Finite Group Databasebeta

← #14679247

Subgroups — #14679247

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622574C211yesmaximal, characteristic
3C2×#10622541C211yesmaximal, characteristic, complemented
4C2×#10622553C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic, complemented
6C2×#10622823C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic, complemented
11#13066851C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, 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
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C4×C11×C22⋊C4—24no—
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43#10622823—24no—
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
56#10622574C418yescomplemented
57#10622553—24no—
58#10622541—24no—
59#10622281—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11D414yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11C2×C414yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4C2×C414yescomplemented
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—41no—
107C2×C42×C11—41no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11C2×C414yescomplemented
117C4×C22⋊D11—232no—
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—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4C2×C414yescomplemented
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×(C2×D11)⋊C4D414yes—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—41no—
138C2×C4⋊Dic11C2×C414yescomplemented
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4D414yes—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C11×#95—22no—
152C11×#95D414yescomplemented
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—41no—
164C11⋊#95C2×C414yescomplemented
165#14185—111nomaximal, Sylow
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×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11#4112yes—
181C24×C11C2411yescharacteristic
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×D11C22×C412yes—
195C23×D11C2×D412yes—
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—28no—
228C22×C4×C11—28no—
229C22×C4×C11—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11C22×C412yes—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11#4112yes—
244C22×C4×C11#4112yes—
245C22×C4×C11#4112yes—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
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×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11C22×C412yes—
296C22×Dic11C22×C412yes—
297C22×Dic11C22×C412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11#4112yes—
302C2×C4×D11—28no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C11×C22⋊C4—28no—
310C11×C22⋊C4—28no—
311C42×C11—44no—
312C42×C11—44no—
313C22⋊Dic11—28no—
314C22⋊Dic11—28no—
315C22⋊Dic11—44no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—28no—
319(C2×D11)⋊C4—44no—
320(C2×D11)⋊C4—44no—
321C4⋊Dic11—28no—
322C4⋊Dic11—44no—
323Dic11⋊C4—28no—
324Dic11⋊C4—44no—
325Dic11⋊C4—44no—
326C4×Dic11—28no—
327C22×C4×D4—111no—
328C2×#394—111no—
329C2×#389—111no—
330C2×#388—111no—
331C2×#385—111no—
332C2×#385—111no—
333C2×C4×C22⋊C4D1111yescharacteristic, complemented
334#1440—111no—
335#1439—111no—
336#1438—111no—
337#1437—111no—
338#1436—111no—
339#1436—111no—
340#1436—111no—
341C22⋊#95—111no—
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—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
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×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11C4×D414yes—
377C23×C11C23×C411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C23×C11C22×D411yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C112−1+411yescharacteristic
391C23×C112−1+411yescharacteristic
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—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
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×D11—41no—
425C22×D11—41no—
426C22×D11C4×D414yes—
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—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—22no—
453C2×C4×C11—22no—
454C2×C4×C11—416no—
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×C11C4×D414yescomplemented
468C2×C4×C11#12014yes—
469C2×C4×C11#12114yes—
470C22⋊D11—232no—
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—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
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×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×Dic11C4×D414yes—
520C4×D11—416no—
521C23×D4—111no—
522C24×C4—111no—
523C24×C4C2×D1111yescharacteristic
524C2×C4×D4—224no—
525C2×C4×D4—224no—
526C2×C4×D4—224no—
527C22×C4⋊C4—111no—
528C22×C4⋊C4—111no—
