Finite Group Databasebeta

← C22×#10623186 #15660712

Subgroups — C22×#10623186 #15660712

Order 2816.

12230 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C23×#4341C211yesmaximal, characteristic, complemented
3C2×#10623186C2148yesmaximal, direct product factor
4C22×#66941C211yesmaximal, characteristic, complemented
5C22×#66947C211yesmaximal, characteristic, complemented
6C22×#66939C211yesmaximal, characteristic, complemented
7C22×#66936C211yesmaximal, characteristic, complemented
8C22×#66949C211yesmaximal, characteristic, complemented
9C22×#66931C211yesmaximal, characteristic, complemented
10C22×#66937C211yesmaximal, characteristic, complemented
11C22×#66992C211yesmaximal, characteristic, complemented
12C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
13C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
14C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4341—216no—
27C22×#4341C22124yescomplemented
28C22×#4339—216no—
29C22×#4339C22124yescomplemented
30C23×D44C2211yescharacteristic
31C23×C4×D11C2211yescharacteristic
32C23×C4×D11C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic
34C23×C4×D11C2211yescharacteristic
35C23×Dic22C2211yescharacteristic
36C23×Dic22C2211yescharacteristic
37C2×C11×#123C22124yescomplemented
38C22×C11×C4⋊C4C2211yescharacteristic
39C22×C11×C4⋊C4C2211yescharacteristic
40C22×C11×C22⋊C4C2211yescharacteristic
41C22×C11×C22⋊C4C2211yescharacteristic
42C22×C11×C22⋊C4C2211yescharacteristic
43C22×C22⋊Dic11C2211yescharacteristic
44C2×#66992C22124yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×C4⋊Dic11C2211yescharacteristic
50C22×C4⋊Dic11C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C22×Dic11⋊C4C2211yescharacteristic
53C22×Dic11⋊C4C2211yescharacteristic
54C22×Dic11⋊C4C2211yescharacteristic
55C22×Dic11⋊C4C2211yescharacteristic
56C22×Dic11⋊C4C2211yescharacteristic
57C22×Dic11⋊C4C22124yescomplemented
58C22×C4×Dic11C2211yescharacteristic
59#10623186C221256yesdirect product factor
60C2×#66949C22124yescomplemented
61C2×#66947C22124yescomplemented
62C2×C4⋊C4×D11C22124yescomplemented
63C2×#66941C22124yescomplemented
64C2×#66939C22124yescomplemented
65C2×#66937C22124yescomplemented
66C2×#66936C22124yescomplemented
67C2×(C22⋊D11)⋊C4C22124yescomplemented
68C2×(C22⋊D11)⋊C4C22124yescomplemented
69C2×#66931C22124yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—28no—
75C22×D4×C11C23112yes—
76C23×C4×C11—28no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C23112yes—
83C22×C22⋊D11—28no—
84C22×C22⋊D11—28no—
85C22×C22⋊D11—28no—
86C22×C22⋊D11D4116yescomplemented
87C22×C22⋊D11C23112yes—
88C22×C22⋊D11C23112yes—
89C22×C22⋊D11C23112yes—
90C22×C22⋊D11C23112yes—
91C23×Dic11—28no—
92C23×Dic11—28no—
93C23×Dic11—28no—
94C23×Dic11C23112yes—
95C23×Dic11C23112yes—
