Finite Group Databasebeta

← D4×C22⋊C4×D11 #14912940

Subgroups — D4×C22⋊C4×D11 #14912940

Order 2816.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic
2C2×C4×D4×D11C212yesmaximal, complemented
3C22×C22⋊C4×D11C212yesmaximal, complemented
4C22⋊C4×D44C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13071437C212yesmaximal, complemented
7#13071436C211yesmaximal, characteristic, complemented
8C22⋊C4×C22⋊D11C212yesmaximal, complemented
9#13071434C214yesmaximal, complemented
10D4×(C2×D11)⋊C4C212yesmaximal, complemented
11#13071432C212yesmaximal, complemented
12D11×#390C212yesmaximal, complemented
13D11×#386C214yesmaximal, complemented
14D11×#380C211yesmaximal, characteristic, complemented
15D11×#379C212yesmaximal, complemented
16C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
17D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
18C25×D11C2212yes—
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2212yes—
21C22×D4×D11—216no—
22C22×D4×D11C4116yescomplemented
23C22×D4×D11C2211yescharacteristic
24C22×D4×D11C2212yes—
25C22×D4×D11C2211yescharacteristic
26C22×D4×D11C2212yes—
27C22×D4×D11C2211yescharacteristic
28C22×D4×D11C2211yescharacteristic
29C23×D44C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×C4×D11C2214yescomplemented
32C2×C4×D4×C11C2212yescomplemented
33C22×C11×C22⋊C4C2212yescomplemented
34C22×C22⋊Dic11C2212yescomplemented
35C2×D4×Dic11C2212yescomplemented
36C2×C4×C22⋊D11C2214yescomplemented
37C22×(C2×D11)⋊C4C2214yescomplemented
38C4×D4×D11—216no—
39C2×#66946C2212yescomplemented
40C2×C4⋊C4×D11C2212yescomplemented
41C2×(C22⋊D11)⋊C4C2214yescomplemented
42C2×C22⋊C4×D11—216no—
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C22⋊C4×D11C2212yes—
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2214yescomplemented
47C2×C22⋊C4×D11C2212yescomplemented
48C2×C22⋊C4×D11C2212yescomplemented
49C2×C22⋊C4×D11C2214yescomplemented
50C2×C22⋊C4×D11C2214yescomplemented
51C2×C22⋊C4×D11C2214yescomplemented
52C2×C4×D44C2212yescomplemented
53C2×C42×D11C2212yescomplemented
54C11×#390C2212yescomplemented
55C11×#386C2214yescomplemented
56C11×#380C2211yescharacteristic, complemented
57C11×#379C2212yescomplemented
58C4×C11×C22⋊C4C2211yescharacteristic, complemented
59#10622860C2212yescomplemented
60#10622834C2212yescomplemented
61#10622833C2214yescomplemented
62#10622826C2214yescomplemented
63#10622825C2211yescharacteristic, complemented
64C4×C22⋊Dic11C2211yescharacteristic, complemented
65#10622601C2212yescomplemented
66#10622600C2212yescomplemented
67#10622571C2214yescomplemented
68#10622570C2214yescomplemented
69#10622570C2214yescomplemented
70#10622569C2214yescomplemented
71#10622569C2214yescomplemented
72#10622568C2214yescomplemented
73#10622568C2214yescomplemented
74#10622568C2212yescomplemented
75#10622568C2212yescomplemented
76#10622555C2212yescomplemented
77C22⋊C4×Dic11C2211yescharacteristic, complemented
