Finite Group Databasebeta

← C2×#13072861 #14921377

Subgroups — C2×#13072861 #14921377

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×#66932C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C211yesmaximal, characteristic
3#13072861C2116yesmaximal, direct product factor
4C2×#10622565C211yesmaximal, characteristic, complemented
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622558C211yesmaximal, characteristic, complemented
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622563C211yesmaximal, characteristic, complemented
12C2×#10622559C211yesmaximal, characteristic, complemented
13C2×#10622555C211yesmaximal, characteristic, complemented
14C2×#10622860C211yesmaximal, characteristic
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#379C211yesmaximal, characteristic
17C26×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11—28no—
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2218yes—
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic, complemented
39C22×C4⋊Dic11C2211yescharacteristic, complemented
40C22×Dic11⋊C4C2211yescharacteristic, complemented
41C22×Dic11⋊C4C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2211yescharacteristic, complemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic11C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46C2×#66932—28no—
47C2×#66932C2218yescomplemented
48C11×#379C2218yes—
49#10622860C2218yes—
50C2×C11⋊#95C2211yescharacteristic, complemented
51C2×C11⋊#95C2211yescharacteristic, complemented
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#10622566C2218yescomplemented
59#10622565C2218yescomplemented
60#10622565C2218yescomplemented
61#10622564C2218yescomplemented
62#10622563C2218yescomplemented
63#10622561C2218yescomplemented
64#10622559C2218yescomplemented
65#10622558C2218yescomplemented
66#10622557C2218yescomplemented
67#10622555C2218yescomplemented
68C22⋊C4×Dic11C2218yescomplemented
69C25×C11—24no—
70C25×C11—24no—
71C25×C11—24no—
72C25×C11—24no—
73C25×C11—24no—
74C25×C11—42no—
75C25×C11—42no—
76C25×C11C2311yescharacteristic
77C25×C11C2311yescharacteristic
78C25×C11C2314yes—
79C25×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11—24no—
87C23×Dic11—24no—
88C23×Dic11—42no—
89C23×Dic11—42no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2314yes—
97C23×Dic11C2314yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—42no—
105C2×C11×C22⋊C4—42no—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—232no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11D418yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11—42no—
135C2×C4⋊Dic11C2314yescomplemented
136C2×C4⋊Dic11C2314yescomplemented
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—24no—
139C2×Dic11⋊C4—42no—
140C2×Dic11⋊C4—42no—
141C2×Dic11⋊C4C2314yescomplemented
142C2×Dic11⋊C4C2314yescomplemented
143C2×Dic11⋊C4C2314yescomplemented
144C2×Dic11⋊C4C2314yescomplemented
145C2×C4×Dic11—24no—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yescomplemented
148C2×C4×Dic11C2314yescomplemented
149#66932—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—232no—
164C24×C11—28no—
165C24×C11—22no—
166C24×C11—28no—
167C24×C11—28no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—28no—
180C24×C11—28no—
181C24×C11—44no—
182C24×C11—44no—
183C24×C11—416no—
184C24×C11—416no—
185C24×C11—416no—
186C24×C11—416no—
187C24×C11—416no—
188C24×C11—416no—
189C24×C11C2×D414yes—
190C24×C11#4114yes—
191C24×C11#4114yes—
192C24×C11#4114yes—
193C24×C11#4114yes—
194C24×C11C2412yes—
195C24×C11C2412yes—
196C24×C11C2412yes—
197C24×C11C2411yescharacteristic
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—22no—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×Dic11—28no—
215C22×Dic11—28no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—28no—
229C22×Dic11—22no—
230C22×Dic11—28no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—44no—
241C22×Dic11—44no—
242C22×Dic11—416no—
243C22×Dic11—416no—
244C22×Dic11C2×D414yes—
245C22×Dic11C2×D414yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—44no—
259C11×C22⋊C4—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—28no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—28no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11C2×D4116yes—
270C4⋊Dic11—28no—
271C4⋊Dic11—44no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—44no—
275Dic11⋊C4—44no—
276C4×Dic11—28no—
277C4×Dic11—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×#379D1111yescharacteristic
