Finite Group Databasebeta

← C2×#13073594 #14925109

Subgroups — C2×#13073594 #14925109

Order 2816.

3310 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66938C211yesmaximal, characteristic
3C22×#66938C211yesmaximal, characteristic
4C22×C4×Dic22C211yesmaximal, characteristic, complemented
5#13073594C2116yesmaximal, direct product factor
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622561C211yesmaximal, characteristic, complemented
9C2×#10622607C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic
12C2×#10622283C211yesmaximal, characteristic, complemented
13C2×#10622553C211yesmaximal, characteristic, complemented
14C2×#10622557C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66941—28no—
47C2×#66941C2218yescomplemented
48C2×#66938—28no—
49C2×#66938—28no—
50C2×#66938C2218yes—
51C2×#66938C2218yes—
52C2×C4×Dic22—28no—
53C2×C4×Dic22C2218yescomplemented
54C11×#388C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622570C2218yes—
63#10622561C2218yescomplemented
64#10622561C2218yescomplemented
65#10622557C2218yescomplemented
66#10622553C2218yescomplemented
67#10622289C2218yescomplemented
68#10622283C2218yescomplemented
69#10622262C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11C2314yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×Dic22—24no—
91C22×Dic22—24no—
92C22×Dic22—24no—
93C22×Dic22—24no—
94C22×Dic22—24no—
95C22×Dic22D418yes—
96C22×Dic22C2314yes—
97C22×Dic22C2314yes—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C42×C11—24no—
107C2×C42×C11C2314yes—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
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—24no—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11—24no—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4—24no—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11D418yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150#66941—232no—
151#66938—232no—
152#66938—232no—
153C4×Dic22—232no—
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C2×#2545—111nomaximal, Sylow
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11C2412yes—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11C2×D414yes—
194C22×C4×C11C2×D414yes—
195C22×C4×C11#4114yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—416no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11C2×D414yes—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×D414yes—
224C22×Dic11C2×D414yes—
225C22×Dic11#4114yes—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C2×Dic22—232no—
235C2×Dic22—28no—
236C2×Dic22—28no—
237C2×Dic22—28no—
238C2×Dic22—28no—
239C2×Dic22—28no—
240C2×Dic22—416no—
241C2×Dic22C2×D4116yes—
242C11×C4⋊C4—28no—
243C11×C22⋊C4—28no—
244C11×C22⋊C4—28no—
245C11×C22⋊C4—28no—
246C42×C11—28no—
247C22⋊Dic11—28no—
248C22⋊Dic11—28no—
249C22⋊Dic11—28no—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—28no—
256C4⋊Dic11—28no—
257C4⋊Dic11—28no—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4—28no—
261Dic11⋊C4—28no—
262Dic11⋊C4—28no—
263Dic11⋊C4—28no—
264C4×Dic11—28no—
265C4×Dic11—28no—
266C4×Dic11—28no—
267C4×Dic11C2×D4116yes—
268C22×C4⋊Q8—111no—
269C22×#124—111no—
270C22×#124—111no—
271C22×C4×Q8—111no—
272#2545—1116no—
273C2×#396—111no—
274C2×#396—111no—
275C2×#396—111no—
276C2×#396—111no—
277C2×#391—111no—
278C2×#390—111no—
279C2×#388—111no—
280C2×#388—111no—
281C2×#388—111no—
282C2×#388D1111yescharacteristic, complemented
283C2×C4×C4⋊C4—111no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11C22×D412yes—
299C23×C11C22×D412yes—
300C23×C11C2×#4112yes—
301C23×C11C2×#4112yes—
302C23×C11C2×#4112yes—
303C23×C112−1+412yes—
304C23×C112−1+412yes—
305C23×C11C2511yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11—44no—
318C22×D11—44no—
319C22×D11—44no—
320C2×C4×C11—28no—
321C2×C4×C11—28no—
322C2×C4×C11—28no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—44no—
339C2×C4×C11—44no—
