Finite Group Databasebeta

← #14685197

Subgroups — #14685197

Order 2816.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
2C2×#10622835C211yesmaximal, characteristic, complemented
3C2×#10622836C211yesmaximal, characteristic
4C2×#10622569C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6#13066879C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C22×C11×#123C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C2×C11×#123—24no—
22C2×C11×#123—24no—
23C2×C11×#123—24no—
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×C4×C22⋊D11—24no—
36C2×C4×C22⋊D11—24no—
37C2×C4×C22⋊D11—24no—
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45#10622836—24no—
46#10622835—24no—
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622602—24no—
60#10622569—24no—
61C25×C11C2311yescharacteristic
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C23×C4×C11—22no—
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—22no—
75C23×C4×C11—41no—
76C23×C4×C11—41no—
77C23×C4×C11D414yescomplemented
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—22no—
88C22×C22⋊D11—22no—
89C22×C22⋊D11—22no—
90C22×C22⋊D11—22no—
91C22×C22⋊D11—22no—
92C22×C22⋊D11—22no—
93C22×C22⋊D11—22no—
94C22×C22⋊D11—41no—
95C22×C22⋊D11—41no—
96C22×C22⋊D11D414yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—22no—
109C22×C4×D11—41no—
110C22×C4×D11—41no—
111C11×#123—232no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—22no—
117C2×C11×C4⋊C4D414yescomplemented
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4D414yescomplemented
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—22no—
131C2×C22⋊Dic11—22no—
132C2×C22⋊Dic11—22no—
133C2×C22⋊Dic11—22no—
134C2×C22⋊Dic11—22no—
135C2×C22⋊Dic11—22no—
136C2×C22⋊Dic11—22no—
137C2×C22⋊Dic11—22no—
138C2×C22⋊Dic11—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—41no—
141C2×C22⋊Dic11—41no—
142C2×C22⋊Dic11—41no—
143C2×C22⋊Dic11—41no—
144C2×C22⋊Dic11D414yescomplemented
145C4×C22⋊D11—232no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—22no—
155C2×(C2×D11)⋊C4—22no—
156C2×(C2×D11)⋊C4—41no—
157C2×(C2×D11)⋊C4—41no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—22no—
160C2×Dic11⋊C4—22no—
161C2×Dic11⋊C4—22no—
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4—41no—
164C2×C4×Dic11—22no—
165C2×C4×Dic11—22no—
166C2×C4×Dic11—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—41no—
177C11⋊#95—41no—
178C11⋊#95—41no—
179#14721—111nomaximal, Sylow
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×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11C2×D412yes—
207C24×C11C2×D412yes—
208C24×C11C2×D412yes—
209C24×C11C2×D412yes—
210C24×C11C2411yescharacteristic
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—21no—
223C23×D11C2×D412yes—
224C23×D11#4112yes—
225C23×D11#4112yes—
226C2×D4×C11—28no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11—44no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—28no—
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—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—28no—
263C22×C4×C11—44no—
264C22×C4×C11—44no—
265C22×C4×C11—44no—
266C22×C4×C11—44no—
267C22×C4×C11—44no—
268C22×C4×C11C2×D412yes—
269C22×C4×C11C2×D412yes—
270C22×C4×C11C2×D412yes—
271C22×C4×C11C2×D412yes—
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D412yes—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—28no—
277C2×C22⋊D11—28no—
278C2×C22⋊D11—28no—
279C2×C22⋊D11—28no—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—28no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—44no—
