Finite Group Databasebeta

← C2×#13072148 #14921237

Subgroups — C2×#13072148 #14921237

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×#66992C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C22×#67006C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5C23×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13072148C2116yesmaximal, direct product factor
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622834C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×#10622563C211yesmaximal, characteristic, complemented
16C22×C11×#120C211yesmaximal, characteristic, complemented
17C26×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic, complemented
25C24×Dic11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C2×C11×#120—28no—
29C2×C11×#120C2218yescomplemented
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C2×#67006—28no—
34C2×#67006C2218yescomplemented
35C22×C22⋊Dic11—28no—
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C22×C22⋊Dic11C2211yescharacteristic
41C22×C22⋊Dic11C2211yescharacteristic
42C22×C22⋊Dic11C2211yescharacteristic
43C22×C22⋊Dic11C2218yescomplemented
44C22×C22⋊Dic11C2211yescharacteristic, complemented
45C22×C22⋊Dic11C2211yescharacteristic, complemented
46C22×C22⋊Dic11C2211yescharacteristic, complemented
47C2×#66992—28no—
48C2×#66992C2218yescomplemented
49C2×#66991—28no—
50C2×#66991C2218yescomplemented
51C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
52C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
53C22×C4⋊Dic11C2211yescharacteristic, complemented
54C22×C4⋊Dic11C2211yescharacteristic, complemented
55C22×Dic11⋊C4C2211yescharacteristic, complemented
56C22×Dic11⋊C4C2211yescharacteristic, complemented
57C22×C4×Dic11C2211yescharacteristic, complemented
58C2×(C22⋊D11)⋊C4—28no—
59C2×(C22⋊D11)⋊C4C2218yescomplemented
60#10622836C2218yescomplemented
61#10622835C2218yescomplemented
62#10622834C2218yescomplemented
63#10622833C2218yescomplemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67C2×C11⋊#95C2211yescharacteristic, complemented
68#10622574C2218yescomplemented
69#10622569C2218yescomplemented
70#10622563C2218yescomplemented
71#10622561C2218yescomplemented
72#10622557C2218yescomplemented
73C25×C11—24no—
74C25×C11—24no—
75C25×C11—24no—
76C25×C11—24no—
77C25×C11—24no—
78C25×C11—42no—
79C25×C11—42no—
80C25×C11C2311yescharacteristic
81C25×C11C2311yescharacteristic
82C25×C11C2311yescharacteristic
83C25×C11C2314yes—
84C25×C11C2311yescharacteristic
85C24×D11C2311yescharacteristic
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—24no—
90C22×D4×C11—24no—
91C22×D4×C11—24no—
92C22×D4×C11—24no—
93C22×D4×C11—42no—
94C22×D4×C11—42no—
95C22×D4×C11C2314yes—
96C22×D4×C11C2314yes—
97C22×D4×C11C2314yes—
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11—24no—
109C22×C22⋊D11—42no—
110C22×C22⋊D11—42no—
111C22×C22⋊D11—42no—
112C22×C22⋊D11D418yescomplemented
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2314yes—
116C22×C22⋊D11C2314yescomplemented
117C23×Dic11—24no—
118C23×Dic11—24no—
119C23×Dic11—24no—
120C23×Dic11—24no—
121C23×Dic11—42no—
122C23×Dic11—42no—
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic
127C23×Dic11C2314yes—
128C23×Dic11C2314yes—
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—42no—
135C22×C4×D11C2314yescomplemented
136C11×#120—232no—
137C2×C11×C22⋊C4—24no—
138C2×C11×C22⋊C4—24no—
139C2×C11×C22⋊C4D418yescomplemented
140C2×C11×C22⋊C4C2314yes—