293C2×C4×C22⋊C4—111no—
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—232no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—416no—
324C23×C11—416no—
325C23×C11—416no—
326C23×C11—416no—
327C23×C11—416no—
328C23×C11—4128no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—416no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11#126116yescomplemented
339C23×C11C22×D414yes—
340C23×C11C22×D412yes—
341C23×C11C2×#4114yes—
342C23×C11C2×#4112yes—
343C23×C11C2×#4114yes—
344C23×C11C2×#4114yes—
345C23×C11C2×#4114yes—
346C23×C11C2×#4112yes—
347C23×C11C2×#4112yes—
348C23×C11C2×#4112yes—
349C23×C11H(5,𝔽2)12yes—
350C23×C11H(5,𝔽2)12yes—
351C23×C11C2511yescharacteristic
352C2×C4×C11—22no—
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—44no—
365C2×C4×C11—44no—
366C2×C4×C11—44no—
367C2×C4×C11—44no—
368C2×Dic11—28no—
369C2×Dic11—28no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
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—416no—
393C2×Dic11—416no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C26C2×D1111yescharacteristic
403C24×C4—111no—
404C24×C4—111no—
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—118no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—228no—
425C22×C22⋊C4C2×D1111yescharacteristic
426C22×C22⋊C4C2×D1111yescharacteristic
427C22×C22⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4C2×D1111yescharacteristic
429C22×C22⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4C2×D1111yescharacteristic
431C22×C42—111no—
432C22×C42—111no—
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#379C2×D1118yes—
445C4×C22⋊C4—118no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—232no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—464no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—416no—
477C22×C11—416no—
478C22×C11#52514yes—
479C22×C11C2×#12614yes—
480C22×C11C2×#12618yescomplemented
481C22×C11#53814yes—
482C22×C11#54614yes—
483C22×C11#54614yes—
484C22×C11#55114yes—
485C22×C11#55114yes—
486C22×C11C23×D411yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C22×#4111yescharacteristic
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×H(5,𝔽2)11yescharacteristic
493C4×C11—42no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497Dic11—24no—
498Dic11—24no—
499Dic11—42no—
500Dic11—42no—
501Dic11—42no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505C25—24no—
506C25—24no—
507C25—24no—
508C25—24no—
509C25—24no—
510C25—42no—
511C25—42no—
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C25C22×D1114yes—
515C25C22×D1111yescharacteristic
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—114no—
525C23×C4—114no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—224no—
530C23×C4—442no—
531C23×C4—442no—
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
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—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—118no—
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—442no—
575C2×C22⋊C4—442no—
576C2×C22⋊C4C22×D1114yes—
577C2×C22⋊C4C22×D1114yes—
578C2×C22⋊C4C22×D1114yes—
579C2×C22⋊C4C22×D1114yes—
580C2×C22⋊C4C22×D1114yes—
581C2×C22⋊C4C22×D1114yes—
582C2×C42—114no—
583C2×C42—114no—
584C2×C42—224no—
585C2×C42—442no—
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95—114no—
591#95—114no—
592#95—114no—
593#95—114no—
594C2×C11—28no—
595C2×C11—44no—
596C2×C11—44no—
597C2×C11#248018yescomplemented
598C2×C11C2×#52511yescharacteristic
599C2×C11C22×#12611yescharacteristic
600C2×C11C2×#53811yescharacteristic
601C2×C11C2×#54611yescharacteristic
602C2×C11C2×#54611yescharacteristic
603C2×C11C2×#55111yescharacteristic
604C2×C11C2×#55111yescharacteristic
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—232no—
610C24—22no—
611C24—22no—
612C24—28no—
613C24—22no—
614C24—28no—
615C24—28no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—28no—
627C24—44no—
628C24—44no—
629C24—416no—
630C24—416no—
631C24—416no—
632C24—416no—
633C24—416no—
634C24—416no—
635C24#433914yes—
636C24D4×D1114yes—
637C24#434114yes—
638C24#434114yes—
639C24#434114yes—
640C24C23×D1112yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—114no—
657C22×C4—114no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—228no—
667C22×C4—228no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—228no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—228no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—444no—
693C22×C4—444no—
694C22×C4—4416no—
695C22×C4—4416no—
