Finite Group Databasebeta

← C22⋊C4×#4339 #14912975

Subgroups — C22⋊C4×#4339 #14912975

Order 2816.

5646 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C2×C4×#4339C212yesmaximal, complemented
3#13071456C212yesmaximal, complemented
4C22⋊C4×Dic22C212yesmaximal, complemented
5#13071447C212yesmaximal, complemented
6#13071443C214yesmaximal, complemented
7C22⋊C4×D44C212yesmaximal, complemented
8C22⋊C4×C22⋊D11C214yesmaximal, complemented
9#13071106C212yesmaximal, complemented
10#13071102C214yesmaximal, complemented
11#13070999C211yesmaximal, characteristic, complemented
12#13070997C212yesmaximal, complemented
13C4×C22⋊C4×D11C212yesmaximal, complemented
14C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C22×#4339—216no—
18C22×#4339C4116yescomplemented
19C22×#4339C2211yescharacteristic
20C22×#4339C2212yes—
21C22×#4339C2211yescharacteristic
22C22×#4339C2211yescharacteristic
23C22×#4339C2212yes—
24C22×#4339C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×C4×D11C2212yes—
27C23×Dic22C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C42×C11C2212yescomplemented
30C2×C4×C22⋊D11C2218yescomplemented
31C2×#66979C2212yescomplemented
32C2×C22⋊C4×D11C2214yes—
33C4×#4339—216no—
34C2×C4×D44C2214yescomplemented
35C2×#66925C2214yescomplemented
36C2×C42×D11C2214yescomplemented
37C2×C4×Dic22C2214yescomplemented
38C4×C11×C22⋊C4C2212yes—
39C4×C11×C22⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4C2211yescharacteristic
41C4×C11×C22⋊C4C2212yescomplemented
42C4×C11×C22⋊C4C2212yescomplemented
43C2×C11×#95C2212yescomplemented
44#10622860C2212yes—
45#10622826C2218yescomplemented
46#10622825C2212yes—
47#10622825C2212yescomplemented
48#10622824C2212yescomplemented
49C4×C22⋊Dic11C2212yes—
50C4×C22⋊Dic11C2212yescomplemented
51#10622570C2218yescomplemented
52#10622569C2218yescomplemented
53#10622568C2214yes—
54#10622555C2214yes—
55C22⋊C4×Dic11C2214yes—
56#10622552C2214yescomplemented
57C4×(C2×D11)⋊C4C2214yescomplemented
58C4×(C2×D11)⋊C4C2214yescomplemented
59#10622542C2214yescomplemented
60#10622280C2214yescomplemented
61#10622279C2214yescomplemented
62#10622278C2218yescomplemented
63#10622277C2214yescomplemented
64D11×#95C2214yescomplemented
65#10622259C2218yescomplemented
66C25×C11C2311yescharacteristic
67C24×D11C2312yes—
68C23×C4×C11—28no—
69C23×C4×C11C2×C418yescomplemented
70C23×C4×C11C2314yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—216no—
78C22×C22⋊D11C2×C4116yescomplemented
79C22×C22⋊D11C2312yes—
80C22×C22⋊D11C2312yes—
81C22×C22⋊D11C2312yes—
82C22×C22⋊D11C2312yes—
83C23×Dic11C2312yes—
84C2×#4339—28no—
85C2×#4339—216no—
86C2×#4339—2128no—
87C2×#4339—28no—
88C2×#4339—216no—
89C2×#4339—28no—
90C2×#4339C2×C418yes—
91C2×#4339C2×C4116yescomplemented
92C2×#4339C2×C418yescomplemented
93C2×#4339C2×C418yescomplemented
94C2×#4339C2×C4116yescomplemented
95C2×#4339C2×C418yescomplemented
