Finite Group Databasebeta

← #14677230

Subgroups — #14677230

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×#66948C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6C2×#10622278C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic, complemented
12#13066854C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C2×#66948—24no—
38C2×#66948—24no—
39C2×#66948C418yescomplemented
40C2×C4×D44—24no—
41C2×C4×D44—24no—
42C2×C4×D44—24no—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622278—24no—
58#10622278—24no—
59#10622278—24no—
60#10622278—24no—
61D11×#95—24no—
62C24×D11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44—22no—
82C22×D44—22no—
83C22×D44—22no—
84C22×D44—22no—
85C22×D44—22no—
86C22×D44—22no—
87C22×D44—22no—
88C22×D44—22no—
89C22×D44—22no—
90C22×D44—22no—
91C22×D44—41no—
92C22×D44—41no—
93C22×D44C2×C414yes—
94C22×D44C2×C414yescomplemented
95C22×D44C2×C414yescomplemented
96C22×D44D414yes—
97C22×D44D414yes—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—22no—
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×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×C4⋊C4—22no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4C2×C414yescomplemented
129C2×C42×C11—22no—
130C2×C42×C11—22no—
131C2×C42×C11—22no—
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—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×(C2×D11)⋊C4—41no—
159C2×(C2×D11)⋊C4—41no—
160C2×(C2×D11)⋊C4—41no—
161C2×(C2×D11)⋊C4—41no—
162C2×(C2×D11)⋊C4C2×C414yescomplemented
163C2×(C2×D11)⋊C4C2×C414yescomplemented
164C2×(C2×D11)⋊C4D414yescomplemented
165C2×C4⋊Dic11—22no—
166C2×C4⋊Dic11—22no—
167C2×C4⋊Dic11—22no—
168#66948—232no—
169C4×D44—232no—
170C11×#95—22no—
171C11×#95—22no—
172C11×#95—22no—
173C11×#95—22no—
174C11×#95D414yescomplemented
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⋊#95—41no—
184#14023—111nomaximal, Sylow
185C24×C11C2411yescharacteristic
186C23×D11—21no—
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×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11C22×C412yes—
221C23×D11C22×C412yes—
222C23×D11C22×C412yes—
223C23×D11C2×D412yes—
224C23×D11C2×D412yes—
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—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—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—21no—
268C22×C4×C11C22×C412yes—
269C22×C4×C11C22×C412yes—
270C22×C4×C11C22×C412yes—
271C22×C4×C11C2×D412yes—
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2×D412yes—
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11#4112yes—
279C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11#4112yes—
315C2×D44—28no—
316C2×D44—28no—
317C2×D44—28no—
318C2×D44—28no—
319C2×D44—28no—
320C2×D44—28no—
321C2×D44—28no—
322C2×D44—28no—
323C2×D44—28no—
324C2×D44—28no—
325C2×D44—28no—
326C2×D44—44no—
327C2×D44—44no—
328C2×D44—44no—
329C2×D44—44no—
330C2×D44—44no—
331C2×D44—44no—
332C2×D44—44no—
333C2×D44—44no—
334C2×D44—44no—
335C2×D44C22⋊C4116yescomplemented
336C2×C4×D11—28no—
337C2×C4×D11—28no—
338C2×C4×D11—28no—
339C2×C4×D11—28no—
340C2×C4×D11—28no—
341C2×C4×D11—28no—
342C2×C4×D11—44no—
343C2×C4×D11—44no—
344C2×C4×D11—44no—
345C2×C4×D11—44no—
346C2×C4×D11—44no—
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—
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×C4⋊C4—28no—
365C42×C11—28no—
366(C2×D11)⋊C4—28no—
367(C2×D11)⋊C4—28no—
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—
375(C2×D11)⋊C4—44no—
376(C2×D11)⋊C4—44no—
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#1436D1111yescharacteristic, complemented
391C22⋊#95—111no—
392C22⋊#95—111no—
393C23×C11C23×C411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C22×D411yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11C2×#4111yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C112−1+411yescharacteristic
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
