Finite Group Databasebeta

← #14676891

Subgroups — #14676891

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic, complemented
5C2×#10622277C211yesmaximal, characteristic, complemented
6C2×#10622279C211yesmaximal, characteristic, complemented
7C2×D11×#95C211yesmaximal, characteristic, complemented
8#13066882C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066845C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1445C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66947—24no—
36C2×#66947—24no—
37C2×#66947C418yescomplemented
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
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
54#10622281—24no—
55#10622279—24no—
56#10622278—24no—
57#10622278—24no—
58#10622277—24no—
59D11×#95—24no—
60C24×D11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44C2×C414yes—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C22×C4×D11C2×C414yes—
102C22×C4×D11D414yes—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4C2×C414yescomplemented
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4C2×C414yes—
128C2×(C2×D11)⋊C4C2×C414yescomplemented
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×(C2×D11)⋊C4D414yes—
131C2×(C2×D11)⋊C4D414yes—
132C2×(C2×D11)⋊C4D414yes—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—41no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4C2×C414yescomplemented
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—41no—
147C2×C4×Dic11—41no—
148#66947—232no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—22no—
154C11×#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165#13996—111nomaximal, Sylow
166C24×C11C2411yescharacteristic
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11C22×C412yes—
190C23×D11C22×C412yes—
191C23×D11C2×D412yes—
192C23×D11C2×D412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11#4112yes—
196C23×D11#4112yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11C22×C412yes—
239C22×C4×C11C22×C412yes—
240C22×C4×C11C22×C412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11#4112yes—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11C22×C412yes—
280C22×Dic11C22×C412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11#4112yes—
286C22×Dic11#4112yes—
287C22×Dic11#4112yes—
288C2×D44—28no—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—44no—
292C2×D44—44no—
293C2×D44—44no—
294C2×D44—44no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C11×C4⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—28no—
319(C2×D11)⋊C4—28no—
320(C2×D11)⋊C4—44no—
321(C2×D11)⋊C4—44no—
322(C2×D11)⋊C4—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
325(C2×D11)⋊C4C22⋊C4116yescomplemented
326C4⋊Dic11—44no—
327Dic11⋊C4—28no—
328Dic11⋊C4—44no—
329C4×Dic11—44no—
330C4×Dic11—44no—
331C22×#123—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#385—111no—
335C2×#381—111no—
336C2×C4×C22⋊C4—111no—
337C22×#95—111no—
338#1445—111no—
339#1445D1111yescharacteristic, complemented
340#1439—111no—
341#1439—111no—
342#1437—111no—
343#1437—111no—
344C4⋊#95—111no—
345C4⋊#95—111no—
346C23×C11C23×C411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11C2×#4111yescharacteristic
353C23×C11C2×#4111yescharacteristic
354C23×C11C2×#4111yescharacteristic
355C23×C11C2×#4111yescharacteristic
356C23×C11C2×#4111yescharacteristic
357C23×C11H(5,𝔽2)11yescharacteristic
358C23×C11H(5,𝔽2)11yescharacteristic
359C23×C112−1+411yescharacteristic
360C23×C112−1+411yescharacteristic
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11C2×C22⋊C414yes—
425C22×D11C4×D414yes—
426C22×D11C4×D414yes—
427C22×D11#12114yes—
428C22×D11#12114yes—
429C22×D11#12414yes—
430C22×D11#12714yes—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11C2×C22⋊C414yes—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11C2×C22⋊C414yes—
521C2×Dic11#12314yescomplemented
522D44—416no—
523C4×D11—416no—
524C4×D11—416no—
525C4×D11—416no—
526C23×D4—111no—
527C24×C4—111no—
528C24×C4—111no—
529C24×C4—111no—
530C2×#123—118no—
531C2×#123—224no—
532C2×#123—224no—
533C22×C4⋊C4—111no—
534C22×C4⋊C4—111no—
535C22×C4⋊C4—111no—
536C22×C4⋊C4C2×D1111yescharacteristic
537C22×C22⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4—111no—
546C22×C42—111no—
547C22×C42—111no—
548#386—224no—
549#386—224no—
550#385—224no—
551#381—224no—
552C4×C22⋊C4—224no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—224no—
