Finite Group Databasebeta

← #14680663

Subgroups — #14680663

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066857C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066852C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C11×#386—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40#10622836C418yescomplemented
41#10622826—24no—
42C4×C22⋊Dic11—24no—
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#10622570—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—41no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11C2×C414yes—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11D414yescomplemented
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11—41no—
86C22×C22⋊D11—41no—
87C22×C22⋊D11—41no—
88C22×C22⋊D11—41no—
89C22×C22⋊D11—41no—
90C22×C22⋊D11C2×C414yes—
91C22×C22⋊D11C2×C414yescomplemented
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11C2×C414yes—
125C2×C22⋊Dic11C2×C414yescomplemented
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4C2×C414yescomplemented
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—41no—
143C2×Dic11⋊C4—41no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—41no—
146C2×C4×Dic11—41no—
147C2×C4×Dic11—41no—
148C2×C4×Dic11—41no—
149C2×C4×Dic11D414yescomplemented
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⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95—41no—
163C11⋊#95C2×C414yescomplemented
164#14311—111nomaximal, Sylow
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×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11C22×C412yes—
192C24×C11C22×C412yes—
193C24×C11C2×D412yes—
194C24×C11#4112yes—
195C24×C11C2411yescharacteristic
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11C22×C412yes—
211C2×D4×C11—28no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—44no—
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—28no—
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×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—44no—
250C22×C4×C11—44no—
251C22×C4×C11—44no—
252C22×C4×C11—44no—
253C22×C4×C11—44no—
254C22×C4×C11—44no—
255C22×C4×C11C22×C412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11#4112yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
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×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11C22×C412yes—
317C22×Dic11C22×C412yes—
318C22×Dic11C22×C412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11#4112yes—
322C22×Dic11#4112yes—
323C11×C22⋊C4—44no—
324C11×C22⋊C4—44no—
325C11×C22⋊C4—44no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—44no—
329C22⋊Dic11—44no—
330C22⋊Dic11—44no—
331C22⋊Dic11—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337Dic11⋊C4—44no—
338C4×Dic11—44no—
339C4×Dic11—44no—
340C2×#392—111no—
341C2×#390—111no—
342C2×#386—111no—
343C2×#386D1111yescharacteristic, complemented
344C2×C4×C22⋊C4—111no—
345#1442—111no—
346#1440—111no—
347#1440—111no—
348#1439—111no—
349#1438—111no—
350#1438—111no—
351#1438—111no—
352#1437—111no—
353#1437—111no—
354#1434—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11C4×D414yes—
425C23×C11C23×C411yescharacteristic
426C23×C11C22×D411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C2×#4111yescharacteristic
429C23×C11C2×#4111yescharacteristic
430C23×C11C2×#4111yescharacteristic
431C23×C11C2×#4111yescharacteristic
432C23×C11H(5,𝔽2)11yescharacteristic
433C23×C11H(5,𝔽2)11yescharacteristic
434C23×C11H(5,𝔽2)11yescharacteristic
435C23×C11H(5,𝔽2)11yescharacteristic
436C23×C11H(5,𝔽2)11yescharacteristic
437C23×C11H(5,𝔽2)11yescharacteristic
438C23×C11H(5,𝔽2)11yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
