Finite Group Databasebeta

← C2×#13073553 #14924942

Subgroups — C2×#13073553 #14924942

Order 2816.

4566 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic, complemented
3C22×#66931C211yesmaximal, characteristic, complemented
4C22×#66937C211yesmaximal, characteristic, complemented
5C22×#66992C211yesmaximal, characteristic, complemented
6C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7#13073553C2116yesmaximal, direct product factor
8C2×#10622562C211yesmaximal, characteristic, complemented
9C2×#10622605C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622552C211yesmaximal, characteristic, complemented
13C2×#10622570C211yesmaximal, characteristic, complemented
14C2×#10622570C211yesmaximal, characteristic, complemented
15C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66949—28no—
53C2×#66949C2218yescomplemented
54C2×#66938—28no—
55C2×#66938C2218yescomplemented
56C2×#66937—28no—
57C2×#66937C2218yescomplemented
58C2×(C22⋊D11)⋊C4—28no—
59C2×(C22⋊D11)⋊C4C2218yescomplemented
60C2×#66931—28no—
61C2×#66931C2218yescomplemented
62C11×#390C2218yescomplemented
63#10622836C2218yescomplemented
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622605C2218yescomplemented
67#10622573C2218yescomplemented
68#10622570C2218yescomplemented
69#10622570C2218yescomplemented
70#10622562C2218yescomplemented
71#10622552C2218yescomplemented
72C4×Dic11⋊C4C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
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—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C23×Dic11—24no—
103C23×Dic11—24no—
104C23×Dic11—24no—
105C23×Dic11C2314yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—42no—
115C22×D44C2314yes—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—24no—
119C22×C4×D11C2314yes—
120C22×Dic22—24no—
121C22×Dic22—24no—
122C22×Dic22—24no—
123C22×Dic22C2314yes—
124C2×C11×C4⋊C4—24no—
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C42×C11—42no—
135C2×C42×C11C2314yes—
136C2×C22⋊Dic11—24no—
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11—24no—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142#66992—232no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×C4⋊Dic11—24no—
158C2×C4⋊Dic11C2314yes—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4—24no—
161C2×Dic11⋊C4—24no—
162C2×Dic11⋊C4D418yescomplemented
163C2×Dic11⋊C4D418yescomplemented
164C2×Dic11⋊C4C2314yes—
165C2×Dic11⋊C4C2314yes—
166C2×Dic11⋊C4C2314yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×C4×Dic11—42no—
170C2×C4×Dic11D418yescomplemented
171C2×C4×Dic11C2314yes—
172C2×C4×Dic11C2314yes—
173#66949—232no—
174#66938—232no—
175#66937—232no—
176(C22⋊D11)⋊C4—232no—
177#66931—232no—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C2×#2540—111nomaximal, Sylow
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×C11—22no—
193C24×C11—22no—
194C24×C11#4114yes—
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×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11#4114yes—
212C23×D11C2412yes—
213C23×D11C2412yes—
214C2×D4×C11—28no—
215C2×D4×C11—28no—
216C2×D4×C11—44no—
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—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11C2×D414yes—
231C22×C4×C11C2×D414yes—
232C22×C4×C11C2×D414yes—
233C22×C4×C11C2412yes—
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—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—416no—
252C2×C22⋊D11—416no—
253C2×C22⋊D11—416no—
254C22×Dic11—28no—
255C22×Dic11—28no—
256C22×Dic11—28no—
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—416no—
270C22×Dic11C2×D414yes—
271C22×Dic11C2×D414yes—
272C22×Dic11C2×D414yes—
273C22×Dic11C2×D414yes—
274C22×Dic11C2×D414yes—
275C22×Dic11C2×D414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—416no—
286C2×C4×D11—28no—
287C2×C4×D11—28no—
288C2×C4×D11—28no—
289C2×C4×D11—416no—
290C2×Dic22—28no—
291C2×Dic22—28no—
292C2×Dic22—28no—
293C2×Dic22—416no—
294C11×C4⋊C4—28no—
295C11×C22⋊C4—28no—
296C11×C22⋊C4—28no—
297C11×C22⋊C4—28no—
