Finite Group Databasebeta

← C2×#13072181 #14922021

Subgroups — C2×#13072181 #14922021

Order 2816.

3678 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×#66949C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic
4C22×C4×Dic22C211yesmaximal, characteristic, complemented
5#13072181C2116yesmaximal, direct product factor
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622607C211yesmaximal, characteristic, complemented
8C2×#10622285C211yesmaximal, characteristic, complemented
9C2×#10622574C211yesmaximal, characteristic, complemented
10C2×#10622552C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622570C211yesmaximal, characteristic, complemented
13C2×#10622260C211yesmaximal, characteristic, complemented
14C2×#10622282C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C42×C11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66949—28no—
49C2×#66949C2218yescomplemented
50C2×#66938—28no—
51C2×#66938C2218yescomplemented
52C2×#66937—28no—
53C2×#66937C2218yes—
54C2×C4×Dic22—28no—
55C2×C4×Dic22C2218yescomplemented
56C11×#388C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58C2×C11×#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622607C2218yescomplemented
62#10622574C2218yescomplemented
63#10622570C2218yescomplemented
64#10622570C2218yescomplemented
65#10622561C2218yescomplemented
66#10622552C2218yescomplemented
67#10622285C2218yescomplemented
68#10622282C2218yescomplemented
69#10622279C2218yescomplemented
70#10622260C2218yescomplemented
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—24no—
95C22×D44—24no—
96C22×D44—42no—
97C22×D44C2314yes—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11C2314yes—
102C22×Dic22—24no—
103C22×Dic22—24no—
104C22×Dic22D418yescomplemented
105C22×Dic22C2314yes—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4—24no—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C42×C11—24no—
115C2×C42×C11C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11—42no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—42no—
146C2×Dic11⋊C4D418yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×C4×Dic11—24no—
153C2×C4×Dic11—24no—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158#66949—232no—
159#66938—232no—
160#66937—232no—
161C4×Dic22—232no—
162C11×#95C2314yes—
163C11×#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2426—111nomaximal, Sylow
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11#4114yes—
190C23×D11C2412yes—
191C23×D11C2412yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
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×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11#4114yes—
210C22×C4×C11C2412yes—
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—28no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
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×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11C2×D414yes—
240C22×Dic11C2×D414yes—
241C22×Dic11#4114yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×D44—28no—
249C2×D44—28no—
250C2×D44—44no—
251C2×D44—416no—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—416no—
256C2×Dic22—232no—
257C2×Dic22—28no—
258C2×Dic22—28no—
259C2×Dic22C2×D4116yescomplemented
260C11×C4⋊C4—28no—
261C11×C22⋊C4—28no—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C42×C11—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—44no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—28no—
273(C2×D11)⋊C4—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—44no—
276C4⋊Dic11—28no—
277C4⋊Dic11—44no—
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—44no—
282Dic11⋊C4C2×D4116yes—
283C4×Dic11—28no—
284C4×Dic11—28no—
285C4×Dic11—28no—
286C22×#124—111no—
287C22×C22⋊Q8—111no—
288C22×#121—111no—
289C22×C4×Q8—111no—
290#2426—1116no—
291C2×#396—111no—
292C2×#396—111no—
293C2×#394—111no—
294C2×#394—111no—
295C2×#390—111no—
296C2×#390—111no—
297C2×#390—111no—
298C2×#389—111no—
299C2×#388—111no—
300C2×#388D1111yescharacteristic, complemented
301C2×C4×C22⋊C4—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D412yes—
317C23×C11C22×D412yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C112−1+412yes—
323C23×C11C2511yescharacteristic
324C22×D11—28no—
