Finite Group Databasebeta

← C2×#13073545 #14923804

Subgroups — C2×#13073545 #14923804

Order 2816.

5726 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×#66935C211yesmaximal, characteristic, complemented
5C22×#66990C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
7#13073545C2116yesmaximal, 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×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×D44C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C4⋊C4C2211yescharacteristic, complemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic, complemented
31C22×C11×C22⋊C4C2211yescharacteristic, complemented
32C22×C42×C11C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic, complemented
36C2×#66990—28no—
37C2×#66990C2218yescomplemented
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×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C22×C4⋊Dic11C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×Dic11⋊C4C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×#66947—28no—
53C2×#66947C2218yescomplemented
54C2×#66937—28no—
55C2×#66937C2218yescomplemented
56C2×#66936—28no—
57C2×#66936C2218yescomplemented
58C2×#66935—28no—
59C2×#66935C2218yescomplemented
60C2×C22⋊C4×D11—28no—
61C2×C22⋊C4×D11C2218yescomplemented
62C11×#390C2218yescomplemented
63#10622836C2218yescomplemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66#10622605C2218yescomplemented
67#10622573C2218yescomplemented
68#10622570C2218yescomplemented
69#10622570C2218yescomplemented
70#10622562C2218yescomplemented
71#10622552C2218yescomplemented
72C4×(C2×D11)⋊C4C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—42no—
81C24×D11—42no—
82C24×D11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C24×D11C2314yes—
85C24×D11C2311yescharacteristic
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—42no—
89C22×D4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
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—24no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11—42no—
105C22×C22⋊D11—42no—
106C22×C22⋊D11—42no—
107C22×C22⋊D11C2314yes—
108C22×C22⋊D11C2314yes—
109C22×C22⋊D11C2314yes—
110C22×C22⋊D11C2314yescomplemented
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C22×D44—24no—
117C22×D44—24no—
118C22×D44—24no—
119C22×D44—24no—
120C22×D44—24no—
121C22×D44—42no—
122C22×D44C2314yes—
123C22×D44C2314yes—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—42no—
128C22×C4×D11—42no—
129C22×C4×D11D418yescomplemented
130C22×C4×D11C2314yes—
131C22×C4×D11C2314yes—
132C2×C11×C4⋊C4—24no—
133C2×C11×C4⋊C4C2314yescomplemented
134C2×C11×C22⋊C4—24no—
135C2×C11×C22⋊C4—24no—
136C2×C11×C22⋊C4—24no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yescomplemented
141C2×C11×C22⋊C4C2314yescomplemented
142C2×C42×C11—42no—
143C2×C42×C11C2314yescomplemented
144C2×C22⋊Dic11—24no—
145C2×C22⋊Dic11—24no—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11C2314yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yescomplemented
150#66990—232no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4D418yescomplemented
159C2×(C2×D11)⋊C4D418yescomplemented
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yescomplemented
167C2×(C2×D11)⋊C4C2314yescomplemented
168C2×(C2×D11)⋊C4C2314yescomplemented
169C2×C4⋊Dic11—24no—
170C2×C4⋊Dic11C2314yescomplemented
171C2×Dic11⋊C4—24no—
172C2×Dic11⋊C4—24no—
173C2×Dic11⋊C4—24no—
174C2×Dic11⋊C4C2314yescomplemented
175C2×Dic11⋊C4C2314yescomplemented
176C2×Dic11⋊C4C2314yescomplemented
177C2×C4×Dic11—42no—
178C2×C4×Dic11C2314yescomplemented
179#66947—232no—
180#66937—232no—
181#66936—232no—
182#66935—232no—
183C22⋊C4×D11—232no—
184C11⋊#95C2314yescomplemented
185C11⋊#95C2314yescomplemented
186C2×#2539—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11#4114yes—
201C24×C11C2412yes—
202C24×C11C2412yes—
203C24×C11C2411yescharacteristic