298C11×C22⋊C4—28no—
299C42×C11—44no—
300C22⋊Dic11—28no—
301C22⋊Dic11—28no—
302C22⋊Dic11—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—28no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—28no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310C4⋊Dic11—28no—
311Dic11⋊C4—28no—
312Dic11⋊C4—28no—
313Dic11⋊C4—28no—
314Dic11⋊C4C2×D4116yescomplemented
315Dic11⋊C4C2×D4116yescomplemented
316C4×Dic11—44no—
317C4×Dic11C2×D4116yescomplemented
318C22×#124—111no—
319C22×C22⋊Q8—111no—
320C22×C22⋊Q8—111no—
321C22×#121—111no—
322C22×#121—111no—
323C22×C4×D4—111no—
324#2540—1116no—
325C2×#399—111no—
326C2×#399—111no—
327C2×#392—111no—
328C2×#392—111no—
329C2×#390—111no—
330C2×#390—111no—
331C2×#390—111no—
332C2×#390D1111yescharacteristic, complemented
333C2×C4×C4⋊C4—111no—
334C23×C11—28no—
335C23×C11—28no—
336C23×C11—28no—
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—22no—
348C23×C11—22no—
349C23×C11—22no—
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×C11C22×D412yes—
362C23×C11C22×D412yes—
363C23×C11C22×D412yes—
364C23×C11C2×#4114yes—
365C23×C11C2×#4112yes—
366C23×C11C2×#4112yes—
367C23×C11H(5,𝔽2)12yes—
368C23×C112−1+412yes—
369C23×C11C2511yescharacteristic
370C22×D11—28no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—44no—
387C22×D11—44no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11C2×#4114yes—
398D4×C11—416no—
399C2×C4×C11—28no—
400C2×C4×C11—28no—
401C2×C4×C11—28no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—44no—
415C2×C4×C11—44no—
416C2×C4×C11C22×D414yes—
417C2×C4×C11C22×D414yes—
418C2×C4×C11C22×D414yes—
419C22⋊D11—232no—
420C22⋊D11—416no—
421C22⋊D11—416no—
422C22⋊D11—416no—
423C2×Dic11—28no—
424C2×Dic11—28no—
425C2×Dic11—28no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—44no—
439C2×Dic11—44no—
440C2×Dic11—416no—
441C2×Dic11#127116yes—
442C2×Dic11C22×D414yes—
443C2×Dic11C22×D414yes—
444C2×Dic11C22×D414yes—
445C2×Dic11C22×D414yes—
446C2×Dic11C22×D414yes—
447C2×Dic11C22×D414yes—
448D44—416no—
449C4×D11—416no—
450Dic22—416no—
451C23×Q8—111no—
452C23×D4—111no—
453C23×D4—111no—
454C23×D4—111no—
455C23×D4—111no—
456C23×D4—111no—
457C23×D4C2×D1111yescharacteristic
458C24×C4—111no—
459C24×C4—111no—
460C2×#124—118no—
461C2×#124—228no—
462C2×C22⋊Q8—118no—
463C2×C22⋊Q8—118no—
464C2×C22⋊Q8—228no—
465C2×C22⋊Q8—228no—
466C2×#121—118no—
467C2×#121—118no—
468C2×#121—228no—
469C2×#121—228no—
470C2×C4×D4—118no—
471C2×C4×D4—228no—
472C22×C4⋊C4—111no—
473C22×C4⋊C4—111no—
474C22×C4⋊C4—111no—
475C22×C4⋊C4—111no—
476C22×C4⋊C4—111no—
477C22×C4⋊C4—111no—
478C22×C4⋊C4C2×D1111yescharacteristic
479C22×C22⋊C4—111no—
480C22×C22⋊C4—111no—
481C22×C22⋊C4—111no—
482C22×C22⋊C4—111no—
483C22×C22⋊C4—111no—
484C22×C22⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4C2×D1111yescharacteristic
490C22×C22⋊C4C2×D1111yescharacteristic
491C22×C22⋊C4C2×D1111yescharacteristic
492C22×C22⋊C4C2×D1111yescharacteristic
493C22×C42—111no—
494C22×C42—111no—
495C22×C42C2×D1111yescharacteristic
496#399—118no—
497#399—118no—
498#392—118no—
499#392—118no—
500#390—118no—
501#390—118no—
502#390—118no—
503#390C2×D1118yescomplemented
504C4×C4⋊C4—118no—
505C2×#95—111no—
506C2×#95—111no—
507C22×C11—24no—
508C22×C11—24no—
509C22×C11—24no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—416no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—88no—
523C22×C11#52514yes—
524C22×C11C2×#12714yes—
525C22×C11#53714yes—
526C22×C11#54614yes—
527C22×C11#54614yes—
528C22×C11#54814yes—
529C22×C11#54814yes—
530C22×C11C23×D411yescharacteristic
531C22×C11C23×D411yescharacteristic
532C22×C11C23×D411yescharacteristic
533C22×C11C22×#4111yescharacteristic
534C22×C11C22×#4111yescharacteristic
535C22×C11C2×H(5,𝔽2)11yescharacteristic
536C22×C11C2×2−1+411yescharacteristic
537C2×D11—24no—
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—416no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—88no—
553C4×C11—24no—
554C4×C11—24no—
555C4×C11—24no—
556C4×C11—42no—
557C4×C11—42no—
558Dic11—24no—
