Finite Group Databasebeta

← C2×#13071690 #14913383

Subgroups — C2×#13071690 #14913383

Order 2816.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
4#13071690C2116yesmaximal, direct product factor
5C2×#10622259C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic
7C2×#10622558C211yesmaximal, characteristic, complemented
8C2×#10622283C211yesmaximal, characteristic, complemented
9C2×#10622603C211yesmaximal, characteristic, complemented
10C2×#10622563C211yesmaximal, characteristic, complemented
11C2×#10622281C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622262C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66938C4116yescomplemented
45C2×#66938C2218yes—
46C2×(C22⋊D11)⋊C4—28no—
47C2×(C22⋊D11)⋊C4C2218yes—
48C2×C4×Dic22—28no—
49C2×C4×Dic22C2218yescomplemented
50C11×#388C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622603C2218yescomplemented
60C4⋊C4×Dic11C2218yescomplemented
61#10622570C2218yes—
62#10622563C2218yescomplemented
63#10622558C2218yescomplemented
64C22⋊C4×Dic11C2218yescomplemented
65C4×(C2×D11)⋊C4C2218yescomplemented
66#10622283C2218yescomplemented
67#10622281C2218yescomplemented
68#10622262C2218yescomplemented
69#10622259C2218yescomplemented
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11C2×C418yes—
81C22×C22⋊D11C2314yes—
82C23×Dic11—24no—
83C23×Dic11—24no—
84C23×Dic11—42no—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—24no—
95C22×C4×D11—42no—
96C22×C4×D11C2314yes—
97C22×Dic22—24no—
98C22×Dic22—24no—
99C22×Dic22C2×C418yescomplemented
100C22×Dic22C2314yes—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4C2×C418yescomplemented
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2314yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C42×C11—24no—
110C2×C42×C11C2314yes—
111C2×C22⋊Dic11—42no—
112C2×C22⋊Dic11C2×C418yescomplemented
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—42no—
118C2×(C2×D11)⋊C4C2×C418yescomplemented
119C2×(C2×D11)⋊C4C2×C418yescomplemented
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2314yes—
129C2×Dic11⋊C4—24no—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4D418yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—24no—
137C2×C4×Dic11—24no—
138C2×C4×Dic11—42no—
139C2×C4×Dic11—42no—
140C2×C4×Dic11C2×C418yescomplemented
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147#66938C2×C4164yescomplemented
148(C22⋊D11)⋊C4—232no—
149C4×Dic22—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2367—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C22×C414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11C22×C414yes—
175C23×D11C2412yes—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C2×D414yes—
193C22×C4×C11#4114yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C2×C22⋊D11—232no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11C22×C4116yes—
204C22×Dic11—28no—
205C22×Dic11—28no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—44no—
221C22×Dic11—416no—
222C22×Dic11C22×C414yes—
223C22×Dic11C22×C414yes—
224C22×Dic11C22×C414yes—
225C22×Dic11C2×D414yes—
226C22×Dic11C2×D414yes—
227C22×Dic11#4114yes—
228C22×Dic11#4114yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C2×C4×D11—28no—
237C2×C4×D11—28no—
238C2×C4×D11—44no—
239C2×C4×D11—416no—
240C2×Dic22—232no—
241C2×Dic22—28no—
242C2×Dic22—28no—
243C2×Dic22C22×C4116yescomplemented
244C11×C4⋊C4—28no—
245C11×C22⋊C4—28no—
246C11×C22⋊C4—28no—
247C11×C22⋊C4C22×C4116yescomplemented
248C42×C11—28no—
249C22⋊Dic11—44no—
250C22⋊Dic11C22×C4116yescomplemented
