Finite Group Databasebeta

← #14685039

Subgroups — #14685039

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622585C211yesmaximal, characteristic, complemented
5C2×#10622558C211yesmaximal, characteristic, complemented
6C2×#10622553C211yesmaximal, characteristic, complemented
7C2×#10622603C211yesmaximal, characteristic, complemented
8C2×C42×Dic11C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C11×#388—24no—
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
52#10622603—24no—
53#10622585—24no—
54#10622570—24no—
55#10622570—24no—
56#10622570C418yescomplemented
57#10622558—24no—
58#10622553—24no—
59C42×Dic11—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4C2×C414yes—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11D414yescomplemented
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11C2×C414yes—
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)⋊C4C2×C414yes—
123C2×(C2×D11)⋊C4C2×C414yes—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4C2×C414yes—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11C2×C414yes—
151C2×C4×Dic11D414yes—
152C2×C4×Dic11D414yes—
153C2×C4×Dic11D414yescomplemented
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—
164#14700—111nomaximal, Sylow
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11C22×C412yes—
180C24×C11C2411yescharacteristic
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×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11C22×C412yes—
196C22×C4×C11—21no—
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×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C22×Dic11—21no—
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×Dic11C22×C412yes—
278C22×Dic11C22×C412yes—
279C22×Dic11C22×C412yes—
280C22×Dic11C2×D412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11C2×D412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11#4112yes—
287C22×Dic11#4112yes—
288C22×Dic11#4112yes—
289C22×Dic11#4112yes—
290C22×Dic11#4112yes—
291C22×Dic11#4112yes—
292C22×Dic11#4112yes—
293C22×Dic11#4112yes—
294C11×C4⋊C4—44no—
295C11×C22⋊C4—28no—
296C11×C22⋊C4—44no—
297C11×C22⋊C4—44no—
298C42×C11—28no—
299C22⋊Dic11—28no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308Dic11⋊C4—28no—
309Dic11⋊C4—44no—
310Dic11⋊C4—44no—
311Dic11⋊C4—44no—
312C4×Dic11—28no—
313C4×Dic11—28no—
314C4×Dic11—28no—
315C4×Dic11—28no—
316C4×Dic11—28no—
317C4×Dic11—28no—
318C2×#390—111no—
319C2×#390—111no—
320C2×#390—111no—
321C2×#389—111no—
322C2×#388—111no—
323C2×#388—111no—
324C2×#388—111no—
325C2×#388D1111yescharacteristic, complemented
326C2×C43—111no—
327#1437—111no—
328#1437—111no—
329#1437—111no—
330#1437—111no—
331C4⋊#95—111no—
332C4⋊#95—111no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11C23×C411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11C2×#4111yescharacteristic
377C23×C11C2×#4111yescharacteristic
378C23×C11C2×#4111yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
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—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
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—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11C4×D414yes—
458C2×C4×C11#12114yes—
459C2×C4×C11#12714yes—
460C22⋊D11—416no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11#11714yes—
501C2×Dic11C4×D414yes—
502C2×Dic11C4×D414yes—
503C2×Dic11C4×D414yes—
504C2×Dic11#12114yes—
505C2×Dic11#12114yes—
506C2×Dic11#12314yes—
507C2×Dic11#12414yes—
508C2×Dic11#12414yes—
509C2×Dic11#12614yes—
510C23×D4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4—111no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4C2×D1111yescharacteristic
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531C22×C42—111no—
532C22×C42—111no—
533C22×C42—111no—
534C22×C42C2×D1111yescharacteristic
535#390—118no—
536#390—224no—
537#390—224no—
538#389—224no—
539#388—24no—
540#388—224no—
541#388—224no—
542#388—224no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95C2×D1111yescharacteristic
552C2×#95C2×D1111yescharacteristic