286C2×C22⋊D11—44no—
287C2×C22⋊D11—44no—
288C2×C22⋊D11—44no—
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×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11#4112yes—
335C22×Dic11#4112yes—
336C22×Dic11#4112yes—
337C22×Dic11#4112yes—
338C2×C4×D11—28no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C2×C4×D11—44no—
344C2×C4×D11—44no—
345C11×C4⋊C4—28no—
346C11×C4⋊C4—28no—
347C11×C22⋊C4—28no—
348C11×C22⋊C4—28no—
349C11×C22⋊C4—28no—
350C22⋊Dic11—28no—
351C22⋊Dic11—44no—
352C22⋊Dic11—44no—
353C22⋊Dic11—44no—
354C22⋊Dic11—44no—
355C22⋊Dic11—44no—
356(C2×D11)⋊C4—28no—
357(C2×D11)⋊C4—28no—
358(C2×D11)⋊C4—44no—
359(C2×D11)⋊C4—44no—
360Dic11⋊C4—28no—
361Dic11⋊C4—44no—
362C4×Dic11—28no—
363C22×#123D1111yescharacteristic, complemented
364C22×C4×D4—111no—
365C2×#394—111no—
366C2×#392—111no—
367C2×#386—111no—
368C2×#385—111no—
369#1444—111no—
370#1440—111no—
371#1439—111no—
372#1439—111no—
373#1438—111no—
374#1438—111no—
375#1437—111no—
376#1436—111no—
377C22⋊#95—111no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
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×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11#12014yes—
448C23×C11C22×D411yescharacteristic
449C23×C11C22×D411yescharacteristic
450C23×C11C22×D411yescharacteristic
451C23×C11C22×D411yescharacteristic
452C23×C11C22×D411yescharacteristic
453C23×C11C2×#4111yescharacteristic
454C23×C11C2×#4111yescharacteristic
455C23×C11C2×#4111yescharacteristic
456C23×C11C2×#4111yescharacteristic
457C23×C11C2×#4111yescharacteristic
458C23×C11C2×#4111yescharacteristic
459C23×C11H(5,𝔽2)11yescharacteristic
460C23×C11H(5,𝔽2)11yescharacteristic
461C23×C11H(5,𝔽2)11yescharacteristic
462C23×C112−1+411yescharacteristic
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11—41no—
496C22×D11—41no—
497C22×D11#12314yescomplemented
498D4×C11—416no—
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—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—416no—
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—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11#12014yes—
535C22⋊D11—232no—
536C22⋊D11—416no—
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—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
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×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—41no—
584C2×Dic11—41no—
585C2×Dic11#12314yescomplemented
586C4×D11—416no—
587C23×D4—111no—
588C23×D4—111no—
589C23×D4C2×D1111yescharacteristic
590C24×C4—111no—
591C24×C4C2×D1111yescharacteristic
592C2×#123—24no—
593C2×#123—24no—
594C2×#123—24no—
595C2×C4×D4—224no—
596C2×C4×D4—224no—
597C2×C4×D4—224no—
598C22×C4⋊C4—111no—
599C22×C4⋊C4—111no—
600C22×C4⋊C4C2×D1111yescharacteristic
601C22×C4⋊C4C2×D1111yescharacteristic
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4—111no—
605C22×C22⋊C4—111no—
606C22×C22⋊C4—111no—
607C22×C22⋊C4—111no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—111no—
611C22×C22⋊C4—111no—
612C22×C22⋊C4C2×D1111yescharacteristic
613C22×C22⋊C4C2×D1111yescharacteristic
614C22×C22⋊C4C2×D1111yescharacteristic
615C22×C42—111no—
616#394—224no—
617#392—224no—
618#386—224no—
619#385—224no—
620C2×#95—111no—
621C2×#95—111no—
622C2×#95—111no—
623C2×#95—111no—
624C2×#95—111no—
625C2×#95—111no—
626C2×#95—111no—
627C2×#95—111no—
628C2×#95—111no—
629C2×#95—111no—
630C2×#95—111no—
631C2×#95—111no—
632C22×C11—24no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—81no—