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—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—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×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×D11C2×C22⋊C414yes—
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—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
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—41no—
556C2×C4×C11—41no—
557C2×C4×C11—41no—
558C2×C4×C11—41no—
559C2×C4×C11C2×C22⋊C414yes—
560C2×C4×C11C4×D414yescomplemented
561C2×C4×C11#12114yescomplemented
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—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×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11—41no—
592C2×Dic11—41no—
593C2×Dic11—41no—
594C2×Dic11—41no—
595C2×Dic11—41no—
596C2×Dic11—41no—
597D44—232no—
598D44—416no—
599D44—416no—
600C4×D11—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×C4—111no—
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⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
629C22×C22⋊C4—111no—
630C22×C42C2×D1111yescharacteristic
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—224no—
645C2×#95C2×D1111yescharacteristic
646C2×#95C2×D1111yescharacteristic
647C2×#95C2×D1111yescharacteristic
648C2×#95C2×D1111yescharacteristic
649C2×#95C2×D1111yescharacteristic
650C22×C11C22×C22⋊C411yescharacteristic
651C22×C11C2×C4×D411yescharacteristic
652C22×C11C2×C4×D411yescharacteristic
653C22×C11C2×C4×D411yescharacteristic
654C22×C11C4×#4111yescharacteristic
655C22×C11#51811yescharacteristic
656C22×C11#52011yescharacteristic
657C22×C11C2×#12011yescharacteristic
658C22×C11C2×#12111yescharacteristic
659C22×C11C2×#12111yescharacteristic
660C22×C11C2×#12111yescharacteristic
661C22×C11C2×#12311yescharacteristic
662C22×C11#52511yescharacteristic
663C22×C11#52911yescharacteristic
664C22×C11#53211yescharacteristic
665C22×C11#53411yescharacteristic
666C22×C11#53711yescharacteristic
667C22×C11#53811yescharacteristic
668C22×C11#53911yescharacteristic
669C22×C11D4211yescharacteristic
670C22×C11D4211yescharacteristic
671C22×C11D4211yescharacteristic
672C22×C11#54611yescharacteristic
673C22×C11#54611yescharacteristic
674C22×C11#54611yescharacteristic
675C22×C11#54611yescharacteristic
676C22×C11#54611yescharacteristic
677C22×C11#54611yescharacteristic
678C22×C11#54711yescharacteristic
679C22×C11#54711yescharacteristic
680C22×C11#54711yescharacteristic
681C22×C11#54811yescharacteristic
682C22×C11#55311yescharacteristic
683C22×C11#55311yescharacteristic
684C22×C11#55311yescharacteristic
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—24no—
694C2×D11—24no—
695C2×D11—24no—
696C2×D11—24no—
697C2×D11—24no—
698C2×D11—24no—
699C2×D11—24no—
700C2×D11—24no—
701C2×D11—24no—
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—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—24no—
732C4×C11—24no—
733C4×C11—42no—
734C4×C11—42no—
735C4×C11—42no—
736C4×C11—81no—
737Dic11—42no—
738Dic11—42no—
739Dic11—42no—
740Dic11—42no—
741Dic11—81no—
742C25—111no—
743C25—111no—
744C25—111no—
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—111no—
767C23×C4—111no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—114no—
771C23×C4—114no—
772C23×C4—111no—
773C23×C4—222no—
774C23×C4—222no—
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—222no—
787C23×C4—222no—
788C23×C4—222no—
789C23×C4—222no—
790C23×C4—222no—
791C23×C4—441no—
792C23×C4—441no—
793C23×C4—441no—
794C23×C4—441no—
795C23×C4—441no—
796C23×C4—441no—
797C23×C4—441no—
798C23×C4—441no—
799C23×C4C22×D1111yescharacteristic
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—22no—
809C2×C4⋊C4—22no—
810C2×C4⋊C4—222no—
811C2×C4⋊C4—222no—
812C2×C4⋊C4—222no—
813C2×C4⋊C4C4×D1114yescomplemented
814C2×C22⋊C4—114no—
815C2×C22⋊C4—114no—
816C2×C22⋊C4—114no—
