Finite Group Databasebeta

← #14677224

Subgroups — #14677224

Order 2816.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 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×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066867C211yesmaximal, characteristic, complemented
9#13066865C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, 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
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C2×C4×C22⋊D11—24no—
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×C4×Dic11C2211yescharacteristic
40C2×#66937—24no—
41C2×#66937—24no—
42C2×#66937C418yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47#10622826—24no—
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
58#10622569—24no—
59#10622278—24no—
60#10622278—24no—
61D11×#95—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—22no—
103C22×D44—22no—
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—22no—
117C22×C4×D11—22no—
118C22×C4×D11—41no—
119C22×C4×D11—41no—
120C22×C4×D11—41no—
121C22×C4×D11—41no—
122C22×C4×D11—41no—
123C22×C4×D11—41no—
124C22×C4×D11C2×C414yescomplemented
125C22×C4×D11D414yescomplemented
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—41no—
131C2×C11×C22⋊C4C2×C414yescomplemented
132C2×C22⋊Dic11—22no—
133C2×C22⋊Dic11—22no—
134C2×C22⋊Dic11—22no—
135C2×C22⋊Dic11—22no—
136C2×C22⋊Dic11—22no—
137C2×C22⋊Dic11—41no—
138C4×C22⋊D11—232no—
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—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—41no—
155C2×(C2×D11)⋊C4—41no—
156C2×(C2×D11)⋊C4—41no—
157C2×(C2×D11)⋊C4—41no—
158C2×(C2×D11)⋊C4C2×C414yescomplemented
159C2×(C2×D11)⋊C4D414yescomplemented
160C2×Dic11⋊C4—22no—
161C2×Dic11⋊C4—22no—
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4—22no—
164C2×Dic11⋊C4—22no—
165C2×Dic11⋊C4C2×C414yescomplemented
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169#66937—232no—
170C11×#95—22no—
171C11×#95—22no—
172C11×#95—22no—
173C11×#95—41no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—22no—
181C11⋊#95—22no—
182C11⋊#95—41no—
183C11⋊#95D414yescomplemented
184#14023—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×D11C22×C412yes—
224C23×D11C22×C412yes—
225C23×D11C2×D412yes—
226C23×D11C2×D412yes—
227C23×D11C2×D412yes—
228C23×D11C2×D412yes—
229C23×D11#4112yes—
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×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11C22×C412yes—
328C22×Dic11C22×C412yes—
329C22×Dic11C2×D412yes—
330C22×Dic11C2×D412yes—
331C22×Dic11C2×D412yes—
332C22×Dic11C2×D412yes—
333C22×Dic11C2×D412yes—
334C22×Dic11C2×D412yes—
335C22×Dic11#4112yes—
336C2×D44—28no—
337C2×D44—28no—
338C2×D44—28no—
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—28no—
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—
357C2×C4×D11—44no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11—44no—
363C2×C4×D11—44no—
364C11×C22⋊C4—28no—
365C11×C22⋊C4—44no—
366C22⋊Dic11—28no—
367C22⋊Dic11—44no—
368(C2×D11)⋊C4—28no—
369(C2×D11)⋊C4—28no—
370(C2×D11)⋊C4—44no—
371(C2×D11)⋊C4—44no—
372(C2×D11)⋊C4—44no—
373(C2×D11)⋊C4—44no—
374(C2×D11)⋊C4—44no—
375Dic11⋊C4—28no—
376Dic11⋊C4—28no—
377C4×Dic11—28no—
378C22×#121—111no—
379C22×C4×D4—111no—
380C2×#386—111no—
381C2×#386—111no—
382C2×#386—111no—
383C2×#386—111no—
384C22×#95—111no—
385#1441—111no—
386#1440—111no—
387#1439—111no—
388#1438—111no—
389#1437—111no—
390#1436—111no—
391C22⋊#95—111no—
392C22⋊#95D1111yescharacteristic, complemented
