Finite Group Databasebeta

← C2×#13072616 #14921612

Subgroups — C2×#13072616 #14921612

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×#66982C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4#13072616C2116yesmaximal, direct product factor
5C2×#10622597C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622553C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11—28no—
27C2×C4×D4×C11C2218yescomplemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66983—28no—
37C2×#66983C2218yescomplemented
38C2×#66982—28no—
39C2×#66982C2218yescomplemented
40C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66937—28no—
53C2×#66937C2218yescomplemented
54#10622836C2218yescomplemented
55#10622836C2218yescomplemented
56#10622826C2218yescomplemented
57#10622823C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622604C2218yescomplemented
65#10622597C2218yescomplemented
66#10622570C2218yescomplemented
67#10622569C2218yescomplemented
68#10622564C2218yescomplemented
69#10622553C2218yescomplemented
70C4×(C2×D11)⋊C4C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11C2314yes—
79C23×C4×C11—24no—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—42no—
84C23×C4×C11—42no—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2314yes—
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11—42no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C22×C22⋊D11C2314yes—
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×D44—24no—
115C22×D44—24no—
116C22×D44—42no—
117C22×D44C2314yes—
118C22×C4×D11—24no—
119C22×C4×D11—24no—
120C22×C4×D11—42no—
121C22×C4×D11C2314yes—
122C4×D4×C11—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×C42×C11—24no—
130C2×C42×C11C2314yes—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—42no—
134C2×C22⋊Dic11—42no—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139#66983—232no—
140#66982—232no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4—42no—
147C2×(C2×D11)⋊C4D418yescomplemented
148C2×(C2×D11)⋊C4C2314yes—
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—24no—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×Dic11⋊C4C2314yes—
163C2×C4×Dic11—42no—
164C2×C4×Dic11C2314yes—
165#66937—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×C11C2×D414yes—
186C24×C11#4114yes—
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—22no—
203C23×D11C2×D414yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—232no—
207C2×D4×C11—28no—
208C2×D4×C11—28no—
209C2×D4×C11—28no—
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—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—28no—
221C22×C4×C11—22no—
222C22×C4×C11—28no—
223C22×C4×C11—28no—
224C22×C4×C11—28no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11—416no—
228C22×C4×C11—416no—
229C22×C4×C11C2×D414yes—
230C22×C4×C11C2×D414yes—
231C22×C4×C11C2×D414yes—
232C22×C4×C11#4114yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2412yes—
238C2×C22⋊D11—28no—
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—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—416no—
251C2×C22⋊D11—416no—
252C2×C22⋊D11—416no—
253C2×C22⋊D11—416no—
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×Dic11C2×D414yes—
271C22×Dic11#4114yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C2×D44—28no—
279C2×D44—28no—
280C2×D44—44no—
281C2×D44—416no—
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
289C42×C11—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292C22⋊Dic11—44no—
293C22⋊Dic11—44no—
294(C2×D11)⋊C4—28no—
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)⋊C4C2×D4116yescomplemented
301C4⋊Dic11—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—28no—
304Dic11⋊C4—28no—
305C4×Dic11—44no—
306C22×#123—111no—
307C22×#121—111no—
308C22×#121—111no—
309C22×C4×D4D1111yescharacteristic, complemented
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—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11C22×D412yes—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11C2×#4114yes—
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—22no—
362C22×D11—22no—
363C22×D11—22no—
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—44no—
375C22×D11—44no—
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×D11—44no—
385C22×D11C22×D414yes—
386D4×C11—232no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—28no—
390C2×C4×C11—28no—
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—416no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C22×D414yes—
407C2×C4×C11C22×D414yes—
408C2×C4×C11C2×#4114yes—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C22⋊D11—416no—
412C22⋊D11—416no—
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—22no—
431C2×Dic11—44no—
432C2×Dic11—44no—
433C2×Dic11—44no—
434C2×Dic11—44no—
435C2×Dic11C22×D414yes—
436C2×Dic11C2×#4114yes—
437D44—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×C4C2×D1111yescharacteristic
447C24×C4C2×D1111yescharacteristic
448C2×#123—118no—
449C2×#123—228no—
450C2×#121—118no—
451C2×#121—118no—
452C2×#121—228no—
453C2×#121—228no—
454C2×C4×D4—28no—
455C2×C4×D4C2×D1118yescomplemented
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×C42C2×D1111yescharacteristic
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#52514yes—
510C22×C11#53214yes—
511C22×C11#54014yes—
512C22×C11D4214yes—
513C22×C11#54614yes—
514C22×C11#54614yes—
