Finite Group Databasebeta

← C2×#13076625 #14959923

Subgroups — C2×#13076625 #14959923

Order 2816.

3322 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3#13076625C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622604C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622284C211yesmaximal, characteristic, complemented
13C2×#10622573C211yesmaximal, characteristic, complemented
14C2×#10622573C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×C4×D11C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C2×#66947—28no—
47C2×#66947C2218yescomplemented
48C2×#66937—28no—
49C2×#66937C2218yescomplemented
50C11×#396C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622607C2218yescomplemented
58#10622605C2218yescomplemented
59#10622604C2218yescomplemented
60#10622604C2218yescomplemented
61#10622600C2218yescomplemented
62#10622574C2218yescomplemented
63#10622573C2218yescomplemented
64#10622573C2218yescomplemented
65#10622572C2218yescomplemented
66#10622572C2218yescomplemented
67#10622284C2218yescomplemented
68#10622271C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—42no—
99C22×D44—42no—
100C22×D44—42no—
101C22×D44—42no—
102C22×D44—42no—
103C22×D44—42no—
104C22×D44—42no—
105C22×D44C2314yes—
106C22×D44C2314yes—
107C22×D44C2314yes—
108C22×C4×D11—42no—
109C22×C4×D11—42no—
110C22×C4×D11D418yescomplemented
111C22×C4×D11C2314yes—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4—42no—
114C2×C11×C4⋊C4—42no—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—42no—
120C2×C11×C22⋊C4—42no—
121C2×C11×C22⋊C4C2314yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11C2314yes—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×C4⋊Dic11—42no—
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—24no—
152C2×Dic11⋊C4—42no—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156#66947—232no—
157#66937—232no—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2813—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11C2×D414yes—
195C23×D11C2412yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—416no—
232C2×C22⋊D11—416no—
233C2×C22⋊D11—416no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11C2×D414yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C2×D44—28no—
255C2×D44—28no—
256C2×D44—44no—
257C2×D44—44no—
258C2×D44—44no—
259C2×D44—44no—
260C2×D44—44no—
261C2×D44—44no—
262C2×D44—44no—
263C2×D44—416no—
264C2×D44—416no—
265C2×D44—416no—
266C2×C4×D11—416no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11C2×D4116yescomplemented
270C11×C4⋊C4—28no—
271C11×C4⋊C4—44no—
272C11×C4⋊C4—44no—
273C11×C22⋊C4—28no—
274C11×C22⋊C4—44no—
275C11×C22⋊C4—44no—
276C22⋊Dic11—44no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—28no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4—44no—
284(C2×D11)⋊C4—44no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288C4⋊Dic11—44no—
289Dic11⋊C4—28no—
290Dic11⋊C4—28no—
291Dic11⋊C4—44no—
292C22×#123—111no—
293C22×#121—111no—
294#2813—1116no—
295C2×#400—111no—
296C2×#399—111no—
297C2×#396—111no—
298C2×#396D1111yescharacteristic, complemented
299C2×#394—111no—
300C2×#394—111no—
301C2×#394—111no—
302C2×#394—111no—
303C2×#394—111no—
304C2×#392—111no—
305C2×#392—111no—
306C2×#392—111no—
307C2×#380—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11C22×D412yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11H(5,𝔽2)12yes—
328C23×C112−1+412yes—
329C23×C11C2511yescharacteristic
330C22×D11—28no—
331C22×D11—28no—
332C22×D11—28no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11C22×D414yes—
372C2×C4×C11—28no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11—44no—
395C2×C4×C11C22×D414yes—
396C22⋊D11—416no—
397C22⋊D11—416no—
398C22⋊D11—416no—
399C2×Dic11—28no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—44no—
415C2×Dic11—44no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11C22×D414yes—