96C23×Dic11C23112yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C2×#4341—2192no—
104C2×#4341C23164yescomplemented
105C2×#4339—2192no—
106C2×#4339C23164yescomplemented
107C22×D44—28no—
108C22×D44C23112yes—
109C22×C4×D11—28no—
110C22×C4×D11—28no—
111C22×C4×D11—28no—
112C22×C4×D11—28no—
113C22×C4×D11C23112yes—
114C22×C4×D11C23112yes—
115C22×C4×D11C23112yes—
116C22×C4×D11C23112yes—
117C22×Dic22—28no—
118C22×Dic22—28no—
119C22×Dic22C23112yes—
120C22×Dic22C23112yes—
121C11×#123C23164yescomplemented
122C2×C11×C4⋊C4C23112yes—
123C2×C11×C4⋊C4C23112yes—
124C2×C11×C22⋊C4C23112yes—
125C2×C11×C22⋊C4C23112yes—
126C2×C11×C22⋊C4C23112yes—
127C2×C22⋊Dic11C23112yes—
128#66992C23164yescomplemented
129C2×(C2×D11)⋊C4C23112yes—
130C2×(C2×D11)⋊C4C23112yes—
131C2×(C2×D11)⋊C4C23112yes—
132C2×(C2×D11)⋊C4C23112yes—
133C2×C4⋊Dic11C23112yes—
134C2×C4⋊Dic11C23112yes—
135C2×Dic11⋊C4C23112yes—
136C2×Dic11⋊C4C23112yes—
137C2×Dic11⋊C4C23112yes—
138C2×Dic11⋊C4C23112yes—
139C2×Dic11⋊C4C23112yes—
140C2×Dic11⋊C4C23112yes—
141C2×Dic11⋊C4C23164yescomplemented
142C2×C4×Dic11C23112yes—
143#66949C23164yescomplemented
144#66947C23164yescomplemented
145C4⋊C4×D11C23164yescomplemented
146#66941C23164yescomplemented
147#66939C23164yescomplemented
148#66937C23164yescomplemented
149#66936C23164yescomplemented
150(C22⋊D11)⋊C4C23164yescomplemented
151(C22⋊D11)⋊C4C23164yescomplemented
152#66931C23164yescomplemented
153C22×#547—111nomaximal, Sylow
154C24×C11—24no—
155C24×C11—24no—
156C24×C11—24no—
157C24×C11—24no—
158C24×C11—24no—
159C24×C11C2×D418yes—
160C24×C11C2416yes—
161C24×C11C2416yes—
162C24×C11C2411yescharacteristic
163C23×D11—24no—
164C23×D11—24no—
165C23×D11—24no—
166C23×D11—24no—
167C23×D11—24no—
168C23×D11C2×D418yes—
169C23×D11C2416yes—
170C23×D11C2416yes—
171C2×D4×C11—248no—
172C2×D4×C11C24116yes—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—248no—
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11C2416yes—
180C22×C4×C11C2416yes—
181C22×C4×C11C2416yes—
182C22×C4×C11C2416yes—
183C22×C4×C11C2416yes—
184C22×C4×C11C24116yes—
185C2×C22⋊D11—248no—
186C2×C22⋊D11—248no—
187C2×C22⋊D11—248no—
188C2×C22⋊D11C2×D4196yescomplemented
189C2×C22⋊D11C24116yes—
190C2×C22⋊D11C24116yes—
191C2×C22⋊D11C24116yes—
192C2×C22⋊D11C24116yes—
193C22×Dic11—248no—
194C22×Dic11—248no—
195C22×Dic11—24no—
196C22×Dic11—24no—
197C22×Dic11—24no—
198C22×Dic11—248no—
199C22×Dic11—24no—
200C22×Dic11C2×D418yes—
201C22×Dic11#4118yescomplemented
202C22×Dic11C24116yes—
203C22×Dic11C24116yes—
204C22×Dic11C24116yes—
205C22×Dic11C2416yes—
206C22×Dic11C2416yes—
207C22×Dic11C2416yes—
208C22×Dic11C2416yes—
209C22×Dic11C2416yes—
210C22×Dic11C2416yes—
211#4341—2256no—
212#4339—2256no—
213C2×D44—248no—
214C2×D44C24116yes—
215C2×C4×D11—248no—
216C2×C4×D11—248no—
217C2×C4×D11—248no—
218C2×C4×D11—248no—
