Finite Group Databasebeta

← #14684439

Subgroups — #14684439

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622603C211yesmaximal, characteristic, complemented
4#13066871C211yesmaximal, characteristic, complemented
5#13066865C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066855C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622603—24no—
52#10622573C418yescomplemented
53#10622570—24no—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—41no—
66C22×C22⋊D11—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11—41no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11C2×C414yes—
76C22×C22⋊D11C2×C414yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×D44—41no—
84C22×D44—41no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44C2×C414yes—
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⋊C4—41no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4C2×C414yes—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×(C2×D11)⋊C4—22no—
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—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
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)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4C2×C414yes—
137C2×(C2×D11)⋊C4C2×C414yes—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×C4×Dic11—41no—
142C2×C4×Dic11—41no—
143C2×C4×Dic11D414yescomplemented
144C11×#95—41no—
145C11×#95—41no—
146C11×#95—41no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95C2×C414yes—
158#14623—111nomaximal, Sylow
159C24×C11—21no—
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×C11—21no—
173C24×C11C22×C412yes—
174C24×C11C2411yescharacteristic
175C23×D11—21no—
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×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11C22×C412yes—
204C23×D11C22×C412yes—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C2×D412yes—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
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×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11C22×C412yes—
299C22×Dic11C22×C412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11#4112yes—
303C2×D44—44no—
304C2×D44—44no—
305C2×D44—44no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—44no—
310C11×C4⋊C4—44no—
311C11×C22⋊C4—44no—
312C11×C22⋊C4—44no—
313C11×C22⋊C4—44no—
314C22⋊Dic11—44no—
315C22⋊Dic11—44no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—44no—
318(C2×D11)⋊C4—44no—
319(C2×D11)⋊C4—44no—
320(C2×D11)⋊C4—44no—
321(C2×D11)⋊C4—44no—
322(C2×D11)⋊C4—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
325(C2×D11)⋊C4—44no—
326Dic11⋊C4—44no—
327C4×Dic11—44no—
328C2×#392—111no—
329C2×#390—111no—
330C2×#388—111no—
331#1442—111no—
332#1440—111no—
333#1440—111no—
334#1439—111no—
335#1439—111no—
336#1439D1111yescharacteristic, complemented
337#1438—111no—
338#1438—111no—
339#1438—111no—
340#1438—111no—
341#1438—111no—
342#1434—111no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
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×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11C23×C411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C11H(5,𝔽2)11yescharacteristic
383C23×C11H(5,𝔽2)11yescharacteristic
384C23×C11H(5,𝔽2)11yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C11H(5,𝔽2)11yescharacteristic
392C23×C112−1+411yescharacteristic
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C22⋊D11—416no—
506C22⋊D11—416no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11C4×D414yes—
549D44—416no—
550C23×D4—111no—
551C23×D4—111no—
552C23×D4—111no—