529C22×C4⋊C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4C2×D1111yescharacteristic
541C22×C22⋊C4C2×D1111yescharacteristic
542C22×C42—111no—
543C22×C42C2×D1111yescharacteristic
544C22×C42C2×D1111yescharacteristic
545#394—118no—
546#389—224no—
547#388—224no—
548#385—224no—
549#385—224no—
550C4×C22⋊C4—24no—
551C2×#95—111no—
552C2×#95—111no—
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×#95C2×D1111yescharacteristic
564C2×#95C2×D1111yescharacteristic
565C22×C11—24no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11C2×C4×D411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11C2×C4×D411yescharacteristic
583C22×C11C2×C4×D411yescharacteristic
584C22×C11C4×#4111yescharacteristic
585C22×C11#52011yescharacteristic
586C22×C11#52011yescharacteristic
587C22×C11C2×#12011yescharacteristic
588C22×C11C2×#12111yescharacteristic
589C22×C11#52511yescharacteristic
590C22×C11#52511yescharacteristic
591C22×C11#52511yescharacteristic
592C22×C11#52511yescharacteristic
593C22×C11#52911yescharacteristic
594C22×C11#53211yescharacteristic
595C22×C11#53411yescharacteristic
596C22×C11#53611yescharacteristic
597C22×C11#53911yescharacteristic
598C22×C11#53911yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11#54711yescharacteristic
605C22×C11#54711yescharacteristic
606C22×C11#54811yescharacteristic
607C22×C11#54811yescharacteristic
608C22×C11#54811yescharacteristic
609C22×C11#55111yescharacteristic
610C22×C11#55211yescharacteristic
611C22×C11#55311yescharacteristic
612C22×C11#55311yescharacteristic
613C22×C11#55611yescharacteristic
614C22×C11#55911yescharacteristic
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C4×C11—24no—
631C4×C11—24no—
632C4×C11—24no—
633C4×C11—42no—
634C4×C11—42no—
635C4×C11—42no—
636Dic11—24no—
637Dic11—42no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641Dic11—81no—
642Dic11—81no—
643C25—111no—
644C25C22×D1111yescharacteristic
645C22×D4—114no—
646C22×D4—222no—
647C22×D4—222no—
648C22×D4—222no—
649C22×D4—222no—
650C22×D4—222no—
651C22×D4—222no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—111no—
665C23×C4—222no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—441no—
671C23×C4—441no—
672C23×C4D4414yes—
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678C23×C4C22×D1111yescharacteristic
679C4×D4—2232no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—222no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—222no—
687C2×C4⋊C4—222no—
688C2×C4⋊C4—222no—
689C2×C4⋊C4—222no—
690C2×C4⋊C4—222no—
691C2×C4⋊C4—222no—
692C2×C4⋊C4—222no—
693C2×C4⋊C4—222no—
694C2×C4⋊C4—441no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
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—441no—
721C2×C22⋊C4—441no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4C4×D1114yescomplemented
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42—222no—
732C2×C42—222no—
733C2×C42—222no—
734#95—22no—
735#95—114no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—441no—
747#95C22⋊D1114yescomplemented
748C2×C11—44no—
749C2×C11C4×#12011yescharacteristic
750C2×C11C4×#12111yescharacteristic
751C2×C11#232211yescharacteristic
752C2×C11#235911yescharacteristic
753C2×C11#236111yescharacteristic
754C2×C11#236111yescharacteristic
755C2×C11#236711yescharacteristic
756C2×C11#241011yescharacteristic
757C2×C11#241511yescharacteristic
758C2×C11#243211yescharacteristic
759C2×C11#245511yescharacteristic
760C2×C11#246011yescharacteristic
761C2×C11#246311yescharacteristic
762C2×C11#246611yescharacteristic
763C2×C11#260211yescharacteristic
764D11—44no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—112no—
778C24—112no—
779C24—112no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24C2×C4×D1112yes—
793C24C2×D4412yes—
794C24#433912yes—
795C24C23×D1111yescharacteristic
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—228no—
802C2×D4—228no—
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—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—28no—
834C22×C4—28no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—228no—
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—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—444no—
891C22×C4—444no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4—444no—
895C22×C4—444no—
896C22×C4C2×C4×D1112yes—
897C22×C4C2×C4×D1112yes—
898C22×C4C2×D4412yes—
899C22×C4C2×D4412yes—
900C22×C4#433912yes—
901C22×C4#433912yes—
902C22×C4#433912yes—
903C22×C4D4×D1112yes—
904C22×C4D4×D1112yes—
905C22×C4C2×C22⋊D1112yes—
906C22×C4C2×C22⋊D1112yes—
907C22×C4C2×C22⋊D1112yes—
908C4⋊C4—228no—
909C4⋊C4—228no—
910C4⋊C4—444no—
911C4⋊C4—444no—
912C4⋊C4—444no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—228no—
916C22⋊C4—228no—
917C22⋊C4—228no—