96C2×#4339D4116yes—
97C22×D44—28no—
98C22×D44C2×C418yescomplemented
99C22×D44C2312yes—
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—216no—
103C22×C4×D11C2×C4116yescomplemented
104C22×C4×D11C2318yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×C4×D11C2312yes—
108C22×C4×D11C2312yes—
109C22×Dic22—28no—
110C22×Dic22C2×C418yescomplemented
111C22×Dic22C2312yes—
112C22×Dic22C2311yescharacteristic
113C22×Dic22C2311yescharacteristic
114C2×C11×C22⋊C4—28no—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C42×C11—28no—
119C2×C42×C11C2314yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C4×C22⋊D11—232no—
126C2×(C2×D11)⋊C4C2318yes—
127C2×(C2×D11)⋊C4C2318yes—
128C2×(C2×D11)⋊C4C2318yes—
129#66979—28no—
130C2×C4⋊Dic11C2314yes—
131C2×Dic11⋊C4C2318yes—
132C2×C4×Dic11C2318yes—
133C2×C4×Dic11C2314yes—
134C22⋊C4×D11—216no—
135C4×D44—216no—
136#66925—216no—
137C42×D11—216no—
138C4×Dic22—216no—
139C11×#95C2314yes—
140C11×#95C2312yes—
141C11×#95C2312yes—
142C11⋊#95C2314yes—
143C11⋊#95C2318yes—
144C11⋊#95C2318yes—
145C11⋊#95C2314yes—
146C22⋊C4×#41—111nomaximal, Sylow
147C24×C11—24no—
148C24×C11—24no—
149C24×C11—42no—
150C24×C11C22×C414yes—
151C24×C11C2411yescharacteristic
152C24×C11C2411yescharacteristic
153C24×C11C2411yescharacteristic
154C23×D11—28no—
155C23×D11—28no—
156C23×D11—44no—
157C23×D11C22×C418yes—
158C23×D11C2412yes—
159C23×D11C2412yes—
160C22×C4×C11—24no—
161C22×C4×C11—232no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—28no—
167C22×C4×C11—28no—
168C22×C4×C11—44no—
169C22×C4×C11C22×C414yes—
170C22×C4×C11C22×C414yes—
171C22×C4×C11C22×C414yes—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C22×C414yes—
175C22×C4×C11C2×D418yes—
176C22×C4×C11C2414yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2414yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—264no—
183C2×C22⋊D11—28no—
184C2×C22⋊D11—28no—
185C2×C22⋊D11—28no—
186C2×C22⋊D11C22×C418yes—
187C2×C22⋊D11C22×C418yes—
188C2×C22⋊D11C22×C418yes—
189C2×C22⋊D11C22×C418yes—
190C2×C22⋊D11C2×D4116yes—
191C22×Dic11—28no—
192C22×Dic11C22×C418yes—
193C22×Dic11C2418yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196#4339—264no—
197#4339—232no—
198#4339—264no—
199#4339—232no—
200#4339—232no—
201#4339C22⋊C4164yesdirect product factor
202C2×D44—232no—
203C2×D44—28no—
204C2×D44—24no—
205C2×D44C22×C418yes—
206C2×D44C22×C414yes—
207C2×D44C22×C414yes—
208C2×D44C2×D418yes—
209C2×C4×D11—28no—
210C2×C4×D11—264no—
211C2×C4×D11—28no—
212C2×C4×D11—216no—
213C2×C4×D11—28no—
214C2×C4×D11—216no—
215C2×C4×D11—48no—
216C2×C4×D11C22×C418yes—
217C2×C4×D11C22×C418yes—
218C2×C4×D11C22×C418yes—
219C2×C4×D11C22×C418yes—
220C2×C4×D11C2×D4116yes—
221C2×Dic22—28no—
222C2×Dic22—232no—
223C2×Dic22—24no—
224C2×Dic22C22×C418yes—
225C2×Dic22C22×C414yes—
226C2×Dic22C22×C414yes—
227C2×Dic22C2×D418yes—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—28no—
