Finite Group Databasebeta

← C2×#13072157 #14921242

Subgroups — C2×#13072157 #14921242

Order 2816.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic, complemented
4C22×#66935C211yesmaximal, characteristic, complemented
5C22×C4×D44C211yesmaximal, characteristic, complemented
6C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
7#13072157C2116yesmaximal, direct product factor
8C2×#10622607C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622284C211yesmaximal, characteristic, complemented
12C2×#10622552C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622278C211yesmaximal, characteristic, complemented
15C2×#10622281C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×D44C2211yescharacteristic, complemented
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic, complemented
33C22×C22⋊Dic11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×C4⋊Dic11C2211yescharacteristic, complemented
46C22×C4⋊Dic11C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C2×#66948—28no—
49C2×#66948C2218yescomplemented
50C2×#66937—28no—
51C2×#66937C2218yescomplemented
52C2×#66935—28no—
53C2×#66935—28no—
54C2×#66935C2218yescomplemented
55C2×#66935C2218yescomplemented
56C2×C22⋊C4×D11—28no—
57C2×C22⋊C4×D11C2218yescomplemented
58C2×C4×D44—28no—
59C2×C4×D44C2218yescomplemented
60C11×#388C2218yescomplemented
61C2×C11×#95C2211yescharacteristic, complemented
62C2×C11×#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622607C2218yescomplemented
66#10622574C2218yescomplemented
67#10622574C2218yescomplemented
68#10622552C2218yescomplemented
69#10622284C2218yescomplemented
70#10622281C2218yescomplemented
71#10622278C2218yescomplemented
72#10622278C2218yescomplemented
73C25×C11C2311yescharacteristic
74C24×D11—24no—
75C24×D11—24no—
76C24×D11—24no—
77C24×D11—24no—
78C24×D11—24no—
79C24×D11—42no—
80C24×D11—42no—
81C24×D11C2311yescharacteristic
82C24×D11C2311yescharacteristic
83C24×D11C2311yescharacteristic
84C24×D11C2314yes—
85C24×D11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
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—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—24no—
107C22×D44—24no—
108C22×D44—24no—
109C22×D44—24no—
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—24no—
113C22×D44—24no—
114C22×D44—24no—
115C22×D44—42no—
116C22×D44—42no—
117C22×D44—42no—
118C22×D44D418yescomplemented
119C22×D44C2314yes—
120C22×D44C2314yes—
121C22×D44C2314yes—
122C22×D44C2314yes—
123C22×D44C2314yescomplemented
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—24no—
128C22×C4×D11—24no—
129C22×C4×D11—24no—
130C22×C4×D11—42no—
131C22×C4×D11—42no—
132C22×C4×D11—42no—
133C22×C4×D11C2314yes—
134C22×C4×D11C2314yes—
135C22×C4×D11C2314yescomplemented
136C2×C11×C4⋊C4—24no—
137C2×C11×C4⋊C4C2314yescomplemented
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4—24no—
140C2×C11×C22⋊C4D418yescomplemented
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C42×C11—24no—
145C2×C42×C11C2314yescomplemented
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11C2314yes—
148C2×(C2×D11)⋊C4—24no—
149C2×(C2×D11)⋊C4—24no—
150C2×(C2×D11)⋊C4—24no—
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—42no—
158C2×(C2×D11)⋊C4D418yescomplemented
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yescomplemented
166C2×(C2×D11)⋊C4C2314yescomplemented
167C2×(C2×D11)⋊C4C2314yescomplemented
168C2×(C2×D11)⋊C4C2314yescomplemented
169C2×(C2×D11)⋊C4C2314yescomplemented
170C2×C4⋊Dic11—24no—
171C2×C4⋊Dic11—42no—
172C2×C4⋊Dic11C2314yescomplemented
173C2×C4⋊Dic11C2314yescomplemented
174C2×Dic11⋊C4—24no—
175C2×Dic11⋊C4C2314yescomplemented
176#66948—232no—
177#66937—232no—
178#66935—232no—
179#66935—232no—
180C22⋊C4×D11—232no—
181C4×D44—232no—
182C11×#95C2314yescomplemented
183C11×#95C2314yescomplemented
184C11⋊#95C2314yescomplemented
185C11⋊#95C2314yescomplemented
186C2×#2424—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11C2×D414yes—