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—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—24no—
542C4×C11—24no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×D4—24no—
555C22×D4—24no—
556C22×D4—24no—
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—442no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4—442no—
576C22×D4—442no—
577C22×D4C22×D1114yes—
578C23×C4—24no—
579C23×C4—24no—
580C23×C4—24no—
581C23×C4—24no—
582C23×C4—42no—
583C23×C4—42no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—114no—
591C23×C4—224no—
592C23×C4—224no—
593C23×C4—442no—
594C23×C4C22×D1111yescharacteristic
595C23×C4C22×D1114yes—
596C23×C4C22×D1114yes—
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#123—2232no—
602#121—2232no—
603#121—2232no—
604C4×D4—232no—
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—24no—
642C2×C42—114no—
643C2×C42—442no—
644C2×C42C22×D1114yes—
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#246418yescomplemented
654C2×C11C2×#52511yescharacteristic
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#54011yescharacteristic
657C2×C11C2×D4211yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#54611yescharacteristic
660C2×C11C2×#55311yescharacteristic
661D11—44no—
662D11—82no—
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—114no—
676C24—112no—
677C24—112no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24#433914yes—
692C24C2×C22⋊D1114yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×D4—232no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—228no—
701C2×D4—228no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—444no—
711C2×D4—4416no—
712C2×D4—444no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—4416no—
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—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—416no—
738C22×C4—416no—
739C22×C4—114no—
740C22×C4—114no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—228no—
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#433914yes—
768C22×C4D4×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—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—28no—
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—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—114no—
824C23—228no—
825C23—228no—
826C23—228no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—444no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23C2×#433914yes—
852C23C2×#433912yes—
853C23C2×#433912yes—
854C23C2×D4×D1112yes—
855C23#6703712yes—
856C23#41×D1112yes—
857C23#6704212yes—
858C23C22×C22⋊D1114yes—
859C23C22×C22⋊D1112yes—
860C23C24×D1111yescharacteristic
861D4—232no—
862D4—4416no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
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—416no—
884C2×C4—44no—
885C2×C4—114no—
886C2×C4—114no—
887C2×C4—228no—
888C2×C4—228no—
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—444no—
907C2×C4—444no—
908C2×C4—444no—
909C2×C4—444no—
910C2×C4C2×#433914yes—
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—224no—
931C22—224no—
932C22—224no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—4416no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062307114yes—
947C22#1062307914yes—
948C22#1062308114yes—
949C22#1062309314yes—
950C22#1062332214yes—
951C22D4×C22⋊D1114yes—
952C22#1062336014yes—
953C22C22×#433911yescharacteristic
954C22C22×#433911yescharacteristic
955C22C22×D4×D1111yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#41×D1111yescharacteristic
958C22C2×#6704211yescharacteristic
959C22C23×C22⋊D1111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—42no—
965C4—224no—
966C4—224no—
967C4—442no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—44no—
973C2—444no—
974C2—882no—
975C2#1307261618yesdirect product factor
976C2C2×#1062332211yescharacteristic
977C2C2×#1062307911yescharacteristic
978C2C2×#1062309311yescharacteristic
979C2C2×D4×C22⋊D1111yescharacteristic
980C2C2×#1062336011yescharacteristic
981C2C2×#1062308111yescharacteristic
982C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#2464
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66983C2semidirect
3. C22×#66937C2semidirect
4. #13072616C2direct (N × H)
5. C2×#10622597C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622553C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622823C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C22×C4×D4×C11C2semidirect
27. C2×C4×D4×C11C22semidirect
37. C2×#66983C22semidirect
39. C2×#66982C22semidirect
53. C2×#66937C22semidirect
54. #10622836C22semidirect
55. #10622836C22semidirect
56. #10622826C22semidirect
57. #10622823C22semidirect
64. #10622604C22semidirect
65. #10622597C22semidirect
66. #10622570C22semidirect
67. #10622569C22semidirect
68. #10622564C22semidirect
69. #10622553C22semidirect
70. C4×(C2×D11)⋊C4C22semidirect
126. C2×C11×C22⋊C4D4semidirect
147. C2×(C2×D11)⋊C4D4semidirect
288. C11×C22⋊C4C2×D4semidirect
300. (C2×D11)⋊C4C2×D4semidirect
309. C22×C4×D4D11semidirect
455. C2×C4×D4C2×D11semidirect
638. C2×C22⋊C4C22⋊D11semidirect
653. C2×C11#2464semidirect
793. C22⋊C4C2×C22⋊D11semidirect
796. C11C2×#2464semidirect
975. C2#13072616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669832
C22×#669372
#130726162
C2×#106225972
C2×#106226042
C2×#106228362
C2×#106225702
C2×#106225642
C2×#106225532
C2×#106228262
C2×#106225692
C2×#106228232
C2×C4×(C2×D11)⋊C42
C22×C4×D4×C112
C2×#246411