Finite Group Databasebeta

← C2×#13072862 #14921383

Subgroups — C2×#13072862 #14921383

Order 2816.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66929C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3#13072862C2116yesmaximal, direct product factor
4C2×#10622288C211yesmaximal, characteristic, complemented
5C2×#10622288C211yesmaximal, characteristic, complemented
6C2×#10622288C211yesmaximal, characteristic, complemented
7C2×#10622289C211yesmaximal, characteristic, complemented
8C2×#10622553C211yesmaximal, characteristic, complemented
9C2×#10622553C211yesmaximal, characteristic, complemented
10C2×#10622553C211yesmaximal, characteristic, complemented
11C2×#10622823C211yesmaximal, characteristic, complemented
12C2×#10622559C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×#10622568C211yesmaximal, characteristic
15C2×#10622568C211yesmaximal, characteristic
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic, complemented
23C22×C42×C11C2211yescharacteristic, complemented
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4—28no—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2218yes—
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×Dic11⋊C4C2211yescharacteristic, complemented
41C22×Dic11⋊C4C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×Dic11⋊C4C2211yescharacteristic, complemented
46C2×#66929—28no—
47C2×#66929C2218yescomplemented
48C4×C11×C22⋊C4C2218yescomplemented
49C2×C11×#95C2211yescharacteristic, complemented
50C2×C11×#95C2211yescharacteristic, complemented
51#10622823C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic, complemented
53C2×C11⋊#95C2211yescharacteristic, complemented
54C2×C11⋊#95C2211yescharacteristic, complemented
55C2×C11⋊#95C2211yescharacteristic, complemented
56C2×C11⋊#95C2211yescharacteristic, complemented
57C2×C11⋊#95C2211yescharacteristic, complemented
58#10622568C2218yes—
59#10622568C2218yes—
60#10622559C2218yescomplemented
61#10622555C2218yescomplemented
62#10622553C2218yescomplemented
63#10622553C2218yescomplemented
64#10622553C2218yescomplemented
65#10622289C2218yescomplemented
66#10622288C2218yescomplemented
67#10622288C2218yescomplemented
68#10622288C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11—24no—
71C24×D11—24no—
72C24×D11—24no—
73C24×D11—24no—
74C24×D11—24no—
75C24×D11—42no—
76C24×D11—42no—
77C24×D11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2314yes—
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—42no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C23×C4×C11C2311yescharacteristic
90C23×Dic11—24no—
91C23×Dic11—24no—
92C23×Dic11—42no—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2314yes—
99C23×Dic11C2311yescharacteristic
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11—24no—
105C2×C42×C11—42no—
106C2×C42×C11C2314yescomplemented
107C2×C42×C11C2314yescomplemented
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—232no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4D418yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—24no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4—42no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4C2314yescomplemented
144C2×Dic11⋊C4C2314yescomplemented
145C2×Dic11⋊C4C2314yescomplemented
146C2×Dic11⋊C4C2314yescomplemented
147C2×Dic11⋊C4C2314yescomplemented
148C2×Dic11⋊C4C2314yescomplemented
149#66929—232no—
150C11×#95C2314yescomplemented
151C11×#95C2314yescomplemented
152C11⋊#95C2314yescomplemented
153C11⋊#95C2314yescomplemented
154C11⋊#95C2314yescomplemented
155C11⋊#95C2314yescomplemented
156C11⋊#95C2314yescomplemented
157C11⋊#95C2314yescomplemented
158C2×#2480—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11#4114yes—
164C24×C11#4114yes—
165C24×C11#4114yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—232no—