219C2×C4×D11C24116yes—
220C2×C4×D11C24116yes—
221C2×C4×D11C24116yes—
222C2×C4×D11C24116yes—
223C2×Dic22—248no—
224C2×Dic22—248no—
225C2×Dic22C24116yes—
226C2×Dic22C24116yes—
227C11×C4⋊C4C24116yes—
228C11×C4⋊C4C24116yes—
229C11×C22⋊C4C24116yes—
230C11×C22⋊C4C24116yes—
231C11×C22⋊C4C24116yes—
232C22⋊Dic11C24116yes—
233(C2×D11)⋊C4C24116yes—
234(C2×D11)⋊C4C24116yes—
235(C2×D11)⋊C4C24116yes—
236(C2×D11)⋊C4C24116yes—
237C4⋊Dic11C24116yes—
238C4⋊Dic11C24116yes—
239Dic11⋊C4C24116yes—
240Dic11⋊C4C24116yes—
241Dic11⋊C4C24116yes—
242Dic11⋊C4C24116yes—
243Dic11⋊C4C24116yes—
244Dic11⋊C4C24116yes—
245C4×Dic11C24116yes—
246C23×#41—111no—
247C23×#41—111no—
248C2×#547—1148no—
249C22×C4⋊Q8—111no—
250C22×#123—111no—
251C22×#123—111no—
252C22×#123—111no—
253C22×#123D1111yescharacteristic, complemented
254C22×C22⋊Q8—111no—
255C22×C22⋊Q8—111no—
256C22×#121—111no—
257C22×#121—111no—
258C22×C4×D4—111no—
259C22×C4×D4—111no—
260C23×C4⋊C4—111no—
261C23×C4⋊C4—111no—
262C23×C11—232no—
263C23×C11—212no—
264C23×C11—212no—
265C23×C11—212no—
266C23×C11—212no—
267C23×C11—212no—
268C23×C11—416no—
269C23×C11C22×D4124yes—
270C23×C11C22×D414yes—
271C23×C11C2×#4114yes—
272C23×C112−1+414yes—
273C23×C11C2514yes—
274C23×C11C2514yes—
275C23×C11C2513yes—
276C22×D11—232no—
277C22×D11—212no—
278C22×D11—212no—
279C22×D11—212no—
280C22×D11—212no—
281C22×D11—212no—
282C22×D11—416no—
283C22×D11C22×D4124yes—
284C22×D11C2514yes—
285C22×D11C2514yes—
286D4×C11—232no—
287C2×C4×C11—212no—
288C2×C4×C11—212no—
289C2×C4×C11—212no—
290C2×C4×C11—232no—
291C2×C4×C11—212no—
292C2×C4×C11—212no—
293C2×C4×C11C2514yes—
294C2×C4×C11C2514yes—
295C2×C4×C11C2514yes—
296C2×C4×C11C2514yes—
297C2×C4×C11C2514yes—
298C22⋊D11—232no—
299C22⋊D11—232no—
300C22⋊D11—232no—
301C22⋊D11C22×D4164yescomplemented
302C2×Dic11—212no—
303C2×Dic11—212no—
304C2×Dic11—212no—
305C2×Dic11—232no—
306C2×Dic11—212no—
307C2×Dic11—232no—
308C2×Dic11—232no—
309C2×Dic11C22×D4124yes—
310C2×Dic11C2×#41124yescomplemented
311C2×Dic11C2514yes—
312C2×Dic11C2514yes—
313C2×Dic11C2514yes—
314C2×Dic11C2514yes—
315C2×Dic11C2514yes—
316C2×Dic11C2514yes—
317D44—232no—
318C4×D11—232no—
319C4×D11—232no—
320C4×D11—232no—
321C4×D11—232no—
322Dic22—232no—
323Dic22—232no—
324C22×#41—1124no—
325C22×#41—1124no—
326C22×#41—2216no—
327C22×#41—2216no—
328C23×Q8—111no—
329C23×Q8—111no—
330C23×D4—111no—
331C23×D4—111no—
332C23×D4—111no—
333C23×D4—111no—
334C23×D4—111no—
335C23×D4C2×D1111yescharacteristic
336C24×C4—111no—
337C24×C4—111no—
338C24×C4—111no—
339C24×C4—111no—
340C24×C4—111no—
341C24×C4—111no—
342C24×C4—111no—
343C24×C4C2×D1111yescharacteristic
344#547—11256no—
345C2×C4⋊Q8—1124no—
346C2×#123—1124no—
347C2×#123—1124no—
348C2×#123—1124no—
349C2×#123C2×D11124yescomplemented
350C2×C22⋊Q8—1124no—
351C2×C22⋊Q8—1124no—
352C2×#121—1124no—
353C2×#121—1124no—