419D44—416no—
420D44—416no—
421D44—416no—
422C4×D11—416no—
423C23×D4—111no—
424C23×D4—111no—
425C23×D4—111no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—111no—
429C24×C4—111no—
430C2×#123—118no—
431C2×#123—228no—
432C2×#121—118no—
433C2×#121—228no—
434C22×C4⋊C4—111no—
435C22×C4⋊C4—111no—
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4C2×D1111yescharacteristic
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456#400—118no—
457#399—118no—
458#396—118no—
459#396C2×D1118yescomplemented
460#394—118no—
461#394—118no—
462#394—118no—
463#394—118no—
464#394—118no—
465#392—118no—
466#392—118no—
467#392—118no—
468#380—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95C2×D1111yescharacteristic
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—88no—
483C22×C11#53414yes—
484C22×C11#53514yes—
485C22×C11#53714yes—
486C22×C11#56014yes—
487C22×C11#56014yes—
488C22×C11#56214yes—
489C22×C11#56214yes—
490C22×C11C23×D411yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×H(5,𝔽2)11yescharacteristic
493C22×C11C2×H(5,𝔽2)11yescharacteristic
494C22×C11C2×H(5,𝔽2)11yescharacteristic
495C22×C11C2×H(5,𝔽2)11yescharacteristic
496C22×C11C2×2−1+411yescharacteristic
497C2×D11—24no—
498C2×D11—24no—
499C2×D11—24no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—416no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—88no—
520C2×D11—88no—
521C4×C11—24no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532C25—111no—
533C25—111no—
534C25—111no—
535C25C22×D1111yescharacteristic
536C22×D4—114no—
537C22×D4—114no—
538C22×D4—114no—
539C22×D4—114no—
540C22×D4—114no—
541C22×D4—114no—
542C22×D4—224no—
543C22×D4—224no—
544C22×D4—224no—
545C22×D4—224no—
546C22×D4—442no—
547C22×D4—442no—
548C22×D4—442no—
549C22×D4—442no—
550C22×D4—442no—
551C22×D4—442no—
552C22×D4—442no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4—442no—
557C22×D4—442no—
558C22×D4—442no—
559C22×D4—442no—
560C23×C4—111no—
561C23×C4—118no—
562C23×C4—114no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—442no—
568C23×C4—442no—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575#123—2232no—
576#121—2232no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—42no—
579C2×C4⋊C4—42no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—224no—
585C2×C4⋊C4—224no—
586C2×C4⋊C4—442no—
587C2×C4⋊C4—442no—
588C2×C4⋊C4C22×D1114yes—
589C2×C4⋊C4C22×D1114yes—
590C2×C4⋊C4C22×D1114yes—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—442no—
611C2×C22⋊C4—442no—
612C2×C22⋊C4—442no—
613C2×C22⋊C4—442no—
614C2×C22⋊C4—442no—
615C2×C22⋊C4—442no—
616C2×C22⋊C4—442no—
617C2×C22⋊C4—442no—
618C2×C22⋊C4C22×D1114yes—
619C2×C22⋊C4C22×D1114yes—
620C2×C22⋊C4C22×D1114yes—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95C22×D1114yes—
627C2×C11—82no—
628C2×C11#281318yescomplemented
629C2×C11C2×#53411yescharacteristic
630C2×C11C2×#53511yescharacteristic
631C2×C11C2×#53711yescharacteristic
632C2×C11C2×#56011yescharacteristic
633C2×C11C2×#56011yescharacteristic
634C2×C11C2×#56211yescharacteristic
635C2×C11C2×#56211yescharacteristic
636D11—44no—
637D11—82no—
638D11—82no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—114no—
647C24—112no—
648C24—112no—
649C24—112no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24—222no—
669C24—222no—
670C24C23×D1112yes—
671C24C23×D1111yescharacteristic
672C2×D4—228no—
673C2×D4—228no—
674C2×D4—228no—
675C2×D4—228no—
676C2×D4—444no—
677C2×D4—444no—
678C2×D4—444no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—444no—
682C2×D4—444no—
683C2×D4—4416no—
684C2×D4—4416no—
685C2×D4—4416no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—444no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—4416no—
694C2×D4—4416no—
695C2×D4—4416no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—114no—
714C22×C4—112no—