194C24×C11C2412yes—
195C24×C11C2411yescharacteristic
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11—232no—
201C23×D11—28no—
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—22no—
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—28no—
215C23×D11—28no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—28no—
224C23×D11—28no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11—416no—
228C23×D11—416no—
229C23×D11—416no—
230C23×D11—416no—
231C23×D11—416no—
232C23×D11—416no—
233C23×D11C2×D414yes—
234C23×D11C2×D414yes—
235C23×D11C2×D414yes—
236C23×D11#4114yes—
237C23×D11#4114yes—
238C23×D11C2412yes—
239C23×D11C2412yes—
240C23×D11C2412yes—
241C23×D11C2412yes—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
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×C11C2×D414yes—
257C22×C4×C11C2×D414yes—
258C22×C4×C11C2×D414yes—
259C22×C4×C11C2×D414yes—
260C22×C4×C11C2412yes—
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—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—416no—
273C2×C22⋊D11—416no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11C2×D414yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C2×D44—232no—
291C2×D44—28no—
292C2×D44—28no—
293C2×D44—28no—
294C2×D44—28no—
295C2×D44—28no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44—28no—
299C2×D44—28no—
300C2×D44—28no—
301C2×D44—28no—
302C2×D44—44no—
303C2×D44—44no—
304C2×D44—44no—
305C2×D44—416no—
306C2×D44—416no—
307C2×D44—416no—
308C2×D44—416no—
309C2×D44C2×D4116yescomplemented
310C2×C4×D11—28no—
311C2×C4×D11—28no—
312C2×C4×D11—28no—
313C2×C4×D11—28no—
314C2×C4×D11—28no—
315C2×C4×D11—28no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—416no—
320C2×C4×D11—416no—
321C2×C4×D11—416no—
322C11×C4⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—28no—
325C11×C22⋊C4C2×D4116yescomplemented
326C42×C11—28no—
327C22⋊Dic11—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)⋊C4—28no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—28no—
337(C2×D11)⋊C4—44no—
338(C2×D11)⋊C4C2×D4116yescomplemented
339C4⋊Dic11—28no—
340C4⋊Dic11—44no—
341Dic11⋊C4—28no—
342C22×#121—111no—
343C22×#121—111no—
344C22×#120—111no—
345C22×#120—111no—
346C22×C4×D4—111no—
347C23×C22⋊C4—111no—
348#2424—1116no—
349C2×#396—111no—
350C2×#394—111no—
351C2×#394—111no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#388D1111yescharacteristic, complemented
355C2×#386—111no—
356C2×#386—111no—
357C2×#385—111no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—28no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11C22×D414yes—
372C23×C11C22×D412yes—
373C23×C11C22×D412yes—
374C23×C11C22×D412yes—
375C23×C11C2×#4112yes—
376C23×C11C2×#4112yes—
377C23×C11H(5,𝔽2)12yes—
378C23×C11H(5,𝔽2)12yes—
379C23×C11C2511yescharacteristic
380C22×D11—28no—
381C22×D11—28no—
382C22×D11—28no—
383C22×D11—28no—
384C22×D11—28no—
385C22×D11—28no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—232no—
391C22×D11—28no—
392C22×D11—28no—
393C22×D11—28no—
394C22×D11—28no—
395C22×D11—28no—
396C22×D11—28no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
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—416no—
417C22×D11—416no—
418C22×D11—416no—
419C22×D11—416no—
420C22×D11—4128no—
421C22×D11—416no—
422C22×D11—44no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
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#121116yescomplemented
439C22×D11C22×D414yes—
440C22×D11C22×D414yes—
441C22×D11C22×D414yes—
442C22×D11C2×#4114yes—
443C22×D11C2×#4114yes—
444C2×C4×C11—28no—
445C2×C4×C11—28no—
446C2×C4×C11—28no—
447C2×C4×C11—28no—
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—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—44no—
463C2×C4×C11—44no—
464C2×C4×C11C22×D414yes—
465C2×C4×C11C22×D414yes—
466C2×C4×C11C22×D414yes—
467C2×C4×C11C22×D414yes—
468C22⋊D11—416no—
469C22⋊D11—416no—
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—44no—
483C2×Dic11—44no—
484C2×Dic11—44no—
