Finite Group Databasebeta

← #14676577

Subgroups — #14676577

Order 2816.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622826C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622280C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066865C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
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×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66937—24no—
43C2×#66937—24no—
44C2×#66937C418yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49#10622826—24no—
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622570—24no—
59#10622280—24no—
60#10622279—24no—
61#10622278—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11C2311yescharacteristic
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—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—41no—
87C22×C22⋊D11—41no—
88C22×C22⋊D11C2×C414yes—
89C22×C22⋊D11C2×C414yescomplemented
90C22×C22⋊D11D414yes—
91C22×C22⋊D11D414yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×D44—22no—
99C22×D44—22no—
100C22×D44—22no—
101C22×D44—22no—
102C22×D44—41no—
103C22×D44—41no—
104C22×D44C2×C414yescomplemented
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C4×D11—22no—
111C22×C4×D11—22no—
112C22×C4×D11—22no—
113C22×C4×D11—22no—
114C22×C4×D11—22no—
115C22×C4×D11—22no—
116C22×C4×D11—41no—
117C22×C4×D11—41no—
118C22×C4×D11C2×C414yescomplemented
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—41no—
124C2×C11×C22⋊C4C2×C414yescomplemented
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—41no—
131C4×C22⋊D11—232no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—41no—
151C2×(C2×D11)⋊C4—41no—
152C2×(C2×D11)⋊C4—41no—
153C2×(C2×D11)⋊C4—41no—
154C2×(C2×D11)⋊C4C2×C414yescomplemented
155C2×(C2×D11)⋊C4D414yescomplemented
156C2×Dic11⋊C4—22no—
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—22no—
160C2×Dic11⋊C4—22no—
161C2×Dic11⋊C4—22no—
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4C2×C414yescomplemented
164C2×Dic11⋊C4D414yescomplemented
165C2×C4×Dic11—22no—
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169C2×C4×Dic11—22no—
170C2×C4×Dic11D414yescomplemented
171#66937—232no—
172C11×#95—22no—
173C11×#95—22no—
174C11×#95—22no—
175C11×#95—41no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—41no—
182C11⋊#95—41no—
183C11⋊#95—41no—
184#13970—111nomaximal, Sylow
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×C11C22×C412yes—
198C24×C11C2×D412yes—
199C24×C11C2×D412yes—
200C24×C11C2411yescharacteristic
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×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×D11—21no—
224C23×D11—21no—
225C23×D11C22×C412yes—
226C23×D11C22×C412yes—
227C23×D11C2×D412yes—
228C23×D11C2×D412yes—
229C23×D11C2×D412yes—
230C23×D11#4112yes—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—28no—
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—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—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—44no—
268C22×C4×C11—44no—
269C22×C4×C11—44no—
270C22×C4×C11—44no—
271C22×C4×C11—44no—
272C22×C4×C11—44no—
273C22×C4×C11C22×C412yes—
274C22×C4×C11C22×C412yes—
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11#4112yes—
279C22×C4×C11#4112yes—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—28no—
283C2×C22⋊D11—28no—
284C2×C22⋊D11—28no—
285C2×C22⋊D11—28no—
286C2×C22⋊D11—28no—
287C2×C22⋊D11—28no—
288C2×C22⋊D11—44no—
289C2×C22⋊D11—44no—
290C2×C22⋊D11—44no—
291C2×C22⋊D11—44no—
292C2×C22⋊D11—44no—
293C2×C22⋊D11C22⋊C4116yescomplemented
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×Dic11C22×C412yes—
326C22×Dic11C22×C412yes—
327C22×Dic11C2×D412yes—
328C22×Dic11C2×D412yes—
329C22×Dic11C2×D412yes—
330C22×Dic11C2×D412yes—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11#4112yes—
