Finite Group Databasebeta

← C2×#13072127 #14921642

Subgroups — C2×#13072127 #14921642

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13072127C2116yesmaximal, direct product factor
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622585C211yesmaximal, characteristic, complemented
11C2×#10622823C211yesmaximal, characteristic, complemented
12C2×#10622602C211yesmaximal, characteristic, complemented
13C2×#10622589C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×#123—28no—
24C2×C11×#123C2218yescomplemented
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yes—
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54#10622835C2218yescomplemented
55#10622823C2218yescomplemented
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622606C2218yescomplemented
63#10622602C2218yescomplemented
64#10622589C2218yescomplemented
65#10622585C2218yescomplemented
66#10622572C2218yescomplemented
67#10622570C2218yescomplemented
68#10622566C2218yescomplemented
69#10622555C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—42no—
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11D418yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2314yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C22×C4×D11—24no—
107C22×C4×D11—24no—
108C22×C4×D11—42no—
109C22×C4×D11C2314yes—
110C11×#123—232no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4—24no—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4D418yescomplemented
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131#66992—232no—
132C4×C22⋊D11—232no—
133C2×(C2×D11)⋊C4—24no—
134C2×(C2×D11)⋊C4—24no—
135C2×(C2×D11)⋊C4—24no—
136C2×(C2×D11)⋊C4—24no—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—42no—
148C2×Dic11⋊C4—42no—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11—24no—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159#66936—232no—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2422—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×C11C2×D414yes—
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×D11C2×D414yes—
191C23×D11C2412yes—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
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—28no—
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×C11—28no—
211C22×C4×C11—44no—
212C22×C4×C11—416no—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2×D414yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C2×C22⋊D11—232no—
221C2×C22⋊D11—28no—
222C2×C22⋊D11—28no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—28no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—416no—
227C2×C22⋊D11C2×D4116yes—
228C22×Dic11—28no—
229C22×Dic11—28no—
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—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—416no—
249C22×Dic11C2×D414yes—
250C22×Dic11#4114yes—
251C22×Dic11#4114yes—
252C22×Dic11#4114yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C2×C4×D11—28no—
261C2×C4×D11—28no—
262C2×C4×D11—44no—
263C2×C4×D11—416no—
264C11×C4⋊C4—28no—
265C11×C4⋊C4—28no—
266C11×C22⋊C4—28no—
267C11×C22⋊C4—28no—
268C11×C22⋊C4C2×D4116yescomplemented
269C22⋊Dic11—28no—
270C22⋊Dic11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—28no—
273C22⋊Dic11—28no—
274(C2×D11)⋊C4—28no—
275(C2×D11)⋊C4—28no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278C4⋊Dic11—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—44no—
284Dic11⋊C4—44no—
285C4×Dic11—28no—
286C4×Dic11—28no—
287C22×#123—111no—
288C22×#123D1111yescharacteristic, complemented
289C22×#121—111no—
290C22×C4×D4—111no—
291#2422—1116no—
292C2×#397—111no—
293C2×#397—111no—
294C2×#394—111no—
295C2×#394—111no—
296C2×#390—111no—
297C2×#389—111no—
298C2×#385—111no—
299C2×#385—111no—
300C2×#384—111no—
301C2×#380—111no—
302C2×C4×C22⋊C4—111no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
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—22no—
320C23×C11—22no—
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×D414yes—
332C23×C11C22×D412yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C112−1+412yes—
338C23×C11C2511yescharacteristic
339C22×D11—28no—
340C22×D11—28no—
