C4—111no—
499C22×C42—111no—
500C22×C42C2×D1111yescharacteristic
501#389—24no—
502#389—224no—
503#385—118no—
504#385—224no—
505#385—224no—
506C4×C22⋊C4—224no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—111no—
513C2×#95—111no—
514C2×#95—111no—
515C2×#95—111no—
516C2×#95—111no—
517C2×#95—111no—
518C2×#95—111no—
519C2×#95—111no—
520C2×#95—111no—
521C2×#95C2×D1111yescharacteristic
522C2×#95C2×D1111yescharacteristic
523C22×C11C22×C4⋊C411yescharacteristic
524C22×C11C2×C4×D411yescharacteristic
525C22×C11C2×C4×D411yescharacteristic
526C22×C11C2×C4×D411yescharacteristic
527C22×C11C2×C4×Q811yescharacteristic
528C22×C11#52011yescharacteristic
529C22×C11#52011yescharacteristic
530C22×C11C2×#12011yescharacteristic
531C22×C11C2×#12111yescharacteristic
532C22×C11C2×C22⋊Q811yescharacteristic
533C22×C11#52511yescharacteristic
534C22×C11#52511yescharacteristic
535C22×C11#52511yescharacteristic
536C22×C11C2×#12511yescharacteristic
537C22×C11C2×C4⋊Q811yescharacteristic
538C22×C11#53411yescharacteristic
539C22×C11#53611yescharacteristic
540C22×C11#53911yescharacteristic
541C22×C11#53911yescharacteristic
542C22×C11D4211yescharacteristic
543C22×C11D4211yescharacteristic
544C22×C11#54611yescharacteristic
545C22×C11#54611yescharacteristic
546C22×C11#54711yescharacteristic
547C22×C11#54711yescharacteristic
548C22×C11D4×Q811yescharacteristic
549C22×C11D4×Q811yescharacteristic
550C22×C11D4×Q811yescharacteristic
551C22×C11D4×Q811yescharacteristic
552C22×C11#55211yescharacteristic
553C22×C11#55211yescharacteristic
554C22×C11#55411yescharacteristic
555C22×C11#55411yescharacteristic
556C22×C11#55411yescharacteristic
557C22×C11#55411yescharacteristic
558C2×D11—24no—
559C2×D11—24no—
560C2×D11—24no—
561C2×D11—24no—
562C2×D11—24no—
563C2×D11—24no—
564C2×D11—24no—
565C2×D11—24no—
566C2×D11—24no—
567C2×D11—24no—
568C2×D11—24no—
569C2×D11—24no—
570C2×D11—24no—
571C2×D11—24no—
572C2×D11#38918yescomplemented
573C4×C11—24no—
574C4×C11—24no—
575C4×C11—24no—
576C4×C11—42no—
577C4×C11—42no—
578C4×C11—42no—
579C4×C11—81no—
580Dic11—24no—
581Dic11—24no—
582Dic11—42no—
583Dic11—42no—
584Dic11—42no—
585Dic11—42no—
586Dic11—81no—
587C25—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—114no—
595C23×C4—114no—
596C23×C4—111no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—222no—
600C23×C4—222no—
601C23×C4—222no—
602C23×C4—222no—
603C23×C4—222no—
604C23×C4—222no—
605C23×C4—222no—
606C23×C4—222no—
607C23×C4—222no—
608C23×C4—222no—
609C23×C4—222no—
610C23×C4—222no—
611C23×C4—222no—
612C23×C4—441no—
613C23×C4—441no—
614C23×C4—441no—
615C23×C4—441no—
616C23×C4C22×D1111yescharacteristic
617C23×C4C22×D1111yescharacteristic
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C23×C4C22×D1111yescharacteristic
621C23×C4C22×D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—2232no—
636C2×C4⋊C4—222no—
637C2×C4⋊C4—222no—
638C2×C4⋊C4—222no—
639C2×C4⋊C4—222no—
640C2×C4⋊C4—222no—
641C2×C4⋊C4—222no—
642C2×C4⋊C4—222no—
643C2×C4⋊C4—222no—
644C2×C4⋊C4—222no—
645C2×C4⋊C4—222no—
646C2×C4⋊C4—222no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—441no—
650C2×C4⋊C4—441no—
651C2×C4⋊C4—441no—
652C2×C4⋊C4C4×D1114yescomplemented
653C2×C4⋊C4C22⋊D1114yes—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4—222no—
661C2×C22⋊C4—222no—
662C2×C22⋊C4—222no—
