Finite Group Databasebeta

← C2×#13071657 #14913329

Subgroups — C2×#13071657 #14913329

Order 2816.

4046 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×#66992C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×#66930C211yesmaximal, characteristic, complemented
4#13071657C2116yesmaximal, direct product factor
5C2×#10622834C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622260C211yesmaximal, characteristic, complemented
9C2×#10622558C211yesmaximal, characteristic, complemented
10C2×#10622283C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622262C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×#66992C4116yescomplemented
32C2×#66992C2218yes—
33C2×C4×C22⋊D11—28no—
34C2×C4×C22⋊D11C2218yescomplemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C2×#66930—28no—
51C2×#66930C2218yescomplemented
52C11×#386C2218yescomplemented
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55#10622834C2218yescomplemented
56C4×C22⋊Dic11C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622570C2218yescomplemented
62#10622570C2218yescomplemented
63#10622569C2218yescomplemented
64#10622558C2218yescomplemented
65C22⋊C4×Dic11C2218yescomplemented
66#10622283C2218yescomplemented
67#10622279C2218yescomplemented
68#10622262C2218yescomplemented
69#10622260C2218yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2×C418yescomplemented
76C22×D4×C11C2314yes—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11—42no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11C2×C418yes—
91C22×C22⋊D11C2×C418yescomplemented
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11C2×C418yescomplemented
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C22×C4×D11—24no—
106C22×C4×D11—24no—
107C22×C4×D11—42no—
108C22×C4×D11C2314yes—
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×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11C2×C418yescomplemented
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125#66992C2×C4164yescomplemented
126C4×C22⋊D11—232no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4C2×C418yescomplemented
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—42no—
136C2×C4⋊Dic11C2314yes—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4C2×C418yescomplemented
140C2×Dic11⋊C4D418yescomplemented
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11—24no—
147C2×C4×Dic11—24no—
148C2×C4×Dic11—24no—
149C2×C4×Dic11—42no—
150C2×C4×Dic11—42no—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2314yes—
157#66930—232no—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2363—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
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×C11C22×C414yes—
178C24×C11C22×C414yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C22×C414yes—
189C23×D11C2412yes—
190C2×D4×C11—416no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11C22×C4116yescomplemented
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—28no—
207C22×C4×C11—28no—
208C22×C4×C11—44no—
209C22×C4×C11—416no—
210C22×C4×C11C22×C414yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11#4114yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—232no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—416no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11C22×C4116yes—
225C2×C22⋊D11C22×C4116yescomplemented
226C22×Dic11—232no—
227C22×Dic11—28no—
228C22×Dic11—28no—
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×Dic11C22×C414yes—
244C22×Dic11C22×C414yes—
245C22×Dic11C22×C414yes—
246C22×Dic11C22×C4116yescomplemented
247C22×Dic11C2×D414yes—
248C22×Dic11C2×D414yes—
249C22×Dic11#4114yes—
250C22×Dic11#4114yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C2×C4×D11—28no—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—416no—
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⋊Dic11C22×C4116yescomplemented
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4C22×C4116yescomplemented
274C4⋊Dic11—44no—
275Dic11⋊C4—28no—
276Dic11⋊C4—44no—
277Dic11⋊C4C22×C4116yescomplemented
278Dic11⋊C4C2×D4116yescomplemented
279C4×Dic11—28no—
280C4×Dic11—28no—
281C4×Dic11—28no—
282C4×Dic11—28no—
283C4×Dic11—44no—
284C4×Dic11—44no—
285C22×#121—111no—
286C22×C4×D4—111no—
287C22×#117—111no—
288#2363—1116no—
289C2×#390—111no—
290C2×#390—111no—
291C2×#390—111no—
292C2×#389—111no—
293C2×#388—111no—
294C2×#388—111no—
295C2×#386—111no—
296C2×#386D1111yescharacteristic, complemented
297C2×C4×C4⋊C4—111no—
298C2×C4×C22⋊C4—111no—
299C2×C4×C22⋊C4—111no—
300C2×C4×C22⋊C4—111no—
301C23×C11—28no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
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—22no—
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×C11C23×C414yes—
328C23×C11C23×C414yes—
329C23×C11C23×C412yes—
330C23×C11C22×D412yes—
331C23×C11C2×#4112yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11H(5,𝔽2)12yes—