485C2×Dic11C22×D414yes—
486D44—232no—
487D44—416no—
488D44—416no—
489D44—416no—
490D44—416no—
491C4×D11—416no—
492C4×D11—416no—
493C4×D11—416no—
494C26—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4—111no—
500C23×D4—111no—
501C23×D4—111no—
502C24×C4—111no—
503C24×C4—111no—
504C24×C4—111no—
505C2×#121—118no—
506C2×#121—118no—
507C2×#121—228no—
508C2×#121—228no—
509C2×#120—118no—
510C2×#120—118no—
511C2×#120—228no—
512C2×#120—228no—
513C2×C4×D4—118no—
514C2×C4×D4—228no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C4⋊C4C2×D1111yescharacteristic, complemented
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—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—118no—
532C22×C22⋊C4—228no—
533C22×C22⋊C4C2×D1111yescharacteristic
534C22×C22⋊C4C2×D1111yescharacteristic
535C22×C22⋊C4C2×D1111yescharacteristic
536C22×C42C2×D1111yescharacteristic, complemented
537#396—118no—
538#394—118no—
539#394—118no—
540#392—118no—
541#390—118no—
542#388C2×D1118yescomplemented
543#386—118no—
544#386—118no—
545#385—118no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95C2×D1111yescharacteristic, complemented
549C2×#95C2×D1111yescharacteristic, complemented
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—24no—
553C22×C11—42no—
554C22×C11—416no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11C2×#12114yes—
559C22×C11#52514yes—
560C22×C11#53814yes—
561C22×C11D4214yes—
562C22×C11D4214yes—
563C22×C11#54614yes—
564C22×C11#54614yes—
565C22×C11C23×D411yescharacteristic
566C22×C11C23×D411yescharacteristic
567C22×C11C23×D411yescharacteristic
568C22×C11C22×#4111yescharacteristic
569C22×C11C22×#4111yescharacteristic
570C22×C11C2×H(5,𝔽2)11yescharacteristic
571C22×C11C2×H(5,𝔽2)11yescharacteristic
572C2×D11—24no—
573C2×D11—232no—
574C2×D11—24no—
575C2×D11—24no—
576C2×D11—24no—
577C2×D11—24no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—464no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—416no—
589C2×D11—416no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—88no—
604C2×D11C2×#12118yescomplemented
605C4×C11—24no—
606C4×C11—24no—
607C4×C11—24no—
608C4×C11—24no—
609C4×C11—42no—
610C4×C11—42no—
611Dic11—24no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615C25—111no—
616C25—111no—
617C25—111no—
618C25—111no—
619C25—114no—
620C25—224no—
621C25—224no—
622C25—224no—
623C25—224no—
624C25—224no—
625C25—442no—
626C25—442no—
627C25C22×D1111yescharacteristic
628C22×D4—114no—
629C22×D4—114no—
630C22×D4—118no—
631C22×D4—114no—
632C22×D4—114no—
633C22×D4—114no—
634C22×D4—114no—
635C22×D4—114no—
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—224no—
649C22×D4—224no—
650C22×D4—224no—
651C22×D4—442no—
652C22×D4—442no—
653C22×D4—442no—
654C22×D4—442no—
655C22×D4—442no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—114no—
661C23×C4—114no—
662C23×C4—114no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—224no—
666C23×C4—224no—
667C23×C4—224no—
668C23×C4—224no—
669C23×C4—442no—
670C23×C4—442no—
671C23×C4—442no—
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678#121—2232no—
679#121—2232no—
680#120—2232no—
681#120—2232no—
682C4×D4—2232no—
683C2×C4⋊C4—24no—
684C2×C4⋊C4—114no—
685C2×C4⋊C4—114no—
686C2×C4⋊C4—114no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—442no—
690C2×C4⋊C4C22×D1114yescomplemented
691C2×C22⋊C4—24no—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—118no—
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—114no—
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⋊C4—2232no—
717C2×C22⋊C4—442no—
718C2×C22⋊C4D4418yescomplemented
719C2×C22⋊C4C22×D1114yes—
720C2×C22⋊C4C22×D1114yes—
721C2×C22⋊C4C22×D1114yes—
722C2×C42—24no—
723C2×C42C22×D1114yescomplemented
724#95—114no—
725#95—114no—
726#95C22×D1114yescomplemented
727#95C22×D1114yescomplemented
728C2×C11—44no—
729C2×C11#242418yescomplemented
730C2×C11C22×#12111yescharacteristic
731C2×C11C2×#52511yescharacteristic
