Finite Group Databasebeta

← C2×#13072239 #14922192

Subgroups — C2×#13072239 #14922192

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×#4341C211yesmaximal, characteristic
2C22×#66941C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×#66931C211yesmaximal, characteristic, complemented
5#13072239C2116yesmaximal, direct product factor
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622563C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C22×#4341—28no—
23C22×#4341—28no—
24C22×#4341—28no—
25C22×#4341C2218yes—
26C23×C4×D11C2211yescharacteristic
27C23×Dic22C2211yescharacteristic
28C23×Dic22C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66941—28no—
51C2×#66941C2218yescomplemented
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54C2×#66931—28no—
55C2×#66931C2218yescomplemented
56C11×#394C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622835C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622602C2218yescomplemented
65#10622574C2218yescomplemented
66#10622572C2218yescomplemented
67#10622570C2218yescomplemented
68#10622563C2218yescomplemented
69#10622559C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71#10622281C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11C2314yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11D418yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11—24no—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11D418yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C23×Dic11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C2×#4341—2128no—
109C2×#4341—232no—
110C2×#4341—232no—
111C2×#4341—232no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—24no—
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⋊C4C2314yes—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—24no—
128C2×C11×C22⋊C4—24no—
129C2×C11×C22⋊C4—24no—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C11×C22⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C22⋊Dic11—24no—
135C2×C22⋊Dic11—24no—
136C2×C22⋊Dic11—24no—
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×C4⋊Dic11—24no—
151C2×C4⋊Dic11—24no—
152C2×C4⋊Dic11C2314yes—
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#66941—232no—
167#66938—232no—
168#66931—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×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11C2×D414yes—
189C24×C11C2×D414yes—
190C24×C11C2412yes—
191C24×C11C2412yes—
192C24×C11C2411yescharacteristic
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11C2×D414yes—
200C23×D11C2412yes—
201C2×D4×C11—232no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
204C2×D4×C11—28no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
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—22no—
217C22×C4×C11—22no—
218C22×C4×C11C2×D414yes—
219C22×C4×C11#4114yescomplemented
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C2×C22⋊D11—232no—
226C2×C22⋊D11—232no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—28no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11C2×D4116yes—
233C22×Dic11—232no—
234C22×Dic11—232no—
235C22×Dic11—28no—
236C22×Dic11—28no—
237C22×Dic11—28no—
238C22×Dic11—28no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—28no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11C2×D4116yes—
256C22×Dic11C2×D414yes—
257C22×Dic11C2×D414yes—
258C22×Dic11C2×D414yes—
259C22×Dic11C2×D414yes—
260C22×Dic11C2×D414yes—
261C22×Dic11#4114yescomplemented
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269#4341—2256no—
270C2×C4×D11—232no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
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×C22⋊C4—28no—
284C11×C22⋊C4—28no—
285C11×C22⋊C4—28no—
286C11×C22⋊C4—28no—
287C22⋊Dic11—28no—
288C22⋊Dic11—28no—
289C22⋊Dic11—28no—
290C22⋊Dic11—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295C4⋊Dic11—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×#394D1111yescharacteristic, complemented
312C2×#391—111no—
313C2×#390—111no—
314C2×#385—111no—
315C2×#385—111no—
316C2×#385—111no—
317C2×#385—111no—
318C2×C4×C22⋊C4—111no—
319C23×C11—28no—
320C23×C11—28no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11C22×D414yes—
346C23×C11C22×D414yes—
347C23×C11C22×D412yes—
348C23×C11C22×D412yes—
349C23×C11C22×D412yes—
350C23×C11C2×#4112yes—
351C23×C11C2×#4112yes—
352C23×C112−1+412yes—
353C23×C112−1+412yes—
354C23×C11C2511yescharacteristic