340C2×C4×C11—44no—
341C2×C4×C11C22×D414yes—
342C2×C4×C11C22×D414yes—
343C2×C4×C11C2×#4114yes—
344C22⋊D11—416no—
345C2×Dic11—28no—
346C2×Dic11—28no—
347C2×Dic11—28no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—44no—
364C2×Dic11—44no—
365C2×Dic11—44no—
366C2×Dic11#121116yes—
367C2×Dic11C22×D414yes—
368C2×Dic11C22×D414yes—
369C2×Dic11C22×D414yes—
370C2×Dic11C22×D414yes—
371C2×Dic11C2×#4114yes—
372C2×Dic11C2×#4114yes—
373Dic22—232no—
374Dic22—416no—
375C23×Q8—111no—
376C23×Q8—111no—
377C23×D4—111no—
378C2×C4⋊Q8—118no—
379C2×C4⋊Q8—228no—
380C2×#124—118no—
381C2×#124—118no—
382C2×#124—228no—
383C2×#124—228no—
384C2×C4×Q8—118no—
385C2×C4×Q8—228no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4C2×D1111yescharacteristic
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4—111no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404C22×C22⋊C4C2×D1111yescharacteristic
405C22×C22⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4C2×D1111yescharacteristic
407C22×C42—111no—
408C22×C42—111no—
409C22×C42—111no—
410C22×C42—111no—
411C22×C42C2×D1111yescharacteristic
412#396—118no—
413#396—118no—
414#396—118no—
415#396—118no—
416#391—118no—
417#390—118no—
418#388—118no—
419#388—118no—
420#388—118no—
421#388C2×D1118yescomplemented
422C4×C4⋊C4—118no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95C2×D1111yescharacteristic
428C2×#95C2×D1111yescharacteristic
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—88no—
437C22×C11C2×#12114yes—
438C22×C11#53214yes—
439C22×C11#53614yes—
440C22×C11#54814yes—
441C22×C11#54814yes—
442C22×C11#55614yes—
443C22×C11#55614yes—
444C22×C11C23×D411yescharacteristic
445C22×C11C23×D411yescharacteristic
446C22×C11C22×#4111yescharacteristic
447C22×C11C22×#4111yescharacteristic
448C22×C11C22×#4111yescharacteristic
449C22×C11C2×2−1+411yescharacteristic
450C22×C11C2×2−1+411yescharacteristic
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—88no—
459C4×C11—24no—
460C4×C11—24no—
461C4×C11—24no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—42no—
465Dic11—24no—
466Dic11—24no—
467Dic11—24no—
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11C2×#12118yes—
472C25—111no—
473C25C22×D1111yescharacteristic
474C22×Q8—118no—
475C22×Q8—114no—
476C22×Q8—114no—
477C22×Q8—224no—
478C22×Q8—224no—
479C22×Q8—224no—
480C22×Q8—224no—
481C22×Q8—224no—
482C22×D4—114no—
483C22×D4—224no—
484C22×D4—224no—
485C22×D4—224no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—111no—
493C23×C4C22×D1111yescharacteristic
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C4⋊Q8—2232no—
500#124—2232no—
501#124—2232no—
502C4×Q8—2232no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—224no—
514C2×C4⋊C4—224no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4—224no—
517C2×C4⋊C4—224no—
518C2×C4⋊C4—224no—
519C2×C4⋊C4—224no—
520C2×C4⋊C4C22×D1114yes—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—224no—
537C2×C22⋊C4—224no—
538C2×C22⋊C4—224no—
539C2×C22⋊C4—224no—
540C2×C22⋊C4—224no—
541C2×C22⋊C4—224no—
542C2×C22⋊C4C22×D1114yes—
543C2×C22⋊C4C22×D1114yes—
544C2×C22⋊C4C22×D1114yes—
545C2×C42—24no—
546C2×C42—118no—
547C2×C42—114no—
548C2×C42—114no—
549C2×C42—114no—
550C2×C42—114no—
551C2×C42—224no—
552C2×C42—224no—
553C2×C42—224no—
554C2×C42C22×D1114yes—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95C22×D1114yes—
560#95C22×D1114yes—
561C2×C11—82no—
562C2×C11#254518yescomplemented
563C2×C11C22×#12111yescharacteristic
564C2×C11C2×#53211yescharacteristic
565C2×C11C2×#53611yescharacteristic
566C2×C11C2×#54811yescharacteristic
567C2×C11C2×#54811yescharacteristic
568C2×C11C2×#55611yescharacteristic
569C2×C11C2×#55611yescharacteristic
570D11—82no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—112no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24C23×D1112yes—
587C24C23×D1111yescharacteristic
588C2×Q8—1116no—
589C2×Q8—228no—
590C2×Q8—2232no—
591C2×Q8—228no—