335C22×Dic11#4112yes—
336C2×D44—28no—
337C2×D44—28no—
338C2×D44—44no—
339C2×D44—44no—
340C2×D44—44no—
341C2×D44—44no—
342C2×D44—44no—
343C2×C4×D11—28no—
344C2×C4×D11—28no—
345C2×C4×D11—28no—
346C2×C4×D11—28no—
347C2×C4×D11—44no—
348C2×C4×D11—44no—
349C2×C4×D11—44no—
350C2×C4×D11—44no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C11×C22⋊C4—28no—
358C11×C22⋊C4—44no—
359C22⋊Dic11—28no—
360C22⋊Dic11—44no—
361(C2×D11)⋊C4—28no—
362(C2×D11)⋊C4—28no—
363(C2×D11)⋊C4—28no—
364(C2×D11)⋊C4—28no—
365(C2×D11)⋊C4—44no—
366(C2×D11)⋊C4—44no—
367(C2×D11)⋊C4—44no—
368(C2×D11)⋊C4—44no—
369Dic11⋊C4—28no—
370Dic11⋊C4—28no—
371Dic11⋊C4—44no—
372C4×Dic11—28no—
373C4×Dic11—44no—
374C22×#121—111no—
375C22×C4×D4—111no—
376C2×#390—111no—
377C2×#386—111no—
378C2×#386—111no—
379C2×#380—111no—
380C2×C4×C22⋊C4—111no—
381#1440—111no—
382#1440—111no—
383#1438—111no—
384#1438—111no—
385C4⋊#95—111no—
386C4⋊#95—111no—
387C22⋊#95—111no—
388C22⋊#95D1111yescharacteristic, complemented
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—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
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×C11C2×C22⋊C414yes—
424C23×C11C23×C411yescharacteristic
425C23×C11C22×D411yescharacteristic
426C23×C11C22×D411yescharacteristic
427C23×C11C22×D411yescharacteristic
428C23×C11C22×D411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C2×#4111yescharacteristic
431C23×C11C2×#4111yescharacteristic
432C23×C11C2×#4111yescharacteristic
433C23×C11C2×#4111yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11H(5,𝔽2)11yescharacteristic
436C23×C11H(5,𝔽2)11yescharacteristic
437C23×C11H(5,𝔽2)11yescharacteristic
438C23×C112−1+411yescharacteristic
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
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—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×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—41no—
498C22×D11—41no—
499C22×D11—41no—
500C22×D11—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11C2×C22⋊C414yes—
508C22×D11C4×D414yescomplemented
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—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—416no—
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—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11—41no—
546C2×C4×C11—41no—
547C2×C4×C11—41no—
548C2×C4×C11—41no—
549C2×C4×C11—41no—
550C2×C4×C11—41no—
551C2×C4×C11#12114yescomplemented
552C22⋊D11—232no—
553C22⋊D11—416no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
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—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11C2×C22⋊C414yes—
590C2×Dic11C4×D414yes—
591C2×Dic11C4×D414yes—
592C2×Dic11#12014yes—
593C2×Dic11#12114yes—
594C2×Dic11#12114yes—
595C2×Dic11#12314yes—
596D44—416no—
597C4×D11—416no—
598C4×D11—416no—
599C23×D4—111no—
600C23×D4—111no—
601C23×D4—111no—
602C24×C4—111no—
603C24×C4—111no—
604C24×C4C2×D1111yescharacteristic
605C2×#121—118no—
606C2×#121—224no—
607C2×#121—224no—
608C2×C4×D4—224no—
609C2×C4×D4—224no—
610C2×C4×D4—224no—
611C22×C4⋊C4—111no—
612C22×C4⋊C4—111no—
613C22×C4⋊C4—111no—
614C22×C22⋊C4—111no—
615C22×C22⋊C4—111no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4C2×D1111yescharacteristic
625C22×C22⋊C4C2×D1111yescharacteristic
626C22×C42—111no—
627C22×C42—111no—
628#390—224no—
629#386—224no—
630#386—224no—
631#380—224no—
632C4×C22⋊C4—224no—
633C2×#95—111no—
634C2×#95—111no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95C2×D1111yescharacteristic
642C2×#95C2×D1111yescharacteristic
643C2×#95C2×D1111yescharacteristic
644C2×#95C2×D1111yescharacteristic
645C22×C11—24no—
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11C22×C22⋊C411yescharacteristic
661C22×C11C2×C4×D411yescharacteristic