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—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⋊C4—441no—
847C2×C42—22no—
848C2×C42—22no—
849C2×C42—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—222no—
855#95—222no—
856#95—222no—
857#95—222no—
858#95—222no—
859#95—222no—
860#95—222no—
861#95—441no—
862#95—441no—
863#95D4414yescomplemented
864C2×C11C2×#38611yescharacteristic
865C2×C11C4×#12111yescharacteristic
866C2×C11#232511yescharacteristic
867C2×C11D4×C22⋊C411yescharacteristic
868C2×C11#233911yescharacteristic
869C2×C11#236111yescharacteristic
870C2×C11#236411yescharacteristic
871C2×C11#241011yescharacteristic
872C2×C11#241611yescharacteristic
873C2×C11#242411yescharacteristic
874C2×C11#242511yescharacteristic
875C2×C11#243011yescharacteristic
876C2×C11#244311yescharacteristic
877C2×C11#244411yescharacteristic
878C2×C11#254311yescharacteristic
879D11—28no—
880D11—44no—
881D11—82no—
882C24—112no—
883C24—112no—
884C24—112no—
885C24—112no—
886C24—112no—
887C24—112no—
888C24—112no—
889C24—112no—
890C24—112no—
891C24—112no—
892C24—112no—
893C24—221no—
894C24—221no—
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—
919C24—221no—
920C24—221no—
921C24—221no—
922C24—221no—
923C24—221no—
924C24—221no—
925C24—221no—
926C24—221no—
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—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—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—228no—
991C22×C4—228no—
992C22×C4—228no—
993C22×C4—228no—
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—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—228no—
1019C22×C4—228no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—444no—
1028C22×C4—444no—
1029C22×C4—444no—
1030C22×C4—444no—
1031C22×C4—444no—
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×C4—444no—
1043C22×C4—444no—
1044C22×C4—444no—
1045C22×C4—444no—
1046C22×C4—444no—
1047C22×C4—444no—
1048C22×C4—444no—
1049C22×C4C2×C4×D1112yes—
1050C22×C4C2×C4×D1112yes—
1051C22×C4C2×C4×D1112yes—
1052C22×C4C2×D4412yes—
1053C22×C4C2×D4412yes—
1054C22×C4C2×D4412yes—
1055C22×C4#433912yes—
1056C22×C4D4×D1112yes—
1057C22×C4D4×D1112yes—
1058C22×C4D4×D1112yes—
1059C22×C4D4×D1112yes—
1060C22×C4#434312yes—
1061C4⋊C4—28no—
1062C4⋊C4—228no—
1063C22⋊C4—228no—
1064C22⋊C4—228no—
1065C22⋊C4—228no—
1066C22⋊C4—228no—
1067C22⋊C4—444no—
1068C22⋊C4—444no—
1069C22⋊C4—444no—
1070C22⋊C4—444no—
1071C22⋊C4—444no—
1072C22⋊C4—444no—
1073C22⋊C4—444no—
1074C42—28no—
1075C11#1402311yescharacteristic, complemented, Sylow
1076C23—114no—
1077C23—114no—
1078C23—114no—
1079C23—114no—
1080C23—114no—
1081C23—114no—
1082C23—114no—
1083C23—114no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
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—441no—
1138C23—441no—
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—
1171C23—441no—
1172C23—441no—
1173C23—441no—
1174C23—441no—
1175C23—441no—
1176C23—441no—
1177C23—441no—
1178C23—441no—
1179C23—441no—
1180C23—441no—
1181C23C22×C4×D1111yescharacteristic
1182C23C22×D4411yescharacteristic
1183C23C2×#433911yescharacteristic
1184C23C2×D4×D1111yescharacteristic
1185C23C2×D4×D1111yescharacteristic
1186C23C2×D4×D1111yescharacteristic
1187C23C2×D4×D1111yescharacteristic
1188C23C2×#434311yescharacteristic
1189C23#6704011yescharacteristic
1190C23#41×D1111yescharacteristic
1191C23#41×D1111yescharacteristic
1192C23#41×D1111yescharacteristic
1193C23#6704211yescharacteristic
1194C23#6704211yescharacteristic
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—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
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—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
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—4416no—
1258C2×C4—4416no—
1259C2×C4—4416no—
1260C2×C4—4416no—
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—441no—
1277C2×C4—441no—