141C2×C11×C22⋊C4C2314yes—
142C2×C11×C22⋊C4C2314yes—
143#67006—232no—
144C2×C22⋊Dic11—24no—
145C2×C22⋊Dic11—24no—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11—24no—
148C2×C22⋊Dic11—24no—
149C2×C22⋊Dic11—24no—
150C2×C22⋊Dic11—24no—
151C2×C22⋊Dic11—24no—
152C2×C22⋊Dic11—232no—
153C2×C22⋊Dic11—42no—
154C2×C22⋊Dic11D418yescomplemented
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C2314yes—
157C2×C22⋊Dic11C2314yes—
158C2×C22⋊Dic11C2314yes—
159C2×C22⋊Dic11C2314yes—
160C2×C22⋊Dic11C2314yes—
161C2×C22⋊Dic11C2314yes—
162C2×C22⋊Dic11C2314yescomplemented
163C2×C22⋊Dic11C2314yescomplemented
164C2×C22⋊Dic11C2314yescomplemented
165#66992—232no—
166#66991—232no—
167C2×(C2×D11)⋊C4—24no—
168C2×(C2×D11)⋊C4—24no—
169C2×(C2×D11)⋊C4C2314yescomplemented
170C2×(C2×D11)⋊C4C2314yescomplemented
171C2×C4⋊Dic11—24no—
172C2×C4⋊Dic11—42no—
173C2×C4⋊Dic11C2314yescomplemented
174C2×C4⋊Dic11C2314yescomplemented
175C2×Dic11⋊C4—24no—
176C2×Dic11⋊C4—24no—
177C2×Dic11⋊C4C2314yescomplemented
178C2×Dic11⋊C4C2314yescomplemented
179C2×C4×Dic11—24no—
180C2×C4×Dic11C2314yescomplemented
181(C22⋊D11)⋊C4—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—232no—
192C24×C11—28no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—28no—
199C24×C11—28no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11—22no—
207C24×C11—22no—
208C24×C11—22no—
209C24×C11—28no—
210C24×C11—28no—
211C24×C11—22no—
212C24×C11—22no—
213C24×C11—22no—
214C24×C11—22no—
215C24×C11—22no—
216C24×C11—44no—
217C24×C11—44no—
218C24×C11—416no—
219C24×C11—416no—
220C24×C11—416no—
221C24×C11—416no—
222C24×C11—416no—
223C24×C11—416no—
224C24×C11C2×D414yes—
225C24×C11C2×D414yes—
226C24×C11C2×D414yes—
227C24×C11#4114yes—
228C24×C11#4114yes—
229C24×C11C2412yes—
230C24×C11C2412yes—
231C24×C11C2412yes—
232C24×C11C2412yes—
233C24×C11C2411yescharacteristic
234C23×D11—22no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—22no—
238C23×D11—22no—
239C23×D11—22no—
240C23×D11C2×D414yes—
241C23×D11C2412yes—
242C2×D4×C11—28no—
243C2×D4×C11—28no—
244C2×D4×C11—28no—
245C2×D4×C11—28no—
246C2×D4×C11—28no—
247C2×D4×C11—28no—
248C2×D4×C11—28no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—416no—
252C2×D4×C11—416no—
253C2×D4×C11—416no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11C2×D414yes—
262C22×C4×C11C2×D414yes—
263C22×C4×C11C2412yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—232no—
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—28no—
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⋊D11C2×D4116yescomplemented
282C22×Dic11—28no—
283C22×Dic11—28no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—28no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—28no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—22no—
301C22×Dic11—22no—
302C22×Dic11—22no—
303C22×Dic11—22no—
304C22×Dic11—44no—
305C22×Dic11—44no—
306C22×Dic11—416no—
307C22×Dic11—416no—
308C22×Dic11C2×D414yes—
309C22×Dic11C2×D414yes—
310C22×Dic11C2×D414yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C2×C4×D11—28no—
319C2×C4×D11—28no—
320C2×C4×D11—44no—
321C2×C4×D11—416no—
322C11×C22⋊C4—28no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4C2×D4116yescomplemented
325C22⋊Dic11—28no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—28no—
329C22⋊Dic11—28no—
330C22⋊Dic11—28no—
331C22⋊Dic11—28no—
332C22⋊Dic11—28no—
333C22⋊Dic11—44no—
334C22⋊Dic11C2×D4116yescomplemented
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—28no—