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—232no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—28no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—28no—
217C23×D11—28no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—28no—
226C23×D11—28no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—416no—
230C23×D11—416no—
231C23×D11—416no—
232C23×D11—416no—
233C23×D11—416no—
234C23×D11—416no—
235C23×D11C2×D414yes—
236C23×D11C2×D414yes—
237C23×D11C2×D414yes—
238C23×D11#4114yes—
239C23×D11C2412yes—
240C23×D11C2412yes—
241C23×D11C2412yes—
242C2×D4×C11—28no—
243C2×D4×C11—28no—
244C2×D4×C11—44no—
245C2×D4×C11—416no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11C2×D414yes—
259C22×C4×C11C2×D414yes—
260C22×C4×C11C2×D414yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2412yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—416no—
279C2×C22⋊D11—416no—
280C2×C22⋊D11—416no—
281C2×C22⋊D11—416no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11C2×D414yes—
295C22×Dic11C2×D414yes—
296C22×Dic11C2×D414yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—28no—
306C2×D44—28no—
307C2×D44—44no—
308C2×D44—416no—
309C2×D44—416no—
310C2×C4×D11—28no—
311C2×C4×D11—28no—
312C2×C4×D11—28no—
313C2×C4×D11—416no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—416no—
317C2×C4×D11C2×D4116yescomplemented
318C11×C4⋊C4—28no—
319C11×C22⋊C4—28no—
320C11×C22⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4—28no—
323C42×C11—44no—
324C22⋊Dic11—28no—
325C22⋊Dic11—28no—
326C22⋊Dic11—28no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4C2×D4116yescomplemented
335(C2×D11)⋊C4C2×D4116yescomplemented
336C4⋊Dic11—28no—
337Dic11⋊C4—28no—
338Dic11⋊C4—28no—
339Dic11⋊C4—28no—
340C4×Dic11—44no—
341C22×#123—111no—
342C22×#123—111no—
343C22×#121—111no—
344C22×#120—111no—
345C22×#120—111no—
346C23×C22⋊C4—111no—
347#2539—1116no—
348C2×#399—111no—
349C2×#399—111no—
350C2×#392—111no—
351C2×#392—111no—
352C2×#390—111no—
353C2×#390—111no—
354C2×#390—111no—
355C2×#390D1111yescharacteristic, complemented
356C2×C4×C22⋊C4—111no—
357C23×C11—28no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11C22×D412yes—
385C23×C11C22×D412yes—
386C23×C11C22×D412yes—
387C23×C11C2×#4114yes—
388C23×C11C2×#4112yes—
389C23×C11C2×#4112yes—
390C23×C11H(5,𝔽2)12yes—
391C23×C11H(5,𝔽2)12yes—
392C23×C11C2511yescharacteristic
393C22×D11—28no—
394C22×D11—28no—
395C22×D11—28no—
396C22×D11—28no—
397C22×D11—28no—
398C22×D11—28no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—232no—
404C22×D11—28no—
405C22×D11—28no—
406C22×D11—28no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—416no—
421C22×D11—416no—
422C22×D11—416no—
423C22×D11—416no—
424C22×D11—416no—
425C22×D11—4128no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—416no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11—44no—
434C22×D11—44no—
435C22×D11—44no—
436C22×D11—44no—
437C22×D11—44no—
438C22×D11#127116yes—
439C22×D11C22×D414yes—
440C22×D11C22×D414yes—
441C22×D11C22×D414yes—
442C22×D11C2×#4114yes—
443D4×C11—416no—
444C2×C4×C11—28no—
445C2×C4×C11—28no—
446C2×C4×C11—28no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—44no—
460C2×C4×C11—44no—
461C2×C4×C11C22×D414yes—
462C2×C4×C11C22×D414yes—
463C2×C4×C11C22×D414yes—
464C22⋊D11—416no—
465C22⋊D11—416no—
466C22⋊D11—416no—
467C22⋊D11—416no—
468C2×Dic11—28no—
469C2×Dic11—28no—
470C2×Dic11—28no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—44no—
484C2×Dic11—44no—
485C2×Dic11C22×D414yes—
486C2×Dic11C22×D414yes—
487C2×Dic11C22×D414yes—
488D44—416no—
489D44—416no—
490C4×D11—416no—
491C4×D11—416no—
492C26—111no—
493C23×D4—111no—
494C23×D4—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4C2×D1111yescharacteristic
500C24×C4—111no—
501C24×C4—111no—
502C2×#123—118no—
503C2×#123—118no—
504C2×#123—228no—
505C2×#123—228no—
506C2×#121—118no—
507C2×#121—228no—