655C22×C11—81no—
656C22×C11—81no—
657C22×C11—81no—
658C22×C11—81no—
659C22×C11—81no—
660C22×C11—81no—
661C22×C11—81no—
662C22×C11C2×#12011yescharacteristic
663C22×C11C2×#12011yescharacteristic
664C22×C11C2×#12311yescharacteristic
665C22×C11C2×#12311yescharacteristic
666C22×C11#52511yescharacteristic
667C22×C11#52511yescharacteristic
668C22×C11#52511yescharacteristic
669C22×C11#52511yescharacteristic
670C22×C11#52511yescharacteristic
671C22×C11#52511yescharacteristic
672C22×C11#53211yescharacteristic
673C22×C11#53211yescharacteristic
674C22×C11#53211yescharacteristic
675C22×C11#53411yescharacteristic
676C22×C11#53711yescharacteristic
677C22×C11#53811yescharacteristic
678C22×C11#53911yescharacteristic
679C22×C11#54011yescharacteristic
680C22×C11#54211yescharacteristic
681C22×C11D4211yescharacteristic
682C22×C11D4211yescharacteristic
683C22×C11D4211yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11#54611yescharacteristic
686C22×C11#54611yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54711yescharacteristic
689C22×C11#54711yescharacteristic
690C22×C11#54711yescharacteristic
691C22×C11#54811yescharacteristic
692C22×C11#55011yescharacteristic
693C22×C11#55111yescharacteristic
694C22×C11#55311yescharacteristic
695C22×C11#55311yescharacteristic
696C22×C11#55911yescharacteristic
697C2×D11—24no—
698C2×D11—24no—
699C2×D11—24no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—42no—
709C2×D11—42no—
710C2×D11—42no—
711C2×D11—42no—
712C4×C11—24no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11—42no—
716C4×C11—42no—
717Dic11—24no—
718Dic11—42no—
719Dic11—42no—
720Dic11—42no—
721Dic11—42no—
722Dic11—81no—
723Dic11—81no—
724C25—111no—
725C25C22×D1111yescharacteristic
726C25C22×D1111yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—114no—
735C22×D4—222no—
736C22×D4—222no—
737C22×D4—222no—
738C22×D4—222no—
739C22×D4—222no—
740C22×D4—222no—
741C22×D4—222no—
742C22×D4—222no—
743C22×D4—222no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4—441no—
747C22×D4—441no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—111no—
759C23×C4—111no—
760C23×C4—111no—
761C23×C4—222no—
762C23×C4—222no—
763C23×C4—222no—
764C23×C4—222no—
765C23×C4—222no—
766C23×C4—441no—
767C23×C4—441no—
768C23×C4C22⋊D1114yescomplemented
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771C23×C4C22×D1111yescharacteristic
772C23×C4C22×D1111yescharacteristic
773C23×C4C22×D1111yescharacteristic
774#123—232no—
775C4×D4—2232no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—222no—
782C2×C4⋊C4—222no—
783C2×C4⋊C4—222no—
784C2×C4⋊C4—222no—
785C2×C4⋊C4—222no—
786C2×C4⋊C4—441no—
787C2×C4⋊C4C22⋊D1114yescomplemented
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—114no—
797C2×C22⋊C4—222no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—222no—
805C2×C22⋊C4—222no—
806C2×C22⋊C4—222no—
807C2×C22⋊C4—222no—
808C2×C22⋊C4—222no—
809C2×C22⋊C4—222no—
810C2×C22⋊C4—222no—
811C2×C22⋊C4—222no—
812C2×C22⋊C4—222no—
813C2×C22⋊C4—222no—
814C2×C22⋊C4—222no—
815C2×C22⋊C4—222no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—222no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—441no—
821C2×C22⋊C4—441no—
822C2×C22⋊C4—441no—
823C2×C22⋊C4—441no—
824C2×C22⋊C4—441no—
825C2×C22⋊C4—441no—
826C2×C22⋊C4C22⋊D1114yescomplemented
827C2×C42—222no—
828C2×C42—222no—
829C2×C42—222no—
830#95—222no—
831#95—222no—
832#95—222no—
833#95—222no—
834#95—222no—
835#95—222no—
836#95—222no—
837#95—222no—