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—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475D4×C11—416no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—416no—
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—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11#12114yes—
512C22⋊D11—416no—
513C22⋊D11—416no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
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×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11C4×D414yes—
563C23×D4—111no—
564C23×D4—111no—
565C23×D4C2×D1111yescharacteristic
566C24×C4C2×D1111yescharacteristic
567C22×C4⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4C2×D1111yescharacteristic
581C22×C22⋊C4C2×D1111yescharacteristic
582C22×C42—111no—
583C22×C42—111no—
584#392—118no—
585#390—224no—
586#386—24no—
587#386—224no—
588C4×C22⋊C4—224no—
589C2×#95—111no—
590C2×#95—111no—
591C2×#95—111no—
592C2×#95—111no—
593C2×#95—111no—
594C2×#95—111no—
595C2×#95—111no—
596C2×#95—111no—
597C2×#95—111no—
598C2×#95—111no—
599C2×#95—111no—
600C2×#95—111no—
601C2×#95C2×D1111yescharacteristic
602C2×#95C2×D1111yescharacteristic
603C22×C11—24no—
604C22×C11—24no—
605C22×C11—24no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11—81no—
629C22×C11—81no—
630C22×C11—81no—
631C22×C11—81no—
632C22×C11—81no—
633C22×C11C2×C4×D411yescharacteristic
634C22×C11C2×C4×D411yescharacteristic
635C22×C11C4×#4111yescharacteristic
636C22×C11#51811yescharacteristic
637C22×C11#51811yescharacteristic
638C22×C11#51811yescharacteristic
639C22×C11#51811yescharacteristic
640C22×C11C2×#12111yescharacteristic
641C22×C11#52511yescharacteristic
642C22×C11#52911yescharacteristic
643C22×C11#53211yescharacteristic
644C22×C11#53411yescharacteristic
645C22×C11#53411yescharacteristic
646C22×C11#53411yescharacteristic
647C22×C11#53511yescharacteristic
648C22×C11#53511yescharacteristic
649C22×C11#53511yescharacteristic
650C22×C11#53511yescharacteristic
651C22×C11#53511yescharacteristic
652C22×C11#53811yescharacteristic
653C22×C11#53811yescharacteristic
654C22×C11#53811yescharacteristic
655C22×C11#53811yescharacteristic
656C22×C11#53811yescharacteristic
657C22×C11#53811yescharacteristic
658C22×C11#53811yescharacteristic
659C22×C11#53811yescharacteristic
660C22×C11#53811yescharacteristic
661C22×C11#53811yescharacteristic
662C22×C11#54011yescharacteristic
663C22×C11#54011yescharacteristic
664C22×C11#54011yescharacteristic
665C22×C11#54011yescharacteristic
666C22×C11#54011yescharacteristic
667C22×C11#54011yescharacteristic
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—81no—
676C2×D11—81no—
677C2×D11—81no—
678C2×D11—81no—
679C2×D11—81no—
680C2×D11—81no—
681C2×D11—81no—
682C2×D11—81no—
683C4×C11—24no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11—81no—
687C4×C11—81no—
688Dic11—24no—
689Dic11—42no—
690Dic11—42no—
691Dic11—42no—
692Dic11—42no—
693Dic11—81no—
694Dic11—81no—
695C25—111no—
696C25C22×D1111yescharacteristic
697C25C22×D1111yescharacteristic
698C22×D4—22no—
699C22×D4—22no—
700C22×D4—41no—
701C22×D4—41no—
702C22×D4—41no—
703C22×D4—41no—
704C22×D4—114no—
705C22×D4—114no—
706C22×D4—222no—
707C22×D4—222no—
708C22×D4—222no—
709C22×D4—222no—
710C22×D4—441no—
711C22×D4—441no—
712C22×D4—441no—
713C22×D4—441no—
714C22×D4—441no—
715C22×D4—441no—
716C22×D4—441no—
717C22×D4—441no—
718C22×D4C4×D1114yes—
719C23×C4—22no—
720C23×C4—22no—
721C23×C4—41no—
722C23×C4—41no—
723C23×C4—41no—
724C23×C4—41no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4C22⋊D1114yescomplemented
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1111yescharacteristic