169C23×D11—22no—
170C23×D11—28no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—28no—
183C23×D11—28no—
184C23×D11—28no—
185C23×D11—28no—
186C23×D11—44no—
187C23×D11—44no—
188C23×D11—416no—
189C23×D11—416no—
190C23×D11—416no—
191C23×D11—416no—
192C23×D11—416no—
193C23×D11—416no—
194C23×D11C2×D414yes—
195C23×D11#4114yes—
196C23×D11C2412yes—
197C23×D11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×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—28no—
217C22×C4×C11—44no—
218C22×C4×C11—416no—
219C22×C4×C11C2×D414yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×Dic11—28no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—28no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—44no—
246C22×Dic11—416no—
247C22×Dic11C2×D414yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—28no—
256C42×C11—28no—
257C42×C11—44no—
258C22⋊Dic11—28no—
259C22⋊Dic11—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4C2×D4116yes—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275Dic11⋊C4—44no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C22×#126—111no—
279C23×C22⋊C4—111no—
280#2480—1116no—
281C2×#397—111no—
282C2×#397—111no—
283C2×#397—111no—
284C2×#396—111no—
285C2×#388—111no—
286C2×#388—111no—
287C2×#388—111no—
288C2×#385—111no—
289C2×#385—111no—
290C2×#380—111no—
291C2×#379—111no—
292C2×#379—111no—
293C2×C4×C22⋊C4D1111yescharacteristic, complemented
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
297C23×C11—28no—
298C23×C11—28no—
299C23×C11—28no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11#126116yescomplemented
305C23×C11C22×D412yes—
306C23×C11C2×#4114yes—
307C23×C11C2×#4114yes—
308C23×C11C2×#4114yes—
309C23×C11C2×#4112yes—
310C23×C11C2×#4112yes—
311C23×C11C2×#4112yes—
312C23×C11C2×#4112yes—
313C23×C11H(5,𝔽2)12yes—
314C23×C11H(5,𝔽2)12yes—
315C23×C11C2511yescharacteristic
316C22×D11—232no—
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—28no—
320C22×D11—28no—
321C22×D11—28no—
322C22×D11—28no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—416no—
336C22×D11—416no—
337C22×D11—416no—
338C22×D11—416no—
339C22×D11—416no—
340C22×D11—4128no—
341C22×D11—44no—
342C22×D11—44no—
343C22×D11—416no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11C22×D414yes—
351C22×D11C2×#4114yes—
352C2×C4×C11—28no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—416no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11C22×D414yes—
377C2×Dic11—28no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—416no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—44no—
401C2×Dic11C22×D414yes—
402C26—111no—
403C24×C4—111no—
404C24×C4C2×D1111yescharacteristic
405C2×#126—118no—
406C2×#126—228no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—118no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—228no—
429C22×C22⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4C2×D1111yescharacteristic
431C22×C42C2×D1111yescharacteristic, complemented
432C22×C42C2×D1111yescharacteristic, complemented
433#397—118no—
434#397—118no—
435#397—118no—
436#396—118no—
437#388—118no—
438#388—118no—
439#388—118no—
440#385—118no—
441#385—118no—
442#380—118no—
443#379—118no—
444#379—118no—
445C4×C22⋊C4C2×D1118yescomplemented
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95C2×D1111yescharacteristic, complemented
453C2×#95C2×D1111yescharacteristic, complemented
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—232no—
461C22×C11#52514yes—
462C22×C11C2×#12614yes—
463C22×C11C2×#12618yescomplemented
464C22×C11#53814yes—
465C22×C11#54614yes—
466C22×C11#54614yes—
467C22×C11#55114yes—
468C22×C11#55114yes—
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—24no—
482C2×D11—464no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—416no—