553C43—224no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11C2×#11711yescharacteristic
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C2×C4×D411yescharacteristic
573C22×C11C2×C4×D411yescharacteristic
574C22×C11C4×#4111yescharacteristic
575C22×C11C4×#4111yescharacteristic
576C22×C11C2×#12111yescharacteristic
577C22×C11C2×#12111yescharacteristic
578C22×C11C2×#12111yescharacteristic
579C22×C11C2×#12311yescharacteristic
580C22×C11#52511yescharacteristic
581C22×C11#52511yescharacteristic
582C22×C11C2×#12411yescharacteristic
583C22×C11C2×#12411yescharacteristic
584C22×C11C2×#12611yescharacteristic
585C22×C11#52911yescharacteristic
586C22×C11#52911yescharacteristic
587C22×C11#52911yescharacteristic
588C22×C11#52911yescharacteristic
589C22×C11#52911yescharacteristic
590C22×C11#52911yescharacteristic
591C22×C11#52911yescharacteristic
592C22×C11#52911yescharacteristic
593C22×C11C2×#12711yescharacteristic
594C22×C11#53211yescharacteristic
595C22×C11#53211yescharacteristic
596C22×C11#53211yescharacteristic
597C22×C11#53211yescharacteristic
598C22×C11#53211yescharacteristic
599C22×C11#53211yescharacteristic
600C22×C11#53211yescharacteristic
601C22×C11#53211yescharacteristic
602C22×C11#53211yescharacteristic
603C22×C11#53211yescharacteristic
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C2×D11—81no—
615C2×D11—81no—
616C2×D11—81no—
617C2×D11—81no—
618C2×D11—81no—
619C4×C11—24no—
620C4×C11—24no—
621C4×C11—24no—
622C4×C11—42no—
623C4×C11—81no—
624C4×C11—81no—
625Dic11—24no—
626Dic11—24no—
627Dic11—24no—
628Dic11—42no—
629Dic11—81no—
630Dic11—81no—
631Dic11#38818yescomplemented
632C25—111no—
633C25C22×D1111yescharacteristic
634C22×D4—114no—
635C22×D4—222no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—222no—
640C22×D4—222no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4C22×D1111yescharacteristic
649C23×C4C22×D1111yescharacteristic
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—114no—
658C2×C4⋊C4—222no—
659C2×C4⋊C4—222no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—222no—
667C2×C4⋊C4—222no—
668C2×C4⋊C4—222no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—114no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4C4×D1114yes—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—114no—
708C2×C42—114no—
709C2×C42—114no—
710C2×C42—114no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—222no—
716C2×C42—222no—
717C2×C42—222no—
718C2×C42—222no—
719C2×C42—222no—
720C2×C42—222no—
721C2×C42—222no—
722C2×C42—222no—
723C2×C42—222no—
724C2×C42—222no—
725C2×C42C22⋊D1114yescomplemented
726#95—22no—
727#95—22no—
728#95—222no—
729#95—222no—
730#95—222no—
731#95—222no—
732#95—222no—
733#95—222no—
734#95—222no—
735#95—222no—
736C2×C11—82no—
737C2×C11C2×#38811yescharacteristic
738C2×C11#229311yescharacteristic
739C2×C11#229311yescharacteristic
740C2×C11C4×#12111yescharacteristic
741C2×C11C4×#12111yescharacteristic
742C2×C11C4×#12411yescharacteristic
743C2×C11C4×#12711yescharacteristic
744C2×C11#285011yescharacteristic
745C2×C11#285411yescharacteristic
746C2×C11#285411yescharacteristic
747C2×C11#285611yescharacteristic
748C2×C11#285811yescharacteristic
749C2×C11#286011yescharacteristic
750C2×C11#286011yescharacteristic
751C2×C11#286111yescharacteristic
752D11—82no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—112no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24C2×C4×D1112yes—
783C24C23×D1111yescharacteristic
784C2×D4—228no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—444no—
788C2×D4—444no—
789C2×D4—444no—
790C2×D4—444no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
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×C4C2×C4×D1112yes—
873C22×C4C2×C4×D1112yes—
874C22×C4#433912yes—
875C22×C4D4×D1112yes—
876C22×C4D4×D1112yes—
877C22×C4D4×D1112yes—
878C22×C4#434112yes—
879C22×C4C2×C22⋊D1112yes—
880C22×C4C2×C22⋊D1112yes—
881C22×C4C2×C22⋊D1112yes—
882C4⋊C4—44no—
883C4⋊C4—228no—
884C4⋊C4—444no—
885C4⋊C4—444no—