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—28no—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—1116no—
713C22⋊C4—228no—
714C22⋊C4—228no—
715C22⋊C4—228no—
716C22⋊C4—228no—
717C22⋊C4—228no—
718C22⋊C4—228no—
719C22⋊C4—228no—
720C22⋊C4—444no—
721C22⋊C4—444no—
722C42—228no—
723C42—444no—
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—232no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—416no—
755C23—416no—
756C23—416no—
757C23—416no—
758C23—416no—
759C23—4128no—
760C23—44no—
761C23—44no—
762C23—416no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23#66932116yescomplemented
770C23C2×#433914yes—
771C23C2×#433912yes—
772C23C2×D4×D1114yes—
773C23C2×D4×D1112yes—
774C23C2×#434114yes—
775C23C2×#434114yes—
776C23C2×#434114yes—
777C23C2×#434112yes—
778C23C2×#434112yes—
779C23C2×#434112yes—
780C23#6703712yes—
781C23#6703712yes—
782C23C24×D1111yescharacteristic
783C2×C4—22no—
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—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—114no—
800C2×C4—114no—
801C2×C4—228no—
802C2×C4—228no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
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—4416no—
826C2×C4—4416no—
827C2×C4—444no—
828C2×C4—444no—
829C2×C4—444no—
830C2×C4—444no—
831C2×C4—444no—
832C2×C4—444no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—232no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—464no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—416no—
856C22—416no—
857C22C2×#6693214yes—
858C22C2×#6693218yescomplemented
859C22#1062302114yes—
860C22#1062302614yes—
861C22#1062311714yes—
862C22#1062311814yes—
863C22#1062312214yes—
864C22#1062312414yes—
865C22C22×#433911yescharacteristic
866C22C22×D4×D1111yescharacteristic
867C22C22×#434111yescharacteristic
868C22C22×#434111yescharacteristic
869C22C22×#434111yescharacteristic
870C22C2×#6703711yescharacteristic
871C22C2×#6703711yescharacteristic
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—224no—
877C4—224no—
878C4—442no—
879C4—442no—
880C4—442no—
881C4—442no—
882C4—442no—
883C4—442no—
884C2—28no—
885C2—44no—
886C2—44no—
887C2#1307286118yesdirect product factor
888C2C2×#1062311711yescharacteristic
889C2C22×#6693211yescharacteristic
890C2C2×#1062312411yescharacteristic
891C2C2×#1062312211yescharacteristic
892C2C2×#1062302111yescharacteristic
893C2C2×#1062302611yescharacteristic
894C2C2×#1062311811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#379C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11C2×#2480
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
3. #13072861C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622565C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622558C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622563C2semidirect
12. C2×#10622559C2semidirect
13. C2×#10622555C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
38. C22×C4⋊Dic11C22semidirect
39. C22×C4⋊Dic11C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×C4×Dic11C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66932C22semidirect
50. C2×C11⋊#95C22semidirect
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. C2×C11⋊#95C22semidirect
54. C2×C11⋊#95C22semidirect
55. C2×C11⋊#95C22semidirect
56. C2×C11⋊#95C22semidirect
57. C2×C11⋊#95C22semidirect
58. #10622566C22semidirect
59. #10622565C22semidirect
60. #10622565C22semidirect
61. #10622564C22semidirect
62. #10622563C22semidirect
63. #10622561C22semidirect
64. #10622559C22semidirect
65. #10622558C22semidirect
66. #10622557C22semidirect
67. #10622555C22semidirect
68. C22⋊C4×Dic11C22semidirect
135. C2×C4⋊Dic11C23semidirect
136. C2×C4⋊Dic11C23semidirect
141. C2×Dic11⋊C4C23semidirect
142. C2×Dic11⋊C4C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
147. C2×C4×Dic11C23semidirect
148. C2×C4×Dic11C23semidirect
150. C11⋊#95C23semidirect
151. C11⋊#95C23semidirect
152. C11⋊#95C23semidirect
153. C11⋊#95C23semidirect
154. C11⋊#95C23semidirect
155. C11⋊#95C23semidirect
156. C11⋊#95C23semidirect
157. C11⋊#95C23semidirect
338. C23×C11#126semidirect
480. C22×C11C2×#126semidirect
597. C2×C11#2480semidirect
724. C11C2×#2480semidirect
769. C23#66932semidirect
858. C22C2×#66932semidirect
887. C2#13072861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C23×C22⋊Dic112
#130728612
C2×#106225652
C2×#106225662
C2×#106225612
C2×#106225582
C2×#106225642
C2×#106225572
C2×#106225632
C2×#106225592
C2×#106225552
C2×#106228602
C2×C22⋊C4×Dic112
C2×C11×#3792
C2×#248011