Finite Group Databasebeta

← #14681090

Subgroups — #14681090

Order 2816.

2062 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
1C22×#66982C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622585C211yesmaximal, characteristic, complemented
4C2×#10622591C211yesmaximal, characteristic, complemented
5#13066867C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×#66982—24no—
26C2×#66982—24no—
27C2×#66982C418yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C11×#380—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
55#10622591—24no—
56#10622585—24no—
57#10622570—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
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
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4D414yes—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11C2×C414yes—
108#66982—232no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
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—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4C2×C414yes—
126C2×(C2×D11)⋊C4C2×C414yes—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—41no—
133C2×Dic11⋊C4—41no—
134C2×Dic11⋊C4—41no—
135C2×Dic11⋊C4C2×C414yes—
136C2×Dic11⋊C4C2×C414yes—
137C2×Dic11⋊C4D414yes—
138C2×Dic11⋊C4D414yes—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—41no—
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—22no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159#14360—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—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
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—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—28no—
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—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
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×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C11×C4⋊C4—44no—
297C11×C4⋊C4—44no—
298C11×C22⋊C4—44no—
299C11×C22⋊C4—44no—
300C22⋊Dic11—28no—
301C22⋊Dic11—44no—
302C22⋊Dic11—44no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308(C2×D11)⋊C4—44no—
309Dic11⋊C4—28no—
310Dic11⋊C4—44no—
311Dic11⋊C4—44no—
312Dic11⋊C4C22⋊C4116yescomplemented
313C4×Dic11—44no—
314C4×Dic11—44no—
315C22×#123—111no—
316C2×#390—111no—
317C2×#389—111no—
318C2×#387—111no—
319C2×#380D1111yescharacteristic, complemented
320#1441—111no—
321#1439—111no—
322#1439—111no—
323#1439—111no—
324#1439—111no—
325#1438—111no—
326#1437—111no—
327#1437—111no—
328#1436—111no—
329C22⋊#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×C11H(5,𝔽2)11yescharacteristic
373C23×C11H(5,𝔽2)11yescharacteristic
374C23×C11H(5,𝔽2)11yescharacteristic
375C23×C11H(5,𝔽2)11yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C112−1+411yescharacteristic
378C23×C112−1+411yescharacteristic
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—22no—
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—416no—
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×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
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×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11C2×C22⋊C414yes—
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—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
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×Dic11C2×C22⋊C414yes—
507C2×Dic11C2×C22⋊C414yes—
508C23×D4—111no—
509C24×C4C2×D1111yescharacteristic
510C2×#123—118no—
511C2×#123—224no—
512C2×#123—224no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4C2×D1111yescharacteristic
518C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4C2×D1111yescharacteristic
529C22×C22⋊C4C2×D1111yescharacteristic
530C22×C42—111no—
531C22×C42—111no—
532#390—224no—
533#389—224no—
534#387—224no—
535#380—24no—
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×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
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×C11C22×C22⋊C411yescharacteristic
566C22×C11C2×C4×D411yescharacteristic
567C22×C11C4×#4111yescharacteristic
568C22×C11#51811yescharacteristic
569C22×C11#52011yescharacteristic
570C22×C11#52011yescharacteristic
571C22×C11#52011yescharacteristic
572C22×C11#53411yescharacteristic
573C22×C11#53511yescharacteristic
574C22×C11#53611yescharacteristic
575C22×C11#53611yescharacteristic
576C22×C11#53711yescharacteristic
577C22×C11#53711yescharacteristic
578C22×C11#53811yescharacteristic
579C22×C11#53911yescharacteristic
580C22×C11#53911yescharacteristic
581C22×C11#53911yescharacteristic
582C22×C11#54011yescharacteristic
583C22×C11#54211yescharacteristic
584C22×C11D4211yescharacteristic
585C22×C11D4211yescharacteristic
586C22×C11#54611yescharacteristic
587C22×C11#54611yescharacteristic
588C22×C11#54611yescharacteristic
589C22×C11#54711yescharacteristic
590C22×C11#54811yescharacteristic
591C22×C11#54811yescharacteristic
592C22×C11#55011yescharacteristic
593C22×C11#55011yescharacteristic
594C22×C11#55111yescharacteristic
595C22×C11#55211yescharacteristic
596C22×C11#56011yescharacteristic
597C22×C11#56211yescharacteristic
598C22×C11#56211yescharacteristic
599C22×C11#56311yescharacteristic
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—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—81no—
620C4×C11—81no—
621Dic11—24no—
622Dic11—24no—
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—41no—
642C23×C4—41no—
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#123—2232no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—114no—
665C2×C4⋊C4—114no—
666C2×C4⋊C4—114no—