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—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
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×C11C2×C22⋊C414yes—
428C23×C11C23×C411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C23×C11C22×D411yescharacteristic
432C23×C11C22×D411yescharacteristic
433C23×C11C22×D411yescharacteristic
434C23×C11C2×#4111yescharacteristic
435C23×C11C2×#4111yescharacteristic
436C23×C11C2×#4111yescharacteristic
437C23×C11C2×#4111yescharacteristic
438C23×C11C2×#4111yescharacteristic
439C23×C11H(5,𝔽2)11yescharacteristic
440C23×C11H(5,𝔽2)11yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C23×C112−1+411yescharacteristic
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—22no—
476C22×D11—22no—
477C22×D11—22no—
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×D11C2×C22⋊C414yes—
507C22×D11C4×D414yes—
508C22×D11C4×D414yes—
509C22×D11#12014yes—
510C22×D11#12114yes—
511C22×D11#12114yes—
512C22×D11#12314yes—
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—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—416no—
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—41no—
552C2×C4×C11—41no—
553C2×C4×C11—41no—
554C2×C4×C11—41no—
555C2×C4×C11#12114yescomplemented
556C22⋊D11—232no—
557C22⋊D11—416no—
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—22no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—22no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—22no—
574C2×Dic11—22no—
575C2×Dic11—22no—
576C2×Dic11—22no—
577C2×Dic11—22no—
578C2×Dic11—22no—
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×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597C2×Dic11—41no—
598C2×Dic11C2×C22⋊C414yes—
599C2×Dic11C4×D414yescomplemented
600D44—416no—
601C4×D11—416no—
602C4×D11—416no—
603C4×D11—416no—
604C23×D4—111no—
605C23×D4—111no—
606C23×D4—111no—
607C24×C4—111no—
608C24×C4—111no—
609C24×C4—111no—
610C24×C4C2×D1111yescharacteristic
611C2×#121—118no—
612C2×#121—224no—
613C2×#121—224no—
614C2×C4×D4—224no—
615C2×C4×D4—224no—
616C2×C4×D4—224no—
617C22×C4⋊C4—111no—
618C22×C4⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4—111no—
625C22×C22⋊C4—111no—
626C22×C22⋊C4—111no—
627C22×C22⋊C4—111no—
628C22×C22⋊C4C2×D1111yescharacteristic
629C22×C22⋊C4C2×D1111yescharacteristic
630C22×C42—111no—
631#386—224no—
632#386—224no—
633#386—224no—
634#386—224no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95—111no—
644C2×#95—111no—
645C2×#95—224no—
646C2×#95C2×D1111yescharacteristic
647C2×#95C2×D1111yescharacteristic
648C2×#95C2×D1111yescharacteristic
649C2×#95C2×D1111yescharacteristic
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11C22×C22⋊C411yescharacteristic
666C22×C11C2×C4×D411yescharacteristic
667C22×C11C2×C4×D411yescharacteristic
668C22×C11C2×C4×D411yescharacteristic
669C22×C11C4×#4111yescharacteristic
670C22×C11#51811yescharacteristic
671C22×C11#52011yescharacteristic
672C22×C11C2×#12011yescharacteristic
673C22×C11C2×#12111yescharacteristic
674C22×C11C2×#12111yescharacteristic
675C22×C11C2×#12111yescharacteristic
676C22×C11C2×#12311yescharacteristic
677C22×C11#52511yescharacteristic
678C22×C11#52911yescharacteristic
679C22×C11#53211yescharacteristic
680C22×C11#53411yescharacteristic
681C22×C11#53711yescharacteristic
682C22×C11#53811yescharacteristic
683C22×C11#53911yescharacteristic
684C22×C11D4211yescharacteristic
685C22×C11D4211yescharacteristic
686C22×C11D4211yescharacteristic
687C22×C11#54611yescharacteristic
688C22×C11#54611yescharacteristic
