Finite Group Databasebeta

← #14677849

Subgroups — #14677849

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic
5#13066879C211yesmaximal, characteristic, complemented
6#13066859C211yesmaximal, characteristic, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic
9#13066854C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C22×C11×#117C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C2×C11×#117—24no—
19C2×C11×#117—24no—
20C2×C11×#117—24no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40#10622826C418yescomplemented
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#10622603—24no—
56#10622570—24no—
57#10622553—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11C2×C414yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C11×#117—232no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D414yescomplemented
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4D414yes—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11D414yescomplemented
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11C2×C414yes—
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)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4C2×C414yes—
132C2×(C2×D11)⋊C4C2×C414yes—
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×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—41no—
144C2×C4×Dic11—41no—
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—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95C2×C414yes—
158C11⋊#95C2×C414yes—
159#14071—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11C22×C412yes—
173C24×C11C2×D412yes—
174C24×C11#4112yes—
175C24×C11C2411yescharacteristic
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
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—
191C22×C4×C11—28no—
192C22×C4×C11—28no—
193C22×C4×C11—28no—
194C22×C4×C11—28no—
195C22×C4×C11—28no—
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—28no—
209C22×C4×C11—28no—
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×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11#4112yes—
239C22×C4×C11#4112yes—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
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×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C22×C412yes—
292C22×Dic11#4112yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C11×C4⋊C4—28no—
297C11×C4⋊C4—28no—
298C11×C22⋊C4—28no—
299C11×C22⋊C4—28no—
300C42×C11—28no—
301C42×C11—28no—
302C22⋊Dic11—44no—
303C22⋊Dic11—44no—
304C22⋊Dic11—44no—
305(C2×D11)⋊C4—28no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—44no—
308(C2×D11)⋊C4—44no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311Dic11⋊C4—44no—
312Dic11⋊C4—44no—
313C4×Dic11—44no—
314C4×Dic11—44no—
315C22×#117D1111yescharacteristic, complemented
316C2×#390—111no—
317C2×#388—111no—
318C2×#388—111no—
319C2×#386—111no—
320#1444—111no—
321#1439—111no—
322#1439—111no—
323#1438—111no—
324#1437—111no—
325#1437—111no—
326#1436—111no—
327#1436—111no—
328C22⋊#95—111no—
329C4×#95—111no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
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×C11C4×D414yes—
365C23×C11C23×C411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11C2×#4111yescharacteristic
371C23×C11C2×#4111yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C11H(5,𝔽2)11yescharacteristic
379C23×C112−1+411yescharacteristic
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C2×C4×C11—232no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
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—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11C4×D414yes—
456C2×C4×C11C4×D414yes—
457C2×C4×C11#12014yes—
458C22⋊D11—416no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
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—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
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#11714yescomplemented
508C23×D4—111no—
509C24×C4C2×D1111yescharacteristic
510C2×#117—24no—
511C2×#117—24no—
512C2×#117—24no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4C2×D1111yescharacteristic
516C22×C4⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42—111no—
530C22×C42C2×D1111yescharacteristic
531C22×C42C2×D1111yescharacteristic