592C2×Q8—228no—
593C2×Q8—228no—
594C2×Q8—228no—
595C2×Q8—4416no—
596C2×D4—228no—
597C2×D4—228no—
598C2×D4—228no—
599C2×D4—4416no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—114no—
616C22×C4—114no—
617C22×C4—114no—
618C22×C4—112no—
619C22×C4—114no—
620C22×C4—114no—
621C22×C4—114no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4#433914yes—
644C22×C4D4×D1114yes—
645C22×C4D4×D1114yes—
646C22×C4C23×D1112yes—
647C22×C4C23×D1112yes—
648C22×C4C23×D1112yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1112yes—
652C4⋊C4—28no—
653C4⋊C4—228no—
654C4⋊C4—228no—
655C4⋊C4—228no—
656C4⋊C4—228no—
657C4⋊C4—228no—
658C4⋊C4—228no—
659C4⋊C4—228no—
660C4⋊C4—228no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—28no—
664C22⋊C4—228no—
665C22⋊C4—228no—
666C22⋊C4—228no—
667C22⋊C4—228no—
668C22⋊C4—228no—
669C22⋊C4—228no—
670C22⋊C4—228no—
671C22⋊C4—228no—
672C22⋊C4—228no—
673C42—28no—
674C42—1116no—
675C42—228no—
676C42—228no—
677C42—228no—
678C11C2×#254511yescharacteristic, complemented, Sylow
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—444no—
701C23—444no—
702C23—444no—
703C23—444no—
704C23—444no—
705C23—444no—
706C23—444no—
707C23C2×#433912yes—
708C23C2×D4×D1112yes—
709C23C2×D4×D1112yes—
710C23#41×D1112yes—
711C23#41×D1112yes—
712C23#6704312yes—
713C23#6704312yes—
714C23C24×D1111yescharacteristic
715Q8—2232no—
716Q8—4416no—
717D4—4416no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—1116no—
740C2×C4—114no—
741C2×C4—114no—
742C2×C4—114no—
743C2×C4—114no—
744C2×C4—114no—
745C2×C4—114no—
746C2×C4—228no—
747C2×C4—228no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—228no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—444no—
765C2×C4—444no—
766C2×C4—444no—
767C2×C4C2×#433914yes—
768C2×C4C2×D4×D1114yes—
769C2×C4C2×D4×D1114yes—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—88no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—888no—
786C22#1062306414yes—
787C22#1062307914yes—
788C22#1062308314yes—
789C22D11×#12114yes—
790C22#1062317914yes—
791C22#1062320814yes—
792C22#1062323314yes—
793C22C22×#433911yescharacteristic
794C22C22×D4×D1111yescharacteristic
795C22C22×D4×D1111yescharacteristic
796C22C2×#41×D1111yescharacteristic
797C22C2×#41×D1111yescharacteristic
798C22C2×#6704311yescharacteristic
799C22C2×#6704311yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—118no—
807C4—224no—
808C4—224no—
809C4—224no—
810C4—442no—
811C4—442no—
812C4—442no—
813C2—82no—
814C2—882no—
815C2#1307359418yesdirect product factor
816C2C2×D11×#12111yescharacteristic
817C2C2×#1062307911yescharacteristic
818C2C2×#1062317911yescharacteristic
819C2C2×#1062320811yescharacteristic
820C2C2×#1062308311yescharacteristic
821C2C2×#1062323311yescharacteristic
822C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11C2×#2545
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
4. C22×C4×Dic22C2semidirect
5. #13073594C2direct (N × H)
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622561C2semidirect
9. C2×#10622607C2semidirect
10. C2×#10622259C2semidirect
12. C2×#10622283C2semidirect
13. C2×#10622553C2semidirect
14. C2×#10622557C2semidirect
15. C2×#10622262C2semidirect
16. C2×C11×#388C2semidirect
47. C2×#66941C22semidirect
53. C2×C4×Dic22C22semidirect
54. C11×#388C22semidirect
61. #10622607C22semidirect
63. #10622561C22semidirect
64. #10622561C22semidirect
65. #10622557C22semidirect
66. #10622553C22semidirect
67. #10622289C22semidirect
68. #10622283C22semidirect
69. #10622262C22semidirect
70. #10622259C22semidirect
282. C2×#388D11semidirect
421. #388C2×D11semidirect
562. C2×C11#2545semidirect
678. C11C2×#2545semidirect
815. C2#13073594direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669382
C22×C4×Dic222
#130735942
C2×#106222892
C2×#106225612
C2×#106226072
C2×#106222592
C2×#106225702
C2×#106222832
C2×#106225532
C2×#106225572
C2×#106222622
C2×C11×#3882
C2×#254511