Finite Group Databasebeta

← C2×#13072627 #14921618

Subgroups — C2×#13072627 #14921618

Order 2816.

4218 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13072627C2116yesmaximal, direct product factor
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622603C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121—28no—
27C2×C11×#121C2218yescomplemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C2×#66992—28no—
40C2×#66992C2218yescomplemented
41C2×C4×C22⋊D11—28no—
42C2×C4×C22⋊D11C2218yescomplemented
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54#10622836C2218yescomplemented
55#10622836C2218yescomplemented
56#10622835C2218yescomplemented
57#10622834C2218yescomplemented
58#10622833C2218yescomplemented
59#10622823C2218yescomplemented
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622603C2218yescomplemented
67#10622596C2218yescomplemented
68#10622569C2218yescomplemented
69#10622558C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11—42no—
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C22×D4×C11C2314yes—
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—42no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2314yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11—42no—
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2314yes—
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—42no—
121C22×C4×D11C2314yes—
122C11×#121—232no—
123C2×C11×C4⋊C4—24no—
124C2×C11×C4⋊C4C2314yes—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4D418yescomplemented
127C2×C11×C22⋊C4C2314yes—
128C2×C11×C22⋊C4C2314yes—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—42no—
136C2×C22⋊Dic11—42no—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145#66992—232no—
146C4×C22⋊D11—232no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—42no—
149C2×(C2×D11)⋊C4D418yescomplemented
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11C2314yes—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—42no—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66936—232no—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2464—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11C2×D414yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11C2×D414yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
210C2×D4×C11—28no—
211C2×D4×C11—28no—
212C2×D4×C11—44no—
213C2×D4×C11—44no—
214C2×D4×C11—44no—
215C2×D4×C11—416no—
216C2×D4×C11—416no—
217C2×D4×C11—416no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—28no—
228C22×C4×C11—28no—
229C22×C4×C11—44no—
230C22×C4×C11—416no—
231C22×C4×C11C2×D414yes—
232C22×C4×C11C2×D414yes—
233C22×C4×C11C2×D414yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C2×C22⋊D11—232no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11—416no—
250C22×Dic11—28no—
251C22×Dic11—28no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—44no—
271C22×Dic11—416no—
272C22×Dic11C2×D414yes—
273C22×Dic11#4114yes—
274C22×Dic11#4114yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—44no—
285C2×C4×D11—416no—
286C11×C4⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4C2×D4116yescomplemented
289C22⋊Dic11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—44no—
296C22⋊Dic11—44no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4C2×D4116yescomplemented
300C4⋊Dic11—28no—
301Dic11⋊C4—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—28no—
304C4×Dic11—28no—
305C4×Dic11—44no—
306C22×#123—111no—
307C22×#121—111no—
308C22×#121D1111yescharacteristic, complemented
309C22×C4×D4—111no—
310#2464—1116no—
311C2×#398—111no—
312C2×#394—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#385—111no—
321C2×C4×C22⋊C4—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
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—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11—44no—
351C23×C11—44no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—44no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11C22×D412yes—
363C23×C11C22×D414yes—
364C23×C11C22×D412yes—
365C23×C11C2×#4114yes—
366C23×C11C2×#4112yes—
367C23×C11C2×#4112yes—
368C23×C11C2×#4112yes—
369C23×C11H(5,𝔽2)12yes—
370C23×C11H(5,𝔽2)12yes—
371C23×C11C2511yescharacteristic
372C22×D11—28no—
373C22×D11—28no—
374C22×D11—28no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11—44no—
385C22×D11C22×D414yes—
386D4×C11—416no—
387D4×C11—416no—
388D4×C11—416no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
391C2×C4×C11—28no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—416no—
402C2×C4×C11—44no—
403C2×C4×C11C22×D414yes—
404C2×C4×C11C22×D414yes—
405C2×C4×C11C22×D414yes—
406C22⋊D11—232no—
407C22⋊D11—416no—
408C22⋊D11—416no—
409C2×Dic11—28no—
410C2×Dic11—28no—
411C2×Dic11—28no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—416no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11—44no—
434C2×Dic11—44no—
435C2×Dic11C22×D414yes—
436C2×Dic11C2×#4114yes—
437C2×Dic11C2×#4114yes—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4C2×D1111yescharacteristic
443C23×D4C2×D1111yescharacteristic
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4C2×D1111yescharacteristic
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—28no—
451C2×#121—118no—
452C2×#121—228no—
453C2×#121C2×D1118yescomplemented
454C2×C4×D4—118no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4C2×D1111yescharacteristic
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—111no—
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42—111no—
476#398—118no—
477#394—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#386—118no—
484#386—118no—
485#385—118no—
486C4×C22⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—416no—
508C22×C11—416no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—88no—
517C22×C11#52514yes—
518C22×C11#53214yes—
519C22×C11#54014yes—
520C22×C11D4214yes—
521C22×C11#54614yes—
522C22×C11#54614yes—
523C22×C11#55314yes—
524C22×C11C23×D411yescharacteristic
525C22×C11C23×D411yescharacteristic
526C22×C11C22×#4111yescharacteristic
527C22×C11C22×#4111yescharacteristic