553C22×C4⋊C4—111no—
554C22×C4⋊C4C2×D1111yescharacteristic
555C22×C22⋊C4—111no—
556C22×C22⋊C4—111no—
557C22×C22⋊C4—111no—
558C22×C22⋊C4—111no—
559C22×C22⋊C4—111no—
560C22×C22⋊C4—111no—
561C22×C22⋊C4—111no—
562C22×C22⋊C4—111no—
563C22×C22⋊C4—111no—
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4C2×D1111yescharacteristic
568C22×C22⋊C4C2×D1111yescharacteristic
569C22×C22⋊C4C2×D1111yescharacteristic
570C22×C42—111no—
571#392—118no—
572#390—224no—
573#388—224no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95—111no—
578C2×#95—111no—
579C2×#95—111no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—111no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95C2×D1111yescharacteristic
586C2×#95C2×D1111yescharacteristic
587C2×#95C2×D1111yescharacteristic
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—42no—
595C22×C11—81no—
596C22×C11—81no—
597C22×C11—81no—
598C22×C11—81no—
599C22×C11—81no—
600C22×C11—81no—
601C22×C11—81no—
602C22×C11—81no—
603C22×C11C2×C4×D411yescharacteristic
604C22×C11#51811yescharacteristic
605C22×C11#51811yescharacteristic
606C22×C11#51811yescharacteristic
607C22×C11#51811yescharacteristic
608C22×C11#51811yescharacteristic
609C22×C11#52011yescharacteristic
610C22×C11#53411yescharacteristic
611C22×C11#53511yescharacteristic
612C22×C11#53511yescharacteristic
613C22×C11#53511yescharacteristic
614C22×C11#53511yescharacteristic
615C22×C11#53711yescharacteristic
616C22×C11#53811yescharacteristic
617C22×C11#53811yescharacteristic
618C22×C11#54011yescharacteristic
619C22×C11#54011yescharacteristic
620C22×C11#54011yescharacteristic
621C22×C11#54211yescharacteristic
622C22×C11#56011yescharacteristic
623C22×C11#56011yescharacteristic
624C22×C11#56011yescharacteristic
625C22×C11#56011yescharacteristic
626C22×C11#56011yescharacteristic
627C22×C11#56011yescharacteristic
628C22×C11#56011yescharacteristic
629C22×C11#56011yescharacteristic
630C22×C11#56011yescharacteristic
631C22×C11#56011yescharacteristic
632C22×C11H(3,𝔽4)11yescharacteristic
633C22×C11H(3,𝔽4)11yescharacteristic
634C22×C11#56211yescharacteristic
635C22×C11#56211yescharacteristic
636C22×C11#56211yescharacteristic
637C22×C11#56211yescharacteristic
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—81no—
653C2×D11—81no—
654C2×D11—81no—
655C2×D11—81no—
656C2×D11—81no—
657C2×D11—81no—
658C2×D11—81no—
659C2×D11—81no—
660C2×D11—81no—
661C2×D11—81no—
662C2×D11—81no—
663C2×D11—81no—
664C2×D11—81no—
665C2×D11—81no—
666C2×D11—81no—
667C2×D11—81no—
668C4×C11—42no—
669C4×C11—42no—
670C4×C11—42no—
671C4×C11—81no—
672C4×C11—81no—
673C4×C11—81no—
674Dic11—24no—
675Dic11—42no—
676Dic11—42no—
677Dic11—81no—
678Dic11—81no—
679Dic11—81no—
680C25—111no—
681C25—111no—
682C25C22×D1111yescharacteristic
683C22×D4—114no—
684C22×D4—114no—
685C22×D4—114no—
686C22×D4—222no—
687C22×D4—222no—
688C22×D4—441no—
689C22×D4—441no—
690C22×D4—441no—
691C22×D4—441no—
692C22×D4—441no—
693C22×D4—441no—
694C22×D4—441no—
695C22×D4—441no—
696C22×D4—441no—
697C22×D4—441no—
698C22×D4—441no—
699C22×D4—441no—
700C22×D4—441no—
701C22×D4—441no—
702C22×D4—441no—
703C22×D4—441no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4C22×D1111yescharacteristic
711C23×C4C22×D1111yescharacteristic
712C23×C4C22×D1111yescharacteristic
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1111yescharacteristic
716C2×C4⋊C4—22no—
717C2×C4⋊C4—41no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—441no—
721C2×C4⋊C4—441no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—441no—
740C2×C22⋊C4—441no—
741C2×C22⋊C4—441no—
742C2×C22⋊C4—441no—
