Finite Group Databasebeta

← C2×#13076624 #14959921

Subgroups — C2×#13076624 #14959921

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×#66939C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3#13076624C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622605C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622572C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622573C211yesmaximal, characteristic, complemented
13C2×#10622573C211yesmaximal, characteristic, complemented
14C2×#10622836C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992—28no—
33C2×#66992C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C2×#66939—28no—
49C2×#66939C2218yescomplemented
50C11×#394C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52#10622836C2218yescomplemented
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622607C2218yescomplemented
59#10622605C2218yescomplemented
60#10622574C2218yescomplemented
61#10622573C2218yescomplemented
62#10622573C2218yescomplemented
63#10622572C2218yescomplemented
64#10622572C2218yescomplemented
65#10622561C2218yescomplemented
66#10622555C2218yescomplemented
67#10622285C2218yescomplemented
68#10622273C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11—42no—
99C23×Dic11—42no—
100C23×Dic11D418yescomplemented
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2314yes—
108C22×D44—42no—
109C22×D44—42no—
110C22×D44—42no—
111C22×D44C2314yes—
112C2×C11×C4⋊C4—42no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4—42no—
116C2×C11×C22⋊C4—42no—
117C2×C11×C22⋊C4—42no—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—42no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#66992—232no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
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×C4⋊Dic11—24no—
146C2×C4⋊Dic11—24no—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C2314yes—
149C2×Dic11⋊C4—24no—
150C2×Dic11⋊C4—42no—
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4—42no—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×Dic11⋊C4C2314yes—
157#66939—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×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11C2×D414yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
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×D11—22no—
195C23×D11—22no—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C2×D4×C11—28no—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—416no—
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×C11—22no—
216C22×C4×C11—22no—
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—28no—
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—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—416no—
235C2×C22⋊D11—416no—
236C2×C22⋊D11—416no—
237C2×C22⋊D11—416no—
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×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—416no—
255C22×Dic11—44no—
256C22×Dic11—44no—
257C22×Dic11C2×D414yes—
258C22×Dic11C2×D414yes—
259C22×Dic11C2×D4116yescomplemented
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—416no—
270C11×C4⋊C4—44no—
271C11×C22⋊C4—28no—
272C11×C22⋊C4—44no—
273C11×C22⋊C4—44no—
274C11×C22⋊C4—44no—
275C22⋊Dic11—28no—
276C22⋊Dic11—44no—
277C22⋊Dic11—44no—
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—
286C4⋊Dic11—28no—
287C4⋊Dic11—28no—
288Dic11⋊C4—28no—
289Dic11⋊C4—44no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292C22×#123—111no—
293C22×#121—111no—
294#2813—1116no—
295C2×#400—111no—
296C2×#399—111no—
297C2×#396—111no—
298C2×#396—111no—
299C2×#394—111no—
300C2×#394—111no—
301C2×#394—111no—
302C2×#394—111no—
303C2×#394D1111yescharacteristic, complemented
304C2×#392—111no—
305C2×#392—111no—
306C2×#392—111no—
307C2×#380—111no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11C22×D414yes—
336C23×C11C22×D412yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C11H(5,𝔽2)12yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C112−1+412yes—
343C23×C11C2511yescharacteristic
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—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
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×D11—44no—
372D4×C11—416no—
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—44no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C22⋊D11—416no—
394C22⋊D11—416no—
395C22⋊D11—416no—
396C22⋊D11—416no—
397C2×Dic11—28no—
398C2×Dic11—28no—
399C2×Dic11—22no—
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—22no—
415C2×Dic11—416no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11C22×D414yes—
421C2×Dic11C22×D414yes—
422D44—416no—
423C23×D4—111no—
424C23×D4—111no—
425C23×D4—111no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4C2×D1111yescharacteristic
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⋊C4—111no—
439C22×C4⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4C2×D1111yescharacteristic
456#400—118no—
457#399—118no—
458#396—118no—
459#396—118no—
460#394—118no—
461#394—118no—
462#394—118no—
463#394—118no—
464#394C2×D1118yescomplemented
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—24no—
476C22×C11—24no—
477C22×C11—24no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—416no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—88no—
491C22×C11#53414yes—
492C22×C11#53514yes—
493C22×C11#53714yes—
494C22×C11#56014yes—
495C22×C11#56014yes—
496C22×C11#56214yes—
497C22×C11#56214yes—
498C22×C11C23×D411yescharacteristic
499C22×C11C2×H(5,𝔽2)11yescharacteristic
500C22×C11C2×H(5,𝔽2)11yescharacteristic
501C22×C11C2×H(5,𝔽2)11yescharacteristic
502C22×C11C2×H(5,𝔽2)11yescharacteristic
503C22×C11C2×H(5,𝔽2)11yescharacteristic
504C22×C11C2×2−1+411yescharacteristic
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—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525C4×C11—42no—
