Finite Group Databasebeta

← C2×#13072242 #14922193

Subgroups — C2×#13072242 #14922193

Order 2816.

5502 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C22×#66941C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×#66949C211yesmaximal, characteristic, complemented
5#13072242C2116yesmaximal, direct product factor
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×#4339—28no—
21C22×#4339—28no—
22C22×#4339—28no—
23C22×#4339C2218yes—
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×Dic22C2211yescharacteristic
28C23×Dic22C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66949—28no—
51C2×#66949C2218yescomplemented
52C2×#66941—28no—
53C2×#66941C2218yescomplemented
54C2×#66938—28no—
55C2×#66938C2218yescomplemented
56C11×#385C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59#10622823C2218yescomplemented
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622604C2218yescomplemented
65#10622602C2218yescomplemented
66#10622574C2218yescomplemented
67#10622572C2218yescomplemented
68#10622570C2218yescomplemented
69#10622285C2218yescomplemented
70#10622281C2218yescomplemented
71#10622279C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11D418yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×#4339—2128no—
101C2×#4339—232no—
102C2×#4339—232no—
103C2×#4339—232no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44—24no—
107C22×D44C2314yes—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11D418yes—
114C22×C4×D11C2314yes—
115C22×C4×D11C2314yes—
116C22×Dic22—24no—
117C22×Dic22—24no—
118C22×Dic22—24no—
119C22×Dic22—24no—
120C22×Dic22—24no—
121C22×Dic22D418yes—
122C22×Dic22C2314yes—
123C22×Dic22C2314yes—
124C2×C11×C4⋊C4—24no—
125C2×C11×C4⋊C4—24no—
126C2×C11×C4⋊C4C2314yes—
127C2×C11×C4⋊C4C2314yes—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4—24no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×C4⋊Dic11—24no—
153C2×C4⋊Dic11C2314yes—
154C2×Dic11⋊C4—24no—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4C2314yes—
159C2×Dic11⋊C4C2314yes—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×C4×Dic11—24no—
163C2×C4×Dic11—24no—
164C2×C4×Dic11C2314yes—
165C2×C4×Dic11C2314yes—
166#66949—232no—
167#66941—232no—
168#66938—232no—
169C11×#95C2314yes—
170C11×#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C2×#2432—111nomaximal, Sylow
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11C2×D414yes—
183C24×C11C2412yes—
184C24×C11C2411yescharacteristic
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11C2×D414yes—
198C23×D11C2×D414yes—
199C23×D11C2412yes—
200C23×D11C2412yes—
201C22×C4×C11—232no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—28no—
208C22×C4×C11—22no—
209C22×C4×C11—28no—
210C22×C4×C11—28no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2×D414yes—
222C22×C4×C11#4114yescomplemented
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C2×C22⋊D11—232no—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11C2×D4116yes—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11C2×D414yes—
251C22×Dic11C2×D414yes—
252C22×Dic11C2×D414yes—
253C22×Dic11C2×D414yes—
254C22×Dic11#4114yescomplemented
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261#4339—2256no—
262C2×D44—232no—
263C2×D44—28no—
264C2×D44—28no—
265C2×D44—28no—
266C2×C4×D11—232no—
267C2×C4×D11—232no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11C2×D4116yes—
274C2×Dic22—232no—
275C2×Dic22—28no—
276C2×Dic22—28no—
277C2×Dic22—28no—
278C2×Dic22—28no—
279C2×Dic22—28no—
280C2×Dic22—416no—
