Finite Group Databasebeta

← C2×#13074504 #14920168

Subgroups — C2×#13074504 #14920168

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074504C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622283C211yesmaximal, characteristic, complemented
13C2×#10622557C211yesmaximal, characteristic, complemented
14C2×#10622826C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2218yescomplemented
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×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66937—28no—
47C2×#66937C2218yescomplemented
48C11×#386C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622836C2218yescomplemented
52#10622836C2218yescomplemented
53#10622826C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622574C2218yescomplemented
61#10622573C2218yescomplemented
62#10622572C2218yescomplemented
63#10622562C2218yescomplemented
64#10622557C2218yescomplemented
65#10622285C2218yescomplemented
66#10622283C2218yescomplemented
67#10622277C2218yescomplemented
68#10622271C2218yescomplemented
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×C11—24no—
78C23×C4×C11—42no—
79C23×C4×C11—42no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C22×D44—24no—
109C22×D44—42no—
110C22×D44—42no—
111C22×D44C2314yes—
112C22×C4×D11—42no—
113C22×C4×D11—42no—
114C22×C4×D11D418yescomplemented
115C22×C4×D11C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—42no—
118C2×C11×C22⋊C4—42no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—42no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C4×C22⋊D11—232no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—42no—
135C2×(C2×D11)⋊C4—42no—
136C2×(C2×D11)⋊C4—42no—
137C2×(C2×D11)⋊C4—42no—
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—42no—
146C2×C4⋊Dic11C2314yes—
147C2×Dic11⋊C4—24no—
148C2×Dic11⋊C4—24no—
149C2×Dic11⋊C4—42no—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11—24no—
154C2×C4×Dic11C2314yes—
155#66937—232no—
156C11×#95C2314yes—
157C11×#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2635—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×C11#4114yes—
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×D11C2×D414yes—
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—28no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—416no—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C2×C22⋊D11—232no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—416no—
240C2×C22⋊D11—416no—
241C2×C22⋊D11—416no—
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—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11C2×D414yes—
259C22×Dic11#4114yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C2×D44—28no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—416no—
270C2×C4×D11—416no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11C2×D4116yescomplemented
274C11×C22⋊C4—28no—
275C11×C22⋊C4—44no—
276C11×C22⋊C4—44no—
277C22⋊Dic11—28no—
278C22⋊Dic11—28no—
279C22⋊Dic11—44no—
280C22⋊Dic11—44no—
281(C2×D11)⋊C4—28no—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—28no—
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—
292C4×Dic11—28no—
293C22×#121—111no—
294C22×C4×D4—111no—
295#2635—1116no—
296C2×#400—111no—
297C2×#399—111no—
298C2×#394—111no—
299C2×#394—111no—
300C2×#394—111no—
301C2×#392—111no—
302C2×#392—111no—
303C2×#392—111no—
304C2×#388—111no—
305C2×#388—111no—
306C2×#386—111no—
307C2×#386D1111yescharacteristic, complemented
308C2×#381—111no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—28no—
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—22no—
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×C11—44no—
336C23×C11C22×D412yes—
337C23×C11C2×#4114yes—
338C23×C11C2×#4112yes—
339C23×C11C2×#4112yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11C2511yescharacteristic
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
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—22no—
359C22×D11—22no—
360C22×D11—22no—
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—
372C22×D11C22×D414yes—
373D4×C11—416no—
374C2×C4×C11—28no—
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—416no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11C22×D414yes—
395C22⋊D11—232no—
396C22⋊D11—416no—
397C22⋊D11—416no—
398C22⋊D11—416no—
399C2×Dic11—28no—
400C2×Dic11—28no—
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—22no—
416C2×Dic11—22no—
417C2×Dic11—44no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11C22×D414yes—
422C2×Dic11C2×#4114yes—
423D44—416no—
424C4×D11—416no—
425C23×D4—111no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—111no—
429C23×D4—111no—
430C23×D4C2×D1111yescharacteristic
431C24×C4—111no—
432C24×C4C2×D1111yescharacteristic
433C2×#121—118no—
434C2×#121—228no—
435C2×C4×D4—118no—
436C2×C4×D4—228no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
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×C42—111no—
456#400—118no—
457#399—118no—
458#394—118no—
459#394—118no—
460#394—118no—
461#392—118no—
462#392—118no—
463#392—118no—
464#388—118no—
465#388—118no—
466#386—118no—
467#386C2×D1118yescomplemented
468#381—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95C2×D1111yescharacteristic
476C2×#95C2×D1111yescharacteristic
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—24no—
480C22×C11—416no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—88no—
493C22×C11#52514yes—
494C22×C11#53414yes—
495C22×C11#53514yes—
496C22×C11#53814yes—
497C22×C11#53814yes—
498C22×C11#54014yes—
499C22×C11#54014yes—
500C22×C11C23×D411yescharacteristic
501C22×C11C22×#4111yescharacteristic
502C22×C11C22×#4111yescharacteristic
503C22×C11C2×H(5,𝔽2)11yescharacteristic
504C22×C11C2×H(5,𝔽2)11yescharacteristic
505C22×C11C2×H(5,𝔽2)11yescharacteristic
506C22×C11C2×H(5,𝔽2)11yescharacteristic
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—416no—
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—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—88no—
523C4×C11—24no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527C4×C11—42no—
528Dic11—24no—
529Dic11—24no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534C25—111no—
535C25—111no—
536C25C22×D1111yescharacteristic
