Finite Group Databasebeta

← #14683110

Subgroups — #14683110

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7C2×#10622281C211yesmaximal, characteristic, complemented
8#13066871C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066861C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic, complemented
13#13066852C211yesmaximal, characteristic, complemented
14#13066840C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622826—24no—
42#10622826—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
53#10622573C418yescomplemented
54#10622570—24no—
55#10622569—24no—
56#10622281—24no—
57#10622278—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
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⋊D11C2×C414yes—
87C22×C22⋊D11C2×C414yescomplemented
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—22no—
95C22×D44—22no—
96C22×D44—41no—
97C22×D44—41no—
98C22×D44—41no—
99C22×D44—41no—
100C22×D44C2×C414yescomplemented
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4C2×C414yescomplemented
113C2×C11×C22⋊C4D414yescomplemented
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
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—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)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4C2×C414yescomplemented
145C2×(C2×D11)⋊C4C2×C414yescomplemented
146C2×(C2×D11)⋊C4D414yescomplemented
147C2×C4⋊Dic11—22no—
148C2×C4⋊Dic11—41no—
149C2×C4⋊Dic11—41no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—41no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—41no—
156C11×#95—22no—
157C11×#95—22no—
158C11×#95—41no—
159C11×#95—41no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95C2×C414yescomplemented
169C11⋊#95D414yescomplemented
170#14519—111nomaximal, Sylow
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×C11C22×C412yes—
184C24×C11C2×D412yes—
185C24×C11#4112yes—
186C24×C11C2411yescharacteristic
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×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11C22×C412yes—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
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×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—44no—
254C22×C4×C11—44no—
255C22×C4×C11—44no—
256C22×C4×C11—44no—
257C22×C4×C11—44no—
258C22×C4×C11—44no—
259C22×C4×C11—44no—
260C22×C4×C11C22×C412yes—
261C22×C4×C11C22×C412yes—
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
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×Dic11C2×D412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11#4112yes—
322C2×D44—28no—
323C2×D44—44no—
324C2×D44—44no—
325C2×D44—44no—
326C2×D44—44no—
327C2×D44—44no—
328C2×D44—44no—
329C2×C4×D11—44no—
330C2×C4×D11—44no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C11×C22⋊C4—44no—
337C11×C22⋊C4—44no—
338C22⋊Dic11—44no—
339C22⋊Dic11—44no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—44no—
349C4⋊Dic11—44no—
350Dic11⋊C4—44no—
351C4×Dic11—44no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#386—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#386—111no—
358C2×#385—111no—
359#1442—111no—
360#1440—111no—
361#1439—111no—
362#1439—111no—
363#1438—111no—
364#1437—111no—
365#1434—111no—
366C22⋊#95D1111yescharacteristic, complemented
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—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
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×C11C4×D414yes—
402C23×C11C23×C411yescharacteristic
403C23×C11C22×D411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C11H(5,𝔽2)11yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C112−1+411yescharacteristic
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
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—
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—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11C4×D414yes—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—416no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C22⋊D11—416no—
531C22⋊D11—416no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
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×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11C4×D414yes—
574D44—416no—
575C4×D11—416no—
576C23×D4—111no—
577C23×D4—111no—
578C23×D4—111no—
579C24×C4—111no—
580C24×C4C2×D1111yescharacteristic
581C22×C4⋊C4—111no—
582C22×C4⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4C2×D1111yescharacteristic
595C22×C22⋊C4C2×D1111yescharacteristic
596C22×C42—111no—
597#392—118no—
598#390—224no—
599#386—224no—
600#386—224no—
601#386—224no—
602#386—224no—
603#385—224no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95C2×D1111yescharacteristic