667C2×C4⋊C4—114no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—441no—
674C2×C4⋊C4—441no—
675C2×C4⋊C4—441no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—114no—
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—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4—441no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4C22⋊D1114yes—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—441no—
713C2×C42—441no—
714C2×C42—441no—
715#95—22no—
716#95—22no—
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—441no—
726#95—441no—
727#95—441no—
728#95—441no—
729C2×C11—44no—
730C2×C11#231111yescharacteristic
731C2×C11#232211yescharacteristic
732C2×C11#233511yescharacteristic
733C2×C11D4×C22⋊C411yescharacteristic
734C2×C11#234111yescharacteristic
735C2×C11#235911yescharacteristic
736C2×C11#237611yescharacteristic
737C2×C11#267311yescharacteristic
738C2×C11#267411yescharacteristic
739C2×C11#268111yescharacteristic
740C2×C11#268211yescharacteristic
741C2×C11#269411yescharacteristic
742C2×C11#269611yescharacteristic
743C2×C11#270511yescharacteristic
744C2×C11#270711yescharacteristic
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—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—28no—
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—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
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×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4C2×C4×D1112yes—
877C22×C4C2×C4×D1112yes—
878C22×C4D4×D1112yes—
879C22×C4D4×D1112yes—
880C22×C4C2×C22⋊D1112yes—
881C22×C4C2×C22⋊D1112yes—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—1116no—
885C4⋊C4—228no—
886C4⋊C4—444no—
887C4⋊C4—444no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C22⋊C4—444no—
898C22⋊C4—444no—
899C42—444no—
900C42—444no—
901C11#1436011yescharacteristic, 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×D4×D1111yescharacteristic
975C23C2×D4×D1111yescharacteristic
976C23#6703711yescharacteristic
977C23#6703711yescharacteristic
978C23#6703711yescharacteristic
979C23#6703711yescharacteristic
980C23#6704011yescharacteristic
981C23#6704011yescharacteristic
982C23#41×D1111yescharacteristic
983C23#41×D1111yescharacteristic
984C23#6704211yescharacteristic
985C23#6704311yescharacteristic
986C23C22×C22⋊D1111yescharacteristic
987D4—4416no—
988C2×C4—22no—
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—416no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
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—41no—
1029C2×C4—41no—
1030C2×C4—114no—
1031C2×C4—114no—
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—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
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×C4—441no—
1078C2×C4—441no—
1079C2×C4C22⋊C4×D1114yes—
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—
1110C22C2×C22⋊C4×D1111yescharacteristic
1111C22#1062301711yescharacteristic
1112C22#1062302111yescharacteristic
1113C22#1062302111yescharacteristic
1114C22#1062303511yescharacteristic
1115C22#1062303511yescharacteristic
1116C22#1062304611yescharacteristic
1117C22#1062304611yescharacteristic
1118C22#1062305311yescharacteristic
1119C22#1062305411yescharacteristic
1120C22#1062305811yescharacteristic
1121C22#1062306211yescharacteristic
1122C22#1062313011yescharacteristic
1123C22#1062313011yescharacteristic
1124C22#1062313811yescharacteristic
1125C22#1062313911yescharacteristic
1126C22#1062314411yescharacteristic
1127C22#1062314611yescharacteristic
1128C22#1062315111yescharacteristic
1129C22#1062315211yescharacteristic
1130C22#1062315911yescharacteristic
1131C22#1062316011yescharacteristic
1132C22#1062316411yescharacteristic
1133C22#1062316411yescharacteristic
1134C22#1062316911yescharacteristic
1135C22#1062317111yescharacteristic
1136C22#1062317711yescharacteristic
1137C22#1062317811yescharacteristic
1138C22C2×C4×C22⋊D1111yescharacteristic
1139C22D4×C22⋊D1111yescharacteristic
1140C22D4×C22⋊D1111yescharacteristic
1141C22#1062333511yescharacteristic
1142C22#1062334711yescharacteristic
1143C22#1062335511yescharacteristic
1144C22#1062336011yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—81no—
1151C4—224no—
1152C4—224no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C4—881no—
1157C4—881no—
1158C2—44no—
1159C2—882no—
1160C2#1307120511yescharacteristic
1161C2#1307128511yescharacteristic
1162C2#1307140211yescharacteristic
1163C2C22⋊C4×C22⋊D1111yescharacteristic
1164C2#1307145311yescharacteristic
1165C2#1307160811yescharacteristic
1166C2#1307176011yescharacteristic
1167C2#1307487811yescharacteristic
1168C2#1307489311yescharacteristic
1169C2#1307496411yescharacteristic
1170C2#1307497711yescharacteristic
1171C2#1307513611yescharacteristic
1172C2#1307516611yescharacteristic
1173C2#1307528911yescharacteristic
1174C2#1307531911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#14360
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#10622585C2semidirect
4. C2×#10622591C2semidirect
5. #13066867C2semidirect
6. #13066860C2semidirect
7. #13066859C2semidirect
8. #13066858C2semidirect
9. #13066858C2semidirect
11. #13066853C2semidirect
12. #13066852C2semidirect
13. #13066847C2semidirect
14. #13066839C2semidirect
15. C2×C11×#380C2semidirect
27. C2×#66982C4semidirect
312. Dic11⋊C4C22⋊C4semidirect
319. C2×#380D11semidirect
901. C11#14360semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C2×#106225702
C2×#106225852
C2×#106225912
#130668672
#130668602
#130668592
#130668582
#130668552
#130668532
#130668522
#130668472
#130668392
C2×C11×#3802
#1436011