78C22⋊C4×Dic11C2211yescharacteristic, complemented
79#10622552C2212yescomplemented
80C4×(C2×D11)⋊C4C2212yescomplemented
81#10622280C2212yescomplemented
82#10622279C2212yescomplemented
83#10622278C2214yescomplemented
84#10622278C2214yescomplemented
85D11×#95C2212yescomplemented
86D11×#95C2212yescomplemented
87C25×C11C2312yes—
88C24×D11—28no—
89C24×D11—216no—
90C24×D11—28no—
91C24×D11—48no—
92C24×D11C2×C4116yescomplemented
93C24×D11C2312yes—
94C24×D11C2312yes—
95C24×D11C2312yes—
96C24×D11C2312yes—
97C24×D11C2312yes—
98C24×D11C2311yescharacteristic
99C22×D4×C11—28no—
100C22×D4×C11C2×C418yescomplemented
101C22×D4×C11C2312yes—
102C22×D4×C11C2311yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2314yescomplemented
106C22×C22⋊D11—216no—
107C22×C22⋊D11C2×C4116yescomplemented
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2314yescomplemented
114C2×D4×D11—216no—
115C2×D4×D11—28no—
116C2×D4×D11—216no—
117C2×D4×D11—2128no—
118C2×D4×D11—28no—
119C2×D4×D11—28no—
120C2×D4×D11C2×C418yes—
121C2×D4×D11C2×C4116yescomplemented
122C2×D4×D11C2×C418yescomplemented
123C2×D4×D11C2×C418yescomplemented
124C2×D4×D11C2×C4116yescomplemented
125C2×D4×D11C2×C418yescomplemented
126C2×D4×D11D4116yes—
127C22×D44—28no—
128C22×D44C2×C418yescomplemented
129C22×D44C2312yes—
130C22×D44C2311yescharacteristic
131C22×D44C2311yescharacteristic
132C22×C4×D11—28no—
133C22×C4×D11—216no—
134C22×C4×D11—216no—
135C22×C4×D11—48no—
136C22×C4×D11C2×C418yescomplemented
137C22×C4×D11C2312yes—
138C22×C4×D11C2314yes—
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2314yescomplemented
145C22×C4×D11C2314yescomplemented
146C4×D4×C11—28no—
147C2×C11×C4⋊C4C2312yescomplemented
148C2×C11×C22⋊C4—28no—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2314yescomplemented
153C2×C11×C22⋊C4C2314yescomplemented
154C2×C11×C22⋊C4C2314yescomplemented
155C2×C42×C11C2312yescomplemented
156C2×C22⋊Dic11—28no—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2311yescharacteristic
159C2×C22⋊Dic11C2311yescharacteristic
160C2×C22⋊Dic11C2314yescomplemented
161C2×C22⋊Dic11C2314yescomplemented
162C2×C22⋊Dic11C2314yescomplemented
163D4×Dic11—28no—
164C4×C22⋊D11—216no—
165C2×(C2×D11)⋊C4—216no—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2314yescomplemented
170C2×(C2×D11)⋊C4C2314yescomplemented
171C2×(C2×D11)⋊C4C2314yescomplemented
172C2×(C2×D11)⋊C4C2314yescomplemented
173C2×(C2×D11)⋊C4C2314yescomplemented
174C2×(C2×D11)⋊C4C2314yescomplemented
175C2×C4⋊Dic11C2312yescomplemented
176C2×Dic11⋊C4C2314yescomplemented
177C2×C4×Dic11C2312yescomplemented
178C2×C4×Dic11C2312yescomplemented
179C2×C4×Dic11C2312yescomplemented
180#66946—28no—
181C4⋊C4×D11—28no—
182(C22⋊D11)⋊C4—216no—
183C22⋊C4×D11—28no—
184C22⋊C4×D11—216no—
185C22⋊C4×D11—24no—
186C22⋊C4×D11—216no—
187C22⋊C4×D11—28no—
188C22⋊C4×D11—28no—
189C22⋊C4×D11—216no—
190C22⋊C4×D11—48no—