230C11×C22⋊C4#4118yescomplemented
231C42×C11—28no—
232C42×C11—24no—
233C42×C11—24no—
234C22⋊Dic11—28no—
235C22⋊Dic11—28no—
236C22⋊Dic11—44no—
237(C2×D11)⋊C4—216no—
238(C2×D11)⋊C4—216no—
239(C2×D11)⋊C4—48no—
240C4⋊Dic11—28no—
241Dic11⋊C4—216no—
242C4×Dic11—216no—
243C4×Dic11—28no—
244C23×#41—111no—
245C2×C4×#41—112no—
246#2341—112no—
247Q8×C22⋊C4—112no—
248#2339—112no—
249#2339—114no—
250D4×C22⋊C4—112no—
251D4×C22⋊C4—114no—
252#2297—112no—
253#2297—114no—
254#2280—112no—
255#2280—111no—
256C2×C4×C22⋊C4—112no—
257C2×C4×C22⋊C4D1111yescharacteristic, complemented
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—28no—
263C23×C11—28no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—44no—
268C23×C11—416no—
269C23×C11C23×C412yes—
270C23×C11C23×C412yes—
271C23×C11C23×C412yes—
272C23×C11C22×D414yes—
273C23×C11C2×#4114yes—
274C23×C11C2511yescharacteristic
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—216no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—216no—
282C22×D11—48no—
283C22×D11—432no—
284C22×D11C23×C414yes—
285C22×D11C23×C414yes—
286C22×D11C22×D418yes—
287C2×C4×C11—28no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—28no—
295C2×C4×C11—28no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—416no—
300C2×C4×C11C2×C22⋊C4116yescomplemented
301C2×C4×C11C23×C412yes—
302C2×C4×C11C23×C412yes—
303C2×C4×C11C23×C412yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C22×D414yes—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C2×#4118yescomplemented
308C22⋊D11—216no—
309C22⋊D11—216no—
310C22⋊D11—216no—
311C22⋊D11C2×C22⋊C4132yescomplemented
312C2×Dic11—24no—
313C2×Dic11—216no—
314C2×Dic11—28no—
315C2×Dic11—28no—
316C2×Dic11—28no—
317C2×Dic11C23×C414yes—
318C2×Dic11C23×C414yes—
319C2×Dic11C22×D418yes—
320D44—216no—
321D44—28no—
322D44C2×C22⋊C4116yescomplemented
323C4×D11—216no—
324C4×D11—216no—
325C4×D11—216no—
326C4×D11—432no—
327C4×D11C2×C22⋊C4132yescomplemented
328Dic22—28no—
329Dic22—216no—
330Dic22C2×C22⋊C4116yescomplemented
331C22×#41—111no—
332C22×#41—111no—
333C22×#41—112no—
334C22×#41—111no—
335C22×#41—112no—
336C22×#41—111no—
337C22×#41—1116no—
338C22×#41—2216no—
339C23×Q8—111no—
340C23×D4—112no—
341C23×D4—111no—
342C24×C4—112no—
343C24×C4C2×D1111yescharacteristic
344C4×#41—2216no—
345C2×C4×Q8—114no—
346C2×C4×D4—118no—
347C2×C4×D4—114no—
348C2×#117—112no—
349C2×#117—114no—
350C22×C22⋊C4—114no—
351C22×C22⋊C4C2×D1112yes—
352C22×C42—114no—
353C22×C42C2×D1112yescomplemented
354#391—114no—
355#391—118no—
356#390—118no—
357#390—114no—
358#386—118no—
359#386—118no—
360#386—118no—
361#381—112no—
362#381—114no—
363#380—112no—
364#380—112no—
365#380—114no—
366#380—114no—
367#379—112no—
368#379—114no—
369C4×C22⋊C4—112no—
370C4×C22⋊C4—112no—
371C4×C22⋊C4—114no—
372C4×C22⋊C4—114no—
373C4×C22⋊C4—114no—
374C4×C22⋊C4—114no—
375C4×C22⋊C4C2×D1112yes—