689C22×C11#54611yescharacteristic
690C22×C11#54611yescharacteristic
691C22×C11#54611yescharacteristic
692C22×C11#54611yescharacteristic
693C22×C11#54711yescharacteristic
694C22×C11#54711yescharacteristic
695C22×C11#54711yescharacteristic
696C22×C11#54811yescharacteristic
697C22×C11#55311yescharacteristic
698C22×C11#55311yescharacteristic
699C22×C11#55311yescharacteristic
700C2×D11—24no—
701C2×D11—24no—
702C2×D11—24no—
703C2×D11—24no—
704C2×D11—24no—
705C2×D11—24no—
706C2×D11—24no—
707C2×D11—24no—
708C2×D11—24no—
709C2×D11—24no—
710C2×D11—24no—
711C2×D11—24no—
712C2×D11—24no—
713C2×D11—24no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—81no—
722C2×D11—81no—
723C2×D11—81no—
724C2×D11—81no—
725C2×D11—81no—
726C2×D11—81no—
727C2×D11—81no—
728C2×D11—81no—
729C2×D11#38618yescomplemented
730C4×C11—24no—
731C4×C11—42no—
732C4×C11—42no—
733C4×C11—42no—
734C4×C11—42no—
735C4×C11—81no—
736Dic11—24no—
737Dic11—24no—
738Dic11—42no—
739Dic11—42no—
740Dic11—42no—
741Dic11—81no—
742C25—111no—
743C25—111no—
744C25C22×D1111yescharacteristic
745C22×D4—114no—
746C22×D4—114no—
747C22×D4—114no—
748C22×D4—114no—
749C22×D4—114no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—222no—
761C22×D4—222no—
762C22×D4—222no—
763C22×D4—222no—
764C22×D4—441no—
765C22×D4—441no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—41no—
772C23×C4—41no—
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—114no—
779C23×C4—114no—
780C23×C4—111no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—222no—
792C23×C4—222no—
793C23×C4—222no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4—441no—
800C23×C4C22×D1111yescharacteristic
801C23×C4C22×D1111yescharacteristic
802C23×C4C22×D1111yescharacteristic
803C23×C4C22×D1111yescharacteristic
804C23×C4C22×D1111yescharacteristic
805C23×C4C22×D1111yescharacteristic
806#121—2232no—
807C4×D4—2232no—
808C2×C4⋊C4—114no—
809C2×C4⋊C4—222no—
810C2×C4⋊C4—222no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4—222no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—114no—
820C2×C22⋊C4—114no—
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—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—222no—
840C2×C22⋊C4—222no—
841C2×C22⋊C4—441no—
842C2×C22⋊C4—441no—
843C2×C22⋊C4—441no—
844C2×C22⋊C4—441no—
845C2×C22⋊C4—441no—
846C2×C22⋊C4C4×D1114yescomplemented
847C2×C42—222no—
848C2×C42—222no—
849C2×C42—222no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—41no—
854#95—114no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—222no—
862#95—222no—
863#95—441no—
864C2×C11—44no—
865C2×C11C2×#38611yescharacteristic
866C2×C11C4×#12111yescharacteristic
867C2×C11#232511yescharacteristic
868C2×C11D4×C22⋊C411yescharacteristic
869C2×C11#233911yescharacteristic
870C2×C11#236111yescharacteristic
871C2×C11#236411yescharacteristic
872C2×C11#241011yescharacteristic
873C2×C11#241611yescharacteristic
874C2×C11#242411yescharacteristic
875C2×C11#242511yescharacteristic
876C2×C11#243011yescharacteristic
877C2×C11#244311yescharacteristic
878C2×C11#244411yescharacteristic
879C2×C11#254311yescharacteristic
880D11—28no—
881D11—82no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—112no—
895C24—112no—
896C24—112no—
897C24—112no—
898C24—112no—
899C24—112no—
900C24—112no—
901C24—112no—
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—
919C24—221no—
920C24—221no—
921C24—221no—
922C24—221no—
923C24—221no—
924C24C2×C4×D1112yes—
925C24D4×D1112yes—
926C24D4×D1112yes—
927C24C23×D1111yescharacteristic