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C2×C4⋊C4—222no—
739C2×C4⋊C4—441no—
740C2×C4⋊C4—441no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4—114no—
751C2×C22⋊C4—114no—
752C2×C22⋊C4—114no—
753C2×C22⋊C4—222no—
754C2×C22⋊C4—222no—
755C2×C22⋊C4—222no—
756C2×C22⋊C4—222no—
757C2×C22⋊C4—222no—
758C2×C22⋊C4—222no—
759C2×C22⋊C4—222no—
760C2×C22⋊C4—222no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—222no—
764C2×C22⋊C4—222no—
765C2×C22⋊C4—222no—
766C2×C22⋊C4—222no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4—441no—
773C2×C22⋊C4—441no—
774C2×C22⋊C4—441no—
775C2×C22⋊C4—441no—
776C2×C22⋊C4—441no—
777C2×C22⋊C4—441no—
778C2×C22⋊C4—441no—
779C2×C22⋊C4—441no—
780C2×C22⋊C4—441no—
781C2×C22⋊C4—441no—
782C2×C22⋊C4—441no—
783C2×C42—114no—
784C2×C42—222no—
785C2×C42—441no—
786C2×C42—441no—
787C2×C42—441no—
788C2×C42—441no—
789#95—22no—
790#95—22no—
791#95—114no—
792#95—222no—
793#95—222no—
794#95—222no—
795#95—222no—
796#95—222no—
797#95—441no—
798#95—441no—
799#95—441no—
800#95—441no—
801#95—441no—
802#95—441no—
803C2×C11—44no—
804C2×C11—82no—
805C2×C11C4×#12111yescharacteristic
806C2×C11#232111yescharacteristic
807C2×C11#232111yescharacteristic
808C2×C11#232111yescharacteristic
809C2×C11#232811yescharacteristic
810C2×C11#233311yescharacteristic
811C2×C11#233311yescharacteristic
812C2×C11#261711yescharacteristic
813C2×C11#261911yescharacteristic
814C2×C11#263111yescharacteristic
815C2×C11#263511yescharacteristic
816C2×C11#264811yescharacteristic
817C2×C11#264811yescharacteristic
818C2×C11#266111yescharacteristic
819C2×C11#266111yescharacteristic
820D11—82no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—112no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24C2×C4×D1112yes—
863C24C2×C4×D1112yes—
864C24#433912yes—
865C24C2×C22⋊D1112yes—
866C24C23×D1111yescharacteristic
867C2×D4—28no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—228no—
875C2×D4—228no—
876C2×D4—444no—
877C2×D4—444no—
878C2×D4—444no—
879C2×D4—444no—
880C2×D4—444no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4—444no—
884C2×D4—444no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
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—28no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—112no—
926C22×C4—112no—
927C22×C4—112no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—112no—
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×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4C2×C4×D1112yes—
975C22×C4D4×D1112yes—
976C22×C4#434112yes—
977C22×C4C2×C22⋊D1112yes—
978C22×C4C2×C22⋊D1112yes—
979C4⋊C4—444no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—228no—
984C22⋊C4—228no—
985C22⋊C4—444no—
986C22⋊C4—444no—
987C22⋊C4—444no—
988C22⋊C4—444no—
989C22⋊C4—444no—
990C22⋊C4—444no—
991C22⋊C4—444no—
992C22⋊C4—444no—
993C22⋊C4—444no—
994C42—444no—
995C42—444no—
996C11#1431111yescharacteristic, complemented, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23C4×C22⋊D1114yes—
1102C23C22×C4×D1111yescharacteristic
1103C23C2×#433911yescharacteristic
1104C23C2×D4×D1111yescharacteristic
1105C23C2×#434111yescharacteristic
1106C23#6703711yescharacteristic
1107C23#6703711yescharacteristic
1108C23#6703711yescharacteristic
1109C23#6703711yescharacteristic
1110C23#6703711yescharacteristic
1111C23#6703711yescharacteristic
1112C23#41×D1111yescharacteristic
1113C23#41×D1111yescharacteristic
1114C23#6704211yescharacteristic
1115C23#6704211yescharacteristic
1116C23C22×C22⋊D1111yescharacteristic
1117D4—416no—
1118D4—4416no—