337C4⋊Dic11—28no—
338C4⋊Dic11—44no—
339Dic11⋊C4—28no—
340Dic11⋊C4—28no—
341C4×Dic11—28no—
342C22×#121—111no—
343C22×#121—111no—
344C22×#120—111no—
345C22×#120D1111yescharacteristic, complemented
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×#388—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#385—111no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—28no—
361C23×C11—28no—
362C23×C11—28no—
363C23×C11—28no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—232no—
369C23×C11—28no—
370C23×C11—28no—
371C23×C11—28no—
372C23×C11—28no—
373C23×C11—28no—
374C23×C11—28no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—416no—
395C23×C11—416no—
396C23×C11—416no—
397C23×C11—416no—
398C23×C11—4128no—
399C23×C11—416no—
400C23×C11—44no—
401C23×C11—44no—
402C23×C11—416no—
403C23×C11—44no—
404C23×C11—44no—
405C23×C11—44no—
406C23×C11—44no—
407C23×C11—44no—
408C23×C11—44no—
409C23×C11—44no—
410C23×C11—44no—
411C23×C11—44no—
412C23×C11—44no—
413C23×C11—44no—
414C23×C11—44no—
415C23×C11—44no—
416C23×C11#121116yescomplemented
417C23×C11C22×D414yes—
418C23×C11C22×D414yes—
419C23×C11C22×D412yes—
420C23×C11C22×D412yes—
421C23×C11C22×D414yes—
422C23×C11C22×D412yes—
423C23×C11C2×#4114yes—
424C23×C11C2×#4114yes—
425C23×C11C2×#4112yes—
426C23×C11C2×#4112yes—
427C23×C11H(5,𝔽2)12yes—
428C23×C11H(5,𝔽2)12yes—
429C23×C11C2511yescharacteristic
430C22×D11—28no—
431C22×D11—28no—
432C22×D11—28no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—44no—
440C22×D11—44no—
441C22×D11—44no—
442C22×D11—44no—
443C22×D11C22×D414yes—
444D4×C11—416no—
445D4×C11—416no—
446D4×C11—416no—
447C2×C4×C11—28no—
448C2×C4×C11—28no—
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—44no—
457C2×C4×C11C22×D414yes—
458C2×C4×C11C22×D414yes—
459C22⋊D11—232no—
460C22⋊D11—416no—
461C22⋊D11—416no—
462C22⋊D11—416no—
463C2×Dic11—28no—
464C2×Dic11—28no—
465C2×Dic11—28no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
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—22no—
484C2×Dic11—416no—
485C2×Dic11—416no—
486C2×Dic11—44no—
487C2×Dic11—44no—
488C2×Dic11—44no—
489C2×Dic11—44no—
490C2×Dic11C22×D414yes—
491C2×Dic11C22×D414yes—
492C2×Dic11C22×D414yes—
493C4×D11—416no—
494C26C2×D1111yescharacteristic
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4C2×D1111yescharacteristic
500C23×D4C2×D1111yescharacteristic
501C23×D4C2×D1111yescharacteristic
502C24×C4—111no—
503C24×C4—111no—
504C24×C4—111no—
505C2×#121—118no—
506C2×#121—118no—
507C2×#121—228no—
508C2×#121—228no—
509C2×#120—28no—
510C2×#120—118no—
511C2×#120—228no—
512C2×#120C2×D1118yescomplemented
513C2×C4×D4—118no—
514C2×C4×D4—228no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C4⋊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—118no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—228no—
533C22×C22⋊C4C2×D1111yescharacteristic
534C22×C22⋊C4C2×D1111yescharacteristic
535C22×C22⋊C4C2×D1111yescharacteristic
536C22×C42—111no—
537#396—118no—
538#394—118no—
539#394—118no—
540#392—118no—
541#390—118no—
542#388—118no—
543#386—118no—
544#386—118no—
545#385—118no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C22×C11—24no—
551C22×C11—232no—
552C22×C11—24no—
553C22×C11—24no—
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—24no—
559C22×C11—24no—
560C22×C11—24no—
561C22×C11—24no—
562C22×C11—24no—
563C22×C11—464no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—416no—