928C2×D4—1116no—
929C2×D4—228no—
930C2×D4—228no—
931C2×D4—228no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—228no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4—444no—
946C2×D4—444no—
947C2×D4—444no—
948C2×D4—444no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—28no—
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—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—112no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—112no—
995C22×C4—112no—
996C22×C4—112no—
997C22×C4—112no—
998C22×C4—112no—
999C22×C4—112no—
1000C22×C4—228no—
1001C22×C4—228no—
1002C22×C4—228no—
1003C22×C4—228no—
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—228no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4—221no—
1035C22×C4—221no—
1036C22×C4—221no—
1037C22×C4—221no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4—444no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4—444no—
1050C22×C4—444no—
1051C22×C4—444no—
1052C22×C4—444no—
1053C22×C4—444no—
1054C22×C4C2×C4×D1112yes—
1055C22×C4C2×C4×D1112yes—
1056C22×C4#433912yes—
1057C22×C4#433912yes—
1058C22×C4D4×D1112yes—
1059C22×C4D4×D1112yes—
1060C22×C4D4×D1112yes—
1061C4⋊C4—228no—
1062C4⋊C4—228no—
1063C22⋊C4—28no—
1064C22⋊C4—44no—
1065C22⋊C4—228no—
1066C22⋊C4—228no—
1067C22⋊C4—228no—
1068C22⋊C4—444no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—228no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
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—114no—
1111C23—114no—
1112C23—114no—
1113C23—114no—
1114C23—114no—
1115C23—114no—
1116C23—114no—
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—222no—
1140C23—222no—
1141C23—222no—
1142C23—222no—
1143C23—222no—
1144C23—222no—
1145C23—222no—
1146C23—222no—
1147C23—222no—
1148C23—222no—
1149C23—222no—
1150C23—222no—
1151C23—222no—
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—
1171C23—441no—
1172C23—441no—
1173C23—441no—
1174C23—441no—
1175C23—441no—
1176C23—441no—
1177C23—441no—
1178C23—441no—
1179C23—441no—
1180C23C22⋊C4×D1114yes—
1181C23C22×C4×D1111yescharacteristic
1182C23C2×#433911yescharacteristic
1183C23C2×#433911yescharacteristic
1184C23C2×D4×D1111yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×D4×D1111yescharacteristic
1187C23C2×D4×D1111yescharacteristic
1188C23C2×D4×D1111yescharacteristic
1189C23#6703711yescharacteristic
1190C23#6703711yescharacteristic
1191C23#6704011yescharacteristic
1192C23#41×D1111yescharacteristic
1193C23#41×D1111yescharacteristic
1194C23#41×D1111yescharacteristic
1195C23#6704211yescharacteristic
1196D4—2232no—
1197D4—4416no—
1198D4—4416no—
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—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—416no—
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—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—114no—
1242C2×C4—114no—
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—222no—
1252C2×C4—222no—
1253C2×C4—222no—
1254C2×C4—222no—
1255C2×C4—222no—
1256C2×C4—222no—
1257C2×C4—222no—
1258C2×C4—222no—
1259C2×C4—222no—
1260C2×C4—222no—
1261C2×C4—222no—
1262C2×C4—222no—
1263C2×C4—222no—
1264C2×C4—4416no—
1265C2×C4—4416no—
1266C2×C4—4416no—
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—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4—441no—
1285C2×C4—441no—
1286C2×C4#6693714yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—118no—
1303C22—224no—
1304C22—224no—
1305C22—224no—
1306C22—224no—
1307C22—224no—
1308C22—224no—