886C4⋊C4—444no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C22⋊C4—444no—
898C22⋊C4—444no—
899C42—28no—
900C42—228no—
901C42—228no—
902C42—228no—
903C42—228no—
904C42—228no—
905C42—228no—
906C11#1470011yescharacteristic, complemented, Sylow
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23C22×C4×D1111yescharacteristic
978C23C2×#433911yescharacteristic
979C23C2×D4×D1111yescharacteristic
980C23C2×D4×D1111yescharacteristic
981C23C2×D4×D1111yescharacteristic
982C23C2×#434111yescharacteristic
983C23#41×D1111yescharacteristic
984C23#41×D1111yescharacteristic
985C23#41×D1111yescharacteristic
986C23#41×D1111yescharacteristic
987C23#41×D1111yescharacteristic
988C23#41×D1111yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23C22×C22⋊D1111yescharacteristic
992D4—4416no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—114no—
1033C2×C4—114no—
1034C2×C4—114no—
1035C2×C4—114no—
1036C2×C4—114no—
1037C2×C4—114no—
1038C2×C4—114no—
1039C2×C4—114no—
1040C2×C4—114no—
1041C2×C4—114no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4C4×C22⋊D1114yes—
1082C2×C4#6699214yes—
1083C2×C4#6699314yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—881no—
1107C22—881no—
1108C22—881no—
1109C22—881no—
1110C22—881no—
1111C22—881no—
1112C22—881no—
1113C22—881no—
1114C22D11×#11711yescharacteristic
1115C22#1062305311yescharacteristic
1116C22#1062305911yescharacteristic
1117C22#1062305911yescharacteristic
1118C22C4×#434111yescharacteristic
1119C22#1062306911yescharacteristic
1120C22C4×D4×D1111yescharacteristic
1121C22C4×D4×D1111yescharacteristic
1122C22C4×D4×D1111yescharacteristic
1123C22#1062307811yescharacteristic
1124C22#1062307911yescharacteristic
1125C22#1062307911yescharacteristic
1126C22#1062312711yescharacteristic
1127C22#1062312711yescharacteristic
1128C22D11×#12111yescharacteristic
1129C22D11×#12111yescharacteristic
1130C22#1062318011yescharacteristic
1131C22#1062318011yescharacteristic
1132C22D11×#12311yescharacteristic
1133C22#1062318711yescharacteristic
1134C22#1062319911yescharacteristic
1135C22#1062319911yescharacteristic
1136C22D11×#12411yescharacteristic
1137C22D11×#12411yescharacteristic
1138C22D11×#12611yescharacteristic
1139C22#1062323711yescharacteristic
1140C22#1062323711yescharacteristic
1141C22#1062323711yescharacteristic
1142C22C2×C4×C22⋊D1111yescharacteristic
1143C22C2×#6699211yescharacteristic
1144C22C2×#6699311yescharacteristic
1145C22#1062336311yescharacteristic
1146C22#1062336311yescharacteristic
1147C22#1062336311yescharacteristic
1148C22#1062336311yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—24no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—118no—
1156C4—224no—
1157C4—224no—
1158C4—224no—
1159C4—442no—
1160C4—881no—
1161C4—881no—
1162C2—82no—
1163C2—882no—
1164C2D11×#38811yescharacteristic
1165C2#1307107511yescharacteristic
1166C2#1307107611yescharacteristic
1167C2C4×#6699211yescharacteristic
1168C2#1307112811yescharacteristic
1169C2#1307115711yescharacteristic
1170C2C4×#6699311yescharacteristic
1171C2#1307691411yescharacteristic
1172C2#1307694311yescharacteristic
1173C2#1307694511yescharacteristic
1174C2#1307695911yescharacteristic
1175C2#1307697111yescharacteristic
1176C2#1307698111yescharacteristic
1177C2#1307698211yescharacteristic
1178C2#1307698511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11#14700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#10622585C2semidirect
5. C2×#10622558C2semidirect
6. C2×#10622553C2semidirect
7. C2×#10622603C2semidirect
8. C2×C42×Dic11C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066852C2semidirect
12. #13066852C2semidirect
13. Dic11⋊#95C2semidirect
14. Dic11⋊#95C2semidirect
15. C2×C11×#388C2semidirect
56. #10622570C4semidirect
96. C2×C42×C11D4semidirect
153. C2×C4×Dic11D4semidirect
325. C2×#388D11semidirect
631. Dic11#388semidirect
725. C2×C42C22⋊D11semidirect
906. C11#14700semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106225852
C2×#106225582
C2×#106225532
C2×#106226032
C2×C42×Dic112
#130668532
#130668522
Dic11⋊#952
C2×C11×#3882
#1470011