532#390—224no—
533#388—224no—
534#388—224no—
535#386—118no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—24no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11C2×#11711yescharacteristic
566C22×C11C2×C4×D411yescharacteristic
567C22×C11C2×C4×D411yescharacteristic
568C22×C11C2×C4×D411yescharacteristic
569C22×C11C4×#4111yescharacteristic
570C22×C11#51811yescharacteristic
571C22×C11#52011yescharacteristic
572C22×C11C2×#12011yescharacteristic
573C22×C11#52511yescharacteristic
574C22×C11#52511yescharacteristic
575C22×C11#52511yescharacteristic
576C22×C11#52911yescharacteristic
577C22×C11#52911yescharacteristic
578C22×C11#53211yescharacteristic
579C22×C11#53211yescharacteristic
580C22×C11#53511yescharacteristic
581C22×C11#53711yescharacteristic
582C22×C11#54011yescharacteristic
583C22×C11#54211yescharacteristic
584C22×C11#54611yescharacteristic
585C22×C11#54611yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#54711yescharacteristic
589C22×C11#54711yescharacteristic
590C22×C11#55011yescharacteristic
591C22×C11#55011yescharacteristic
592C22×C11#55111yescharacteristic
593C22×C11#55111yescharacteristic
594C22×C11#55111yescharacteristic
595C22×C11#55211yescharacteristic
596C22×C11#55311yescharacteristic
597C22×C11#55511yescharacteristic
598C22×C11#55511yescharacteristic
599C22×C11#55611yescharacteristic
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—81no—
608C2×D11—81no—
609C2×D11—81no—
610C2×D11—81no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C2×D11—81no—
615C4×C11—24no—
616C4×C11—24no—
617C4×C11—24no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621Dic11—24no—
622Dic11—42no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—81no—
627Dic11—81no—
628C25—111no—
629C25C22×D1111yescharacteristic
630C22×D4—114no—
631C22×D4—222no—
632C22×D4—222no—
633C22×D4—222no—
634C22×D4—222no—
635C22×D4—441no—
636C22×D4—441no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4C4×D1114yes—
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657#117—232no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—441no—
667C2×C4⋊C4—441no—
668C2×C4⋊C4—441no—
669C2×C4⋊C4C22⋊D1114yescomplemented
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—114no—
676C2×C22⋊C4—114no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
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—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—441no—
695C2×C22⋊C4—441no—
696C2×C22⋊C4—441no—
697C2×C22⋊C4—441no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4—441no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4C22⋊D1114yes—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—441no—
713C2×C42—441no—
714C2×C42C22⋊D1114yescomplemented
715#95—114no—
716#95—114no—
717#95—222no—
718#95—222no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—441no—
727#95—441no—
728#95—441no—
729C2×C11—44no—
730C2×C11#229311yescharacteristic
731C2×C11C4×#12011yescharacteristic
732C2×C11#232411yescharacteristic
733C2×C11#234211yescharacteristic
734C2×C11#235411yescharacteristic
735C2×C11#235911yescharacteristic
736C2×C11#236311yescharacteristic
737C2×C11#243011yescharacteristic
738C2×C11#243111yescharacteristic
739C2×C11#247111yescharacteristic
740C2×C11#247411yescharacteristic
741C2×C11#247611yescharacteristic
742C2×C11#247911yescharacteristic
743C2×C11#260111yescharacteristic
744C2×C11#261011yescharacteristic
745D11—82no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—112no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24C2×C4×D1112yes—
774C24#433912yes—
775C24C2×C22⋊D1112yes—
776C24C23×D1111yescharacteristic
777C2×D4—228no—
778C2×D4—228no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—444no—
783C2×D4—444no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—112no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
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—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
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×C4C2×C4×D1112yes—
871C22×C4C2×C4×D1112yes—
872C22×C4#433912yes—
873C22×C4#433912yes—
874C22×C4C2×C22⋊D1112yes—
875C22×C4C2×C22⋊D1112yes—
876C22×C4C2×C22⋊D1112yes—
877C22×C4C2×C22⋊D1112yes—
878C22×C4C2×C22⋊D1112yes—