1119D4—4416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—416no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—114no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—222no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—222no—
1164C2×C4—222no—
1165C2×C4—222no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—441no—
1175C2×C4—441no—
1176C2×C4—441no—
1177C2×C4—441no—
1178C2×C4—441no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C2×C4—441no—
1190C2×C4—441no—
1191C2×C4—441no—
1192C2×C4—441no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—441no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4#6699214yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—442no—
1236C22—442no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—881no—
1243C22—881no—
1244C22—881no—
1245C22—881no—
1246C22—881no—
1247C22—881no—
1248C22—881no—
1249C22—881no—
1250C22#1062301711yescharacteristic
1251C22#1062301711yescharacteristic
1252C22#1062302511yescharacteristic
1253C22#1062302511yescharacteristic
1254C22C4×#434111yescharacteristic
1255C22#1062306911yescharacteristic
1256C22C4×D4×D1111yescharacteristic
1257C22#1062307611yescharacteristic
1258C22#1062307611yescharacteristic
1259C22#1062307811yescharacteristic
1260C22#1062309111yescharacteristic
1261C22#1062309111yescharacteristic
1262C22#1062312011yescharacteristic
1263C22#1062312311yescharacteristic
1264C22#1062312411yescharacteristic
1265C22#1062312411yescharacteristic
1266C22#1062313811yescharacteristic
1267C22#1062313811yescharacteristic
1268C22#1062314411yescharacteristic
1269C22#1062314411yescharacteristic
1270C22#1062314611yescharacteristic
1271C22#1062314611yescharacteristic
1272C22#1062315011yescharacteristic
1273C22#1062315011yescharacteristic
1274C22#1062318811yescharacteristic
1275C22#1062318811yescharacteristic
1276C22#1062319411yescharacteristic
1277C22#1062319411yescharacteristic
1278C22C2×C4×C22⋊D1111yescharacteristic
1279C22C2×#6699211yescharacteristic
1280C22#1062333511yescharacteristic
1281C22#1062333511yescharacteristic
1282C22#1062333611yescharacteristic
1283C22#1062336111yescharacteristic
1284C22#1062336311yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—81no—
1289C4—81no—
1290C4—224no—
1291C4—442no—
1292C4—442no—
1293C4—442no—
1294C4—442no—
1295C4—881no—
1296C4—881no—
1297C2—44no—
1298C2—82no—
1299C2—882no—
1300C2C4×#6699211yescharacteristic
1301C2#1307127011yescharacteristic
1302C2#1307127211yescharacteristic
1303C2#1307127411yescharacteristic
1304C2#1307133711yescharacteristic
1305C2#1307137711yescharacteristic
1306C2#1307138211yescharacteristic
1307C2#1307435411yescharacteristic
1308C2#1307437011yescharacteristic
1309C2#1307447211yescharacteristic
1310C2#1307450411yescharacteristic
1311C2#1307460411yescharacteristic
1312C2#1307460611yescharacteristic
1313C2#1307474411yescharacteristic
1314C2#1307474511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622826C2semidirect
4. C2×C4×C22⋊Dic11C2semidirect
5. #13066871C2semidirect
6. #13066864C2semidirect
7. #13066863C2semidirect
8. #13066859C2semidirect
9. #13066857C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066853C2semidirect
13. #13066852C2semidirect
14. #13066842C2semidirect
15. C2×C11×#386C2semidirect
40. #10622836C4semidirect
72. C23×C4×C11D4semidirect
91. C22×C22⋊D11C2×C4semidirect
125. C2×C22⋊Dic11C2×C4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
149. C2×C4×Dic11D4semidirect
163. C11⋊#95C2×C4semidirect
343. C2×#386D11semidirect
732. C23×C4C22⋊D11semidirect
996. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225702
C2×#106228262
C2×C4×C22⋊Dic112
#130668712
#130668642
#130668632
#130668592
#130668572
#130668552
#130668532
#130668522
#130668422
C2×C11×#3862
#1431111