615C2×#95C2×D1111yescharacteristic
616C2×#95C2×D1111yescharacteristic
617C2×#95C2×D1111yescharacteristic
618C22×C11—24no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11C2×C4×D411yescharacteristic
634C22×C11C2×C4×D411yescharacteristic
635C22×C11C2×C4×D411yescharacteristic
636C22×C11#51811yescharacteristic
637C22×C11#51811yescharacteristic
638C22×C11#51811yescharacteristic
639C22×C11#52011yescharacteristic
640C22×C11#53411yescharacteristic
641C22×C11#53411yescharacteristic
642C22×C11#53511yescharacteristic
643C22×C11#53511yescharacteristic
644C22×C11#53511yescharacteristic
645C22×C11#53711yescharacteristic
646C22×C11#53811yescharacteristic
647C22×C11#53811yescharacteristic
648C22×C11#53811yescharacteristic
649C22×C11#53911yescharacteristic
650C22×C11#54011yescharacteristic
651C22×C11#54011yescharacteristic
652C22×C11D4211yescharacteristic
653C22×C11D4211yescharacteristic
654C22×C11D4211yescharacteristic
655C22×C11#54611yescharacteristic
656C22×C11#54611yescharacteristic
657C22×C11#54611yescharacteristic
658C22×C11#54611yescharacteristic
659C22×C11#54711yescharacteristic
660C22×C11#54811yescharacteristic
661C22×C11#55111yescharacteristic
662C22×C11#55111yescharacteristic
663C22×C11#55311yescharacteristic
664C22×C11#56011yescharacteristic
665C22×C11#56011yescharacteristic
666C22×C11#56211yescharacteristic
667C22×C11#56211yescharacteristic
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C2×D11—81no—
694C2×D11—81no—
695C2×D11—81no—
696C2×D11—81no—
697C2×D11—81no—
698C4×C11—42no—
699C4×C11—42no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—42no—
704Dic11—24no—
705Dic11—42no—
706Dic11—42no—
707Dic11—42no—
708Dic11—81no—
709Dic11—81no—
710C25—111no—
711C25—111no—
712C25C22×D1111yescharacteristic
713C22×D4—114no—
714C22×D4—114no—
715C22×D4—114no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—222no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4—441no—
730C22×D4—441no—
731C22×D4—441no—
732C22×D4—441no—
733C22×D4—441no—
734C23×C4—22no—
735C23×C4—22no—
736C23×C4—22no—
737C23×C4—41no—
738C23×C4—41no—
739C23×C4—41no—
740C23×C4—41no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—222no—
748C23×C4—222no—
749C23×C4—222no—
750C23×C4—441no—
751C23×C4—441no—
752C23×C4—441no—
753C23×C4—441no—
754C23×C4C22×D1111yescharacteristic
755C23×C4C22×D1111yescharacteristic
756C23×C4C22×D1111yescharacteristic
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C2×C4⋊C4—222no—
761C2×C4⋊C4—222no—
762C2×C4⋊C4—222no—
763C2×C4⋊C4—441no—
764C2×C4⋊C4—441no—
765C2×C4⋊C4—441no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—114no—
771C2×C22⋊C4—114no—
772C2×C22⋊C4—114no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—222no—
788C2×C22⋊C4—222no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4C4×D1114yescomplemented
804C2×C22⋊C4D4414yescomplemented
805C2×C42—222no—
806C2×C42—222no—
807C2×C42—441no—
808#95—22no—
809#95—22no—
810#95—41no—
811#95—41no—
812#95—114no—
813#95—114no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—441no—
821#95—441no—
822C2×C11—44no—
823C2×C11#232111yescharacteristic
824C2×C11#232511yescharacteristic
825C2×C11#232811yescharacteristic
826C2×C11#235811yescharacteristic
827C2×C11#235811yescharacteristic
828C2×C11#236111yescharacteristic
829C2×C11#237711yescharacteristic
830C2×C11#266911yescharacteristic
831C2×C11#267111yescharacteristic
832C2×C11#267611yescharacteristic
833C2×C11#267811yescharacteristic
834C2×C11#268811yescharacteristic
835C2×C11#269611yescharacteristic
836C2×C11#270611yescharacteristic
837C2×C11#274911yescharacteristic
838D11—44no—
839D11—82no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—112no—
853C24—112no—
854C24—112no—
855C24—112no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24C2×C4×D1112yes—
883C24C2×D4412yes—
884C24#433912yes—
885C24C23×D1111yescharacteristic
886C2×D4—228no—
887C2×D4—228no—
888C2×D4—228no—
889C2×D4—228no—
890C2×D4—228no—
891C2×D4—444no—
892C2×D4—444no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
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—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—112no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
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×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—444no—
993C22×C4—444no—
994C22×C4—444no—
995C22×C4—444no—
996C22×C4—444no—
997C22×C4—444no—
998C22×C4—444no—
999C22×C4C2×C4×D1112yes—
1000C22×C4C2×C4×D1112yes—
1001C22×C4C2×D4412yes—
1002C22×C4C2×D4412yes—
1003C22×C4D4×D1112yes—
1004C22×C4D4×D1112yes—
1005C4⋊C4—444no—
1006C4⋊C4—444no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—228no—
1010C22⋊C4—444no—
1011C22⋊C4—444no—
