Finite Group Databasebeta

← C2×#13072504 #14921280

Subgroups — C2×#13072504 #14921280

Order 2816.

4282 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×#66991C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13072504C2116yesmaximal, direct product factor
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622573C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622594C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622602C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, 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
25C23×C4×D11C2211yescharacteristic
26C2×C11×#123—28no—
27C2×C11×#123C2218yescomplemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66991—28no—
38C2×#66991C2218yescomplemented
39C2×C4×C22⋊D11—28no—
40C2×C4×C22⋊D11C2218yescomplemented
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×C4⋊Dic11C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66946—28no—
53C2×#66946C2218yescomplemented
54#10622836C2218yescomplemented
55#10622826C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622607C2218yescomplemented
63#10622602C2218yescomplemented
64#10622594C2218yescomplemented
65#10622573C2218yescomplemented
66#10622573C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622557C2218yescomplemented
70#10622557C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—42no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
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⋊D11—42no—
99C22×C22⋊D11—42no—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—42no—
119C22×C4×D11—42no—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C11×#123—232no—
123C2×C11×C4⋊C4—24no—
124C2×C11×C4⋊C4D418yescomplemented
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C4⋊C4C2314yes—
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×C22⋊Dic11—24no—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—42no—
136C2×C22⋊Dic11D418yescomplemented
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141#66991—232no—
142C4×C22⋊D11—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—42no—
148C2×(C2×D11)⋊C4—42no—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×C4⋊Dic11—24no—
156C2×C4⋊Dic11C2314yes—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4—42no—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×C4×Dic11—24no—
162C2×C4×Dic11—24no—
163C2×C4×Dic11C2314yes—
164C2×C4×Dic11C2314yes—
165#66946—232no—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2456—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×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11#4114yes—
203C23×D11#4114yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
209C2×D4×C11—416no—
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×C11—28no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—28no—
224C22×C4×C11—44no—
225C22×C4×C11—416no—
226C22×C4×C11C2×D414yes—
227C22×C4×C11C2×D414yes—
228C22×C4×C11C2×D414yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C2×C22⋊D11—232no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—416no—
248C2×C22⋊D11—416no—
249C2×C22⋊D11—416no—
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×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D414yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—232no—
275C2×D44—28no—
276C2×D44—28no—
277C2×D44—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—416no—
285C2×C4×D11—416no—
286C11×C4⋊C4—28no—
287C11×C4⋊C4C2×D4116yescomplemented
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—44no—
294C22⋊Dic11C2×D4116yescomplemented
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301C4⋊Dic11—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—44no—
304C4×Dic11—28no—
305C4×Dic11—28no—
306C22×#123D1111yescharacteristic, complemented
307C22×#121—111no—
308C22×C4×D4—111no—
309C22×C4×D4—111no—
310#2456—1116no—
311C2×#396—111no—
312C2×#392—111no—
313C2×#392—111no—
314C2×#392—111no—
315C2×#390—111no—
316C2×#388—111no—
317C2×#388—111no—
318C2×#387—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
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—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11C22×D412yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11C2511yescharacteristic
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—28no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—44no—
384C22×D11C2×#4114yes—
385C22×D11C2×#4114yes—
386D4×C11—416no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
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—22no—
402C2×C4×C11—416no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C22×D414yes—
408C22⋊D11—232no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C22⋊D11—416no—
412C2×Dic11—28no—
413C2×Dic11—28no—
414C2×Dic11—28no—
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—44no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C2×#4114yes—
436D44—232no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4C2×D1111yescharacteristic
448C2×#123—28no—
449C2×#123C2×D1118yescomplemented
450C2×#121—118no—
451C2×#121—228no—
452C2×C4×D4—118no—
453C2×C4×D4—118no—
454C2×C4×D4—228no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C22⋊C4C2×D1111yescharacteristic
474C22×C42—111no—
475C22×C42—111no—
476#396—118no—
477#392—118no—
478#392—118no—
479#392—118no—
480#390—118no—
481#388—118no—
482#388—118no—
483#387—118no—
484#386—118no—
485#386—118no—
486#385—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—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—88no—
509C22×C11#52514yes—
510C22×C11#52514yes—
511C22×C11#53814yes—
512C22×C11D4214yes—
513C22×C11#54614yes—
514C22×C11#55014yes—
515C22×C11#55314yes—
516C22×C11C23×D411yescharacteristic
517C22×C11C23×D411yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—416no—
538C2×D11—416no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—42no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—114no—
562C22×D4—224no—
563C22×D4—224no—
564C22×D4—224no—
565C22×D4—224no—