732C2×C11C2×#53811yescharacteristic
733C2×C11C2×D4211yescharacteristic
734C2×C11C2×D4211yescharacteristic
735C2×C11C2×#54611yescharacteristic
736C2×C11C2×#54611yescharacteristic
737D11—28no—
738D11—44no—
739D11—44no—
740D11—82no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—114no—
748C24—114no—
749C24—114no—
750C24—112no—
751C24—114no—
752C24—114no—
753C24—112no—
754C24—112no—
755C24—112no—
756C24—228no—
757C24—228no—
758C24—228no—
759C24—228no—
760C24—2232no—
761C24—222no—
762C24—222no—
763C24—222no—
764C24—222no—
765C24—228no—
766C24—222no—
767C24—222no—
768C24—222no—
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—222no—
783C24—222no—
784C24—222no—
785C24—444no—
786C24—444no—
787C24—4416no—
788C24—4416no—
789C24—4416no—
790C24—4416no—
791C24—4416no—
792C24—4416no—
793C24C2×D4414yes—
794C24C23×D1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—1116no—
797C2×D4—228no—
798C2×D4—2232no—
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—228no—
812C2×D4—228no—
813C2×D4—444no—
814C2×D4—444no—
815C2×D4—444no—
816C2×D4—4416no—
817C2×D4—4416no—
818C2×D4—4416no—
819C2×D4—4416no—
820C2×D4—444no—
821C2×D4—444no—
822C2×D4—4416no—
823C2×D4—4416no—
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—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—114no—
839C22×C4—112no—
840C22×C4—112no—
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—228no—
858C22×C4—228no—
859C22×C4—228no—
860C22×C4—444no—
861C22×C4—444no—
862C22×C4—444no—
863C22×C4—4416no—
864C22×C4—4416no—
865C22×C4—4416no—
866C22×C4C2×D4414yes—
867C22×C4C2×D4414yes—
868C22×C4D4×D1114yes—
869C22×C4D4×D1114yes—
870C22×C4C23×D1112yes—
871C22×C4C23×D1112yes—
872C22×C4C23×D1112yes—
873C22×C4C23×D1112yes—
874C22×C4C23×D1112yes—
875C22×C4C23×D1112yes—
876C4⋊C4—28no—
877C4⋊C4—228no—
878C4⋊C4—228no—
879C4⋊C4—444no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—1116no—
883C22⋊C4—228no—
884C22⋊C4—228no—
885C22⋊C4—228no—
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—228no—
891C22⋊C4—228no—
892C22⋊C4—228no—
893C22⋊C4—444no—
894C22⋊C4C2×D44116yescomplemented
895C42—28no—
896C11C2×#242411yescharacteristic, complemented, Sylow
897C23—28no—
898C23—28no—
899C23—28no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—44no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—1116no—
911C23—114no—
912C23—114no—
913C23—114no—
914C23—114no—
915C23—114no—
916C23—2232no—
917C23—228no—
918C23—228no—
919C23—228no—
920C23—228no—
921C23—228no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—228no—
927C23—228no—
928C23—228no—
929C23—228no—
930C23—228no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—228no—
944C23—228no—
945C23—222no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—4416no—
953C23—4416no—
954C23—4416no—
955C23—4416no—
956C23—4416no—
957C23—44128no—
958C23—4416no—
959C23—444no—
960C23—444no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—444no—
965C23—444no—
966C23—444no—
967C23—444no—
968C23—444no—
969C23—444no—
970C23—444no—
971C23—444no—
972C23—444no—
973C23—444no—
974C23C22×D4414yes—
975C23C22×D4412yes—
976C23C2×D4×D1112yes—
977C23C2×D4×D1112yes—
978C23#41×D1112yes—
979C23#41×D1112yes—
980C23#6704212yes—
981C23#6704212yes—
982C23C24×D1111yescharacteristic
983D4—2232no—
984D4—4416no—
985D4—4416no—
986D4—4416no—
987D4—4416no—
988D4—4416no—
989D4—4416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
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—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—114no—
1011C2×C4—228no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—4416no—
1024C2×C4—4416no—
1025C2×C4—4416no—
1026C2×C4—444no—
1027C2×C4—444no—
1028C2×C4—444no—
1029C2×C4C22×D4414yes—
1030C2×C4C22×D4414yes—
1031C2×C4C2×D4×D1114yes—
1032C2×C4C2×D4×D1114yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—416no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—118no—
1042C22—224no—
1043C22—2232no—
1044C22—224no—
1045C22—224no—