567C22×C11—416no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—88no—
582C22×C11C2×#12114yes—
583C22×C11C2×#12118yescomplemented
584C22×C11#52514yes—
585C22×C11#53814yes—
586C22×C11D4214yes—
587C22×C11D4214yes—
588C22×C11#54614yes—
589C22×C11#54614yes—
590C22×C11C23×D411yescharacteristic
591C22×C11C23×D411yescharacteristic
592C22×C11C23×D411yescharacteristic
593C22×C11C22×#4111yescharacteristic
594C22×C11C22×#4111yescharacteristic
595C22×C11C2×H(5,𝔽2)11yescharacteristic
596C22×C11C2×H(5,𝔽2)11yescharacteristic
597C2×D11—24no—
598C2×D11—24no—
599C2×D11—24no—
600C2×D11—42no—
601C2×D11—416no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C4×C11—24no—
606C4×C11—24no—
607C4×C11—42no—
608Dic11—24no—
609Dic11—24no—
610Dic11—24no—
611Dic11—42no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615C25—24no—
616C25—24no—
617C25—24no—
618C25—24no—
619C25—24no—
620C25—42no—
621C25—42no—
622C25—111no—
623C25C22×D1111yescharacteristic
624C25C22×D1111yescharacteristic
625C25C22×D1111yescharacteristic
626C25C22×D1114yes—
627C25C22×D1111yescharacteristic
628C22×D4—24no—
629C22×D4—24no—
630C22×D4—24no—
631C22×D4—24no—
632C22×D4—24no—
633C22×D4—24no—
634C22×D4—24no—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—118no—
638C22×D4—114no—
639C22×D4—114no—
640C22×D4—114no—
641C22×D4—114no—
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—442no—
651C22×D4—442no—
652C22×D4—442no—
653C22×D4C22×D1114yes—
654C22×D4C22×D1114yes—
655C22×D4C22×D1114yes—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—114no—
664C23×C4—114no—
665C23×C4—114no—
666C23×C4—224no—
667C23×C4—224no—
668C23×C4—224no—
669C23×C4—224no—
670C23×C4—224no—
671C23×C4—224no—
672C23×C4—442no—
673C23×C4—442no—
674C23×C4—442no—
675C23×C4C22×D1111yescharacteristic
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1111yescharacteristic
678#121—2232no—
679#121—2232no—
680#120—232no—
681#120—2232no—
682C4×D4—2232no—
683C2×C4⋊C4—114no—
684C2×C4⋊C4—114no—
685C2×C4⋊C4—114no—
686C2×C4⋊C4—114no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—224no—
690C2×C4⋊C4—442no—
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—2232no—
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—224no—
717C2×C22⋊C4—442no—
718C2×C22⋊C4C22⋊D1118yescomplemented
719C2×C22⋊C4C22×D1114yes—
720C2×C22⋊C4C22×D1114yes—
721C2×C22⋊C4C22×D1114yes—
722C2×C42—114no—
723C2×C42—224no—
724#95—114no—
725#95—114no—
726#95—114no—
727#95—114no—
728C2×C11—28no—
729C2×C11—44no—
730C2×C11—44no—
731C2×C11—82no—
732C2×C11#242418yescomplemented
733C2×C11C22×#12111yescharacteristic
734C2×C11C2×#52511yescharacteristic
735C2×C11C2×#53811yescharacteristic
736C2×C11C2×D4211yescharacteristic
737C2×C11C2×D4211yescharacteristic
738C2×C11C2×#54611yescharacteristic
739C2×C11C2×#54611yescharacteristic
740D11—44no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—232no—
746C24—28no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—28no—
751C24—28no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—22no—
757C24—22no—
758C24—22no—
759C24—22no—
760C24—22no—
761C24—22no—
762C24—22no—
763C24—28no—
764C24—22no—
765C24—22no—
766C24—22no—
767C24—22no—
768C24—28no—
769C24—22no—
770C24—44no—
771C24—44no—
772C24—416no—
773C24—416no—
774C24—416no—
775C24—416no—
776C24—416no—
777C24—416no—
778C24—114no—
779C24—112no—
780C24—222no—
781C24—222no—
782C24—222no—
783C24—222no—
784C24—222no—
785C24—222no—
786C24D4×D1114yes—