838#95—222no—
839#95—441no—
840#95—441no—
841#95—441no—
842C2×C11—44no—
843C2×C11—82no—
844C2×C11#238811yescharacteristic
845C2×C11#240311yescharacteristic
846C2×C11#240711yescharacteristic
847C2×C11#241811yescharacteristic
848C2×C11#242211yescharacteristic
849C2×C11#243011yescharacteristic
850C2×C11#244311yescharacteristic
851C2×C11#244511yescharacteristic
852C2×C11#245511yescharacteristic
853C2×C11#245611yescharacteristic
854C2×C11#246111yescharacteristic
855C2×C11#246411yescharacteristic
856C2×C11#260211yescharacteristic
857C2×C11#263011yescharacteristic
858C2×C11#284911yescharacteristic
859D11—44no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—112no—
887C24—112no—
888C24—112no—
889C24—221no—
890C24—221no—
891C24—221no—
892C24—221no—
893C24—221no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24—221no—
899C24—221no—
900C24—221no—
901C24D4×D1112yes—
902C24D4×D1112yes—
903C24C2×C22⋊D1112yes—
904C24C2×C22⋊D1112yes—
905C24C23×D1111yescharacteristic
906C2×D4—28no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—228no—
914C2×D4—228no—
915C2×D4—228no—
916C2×D4—228no—
917C2×D4—228no—
918C2×D4—228no—
919C2×D4—228no—
920C2×D4—228no—
921C2×D4—444no—
922C2×D4—444no—
923C2×D4—444no—
924C2×D4—444no—
925C2×D4—444no—
926C2×D4—444no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—28no—
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—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—28no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—112no—
967C22×C4—112no—
968C22×C4—112no—
969C22×C4—228no—
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—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4—444no—
1015C22×C4—444no—
1016C22×C4—444no—
1017C22×C4—444no—
1018C22×C4C2×C22⋊D1112yes—
1019C22×C4C2×C22⋊D1112yes—
1020C22×C4C2×C22⋊D1112yes—
1021C22×C4C2×C22⋊D1112yes—
1022C22×C4C2×C22⋊D1112yes—
1023C22×C4C2×C22⋊D1112yes—
1024C22×C4C2×C22⋊D1112yes—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—228no—
1028C4⋊C4—444no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—228no—
1033C22⋊C4—228no—
1034C22⋊C4—228no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4—444no—
1038C22⋊C4—444no—
1039C22⋊C4—444no—
1040C22⋊C4—444no—
1041C22⋊C4—444no—
1042C42—228no—
1043C11#1472111yescharacteristic, complemented, Sylow
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—114no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—222no—
1121C23—222no—
1122C23—222no—
1123C23—222no—
1124C23—222no—
1125C23—222no—
1126C23—222no—
1127C23—222no—
1128C23—222no—
1129C23—222no—
1130C23—222no—
1131C23—222no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23#6699014yes—
1149C23C2×D4×D1111yescharacteristic
1150C23C2×D4×D1111yescharacteristic
1151C23#6703711yescharacteristic
1152C23#6703711yescharacteristic
1153C23#41×D1111yescharacteristic
1154C23#41×D1111yescharacteristic
1155C23#41×D1111yescharacteristic
1156C23#41×D1111yescharacteristic
1157C23#41×D1111yescharacteristic
1158C23#41×D1111yescharacteristic
1159C23#6704211yescharacteristic
1160C23#6704311yescharacteristic
1161C23C22×C22⋊D1111yescharacteristic
1162C23C22×C22⋊D1111yescharacteristic
1163C23C22×C22⋊D1111yescharacteristic
1164D4—416no—
1165D4—2232no—
1166D4—4416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—416no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—114no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—222no—
1220C2×C4—222no—
1221C2×C4—4416no—