281C2×Dic22C2×D4116yes—
282C11×C4⋊C4—28no—
283C11×C4⋊C4—28no—
284C11×C22⋊C4—28no—
285C11×C22⋊C4—28no—
286C22⋊Dic11—28no—
287C22⋊Dic11—28no—
288(C2×D11)⋊C4—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296C4⋊Dic11—28no—
297Dic11⋊C4—28no—
298Dic11⋊C4—28no—
299Dic11⋊C4—28no—
300Dic11⋊C4—28no—
301C4×Dic11—28no—
302C4×Dic11—28no—
303C23×#41—111no—
304C22×C4⋊Q8—111no—
305C22×#124—111no—
306C22×C22⋊Q8—111no—
307#2432—1116no—
308C2×#394—111no—
309C2×#394—111no—
310C2×#394—111no—
311C2×#394—111no—
312C2×#391—111no—
313C2×#390—111no—
314C2×#385—111no—
315C2×#385—111no—
316C2×#385—111no—
317C2×#385D1111yescharacteristic, complemented
318C2×C4×C22⋊C4—111no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—28no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11C22×D414yes—
333C23×C11C22×D412yes—
334C23×C11C22×D412yes—
335C23×C11C22×D412yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4112yes—
338C23×C112−1+412yes—
339C23×C112−1+412yes—
340C23×C11C2511yescharacteristic
341C22×D11—28no—
342C22×D11—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—44no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11C22×D414yes—
368C22×D11C22×D414yes—
369C2×C4×C11—232no—
370C2×C4×C11—28no—
371C2×C4×C11—28no—
372C2×C4×C11—28no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C2×C4×C11C22×D414yes—
392C2×C4×C11C22×D414yes—
393C2×C4×C11C2×#4114yescomplemented
394C22⋊D11—232no—
395C22⋊D11—232no—
396C2×Dic11—28no—
397C2×Dic11—28no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—44no—
412C2×Dic11—44no—
413C2×Dic11—44no—
414C2×Dic11#120116yes—
415C2×Dic11C22×D414yes—
416C2×Dic11C22×D414yes—
417C2×Dic11C22×D414yes—
418C2×Dic11C22×D414yes—
419C2×Dic11C2×#4114yescomplemented
420D44—232no—
421C4×D11—232no—
422C4×D11—232no—
423Dic22—232no—
424Dic22—416no—
425C22×#41—118no—
426C22×#41—228no—
427C22×#41—228no—
428C22×#41—228no—
429C23×Q8—111no—
430C23×Q8—111no—
431C23×D4—111no—
432C23×D4—111no—
433C23×D4—111no—
434C24×C4—111no—
435C24×C4—111no—
436C24×C4C2×D1111yescharacteristic
437C2×C4⋊Q8—118no—
438C2×C4⋊Q8—228no—
439C2×#124—118no—
440C2×#124—228no—
441C2×C22⋊Q8—118no—
442C2×C22⋊Q8—228no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4C2×D1111yescharacteristic
449C22×C4⋊C4C2×D1111yescharacteristic
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4C2×D1111yescharacteristic
461C22×C22⋊C4C2×D1111yescharacteristic
462C22×C42—111no—
463C22×C42—111no—
464#394—118no—
465#394—118no—
466#394—118no—
467#394—118no—
468#391—118no—
469#390—118no—
470#385—118no—
471#385—118no—
472#385—118no—
473#385C2×D1118yescomplemented
474C4×C22⋊C4—118no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95C2×D1111yescharacteristic
480C2×#95C2×D1111yescharacteristic
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—416no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11C2×#12014yes—
490C22×C11#53214yes—
491C22×C11#53614yes—
492C22×C11#54714yes—
493C22×C11#54714yes—
494C22×C11#54814yes—
495C22×C11#54814yes—
496C22×C11C23×D411yescharacteristic
497C22×C11C23×D411yescharacteristic
498C22×C11C23×D411yescharacteristic
499C22×C11C22×#4111yescharacteristic
500C22×C11C22×#4111yescharacteristic
501C22×C11C2×2−1+411yescharacteristic
502C22×C11C2×2−1+411yescharacteristic
503C2×D11—24no—
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—416no—
512C2×D11—416no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C4×C11—24no—
520C4×C11—24no—
521C4×C11—24no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—42no—
525Dic11—24no—