559Dic11—24no—
560Dic11—24no—
561Dic11—42no—
562Dic11—42no—
563Dic11C2×#12718yes—
564C25—111no—
565C25—111no—
566C25C22×D1111yescharacteristic
567C25C22×D1111yescharacteristic
568C22×Q8—114no—
569C22×Q8—224no—
570C22×Q8—224no—
571C22×Q8—224no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—42no—
575C22×D4—114no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—114no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—224no—
587C22×D4—224no—
588C22×D4—224no—
589C22×D4—224no—
590C22×D4—224no—
591C22×D4—224no—
592C22×D4—442no—
593C22×D4—442no—
594C22×D4—442no—
595C22×D4C22×D1114yes—
596C23×C4—111no—
597C23×C4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—114no—
601C23×C4—111no—
602C23×C4—111no—
603C23×C4—114no—
604C23×C4—224no—
605C23×C4—224no—
606C23×C4—224no—
607C23×C4—224no—
608C23×C4—224no—
609C23×C4—224no—
610C23×C4C22×D1111yescharacteristic
611C23×C4C22×D1111yescharacteristic
612C23×C4C22×D1111yescharacteristic
613C23×C4C22×D1111yescharacteristic
614C23×C4C22×D1111yescharacteristic
615#124—2232no—
616C22⋊Q8—2232no—
617C22⋊Q8—2232no—
618#121—2232no—
619#121—2232no—
620C4×D4—2232no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—118no—
623C2×C4⋊C4—118no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—114no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—224no—
631C2×C4⋊C4—224no—
632C2×C4⋊C4—224no—
633C2×C4⋊C4—224no—
634C2×C4⋊C4C22×D1114yes—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—114no—
640C2×C22⋊C4—114no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—114no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—114no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—224no—
650C2×C22⋊C4—224no—
651C2×C22⋊C4—224no—
652C2×C22⋊C4—224no—
653C2×C22⋊C4—224no—
654C2×C22⋊C4—224no—
655C2×C22⋊C4—224no—
656C2×C22⋊C4—224no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4C22×D1114yes—
660C2×C22⋊C4C22×D1114yes—
661C2×C22⋊C4C22×D1114yes—
662C2×C22⋊C4C22×D1114yes—
663C2×C42—42no—
664C2×C42—118no—
665C2×C42—114no—
666C2×C42—114no—
667C2×C42—442no—
668C2×C42C22×D1114yes—
669#95—114no—
670#95—114no—
671C2×C11—44no—
672C2×C11—82no—
673C2×C11#254018yescomplemented
674C2×C11C2×#52511yescharacteristic
675C2×C11C22×#12711yescharacteristic
676C2×C11C2×#53711yescharacteristic
677C2×C11C2×#54611yescharacteristic
678C2×C11C2×#54611yescharacteristic
679C2×C11C2×#54811yescharacteristic
680C2×C11C2×#54811yescharacteristic
681D11—44no—
682D11—82no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—114no—
697C24—112no—
698C24—112no—
699C24—222no—
700C24—222no—
701C24—222no—
702C24—222no—
703C24—222no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24#433914yes—
713C24C23×D1112yes—
714C24C23×D1112yes—
715C24C23×D1111yescharacteristic
716C2×Q8—228no—
717C2×Q8—228no—
718C2×Q8—228no—
719C2×Q8—4416no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—44no—
723C2×D4—416no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—228no—
732C2×D4—2232no—
733C2×D4—228no—
734C2×D4—228no—
735C2×D4—228no—
736C2×D4—228no—
737C2×D4—444no—
738C2×D4—4416no—
739C2×D4—4416no—
740C2×D4—444no—
741C2×D4—444no—
742C2×D4—4416no—
743C2×D4—4416no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—114no—
757C22×C4—114no—
758C22×C4—114no—
759C22×C4—112no—
760C22×C4—114no—
761C22×C4—114no—
762C22×C4—114no—
763C22×C4—112no—
764C22×C4—112no—
765C22×C4—112no—
766C22×C4—112no—
767C22×C4—112no—
768C22×C4—228no—
769C22×C4—228no—
770C22×C4—228no—
771C22×C4—228no—
772C22×C4—228no—
773C22×C4—228no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—4416no—
787C22×C4—4416no—
788C22×C4D4×D1114yes—
789C22×C4D4×D1114yes—
790C22×C4D4×D1114yes—
791C22×C4C23×D1112yes—
792C22×C4C23×D1112yes—
793C22×C4C23×D1112yes—
794C22×C4C23×D1112yes—
795C22×C4C23×D1112yes—
796C4⋊C4—28no—
797C4⋊C4—1116no—
798C4⋊C4—1116no—
799C4⋊C4—228no—
800C4⋊C4—228no—
801C4⋊C4—228no—
802C4⋊C4—228no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—228no—
808C22⋊C4—228no—
809C22⋊C4—228no—
810C22⋊C4—228no—
811C22⋊C4—228no—