663C2×C22⋊C4—222no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—41no—
669C2×C42—222no—
670C2×C42—222no—
671C2×C42—441no—
672#95—22no—
673#95—22no—
674#95—114no—
675#95—114no—
676#95—222no—
677#95—222no—
678#95—222no—
679#95—222no—
680#95—222no—
681#95—222no—
682#95—222no—
683#95—222no—
684#95—222no—
685#95—222no—
686#95—441no—
687#95—441no—
688C2×C11C2×#38911yescharacteristic
689C2×C11C4×#12011yescharacteristic
690C2×C11#232211yescharacteristic
691C2×C11D4×C4⋊C411yescharacteristic
692C2×C11D4×C4⋊C411yescharacteristic
693C2×C11#236011yescharacteristic
694C2×C11#236011yescharacteristic
695C2×C11#241011yescharacteristic
696C2×C11#241311yescharacteristic
697C2×C11#243411yescharacteristic
698C2×C11#244911yescharacteristic
699C2×C11#244911yescharacteristic
700C2×C11#247311yescharacteristic
701C2×C11#247311yescharacteristic
702C2×C11#258311yescharacteristic
703D11—28no—
704C24—112no—
705C24—112no—
706C24—112no—
707C24—112no—
708C24—112no—
709C24—112no—
710C24—112no—
711C24—221no—
712C24—221no—
713C24—221no—
714C24—221no—
715C24—221no—
716C24—221no—
717C24—221no—
718C24—221no—
719C24C23×D1111yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
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—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—228no—
768C22×C4—228no—
769C22×C4—228no—
770C22×C4—228no—
771C22×C4—228no—
772C22×C4—228no—
773C22×C4—228no—
774C22×C4—228no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—228no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—228no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—444no—
817C22×C4—444no—
818C22×C4—444no—
819C22×C4—444no—
820C22×C4—444no—
821C22×C4—444no—
822C22×C4—444no—
823C22×C4—444no—
824C22×C4—444no—
825C22×C4—444no—
826C22×C4—444no—
827C22×C4C2×C4×D1112yes—
828C22×C4C2×C4×D1112yes—
829C22×C4C2×C4×D1112yes—
830C22×C4#433912yes—
831C22×C4D4×D1112yes—
832C22×C4D4×D1112yes—
833C22×C4D4×D1112yes—
834C22×C4Q8×D1112yes—
835C22×C4Q8×D1112yes—
836C22×C4C2×C22⋊D1112yes—
837C22×C4C2×C22⋊D1112yes—
838C22×C4C2×C22⋊D1112yes—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—228no—
844C4⋊C4—228no—
845C4⋊C4—228no—
846C4⋊C4—228no—
847C4⋊C4—444no—
848C4⋊C4—444no—
849C22⋊C4—1116no—
850C22⋊C4—228no—
851C22⋊C4—228no—
852C22⋊C4—444no—
853C42—44no—
854C42—444no—
855C11#1404311yescharacteristic, complemented, Sylow
856C23—114no—
857C23—114no—
858C23—114no—
859C23—114no—
860C23—114no—
861C23—114no—
862C23—114no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23C22×C4×D1111yescharacteristic
892C23C2×#433911yescharacteristic
893C23C2×D4×D1111yescharacteristic
894C23C2×D4×D1111yescharacteristic
895C23C2×D4×D1111yescharacteristic
896C23#6703711yescharacteristic
897C23C2×Q8×D1111yescharacteristic
898C23C2×Q8×D1111yescharacteristic
899C23#6704011yescharacteristic
900C23#6704011yescharacteristic
901C23#41×D1111yescharacteristic
902C23#41×D1111yescharacteristic
903C23#41×D1111yescharacteristic
904C23#6704211yescharacteristic
905C23C22×C22⋊D1111yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—114no—
953C2×C4—114no—
954C2×C4—2232no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—4416no—
980C2×C4—4416no—
981C2×C4—441no—
982C2×C4—441no—
983C2×C4—441no—
984C2×C4—441no—
985C2×C4—441no—
986C2×C4—441no—
987C2×C4—441no—
988C2×C4—441no—
989C2×C4—441no—
990C2×C4—441no—
991C2×C4—441no—