918C22⋊C4—228no—
919C22⋊C4—228no—
920C22⋊C4—444no—
921C22⋊C4—444no—
922C22⋊C4—444no—
923C42—44no—
924C42—44no—
925C42—228no—
926C11#1418511yescharacteristic, complemented, Sylow
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—114no—
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—222no—
979C23—222no—
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—
996C23C4×D4414yes—
997C23C22×C4×D1111yescharacteristic
998C23C22×D4411yescharacteristic
999C23C2×#433911yescharacteristic
1000C23C2×#433911yescharacteristic
1001C23C2×#433911yescharacteristic
1002C23C2×#433911yescharacteristic
1003C23C2×D4×D1111yescharacteristic
1004C23C2×D4×D1111yescharacteristic
1005C23#6703711yescharacteristic
1006C23#6703711yescharacteristic
1007C23#41×D1111yescharacteristic
1008C23#41×D1111yescharacteristic
1009C23#6704311yescharacteristic
1010C23#6704311yescharacteristic
1011C23C22×C22⋊D1111yescharacteristic
1012D4—2232no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
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—416no—
1041C2×C4—41no—
1042C2×C4—41no—
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—114no—
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—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—4416no—
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—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4#6693514yes—
1104C2×C4C4×C22⋊D1114yescomplemented
1105C2×C4#6698314yes—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—224no—
1122C22—224no—
1123C22—224no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22—442no—
1133C22—442no—
1134C22—442no—
1135C22—442no—
1136C22C2×C4×D4411yescharacteristic
1137C22C4×#433911yescharacteristic
1138C22#1062300811yescharacteristic
1139C22#1062301011yescharacteristic
1140C22C2×#6693511yescharacteristic
1141C22#1062302111yescharacteristic
1142C22#1062302111yescharacteristic
1143C22#1062302411yescharacteristic
1144C22#1062305511yescharacteristic
1145C22#1062305711yescharacteristic
1146C22#1062306011yescharacteristic
1147C22#1062306411yescharacteristic
1148C22#1062307111yescharacteristic
1149C22C4×D4×D1111yescharacteristic
1150C22C4×D4×D1111yescharacteristic
1151C22#1062307711yescharacteristic
1152C22#1062307711yescharacteristic
1153C22#1062307811yescharacteristic
1154C22#1062307811yescharacteristic
1155C22#1062308211yescharacteristic
1156C22#1062308211yescharacteristic
1157C22#1062308311yescharacteristic
1158C22#1062308311yescharacteristic
1159C22#1062308711yescharacteristic
1160C22#1062308911yescharacteristic
1161C22#1062309011yescharacteristic
1162C22#1062309511yescharacteristic
1163C22#1062309511yescharacteristic
1164C22C2×C4×C22⋊D1111yescharacteristic
1165C22C2×#6698311yescharacteristic
1166C22#1062332211yescharacteristic
1167C22D4×C22⋊D1111yescharacteristic
1168C22D4×C22⋊D1111yescharacteristic
1169C22#1062335511yescharacteristic
1170C22#1062336211yescharacteristic
1171C4—24no—
1172C4—24no—
1173C4—24no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—224no—
1178C4—442no—
1179C4—442no—
1180C4—442no—
1181C4—442no—
1182C4—881no—
1183C4—881no—
1184C2—44no—
1185C2—444no—
1186C2C4×#6693511yescharacteristic
1187C2C4×#6698311yescharacteristic
1188C2#1307128711yescharacteristic
1189C2#1307160911yescharacteristic
1190C2#1307162811yescharacteristic
1191C2#1307163311yescharacteristic
1192C2#1307168811yescharacteristic
1193C2#1307198411yescharacteristic
1194C2#1307203911yescharacteristic
1195C2#1307224411yescharacteristic
1196C2#1307249311yescharacteristic
1197C2#1307256811yescharacteristic
1198C2#1307260711yescharacteristic
1199C2#1307265211yescharacteristic
1200C2#1307422211yescharacteristic
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#14185
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#10622541C2semidirect
4. C2×#10622553C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622823C2semidirect
7. #13066863C2semidirect
8. #13066861C2semidirect
10. #13066854C2semidirect
11. #13066851C2semidirect
12. #13066850C2semidirect
13. #13066849C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
56. #10622574C4semidirect
101. C2×C11×C22⋊C4C2×C4semidirect
116. C2×C22⋊Dic11C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×C4⋊Dic11C2×C4semidirect
152. C11×#95D4semidirect
164. C11⋊#95C2×C4semidirect
333. C2×C4×C22⋊C4D11semidirect
467. C2×C4×C11C4×D4semidirect
724. C2×C22⋊C4C4×D11semidirect
747. #95C22⋊D11semidirect
926. C11#14185semidirect
1104. C2×C4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225742
C2×#106225412
C2×#106225532
C2×#106222812
C2×#106228232
#130668632
#130668612
#130668552
#130668542
#130668512
#130668502
#130668492
(C2×D11)⋊#952
C2×C4×C11×C22⋊C42
#1418511