341C22×D11—28no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11C22×D414yes—
353D4×C11—416no—
354C2×C4×C11—28no—
355C2×C4×C11—28no—
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—416no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11—44no—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D414yes—
375C22⋊D11—232no—
376C22⋊D11—416no—
377C2×Dic11—28no—
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—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—44no—
396C2×Dic11—44no—
397C2×Dic11—44no—
398C2×Dic11—44no—
399C2×Dic11—44no—
400C2×Dic11—416no—
401C2×Dic11#123116yescomplemented
402C2×Dic11C22×D414yes—
403C2×Dic11C2×#4114yes—
404C2×Dic11C2×#4114yes—
405C2×Dic11C2×#4114yes—
406C4×D11—416no—
407C23×D4—111no—
408C23×D4—111no—
409C23×D4C2×D1111yescharacteristic
410C24×C4—111no—
411C24×C4—111no—
412C24×C4C2×D1111yescharacteristic
413C2×#123—28no—
414C2×#123—118no—
415C2×#123—228no—
416C2×#123C2×D1118yescomplemented
417C2×#121—118no—
418C2×#121—228no—
419C2×C4×D4—118no—
420C2×C4×D4—228no—
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⋊C4—111no—
428C22×C4⋊C4C2×D1111yescharacteristic
429C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C42—111no—
443C22×C42—111no—
444#397—118no—
445#397—118no—
446#394—118no—
447#394—118no—
448#390—118no—
449#389—118no—
450#385—118no—
451#385—118no—
452#384—118no—
453#380—118no—
454C4×C22⋊C4—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—416no—
470C22×C11—416no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11C2×#12314yes—
478C22×C11#53214yes—
479C22×C11#54214yes—
480C22×C11D4214yes—
481C22×C11#54714yes—
482C22×C11#54714yes—
483C22×C11#55314yes—
484C22×C11C23×D411yescharacteristic
485C22×C11C23×D411yescharacteristic
486C22×C11C22×#4111yescharacteristic
487C22×C11C22×#4111yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×2−1+411yescharacteristic
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—42no—
495C2×D11—416no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C4×C11—24no—
500C4×C11—24no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504Dic11—24no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11C2×#12318yescomplemented
511C25—111no—
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C22×D4—24no—
515C22×D4—24no—
516C22×D4—42no—
517C22×D4—118no—
518C22×D4—114no—
519C22×D4—114no—
520C22×D4—224no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—224no—
524C22×D4—442no—
525C22×D4C22×D1114yes—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—114no—
538C23×C4—224no—
539C23×C4—224no—
540C23×C4—224no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—442no—
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C23×C4C22×D1111yescharacteristic
547C23×C4C22×D1114yes—
548C23×C4C22×D1111yescharacteristic
549C23×C4C22×D1111yescharacteristic
550#123—232no—
551#123—2232no—
552#121—2232no—
553C4×D4—2232no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—224no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—442no—
569C2×C4⋊C4—442no—
570C2×C4⋊C4C22×D1114yes—
571C2×C4⋊C4C22×D1114yes—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
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—114no—
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—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4C22⋊D1118yescomplemented
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C22⋊C4C22×D1114yes—
596C2×C42—114no—
597C2×C42—114no—
598C2×C42—224no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606C2×C11—44no—
607C2×C11—44no—
608C2×C11#242218yescomplemented
609C2×C11C22×#12311yescharacteristic
610C2×C11C2×#53211yescharacteristic
611C2×C11C2×#54211yescharacteristic
612C2×C11C2×D4211yescharacteristic
613C2×C11C2×#54711yescharacteristic
614C2×C11C2×#54711yescharacteristic
615C2×C11C2×#55311yescharacteristic
616D11—44no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—114no—
630C24—112no—
631C24—222no—
632C24—222no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24D4×D1114yes—
638C24C2×C22⋊D1114yes—
639C24C23×D1112yes—
640C24C23×D1112yes—
641C24C23×D1111yescharacteristic
642C2×D4—28no—
643C2×D4—28no—
644C2×D4—44no—
645C2×D4—416no—
646C2×D4—1116no—