1012C22⋊C4—444no—
1013C22⋊C4—444no—
1014C22⋊C4—444no—
1015C22⋊C4—444no—
1016C22⋊C4—444no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C42—444no—
1021C11#1451911yescharacteristic, complemented, Sylow
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
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—114no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23—222no—
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—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23C4×D4414yes—
1127C23C22×C4×D1111yescharacteristic
1128C23C22×D4411yescharacteristic
1129C23C2×#433911yescharacteristic
1130C23C2×D4×D1111yescharacteristic
1131C23C2×D4×D1111yescharacteristic
1132C23#6703711yescharacteristic
1133C23#6703711yescharacteristic
1134C23#6703711yescharacteristic
1135C23#6703711yescharacteristic
1136C23#6703711yescharacteristic
1137C23#6704011yescharacteristic
1138C23#41×D1111yescharacteristic
1139C23#41×D1111yescharacteristic
1140C23#6704211yescharacteristic
1141C23#6704211yescharacteristic
1142D4—4416no—
1143D4—4416no—
1144D4—4416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—416no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—114no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—4416no—
1205C2×C4—441no—
1206C2×C4—441no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—224no—
1247C22—224no—
1248C22—224no—
1249C22—442no—
1250C22—442no—
1251C22—442no—
1252C22—442no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—442no—
1260C22—442no—
1261C22—442no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—881no—
1269C22—881no—
1270C22—881no—
1271C22—881no—
1272C22—881no—
1273C22—881no—
1274C22—881no—
1275C22—881no—
1276C22C2×C4×D4411yescharacteristic
1277C22#1062301711yescharacteristic
1278C22#1062302111yescharacteristic
1279C22#1062302111yescharacteristic
1280C22#1062302411yescharacteristic
1281C22#1062302511yescharacteristic
1282C22#1062303511yescharacteristic
1283C22#1062304111yescharacteristic
1284C22#1062304611yescharacteristic
1285C22#1062305811yescharacteristic
1286C22#1062305811yescharacteristic
1287C22C4×D4×D1111yescharacteristic
1288C22C4×D4×D1111yescharacteristic
1289C22#1062307611yescharacteristic
1290C22#1062307611yescharacteristic
1291C22D4×D4411yescharacteristic
1292C22D4×D4411yescharacteristic
1293C22#1062308511yescharacteristic
1294C22#1062308511yescharacteristic
1295C22#1062312011yescharacteristic
1296C22#1062312111yescharacteristic
1297C22#1062312311yescharacteristic
1298C22#1062312611yescharacteristic
1299C22#1062313811yescharacteristic
1300C22#1062313811yescharacteristic
1301C22#1062314411yescharacteristic
1302C22#1062314611yescharacteristic
1303C22#1062316211yescharacteristic
1304C22#1062316411yescharacteristic
1305C22#1062317811yescharacteristic
1306C22#1062317811yescharacteristic
1307C22#1062318811yescharacteristic
1308C22#1062319211yescharacteristic
1309C22#1062319411yescharacteristic
1310C22#1062319711yescharacteristic
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—224no—
1318C4—442no—
1319C4—442no—
1320C4—442no—
1321C4—881no—
1322C4—881no—
1323C2—44no—
1324C2—444no—
1325C2—882no—
1326C2#1307127211yescharacteristic
1327C2#1307131911yescharacteristic
1328C2#1307133711yescharacteristic
1329C2#1307159811yescharacteristic
1330C2#1307159811yescharacteristic
1331C2#1307163511yescharacteristic
1332C2#1307177211yescharacteristic
1333C2#1307483411yescharacteristic
1334C2#1307485511yescharacteristic
1335C2#1307492011yescharacteristic
1336C2#1307494511yescharacteristic
1337C2#1307505011yescharacteristic
1338C2#1307516611yescharacteristic
1339C2#1307530411yescharacteristic
1340C2#1307583511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22⋊#95D11
hypocenterC11#14519
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622569C2semidirect
7. C2×#10622281C2semidirect
8. #13066871C2semidirect
9. #13066864C2semidirect
10. #13066862C2semidirect
11. #13066861C2semidirect
12. #13066856C2semidirect
13. #13066852C2semidirect
14. #13066840C2semidirect
15. C11×C22⋊#95C2semidirect
53. #10622573C4semidirect
87. C22×C22⋊D11C2×C4semidirect
100. C22×D44C2×C4semidirect
112. C2×C11×C22⋊C4C2×C4semidirect
113. C2×C11×C22⋊C4D4semidirect
144. C2×(C2×D11)⋊C4C2×C4semidirect
145. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×(C2×D11)⋊C4D4semidirect
168. C11⋊#95C2×C4semidirect
169. C11⋊#95D4semidirect
366. C22⋊#95D11semidirect
803. C2×C22⋊C4C4×D11semidirect
804. C2×C22⋊C4D44semidirect
1021. C11#14519semidirect

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×#106228262
C2×#106222782
C2×#106225692
C2×#106222812
#130668712
#130668642
#130668622
#130668612
#130668562
#130668522
#130668402
C11×C22⋊#952
#1451911