526Dic11—24no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11C2×#12018yes—
531C25—111no—
532C25—111no—
533C25C22×D1111yescharacteristic
534C2×#41—2232no—
535C2×#41—2232no—
536C2×#41—2232no—
537C2×#41—22128no—
538C22×Q8—118no—
539C22×Q8—114no—
540C22×Q8—114no—
541C22×Q8—224no—
542C22×Q8—224no—
543C22×Q8—224no—
544C22×Q8—224no—
545C22×Q8—224no—
546C22×D4—118no—
547C22×D4—114no—
548C22×D4—114no—
549C22×D4—114no—
550C22×D4—224no—
551C22×D4—224no—
552C22×D4—224no—
553C22×D4—224no—
554C22×D4—224no—
555C22×D4—224no—
556C22×D4—224no—
557C22×D4—224no—
558C23×C4—24no—
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—118no—
565C23×C4—114no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—114no—
570C23×C4—224no—
571C23×C4—224no—
572C23×C4—224no—
573C23×C4—224no—
574C23×C4—224no—
575C23×C4C22×D1114yes—
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C4⋊Q8—2232no—
583#124—2232no—
584C22⋊Q8—2232no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—224no—
593C2×C4⋊C4—224no—
594C2×C4⋊C4—224no—
595C2×C4⋊C4—224no—
596C2×C4⋊C4—224no—
597C2×C4⋊C4C22×D1114yes—
598C2×C4⋊C4C22×D1114yes—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—224no—
612C2×C22⋊C4—224no—
613C2×C22⋊C4—224no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—224no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4C22×D1114yes—
622C2×C22⋊C4C22×D1114yes—
623C2×C42—114no—
624C2×C42—114no—
625C2×C42—224no—
626C2×C42—224no—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—114no—
631#95C22×D1114yes—
632#95C22×D1114yes—
633C2×C11—44no—
634C2×C11#243218yescomplemented
635C2×C11C22×#12011yescharacteristic
636C2×C11C2×#53211yescharacteristic
637C2×C11C2×#53611yescharacteristic
638C2×C11C2×#54711yescharacteristic
639C2×C11C2×#54711yescharacteristic
640C2×C11C2×#54811yescharacteristic
641C2×C11C2×#54811yescharacteristic
642D11—44no—
643D11—44no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—114no—
651C24—114no—
652C24—112no—
653C24—112no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24D4×D1114yes—
667C24C23×D1112yes—
668C24C23×D1111yescharacteristic
669#41—22256no—
670C2×Q8—1116no—
671C2×Q8—2232no—
672C2×Q8—228no—
673C2×Q8—228no—
674C2×Q8—228no—
675C2×Q8—228no—
676C2×Q8—228no—
677C2×Q8—4416no—
678C2×D4—1116no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—2232no—
682C2×D4—2232no—
683C2×D4—228no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—228no—
687C2×D4—2232no—
688C2×D4—228no—
689C2×D4—228no—
690C22×C4—232no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—114no—
710C22×C4—114no—
711C22×C4—114no—
712C22×C4—112no—
713C22×C4—114no—
714C22×C4—114no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—1116no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
721C22×C4—2232no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—2232no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—228no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4#433914yescomplemented
742C22×C4D4×D1114yes—
743C22×C4D4×D1114yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—228no—
753C4⋊C4—228no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C22⋊C4—28no—
758C22⋊C4—28no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C22⋊C4—228no—
762C22⋊C4—228no—
763C22⋊C4—228no—
764C22⋊C4—228no—
765C22⋊C4—228no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C42—228no—
770C42—228no—
771C11C2×#243211yescharacteristic, complemented, Sylow
772C23—28no—
773C23—28no—
774C23—28no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—114no—