662C22×C11C2×C4×D411yescharacteristic
663C22×C11C2×C4×D411yescharacteristic
664C22×C11C4×#4111yescharacteristic
665C22×C11#51811yescharacteristic
666C22×C11#52011yescharacteristic
667C22×C11C2×#12011yescharacteristic
668C22×C11C2×#12111yescharacteristic
669C22×C11C2×#12111yescharacteristic
670C22×C11C2×#12111yescharacteristic
671C22×C11C2×#12311yescharacteristic
672C22×C11#52511yescharacteristic
673C22×C11#52911yescharacteristic
674C22×C11#53211yescharacteristic
675C22×C11#53511yescharacteristic
676C22×C11#53711yescharacteristic
677C22×C11#54011yescharacteristic
678C22×C11#54211yescharacteristic
679C22×C11D4211yescharacteristic
680C22×C11D4211yescharacteristic
681C22×C11D4211yescharacteristic
682C22×C11#54611yescharacteristic
683C22×C11#54611yescharacteristic
684C22×C11#54611yescharacteristic
685C22×C11#54611yescharacteristic
686C22×C11#54611yescharacteristic
687C22×C11#54711yescharacteristic
688C22×C11#54711yescharacteristic
689C22×C11#54711yescharacteristic
690C22×C11#54811yescharacteristic
691C22×C11#55011yescharacteristic
692C22×C11#55311yescharacteristic
693C22×C11#55311yescharacteristic
694C22×C11#55511yescharacteristic
695C2×D11—24no—
696C2×D11—24no—
697C2×D11—24no—
698C2×D11—24no—
699C2×D11—24no—
700C2×D11—24no—
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—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—42no—
724C2×D11—42no—
725C4×C11—24no—
726C4×C11—42no—
727C4×C11—42no—
728C4×C11—42no—
729C4×C11—42no—
730C4×C11—81no—
731Dic11—42no—
732Dic11—42no—
733Dic11—42no—
734Dic11—42no—
735Dic11—81no—
736Dic11#38618yescomplemented
737C25—111no—
738C25—111no—
739C25C22×D1111yescharacteristic
740C22×D4—114no—
741C22×D4—114no—
742C22×D4—114no—
743C22×D4—114no—
744C22×D4—114no—
745C22×D4—222no—
746C22×D4—222no—
747C22×D4—222no—
748C22×D4—222no—
749C22×D4—222no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—441no—
758C22×D4—441no—
759C22×D4—441no—
760C22×D4—441no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—114no—
774C23×C4—111no—
775C23×C4—222no—
776C23×C4—222no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—441no—
787C23×C4—441no—
788C23×C4C22×D1111yescharacteristic
789C23×C4C22×D1111yescharacteristic
790C23×C4C22×D1111yescharacteristic
791C23×C4C22×D1111yescharacteristic
792C23×C4C22×D1111yescharacteristic
793C23×C4C22×D1111yescharacteristic
794#121—2232no—
795C4×D4—2232no—
796C2×C4⋊C4—114no—
797C2×C4⋊C4—114no—
798C2×C4⋊C4—222no—
799C2×C4⋊C4—222no—
800C2×C4⋊C4—222no—
801C2×C4⋊C4—222no—
802C2×C4⋊C4—222no—
803C2×C4⋊C4—222no—
804C2×C4⋊C4—222no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—114no—
811C2×C22⋊C4—114no—
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—222no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—441no—
836C2×C22⋊C4—441no—
837C2×C22⋊C4—441no—
838C2×C22⋊C4—441no—
839C2×C22⋊C4—441no—
840C2×C22⋊C4C4×D1114yescomplemented
841C2×C42—114no—
842C2×C42—222no—
843C2×C42—222no—
844C2×C42—222no—
845C2×C42—222no—
846C2×C42—222no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—41no—
851#95—222no—
852#95—222no—
853#95—222no—
854#95—222no—
855#95—222no—
856#95—441no—
857#95—441no—
858#95—441no—
859C2×C11—44no—
860C2×C11C2×#38611yescharacteristic
861C2×C11C4×#12111yescharacteristic
862C2×C11#232411yescharacteristic
863C2×C11D4×C22⋊C411yescharacteristic
864C2×C11#233911yescharacteristic
865C2×C11#236111yescharacteristic
866C2×C11#236311yescharacteristic
867C2×C11#240711yescharacteristic
868C2×C11#240811yescharacteristic
869C2×C11#242011yescharacteristic
870C2×C11#242211yescharacteristic
871C2×C11#242711yescharacteristic
872C2×C11#242811yescharacteristic
873C2×C11#253511yescharacteristic
874C2×C11#253711yescharacteristic
875D11—44no—
876D11—44no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—112no—
890C24—112no—
