Finite Group Databasebeta

← C2×#13074372 #14920825

Subgroups — C2×#13074372 #14920825

Order 2816.

3566 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic
4C22×#66930C211yesmaximal, characteristic, complemented
5#13074372C2116yesmaximal, direct product factor
6C2×#10622289C211yesmaximal, characteristic, complemented
7C2×#10622561C211yesmaximal, characteristic, complemented
8C2×#10622561C211yesmaximal, characteristic, complemented
9C2×#10622607C211yesmaximal, characteristic, complemented
10C2×#10622574C211yesmaximal, characteristic, complemented
11C2×#10622572C211yesmaximal, characteristic, complemented
12C2×#10622835C211yesmaximal, characteristic, complemented
13C2×#10622259C211yesmaximal, characteristic, complemented
14C2×#10622570C211yesmaximal, characteristic, complemented
15C2×#10622589C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992—28no—
33C2×#66992C2218yes—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66938—28no—
51C2×#66938C2218yescomplemented
52C2×#66931—28no—
53C2×#66931C2218yescomplemented
54C2×#66930—28no—
55C2×#66930C2218yescomplemented
56C11×#394C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622835C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622607C2218yescomplemented
63#10622589C2218yescomplemented
64#10622574C2218yescomplemented
65#10622572C2218yescomplemented
66#10622570C2218yescomplemented
67#10622561C2218yescomplemented
68#10622561C2218yescomplemented
69#10622289C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—42no—
76C22×D4×C11—42no—
77C22×D4×C11C2314yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11—24no—
92C23×Dic11—24no—
93C23×Dic11D418yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×Dic22—24no—
103C22×Dic22—24no—
104C22×Dic22—24no—
105C22×Dic22C2314yes—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126#66992—232no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11—24no—
138C2×C4⋊Dic11—42no—
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2314yes—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—42no—
147C2×Dic11⋊C4—42no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11D418yescomplemented
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159#66938—232no—
160#66931—232no—
161#66930—232no—
162C11×#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2620—111nomaximal, Sylow
167C24×C11—22no—
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—22no—
180C24×C11C2×D414yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—416no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
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×C11C2×D414yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
224C22×Dic11—232no—
225C22×Dic11—28no—
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—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11C2×D4116yes—
244C22×Dic11C2×D414yes—
245C22×Dic11C2×D414yes—
246C22×Dic11C2×D414yes—
247C22×Dic11C2×D414yes—
248C22×Dic11#4114yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C2×Dic22—28no—
257C2×Dic22—28no—
258C2×Dic22—28no—
259C2×Dic22—416no—
260C11×C4⋊C4—44no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—44no—
265C22⋊Dic11—28no—
266C22⋊Dic11—28no—
267C22⋊Dic11—28no—
268C22⋊Dic11—28no—
269C22⋊Dic11—44no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—44no—
275C4⋊Dic11—28no—
276C4⋊Dic11—44no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—44no—
283Dic11⋊C4—44no—
284C4×Dic11—28no—
285C4×Dic11C2×D4116yescomplemented
286C22×#124—111no—
287C22×C22⋊Q8—111no—
288C22×#121—111no—
289C22×#117—111no—
290#2620—1116no—
291C2×#396—111no—
292C2×#396—111no—
293C2×#396—111no—
294C2×#396—111no—
295C2×#394—111no—
296C2×#394—111no—
297C2×#394—111no—
298C2×#394D1111yescharacteristic, complemented
299C2×#391—111no—
300C2×#390—111no—
301C2×#384—111no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11C22×D414yes—
330C23×C11C22×D412yes—
331C23×C11C22×D412yes—
332C23×C11C2×#4112yes—