812C22⋊C4—228no—
813C22⋊C4—228no—
814C22⋊C4—228no—
815C22⋊C4—228no—
816C22⋊C4—228no—
817C42—44no—
818C42—1116no—
819C42—444no—
820C11C2×#254011yescharacteristic, complemented, Sylow
821C23—28no—
822C23—28no—
823C23—28no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23—44no—
843C23—44no—
844C23—44no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—114no—
849C23—228no—
850C23—228no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—228no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23—444no—
870C23—444no—
871C23—444no—
872C23—444no—
873C23—444no—
874C23—444no—
875C23—444no—
876C23C2×#433914yes—
877C23C2×#433912yes—
878C23C2×D4×D1112yes—
879C23C2×D4×D1112yes—
880C23C2×D4×D1112yes—
881C23#6703712yes—
882C23#41×D1112yes—
883C23#6704312yes—
884C23C24×D1111yescharacteristic
885Q8—4416no—
886D4—416no—
887D4—2232no—
888D4—4416no—
889D4—4416no—
890D4—4416no—
891D4—4416no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—1116no—
910C2×C4—114no—
911C2×C4—114no—
912C2×C4—114no—
913C2×C4—114no—
914C2×C4—114no—
915C2×C4—114no—
916C2×C4—228no—
917C2×C4—228no—
918C2×C4—228no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—4416no—
932C2×C4—4416no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4C2×D4×D1114yes—
936C2×C4C2×D4×D1114yes—
937C2×C4C2×D4×D1114yes—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—42no—
942C22—42no—
943C22—416no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—88no—
954C22—224no—
955C22—224no—
956C22—224no—
957C22—442no—
958C22—442no—
959C22—4416no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—888no—
970C22#1062302114yes—
971C22#1062307814yes—
972C22#1062308314yes—
973C22#1062312814yes—
974C22#1062314114yes—
975C22#1062320814yes—
976C22D11×#12714yes—
977C22C22×#433911yescharacteristic
978C22C22×D4×D1111yescharacteristic
979C22C22×D4×D1111yescharacteristic
980C22C22×D4×D1111yescharacteristic
981C22C2×#6703711yescharacteristic
982C22C2×#41×D1111yescharacteristic
983C22C2×#6704311yescharacteristic
984C4—24no—
985C4—24no—
986C4—24no—
987C4—42no—
988C4—42no—
989C4—118no—
990C4—224no—
991C4—224no—
992C4—224no—
993C4—442no—
994C4—442no—
995C2—44no—
996C2—82no—
997C2—444no—
998C2—882no—
999C2#1307355318yesdirect product factor
1000C2C2×#1062307811yescharacteristic
1001C2C2×D11×#12711yescharacteristic
1002C2C2×#1062312811yescharacteristic
1003C2C2×#1062314111yescharacteristic
1004C2C2×#1062302111yescharacteristic
1005C2C2×#1062320811yescharacteristic
1006C2C2×#1062308311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
hypercenterC2×#390D11
hypocenterC11C2×#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66949C2semidirect
3. C22×#66931C2semidirect
4. C22×#66937C2semidirect
5. C22×#66992C2semidirect
6. C22×(C22⋊D11)⋊C4C2semidirect
7. #13073553C2direct (N × H)
8. C2×#10622562C2semidirect
9. C2×#10622605C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622552C2semidirect
13. C2×#10622570C2semidirect
14. C2×#10622570C2semidirect
15. C2×C4×Dic11⋊C4C2semidirect
16. C2×C11×#390C2semidirect
36. C2×#66992C22semidirect
53. C2×#66949C22semidirect
55. C2×#66938C22semidirect
57. C2×#66937C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
61. C2×#66931C22semidirect
62. C11×#390C22semidirect
63. #10622836C22semidirect
66. #10622605C22semidirect
67. #10622573C22semidirect
68. #10622570C22semidirect
69. #10622570C22semidirect
70. #10622562C22semidirect
71. #10622552C22semidirect
72. C4×Dic11⋊C4C22semidirect
162. C2×Dic11⋊C4D4semidirect
163. C2×Dic11⋊C4D4semidirect
170. C2×C4×Dic11D4semidirect
314. Dic11⋊C4C2×D4semidirect
315. Dic11⋊C4C2×D4semidirect
317. C4×Dic11C2×D4semidirect
332. C2×#390D11semidirect
503. #390C2×D11semidirect
673. C2×C11#2540semidirect
820. C11C2×#2540semidirect
999. C2#13073553direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669492
C22×#669312
C22×#669372
C22×#669922
C22×(C22⋊D11)⋊C42
#130735532
C2×#106225622
C2×#106226052
C2×#106225732
C2×#106228362
C2×#106225522
C2×#106225702
C2×C4×Dic11⋊C42
C2×C11×#3902
C2×#254011