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—44no—
341C22×D11—44no—
342C22×D11—44no—
343C22×D11—44no—
344C22×D11—44no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11C2×#4114yes—
352C2×C4×C11—28no—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
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—22no—
369C2×C4×C11—22no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D414yes—
375C2×C4×C11C2×#4114yes—
376C22⋊D11—416no—
377C22⋊D11—416no—
378C2×Dic11—28no—
379C2×Dic11—28no—
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—22no—
393C2×Dic11—44no—
394C2×Dic11—44no—
395C2×Dic11—44no—
396C2×Dic11#121116yes—
397C2×Dic11C22×D414yes—
398C2×Dic11C22×D414yes—
399C2×Dic11C22×D414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C2×#4114yes—
402D44—416no—
403C4×D11—416no—
404Dic22—232no—
405C23×Q8—111no—
406C23×D4—111no—
407C23×D4—111no—
408C23×D4—111no—
409C24×C4—111no—
410C2×#124—118no—
411C2×#124—228no—
412C2×C22⋊Q8—118no—
413C2×C22⋊Q8—228no—
414C2×#121—118no—
415C2×#121—228no—
416C2×C4×Q8—118no—
417C2×C4×Q8—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⋊C4C2×D1111yescharacteristic
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C42—111no—
441C22×C42—111no—
442C22×C42—111no—
443C22×C42C2×D1111yescharacteristic
444#396—118no—
445#396—118no—
446#394—118no—
447#394—118no—
448#390—118no—
449#390—118no—
450#390—118no—
451#389—118no—
452#388—118no—
453#388C2×D1118yescomplemented
454C4×C22⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—88no—
467C22×C11C2×#12114yes—
468C22×C11#52914yes—
469C22×C11#54214yes—
470C22×C11#54614yes—
471C22×C11#54814yes—
472C22×C11#54814yes—
473C22×C11#55014yes—
474C22×C11C23×D411yescharacteristic
475C22×C11C23×D411yescharacteristic
476C22×C11C22×#4111yescharacteristic
477C22×C11C22×#4111yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C2×H(5,𝔽2)11yescharacteristic
480C22×C11C2×2−1+411yescharacteristic
481C2×D11—24no—
482C2×D11—24no—
483C2×D11—24no—
484C2×D11—42no—
485C2×D11—416no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
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—24no—
499C4×C11—24no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11—42no—
503Dic11—24no—
504Dic11—24no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11C2×#12118yes—
509C25—111no—
510C25—111no—
511C25C22×D1111yescharacteristic
512C22×Q8—118no—
513C22×Q8—114no—
514C22×Q8—224no—
515C22×Q8—224no—
516C22×D4—114no—
517C22×D4—114no—
518C22×D4—114no—
519C22×D4—224no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—224no—
526C22×D4—442no—
527C22×D4—442no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—114no—
535C23×C4—224no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544#124—2232no—
545C22⋊Q8—2232no—
546#121—2232no—
547C4×Q8—2232no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—118no—
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—224no—
558C2×C4⋊C4—224no—
559C2×C4⋊C4—224no—
560C2×C4⋊C4—224no—
561C2×C4⋊C4—442no—
562C2×C4⋊C4—442no—
563C2×C4⋊C4C22×D1114yes—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
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—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4C22×D1114yes—
590C2×C22⋊C4C22×D1114yes—
591C2×C22⋊C4C22×D1114yes—
592C2×C42—24no—
593C2×C42—114no—
594C2×C42—114no—
595C2×C42—114no—
596C2×C42—224no—
597C2×C42—224no—
598C2×C42—224no—
599C2×C42C22×D1114yes—
600#95—114no—
601#95—114no—
602#95C22×D1114yes—
603#95C22×D1114yes—
604C2×C11—82no—
605C2×C11#242618yescomplemented
606C2×C11C22×#12111yescharacteristic
607C2×C11C2×#52911yescharacteristic
608C2×C11C2×#54211yescharacteristic
609C2×C11C2×#54611yescharacteristic
610C2×C11C2×#54811yescharacteristic
611C2×C11C2×#54811yescharacteristic
612C2×C11C2×#55011yescharacteristic
613D11—44no—
614D11—82no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—114no—
623C24—112no—
624C24—112no—
625C24—222no—
626C24—222no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24C23×D1112yes—
639C24C23×D1111yescharacteristic
640C2×Q8—1116no—
641C2×Q8—228no—
642C2×Q8—2232no—
643C2×Q8—228no—
644C2×D4—228no—
645C2×D4—228no—
646C2×D4—228no—
647C2×D4—228no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—444no—
652C2×D4—4416no—