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4C22×C4116yescomplemented
255(C2×D11)⋊C4C22×C4116yescomplemented
256C4⋊Dic11—28no—
257C4⋊Dic11—28no—
258Dic11⋊C4—28no—
259Dic11⋊C4—28no—
260Dic11⋊C4C2×D4116yes—
261C4×Dic11—28no—
262C4×Dic11—28no—
263C4×Dic11—28no—
264C4×Dic11—44no—
265C4×Dic11—44no—
266C4×Dic11C22×C4116yescomplemented
267C22×#124—111no—
268C22×C4×Q8—111no—
269C22×C4×D4—111no—
270#2367—1116no—
271C2×#391—111no—
272C2×#390—111no—
273C2×#388—111no—
274C2×#388—111no—
275C2×#388—111no—
276C2×#388D1111yescharacteristic, complemented
277C2×#385—111no—
278C2×#385—111no—
279C2×C4×C4⋊C4—111no—
280C2×C4×C4⋊C4—111no—
281C2×C4×C22⋊C4—111no—
282C2×C4×C22⋊C4—111no—
283C23×C11—28no—
284C23×C11—28no—
285C23×C11—28no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11C23×C414yes—
297C23×C11C23×C412yes—
298C23×C11C22×D412yes—
299C23×C11C2×#4112yes—
300C23×C11C2×#4112yes—
301C23×C11C2×#4112yes—
302C23×C11H(5,𝔽2)12yes—
303C23×C112−1+412yes—
304C23×C11C2511yescharacteristic
305C22×D11—28no—
306C22×D11—28no—
307C22×D11—28no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—44no—
317C22×D11—44no—
318C22×D11C23×C414yes—
319C2×C4×C11—28no—
320C2×C4×C11—28no—
321C2×C4×C11—28no—
322C2×C4×C11—28no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11C23×C414yes—
340C2×C4×C11C23×C414yes—
341C2×C4×C11C22×D414yes—
342C2×C4×C11C2×#4114yes—
343C22⋊D11—232no—
344C2×Dic11—28no—
345C2×Dic11—28no—
346C2×Dic11—28no—
347C2×Dic11—28no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—416no—
363C2×Dic11—44no—
364C2×Dic11—44no—
365C2×Dic11C4×D4116yes—
366C2×Dic11C23×C414yes—
367C2×Dic11C23×C414yes—
368C2×Dic11C23×C414yes—
369C2×Dic11C22×D414yes—
370C2×Dic11C22×D414yes—
371C2×Dic11C2×#4114yes—
372C2×Dic11C2×#4114yes—
373C4×D11—416no—
374Dic22—232no—
375C23×Q8—111no—
376C23×D4—111no—
377C24×C4—111no—
378C24×C4—111no—
379C2×#124—118no—
380C2×#124—1116no—
381C2×C4×Q8—118no—
382C2×C4×Q8—228no—
383C2×C4×D4—118no—
384C2×C4×D4—228no—
385C22×C4⋊C4—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4C2×D1111yescharacteristic
391C22×C22⋊C4—111no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—111no—
398C22×C22⋊C4C2×D1111yescharacteristic
399C22×C22⋊C4C2×D1111yescharacteristic
400C22×C22⋊C4C2×D1111yescharacteristic
401C22×C42—111no—
402C22×C42—111no—
403C22×C42—111no—
404C22×C42—111no—
405C22×C42—111no—
406C22×C42—111no—
407C22×C42C2×D1111yescharacteristic
408#391—118no—
409#390—118no—
410#388—118no—
411#388—118no—
412#388—118no—
413#388C2×D1118yescomplemented
414#385—118no—
415#385—118no—
416C4×C4⋊C4—118no—
417C4×C4⋊C4—118no—
418C4×C22⋊C4—118no—
419C4×C22⋊C4—118no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95C2×D1111yescharacteristic
427C2×#95C2×D1111yescharacteristic
428C22×C11—24no—
429C22×C11—24no—
430C22×C11—24no—
431C22×C11—416no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11C2×C4×D414yes—
437C22×C11C4×#4114yes—
438C22×C11#52014yes—
439C22×C11#54614yes—
440C22×C11#54814yes—
441C22×C11#55614yes—
442C22×C11#55914yes—
443C22×C11C24×C411yescharacteristic
444C22×C11C23×D411yescharacteristic
445C22×C11C22×#4111yescharacteristic
446C22×C11C22×#4111yescharacteristic
447C22×C11C22×#4111yescharacteristic
448C22×C11C2×H(5,𝔽2)11yescharacteristic
449C22×C11C2×2−1+411yescharacteristic
450C2×D11—24no—
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—416no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C4×C11—24no—
459C4×C11—24no—
460C4×C11—24no—
461C4×C11—24no—
462C4×C11—42no—
463C4×C11—42no—
464Dic11—24no—