333C23×C11H(5,𝔽2)12yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C112−1+412yes—
336C23×C112−1+412yes—
337C23×C11C2511yescharacteristic
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352D4×C11—416no—
353C2×C4×C11—28no—
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—44no—
369C2×C4×C11—44no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11C22×D414yes—
373C22⋊D11—416no—
374C22⋊D11—416no—
375C2×Dic11—28no—
376C2×Dic11—28no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—232no—
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—44no—
395C2×Dic11—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11#121116yes—
399C2×Dic11C22×D414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C22×D414yes—
403C2×Dic11C2×#4114yes—
404Dic22—416no—
405C23×Q8—111no—
406C23×D4—111no—
407C23×D4—111no—
408C23×D4C2×D1111yescharacteristic
409C24×C4—111no—
410C2×#124—118no—
411C2×#124—228no—
412C2×C22⋊Q8—118no—
413C2×C22⋊Q8—228no—
414C2×#121—118no—
415C2×#121—228no—
416C2×#117—118no—
417C2×#117—228no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4C2×D1111yescharacteristic
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#396—118no—
445#396—118no—
446#396—118no—
447#396—118no—
448#394—118no—
449#394—118no—
450#394—118no—
451#394C2×D1118yescomplemented
452#391—118no—
453#390—118no—
454#384—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95C2×D1111yescharacteristic
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—416no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—88no—
475C22×C11C2×#12114yes—
476C22×C11#53514yes—
477C22×C11#53614yes—
478C22×C11#53714yes—
479C22×C11#53714yes—
480C22×C11#54214yes—
481C22×C11#54214yes—
482C22×C11C23×D411yescharacteristic
483C22×C11C23×D411yescharacteristic
484C22×C11C22×#4111yescharacteristic
485C22×C11C2×H(5,𝔽2)11yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C22×C11C2×2−1+411yescharacteristic
488C22×C11C2×2−1+411yescharacteristic
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—88no—
497C4×C11—24no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502Dic11—24no—
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11C2×#12118yes—
509C25—111no—
510C25C22×D1111yescharacteristic
511C25C22×D1111yescharacteristic
512C22×Q8—114no—
513C22×Q8—224no—
514C22×Q8—224no—
515C22×Q8—224no—
516C22×D4—24no—
517C22×D4—42no—
518C22×D4—42no—
519C22×D4—114no—
520C22×D4—114no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—442no—
526C22×D4—442no—
527C22×D4C22×D1114yes—
528C23×C4—111no—
529C23×C4—118no—
530C23×C4—114no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544#124—2232no—
545C22⋊Q8—2232no—
546#121—2232no—
547#117—2232no—
548C2×C4⋊C4—42no—
549C2×C4⋊C4—114no—
550C2×C4⋊C4—114no—
551C2×C4⋊C4—114no—
552C2×C4⋊C4—114no—
553C2×C4⋊C4—114no—
554C2×C4⋊C4—114no—
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—224no—
559C2×C4⋊C4—224no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—224no—
562C2×C4⋊C4—224no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—442no—
565C2×C4⋊C4—442no—
566C2×C4⋊C4—442no—
567C2×C4⋊C4C22×D1114yes—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4—442no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C42—118no—
597C2×C42—114no—
598C2×C42—114no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95C22×D1114yes—
604C2×C11—44no—
605C2×C11—82no—
606C2×C11#262018yescomplemented
607C2×C11C22×#12111yescharacteristic
608C2×C11C2×#53511yescharacteristic
609C2×C11C2×#53611yescharacteristic
610C2×C11C2×#53711yescharacteristic
611C2×C11C2×#53711yescharacteristic
612C2×C11C2×#54211yescharacteristic
613C2×C11C2×#54211yescharacteristic
614D11—82no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—112no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24D4×D1114yes—
637C24C23×D1112yes—
638C24C23×D1112yes—
639C24C23×D1111yescharacteristic
640C2×Q8—228no—
641C2×Q8—228no—
642C2×Q8—228no—
643C2×Q8—4416no—
644C2×D4—28no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—416no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—4416no—
