Finite Group Databasebeta

← #14679196

Subgroups — #14679196

Order 2816.

2162 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622572C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622569C211yesmaximal, characteristic
5C2×#10622823C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13066877C211yesmaximal, characteristic, complemented
8#13066865C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
35C4×C11×C22⋊C4—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622826—24no—
39#10622823—24no—
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#10622572C418yescomplemented
55#10622569—24no—
56#10622553—24no—
57C4×(C2×D11)⋊C4—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4C2×C414yescomplemented
99C2×C11×C22⋊C4D414yes—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11—41no—
105C2×C42×C11—41no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11C2×C414yescomplemented
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—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4C2×C414yescomplemented
128C2×(C2×D11)⋊C4C2×C414yescomplemented
129C2×(C2×D11)⋊C4D414yes—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—41no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×Dic11⋊C4C2×C414yescomplemented
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—41no—
142C11×#95—22no—
143C11×#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95C2×C414yescomplemented
157C11⋊#95D414yescomplemented
158#14182—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11C22×C412yes—
172C24×C11C2×D412yes—
173C24×C11#4112yes—
174C24×C11C2411yescharacteristic
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×D11C22×C412yes—
188C23×D11C2×D412yes—
189C23×D11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—28no—
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—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11—44no—
228C22×C4×C11—44no—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
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×Dic11—21no—
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×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C2×C4×D11—28no—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C11×C22⋊C4—28no—
303C11×C22⋊C4—28no—
304C42×C11—44no—
305C42×C11—44no—
306C22⋊Dic11—28no—
307C22⋊Dic11—44no—
308C22⋊Dic11—44no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—28no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314Dic11⋊C4—44no—
315Dic11⋊C4—44no—
316Dic11⋊C4—44no—
317C4×Dic11—44no—
318C2×#394—111no—
319C2×#388—111no—
320C2×#386—111no—
321C2×#386—111no—
322C2×#385—111no—
323C2×C4×C22⋊C4—111no—
324C2×C4×C22⋊C4D1111yescharacteristic, complemented
325#1443—111no—
326#1440—111no—
327#1439—111no—
328#1437—111no—
329#1436—111no—
330#1436—111no—
331C4⋊#95—111no—
332C22⋊#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—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
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×C11C4×D414yes—
368C23×C11C23×C411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11C2×#4111yescharacteristic
377C23×C11C2×#4111yescharacteristic
378C23×C11C2×#4111yescharacteristic
379C23×C11H(5,𝔽2)11yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C112−1+411yescharacteristic
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—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
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×D11C4×D414yes—
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—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—416no—
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×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11#12114yes—
460C2×C4×C11#12314yes—
461C22⋊D11—416no—
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—41no—
481C2×Dic11—41no—
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—41no—
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×Dic11C4×D414yes—
511C4×D11—416no—
512C23×D4—111no—
513C24×C4—111no—
514C24×C4C2×D1111yescharacteristic
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊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⋊C4—111no—
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42C2×D1111yescharacteristic
530C22×C42C2×D1111yescharacteristic
531#394—118no—
532#388—224no—
533#386—224no—
534#386—224no—
535#385—224no—
536C4×C22⋊C4—24no—
537C4×C22⋊C4—224no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
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×#95—111no—
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11C2×C4×D411yescharacteristic
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C4×#4111yescharacteristic
573C22×C11C4×#4111yescharacteristic
574C22×C11#51811yescharacteristic
575C22×C11#52011yescharacteristic
576C22×C11C2×#12111yescharacteristic
577C22×C11C2×#12311yescharacteristic
578C22×C11#52511yescharacteristic
579C22×C11#52511yescharacteristic
580C22×C11#52911yescharacteristic
581C22×C11#52911yescharacteristic
582C22×C11#52911yescharacteristic
583C22×C11#53211yescharacteristic
584C22×C11#53811yescharacteristic
585C22×C11#53811yescharacteristic
586C22×C11#54211yescharacteristic
587C22×C11#54211yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11D4211yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54711yescharacteristic
596C22×C11#54711yescharacteristic
597C22×C11#54811yescharacteristic
598C22×C11#55111yescharacteristic
599C22×C11#55111yescharacteristic
600C22×C11#55211yescharacteristic
601C22×C11#55311yescharacteristic
602C22×C11#55311yescharacteristic
603C22×C11#55311yescharacteristic
604C2×D11—24no—
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C4×C11—24no—
620C4×C11—24no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625Dic11—24no—
626Dic11—42no—
627Dic11—42no—
628Dic11—42no—
629Dic11—42no—
630Dic11—81no—
631Dic11—81no—
632C25—111no—
633C25C22×D1111yescharacteristic
634C22×D4—114no—
635C22×D4—222no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—441no—
640C22×D4—441no—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—41no—
647C23×C4—41no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—222no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C2×C4⋊C4—114no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—222no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—441no—
675C2×C4⋊C4—441no—
676C2×C4⋊C4—441no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—114no—
682C2×C22⋊C4—114no—
683C2×C22⋊C4—114no—
684C2×C22⋊C4—114no—