528C22×C11C22×#4111yescharacteristic
529C22×C11C2×H(5,𝔽2)11yescharacteristic
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25C22×D1111yescharacteristic
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4C22×D1114yes—
576C22×D4C22×D1114yes—
577C22×D4C22×D1114yes—
578C23×C4—24no—
579C23×C4—24no—
580C23×C4—42no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—114no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—224no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1114yes—
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—232no—
603#121—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—114no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—224no—
612C2×C4⋊C4—224no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4C22×D1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—118no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—224no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—442no—
636C2×C22⋊C4—442no—
637C2×C22⋊C4—442no—
638C2×C22⋊C4C22⋊D1118yescomplemented
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—442no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651C2×C11—44no—
652C2×C11—44no—
653C2×C11—82no—
654C2×C11#246418yescomplemented
655C2×C11C2×#52511yescharacteristic
656C2×C11C2×#53211yescharacteristic
657C2×C11C2×#54011yescharacteristic
658C2×C11C2×D4211yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#54611yescharacteristic
661C2×C11C2×#55311yescharacteristic
662D11—44no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—114no—
683C24—112no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24#434114yes—
691C24C2×C22⋊D1114yes—
692C24C23×D1112yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—416no—
706C2×D4—416no—
707C2×D4—416no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—2232no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—444no—
717C2×D4—444no—
718C2×D4—4416no—
719C2×D4—4416no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—44no—
732C22×C4—416no—
733C22×C4—114no—
734C22×C4—114no—
735C22×C4—114no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—228no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—222no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—228no—
765C22×C4—444no—
766C22×C4—4416no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4D4×D1114yes—
770C22×C4C2×C22⋊D1114yes—
771C22×C4C2×C22⋊D1114yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—28no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—228no—
781C22⋊C4—28no—
782C22⋊C4—1116no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C22⋊C4C2×C22⋊D11116yescomplemented
794C42—228no—
795C42—444no—
796C11C2×#246411yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—28no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—44no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—114no—
838C23—228no—
839C23—228no—
840C23—228no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23C2×D4×D1112yes—
852C23C2×#434114yes—
853C23C2×#434112yes—
854C23#6703712yes—
855C23#6703712yes—
856C23#41×D1112yes—
857C23#41×D1112yes—
858C23C22×C22⋊D1114yes—
859C23C22×C22⋊D1112yes—
860C23C24×D1111yescharacteristic
861D4—416no—
862D4—416no—
863D4—416no—
864D4—2232no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—416no—
880C2×C4—44no—
881C2×C4—114no—
882C2×C4—114no—
883C2×C4—114no—
884C2×C4—228no—
885C2×C4—228no—
886C2×C4—228no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—4416no—
906C2×C4—4416no—
907C2×C4—444no—
908C2×C4—444no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4C2×D4×D1114yes—
912C2×C4C22×C22⋊D1114yes—
913C2×C4C22×C22⋊D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—416no—
929C22—416no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—88no—
938C22—224no—
939C22—224no—
940C22—224no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—4416no—
946C22#1062313214yes—
947C22#1062313714yes—
948C22#1062314314yes—
949C22#1062314614yes—
950C22D4×C22⋊D1114yes—
951C22#1062333714yes—
952C22#1062336314yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×#434111yescharacteristic
955C22C2×#6703711yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C23×C22⋊D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—224no—
965C4—224no—
966C4—224no—
967C4—442no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—44no—
973C2—82no—
974C2—444no—
975C2#1307262718yesdirect product factor
976C2C2×#1062313711yescharacteristic
977C2C2×#1062336311yescharacteristic
978C2C2×#1062314611yescharacteristic
979C2C2×D4×C22⋊D1111yescharacteristic
980C2C2×#1062333711yescharacteristic
981C2C2×#1062314311yescharacteristic
982C2C2×#1062313211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2464
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66992C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13072627C2direct (N × H)
5. C2×#10622596C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622603C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622823C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C22×C11×#121C2semidirect
27. C2×C11×#121C22semidirect
40. C2×#66992C22semidirect
42. C2×C4×C22⋊D11C22semidirect
53. C2×#66936C22semidirect
54. #10622836C22semidirect
55. #10622836C22semidirect
56. #10622835C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
59. #10622823C22semidirect
66. #10622603C22semidirect
67. #10622596C22semidirect
68. #10622569C22semidirect
69. #10622558C22semidirect
70. C22⋊C4×Dic11C22semidirect
126. C2×C11×C22⋊C4D4semidirect
149. C2×(C2×D11)⋊C4D4semidirect
288. C11×C22⋊C4C2×D4semidirect
299. (C2×D11)⋊C4C2×D4semidirect
308. C22×#121D11semidirect
453. C2×#121C2×D11semidirect
638. C2×C22⋊C4C22⋊D11semidirect
654. C2×C11#2464semidirect
793. C22⋊C4C2×C22⋊D11semidirect
796. C11C2×#2464semidirect
975. C2#13072627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669922
C22×C4×C22⋊D112
#130726272
C2×#106225962
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106225582
C2×#106226032
C2×#106228332
C2×#106225692
C2×#106228232
C2×C22⋊C4×Dic112
C22×C11×#1212
C2×#246411