508C2×#120—118no—
509C2×#120—118no—
510C2×#120—228no—
511C2×#120—228no—
512C22×C4⋊C4—111no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4C2×D1111yescharacteristic, complemented
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—118no—
530C22×C22⋊C4—228no—
531C22×C22⋊C4C2×D1111yescharacteristic
532C22×C22⋊C4C2×D1111yescharacteristic
533C22×C22⋊C4C2×D1111yescharacteristic, complemented
534C22×C22⋊C4C2×D1111yescharacteristic, complemented
535C22×C42—111no—
536C22×C42C2×D1111yescharacteristic, complemented
537#399—118no—
538#399—118no—
539#392—118no—
540#392—118no—
541#390—118no—
542#390—118no—
543#390—118no—
544#390C2×D1118yescomplemented
545C4×C22⋊C4—118no—
546C2×#95—111no—
547C2×#95—111no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—24no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—416no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—88no—
564C22×C11#52514yes—
565C22×C11C2×#12714yes—
566C22×C11#53414yes—
567C22×C11#54614yes—
568C22×C11#54614yes—
569C22×C11#54614yes—
570C22×C11#54614yes—
571C22×C11C23×D411yescharacteristic
572C22×C11C23×D411yescharacteristic
573C22×C11C23×D411yescharacteristic
574C22×C11C22×#4111yescharacteristic
575C22×C11C22×#4111yescharacteristic
576C22×C11C2×H(5,𝔽2)11yescharacteristic
577C22×C11C2×H(5,𝔽2)11yescharacteristic
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—232no—
585C2×D11—24no—
586C2×D11—24no—
587C2×D11—24no—
588C2×D11—464no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—416no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—88no—
602C2×D11C2×#12718yes—
603C4×C11—24no—
604C4×C11—24no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608Dic11—24no—
609Dic11—24no—
610Dic11—24no—
611Dic11—42no—
612Dic11—42no—
613C25—111no—
614C25—111no—
615C25—111no—
616C25—114no—
617C25—224no—
618C25—224no—
619C25—224no—
620C25—224no—
621C25—224no—
622C25—442no—
623C25—442no—
624C25C22×D1111yescharacteristic
625C25C22×D1111yescharacteristic
626C22×D4—24no—
627C22×D4—24no—
628C22×D4—42no—
629C22×D4—114no—
630C22×D4—114no—
631C22×D4—114no—
632C22×D4—114no—
633C22×D4—114no—
634C22×D4—114no—
635C22×D4—224no—
636C22×D4—224no—
637C22×D4—224no—
638C22×D4—224no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—224no—
643C22×D4—224no—
644C22×D4—224no—
645C22×D4—224no—
646C22×D4—224no—
647C22×D4—224no—
648C22×D4—442no—
649C22×D4—442no—
650C22×D4—442no—
651C22×D4—442no—
652C22×D4—442no—
653C22×D4C22×D1114yes—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—118no—
658C23×C4—114no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—114no—
662C23×C4—224no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—442no—
666C23×C4—442no—
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672#123—2232no—
673#123—2232no—
674#121—2232no—
675#120—2232no—
676#120—2232no—
677C2×C4⋊C4—24no—
678C2×C4⋊C4—114no—
679C2×C4⋊C4—114no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—224no—
683C2×C4⋊C4—224no—
684C2×C4⋊C4—224no—
685C2×C4⋊C4—224no—
686C2×C4⋊C4C22×D1114yescomplemented
687C2×C22⋊C4—24no—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—118no—
692C2×C22⋊C4—118no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—114no—
704C2×C22⋊C4—114no—
705C2×C22⋊C4—2232no—
706C2×C22⋊C4—224no—
707C2×C22⋊C4—224no—
708C2×C22⋊C4—224no—
709C2×C22⋊C4—224no—
710C2×C22⋊C4—224no—
711C2×C22⋊C4—224no—
712C2×C22⋊C4—224no—
713C2×C22⋊C4—224no—
714C2×C22⋊C4—224no—
715C2×C22⋊C4—224no—
716C2×C22⋊C4C22×D1114yes—
717C2×C22⋊C4C22×D1114yes—
718C2×C22⋊C4C22×D1114yescomplemented
719C2×C22⋊C4C22×D1114yescomplemented
720C2×C42—42no—
721C2×C42—114no—
722C2×C42—442no—
723C2×C42C22×D1114yescomplemented
724#95—114no—
725#95—114no—
726C2×C11—44no—
727C2×C11—82no—
728C2×C11#253918yescomplemented
729C2×C11C2×#52511yescharacteristic
730C2×C11C22×#12711yescharacteristic
731C2×C11C2×#53411yescharacteristic
732C2×C11C2×#54611yescharacteristic