743C2×C22⋊C4—441no—
744C2×C22⋊C4—441no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C22⋊C4—441no—
751C2×C22⋊C4—441no—
752C2×C22⋊C4—441no—
753C2×C22⋊C4—441no—
754C2×C22⋊C4—441no—
755C2×C22⋊C4—441no—
756C2×C22⋊C4—441no—
757C2×C22⋊C4—441no—
758C2×C22⋊C4—441no—
759C2×C22⋊C4—441no—
760C2×C22⋊C4—441no—
761C2×C22⋊C4—441no—
762C2×C22⋊C4—441no—
763C2×C22⋊C4—441no—
764C2×C22⋊C4—441no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4C4×D1114yes—
767C2×C42—114no—
768C2×C42—441no—
769C2×C42—441no—
770#95—41no—
771#95—41no—
772#95—41no—
773#95—114no—
774#95—222no—
775#95—222no—
776#95—222no—
777#95—441no—
778#95—441no—
779#95—441no—
780#95—441no—
781#95—441no—
782#95—441no—
783#95—441no—
784C2×C11—82no—
785C2×C11#232111yescharacteristic
786C2×C11#232411yescharacteristic
787C2×C11#232811yescharacteristic
788C2×C11#237511yescharacteristic
789C2×C11#237511yescharacteristic
790C2×C11#237711yescharacteristic
791C2×C11#237711yescharacteristic
792C2×C11#281311yescharacteristic
793C2×C11#281511yescharacteristic
794C2×C11#281811yescharacteristic
795C2×C11#281911yescharacteristic
796C2×C11#282811yescharacteristic
797C2×C11#282811yescharacteristic
798C2×C11#282911yescharacteristic
799C2×C11#282911yescharacteristic
800D11—82no—
801D11—82no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—112no—
817C24—112no—
818C24—221no—
819C24—221no—
820C24—221no—
821C24—221no—
822C24—221no—
823C24—221no—
824C24—221no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24—221no—
832C24—221no—
833C24—221no—
834C24—221no—
835C24—221no—
836C24—221no—
837C24—221no—
838C24—221no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24C2×C4×D1112yes—
847C24C23×D1111yescharacteristic
848C2×D4—228no—
849C2×D4—444no—
850C2×D4—444no—
851C2×D4—444no—
852C2×D4—444no—
853C2×D4—444no—
854C2×D4—444no—
855C2×D4—444no—
856C2×D4—444no—
857C2×D4—444no—
858C2×D4—444no—
859C2×D4—444no—
860C2×D4—444no—
861C2×D4—444no—
862C2×D4—444no—
863C2×D4—444no—
864C2×D4—444no—
865C2×D4—444no—
866C2×D4—444no—
867C2×D4—444no—
868C2×D4—444no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—112no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—221no—
924C22×C4—221no—
925C22×C4—221no—
926C22×C4—221no—
927C22×C4—221no—
928C22×C4—221no—
929C22×C4—221no—
930C22×C4—221no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4C2×C4×D1112yes—
951C22×C4C2×C4×D1112yes—
952C22×C4D4×D1112yes—
953C4⋊C4—44no—
954C4⋊C4—444no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—228no—
959C22⋊C4—444no—
960C22⋊C4—444no—
961C22⋊C4—444no—
962C22⋊C4—444no—
963C22⋊C4—444no—
964C22⋊C4—444no—
965C22⋊C4—444no—
966C22⋊C4—444no—
967C22⋊C4—444no—
968C22⋊C4—444no—
969C22⋊C4—444no—
970C42—444no—
971C11#1462311yescharacteristic, complemented, Sylow
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—441no—
1022C23—441no—
1023C23—441no—
1024C23—441no—
1025C23—441no—
1026C23—441no—
1027C23—441no—
1028C23—441no—
1029C23—441no—
1030C23—441no—
1031C23—441no—
1032C23—441no—
1033C23—441no—
1034C23—441no—
1035C23—441no—
1036C23—441no—
1037C23—441no—
1038C23—441no—
1039C23—441no—
1040C23—441no—
1041C23—441no—
1042C23—441no—
1043C23—441no—
1044C23—441no—
1045C23—441no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23C22×C4×D1111yescharacteristic
1078C23C2×D4×D1111yescharacteristic
1079C23#6703711yescharacteristic
1080C23#6703711yescharacteristic
1081C23#6703711yescharacteristic
1082C23#6703711yescharacteristic
1083C23#6703711yescharacteristic
1084C23#6703711yescharacteristic
1085C23#6704011yescharacteristic
1086C23#41×D1111yescharacteristic