354C2×C4×D4—1124no—
355C2×C4×D4—1124no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C4⋊C4—1124no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—1124no—
366C22×C4⋊C4C2×D1111yescharacteristic
367C22×C4⋊C4C2×D1111yescharacteristic
368C22×C22⋊C4—111no—
369C22×C22⋊C4—111no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4C2×D1111yescharacteristic
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C42—111no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11—248no—
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—424no—
384C22×C11#547116yescomplemented
385C22×C11C23×D418yes—
386C22×C11C23×D416yes—
387C22×C11C22×#4116yes—
388C22×C11C2×2−1+416yes—
389C22×C11C2611yescharacteristic
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—248no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—424no—
397C2×D11C23×D418yes—
398C4×C11—24no—
399C4×C11—24no—
400C4×C11—24no—
401C4×C11—24no—
402C4×C11—24no—
403Dic11—24no—
404Dic11—24no—
405Dic11—24no—
406Dic11—24no—
407Dic11C23×D418yes—
408Dic11C22×#4118yescomplemented
409C25—111no—
410C25—111no—
411C25C22×D1111yescharacteristic
412C25C22×D1111yescharacteristic
413C2×#41—1164no—
414C2×#41—1164no—
415C2×#41—22192no—
416C2×#41—22192no—
417C22×Q8—1112no—
418C22×Q8—1112no—
419C22×Q8—228no—
420C22×Q8—228no—
421C22×D4—28no—
422C22×D4—1116no—
423C22×D4—1112no—
424C22×D4—1112no—
425C22×D4—1112no—
426C22×D4—1112no—
427C22×D4—1112no—
428C22×D4—228no—
429C22×D4—228no—
430C22×D4—228no—
431C22×D4—228no—
432C22×D4C22×D11112yes—
433C23×C4—28no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—1112no—
437C23×C4—1112no—
438C23×C4—1112no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—1112no—
444C23×C4—1112no—
445C23×C4—1112no—
446C23×C4—1112no—
447C23×C4—228no—
448C23×C4—228no—
449C23×C4—228no—
450C23×C4—228no—
451C23×C4—228no—
452C23×C4—228no—
453C23×C4—228no—
454C23×C4C22×D11112yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C4⋊Q8—1164no—
461#123—1164no—
462#123—1164no—
463#123—1164no—
464#123C22×D11164yescomplemented
465C22⋊Q8—1164no—
466C22⋊Q8—1164no—
467#121—1164no—
468#121—1164no—
469C4×D4—1164no—
470C4×D4—1164no—
471C2×C4⋊C4—1112no—
472C2×C4⋊C4—1112no—
473C2×C4⋊C4—1112no—
474C2×C4⋊C4—1112no—
475C2×C4⋊C4—1112no—
476C2×C4⋊C4—1112no—
477C2×C4⋊C4—1164no—
478C2×C4⋊C4—1112no—
479C2×C4⋊C4—1112no—
480C2×C4⋊C4—1164no—
481C2×C4⋊C4C22×D11112yes—
482C2×C4⋊C4C22×D11112yes—
483C2×C22⋊C4—1112no—
484C2×C22⋊C4—1112no—
485C2×C22⋊C4—1112no—
486C2×C22⋊C4—1112no—
487C2×C22⋊C4—1112no—
488C2×C22⋊C4C22×D11112yes—
489C2×C22⋊C4C22×D11112yes—
490C2×C22⋊C4C22×D11112yes—
491C2×C42—1112no—
492C2×C11—28no—
493C2×C11—44no—
494C2×C11C2×#547112yescomplemented
495C2×C11C24×D411yescharacteristic
496C2×C11C23×#4111yescharacteristic
497C2×C11C22×2−1+411yescharacteristic
498D11—28no—