733C2×C11C2×#54611yescharacteristic
734C2×C11C2×#54611yescharacteristic
735C2×C11C2×#54611yescharacteristic
736D11—28no—
737D11—44no—
738D11—82no—
739C24—22no—
740C24—22no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—114no—
753C24—114no—
754C24—114no—
755C24—112no—
756C24—114no—
757C24—112no—
758C24—112no—
759C24—228no—
760C24—228no—
761C24—228no—
762C24—228no—
763C24—2232no—
764C24—222no—
765C24—222no—
766C24—222no—
767C24—222no—
768C24—228no—
769C24—222no—
770C24—222no—
771C24—222no—
772C24—222no—
773C24—222no—
774C24—222no—
775C24—222no—
776C24—222no—
777C24—222no—
778C24—222no—
779C24—222no—
780C24—222no—
781C24—222no—
782C24—444no—
783C24—444no—
784C24—4416no—
785C24—4416no—
786C24—4416no—
787C24—4416no—
788C24—4416no—
789C24—4416no—
790C24#433914yes—
791C24C23×D1112yes—
792C24C23×D1112yes—
793C24C23×D1111yescharacteristic
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—44no—
797C2×D4—416no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—228no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—444no—
812C2×D4—4416no—
813C2×D4—4416no—
814C2×D4—444no—
815C2×D4—444no—
816C2×D4—444no—
817C2×D4—444no—
818C2×D4—4416no—
819C2×D4—4416no—
820C2×D4—4416no—
821C2×D4—4416no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—114no—
835C22×C4—114no—
836C22×C4—114no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—1116no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—228no—
844C22×C4—228no—
845C22×C4—228no—
846C22×C4—222no—
847C22×C4—222no—
848C22×C4—222no—
849C22×C4—222no—
850C22×C4—222no—
851C22×C4—222no—
852C22×C4—222no—
853C22×C4—222no—
854C22×C4—222no—
855C22×C4—222no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—4416no—
859C22×C4—444no—
860C22×C4—444no—
861C22×C4—4416no—
862C22×C4D4×D1114yes—
863C22×C4D4×D1114yes—
864C22×C4D4×D1114yes—
865C22×C4C23×D1112yes—
866C22×C4C23×D1112yes—
867C22×C4C23×D1112yes—
868C22×C4C23×D1112yes—
869C22×C4C23×D1112yes—
870C4⋊C4—28no—
871C4⋊C4—228no—
872C4⋊C4—228no—
873C4⋊C4—228no—
874C4⋊C4—228no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—1116no—
880C22⋊C4—1116no—
881C22⋊C4—228no—
882C22⋊C4—228no—
883C22⋊C4—228no—
884C22⋊C4—228no—
885C22⋊C4—228no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—228no—
891C42—44no—
892C42—444no—
893C11C2×#253911yescharacteristic, complemented, Sylow
894C23—28no—
895C23—28no—
896C23—28no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—1116no—
922C23—114no—
923C23—114no—
924C23—114no—
925C23—114no—
926C23—2232no—
927C23—228no—
928C23—228no—
929C23—228no—
930C23—228no—
931C23—228no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—228no—
937C23—228no—
938C23—228no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—228no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—4416no—
954C23—4416no—
955C23—4416no—
956C23—4416no—
957C23—4416no—
958C23—4416no—
959C23—44128no—
960C23—444no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—444no—
965C23—444no—
966C23—444no—
967C23—444no—
968C23—444no—
969C23—444no—
970C23—444no—
971C23C2×#433914yes—
972C23C2×#433912yes—
973C23C2×D4×D1112yes—
974C23C2×D4×D1112yes—
975C23C2×D4×D1112yes—
976C23#6703712yes—
977C23#41×D1112yes—
978C23#6704212yes—
979C23C24×D1111yescharacteristic
980D4—416no—
981D4—4416no—
982D4—4416no—
983D4—4416no—
984D4—4416no—
985D4—4416no—
986D4—4416no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—28no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—114no—
1005C2×C4—114no—
1006C2×C4—114no—
1007C2×C4—228no—
1008C2×C4—228no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—228no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—4416no—
1023C2×C4—4416no—
1024C2×C4—444no—
1025C2×C4—444no—
1026C2×C4C2×D4×D1114yes—
1027C2×C4C2×D4×D1114yes—
1028C2×C4C2×D4×D1114yes—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—416no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—88no—