465Dic11—24no—
466Dic11—24no—
467Dic11—24no—
468Dic11—42no—
469Dic11—42no—
470Dic11C2×C4×D418yes—
471C25—111no—
472C25C22×D1111yescharacteristic
473C22×Q8—118no—
474C22×Q8—114no—
475C22×Q8—224no—
476C22×Q8—224no—
477C22×D4—118no—
478C22×D4—114no—
479C22×D4—224no—
480C22×D4—224no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—114no—
489C23×C4—114no—
490C23×C4—224no—
491C23×C4—224no—
492C23×C4—224no—
493C23×C4—224no—
494C23×C4—442no—
495C23×C4—442no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502#124—1164no—
503C4×Q8—2232no—
504C4×D4—2232no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—118no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—114no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—224no—
514C2×C4⋊C4—224no—
515C2×C4⋊C4—224no—
516C2×C4⋊C4C22×D1114yes—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—118no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—118no—
522C2×C22⋊C4—118no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—224no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—442no—
532C2×C22⋊C4—442no—
533C2×C22⋊C4C4×D1118yescomplemented
534C2×C22⋊C4C22×D1114yes—
535C2×C22⋊C4C22×D1114yes—
536C2×C22⋊C4C22×D1114yes—
537C2×C42—24no—
538C2×C42—118no—
539C2×C42—114no—
540C2×C42—114no—
541C2×C42—114no—
542C2×C42—114no—
543C2×C42—114no—
544C2×C42—114no—
545C2×C42—224no—
546C2×C42—224no—
547C2×C42—224no—
548C2×C42—442no—
549C2×C42—442no—
550C2×C42C22×D1114yes—
551#95—114no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—114no—
556#95—114no—
557#95C22×D1114yes—
558#95C22×D1114yes—
559C2×C11—44no—
560C2×C11#236718yescomplemented
561C2×C11C22×C4×D411yescharacteristic
562C2×C11C2×C4×#4111yescharacteristic
563C2×C11C2×#52011yescharacteristic
564C2×C11C2×#54611yescharacteristic
565C2×C11C2×#54811yescharacteristic
566C2×C11C2×#55611yescharacteristic
567C2×C11C2×#55911yescharacteristic
568D11—44no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—114no—
576C24—112no—
577C24—222no—
578C24—222no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24C2×C4×D1114yes—
584C24C23×D1112yes—
585C24C23×D1111yescharacteristic
586C2×Q8—1116no—
587C2×Q8—228no—
588C2×Q8—2232no—
589C2×Q8—228no—
590C2×D4—1116no—
591C2×D4—228no—
592C2×D4—2232no—
593C2×D4—228no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—114no—
609C22×C4—114no—
610C22×C4—114no—
611C22×C4—112no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—114no—
615C22×C4—114no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—228no—
623C22×C4—228no—
624C22×C4—228no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—228no—
640C22×C4—444no—
641C22×C4—4416no—
642C22×C4—444no—
643C22×C4—4416no—
644C22×C4C2×C4×D1114yes—
645C22×C4C2×C4×D1114yes—
646C22×C4D4×D1114yes—
647C22×C4#434114yes—
648C22×C4C23×D1112yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1112yes—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C4⋊C4—28no—
655C4⋊C4—1116no—
656C4⋊C4—228no—
657C4⋊C4—228no—
658C4⋊C4—228no—
659C4⋊C4—228no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—1116no—
663C22⋊C4—1116no—
664C22⋊C4—1116no—
665C22⋊C4—228no—
666C22⋊C4—228no—
667C22⋊C4—444no—
668C22⋊C4—444no—
669C22⋊C4C2×C4×D11116yescomplemented
670C42—28no—
671C42—1116no—
672C42—228no—
673C42—228no—
674C42—228no—
675C42—444no—
676C42—444no—
677C11C2×#236711yescharacteristic, complemented, Sylow
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—114no—
692C23—228no—
693C23—228no—
694C23—228no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—444no—