499D11—44no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—118no—
506C24—116no—
507C24—116no—
508C24—224no—
509C24—224no—
510C24—224no—
511C24—224no—
512C24—224no—
513C24D4×D1118yes—
514C24C23×D1116yes—
515C24C23×D1116yes—
516C24C23×D1111yescharacteristic
517#41—22256no—
518#41—22256no—
519C2×Q8—1116no—
520C2×Q8—1116no—
521C2×Q8—2248no—
522C2×Q8—2248no—
523C2×D4—248no—
524C2×D4—1196no—
525C2×D4—1116no—
526C2×D4—1116no—
527C2×D4—1116no—
528C2×D4—1116no—
529C2×D4—1116no—
530C2×D4—2248no—
531C2×D4—2248no—
532C2×D4—2248no—
533C2×D4—2248no—
534C2×D4C23×D11116yes—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—248no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—118no—
542C22×C4—118no—
543C22×C4—116no—
544C22×C4—116no—
545C22×C4—116no—
546C22×C4—116no—
547C22×C4—116no—
548C22×C4—116no—
549C22×C4—1116no—
550C22×C4—1116no—
551C22×C4—1116no—
552C22×C4—1116no—
553C22×C4—1116no—
554C22×C4—1116no—
555C22×C4—1116no—
556C22×C4—2248no—
557C22×C4—2248no—
558C22×C4—2248no—
559C22×C4—2248no—
560C22×C4—2248no—
561C22×C4—2248no—
562C22×C4—224no—
563C22×C4—224no—
564C22×C4—224no—
565C22×C4—2248no—
566C22×C4—224no—
567C22×C4C23×D1116yes—
568C22×C4C23×D1116yes—
569C22×C4C23×D1116yes—
570C22×C4C23×D1116yes—
571C22×C4C23×D1116yes—
572C22×C4C23×D11116yes—
573C4⋊C4—1116no—
574C4⋊C4—1116no—
575C4⋊C4—1116no—
576C4⋊C4—1116no—
577C4⋊C4—1116no—
578C4⋊C4—1116no—
579C4⋊C4—1116no—
580C4⋊C4—1116no—
581C4⋊C4C23×D11116yes—
582C4⋊C4C23×D11116yes—
583C22⋊C4—1116no—
584C22⋊C4—1116no—
585C22⋊C4—1116no—
586C22⋊C4—1116no—
587C22⋊C4—1116no—
588C22⋊C4C23×D11116yes—
589C22⋊C4C23×D11116yes—
590C22⋊C4C23×D11116yes—
591C42—1116no—
592C11C22×#54711yescharacteristic, complemented, Sylow
593C23—232no—
594C23—212no—
595C23—212no—
596C23—212no—
597C23—212no—
598C23—212no—
599C23—416no—
600C23—1124no—
601C23—114no—
602C23—114no—
603C23—2232no—
604C23—2212no—
605C23—2212no—
606C23—2212no—
607C23—2212no—
608C23—2212no—
609C23—4416no—
610C23C2×D4×D11124yes—
611C23C2×D4×D1114yes—
612C23#41×D1114yes—
613C23#6704314yes—
614C23C24×D1114yes—
615C23C24×D1114yes—
616C23C24×D1113yes—
617Q8—2232no—
618Q8—2232no—
619D4—232no—
620D4—1164no—
621D4—2232no—
622D4—2232no—
623D4—2232no—
624D4—2232no—
625C2×C4—212no—
626C2×C4—212no—
627C2×C4—232no—
628C2×C4—212no—
629C2×C4—212no—
630C2×C4—212no—
631C2×C4—1124no—
632C2×C4—1124no—
633C2×C4—114no—
634C2×C4—114no—
635C2×C4—114no—
636C2×C4—114no—
637C2×C4—114no—
638C2×C4—114no—
639C2×C4—2232no—
640C2×C4—2232no—
641C2×C4—2232no—
642C2×C4—2232no—
643C2×C4—2232no—
644C2×C4—2232no—
645C2×C4—2212no—
646C2×C4—2212no—
647C2×C4—2212no—
648C2×C4—2232no—
649C2×C4—2212no—
650C2×C4C24×D1114yes—
651C2×C4C24×D1114yes—
652C2×C4C24×D1114yes—
653C2×C4C24×D1114yes—
654C2×C4C24×D1114yes—
655C22—24no—
656C22—24no—