787C24D4×D1114yes—
788C24#434114yes—
789C24#434114yes—
790C24C2×C22⋊D1114yes—
791C24C23×D1112yes—
792C24C23×D1112yes—
793C24C23×D1112yes—
794C24C23×D1112yes—
795C24C23×D1111yescharacteristic
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—416no—
806C2×D4—416no—
807C2×D4—416no—
808C2×D4—1116no—
809C2×D4—228no—
810C2×D4—2232no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C2×D4—228no—
816C2×D4—228no—
817C2×D4—228no—
818C2×D4—444no—
819C2×D4—444no—
820C2×D4—444no—
821C2×D4—4416no—
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—114no—
832C22×C4—114no—
833C22×C4—114no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—112no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—228no—
842C22×C4—228no—
843C22×C4—228no—
844C22×C4—222no—
845C22×C4—222no—
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—228no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—222no—
860C22×C4—222no—
861C22×C4—222no—
862C22×C4—222no—
863C22×C4—228no—
864C22×C4—228no—
865C22×C4—444no—
866C22×C4—4416no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—4416no—
870C22×C4—4416no—
871C22×C4C2×C22⋊D1114yes—
872C22×C4C2×C22⋊D1114yes—
873C22×C4C23×D1112yes—
874C22×C4C23×D1112yes—
875C22×C4C23×D1112yes—
876C4⋊C4—228no—
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×C22⋊D11116yescomplemented
895C42—228no—
896C11C2×#242411yescharacteristic, complemented, Sylow
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—28no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—232no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—416no—
934C23—416no—
935C23—416no—
936C23—416no—
937C23—4128no—
938C23—416no—
939C23—44no—
940C23—44no—
941C23—416no—
942C23—44no—
943C23—44no—
944C23—44no—
945C23—44no—
946C23—44no—
947C23—44no—
948C23—44no—
949C23—44no—
950C23—44no—
951C23—44no—
952C23—44no—
953C23—44no—
954C23—44no—
955C23—114no—
956C23—228no—
957C23—228no—
958C23—228no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—444no—
966C23—444no—
967C23—444no—
968C23—444no—
969C23#66991116yescomplemented
970C23C2×D4×D1114yes—
971C23C2×D4×D1114yes—
972C23C2×D4×D1112yes—
973C23C2×D4×D1112yes—
974C23C2×#434114yes—
975C23C2×#434114yes—
976C23C2×#434112yes—
977C23C2×#434112yes—
978C23#6703712yes—
979C23#6703712yes—
980C23C22×C22⋊D1114yes—
981C23C22×C22⋊D1112yes—
982C23C24×D1111yescharacteristic
983D4—416no—
984D4—416no—
985D4—416no—
986D4—2232no—
987D4—4416no—
988D4—4416no—
989D4—4416no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—44no—
1000C2×C4—114no—
1001C2×C4—114no—
1002C2×C4—114no—
1003C2×C4—228no—
1004C2×C4—228no—
1005C2×C4—228no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
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—222no—
1024C2×C4—4416no—
1025C2×C4—4416no—
1026C2×C4—4416no—
1027C2×C4—444no—
1028C2×C4—444no—
1029C2×C4—444no—
1030C2×C4—444no—
1031C2×C4C22×C22⋊D1114yes—
1032C2×C4C22×C22⋊D1114yes—
1033C22—232no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—24no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—464no—
1047C22—416no—
1048C22—416no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—88no—
1065C22—224no—
1066C22—224no—
1067C22—224no—
1068C22—4416no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22#1062311714yes—
1074C22#1062312114yes—
1075C22#1062312214yes—
1076C22#1062312414yes—
1077C22C2×#6699114yes—
1078C22C2×#6699118yescomplemented
1079C22D4×C22⋊D1114yes—
1080C22#1062333714yes—