647C2×D4—2232no—
648C2×D4—228no—
649C2×D4—228no—
650C2×D4—228no—
651C2×D4—228no—
652C2×D4—444no—
653C2×D4—4416no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—28no—
669C22×C4—44no—
670C22×C4—416no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—114no—
676C22×C4—112no—
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—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×C4—222no—
703C22×C4—228no—
704C22×C4—444no—
705C22×C4—4416no—
706C22×C4—4416no—
707C22×C4C2×C22⋊D1114yes—
708C22×C4C2×C22⋊D1114yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—228no—
717C4⋊C4—228no—
718C4⋊C4—228no—
719C4⋊C4—228no—
720C4⋊C4—228no—
721C4⋊C4—444no—
722C4⋊C4—444no—
723C22⋊C4—28no—
724C22⋊C4—28no—
725C22⋊C4—228no—
726C22⋊C4—228no—
727C22⋊C4—228no—
728C22⋊C4—228no—
729C22⋊C4—228no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4C2×C22⋊D11116yescomplemented
735C42—228no—
736C42—228no—
737C11C2×#242211yescharacteristic, complemented, Sylow
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—114no—
765C23—228no—
766C23—228no—
767C23—228no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—444no—
775C23—444no—
776C23—444no—
777C23—444no—
778C23C2×D4×D1114yes—
779C23C2×D4×D1112yes—
780C23#6703712yes—
781C23#41×D1112yes—
782C23#41×D1112yes—
783C23#41×D1112yes—
784C23#6704312yes—
785C23C22×C22⋊D1114yes—
786C23C22×C22⋊D1112yes—
787C23C24×D1111yescharacteristic
788D4—416no—
789D4—2232no—
790D4—4416no—
791C2×C4—28no—
792C2×C4—28no—
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—416no—
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—222no—
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—4416no—
834C2×C4—4416no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4C22×C22⋊D1114yes—
841C2×C4C22×C22⋊D1114yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—224no—
859C22—224no—
860C22—224no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—4416no—
866C22D11×#12314yes—
867C22#1062318614yes—
868C22#1062319214yes—
869C22#1062319314yes—
870C22D4×C22⋊D1114yes—
871C22#1062335514yes—
872C22#1062336314yes—
873C22C22×D4×D1111yescharacteristic
874C22C2×#6703711yescharacteristic
875C22C2×#41×D1111yescharacteristic
876C22C2×#41×D1111yescharacteristic
877C22C2×#41×D1111yescharacteristic
878C22C2×#6704311yescharacteristic
879C22C23×C22⋊D1111yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—118no—
886C4—224no—
887C4—442no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4—442no—
892C2—44no—
893C2—44no—
894C2—444no—
895C2#1307212718yesdirect product factor
896C2C2×D11×#12311yescharacteristic
897C2C2×#1062336311yescharacteristic
898C2C2×#1062319311yescharacteristic
899C2C2×D4×C22⋊D1111yescharacteristic
900C2C2×#1062318611yescharacteristic
901C2C2×#1062335511yescharacteristic
902C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC22×#123D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13072127C2direct (N × H)
5. C2×#10622606C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622585C2semidirect
11. C2×#10622823C2semidirect
12. C2×#10622602C2semidirect
13. C2×#10622589C2semidirect
14. C2×#10622555C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C22×C11×#123C2semidirect
24. C2×C11×#123C22semidirect
38. C2×C4×C22⋊D11C22semidirect
53. C2×#66936C22semidirect
54. #10622835C22semidirect
55. #10622823C22semidirect
62. #10622606C22semidirect
63. #10622602C22semidirect
64. #10622589C22semidirect
65. #10622585C22semidirect
66. #10622572C22semidirect
67. #10622570C22semidirect
68. #10622566C22semidirect
69. #10622555C22semidirect
70. C22⋊C4×Dic11C22semidirect
117. C2×C11×C22⋊C4D4semidirect
268. C11×C22⋊C4C2×D4semidirect
288. C22×#123D11semidirect
401. C2×Dic11#123semidirect
416. C2×#123C2×D11semidirect
510. Dic11C2×#123semidirect
592. C2×C22⋊C4C22⋊D11semidirect
608. C2×C11#2422semidirect
734. C22⋊C4C2×C22⋊D11semidirect
737. C11C2×#2422semidirect
895. C2#13072127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669922
C22×C4×C22⋊D112
#130721272
C2×#106226062
C2×#106225662
C2×#106225722
C2×#106228352
C2×#106225702
C2×#106225852
C2×#106228232
C2×#106226022
C2×#106225892
C2×#106225552
C2×C22⋊C4×Dic112
C22×C11×#1232
C2×#242211