1046C22—224no—
1047C22—224no—
1048C22—224no—
1049C22—224no—
1050C22—224no—
1051C22—224no—
1052C22—224no—
1053C22—224no—
1054C22—224no—
1055C22—4464no—
1056C22—442no—
1057C22—4416no—
1058C22—4416no—
1059C22—442no—
1060C22—442no—
1061C22—442no—
1062C22—442no—
1063C22—442no—
1064C22—442no—
1065C22—442no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22—888no—
1074C22#1062305514yes—
1075C22D4×D4414yes—
1076C22D4×D4414yes—
1077C22D11×#12114yes—
1078C22#1062318514yes—
1079C22#1062320714yes—
1080C22#1062323514yes—
1081C22C23×D4411yescharacteristic
1082C22C22×D4×D1111yescharacteristic
1083C22C22×D4×D1111yescharacteristic
1084C22C2×#41×D1111yescharacteristic
1085C22C2×#41×D1111yescharacteristic
1086C22C2×#6704211yescharacteristic
1087C22C2×#6704211yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—42no—
1093C4—42no—
1094C4—224no—
1095C4—442no—
1096C4—442no—
1097C4—442no—
1098C2—44no—
1099C2—228no—
1100C2—444no—
1101C2—444no—
1102C2—882no—
1103C2#1307215718yesdirect product factor
1104C2C2×D11×#12111yescharacteristic
1105C2C2×#1062305511yescharacteristic
1106C2C2×#1062323511yescharacteristic
1107C2C2×D4×D4411yescharacteristic
1108C2C2×D4×D4411yescharacteristic
1109C2C2×#1062318511yescharacteristic
1110C2C2×#1062320711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
hypercenterC2×#388D11
hypocenterC11C2×#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66937C2semidirect
3. C22×#66935C2semidirect
4. C22×#66935C2semidirect
5. C22×C4×D44C2semidirect
6. C22×C22⋊C4×D11C2semidirect
7. #13072157C2direct (N × H)
8. C2×#10622607C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622284C2semidirect
12. C2×#10622552C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622278C2semidirect
15. C2×#10622281C2semidirect
16. C2×C11×#388C2semidirect
24. C23×D44C22semidirect
27. C23×C4×D11C22semidirect
28. C22×C11×C4⋊C4C22semidirect
32. C22×C42×C11C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×(C2×D11)⋊C4C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×C4⋊Dic11C22semidirect
46. C22×C4⋊Dic11C22semidirect
47. C22×Dic11⋊C4C22semidirect
49. C2×#66948C22semidirect
51. C2×#66937C22semidirect
54. C2×#66935C22semidirect
55. C2×#66935C22semidirect
57. C2×C22⋊C4×D11C22semidirect
59. C2×C4×D44C22semidirect
60. C11×#388C22semidirect
61. C2×C11×#95C22semidirect
62. C2×C11×#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622607C22semidirect
66. #10622574C22semidirect
67. #10622574C22semidirect
68. #10622552C22semidirect
69. #10622284C22semidirect
70. #10622281C22semidirect
71. #10622278C22semidirect
72. #10622278C22semidirect
118. C22×D44D4semidirect
123. C22×D44C23semidirect
135. C22×C4×D11C23semidirect
137. C2×C11×C4⋊C4C23semidirect
140. C2×C11×C22⋊C4D4semidirect
145. C2×C42×C11C23semidirect
158. C2×(C2×D11)⋊C4D4semidirect
165. C2×(C2×D11)⋊C4C23semidirect
166. C2×(C2×D11)⋊C4C23semidirect
167. C2×(C2×D11)⋊C4C23semidirect
168. C2×(C2×D11)⋊C4C23semidirect
169. C2×(C2×D11)⋊C4C23semidirect
172. C2×C4⋊Dic11C23semidirect
173. C2×C4⋊Dic11C23semidirect
175. C2×Dic11⋊C4C23semidirect
182. C11×#95C23semidirect
183. C11×#95C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
309. C2×D44C2×D4semidirect
325. C11×C22⋊C4C2×D4semidirect
338. (C2×D11)⋊C4C2×D4semidirect
354. C2×#388D11semidirect
438. C22×D11#121semidirect
518. C22×C4⋊C4C2×D11semidirect
536. C22×C42C2×D11semidirect
542. #388C2×D11semidirect
548. C2×#95C2×D11semidirect
549. C2×#95C2×D11semidirect
604. C2×D11C2×#121semidirect
690. C2×C4⋊C4C22×D11semidirect
718. C2×C22⋊C4D44semidirect
723. C2×C42C22×D11semidirect
726. #95C22×D11semidirect
727. #95C22×D11semidirect
729. C2×C11#2424semidirect
894. C22⋊C4C2×D44semidirect
896. C11C2×#2424semidirect
1103. C2#13072157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669372
C22×#669352
C22×C4×D442
C22×C22⋊C4×D112
#130721572
C2×#106226072
C2×#106225742
C2×#106222842
C2×#106225522
C2×#106222782
C2×#106222812
C2×C11×#3882
C2×#242411