992C2×C4—441no—
993C2×C4—441no—
994C2×C4—441no—
995C2×C4—441no—
996C2×C4—441no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4C4⋊C4×D1114yescomplemented
1005C2×C4C4×C22⋊D1114yes—
1006C2×C4#6699014yes—
1007C22—118no—
1008C22—224no—
1009C22—224no—
1010C22—224no—
1011C22—224no—
1012C22—224no—
1013C22—224no—
1014C22—224no—
1015C22—224no—
1016C22—224no—
1017C22—224no—
1018C22—224no—
1019C22—224no—
1020C22—224no—
1021C22—224no—
1022C22C2×C4⋊C4×D1111yescharacteristic
1023C22#1062303511yescharacteristic
1024C22#1062303811yescharacteristic
1025C22#1062304211yescharacteristic
1026C22C4×D4×D1111yescharacteristic
1027C22C4×D4×D1111yescharacteristic
1028C22#1062307811yescharacteristic
1029C22#1062307811yescharacteristic
1030C22C4×Q8×D1111yescharacteristic
1031C22#1062310511yescharacteristic
1032C22#1062311011yescharacteristic
1033C22#1062311211yescharacteristic
1034C22D11×#12111yescharacteristic
1035C22#1062313611yescharacteristic
1036C22#1062314011yescharacteristic
1037C22#1062314111yescharacteristic
1038C22D11×C22⋊Q811yescharacteristic
1039C22#1062316211yescharacteristic
1040C22#1062316711yescharacteristic
1041C22#1062316911yescharacteristic
1042C22D11×#12511yescharacteristic
1043C22#1062322111yescharacteristic
1044C22#1062322311yescharacteristic
1045C22#1062322411yescharacteristic
1046C22D11×C4⋊Q811yescharacteristic
1047C22#1062325511yescharacteristic
1048C22#1062325811yescharacteristic
1049C22#1062325811yescharacteristic
1050C22C2×C4×C22⋊D1111yescharacteristic
1051C22C2×#6699011yescharacteristic
1052C22D4×C22⋊D1111yescharacteristic
1053C22Q8×C22⋊D1111yescharacteristic
1054C22Q8×C22⋊D1111yescharacteristic
1055C22#1062335911yescharacteristic
1056C22#1062336011yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—24no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—81no—
1064C4—224no—
1065C4—224no—
1066C4—442no—
1067C4—442no—
1068C4—442no—
1069C4—442no—
1070C4—881no—
1071C2—228no—
1072C2D11×#38911yescharacteristic
1073C2C4×#6699011yescharacteristic
1074C2#1307128011yescharacteristic
1075C2C4⋊C4×C22⋊D1111yescharacteristic
1076C2#1307151711yescharacteristic
1077C2#1307161711yescharacteristic
1078C2#1307161811yescharacteristic
1079C2#1307198711yescharacteristic
1080C2#1307202011yescharacteristic
1081C2#1307225711yescharacteristic
1082C2#1307242211yescharacteristic
1083C2#1307243211yescharacteristic
1084C2#1307275311yescharacteristic
1085C2#1307276311yescharacteristic
1086C2#1307399411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11#14043
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
7. #13066880C2semidirect
8. #13066879C2semidirect
9. #13066869C2semidirect
10. #13066867C2semidirect
11. #13066849C2semidirect
12. #13066848C2semidirect
15. C2×C11×#389C2semidirect
57. #10622602C4semidirect
106. C2×C11×C4⋊C4C2×C4semidirect
139. C2×Dic11⋊C4C2×C4semidirect
159. C11⋊#95C2×C4semidirect
160. C11⋊#95C2×C4semidirect
305. (C2×D11)⋊C4C4⋊C4semidirect
315. C2×#389D11semidirect
424. C2×C4×C11C2×C4⋊C4semidirect
474. C2×Dic11C2×C4⋊C4semidirect
572. C2×D11#389semidirect
652. C2×C4⋊C4C4×D11semidirect
855. C11#14043semidirect
1004. C2×C4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106225852
C2×#106226022
C2×C4×(C2×D11)⋊C42
#130668802
#130668792
#130668692
#130668672
#130668492
#130668482
(C2×D11)⋊#952
C2×C11×#3892
#1404311