657C22—248no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—424no—
662C22—118no—
663C22—224no—
664C22—224no—
665C22—2248no—
666C22—224no—
667C22—224no—
668C22—224no—
669C22—4424no—
670C22#10623186116yesdirect product factor
671C22C22×D4×D1118yes—
672C22C22×D4×D1116yes—
673C22C2×#41×D1116yes—
674C22C2×#6704316yes—
675C22C25×D1111yescharacteristic
676C4—24no—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—24no—
681C4—118no—
682C4—118no—
683C4—224no—
684C4—224no—
685C4—224no—
686C4—224no—
687C2—28no—
688C2—44no—
689C2—228no—
690C2—444no—
691C2C2×#10623186112yesdirect product factor
692C2C23×D4×D1111yescharacteristic
693C2C22×#41×D1111yescharacteristic
694C2C22×#6704311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#123C2
socleC24×C11C24
hypercenterC22×#123D11
hypocenterC11C22×#547
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C23×#4341C2semidirect
3. C2×#10623186C2direct (N × H)
4. C22×#66941C2semidirect
5. C22×#66947C2semidirect
6. C22×#66939C2semidirect
7. C22×#66936C2semidirect
8. C22×#66949C2semidirect
9. C22×#66931C2semidirect
10. C22×#66937C2semidirect
11. C22×#66992C2semidirect
12. C22×(C22⋊D11)⋊C4C2semidirect
13. C22×(C22⋊D11)⋊C4C2semidirect
14. C23×Dic11⋊C4C2semidirect
15. C22×C4⋊C4×D11C2semidirect
16. C22×C11×#123C2semidirect
27. C22×#4341C22semidirect
29. C22×#4339C22semidirect
37. C2×C11×#123C22semidirect
44. C2×#66992C22semidirect
57. C22×Dic11⋊C4C22semidirect
59. #10623186C22direct (N × H)
60. C2×#66949C22semidirect
61. C2×#66947C22semidirect
62. C2×C4⋊C4×D11C22semidirect
63. C2×#66941C22semidirect
64. C2×#66939C22semidirect
65. C2×#66937C22semidirect
66. C2×#66936C22semidirect
67. C2×(C22⋊D11)⋊C4C22semidirect
68. C2×(C22⋊D11)⋊C4C22semidirect
69. C2×#66931C22semidirect
86. C22×C22⋊D11D4semidirect
104. C2×#4341C23semidirect
106. C2×#4339C23semidirect
121. C11×#123C23semidirect
128. #66992C23semidirect
141. C2×Dic11⋊C4C23semidirect
143. #66949C23semidirect
144. #66947C23semidirect
145. C4⋊C4×D11C23semidirect
146. #66941C23semidirect
147. #66939C23semidirect
148. #66937C23semidirect
149. #66936C23semidirect
150. (C22⋊D11)⋊C4C23semidirect
151. (C22⋊D11)⋊C4C23semidirect
152. #66931C23semidirect
188. C2×C22⋊D11C2×D4semidirect
201. C22×Dic11#41semidirect
253. C22×#123D11semidirect
301. C22⋊D11C22×D4semidirect
310. C2×Dic11C2×#41semidirect
349. C2×#123C2×D11semidirect
384. C22×C11#547semidirect
408. Dic11C22×#41semidirect
464. #123C22×D11semidirect
494. C2×C11C2×#547semidirect
592. C11C22×#547semidirect
670. C22#10623186direct (N × H)
691. C2C2×#10623186direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C23×#43412
C2×#106231862
C22×#669412
C22×#669472
C22×#669392
C22×#669362
C22×#669492
C22×#669312
C22×#669372
C22×#669922
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
C22×C4⋊C4×D112
C22×C11×#1232
C22×#54711