1309C22—224no—
1310C22—224no—
1311C22—224no—
1312C22—224no—
1313C22—224no—
1314C22—224no—
1315C22—224no—
1316C22—224no—
1317C22—442no—
1318C22—442no—
1319C22—442no—
1320C22—442no—
1321C22—442no—
1322C22—442no—
1323C22—442no—
1324C22—881no—
1325C22—881no—
1326C22—881no—
1327C22—881no—
1328C22—881no—
1329C22—881no—
1330C22—881no—
1331C22—881no—
1332C22C4×#433911yescharacteristic
1333C22C2×C22⋊C4×D1111yescharacteristic
1334C22C2×#6693711yescharacteristic
1335C22#1062302111yescharacteristic
1336C22#1062302111yescharacteristic
1337C22#1062302111yescharacteristic
1338C22#1062303511yescharacteristic
1339C22#1062303811yescharacteristic
1340C22#1062303811yescharacteristic
1341C22#1062305911yescharacteristic
1342C22#1062306111yescharacteristic
1343C22C4×D4×D1111yescharacteristic
1344C22C4×D4×D1111yescharacteristic
1345C22C4×D4×D1111yescharacteristic
1346C22#1062307611yescharacteristic
1347C22#1062307811yescharacteristic
1348C22#1062307911yescharacteristic
1349C22#1062308111yescharacteristic
1350C22#1062308911yescharacteristic
1351C22D11×#12011yescharacteristic
1352C22#1062312011yescharacteristic
1353C22#1062312111yescharacteristic
1354C22#1062312111yescharacteristic
1355C22D11×#12111yescharacteristic
1356C22D11×#12111yescharacteristic
1357C22#1062314011yescharacteristic
1358C22#1062314111yescharacteristic
1359C22#1062316011yescharacteristic
1360C22#1062316211yescharacteristic
1361C22#1062316411yescharacteristic
1362C22#1062316911yescharacteristic
1363C22D11×#12311yescharacteristic
1364C22#1062318511yescharacteristic
1365C22#1062318811yescharacteristic
1366C22#1062319211yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—81no—
1373C4—224no—
1374C4—224no—
1375C4—442no—
1376C4—442no—
1377C4—442no—
1378C4—881no—
1379C2—44no—
1380C2—228no—
1381C2—882no—
1382C2D11×#38611yescharacteristic
1383C2C4×#6693711yescharacteristic
1384C2#1307131311yescharacteristic
1385C2#1307143411yescharacteristic
1386C2#1307144311yescharacteristic
1387C2#1307163511yescharacteristic
1388C2#1307166711yescharacteristic
1389C2#1307199211yescharacteristic
1390C2#1307205811yescharacteristic
1391C2#1307215111yescharacteristic
1392C2#1307216411yescharacteristic
1393C2#1307222511yescharacteristic
1394C2#1307235011yescharacteristic
1395C2#1307236511yescharacteristic
1396C2#1307357511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenterC22⋊#95D11
hypocenterC11#14023
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×#10622826C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622569C2semidirect
7. C2×D11×#95C2semidirect
8. #13066867C2semidirect
9. #13066865C2semidirect
10. #13066860C2semidirect
11. #13066855C2semidirect
12. #13066852C2semidirect
13. #13066847C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×C22⋊#95C2semidirect
42. C2×#66937C4semidirect
89. C22×C22⋊D11C2×C4semidirect
104. C22×D44C2×C4semidirect
124. C22×C4×D11C2×C4semidirect
125. C22×C4×D11D4semidirect
131. C2×C11×C22⋊C4C2×C4semidirect
158. C2×(C2×D11)⋊C4C2×C4semidirect
159. C2×(C2×D11)⋊C4D4semidirect
165. C2×Dic11⋊C4C2×C4semidirect
183. C11⋊#95D4semidirect
293. C2×C22⋊D11C22⋊C4semidirect
392. C22⋊#95D11semidirect
555. C2×C4×C11#121semidirect
599. C2×Dic11C4×D4semidirect
729. C2×D11#386semidirect
846. C2×C22⋊C4C4×D11semidirect
1075. C11#14023semidirect
1286. 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×#106228262
C2×#106222782
C2×#106225692
C2×D11×#952
#130668672
#130668652
#130668602
#130668552
#130668522
#130668472
(C2×D11)⋊#952
C11×C22⋊#952
#1402311