492C2×D11—416no—
493C4×C11—24no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499Dic11—24no—
500Dic11—42no—
501Dic11—42no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505C25—111no—
506C25—111no—
507C25—114no—
508C25—224no—
509C25—224no—
510C25—224no—
511C25—224no—
512C25—224no—
513C25—442no—
514C25—442no—
515C25C22×D1111yescharacteristic
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—42no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—114no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1114yes—
535C23×C4C22×D1111yescharacteristic
536#126—2232no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4—442no—
548C2×C4⋊C4—442no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—118no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—2232no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4—224no—
569C2×C22⋊C4—224no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—224no—
572C2×C22⋊C4—224no—
573C2×C22⋊C4—224no—
574C2×C22⋊C4—224no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—442no—
577C2×C22⋊C4—442no—
578C2×C22⋊C4—442no—
579C2×C22⋊C4—442no—
580C2×C22⋊C4C22×D1114yes—
581C2×C22⋊C4C22×D1114yes—
582C2×C42—24no—
583C2×C42—42no—
584C2×C42C22×D1114yescomplemented
585C2×C42C22×D1114yescomplemented
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95—114no—
591#95—114no—
592#95C22×D1114yescomplemented
593#95C22×D1114yescomplemented
594C2×C11—28no—
595C2×C11#248018yescomplemented
596C2×C11C2×#52511yescharacteristic
597C2×C11C22×#12611yescharacteristic
598C2×C11C2×#53811yescharacteristic
599C2×C11C2×#54611yescharacteristic
600C2×C11C2×#54611yescharacteristic
601C2×C11C2×#55111yescharacteristic
602C2×C11C2×#55111yescharacteristic
603D11—44no—
604D11—44no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—114no—
610C24—114no—
611C24—112no—
612C24—112no—
613C24—228no—
614C24—228no—
615C24—2232no—
616C24—228no—
617C24—222no—
618C24—222no—
619C24—222no—
620C24—222no—
621C24—222no—
622C24—222no—
623C24—222no—
624C24—222no—
625C24—222no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—228no—
630C24—228no—
631C24—444no—
632C24—444no—
633C24—4416no—
634C24—4416no—
635C24—4416no—
636C24—4416no—
637C24—4416no—
638C24—4416no—
639C24#433914yes—
640C24#433914yes—
641C24#433914yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—28no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—416no—
665C22×C4—114no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—228no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—228no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—444no—
692C22×C4—4416no—
693C22×C4D4×D1114yes—
694C22×C4C23×D1112yes—
695C22×C4C23×D1112yes—
696C22×C4C23×D1112yes—
697C22×C4C23×D1112yes—
698C22×C4C23×D1112yes—
699C22×C4C23×D1112yes—
700C4⋊C4—228no—
701C4⋊C4—228no—
702C4⋊C4—228no—
703C4⋊C4—444no—
704C4⋊C4—444no—
705C4⋊C4—444no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—1116no—
709C22⋊C4—228no—
710C22⋊C4—228no—
711C22⋊C4—228no—
712C22⋊C4—228no—
713C22⋊C4—228no—
714C22⋊C4—228no—
715C22⋊C4—228no—
716C22⋊C4—228no—
717C22⋊C4—228no—
718C22⋊C4—444no—
719C22⋊C4—444no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C42—28no—
723C42—44no—
724C11C2×#248011yescharacteristic, complemented, Sylow
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—114no—
736C23—114no—
737C23—2232no—
738C23—228no—
739C23—228no—
740C23—228no—
741C23—228no—
742C23—228no—
743C23—228no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—4416no—
757C23—4416no—
758C23—4416no—
759C23—4416no—
760C23—4416no—
761C23—44128no—
762C23—444no—
763C23—444no—
764C23—4416no—
765C23—444no—
766C23—444no—
767C23—444no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23#66929116yescomplemented