702C23—444no—
703C23—444no—
704C23—444no—
705C23C22×C4×D1114yes—
706C23C22×C4×D1112yes—
707C23C2×D4×D1112yes—
708C23C2×#434112yes—
709C23#41×D1112yes—
710C23#41×D1112yes—
711C23#6704212yes—
712C23#6704312yes—
713C23C24×D1111yescharacteristic
714Q8—2232no—
715D4—2232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—1116no—
737C2×C4—114no—
738C2×C4—114no—
739C2×C4—114no—
740C2×C4—114no—
741C2×C4—114no—
742C2×C4—114no—
743C2×C4—114no—
744C2×C4—228no—
745C2×C4—228no—
746C2×C4—228no—
747C2×C4—228no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—4416no—
763C2×C4—4416no—
764C2×C4—444no—
765C2×C4—444no—
766C2×C4C22×C4×D1114yes—
767C2×C4C22×C4×D1114yes—
768C2×C4C2×D4×D1114yes—
769C2×C4C2×#434114yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—416no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—224no—
779C22—224no—
780C22—224no—
781C22—442no—
782C22—4416no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22#1062305414yes—
787C22C4×#434114yes—
788C22C4×D4×D1114yes—
789C22#1062312914yes—
790C22#1062318514yes—
791C22#1062321214yes—
792C22#1062323314yes—
793C22C23×C4×D1111yescharacteristic
794C22C22×D4×D1111yescharacteristic
795C22C22×#434111yescharacteristic
796C22C2×#41×D1111yescharacteristic
797C22C2×#41×D1111yescharacteristic
798C22C2×#6704211yescharacteristic
799C22C2×#6704311yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—118no—
807C4—224no—
808C4—224no—
809C4—224no—
810C4—224no—
811C4—442no—
812C4—442no—
813C2—44no—
814C2—444no—
815C2#1307169018yesdirect product factor
816C2C2×C4×D4×D1111yescharacteristic
817C2C2×C4×#434111yescharacteristic
818C2C2×#1062305411yescharacteristic
819C2C2×#1062318511yescharacteristic
820C2C2×#1062312911yescharacteristic
821C2C2×#1062323311yescharacteristic
822C2C2×#1062321211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2367
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. #13071690C2direct (N × H)
5. C2×#10622259C2semidirect
7. C2×#10622558C2semidirect
8. C2×#10622283C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622563C2semidirect
11. C2×#10622281C2semidirect
12. C2×C4⋊C4×Dic11C2semidirect
13. C2×#10622262C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
44. C2×#66938C4semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#388C22semidirect
59. #10622603C22semidirect
60. C4⋊C4×Dic11C22semidirect
62. #10622563C22semidirect
63. #10622558C22semidirect
64. C22⋊C4×Dic11C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622283C22semidirect
67. #10622281C22semidirect
68. #10622262C22semidirect
69. #10622259C22semidirect
99. C22×Dic22C2×C4semidirect
105. C2×C11×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic11C2×C4semidirect
118. C2×(C2×D11)⋊C4C2×C4semidirect
119. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×C4×Dic11C2×C4semidirect
147. #66938C2×C4semidirect
243. C2×Dic22C22×C4semidirect
247. C11×C22⋊C4C22×C4semidirect
250. C22⋊Dic11C22×C4semidirect
254. (C2×D11)⋊C4C22×C4semidirect
255. (C2×D11)⋊C4C22×C4semidirect
266. C4×Dic11C22×C4semidirect
276. C2×#388D11semidirect
413. #388C2×D11semidirect
533. C2×C22⋊C4C4×D11semidirect
560. C2×C11#2367semidirect
669. C22⋊C4C2×C4×D11semidirect
677. C11C2×#2367semidirect
815. C2#13071690direct (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×C4×Dic222
C22×(C22⋊D11)⋊C42
#130716902
C2×#106222592
C2×#106225702
C2×#106225582
C2×#106222832
C2×#106226032
C2×#106225632
C2×#106222812
C2×C4⋊C4×Dic112
C2×#106222622
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#236711