1087C23#6704211yescharacteristic
1088C23#6704211yescharacteristic
1089C23#6704211yescharacteristic
1090C23#6704211yescharacteristic
1091C23#6704211yescharacteristic
1092D4—4416no—
1093D4—4416no—
1094D4—4416no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—114no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—441no—
1153C2×C4—441no—
1154C2×C4—441no—
1155C2×C4—441no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—441no—
1166C2×C4—441no—
1167C2×C4—441no—
1168C2×C4—441no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—441no—
1176C2×C4—441no—
1177C2×C4—441no—
1178C2×C4—441no—
1179C22—42no—
1180C22—42no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—442no—
1207C22—442no—
1208C22—881no—
1209C22—881no—
1210C22—881no—
1211C22—881no—
1212C22—881no—
1213C22—881no—
1214C22—881no—
1215C22—881no—
1216C22—881no—
1217C22—881no—
1218C22—881no—
1219C22—881no—
1220C22—881no—
1221C22—881no—
1222C22—881no—
1223C22—881no—
1224C22#1062301711yescharacteristic
1225C22#1062303511yescharacteristic
1226C22#1062305211yescharacteristic
1227C22C4×D4×D1111yescharacteristic
1228C22#1062307611yescharacteristic
1229C22#1062307611yescharacteristic
1230C22#1062307611yescharacteristic
1231C22#1062312311yescharacteristic
1232C22#1062312311yescharacteristic
1233C22#1062312611yescharacteristic
1234C22#1062313611yescharacteristic
1235C22#1062313811yescharacteristic
1236C22#1062314611yescharacteristic
1237C22#1062315111yescharacteristic
1238C22#1062315111yescharacteristic
1239C22#1062315111yescharacteristic
1240C22#1062315111yescharacteristic
1241C22#1062315111yescharacteristic
1242C22#1062316011yescharacteristic
1243C22#1062317111yescharacteristic
1244C22#1062317811yescharacteristic
1245C22#1062317811yescharacteristic
1246C22#1062317811yescharacteristic
1247C22#1062317811yescharacteristic
1248C22#1062318811yescharacteristic
1249C22#1062319411yescharacteristic
1250C22#1062319411yescharacteristic
1251C22#1062319711yescharacteristic
1252C22#1062319711yescharacteristic
1253C22#1062320511yescharacteristic
1254C22#1062321411yescharacteristic
1255C22#1062321411yescharacteristic
1256C22#1062323511yescharacteristic
1257C22#1062324211yescharacteristic
1258C22#1062325111yescharacteristic
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—224no—
1266C4—442no—
1267C4—442no—
1268C4—881no—
1269C4—881no—
1270C4—881no—
1271C2—82no—
1272C2—882no—
1273C2—882no—
1274C2#1307126911yescharacteristic
1275C2#1307130811yescharacteristic
1276C2#1307133711yescharacteristic
1277C2#1307175311yescharacteristic
1278C2#1307175611yescharacteristic
1279C2#1307177011yescharacteristic
1280C2#1307177211yescharacteristic
1281C2#1307662511yescharacteristic
1282C2#1307664111yescharacteristic
1283C2#1307665811yescharacteristic
1284C2#1307666411yescharacteristic
1285C2#1307673211yescharacteristic
1286C2#1307673711yescharacteristic
1287C2#1307675311yescharacteristic
1288C2#1307675511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622603C2semidirect
4. #13066871C2semidirect
5. #13066865C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
8. #13066858C2semidirect
9. #13066856C2semidirect
10. #13066856C2semidirect
11. #13066855C2semidirect
12. #13066855C2semidirect
13. #13066855C2semidirect
14. #13066840C2semidirect
15. C11×#1439C2semidirect
52. #10622573C4semidirect
143. C2×C4×Dic11D4semidirect
336. #1439D11semidirect
971. C11#14623semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225702
C2×#106226032
#130668712
#130668652
#130668642
#130668602
#130668582
#130668562
#130668552
#130668402
C11×#14392
#1462311