355C22×D11—28no—
356C22×D11—28no—
357C22×D11—28no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—44no—
365C22×D11—44no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11C22×D414yes—
369D4×C11—232no—
370C2×C4×C11—28no—
371C2×C4×C11—28no—
372C2×C4×C11—22no—
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—44no—
386C2×C4×C11—44no—
387C2×C4×C11—44no—
388C2×C4×C11C22×D414yes—
389C2×C4×C11C2×#4114yescomplemented
390C22⋊D11—232no—
391C22⋊D11—232no—
392C2×Dic11—232no—
393C2×Dic11—28no—
394C2×Dic11—28no—
395C2×Dic11—28no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—232no—
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—22no—
412C2×Dic11—44no—
413C2×Dic11—44no—
414C2×Dic11—44no—
415C2×Dic11#120116yes—
416C2×Dic11C22×D414yes—
417C2×Dic11C22×D414yes—
418C2×Dic11C22×D414yes—
419C2×Dic11C22×D414yes—
420C2×Dic11C22×D414yes—
421C2×Dic11C2×#4114yescomplemented
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×D4C2×D1111yescharacteristic
434C24×C4—111no—
435C24×C4—111no—
436C24×C4—111no—
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⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
459C22×C22⋊C4C2×D1111yescharacteristic
460C22×C22⋊C4C2×D1111yescharacteristic
461C22×C22⋊C4C2×D1111yescharacteristic
462C22×C42—111no—
463C22×C42—111no—
464#394—118no—
465#394—118no—
466#394—118no—
467#394C2×D1118yescomplemented
468#391—118no—
469#390—118no—
470#385—118no—
471#385—118no—
472#385—118no—
473#385—118no—
474C4×C22⋊C4—118no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95C2×D1111yescharacteristic
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—24no—
486C22×C11—24no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—416no—
490C22×C11—416no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11C2×#12014yes—
498C22×C11#53214yes—
499C22×C11#53614yes—
500C22×C11#54714yes—
501C22×C11#54714yes—
502C22×C11#54814yes—
503C22×C11#54814yes—
504C22×C11C23×D411yescharacteristic
505C22×C11C23×D411yescharacteristic
506C22×C11C23×D411yescharacteristic
507C22×C11C22×#4111yescharacteristic
508C22×C11C22×#4111yescharacteristic
509C22×C11C2×2−1+411yescharacteristic
510C22×C11C2×2−1+411yescharacteristic
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—416no—
517C2×D11—42no—
518C2×D11—42no—
519C4×C11—24no—
520C4×C11—24no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524Dic11—24no—
525Dic11—24no—
526Dic11—24no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530Dic11C2×#12018yes—
531C25—111no—
532C25C22×D1111yescharacteristic
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—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—118no—
550C22×D4—114no—
551C22×D4—114no—
552C22×D4—224no—
553C22×D4—224no—
554C22×D4—224no—
555C22×D4—224no—
556C22×D4—224no—
557C22×D4C22×D1114yes—
558C23×C4—111no—
559C23×C4—118no—
560C23×C4—114no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—114no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—114no—
569C23×C4—224no—
570C23×C4—224no—
571C23×C4—224no—
572C23×C4—224no—
573C23×C4—224no—
574C23×C4—224no—
575C23×C4—224no—
576C23×C4—224no—
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—114no—
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⋊C4—224no—
598C2×C4⋊C4C22×D1114yes—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
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⋊C4C22×D1114yes—
620C2×C22⋊C4C22×D1114yes—
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#95—114no—
632#95C22×D1114yes—
633C2×C11—44no—
634C2×C11—44no—
635C2×C11#243218yescomplemented
636C2×C11C22×#12011yescharacteristic
637C2×C11C2×#53211yescharacteristic
638C2×C11C2×#53611yescharacteristic
639C2×C11C2×#54711yescharacteristic
640C2×C11C2×#54711yescharacteristic
641C2×C11C2×#54811yescharacteristic
642C2×C11C2×#54811yescharacteristic
643D11—44no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—114no—
657C24—112no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24D4×D1114yes—
665C24D4×D1114yes—
666C24C23×D1112yes—
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—232no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—1116no—
683C2×D4—2232no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—228no—
687C2×D4—228no—
688C2×D4—2232no—
689C2×D4—228no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—114no—
704C22×C4—114no—
705C22×C4—114no—
706C22×C4—112no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—1116no—