1278C2×C4—441no—
1279C2×C4—441no—
1280C2×C4—441no—
1281C2×C4—441no—
1282C2×C4—441no—
1283C2×C4—441no—
1284C2×C4C4×D4414yescomplemented
1285C2×C4C22⋊C4×D1114yes—
1286C2×C4#6694814yescomplemented
1287C22—118no—
1288C22—224no—
1289C22—224no—
1290C22—224no—
1291C22—224no—
1292C22—224no—
1293C22—224no—
1294C22—224no—
1295C22—224no—
1296C22—224no—
1297C22—224no—
1298C22—224no—
1299C22—224no—
1300C22—224no—
1301C22—224no—
1302C22—224no—
1303C22—224no—
1304C22—224no—
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—
1322C22—442no—
1323C22—442no—
1324C22—881no—
1325C22—881no—
1326C22—881no—
1327C22—881no—
1328C22—881no—
1329C22—881no—
1330C22—881no—
1331C22—881no—
1332C22C2×C4×D4411yescharacteristic
1333C22C2×C22⋊C4×D1111yescharacteristic
1334C22C2×#6694811yescharacteristic
1335C22#1062303811yescharacteristic
1336C22#1062305211yescharacteristic
1337C22#1062305511yescharacteristic
1338C22#1062306111yescharacteristic
1339C22C4×D4×D1111yescharacteristic
1340C22C4×D4×D1111yescharacteristic
1341C22#1062307911yescharacteristic
1342C22D4×D4411yescharacteristic
1343C22D4×D4411yescharacteristic
1344C22D4×D4411yescharacteristic
1345C22#1062308111yescharacteristic
1346C22#1062308111yescharacteristic
1347C22C4×#434311yescharacteristic
1348C22#1062310511yescharacteristic
1349C22#1062310711yescharacteristic
1350C22#1062311111yescharacteristic
1351C22D11×#12011yescharacteristic
1352C22D11×#12111yescharacteristic
1353C22D11×#12111yescharacteristic
1354C22#1062316011yescharacteristic
1355C22#1062316111yescharacteristic
1356C22#1062316111yescharacteristic
1357C22#1062316211yescharacteristic
1358C22D11×#12311yescharacteristic
1359C22#1062318411yescharacteristic
1360C22#1062318511yescharacteristic
1361C22#1062320711yescharacteristic
1362C22#1062322311yescharacteristic
1363C22#1062322611yescharacteristic
1364C22#1062323511yescharacteristic
1365C22#1062324011yescharacteristic
1366C22#1062325711yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—24no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—81no—
1374C4—442no—
1375C4—442no—
1376C4—442no—
1377C4—442no—
1378C4—881no—
1379C2—228no—
1380C2—444no—
1381C2—882no—
1382C2D11×#38611yescharacteristic
1383C2C4×#6694811yescharacteristic
1384C2#1307131511yescharacteristic
1385C2C22⋊C4×D4411yescharacteristic
1386C2#1307144511yescharacteristic
1387C2#1307163411yescharacteristic
1388C2#1307166211yescharacteristic
1389C2#1307198811yescharacteristic
1390C2#1307205411yescharacteristic
1391C2#1307215711yescharacteristic
1392C2#1307217411yescharacteristic
1393C2#1307222511yescharacteristic
1394C2#1307235611yescharacteristic
1395C2#1307237111yescharacteristic
1396C2#1307358111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenter#1436D11
hypocenterC11#14023
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. C2×#10622278C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622278C2semidirect
6. C2×#10622278C2semidirect
7. C2×D11×#95C2semidirect
8. #13066869C2semidirect
9. #13066864C2semidirect
10. #13066862C2semidirect
11. #13066856C2semidirect
12. #13066854C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
39. C2×#66948C4semidirect
94. C22×D44C2×C4semidirect
95. C22×D44C2×C4semidirect
124. C22×C4×D11C2×C4semidirect
125. C22×C4×D11D4semidirect
128. C2×C11×C4⋊C4C2×C4semidirect
162. C2×(C2×D11)⋊C4C2×C4semidirect
163. C2×(C2×D11)⋊C4C2×C4semidirect
164. C2×(C2×D11)⋊C4D4semidirect
174. C11×#95D4semidirect
335. C2×D44C22⋊C4semidirect
390. #1436D11semidirect
560. C2×C4×C11C4×D4semidirect
561. C2×C4×C11#121semidirect
729. C2×D11#386semidirect
813. C2×C4⋊C4C4×D11semidirect
863. #95D44semidirect
1075. C11#14023semidirect
1284. C2×C4C4×D44semidirect
1286. C2×C4#66948semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C22×C4×D442
C2×#106222782
C2×D11×#952
#130668692
#130668642
#130668622
#130668562
#130668542
(C2×D11)⋊#952
C11×#14362
#1402311