653C2×D4—4416no—
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—22no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—228no—
683C22×C4—228no—
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—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—4416no—
699C22×C4#433914yes—
700C22×C4D4×D1114yes—
701C22×C4D4×D1114yes—
702C22×C4C23×D1112yes—
703C22×C4C23×D1112yes—
704C22×C4C23×D1112yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C4⋊C4—28no—
709C4⋊C4—1116no—
710C4⋊C4—228no—
711C4⋊C4—228no—
712C4⋊C4—228no—
713C4⋊C4—228no—
714C4⋊C4—444no—
715C4⋊C4—444no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—228no—
720C22⋊C4—228no—
721C22⋊C4—228no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—228no—
728C22⋊C4—444no—
729C22⋊C4—444no—
730C42—28no—
731C42—228no—
732C42—228no—
733C42—228no—
734C11C2×#242611yescharacteristic, complemented, Sylow
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—114no—
750C23—228no—
751C23—228no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—228no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—444no—
767C23—444no—
768C23—444no—
769C23—444no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23C2×#433912yes—
778C23C2×D4×D1112yes—
779C23C2×D4×D1112yes—
780C23#41×D1112yes—
781C23#41×D1112yes—
782C23#6704212yes—
783C23#6704312yes—
784C23C24×D1111yescharacteristic
785Q8—2232no—
786D4—4416no—
787D4—4416no—
788D4—4416no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
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—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—1116no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—114no—
816C2×C4—228no—
817C2×C4—228no—
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—4416no—
832C2×C4—444no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4C2×#433914yes—
836C2×C4C2×D4×D1114yes—
837C2×C4C2×D4×D1114yes—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—88no—
846C22—224no—
847C22—224no—
848C22—224no—
849C22—4416no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—888no—
862C22#1062305914yes—
863C22#1062308314yes—
864C22#1062308414yes—
865C22D11×#12114yes—
866C22#1062318514yes—
867C22#1062320814yes—
868C22#1062324114yes—
869C22C22×#433911yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C22×D4×D1111yescharacteristic
872C22C2×#41×D1111yescharacteristic
873C22C2×#41×D1111yescharacteristic
874C22C2×#6704211yescharacteristic
875C22C2×#6704311yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—118no—
883C4—224no—
884C4—224no—
885C4—442no—
886C4—442no—
887C4—442no—
888C2—82no—
889C2—444no—
890C2—882no—
891C2#1307218118yesdirect product factor
892C2C2×D11×#12111yescharacteristic
893C2C2×#1062305911yescharacteristic
894C2C2×#1062324111yescharacteristic
895C2C2×#1062318511yescharacteristic
896C2C2×#1062320811yescharacteristic
897C2C2×#1062308311yescharacteristic
898C2C2×#1062308411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#388D11
hypocenterC11C2×#2426
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66949C2semidirect
4. C22×C4×Dic22C2semidirect
5. #13072181C2direct (N × H)
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622285C2semidirect
9. C2×#10622574C2semidirect
10. C2×#10622552C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622570C2semidirect
13. C2×#10622260C2semidirect
14. C2×#10622282C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#388C2semidirect
49. C2×#66949C22semidirect
51. C2×#66938C22semidirect
55. C2×C4×Dic22C22semidirect
56. C11×#388C22semidirect
61. #10622607C22semidirect
62. #10622574C22semidirect
63. #10622570C22semidirect
64. #10622570C22semidirect
65. #10622561C22semidirect
66. #10622552C22semidirect
67. #10622285C22semidirect
68. #10622282C22semidirect
69. #10622279C22semidirect
70. #10622260C22semidirect
104. C22×Dic22D4semidirect
259. C2×Dic22C2×D4semidirect
300. C2×#388D11semidirect
453. #388C2×D11semidirect
605. C2×C11#2426semidirect
734. C11C2×#2426semidirect
891. C2#13072181direct (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×#669492
C22×#669372
C22×C4×Dic222
#130721812
C2×#106225612
C2×#106226072
C2×#106222852
C2×#106225742
C2×#106225522
C2×#106225702
C2×#106222602
C2×#106222822
C2×#106222792
C2×C11×#3882
C2×#242611