879C22×C4C2×C22⋊D1112yes—
880C22×C4C2×C22⋊D1112yes—
881C22×C4C2×C22⋊D1112yes—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—444no—
885C4⋊C4—444no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—444no—
891C22⋊C4—444no—
892C22⋊C4—444no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C42—28no—
898C42—28no—
899C42—444no—
900C42—444no—
901C11#1407111yescharacteristic, complemented, Sylow
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23C4×C22⋊D1114yes—
972C23C22×C4×D1111yescharacteristic
973C23C2×#433911yescharacteristic
974C23C2×#433911yescharacteristic
975C23C2×#433911yescharacteristic
976C23#41×D1111yescharacteristic
977C23#41×D1111yescharacteristic
978C23#41×D1111yescharacteristic
979C23#41×D1111yescharacteristic
980C23#6704211yescharacteristic
981C23#6704211yescharacteristic
982C23#6704211yescharacteristic
983C23#6704311yescharacteristic
984C23C22×C22⋊D1111yescharacteristic
985C23C22×C22⋊D1111yescharacteristic
986C23C22×C22⋊D1111yescharacteristic
987D4—4416no—
988C2×C4—232no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—114no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4C4×C22⋊D1114yes—
1078C2×C4C4×C22⋊D1114yes—
1079C2×C4#6700614yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—881no—
1103C22—881no—
1104C22—881no—
1105C22—881no—
1106C22—881no—
1107C22—881no—
1108C22—881no—
1109C22—881no—
1110C22D11×#11711yescharacteristic
1111C22#1062305211yescharacteristic
1112C22#1062305311yescharacteristic
1113C22#1062305411yescharacteristic
1114C22#1062305811yescharacteristic
1115C22#1062305811yescharacteristic
1116C22#1062305811yescharacteristic
1117C22#1062305911yescharacteristic
1118C22#1062305911yescharacteristic
1119C22#1062306111yescharacteristic
1120C22#1062306211yescharacteristic
1121C22#1062306311yescharacteristic
1122C22#1062306311yescharacteristic
1123C22#1062306411yescharacteristic
1124C22#1062306511yescharacteristic
1125C22#1062306611yescharacteristic
1126C22C2×C4×C22⋊D1111yescharacteristic
1127C22C2×C4×C22⋊D1111yescharacteristic
1128C22C2×C4×C22⋊D1111yescharacteristic
1129C22#1062332211yescharacteristic
1130C22#1062332211yescharacteristic
1131C22#1062332211yescharacteristic
1132C22#1062335511yescharacteristic
1133C22#1062335511yescharacteristic
1134C22#1062336011yescharacteristic
1135C22#1062336011yescharacteristic
1136C22#1062336011yescharacteristic
1137C22#1062336011yescharacteristic
1138C22#1062336111yescharacteristic
1139C22#1062336311yescharacteristic
1140C22#1062336311yescharacteristic
1141C22#1062336411yescharacteristic
1142C22#1062336511yescharacteristic
1143C22#1062336511yescharacteristic
1144C22C2×#6700611yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—224no—
1152C4—442no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C4—881no—
1157C4—881no—
1158C2—44no—
1159C2—882no—
1160C2#1307107511yescharacteristic
1161C2C4×#6700611yescharacteristic
1162C2#1307130911yescharacteristic
1163C2#1307146611yescharacteristic
1164C2#1307156611yescharacteristic
1165C2#1307160811yescharacteristic
1166C2#1307165411yescharacteristic
1167C2#1307222011yescharacteristic
1168C2#1307223111yescharacteristic
1169C2#1307272111yescharacteristic
1170C2#1307276611yescharacteristic
1171C2#1307279611yescharacteristic
1172C2#1307284111yescharacteristic
1173C2#1307421311yescharacteristic
1174C2#1307430311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#117C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#117D11
hypocenterC11#14071
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622603C2semidirect
5. #13066879C2semidirect
6. #13066859C2semidirect
7. #13066858C2semidirect
9. #13066854C2semidirect
10. #13066853C2semidirect
11. #13066849C2semidirect
12. #13066848C2semidirect
13. #13066839C2semidirect
14. C4×C11⋊#95C2semidirect
15. C22×C11×#117C2semidirect
40. #10622826C4semidirect
93. C2×C11×C4⋊C4D4semidirect
105. C2×C42×C11D4semidirect
315. C22×#117D11semidirect
507. C2×Dic11#117semidirect
669. C2×C4⋊C4C22⋊D11semidirect
714. C2×C42C22⋊D11semidirect
901. C11#14071semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106225532
C2×#106226032
C2×#106228262
#130668792
#130668592
#130668582
#130668552
#130668542
#130668532
#130668492
#130668482
#130668392
C4×C11⋊#952
C22×C11×#1172
#1407111