564C2×#95C2×D1111yescharacteristic
565C2×#95C2×D1111yescharacteristic
566C2×#95C2×D1111yescharacteristic
567C2×#95C2×D1111yescharacteristic
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C22×C11C22×C22⋊C411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C2×C4×D411yescharacteristic
573C22×C11C4×#4111yescharacteristic
574C22×C11C4×#4111yescharacteristic
575C22×C11#52011yescharacteristic
576C22×C11#52011yescharacteristic
577C22×C11C2×#12111yescharacteristic
578C22×C11C2×#12111yescharacteristic
579C22×C11C2×#12311yescharacteristic
580C22×C11#52511yescharacteristic
581C22×C11C2×#12411yescharacteristic
582C22×C11#52911yescharacteristic
583C22×C11#52911yescharacteristic
584C22×C11C2×#12711yescharacteristic
585C22×C11#53411yescharacteristic
586C22×C11#53611yescharacteristic
587C22×C11#53911yescharacteristic
588C22×C11#53911yescharacteristic
589C22×C11#54611yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54711yescharacteristic
596C22×C11#54711yescharacteristic
597C22×C11#54711yescharacteristic
598C22×C11#54711yescharacteristic
599C22×C11#54711yescharacteristic
600C22×C11#54711yescharacteristic
601C22×C11#55111yescharacteristic
602C22×C11#55111yescharacteristic
603C22×C11#55211yescharacteristic
604C22×C11#55211yescharacteristic
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—24no—
608C2×D11—24no—
609C2×D11—24no—
610C2×D11—24no—
611C2×D11—24no—
612C2×D11—24no—
613C2×D11—24no—
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—24no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—81no—
627C2×D11—81no—
628C2×D11—81no—
629C2×D11—81no—
630C2×D11—81no—
631C2×D11—81no—
632C2×D11—81no—
633C2×D11—81no—
634C2×D11#39018yes—
635C4×C11—24no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—81no—
642Dic11—24no—
643Dic11—24no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648C25—111no—
649C25—111no—
650C22×D4—114no—
651C22×D4—222no—
652C22×D4—222no—
653C22×D4—222no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—114no—
663C23×C4—114no—
664C23×C4—111no—
665C23×C4—222no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—441no—
681C23×C4—441no—
682C23×C4—441no—
683C23×C4—441no—
684C23×C4C22×D1111yescharacteristic
685C23×C4C22×D1111yescharacteristic
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691#123—2232no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—114no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C4⋊C4—222no—
701C2×C4⋊C4—441no—
702C2×C4⋊C4—441no—
703C2×C4⋊C4C4×D1114yescomplemented
704C2×C22⋊C4—114no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—114no—
708C2×C22⋊C4—114no—
709C2×C22⋊C4—114no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C42—222no—
732C2×C42—222no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—441no—
736C2×C42—441no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—222no—
753C2×C11C2×#39011yescharacteristic
754C2×C11C4×#12311yescharacteristic
755C2×C11#232211yescharacteristic
756C2×C11#233911yescharacteristic
757C2×C11#233911yescharacteristic
758C2×C11#235911yescharacteristic
759C2×C11#235911yescharacteristic
760C2×C11#241211yescharacteristic
761C2×C11#241311yescharacteristic
762C2×C11#242511yescharacteristic
763C2×C11#242511yescharacteristic
764C2×C11#248811yescharacteristic
765C2×C11#248811yescharacteristic
766C2×C11#250111yescharacteristic
767C2×C11#253911yescharacteristic
768D11—28no—
769D11—82no—
770C24—112no—
771C24—112no—
772C24—112no—
773C24—112no—
774C24—112no—
775C24—112no—
776C24—112no—
777C24—112no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24C23×D1111yescharacteristic
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C2×D4—444no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—228no—
859C22×C4—228no—
860C22×C4—228no—
861C22×C4—228no—
862C22×C4—228no—
863C22×C4—228no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—444no—
898C22×C4—444no—
899C22×C4—444no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4C2×C4×D1112yes—
913C22×C4C2×C4×D1112yes—
914C22×C4C2×C4×D1112yes—
915C22×C4D4×D1112yes—
916C22×C4D4×D1112yes—
917C22×C4D4×D1112yes—
918C22×C4D4×D1112yes—
919C22×C4#434312yes—
920C4⋊C4—28no—
921C4⋊C4—228no—
922C4⋊C4—444no—
923C4⋊C4—444no—
924C22⋊C4—1116no—
925C22⋊C4—228no—
926C22⋊C4—228no—
927C22⋊C4—228no—
928C22⋊C4—444no—
929C22⋊C4—444no—
930C22⋊C4—444no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C42—444no—
934C42—444no—