891C24—112no—
892C24—112no—
893C24—112no—
894C24—112no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24—221no—
899C24—221no—
900C24—221no—
901C24—221no—
902C24—221no—
903C24—221no—
904C24—221no—
905C24—221no—
906C24—221no—
907C24—221no—
908C24—221no—
909C24—221no—
910C24—221no—
911C24—221no—
912C24—221no—
913C24—221no—
914C24—221no—
915C24—221no—
916C24—221no—
917C24—221no—
918C24—221no—
919C24C2×C4×D1112yes—
920C24D4×D1112yes—
921C24D4×D1112yes—
922C24C23×D1111yescharacteristic
923C2×D4—1116no—
924C2×D4—228no—
925C2×D4—228no—
926C2×D4—228no—
927C2×D4—228no—
928C2×D4—228no—
929C2×D4—228no—
930C2×D4—228no—
931C2×D4—228no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4—444no—
937C2×D4—444no—
938C2×D4—444no—
939C2×D4—444no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—28no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—112no—
995C22×C4—112no—
996C22×C4—112no—
997C22×C4—228no—
998C22×C4—228no—
999C22×C4—228no—
1000C22×C4—228no—
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—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—444no—
1033C22×C4—444no—
1034C22×C4—444no—
1035C22×C4—444no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4C2×C4×D1112yes—
1043C22×C4C2×C4×D1112yes—
1044C22×C4#433912yes—
1045C22×C4#433912yes—
1046C22×C4D4×D1112yes—
1047C22×C4D4×D1112yes—
1048C22×C4D4×D1112yes—
1049C4⋊C4—228no—
1050C4⋊C4—228no—
1051C4⋊C4—444no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—228no—
1055C22⋊C4—228no—
1056C22⋊C4—228no—
1057C22⋊C4—228no—
1058C22⋊C4—228no—
1059C22⋊C4—444no—
1060C22⋊C4—444no—
1061C22⋊C4—444no—
1062C22⋊C4—444no—
1063C22⋊C4—444no—
1064C42—228no—
1065C42—444no—
1066C11#1397011yescharacteristic, complemented, Sylow
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
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—114no—
1102C23—114no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23—222no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
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—222no—
1133C23—222no—
1134C23—222no—
1135C23—222no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23—441no—
1145C23—441no—
1146C23—441no—
1147C23—441no—
1148C23—441no—
1149C23—441no—
1150C23—441no—
1151C23—441no—
1152C23—441no—
1153C23—441no—
1154C23—441no—
1155C23—441no—
1156C23—441no—
1157C23—441no—
1158C23—441no—
1159C23—441no—
1160C23—441no—
1161C23—441no—
1162C23—441no—
1163C23—441no—
1164C23—441no—
1165C23—441no—
1166C23—441no—
1167C23—441no—
1168C23—441no—
1169C23—441no—
1170C23—441no—
1171C23C22⋊C4×D1114yes—
1172C23C22×C4×D1111yescharacteristic
1173C23C2×#433911yescharacteristic
1174C23C2×#433911yescharacteristic
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177C23C2×D4×D1111yescharacteristic
1178C23C2×D4×D1111yescharacteristic
1179C23C2×D4×D1111yescharacteristic
1180C23#6703711yescharacteristic
1181C23#6703711yescharacteristic
1182C23#6704011yescharacteristic
1183C23#41×D1111yescharacteristic
1184C23#41×D1111yescharacteristic
1185C23#41×D1111yescharacteristic
1186C23#6704211yescharacteristic
1187D4—2232no—
1188D4—4416no—
1189D4—4416no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—416no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—114no—
1233C2×C4—114no—
1234C2×C4—114no—
1235C2×C4—114no—
1236C2×C4—114no—
1237C2×C4—114no—
1238C2×C4—114no—
1239C2×C4—222no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—222no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—222no—
1248C2×C4—222no—
1249C2×C4—222no—
1250C2×C4—222no—
1251C2×C4—4416no—
1252C2×C4—4416no—
1253C2×C4—441no—
1254C2×C4—441no—
1255C2×C4—441no—
1256C2×C4—441no—
1257C2×C4—441no—
1258C2×C4—441no—
1259C2×C4—441no—
1260C2×C4—441no—
1261C2×C4—441no—
1262C2×C4—441no—
1263C2×C4—441no—
1264C2×C4—441no—
1265C2×C4—441no—
1266C2×C4—441no—