653C2×D4—444no—
654C2×D4—444no—
655C2×D4—4416no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—112no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—1116no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—112no—
683C22×C4—228no—
684C22×C4—2232no—
685C22×C4—228no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4D4×D1114yes—
703C22×C4C23×D1112yes—
704C22×C4C23×D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C4⋊C4—44no—
709C4⋊C4—228no—
710C4⋊C4—228no—
711C4⋊C4—228no—
712C4⋊C4—228no—
713C4⋊C4—228no—
714C4⋊C4—228no—
715C4⋊C4—444no—
716C4⋊C4—444no—
717C4⋊C4—444no—
718C22⋊C4—28no—
719C22⋊C4—28no—
720C22⋊C4—28no—
721C22⋊C4—44no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—228no—
728C22⋊C4—228no—
729C22⋊C4—444no—
730C22⋊C4—444no—
731C22⋊C4—444no—
732C42—1116no—
733C42—228no—
734C11C2×#262011yescharacteristic, complemented, Sylow
735C23—28no—
736C23—28no—
737C23—28no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23C2×D4×D1114yes—
777C23C2×D4×D1112yes—
778C23C2×D4×D1112yes—
779C23#6703712yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#6704312yes—
783C23#6704312yes—
784C23C24×D1111yescharacteristic
785Q8—4416no—
786D4—416no—
787D4—4416no—
788D4—4416no—
789C2×C4—28no—
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—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—1116no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—2232no—
815C2×C4—228no—
816C2×C4—228no—
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—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4C2×D4×D1114yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—416no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—88no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—888no—
862C22#1062312314yes—
863C22#1062312814yes—
864C22D11×#12114yes—
865C22#1062313914yes—
866C22#1062317914yes—
867C22#1062319314yes—
868C22#1062320014yes—
869C22C22×D4×D1111yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C2×#6703711yescharacteristic
872C22C2×#6703711yescharacteristic
873C22C2×#41×D1111yescharacteristic
874C22C2×#6704311yescharacteristic
875C22C2×#6704311yescharacteristic
876C4—24no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—118no—
882C4—224no—
883C4—224no—
884C4—442no—
885C4—442no—
886C4—442no—
887C4—442no—
888C2—44no—
889C2—82no—
890C2—882no—
891C2#1307437218yesdirect product factor
892C2C2×D11×#12111yescharacteristic
893C2C2×#1062312311yescharacteristic
894C2C2×#1062317911yescharacteristic
895C2C2×#1062312811yescharacteristic
896C2C2×#1062313911yescharacteristic
897C2C2×#1062320011yescharacteristic
898C2C2×#1062319311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#394D11
hypocenterC11C2×#2620
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66931C2semidirect
4. C22×#66930C2semidirect
5. #13074372C2direct (N × H)
6. C2×#10622289C2semidirect
7. C2×#10622561C2semidirect
8. C2×#10622561C2semidirect
9. C2×#10622607C2semidirect
10. C2×#10622574C2semidirect
11. C2×#10622572C2semidirect
12. C2×#10622835C2semidirect
13. C2×#10622259C2semidirect
14. C2×#10622570C2semidirect
15. C2×#10622589C2semidirect
16. C2×C11×#394C2semidirect
51. C2×#66938C22semidirect
53. C2×#66931C22semidirect
55. C2×#66930C22semidirect
56. C11×#394C22semidirect
58. #10622835C22semidirect
62. #10622607C22semidirect
63. #10622589C22semidirect
64. #10622574C22semidirect
65. #10622572C22semidirect
66. #10622570C22semidirect
67. #10622561C22semidirect
68. #10622561C22semidirect
69. #10622289C22semidirect
70. #10622259C22semidirect
156. C2×C4×Dic11D4semidirect
285. C4×Dic11C2×D4semidirect
298. C2×#394D11semidirect
451. #394C2×D11semidirect
606. C2×C11#2620semidirect
734. C11C2×#2620semidirect
891. C2#13074372direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669312
C22×#669922
C22×#669302
#130743722
C2×#106222892
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106222592
C2×#106225702
C2×#106225892
C2×C11×#3942
C2×#262011