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—441no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4C4×D1114yescomplemented
706C2×C22⋊C4C22⋊D1114yes—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—441no—
716#95—22no—
717#95—22no—
718#95—114no—
719#95—114no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—441no—
731#95—441no—
732C2×C11—44no—
733C2×C11C4×#12111yescharacteristic
734C2×C11C4×#12311yescharacteristic
735C2×C11#233711yescharacteristic
736C2×C11#235811yescharacteristic
737C2×C11#235911yescharacteristic
738C2×C11#236111yescharacteristic
739C2×C11#236411yescharacteristic
740C2×C11#241811yescharacteristic
741C2×C11#242211yescharacteristic
742C2×C11#242411yescharacteristic
743C2×C11#242711yescharacteristic
744C2×C11#247011yescharacteristic
745C2×C11#247711yescharacteristic
746C2×C11#255911yescharacteristic
747C2×C11#257611yescharacteristic
748D11—44no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—112no—
762C24—112no—
763C24—112no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24C2×C4×D1112yes—
777C24#433912yes—
778C24C2×C22⋊D1112yes—
779C24C23×D1111yescharacteristic
780C2×D4—228no—
781C2×D4—228no—
782C2×D4—444no—
783C2×D4—444no—
784C2×D4—444no—
785C2×D4—444no—
786C2×D4—444no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
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—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—228no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
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×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—444no—
877C22×C4—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4C2×C4×D1112yes—
883C22×C4C2×C4×D1112yes—
884C22×C4#433912yes—
885C22×C4#433912yes—
886C22×C4#433912yes—
887C22×C4#433912yes—
888C22×C4D4×D1112yes—
889C22×C4D4×D1112yes—
890C22×C4C2×C22⋊D1112yes—
891C22×C4C2×C22⋊D1112yes—
892C4⋊C4—444no—
893C4⋊C4—444no—
894C4⋊C4—444no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—228no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—444no—
902C22⋊C4—444no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C42—44no—
906C42—44no—
907C42—444no—
908C11#1418211yescharacteristic, complemented, Sylow
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—41no—
943C23—114no—
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—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—
977C23—441no—
978C23C4×C22⋊D1114yes—
979C23C22×C4×D1111yescharacteristic
980C23C2×#433911yescharacteristic
981C23C2×#433911yescharacteristic
982C23C2×#433911yescharacteristic
983C23C2×#433911yescharacteristic
984C23C2×#433911yescharacteristic
985C23C2×D4×D1111yescharacteristic
986C23C2×D4×D1111yescharacteristic
987C23#6703711yescharacteristic
988C23#6703711yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23#6704211yescharacteristic
992C23#6704311yescharacteristic
993C23C22×C22⋊D1111yescharacteristic
994D4—4416no—
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—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—416no—
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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—114no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
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—4416no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
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×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4#6693714yes—
1087C2×C4#6698214yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—224no—
1104C22—224no—
1105C22—224no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22C4×#433911yescharacteristic
1119C22C4×#433911yescharacteristic
1120C22#1062301011yescharacteristic
1121C22#1062301011yescharacteristic
1122C22C2×#6693711yescharacteristic
1123C22#1062302111yescharacteristic
1124C22#1062302111yescharacteristic
1125C22#1062302511yescharacteristic
1126C22#1062305911yescharacteristic
1127C22#1062306011yescharacteristic
1128C22#1062306111yescharacteristic
1129C22#1062306511yescharacteristic
1130C22#1062307111yescharacteristic
1131C22C4×D4×D1111yescharacteristic
1132C22C4×D4×D1111yescharacteristic
1133C22#1062307611yescharacteristic
1134C22#1062307711yescharacteristic
1135C22#1062307811yescharacteristic
1136C22#1062307911yescharacteristic
1137C22#1062308111yescharacteristic
1138C22#1062308111yescharacteristic
1139C22#1062308211yescharacteristic
1140C22#1062308311yescharacteristic
1141C22#1062308711yescharacteristic
1142C22#1062308711yescharacteristic
1143C22#1062308911yescharacteristic
1144C22#1062309111yescharacteristic
1145C22#1062309211yescharacteristic
1146C22C2×C4×C22⋊D1111yescharacteristic
1147C22C2×#6698211yescharacteristic
1148C22#1062332211yescharacteristic
1149C22D4×C22⋊D1111yescharacteristic
1150C22D4×C22⋊D1111yescharacteristic
1151C22#1062335511yescharacteristic
1152C22#1062336011yescharacteristic
1153C4—24no—
1154C4—24no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—224no—
1160C4—442no—
1161C4—442no—
1162C4—442no—
1163C4—442no—
1164C4—881no—
1165C4—881no—
1166C2—44no—
1167C2—444no—
1168C2C4×#6693711yescharacteristic
1169C2C4×#6698211yescharacteristic
1170C2#1307142411yescharacteristic
1171C2#1307159311yescharacteristic
1172C2#1307160911yescharacteristic
1173C2#1307163311yescharacteristic
1174C2#1307166711yescharacteristic
1175C2#1307207211yescharacteristic
1176C2#1307212411yescharacteristic
1177C2#1307215211yescharacteristic
1178C2#1307219311yescharacteristic
1179C2#1307270611yescharacteristic
1180C2#1307281711yescharacteristic
1181C2#1307374511yescharacteristic
1182C2#1307391411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14182
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
5. C2×#10622823C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. #13066877C2semidirect
8. #13066865C2semidirect
9. #13066860C2semidirect
10. #13066853C2semidirect
11. #13066849C2semidirect
12. #13066849C2semidirect
13. Dic11⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
54. #10622572C4semidirect
98. C2×C11×C22⋊C4C2×C4semidirect
114. C2×C22⋊Dic11C2×C4semidirect
127. C2×(C2×D11)⋊C4C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×Dic11⋊C4C2×C4semidirect
156. C11⋊#95C2×C4semidirect
157. C11⋊#95D4semidirect
324. C2×C4×C22⋊C4D11semidirect
705. C2×C22⋊C4C4×D11semidirect
908. C11#14182semidirect

Maximal subgroups

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

subgroupindex
C2×#106225722
C2×#106225532
C2×#106228262
C2×#106225692
C2×#106228232
C2×C4×(C2×D11)⋊C42
#130668772
#130668652
#130668602
#130668532
#130668492
Dic11⋊#952
(C2×D11)⋊#952
C2×C4×C11×C22⋊C42
#1418211