526Dic11—24no—
527Dic11—24no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532C25—111no—
533C25—111no—
534C25C22×D1111yescharacteristic
535C25C22×D1111yescharacteristic
536C22×D4—24no—
537C22×D4—42no—
538C22×D4—42no—
539C22×D4—114no—
540C22×D4—114no—
541C22×D4—114no—
542C22×D4—114no—
543C22×D4—114no—
544C22×D4—224no—
545C22×D4—224no—
546C22×D4—224no—
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×D4C22×D1114yes—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—118no—
563C23×C4—114no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—442no—
569C23×C4—442no—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573C23×C4C22×D1111yescharacteristic
574C23×C4C22×D1111yescharacteristic
575#123—2232no—
576#121—2232no—
577C2×C4⋊C4—42no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
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—224no—
587C2×C4⋊C4—442no—
588C2×C4⋊C4—442no—
589C2×C4⋊C4—442no—
590C2×C4⋊C4C22×D1114yes—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
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⋊C4C22×D1114yes—
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—44no—
628C2×C11—82no—
629C2×C11#281318yescomplemented
630C2×C11C2×#53411yescharacteristic
631C2×C11C2×#53511yescharacteristic
632C2×C11C2×#53711yescharacteristic
633C2×C11C2×#56011yescharacteristic
634C2×C11C2×#56011yescharacteristic
635C2×C11C2×#56211yescharacteristic
636C2×C11C2×#56211yescharacteristic
637D11—82no—
638D11—82no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—112no—
653C24—112no—
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—
668C24D4×D1114yes—
669C24C23×D1112yes—
670C24C23×D1112yes—
671C24C23×D1111yescharacteristic
672C2×D4—28no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—416no—
676C2×D4—228no—
677C2×D4—228no—
678C2×D4—228no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—444no—
682C2×D4—4416no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—444no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—4416no—
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—114no—
712C22×C4—114no—
713C22×C4—112no—
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—222no—
735C22×C4—222no—
736C22×C4—4416no—
737C22×C4—444no—
738C22×C4—444no—
739C22×C4C23×D1112yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C4⋊C4—44no—
745C4⋊C4—228no—
746C4⋊C4—228no—
747C4⋊C4—228no—
748C4⋊C4—444no—
749C4⋊C4—444no—
750C4⋊C4—444no—
751C22⋊C4—28no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—228no—
756C22⋊C4—228no—
757C22⋊C4—228no—
758C22⋊C4—228no—
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—28no—
768C23—28no—
769C23—28no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
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—
822C23C2×D4×D1114yes—
823C23C2×D4×D1112yes—
824C23#6703712yes—
825C23#6703712yes—
826C23#6703712yes—
827C23#6704212yes—
828C23#6704212yes—
829C23#6704312yes—
830C23C24×D1111yescharacteristic
831D4—416no—
832D4—4416no—
833D4—4416no—
834D4—4416no—
835D4—4416no—
836D4—4416no—
837C2×C4—22no—
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—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—114no—
858C2×C4—114no—
859C2×C4—228no—
860C2×C4—228no—
861C2×C4—222no—
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—222no—
877C2×C4—4416no—
878C2×C4—444no—
879C2×C4—444no—
880C2×C4—444no—
881C2×C4—444no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—416no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—88no—
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#1062312314yes—
915C22#1062312814yes—
916C22#1062315114yes—
917C22#1062315114yes—
918C22#1062318414yes—
919C22#1062319814yes—
920C22#1062321514yes—
921C22C22×D4×D1111yescharacteristic
922C22C2×#6703711yescharacteristic
923C22C2×#6703711yescharacteristic
924C22C2×#6703711yescharacteristic
925C22C2×#6704211yescharacteristic
926C22C2×#6704211yescharacteristic
927C22C2×#6704311yescharacteristic
928C4—42no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—224no—
934C4—224no—
935C4—442no—
936C4—442no—
937C4—442no—
938C4—442no—
939C2—44no—
940C2—82no—
941C2—882no—
942C2—882no—
943C2#1307662418yesdirect product factor
944C2C2×#1062318411yescharacteristic
945C2C2×#1062312311yescharacteristic
946C2C2×#1062312811yescharacteristic
947C2C2×#1062315111yescharacteristic
948C2C2×#1062315111yescharacteristic
949C2C2×#1062321511yescharacteristic
950C2C2×#1062319811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66939C2semidirect
2. C22×#66992C2semidirect
3. #13076624C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622605C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622285C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622572C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622573C2semidirect
13. C2×#10622573C2semidirect
14. C2×#10622836C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#394C2semidirect
33. C2×#66992C22semidirect
49. C2×#66939C22semidirect
50. C11×#394C22semidirect
52. #10622836C22semidirect
58. #10622607C22semidirect
59. #10622605C22semidirect
60. #10622574C22semidirect
61. #10622573C22semidirect
62. #10622573C22semidirect
63. #10622572C22semidirect
64. #10622572C22semidirect
65. #10622561C22semidirect
66. #10622555C22semidirect
67. #10622285C22semidirect
68. #10622273C22semidirect
100. C23×Dic11D4semidirect
259. C22×Dic11C2×D4semidirect
303. C2×#394D11semidirect
464. #394C2×D11semidirect
629. C2×C11#2813semidirect
766. C11C2×#2813semidirect
943. C2#13076624direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669392
C22×#669922
#130766242
C2×#106222732
C2×#106226052
C2×#106225612
C2×#106226072
C2×#106222852
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225552
C2×C11×#3942
C2×#281311