376C4×C22⋊C4C2×D1111yescharacteristic
377C4×C22⋊C4C2×D1111yescharacteristic
378C4×C22⋊C4C2×D1112yescomplemented
379C4×C22⋊C4C2×D1112yescomplemented
380C2×#95—114no—
381C2×#95C2×D1112yescomplemented
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—28no—
387C22×C11—28no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—416no—
392C22×C11—44no—
393C22×C11C22×C22⋊C414yes—
394C22×C11C4×#4114yescomplemented
395C22×C11C24×C411yescharacteristic
396C22×C11C23×D412yes—
397C22×C11C22×#4112yes—
398C22×C11#58512yes—
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—216no—
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—24no—
405C2×D11—432no—
406C2×D11—48no—
407C2×D11C22×C22⋊C418yes—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—28no—
411C4×C11—44no—
412C4×C11C22×C22⋊C414yes—
413C4×C11C22×C22⋊C414yes—
414Dic11—24no—
415Dic11—48no—
416Dic11C22×C22⋊C418yes—
417C25—112no—
418C25C22×D1111yescharacteristic
419C2×#41—118no—
420C2×#41—1116no—
421C2×#41—1116no—
422C2×#41—118no—
423C2×#41—118no—
424C2×#41—118no—
425C2×#41—1116no—
426C2×#41—2216no—
427C2×#41—2216no—
428C2×#41—228no—
429C2×#41—228no—
430C2×#41—22128no—
431C2×#41—228no—
432C22×Q8—118no—
433C22×Q8—111no—
434C22×Q8—112no—
435C22×Q8—111no—
436C22×Q8—228no—
437C22×D4—112no—
438C22×D4—1116no—
439C22×D4—112no—
440C22×D4—112no—
441C22×D4—112no—
442C22×D4—118no—
443C22×D4—111no—
444C22×D4—112no—
445C22×D4—111no—
446C22×D4—228no—
447C22×D4—2216no—
448C23×C4—28no—
449C23×C4—112no—
450C23×C4—112no—
451C23×C4—1116no—
452C23×C4—112no—
453C23×C4—112no—
454C23×C4—112no—
455C23×C4—118no—
456C23×C4—2216no—
457C23×C4C4×D1118yescomplemented
458C23×C4C22×D1114yes—
459C23×C4C22×D1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C4×Q8—2216no—
466C4×D4—2216no—
467C4×D4—2232no—
468#117—2216no—
469#117—228no—
470C2×C4⋊C4—118no—
471C2×C4⋊C4—114no—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—114no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—2216no—
480C2×C22⋊C4C22×D1112yes—
481C2×C22⋊C4C22×D1114yes—
482C2×C22⋊C4C22×D1112yes—
483C2×C42—28no—
484C2×C42—118no—
485C2×C42—114no—
486C2×C42—2216no—
487C2×C42C22×D1114yes—
488C2×C42C22×D1112yes—
489C2×C42C22×D1112yes—
490#95—114no—
491#95—118no—
492#95—118no—
493#95—114no—
494#95C22×D1112yes—
495#95C22×D1112yes—
496#95C22×D1114yes—
497C2×C11—24no—
498C2×C11—24no—
499C2×C11—42no—
500C2×C11C23×C22⋊C411yescharacteristic
501C2×C11C2×C4×#4111yescharacteristic
502C2×C11#342811yescharacteristic
503C2×C11D4×#4114yes—
504D11—28no—
505D11—44no—
506C24—24no—
507C24—24no—
508C24—42no—
509C24—112no—
510C24—112no—
511C24—118no—
512C24—228no—
513C24—228no—
514C24—444no—
515C24C2×C4×D1114yes—
516C24C23×D1111yescharacteristic
517C24C23×D1111yescharacteristic
518C24C23×D1111yescharacteristic
519#41—1164no—
520#41—2264no—
521#41—2264no—
522#41—2232no—
523#41—2232no—
524#41—2232no—
525C2×Q8—114no—