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—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4—441no—
1248C2×C4—441no—
1249C2×C4—441no—
1250C2×C4—441no—
1251C2×C4—441no—
1252C2×C4#6700614yes—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—224no—
1284C22—224no—
1285C22—224no—
1286C22—442no—
1287C22—442no—
1288C22—442no—
1289C22—442no—
1290C22—442no—
1291C22—442no—
1292C22—442no—
1293C22—442no—
1294C22—442no—
1295C22—442no—
1296C22—442no—
1297C22—442no—
1298C22D11×#12311yescharacteristic
1299C22D11×#12311yescharacteristic
1300C22#1062318511yescharacteristic
1301C22#1062318511yescharacteristic
1302C22#1062318611yescharacteristic
1303C22#1062318611yescharacteristic
1304C22#1062318711yescharacteristic
1305C22#1062318711yescharacteristic
1306C22#1062318811yescharacteristic
1307C22#1062319011yescharacteristic
1308C22#1062319111yescharacteristic
1309C22#1062319211yescharacteristic
1310C22#1062319211yescharacteristic
1311C22#1062319311yescharacteristic
1312C22#1062319411yescharacteristic
1313C22#1062319511yescharacteristic
1314C22C2×#6699011yescharacteristic
1315C22D4×C22⋊D1111yescharacteristic
1316C22D4×C22⋊D1111yescharacteristic
1317C22D4×C22⋊D1111yescharacteristic
1318C22D4×C22⋊D1111yescharacteristic
1319C22#1062333511yescharacteristic
1320C22#1062335511yescharacteristic
1321C22#1062335911yescharacteristic
1322C22#1062335911yescharacteristic
1323C22#1062335911yescharacteristic
1324C22#1062335911yescharacteristic
1325C22#1062336011yescharacteristic
1326C22#1062336211yescharacteristic
1327C22#1062336311yescharacteristic
1328C22#1062336311yescharacteristic
1329C22#1062336311yescharacteristic
1330C22#1062336411yescharacteristic
1331C22#1062336511yescharacteristic
1332C22C2×#6700611yescharacteristic
1333C4—24no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—224no—
1339C4—442no—
1340C4—442no—
1341C4—442no—
1342C4—442no—
1343C4—881no—
1344C4—881no—
1345C2—44no—
1346C2—82no—
1347C2—444no—
1348C2#1307182911yescharacteristic
1349C2#1307192611yescharacteristic
1350C2#1307195511yescharacteristic
1351C2#1307207511yescharacteristic
1352C2#1307212711yescharacteristic
1353C2#1307222811yescharacteristic
1354C2#1307234811yescharacteristic
1355C2#1307238011yescharacteristic
1356C2#1307249511yescharacteristic
1357C2#1307250411yescharacteristic
1358C2#1307258211yescharacteristic
1359C2#1307261911yescharacteristic
1360C2#1307423011yescharacteristic
1361C2#1307445511yescharacteristic
1362C2#1307690511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C11×#123C2
prime radicalC2×#10622836C2
hypercenterC22×#123D11
hypocenterC11#14721
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D11C2semidirect
2. C2×#10622835C2semidirect
4. C2×#10622569C2semidirect
5. C2×#10622602C2semidirect
6. #13066879C2semidirect
7. #13066863C2semidirect
8. #13066859C2semidirect
9. #13066858C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066853C2semidirect
13. #13066848C2semidirect
14. #13066839C2semidirect
15. C22×C11×#123C2semidirect
77. C23×C4×C11D4semidirect
117. C2×C11×C4⋊C4D4semidirect
126. C2×C11×C22⋊C4D4semidirect
144. C2×C22⋊Dic11D4semidirect
363. C22×#123D11semidirect
497. C22×D11#123semidirect
585. C2×Dic11#123semidirect
768. C23×C4C22⋊D11semidirect
787. C2×C4⋊C4C22⋊D11semidirect
826. C2×C22⋊C4C22⋊D11semidirect
1043. C11#14721semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228352
C2×#106228362
C2×#106225692
C2×#106226022
#130668792
#130668632
#130668592
#130668582
#130668552
#130668532
#130668482
#130668392
C22×C11×#1232
#1472111