1267C2×C4—441no—
1268C2×C4—441no—
1269C2×C4—441no—
1270C2×C4—441no—
1271C2×C4—441no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4#6693714yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—224no—
1293C22—224no—
1294C22—224no—
1295C22—224no—
1296C22—224no—
1297C22—224no—
1298C22—442no—
1299C22—442no—
1300C22—442no—
1301C22—442no—
1302C22—442no—
1303C22—442no—
1304C22—442no—
1305C22—442no—
1306C22—442no—
1307C22—442no—
1308C22—442no—
1309C22—442no—
1310C22—442no—
1311C22—442no—
1312C22—442no—
1313C22—442no—
1314C22—442no—
1315C22—442no—
1316C22—442no—
1317C22—442no—
1318C22—442no—
1319C22—442no—
1320C22—442no—
1321C22—442no—
1322C22C4×#433911yescharacteristic
1323C22C2×C22⋊C4×D1111yescharacteristic
1324C22C2×#6693711yescharacteristic
1325C22#1062302111yescharacteristic
1326C22#1062302111yescharacteristic
1327C22#1062302111yescharacteristic
1328C22#1062303511yescharacteristic
1329C22#1062303811yescharacteristic
1330C22#1062303811yescharacteristic
1331C22#1062305911yescharacteristic
1332C22#1062306311yescharacteristic
1333C22#1062307111yescharacteristic
1334C22C4×D4×D1111yescharacteristic
1335C22C4×D4×D1111yescharacteristic
1336C22C4×D4×D1111yescharacteristic
1337C22#1062307611yescharacteristic
1338C22#1062307811yescharacteristic
1339C22#1062307911yescharacteristic
1340C22#1062308411yescharacteristic
1341C22D11×#12011yescharacteristic
1342C22#1062312111yescharacteristic
1343C22#1062312111yescharacteristic
1344C22#1062312311yescharacteristic
1345C22D11×#12111yescharacteristic
1346C22D11×#12111yescharacteristic
1347C22#1062314011yescharacteristic
1348C22#1062314111yescharacteristic
1349C22#1062316011yescharacteristic
1350C22#1062316211yescharacteristic
1351C22#1062316411yescharacteristic
1352C22#1062317111yescharacteristic
1353C22D11×#12311yescharacteristic
1354C22#1062318511yescharacteristic
1355C22#1062319211yescharacteristic
1356C22#1062319411yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—81no—
1363C4—118no—
1364C4—442no—
1365C4—442no—
1366C4—442no—
1367C4—442no—
1368C4—881no—
1369C2—44no—
1370C2—444no—
1371C2—444no—
1372C2D11×#38611yescharacteristic
1373C2C4×#6693711yescharacteristic
1374C2#1307130811yescharacteristic
1375C2#1307143411yescharacteristic
1376C2#1307144311yescharacteristic
1377C2#1307163511yescharacteristic
1378C2#1307165511yescharacteristic
1379C2#1307196011yescharacteristic
1380C2#1307197111yescharacteristic
1381C2#1307210711yescharacteristic
1382C2#1307212911yescharacteristic
1383C2#1307219211yescharacteristic
1384C2#1307220311yescharacteristic
1385C2#1307351611yescharacteristic
1386C2#1307353111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenterC22⋊#95D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622826C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622280C2semidirect
7. C2×#10622279C2semidirect
8. #13066865C2semidirect
9. #13066864C2semidirect
10. #13066856C2semidirect
11. #13066855C2semidirect
12. Dic11⋊#95C2semidirect
13. Dic11⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
44. C2×#66937C4semidirect
89. C22×C22⋊D11C2×C4semidirect
104. C22×D44C2×C4semidirect
118. C22×C4×D11C2×C4semidirect
124. C2×C11×C22⋊C4C2×C4semidirect
154. C2×(C2×D11)⋊C4C2×C4semidirect
155. C2×(C2×D11)⋊C4D4semidirect
163. C2×Dic11⋊C4C2×C4semidirect
164. C2×Dic11⋊C4D4semidirect
170. C2×C4×Dic11D4semidirect
293. C2×C22⋊D11C22⋊C4semidirect
388. C22⋊#95D11semidirect
508. C22×D11C4×D4semidirect
551. C2×C4×C11#121semidirect
736. Dic11#386semidirect
840. C2×C22⋊C4C4×D11semidirect
1066. C11#13970semidirect
1276. C2×C4#66937semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×C22⋊D112
C2×#106225702
C2×#106228262
C2×#106222782
C2×#106222802
C2×#106222792
#130668652
#130668642
#130668562
#130668552
Dic11⋊#952
(C2×D11)⋊#952
C11×C22⋊#952
#1397011