935C11#1399611yescharacteristic, complemented, Sylow
936C23—114no—
937C23—114no—
938C23—114no—
939C23—114no—
940C23—114no—
941C23—114no—
942C23—114no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23—441no—
991C23—441no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23C22×C4×D1111yescharacteristic
1007C23C2×D4×D1111yescharacteristic
1008C23C2×D4×D1111yescharacteristic
1009C23C2×D4×D1111yescharacteristic
1010C23C2×D4×D1111yescharacteristic
1011C23C2×#434311yescharacteristic
1012C23#6704011yescharacteristic
1013C23#41×D1111yescharacteristic
1014C23#41×D1111yescharacteristic
1015C23#41×D1111yescharacteristic
1016C23#41×D1111yescharacteristic
1017C23#41×D1111yescharacteristic
1018C23#6704211yescharacteristic
1019C23#6704211yescharacteristic
1020C23#6704311yescharacteristic
1021D4—4416no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—114no—
1071C2×C4—114no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—4416no—
1094C2×C4—4416no—
1095C2×C4—4416no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4C22⋊C4×D1114yes—
1116C22—118no—
1117C22—224no—
1118C22—224no—
1119C22—224no—
1120C22—224no—
1121C22—224no—
1122C22—224no—
1123C22—224no—
1124C22—224no—
1125C22—224no—
1126C22—224no—
1127C22—224no—
1128C22—224no—
1129C22—224no—
1130C22—224no—
1131C22—442no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22—442no—
1137C22—442no—
1138C22—881no—
1139C22—881no—
1140C22—881no—
1141C22—881no—
1142C22—881no—
1143C22—881no—
1144C22—881no—
1145C22—881no—
1146C22C2×C22⋊C4×D1111yescharacteristic
1147C22#1062305311yescharacteristic
1148C22#1062305411yescharacteristic
1149C22C4×D4×D1111yescharacteristic
1150C22C4×D4×D1111yescharacteristic
1151C22C4×#434311yescharacteristic
1152C22#1062310511yescharacteristic
1153C22D11×#12111yescharacteristic
1154C22D11×#12111yescharacteristic
1155C22#1062315811yescharacteristic
1156C22#1062315911yescharacteristic
1157C22#1062316111yescharacteristic
1158C22#1062316111yescharacteristic
1159C22#1062316211yescharacteristic
1160C22#1062316211yescharacteristic
1161C22D11×#12311yescharacteristic
1162C22#1062318411yescharacteristic
1163C22#1062318511yescharacteristic
1164C22#1062318511yescharacteristic
1165C22#1062318511yescharacteristic
1166C22#1062318611yescharacteristic
1167C22#1062318611yescharacteristic
1168C22#1062318611yescharacteristic
1169C22D11×#12411yescharacteristic
1170C22#1062320711yescharacteristic
1171C22#1062322211yescharacteristic
1172C22#1062322311yescharacteristic
1173C22#1062322411yescharacteristic
1174C22#1062322511yescharacteristic
1175C22#1062323611yescharacteristic
1176C22#1062323611yescharacteristic
1177C22#1062323711yescharacteristic
1178C22#1062323811yescharacteristic
1179C22D11×#12711yescharacteristic
1180C22#1062325711yescharacteristic
1181C4—24no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—81no—
1188C4—224no—
1189C4—224no—
1190C4—442no—
1191C4—442no—
1192C4—442no—
1193C4—881no—
1194C2—228no—
1195C2—882no—
1196C2D11×#39011yescharacteristic
1197C2#1307113711yescharacteristic
1198C2#1307128911yescharacteristic
1199C2#1307144011yescharacteristic
1200C2#1307144511yescharacteristic
1201C2#1307160111yescharacteristic
1202C2#1307161511yescharacteristic
1203C2#1307200511yescharacteristic
1204C2#1307201611yescharacteristic
1205C2#1307216011yescharacteristic
1206C2#1307217011yescharacteristic
1207C2#1307293711yescharacteristic
1208C2#1307294311yescharacteristic
1209C2#1307308211yescharacteristic
1210C2#1307354311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1445D11
hypocenterC11#13996
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
4. C2×#10622281C2semidirect
5. C2×#10622277C2semidirect
6. C2×#10622279C2semidirect
7. C2×D11×#95C2semidirect
8. #13066882C2semidirect
9. #13066862C2semidirect
10. #13066860C2semidirect
11. #13066852C2semidirect
12. #13066852C2semidirect
13. #13066845C2semidirect
14. Dic11⋊#95C2semidirect
15. C11×#1445C2semidirect
37. C2×#66947C4semidirect
105. C2×C11×C4⋊C4C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
141. C2×Dic11⋊C4C2×C4semidirect
325. (C2×D11)⋊C4C22⋊C4semidirect
339. #1445D11semidirect
521. C2×Dic11#123semidirect
703. C2×C4⋊C4C4×D11semidirect
935. C11#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106222782
C2×#106222812
C2×#106222772
C2×#106222792
C2×D11×#952
#130668822
#130668622
#130668602
#130668522
#130668452
Dic11⋊#952
C11×#14452
#1399611