526C2×Q8—118no—
527C2×Q8—114no—
528C2×Q8—118no—
529C2×Q8—228no—
530C2×Q8—2232no—
531C2×Q8—224no—
532C2×D4—118no—
533C2×D4—1116no—
534C2×D4—118no—
535C2×D4—118no—
536C2×D4—118no—
537C2×D4—114no—
538C2×D4—118no—
539C2×D4—114no—
540C2×D4—118no—
541C2×D4—2232no—
542C2×D4—228no—
543C2×D4—228no—
544C2×D4—2264no—
545C2×D4—228no—
546C2×D4—228no—
547C2×D4—224no—
548C22×C4—24no—
549C22×C4—232no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—44no—
557C22×C4—112no—
558C22×C4—118no—
559C22×C4—1116no—
560C22×C4—118no—
561C22×C4—112no—
562C22×C4—118no—
563C22×C4—118no—
564C22×C4—118no—
565C22×C4—118no—
566C22×C4—228no—
567C22×C4—2264no—
568C22×C4—228no—
569C22×C4—2216no—
570C22×C4—228no—
571C22×C4—228no—
572C22×C4—2216no—
573C22×C4—448no—
574C22×C4C2×C4×D1114yes—
575C22×C4C2×C4×D1114yes—
576C22×C4C2×C4×D1114yes—
577C22×C4C2×C4×D1114yes—
578C22×C4C2×C4×D1114yes—
579C22×C4C2×C4×D1114yes—
580C22×C4D4×D1118yes—
581C22×C4C23×D1114yes—
582C22×C4C23×D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584C22×C4C23×D1114yes—
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1111yescharacteristic
587C4⋊C4—2216no—
588C4⋊C4—228no—
589C22⋊C4—24no—
590C22⋊C4—28no—
591C22⋊C4—2216no—
592C22⋊C4—228no—
593C22⋊C4—228no—
594C22⋊C4—2216no—
595C22⋊C4—448no—
596C22⋊C4—444no—
597C22⋊C4#433918yesdirect product factor
598C42—24no—
599C42—24no—
600C42—28no—
601C42—2216no—
602C42—228no—
603C11C22⋊C4×#4111yescharacteristic, complemented, Sylow
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—416no—
615C23—114no—
616C23—118no—
617C23—114no—
618C23—2216no—
619C23—224no—
620C23—224no—
621C23—2216no—
622C23—224no—
623C23—224no—
624C23—224no—
625C23—448no—
626C23—4432no—
627C23C22×C4×D1112yes—
628C23C22×C4×D1112yes—
629C23C22×C4×D1112yes—
630C23C2×#433914yes—
631C23C2×D4×D1114yes—
632C23C24×D1111yescharacteristic
633Q8—1116no—
634Q8—2216no—
635Q8—228no—
636D4—1132no—
637D4—1116no—
638D4—2216no—
639D4—2216no—
640D4—2216no—
641D4—2216no—
642D4—228no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—416no—
656C2×C4—114no—
657C2×C4—118no—
658C2×C4—1132no—
659C2×C4—114no—
660C2×C4—2216no—
661C2×C4—2216no—
662C2×C4—2216no—
663C2×C4—224no—
664C2×C4—2216no—
665C2×C4—228no—
666C2×C4—228no—
667C2×C4—228no—
668C2×C4—4432no—
669C2×C4C22⋊C4×D11116yescomplemented
670C2×C4C22×C4×D1112yes—
671C2×C4C22×C4×D1112yes—
672C2×C4C22×C4×D1112yes—
673C2×C4C22×C4×D1112yes—
674C2×C4C2×#433918yescomplemented
675C2×C4C2×D4×D1114yes—
676C2×C4C2×D4×D1114yes—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—28no—
682C22—28no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—416no—
687C22—44no—
688C22—118no—
689C22—224no—
690C22—224no—
691C22—2216no—
692C22—224no—
693C22—224no—
694C22—224no—
695C22—4432no—
696C22—448no—
697C22C4×#433914yescomplemented
698C22C2×C22⋊C4×D1114yes—
699C22C23×C4×D1111yescharacteristic
700C22C22×#433912yes—