335C23×C11H(5,𝔽2)12yes—
336C23×C11C2511yescharacteristic
337C22×D11—28no—
338C22×D11—28no—
339C22×D11—28no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11C23×C414yes—
351D4×C11—416no—
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—416no—
368C2×C4×C11—44no—
369C2×C4×C11—44no—
370C2×C4×C11C23×C414yes—
371C2×C4×C11C22×D414yes—
372C2×C4×C11C2×#4114yes—
373C22⋊D11—232no—
374C22⋊D11—416no—
375C2×Dic11—28no—
376C2×Dic11—28no—
377C2×Dic11—28no—
378C2×Dic11—28no—
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—232no—
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×Dic11C4×D4116yes—
397C2×Dic11C23×C414yes—
398C2×Dic11C23×C414yes—
399C2×Dic11C23×C414yes—
400C2×Dic11C22×D414yes—
401C2×Dic11C22×D414yes—
402C2×Dic11C2×#4114yes—
403C2×Dic11C2×#4114yes—
404C4×D11—416no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4C2×D1111yescharacteristic
408C24×C4—111no—
409C24×C4—111no—
410C24×C4C2×D1111yescharacteristic
411C2×#121—118no—
412C2×#121—1116no—
413C2×C4×D4—118no—
414C2×C4×D4—228no—
415C2×#117—118no—
416C2×#117—228no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420C22×C4⋊C4—111no—
421C22×C4⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C42—111no—
435C22×C42—111no—
436C22×C42—111no—
437C22×C42—111no—
438C22×C42—111no—
439C22×C42—111no—
440#390—118no—
441#390—118no—
442#390—118no—
443#389—118no—
444#388—118no—
445#388—118no—
446#386—118no—
447#386C2×D1118yescomplemented
448C4×C4⋊C4—118no—
449C4×C22⋊C4—118no—
450C4×C22⋊C4—118no—
451C4×C22⋊C4—118no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—416no—
465C22×C11—416no—
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×C11C2×C4×D414yes—
475C22×C11C4×#4114yes—
476C22×C11#51814yes—
477C22×C11#54614yes—
478C22×C11#55014yes—
479C22×C11#55314yes—
480C22×C11#55514yes—
481C22×C11C24×C411yescharacteristic
482C22×C11C23×D411yescharacteristic
483C22×C11C22×#4111yescharacteristic
484C22×C11C22×#4111yescharacteristic
485C22×C11C22×#4111yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C22×C11C2×H(5,𝔽2)11yescharacteristic
488C2×D11—24no—
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—416no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C4×C11—24no—
497C4×C11—24no—
498C4×C11—24no—
499C4×C11—42no—
500C4×C11—42no—
501Dic11—24no—
502Dic11—24no—
503Dic11—24no—
504Dic11—24no—
505Dic11—42no—
506Dic11—42no—
507Dic11C2×C4×D418yes—
508C25—111no—
509C25C22×D1111yescharacteristic
510C25C22×D1111yescharacteristic
511C22×D4—42no—
512C22×D4—42no—
513C22×D4—118no—
514C22×D4—114no—
515C22×D4—118no—
516C22×D4—114no—
517C22×D4—224no—
518C22×D4—224no—
519C22×D4—442no—
520C22×D4—442no—
521C22×D4C4×D1118yescomplemented
522C22×D4C22×D1114yes—
523C23×C4—24no—
524C23×C4—24no—
525C23×C4—42no—
526C23×C4—111no—
527C23×C4—118no—
528C23×C4—114no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—114no—
536C23×C4—224no—
537C23×C4—224no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—442no—
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1114yes—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547#121—1164no—
548C4×D4—2232no—
549#117—2232no—
550C2×C4⋊C4—118no—
551C2×C4⋊C4—118no—
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—442no—
559C2×C4⋊C4—442no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—118no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—118no—
566C2×C22⋊C4—114no—
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—224no—
575C2×C22⋊C4—224no—
576C2×C22⋊C4—224no—
577C2×C22⋊C4—224no—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—442no—
581C2×C22⋊C4C22×D1114yes—
582C2×C22⋊C4C22×D1114yes—
583C2×C22⋊C4C22×D1114yes—
584C2×C42—114no—
585C2×C42—114no—
586C2×C42—114no—
587C2×C42—114no—
588C2×C42—114no—
589C2×C42—114no—
590C2×C42—224no—
591C2×C42—224no—
592C2×C42—224no—
593C2×C42—224no—
594C2×C42—442no—
595C2×C42—442no—
596#95—114no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95C22×D1114yes—
601#95C22×D1114yes—
602C2×C11—44no—
603C2×C11—44no—
604C2×C11#236318yescomplemented
605C2×C11C22×C4×D411yescharacteristic
606C2×C11C2×C4×#4111yescharacteristic
607C2×C11C2×#51811yescharacteristic
608C2×C11C2×#54611yescharacteristic
609C2×C11C2×#55011yescharacteristic
610C2×C11C2×#55311yescharacteristic
611C2×C11C2×#55511yescharacteristic
612D11—44no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—114no—
626C24—112no—
627C24—222no—
628C24—222no—
629C24—222no—
630C24—222no—
631C24—222no—
632C24—222no—
633C24C2×C4×D1114yes—
634C24C2×C4×D1114yes—
635C24C23×D1112yes—
636C24C23×D1112yes—
637C24C23×D1111yescharacteristic
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—416no—
641C2×D4—1116no—
642C2×D4—1116no—
643C2×D4—228no—
644C2×D4—2232no—
645C2×D4—228no—
646C2×D4—4416no—
647C2×D4—444no—
648C2×D4—444no—
649C2×D4C2×C4×D11116yescomplemented
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—114no—