786C23—114no—
787C23—228no—
788C23—228no—
789C23—228no—
790C23—228no—
791C23—228no—
792C23—228no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—444no—
806C23—444no—
807C23—444no—
808C23—444no—
809C23—444no—
810C23—444no—
811C23—444no—
812C23—444no—
813C23C2×#433912yes—
814C23C2×D4×D1114yes—
815C23C2×D4×D1112yes—
816C23C2×D4×D1112yes—
817C23C2×D4×D1112yes—
818C23#6704012yes—
819C23#41×D1112yes—
820C23#6704312yes—
821C23C24×D1111yescharacteristic
822Q8—2232no—
823Q8—4416no—
824D4—2232no—
825D4—2232no—
826D4—2232no—
827C2×C4—232no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—1116no—
850C2×C4—114no—
851C2×C4—114no—
852C2×C4—114no—
853C2×C4—114no—
854C2×C4—114no—
855C2×C4—2232no—
856C2×C4—2232no—
857C2×C4—228no—
858C2×C4—228no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—444no—
873C2×C4—444no—
874C2×C4—444no—
875C2×C4C2×#433914yescomplemented
876C2×C4C2×D4×D1114yes—
877C2×C4C2×D4×D1114yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—42no—
882C22—42no—
883C22—416no—
884C22—42no—
885C22—42no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—224no—
890C22—224no—
891C22—224no—
892C22—442no—
893C22—442no—
894C22—4416no—
895C22—4416no—
896C22—442no—
897C22—442no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22#1062303814yes—
903C22#1062307914yes—
904C22#1062308314yes—
905C22D11×#12014yes—
906C22#1062315914yes—
907C22#1062316414yes—
908C22#1062318614yes—
909C22C22×#433911yescharacteristic
910C22C22×D4×D1111yescharacteristic
911C22C22×D4×D1111yescharacteristic
912C22C22×D4×D1111yescharacteristic
913C22C2×#6704011yescharacteristic
914C22C2×#41×D1111yescharacteristic
915C22C2×#6704311yescharacteristic
916C4—24no—
917C4—24no—
918C4—24no—
919C4—42no—
920C4—42no—
921C4—42no—
922C4—118no—
923C4—224no—
924C4—224no—
925C4—442no—
926C4—442no—
927C4—442no—
928C2—44no—
929C2—444no—
930C2—444no—
931C2#1307224218yesdirect product factor
932C2C2×D11×#12011yescharacteristic
933C2C2×#1062307911yescharacteristic
934C2C2×#1062315911yescharacteristic
935C2C2×#1062318611yescharacteristic
936C2C2×#1062303811yescharacteristic
937C2C2×#1062308311yescharacteristic
938C2C2×#1062316411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC23×#4339C2
hypercenterC2×#385D11
hypocenterC11C2×#2432
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#66941C2semidirect
3. C22×#66938C2semidirect
4. C22×#66949C2semidirect
5. #13072242C2direct (N × H)
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622259C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#385C2semidirect
51. C2×#66949C22semidirect
53. C2×#66941C22semidirect
55. C2×#66938C22semidirect
56. C11×#385C22semidirect
59. #10622823C22semidirect
64. #10622604C22semidirect
65. #10622602C22semidirect
66. #10622574C22semidirect
67. #10622572C22semidirect
68. #10622570C22semidirect
69. #10622285C22semidirect
70. #10622281C22semidirect
71. #10622279C22semidirect
72. #10622259C22semidirect
222. C22×C4×C11#41semidirect
254. C22×Dic11#41semidirect
317. C2×#385D11semidirect
393. C2×C4×C11C2×#41semidirect
419. C2×Dic11C2×#41semidirect
473. #385C2×D11semidirect
634. C2×C11#2432semidirect
741. C22×C4#4339semidirect
771. C11C2×#2432semidirect
875. C2×C4C2×#4339semidirect
931. C2#13072242direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669412
C22×#669382
C22×#669492
#130722422
C2×#106222852
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106222592
C2×#106225702
C2×#106222812
C2×#106228232
C2×#106226022
C2×#106222792
C2×C11×#3852
C2×#243211