715C22×C4—1116no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—4416no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4D4×D1114yes—
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C4⋊C4—28no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—228no—
748C4⋊C4—228no—
749C4⋊C4—444no—
750C4⋊C4—444no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—228no—
755C22⋊C4—228no—
756C22⋊C4—228no—
757C22⋊C4—228no—
758C22⋊C4—444no—
759C22⋊C4—444no—
760C22⋊C4—444no—
761C22⋊C4—444no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C11C2×#281311yescharacteristic, complemented, Sylow
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—114no—
782C23—228no—
783C23—228no—
784C23—228no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—444no—
806C23—444no—
807C23—444no—
808C23—444no—
809C23—444no—
810C23—444no—
811C23—444no—
812C23—444no—
813C23—444no—
814C23—444no—
815C23—444no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23—444no—
823C23C2×D4×D1112yes—
824C23#6703712yes—
825C23#6703712yes—
826C23#6704012yes—
827C23#6704212yes—
828C23#6704212yes—
829C23#6704212yes—
830C23C24×D1111yescharacteristic
831D4—4416no—
832D4—4416no—
833D4—4416no—
834D4—4416no—
835D4—4416no—
836D4—4416no—
837C2×C4—28no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—114no—
861C2×C4—228no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—4416no—
877C2×C4—444no—
878C2×C4—444no—
879C2×C4—444no—
880C2×C4—444no—
881C2×C4C2×D4×D1114yes—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—88no—
890C22—224no—
891C22—224no—
892C22—224no—
893C22—442no—
894C22—442no—
895C22—442no—
896C22—442no—
897C22—4416no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—888no—
913C22—888no—
914C22#1062313614yes—
915C22#1062313814yes—
916C22#1062315114yes—
917C22#1062316014yes—
918C22#1062317814yes—
919C22#1062317814yes—
920C22#1062324214yes—
921C22C22×D4×D1111yescharacteristic
922C22C2×#6703711yescharacteristic
923C22C2×#6703711yescharacteristic
924C22C2×#6704011yescharacteristic
925C22C2×#6704211yescharacteristic
926C22C2×#6704211yescharacteristic
927C22C2×#6704211yescharacteristic
928C4—24no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—224no—
935C4—442no—
936C4—442no—
937C4—442no—
938C4—442no—
939C2—82no—
940C2—444no—
941C2—882no—
942C2—882no—
943C2#1307662518yesdirect product factor
944C2C2×#1062313611yescharacteristic
945C2C2×#1062313811yescharacteristic
946C2C2×#1062316011yescharacteristic
947C2C2×#1062315111yescharacteristic
948C2C2×#1062324211yescharacteristic
949C2C2×#1062317811yescharacteristic
950C2C2×#1062317811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
hypercenterC2×#396D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66937C2semidirect
3. #13076625C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622607C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622604C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622284C2semidirect
13. C2×#10622573C2semidirect
14. C2×#10622573C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#396C2semidirect
47. C2×#66947C22semidirect
49. C2×#66937C22semidirect
50. C11×#396C22semidirect
57. #10622607C22semidirect
58. #10622605C22semidirect
59. #10622604C22semidirect
60. #10622604C22semidirect
61. #10622600C22semidirect
62. #10622574C22semidirect
63. #10622573C22semidirect
64. #10622573C22semidirect
65. #10622572C22semidirect
66. #10622572C22semidirect
67. #10622284C22semidirect
68. #10622271C22semidirect
110. C22×C4×D11D4semidirect
269. C2×C4×D11C2×D4semidirect
298. C2×#396D11semidirect
459. #396C2×D11semidirect
628. C2×C11#2813semidirect
766. C11C2×#2813semidirect
943. C2#13076625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669372
#130766252
C2×#106222712
C2×#106226052
C2×#106226072
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222842
C2×#106225732
C2×#106226002
C2×C11×#3962
C2×#281311