667C22×C4—114no—
668C22×C4—114no—
669C22×C4—112no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—1116no—
673C22×C4—114no—
674C22×C4—114no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—2232no—
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—222no—
699C22×C4—228no—
700C22×C4—444no—
701C22×C4—4416no—
702C22×C4C2×C4×D1114yes—
703C22×C4D4×D1114yes—
704C22×C4#434114yes—
705C22×C4C23×D1112yes—
706C22×C4C23×D1112yes—
707C22×C4C23×D1112yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1112yes—
710C4⋊C4—1116no—
711C4⋊C4—1116no—
712C4⋊C4—228no—
713C4⋊C4—444no—
714C4⋊C4—444no—
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—44no—
718C22⋊C4—1116no—
719C22⋊C4—1116no—
720C22⋊C4—228no—
721C22⋊C4—228no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C22⋊C4—228no—
725C22⋊C4—228no—
726C22⋊C4—444no—
727C42—228no—
728C42—228no—
729C42—228no—
730C42—228no—
731C42—444no—
732C42—444no—
733C11C2×#236311yescharacteristic, complemented, Sylow
734C23—28no—
735C23—28no—
736C23—28no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—114no—
761C23—228no—
762C23—228no—
763C23—228no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—444no—
771C23—444no—
772C23—444no—
773C23—444no—
774C23C22×C4×D1114yes—
775C23C22×C4×D1114yes—
776C23C22×C4×D1112yes—
777C23C2×D4×D1112yes—
778C23C2×#434112yes—
779C23#6703712yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#41×D1112yes—
783C23C24×D1111yescharacteristic
784D4—416no—
785D4—2232no—
786D4—4416no—
787C2×C4—28no—
788C2×C4—28no—
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—416no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—1116no—
806C2×C4—114no—
807C2×C4—114no—
808C2×C4—114no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—114no—
813C2×C4—2232no—
814C2×C4—228no—
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—228no—
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—4416no—
833C2×C4—444no—
834C2×C4—444no—
835C2×C4C22×C4×D1114yes—
836C2×C4C2×D4×D1114yes—
837C2×C4C2×#434114yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—416no—
847C22—416no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—224no—
855C22—224no—
856C22—224no—
857C22—442no—
858C22—4416no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22#1062301714yes—
863C22C4×#434114yes—
864C22C4×D4×D1114yes—
865C22#1062312214yes—
866C22#1062313014yes—
867C22#1062314714yes—
868C22#1062319214yes—
869C22C23×C4×D1111yescharacteristic
870C22C22×D4×D1111yescharacteristic
871C22C22×#434111yescharacteristic
872C22C2×#6703711yescharacteristic
873C22C2×#6703711yescharacteristic
874C22C2×#41×D1111yescharacteristic
875C22C2×#41×D1111yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—118no—
882C4—224no—
883C4—224no—
884C4—224no—
885C4—224no—
886C4—442no—
887C4—442no—
888C2—44no—
889C2—44no—
890C2—444no—
891C2#1307165718yesdirect product factor
892C2C2×C4×D4×D1111yescharacteristic
893C2C2×C4×#434111yescharacteristic
894C2C2×#1062301711yescharacteristic
895C2C2×#1062312211yescharacteristic
896C2C2×#1062313011yescharacteristic
897C2C2×#1062319211yescharacteristic
898C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×#66930C2semidirect
4. #13071657C2direct (N × H)
5. C2×#10622834C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622260C2semidirect
9. C2×#10622558C2semidirect
10. C2×#10622283C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622262C2semidirect
13. C2×C22⋊C4×Dic11C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#386C2semidirect
31. C2×#66992C4semidirect
34. C2×C4×C22⋊D11C22semidirect
51. C2×#66930C22semidirect
52. C11×#386C22semidirect
55. #10622834C22semidirect
56. C4×C22⋊Dic11C22semidirect
61. #10622570C22semidirect
62. #10622570C22semidirect
63. #10622569C22semidirect
64. #10622558C22semidirect
65. C22⋊C4×Dic11C22semidirect
66. #10622283C22semidirect
67. #10622279C22semidirect
68. #10622262C22semidirect
69. #10622260C22semidirect
75. C22×D4×C11C2×C4semidirect
91. C22×C22⋊D11C2×C4semidirect
96. C23×Dic11C2×C4semidirect
119. C2×C22⋊Dic11C2×C4semidirect
125. #66992C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×Dic11⋊C4C2×C4semidirect
140. C2×Dic11⋊C4D4semidirect
193. C2×D4×C11C22×C4semidirect
225. C2×C22⋊D11C22×C4semidirect
246. C22×Dic11C22×C4semidirect
269. C22⋊Dic11C22×C4semidirect
273. (C2×D11)⋊C4C22×C4semidirect
277. Dic11⋊C4C22×C4semidirect
278. Dic11⋊C4C2×D4semidirect
296. C2×#386D11semidirect
447. #386C2×D11semidirect
521. C22×D4C4×D11semidirect
604. C2×C11#2363semidirect
649. C2×D4C2×C4×D11semidirect
733. C11C2×#2363semidirect
891. C2#13071657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×C4×C22⋊D112
C22×#669302
#130716572
C2×#106228342
C2×#106225702
C2×#106222602
C2×#106225582
C2×#106222832
C2×#106225692
C2×#106222622
C2×C22⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×#106222792
C2×C11×#3862
C2×#236311