710C22×C4—114no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—228no—
718C22×C4—228no—
719C22×C4—2232no—
720C22×C4—2232no—
721C22×C4—228no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4—228no—
725C22×C4—2232no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—228no—
732C22×C4—222no—
733C22×C4—228no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4D4×D1114yes—
744C22×C4#434114yescomplemented
745C22×C4C23×D1112yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—28no—
751C4⋊C4—228no—
752C4⋊C4—228no—
753C4⋊C4—228no—
754C4⋊C4—228no—
755C4⋊C4—228no—
756C4⋊C4—228no—
757C22⋊C4—28no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
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—28no—
776C23—28no—
777C23—28no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—114no—
799C23—228no—
800C23—228no—
801C23—228no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—444no—
809C23—444no—
810C23—444no—
811C23—444no—
812C23C2×D4×D1114yes—
813C23C2×D4×D1114yes—
814C23C2×D4×D1112yes—
815C23C2×D4×D1112yes—
816C23C2×D4×D1112yes—
817C23C2×#434112yes—
818C23#41×D1112yes—
819C23#6704312yes—
820C23#6704312yes—
821C23C24×D1111yescharacteristic
822Q8—2232no—
823Q8—4416no—
824D4—232no—
825D4—2232no—
826D4—2232no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
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—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—1116no—
846C2×C4—114no—
847C2×C4—114no—
848C2×C4—114no—
849C2×C4—114no—
850C2×C4—114no—
851C2×C4—114no—
852C2×C4—2232no—
853C2×C4—2232no—
854C2×C4—2232no—
855C2×C4—228no—
856C2×C4—228no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—228no—
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—222no—
873C2×C4—444no—
874C2×C4—444no—
875C2×C4—444no—
876C2×C4C2×D4×D1114yes—
877C2×C4C2×#434114yescomplemented
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—42no—
885C22—42no—
886C22—416no—
887C22—416no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—224no—
895C22—224no—
896C22—224no—
897C22—442no—
898C22—442no—
899C22—4416no—
900C22—442no—
901C22—442no—
902C22D11×#12014yes—
903C22#1062312714yes—
904C22#1062312914yes—
905C22#1062314214yes—
906C22#1062317914yes—
907C22#1062318614yes—
908C22#1062320814yes—
909C22C22×D4×D1111yescharacteristic
910C22C22×D4×D1111yescharacteristic
911C22C22×D4×D1111yescharacteristic
912C22C22×#434111yescharacteristic
913C22C2×#41×D1111yescharacteristic
914C22C2×#6704311yescharacteristic
915C22C2×#6704311yescharacteristic
916C4—24no—
917C4—24no—
918C4—42no—
919C4—42no—
920C4—42no—
921C4—118no—
922C4—224no—
923C4—224no—
924C4—224no—
925C4—442no—
926C4—442no—
927C4—442no—
928C2—44no—
929C2—44no—
930C2—444no—
931C2#1307223918yesdirect product factor
932C2C2×D11×#12011yescharacteristic
933C2C2×#1062312711yescharacteristic
934C2C2×#1062317911yescharacteristic
935C2C2×#1062318611yescharacteristic
936C2C2×#1062314211yescharacteristic
937C2C2×#1062312911yescharacteristic
938C2C2×#1062320811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC23×#4341C2
hypercenterC2×#394D11
hypocenterC11C2×#2432
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#66941C2semidirect
3. C22×#66938C2semidirect
4. C22×#66931C2semidirect
5. #13072239C2direct (N × H)
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622563C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622602C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
51. C2×#66941C22semidirect
53. C2×#66938C22semidirect
55. C2×#66931C22semidirect
56. C11×#394C22semidirect
58. #10622835C22semidirect
64. #10622602C22semidirect
65. #10622574C22semidirect
66. #10622572C22semidirect
67. #10622570C22semidirect
68. #10622563C22semidirect
69. #10622559C22semidirect
70. C22⋊C4×Dic11C22semidirect
71. #10622281C22semidirect
72. #10622259C22semidirect
219. C22×C4×C11#41semidirect
261. C22×Dic11#41semidirect
311. C2×#394D11semidirect
389. C2×C4×C11C2×#41semidirect
421. C2×Dic11C2×#41semidirect
467. #394C2×D11semidirect
635. C2×C11#2432semidirect
744. C22×C4#4341semidirect
771. C11C2×#2432semidirect
877. C2×C4C2×#4341semidirect
931. C2#13072239direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669412
C22×#669382
C22×#669312
#130722392
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106222592
C2×#106225702
C2×#106225632
C2×#106222812
C2×#106225592
C2×#106226022
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#243211