1045C22—118no—
1046C22—224no—
1047C22—224no—
1048C22—2232no—
1049C22—224no—
1050C22—224no—
1051C22—224no—
1052C22—224no—
1053C22—224no—
1054C22—224no—
1055C22—224no—
1056C22—4464no—
1057C22—442no—
1058C22—442no—
1059C22—4416no—
1060C22—442no—
1061C22—442no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—888no—
1070C22#1062302114yes—
1071C22#1062307814yes—
1072C22#1062308114yes—
1073C22#1062313614yes—
1074C22#1062314114yes—
1075C22#1062320714yes—
1076C22D11×#12714yes—
1077C22C22×#433911yescharacteristic
1078C22C22×D4×D1111yescharacteristic
1079C22C22×D4×D1111yescharacteristic
1080C22C22×D4×D1111yescharacteristic
1081C22C2×#6703711yescharacteristic
1082C22C2×#41×D1111yescharacteristic
1083C22C2×#6704211yescharacteristic
1084C4—24no—
1085C4—24no—
1086C4—24no—
1087C4—42no—
1088C4—42no—
1089C4—224no—
1090C4—224no—
1091C4—224no—
1092C4—442no—
1093C4—442no—
1094C2—44no—
1095C2—82no—
1096C2—228no—
1097C2—444no—
1098C2—882no—
1099C2#1307354518yesdirect product factor
1100C2C2×#1062307811yescharacteristic
1101C2C2×D11×#12711yescharacteristic
1102C2C2×#1062313611yescharacteristic
1103C2C2×#1062314111yescharacteristic
1104C2C2×#1062302111yescharacteristic
1105C2C2×#1062320711yescharacteristic
1106C2C2×#1062308111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
hypercenterC2×#390D11
hypocenterC11C2×#2539
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66936C2semidirect
3. C22×#66937C2semidirect
4. C22×#66935C2semidirect
5. C22×#66990C2semidirect
6. C22×C22⋊C4×D11C2semidirect
7. #13073545C2direct (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×(C2×D11)⋊C4C2semidirect
16. C2×C11×#390C2semidirect
22. C23×C22⋊D11C22semidirect
27. C22×C11×C4⋊C4C22semidirect
30. C22×C11×C22⋊C4C22semidirect
31. C22×C11×C22⋊C4C22semidirect
32. C22×C42×C11C22semidirect
35. C22×C22⋊Dic11C22semidirect
37. C2×#66990C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×(C2×D11)⋊C4C22semidirect
46. C22×(C2×D11)⋊C4C22semidirect
47. C22×C4⋊Dic11C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×Dic11⋊C4C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×#66947C22semidirect
55. C2×#66937C22semidirect
57. C2×#66936C22semidirect
59. C2×#66935C22semidirect
61. C2×C22⋊C4×D11C22semidirect
62. C11×#390C22semidirect
63. #10622836C22semidirect
64. C2×C11⋊#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622605C22semidirect
67. #10622573C22semidirect
68. #10622570C22semidirect
69. #10622570C22semidirect
70. #10622562C22semidirect
71. #10622552C22semidirect
72. C4×(C2×D11)⋊C4C22semidirect
110. C22×C22⋊D11C23semidirect
129. C22×C4×D11D4semidirect
133. C2×C11×C4⋊C4C23semidirect
140. C2×C11×C22⋊C4C23semidirect
141. C2×C11×C22⋊C4C23semidirect
143. C2×C42×C11C23semidirect
149. C2×C22⋊Dic11C23semidirect
158. C2×(C2×D11)⋊C4D4semidirect
159. C2×(C2×D11)⋊C4D4semidirect
166. C2×(C2×D11)⋊C4C23semidirect
167. C2×(C2×D11)⋊C4C23semidirect
168. C2×(C2×D11)⋊C4C23semidirect
170. C2×C4⋊Dic11C23semidirect
174. C2×Dic11⋊C4C23semidirect
175. C2×Dic11⋊C4C23semidirect
176. C2×Dic11⋊C4C23semidirect
178. C2×C4×Dic11C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
317. C2×C4×D11C2×D4semidirect
334. (C2×D11)⋊C4C2×D4semidirect
335. (C2×D11)⋊C4C2×D4semidirect
355. C2×#390D11semidirect
516. C22×C4⋊C4C2×D11semidirect
533. C22×C22⋊C4C2×D11semidirect
534. C22×C22⋊C4C2×D11semidirect
536. C22×C42C2×D11semidirect
544. #390C2×D11semidirect
686. C2×C4⋊C4C22×D11semidirect
718. C2×C22⋊C4C22×D11semidirect
719. C2×C22⋊C4C22×D11semidirect
723. C2×C42C22×D11semidirect
728. C2×C11#2539semidirect
893. C11C2×#2539semidirect
1099. C2#13073545direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669362
C22×#669372
C22×#669352
C22×#669902
C22×C22⋊C4×D112
#130735452
C2×#106225622
C2×#106226052
C2×#106225732
C2×#106228362
C2×#106225522
C2×#106225702
C2×C4×(C2×D11)⋊C42
C2×C11×#3902
C2×#253911