537C25C22×D1111yescharacteristic
538C22×D4—24no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—114no—
542C22×D4—114no—
543C22×D4—114no—
544C22×D4—114no—
545C22×D4—114no—
546C22×D4—224no—
547C22×D4—224no—
548C22×D4—224no—
549C22×D4—224no—
550C22×D4—224no—
551C22×D4—224no—
552C22×D4—224no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4—442no—
557C22×D4—442no—
558C22×D4—442no—
559C22×D4—442no—
560C22×D4—442no—
561C22×D4C22×D1114yes—
562C23×C4—24no—
563C23×C4—42no—
564C23×C4—42no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—118no—
568C23×C4—114no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—442no—
574C23×C4—442no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1114yes—
581#121—2232no—
582C4×D4—2232no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—442no—
590C2×C4⋊C4—442no—
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—224no—
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⋊C4C22×D1114yes—
617C2×C22⋊C4C22×D1114yes—
618C2×C22⋊C4C22×D1114yes—
619C2×C42—114no—
620C2×C42—224no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95C22×D1114yes—
628#95C22×D1114yes—
629C2×C11—44no—
630C2×C11—82no—
631C2×C11#263518yescomplemented
632C2×C11C2×#52511yescharacteristic
633C2×C11C2×#53411yescharacteristic
634C2×C11C2×#53511yescharacteristic
635C2×C11C2×#53811yescharacteristic
636C2×C11C2×#53811yescharacteristic
637C2×C11C2×#54011yescharacteristic
638C2×C11C2×#54011yescharacteristic
639D11—44no—
640D11—82no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—114no—
655C24—112no—
656C24—112no—
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—
670C24#433914yes—
671C24C23×D1112yes—
672C24C23×D1112yes—
673C24C23×D1111yescharacteristic
674C2×D4—28no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—416no—
678C2×D4—228no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—228no—
682C2×D4—2232no—
683C2×D4—228no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—4416no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4—4416no—
696C2×D4—4416no—
697C2×D4—4416no—
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—28no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—416no—
716C22×C4—114no—
717C22×C4—114no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—1116no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
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—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—4416no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4D4×D1114yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—228no—
751C4⋊C4—228no—
752C4⋊C4—444no—
753C4⋊C4—444no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—228no—
758C22⋊C4—228no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C22⋊C4—228no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C22⋊C4—444no—
768C42—228no—
769C11C2×#263511yescharacteristic, complemented, Sylow
770C23—28no—
771C23—28no—
772C23—28no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—114no—
798C23—228no—
799C23—228no—
800C23—228no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—444no—
815C23—444no—
816C23—444no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23—444no—
823C23—444no—
824C23—444no—
825C23C2×#433914yes—
826C23C2×#433912yes—
827C23C2×D4×D1112yes—
828C23#6703712yes—
829C23#6703712yes—
830C23#6703712yes—
831C23#41×D1112yes—
832C23#6704212yes—
833C23C24×D1111yescharacteristic
834D4—416no—
835D4—2232no—
836D4—4416no—
837D4—4416no—
838D4—4416no—
839D4—4416no—
840C2×C4—28no—
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—416no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—114no—
861C2×C4—114no—
862C2×C4—228no—
863C2×C4—228no—
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—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—4416no—
881C2×C4—444no—
882C2×C4—444no—
883C2×C4—444no—
884C2×C4—444no—
885C2×C4C2×D4×D1114yes—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—42no—
890C22—42no—
891C22—416no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—88no—
902C22—224no—
903C22—224no—
904C22—224no—
905C22—4416no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—888no—
918C22#1062302514yes—
919C22#1062307814yes—
920C22#1062309114yes—
921C22#1062312014yes—
922C22#1062313814yes—
923C22#1062314614yes—
924C22#1062319414yes—
925C22C22×#433911yescharacteristic
926C22C22×D4×D1111yescharacteristic
927C22C2×#6703711yescharacteristic
928C22C2×#6703711yescharacteristic
929C22C2×#6703711yescharacteristic
930C22C2×#41×D1111yescharacteristic
931C22C2×#6704211yescharacteristic
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—224no—
938C4—224no—
939C4—442no—
940C4—442no—
941C4—442no—
942C4—442no—
943C2—44no—
944C2—82no—
945C2—444no—
946C2—882no—
947C2#1307450418yesdirect product factor
948C2C2×#1062307811yescharacteristic
949C2C2×#1062312011yescharacteristic
950C2C2×#1062313811yescharacteristic
951C2C2×#1062309111yescharacteristic
952C2C2×#1062302511yescharacteristic
953C2C2×#1062314611yescharacteristic
954C2C2×#1062319411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66937C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074504C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622283C2semidirect
13. C2×#10622557C2semidirect
14. C2×#10622826C2semidirect
15. C2×#10622277C2semidirect
16. C2×C11×#386C2semidirect
33. C2×C4×C22⋊D11C22semidirect
47. C2×#66937C22semidirect
48. C11×#386C22semidirect
51. #10622836C22semidirect
52. #10622836C22semidirect
53. #10622826C22semidirect
60. #10622574C22semidirect
61. #10622573C22semidirect
62. #10622572C22semidirect
63. #10622562C22semidirect
64. #10622557C22semidirect
65. #10622285C22semidirect
66. #10622283C22semidirect
67. #10622277C22semidirect
68. #10622271C22semidirect
114. C22×C4×D11D4semidirect
273. C2×C4×D11C2×D4semidirect
307. C2×#386D11semidirect
467. #386C2×D11semidirect
631. C2×C11#2635semidirect
769. C11C2×#2635semidirect
947. C2#13074504direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4×C22⋊D112
#130745042
C2×#106222712
C2×#106225622
C2×#106222852
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106222832
C2×#106225572
C2×#106228262
C2×#106222772
C2×C11×#3862
C2×#263511