772C23C2×#433914yes—
773C23C2×#433914yes—
774C23C2×#433914yes—
775C23C2×#433912yes—
776C23C2×#433912yes—
777C23C2×#433912yes—
778C23C2×D4×D1112yes—
779C23#6703712yes—
780C23#41×D1112yes—
781C23#6704212yes—
782C23C24×D1111yescharacteristic
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—114no—
808C2×C4—228no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—4416no—
827C2×C4—444no—
828C2×C4—444no—
829C2×C4—444no—
830C2×C4—444no—
831C2×C4—444no—
832C2×C4C2×D4×D1114yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—232no—
839C22—24no—
840C22—224no—
841C22—224no—
842C22—224no—
843C22—224no—
844C22—224no—
845C22—224no—
846C22—4464no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—4416no—
855C22—4416no—
856C22—442no—
857C22C2×#6692914yes—
858C22C2×#6692918yescomplemented
859C22#1062302114yes—
860C22#1062305814yes—
861C22#1062307814yes—
862C22#1062308114yes—
863C22#1062308714yes—
864C22#1062309114yes—
865C22C22×#433911yescharacteristic
866C22C22×#433911yescharacteristic
867C22C22×#433911yescharacteristic
868C22C22×D4×D1111yescharacteristic
869C22C2×#6703711yescharacteristic
870C22C2×#41×D1111yescharacteristic
871C22C2×#6704211yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—224no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4—442no—
883C4—442no—
884C2—28no—
885C2—444no—
886C2—444no—
887C2#1307286218yesdirect product factor
888C2C2×#1062307811yescharacteristic
889C2C22×#6692911yescharacteristic
890C2C2×#1062309111yescharacteristic
891C2C2×#1062302111yescharacteristic
892C2C2×#1062308111yescharacteristic
893C2C2×#1062305811yescharacteristic
894C2C2×#1062308711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2480
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66929C2semidirect
3. #13072862C2direct (N × H)
4. C2×#10622288C2semidirect
5. C2×#10622288C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622289C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622553C2semidirect
11. C2×#10622823C2semidirect
12. C2×#10622559C2semidirect
13. C2×#10622555C2semidirect
16. C2×C4×C11×C22⋊C4C2semidirect
22. C22×C42×C11C22semidirect
23. C22×C42×C11C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×Dic11⋊C4C22semidirect
47. C2×#66929C22semidirect
48. C4×C11×C22⋊C4C22semidirect
49. C2×C11×#95C22semidirect
50. C2×C11×#95C22semidirect
51. #10622823C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
60. #10622559C22semidirect
61. #10622555C22semidirect
62. #10622553C22semidirect
63. #10622553C22semidirect
64. #10622553C22semidirect
65. #10622289C22semidirect
66. #10622288C22semidirect
67. #10622288C22semidirect
68. #10622288C22semidirect
106. C2×C42×C11C23semidirect
107. C2×C42×C11C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
145. C2×Dic11⋊C4C23semidirect
146. C2×Dic11⋊C4C23semidirect
147. C2×Dic11⋊C4C23semidirect
148. C2×Dic11⋊C4C23semidirect
150. C11×#95C23semidirect
151. C11×#95C23semidirect
152. C11⋊#95C23semidirect
153. C11⋊#95C23semidirect
154. C11⋊#95C23semidirect
155. C11⋊#95C23semidirect
156. C11⋊#95C23semidirect
157. C11⋊#95C23semidirect
293. C2×C4×C22⋊C4D11semidirect
304. C23×C11#126semidirect
431. C22×C42C2×D11semidirect
432. C22×C42C2×D11semidirect
445. C4×C22⋊C4C2×D11semidirect
452. C2×#95C2×D11semidirect
453. C2×#95C2×D11semidirect
463. C22×C11C2×#126semidirect
584. C2×C42C22×D11semidirect
585. C2×C42C22×D11semidirect
592. #95C22×D11semidirect
593. #95C22×D11semidirect
595. C2×C11#2480semidirect
724. C11C2×#2480semidirect
771. C23#66929semidirect
858. C22C2×#66929semidirect
887. C2#13072862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669292
C23×(C2×D11)⋊C42
#130728622
C2×#106222882
C2×#106222892
C2×#106225532
C2×#106228232
C2×#106225592
C2×#106225552
C2×#106225682
C2×C4×C11×C22⋊C42
C2×#248011