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×D4—442no—
576C22×D4—442no—
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—114no—
588C23×C4—114no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4C22×D1111yescharacteristic
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1114yes—
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—232no—
602#121—2232no—
603C4×D4—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4—224no—
611C2×C4⋊C4—442no—
612C2×C4⋊C4C22⋊D1118yescomplemented
613C2×C4⋊C4C22×D1114yes—
614C2×C4⋊C4C22×D1114yes—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—118no—
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—114no—
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×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C22⋊C4C22×D1114yes—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95—114no—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#245618yescomplemented
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#52511yescharacteristic
656C2×C11C2×#53811yescharacteristic
657C2×C11C2×D4211yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#55011yescharacteristic
660C2×C11C2×#55311yescharacteristic
661D11—44no—
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—114no—
677C24—114no—
678C24—112no—
679C24—112no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24D4×D1114yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—44no—
699C2×D4—416no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—2232no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—2232no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—4416no—
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—28no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—28no—
734C22×C4—44no—
735C22×C4—416no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—228no—
746C22×C4—228no—
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—228no—
763C22×C4—228no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—4416no—
767C22×C4—4416no—
768C22×C4C2×C22⋊D1114yes—
769C22×C4C2×C22⋊D1114yes—
770C22×C4C2×C22⋊D1114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—28no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—444no—
780C4⋊C4C2×C22⋊D11116yescomplemented
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—1116no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—228no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C22⋊C4—444no—
794C42—228no—
795C42—228no—
796C11C2×#245611yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—114no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—228no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—228no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1114yes—
853C23C2×D4×D1112yes—
854C23#6703712yes—
855C23#41×D1112yes—
856C23#41×D1112yes—
857C23#41×D1112yes—
858C23#6704212yes—
859C23C22×C22⋊D1112yes—
860C23C24×D1111yescharacteristic
861D4—416no—
862D4—2232no—
863D4—2232no—
864D4—4416no—
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—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—416no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—228no—
889C2×C4—228no—
890C2×C4—228no—
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—222no—
906C2×C4—4416no—
907C2×C4—4416no—
908C2×C4—444no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4C22×C22⋊D1114yes—
912C2×C4C22×C22⋊D1114yes—
913C2×C4C22×C22⋊D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—416no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—88no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—224no—
934C22—224no—
935C22—224no—
936C22—442no—
937C22—442no—
938C22—4416no—
939C22—4416no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22#1062318514yes—
947C22#1062318714yes—
948C22#1062318814yes—
949C22#1062319214yes—
950C22D4×C22⋊D1114yes—
951C22#1062335914yes—
952C22#1062336514yes—
953C22C22×D4×D1111yescharacteristic
954C22C2×#6703711yescharacteristic
955C22C2×#41×D1111yescharacteristic
956C22C2×#41×D1111yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#6704211yescharacteristic
959C22C23×C22⋊D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—42no—
964C4—42no—
965C4—224no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—82no—
973C2—444no—
974C2—444no—
975C2#1307250418yesdirect product factor
976C2C2×#1062335911yescharacteristic
977C2C2×#1062318711yescharacteristic
978C2C2×#1062318811yescharacteristic
979C2C2×D4×C22⋊D1111yescharacteristic
980C2C2×#1062318511yescharacteristic
981C2C2×#1062336511yescharacteristic
982C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
hypercenterC22×#123D11
hypocenterC11C2×#2456
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66991C2semidirect
2. C22×#66946C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13072504C2direct (N × H)
5. C2×#10622607C2semidirect
6. C2×#10622573C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622594C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622602C2semidirect
16. C22×C11×#123C2semidirect
27. C2×C11×#123C22semidirect
38. C2×#66991C22semidirect
40. C2×C4×C22⋊D11C22semidirect
53. C2×#66946C22semidirect
54. #10622836C22semidirect
55. #10622826C22semidirect
62. #10622607C22semidirect
63. #10622602C22semidirect
64. #10622594C22semidirect
65. #10622573C22semidirect
66. #10622573C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622557C22semidirect
70. #10622557C22semidirect
124. C2×C11×C4⋊C4D4semidirect
136. C2×C22⋊Dic11D4semidirect
287. C11×C4⋊C4C2×D4semidirect
294. C22⋊Dic11C2×D4semidirect
306. C22×#123D11semidirect
449. C2×#123C2×D11semidirect
612. C2×C4⋊C4C22⋊D11semidirect
653. C2×C11#2456semidirect
780. C4⋊C4C2×C22⋊D11semidirect
796. C11C2×#2456semidirect
975. C2#13072504direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×#669462
C22×C4×C22⋊D112
#130725042
C2×#106226072
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106225572
C2×#106225942
C2×#106228262
C2×#106225692
C2×#106226022
C22×C11×#1232
C2×#245611