701C22C22×D4×D1112yes—
702C22#1062345312yes—
703C4—22no—
704C4—22no—
705C4—28no—
706C4—44no—
707C4—118no—
708C4—224no—
709C4—448no—
710C4C2×C22⋊C4×D1114yes—
711C4C2×C22⋊C4×D1114yes—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—228no—
716C2—444no—
717C2C22×C22⋊C4×D1111yescharacteristic
718C2C2×C4×#433911yescharacteristic
719C2#1308181711yescharacteristic
720C2D4×#433914yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×#4339C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C22⋊C4×#41
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4339C2semidirect
3. #13071456C2semidirect
4. C22⋊C4×Dic22C2semidirect
5. #13071447C2semidirect
6. #13071443C2semidirect
7. C22⋊C4×D44C2semidirect
8. C22⋊C4×C22⋊D11C2semidirect
9. #13071106C2semidirect
10. #13071102C2semidirect
11. #13070999C2semidirect
12. #13070997C2semidirect
13. C4×C22⋊C4×D11C2semidirect
14. C2×C4×C11×C22⋊C4C2semidirect
18. C22×#4339C4semidirect
29. C22×C42×C11C22semidirect
30. C2×C4×C22⋊D11C22semidirect
31. C2×#66979C22semidirect
34. C2×C4×D44C22semidirect
35. C2×#66925C22semidirect
36. C2×C42×D11C22semidirect
37. C2×C4×Dic22C22semidirect
41. C4×C11×C22⋊C4C22semidirect
42. C4×C11×C22⋊C4C22semidirect
43. C2×C11×#95C22semidirect
45. #10622826C22semidirect
47. #10622825C22semidirect
48. #10622824C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. #10622570C22semidirect
52. #10622569C22semidirect
56. #10622552C22semidirect
57. C4×(C2×D11)⋊C4C22semidirect
58. C4×(C2×D11)⋊C4C22semidirect
59. #10622542C22semidirect
60. #10622280C22semidirect
61. #10622279C22semidirect
62. #10622278C22semidirect
63. #10622277C22semidirect
64. D11×#95C22semidirect
65. #10622259C22semidirect
69. C23×C4×C11C2×C4semidirect
78. C22×C22⋊D11C2×C4semidirect
91. C2×#4339C2×C4semidirect
92. C2×#4339C2×C4semidirect
93. C2×#4339C2×C4semidirect
94. C2×#4339C2×C4semidirect
95. C2×#4339C2×C4semidirect
98. C22×D44C2×C4semidirect
103. C22×C4×D11C2×C4semidirect
110. C22×Dic22C2×C4semidirect
201. #4339C22⋊C4direct (N × H)
230. C11×C22⋊C4#41semidirect
257. C2×C4×C22⋊C4D11semidirect
300. C2×C4×C11C2×C22⋊C4semidirect
307. C2×C4×C11C2×#41semidirect
311. C22⋊D11C2×C22⋊C4semidirect
322. D44C2×C22⋊C4semidirect
327. C4×D11C2×C22⋊C4semidirect
330. Dic22C2×C22⋊C4semidirect
353. C22×C42C2×D11semidirect
378. C4×C22⋊C4C2×D11semidirect
379. C4×C22⋊C4C2×D11semidirect
381. C2×#95C2×D11semidirect
394. C22×C11C4×#41semidirect
457. C23×C4C4×D11semidirect
597. C22⋊C4#4339direct (N × H)
603. C11C22⋊C4×#41semidirect
669. C2×C4C22⋊C4×D11semidirect
674. C2×C4C2×#4339semidirect
697. C22C4×#4339semidirect

Maximal subgroups

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

subgroupindex
C23×#43392
C2×C4×#43392
#130714562
C22⋊C4×Dic222
#130714472
#130714432
C22⋊C4×D442
C22⋊C4×C22⋊D112
#130711062
#130711022
#130709992
#130709972
C4×C22⋊C4×D112
C2×C4×C11×C22⋊C42
C22⋊C4×#4111