1081C22C22×D4×D1111yescharacteristic
1082C22C22×D4×D1111yescharacteristic
1083C22C22×#434111yescharacteristic
1084C22C22×#434111yescharacteristic
1085C22C2×#6703711yescharacteristic
1086C22C2×#6703711yescharacteristic
1087C22C23×C22⋊D1111yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—42no—
1091C4—224no—
1092C4—224no—
1093C4—224no—
1094C4—442no—
1095C4—442no—
1096C4—442no—
1097C4—442no—
1098C2—28no—
1099C2—44no—
1100C2—44no—
1101C2—82no—
1102C2—444no—
1103C2#1307214818yesdirect product factor
1104C2C22×#6699111yescharacteristic
1105C2C2×#1062311711yescharacteristic
1106C2C2×#1062312411yescharacteristic
1107C2C2×#1062312111yescharacteristic
1108C2C2×D4×C22⋊D1111yescharacteristic
1109C2C2×#1062312211yescharacteristic
1110C2C2×#1062333711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#120C2
socleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C2×#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#66991C2semidirect
3. C22×#67006C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. C23×C22⋊Dic11C2semidirect
6. #13072148C2direct (N × H)
7. C2×#10622561C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622834C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622569C2semidirect
15. C2×#10622563C2semidirect
16. C22×C11×#120C2semidirect
24. C23×C22⋊D11C22semidirect
27. C23×C4×D11C22semidirect
29. C2×C11×#120C22semidirect
34. C2×#67006C22semidirect
43. C22×C22⋊Dic11C22semidirect
44. C22×C22⋊Dic11C22semidirect
45. C22×C22⋊Dic11C22semidirect
46. C22×C22⋊Dic11C22semidirect
48. C2×#66992C22semidirect
50. C2×#66991C22semidirect
51. C22×(C2×D11)⋊C4C22semidirect
52. C22×(C2×D11)⋊C4C22semidirect
53. C22×C4⋊Dic11C22semidirect
54. C22×C4⋊Dic11C22semidirect
55. C22×Dic11⋊C4C22semidirect
56. C22×Dic11⋊C4C22semidirect
57. C22×C4×Dic11C22semidirect
59. C2×(C22⋊D11)⋊C4C22semidirect
60. #10622836C22semidirect
61. #10622835C22semidirect
62. #10622834C22semidirect
63. #10622833C22semidirect
64. C2×C11⋊#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. C2×C11⋊#95C22semidirect
67. C2×C11⋊#95C22semidirect
68. #10622574C22semidirect
69. #10622569C22semidirect
70. #10622563C22semidirect
71. #10622561C22semidirect
72. #10622557C22semidirect
112. C22×C22⋊D11D4semidirect
116. C22×C22⋊D11C23semidirect
135. C22×C4×D11C23semidirect
139. C2×C11×C22⋊C4D4semidirect
154. C2×C22⋊Dic11D4semidirect
162. C2×C22⋊Dic11C23semidirect
163. C2×C22⋊Dic11C23semidirect
164. C2×C22⋊Dic11C23semidirect
169. C2×(C2×D11)⋊C4C23semidirect
170. C2×(C2×D11)⋊C4C23semidirect
173. C2×C4⋊Dic11C23semidirect
174. C2×C4⋊Dic11C23semidirect
177. C2×Dic11⋊C4C23semidirect
178. C2×Dic11⋊C4C23semidirect
180. C2×C4×Dic11C23semidirect
182. C11⋊#95C23semidirect
183. C11⋊#95C23semidirect
184. C11⋊#95C23semidirect
185. C11⋊#95C23semidirect
281. C2×C22⋊D11C2×D4semidirect
324. C11×C22⋊C4C2×D4semidirect
334. C22⋊Dic11C2×D4semidirect
345. C22×#120D11semidirect
416. C23×C11#121semidirect
512. C2×#120C2×D11semidirect
583. C22×C11C2×#121semidirect
718. C2×C22⋊C4C22⋊D11semidirect
732. C2×C11#2424semidirect
894. C22⋊C4C2×C22⋊D11semidirect
896. C11C2×#2424semidirect
969. C23#66991semidirect
1078. C22C2×#66991semidirect
1103. C2#13072148direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×#669912
C22×#670062
C22×(C22⋊D11)⋊C42
C23×C22⋊Dic112
#130721482
C2×#106225612
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106225572
C2×#106228332
C2×#106225692
C2×#106225632
C22×C11×#1202
C2×#242411