191C22⋊C4×D11D418yesdirect product factor
192C4×D44—28no—
193C42×D11—28no—
194C11×#95C2312yescomplemented
195C11×#95C2312yescomplemented
196C11⋊#95C2312yescomplemented
197C11⋊#95C2312yescomplemented
198C11⋊#95C2312yescomplemented
199C11⋊#95C2312yescomplemented
200C11⋊#95C2314yescomplemented
201C2×D4×C22⋊C4—111nomaximal, Sylow
202C24×C11—24no—
203C24×C11—28no—
204C24×C11—24no—
205C24×C11—44no—
206C24×C11C22×C418yescomplemented
207C24×C11C2412yes—
208C24×C11C2412yes—
209C24×C11C2411yescharacteristic
210C23×D11—24no—
211C23×D11—24no—
212C23×D11—24no—
213C23×D11—28no—
214C23×D11—24no—
215C23×D11—24no—
216C23×D11—28no—
217C23×D11—24no—
218C23×D11—264no—
219C23×D11—264no—
220C23×D11—24no—
221C23×D11—24no—
222C23×D11—24no—
223C23×D11—28no—
224C23×D11—28no—
225C23×D11—28no—
226C23×D11—24no—
227C23×D11—24no—
228C23×D11—24no—
229C23×D11—28no—
230C23×D11—432no—
231C23×D11—44no—
232C23×D11—44no—
233C23×D11—44no—
234C23×D11—464no—
235C23×D11—464no—
236C23×D11C22×C418yes—
237C23×D11C22×C418yes—
238C23×D11C22×C414yes—
239C23×D11C22×C418yescomplemented
240C23×D11C22×C418yescomplemented
241C23×D11C22×C418yescomplemented
242C23×D11C2×D4116yes—
243C23×D11C2×D414yes—
244C23×D11#4114yes—
245C23×D11C2412yes—
246C23×D11C2412yes—
247C23×D11C2411yescharacteristic
248C23×D11C2411yescharacteristic
249C2×D4×C11—28no—
250C2×D4×C11—232no—
251C2×D4×C11—24no—
252C2×D4×C11C22×C414yes—
253C2×D4×C11C22×C418yescomplemented
254C2×D4×C11C22×C414yescomplemented
255C2×D4×C11C2×D418yes—
256C22×C4×C11—24no—
257C22×C4×C11—28no—
258C22×C4×C11—28no—
259C22×C4×C11—44no—
260C22×C4×C11C22×C414yescomplemented
261C22×C4×C11C2412yes—
262C22×C4×C11C2414yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2412yes—
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—264no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11C22×C418yes—
271C2×C22⋊D11C22×C418yescomplemented
272C2×C22⋊D11C22×C418yescomplemented
273C2×C22⋊D11C22×C418yescomplemented
274C2×C22⋊D11C2×D4116yes—
275C22×Dic11—24no—
276C22×Dic11—28no—
277C22×Dic11—28no—
278C22×Dic11—44no—
279C22×Dic11C22×C414yescomplemented
280C22×Dic11C2412yes—
281C22×Dic11C2414yes—
282C22×Dic11C2411yescharacteristic
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285D4×D11—264no—
286D4×D11—232no—
287D4×D11—232no—
288D4×D11—264no—
289D4×D11—232no—
290D4×D11C22⋊C4164yesdirect product factor
291C2×D44—232no—
292C2×D44—28no—
293C2×D44—24no—
294C2×D44C22×C414yes—
295C2×D44C22×C418yescomplemented
296C2×D44C22×C414yescomplemented
297C2×D44C2×D418yes—
298C2×C4×D11—24no—
299C2×C4×D11—232no—
300C2×C4×D11—28no—
301C2×C4×D11—24no—
302C2×C4×D11—24no—
303C2×C4×D11—24no—
304C2×C4×D11—28no—
305C2×C4×D11—28no—
306C2×C4×D11—28no—
307C2×C4×D11—28no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—28no—
312C2×C4×D11—24no—
313C2×C4×D11—28no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—464no—
317C2×C4×D11C22×C414yes—
318C2×C4×D11C22×C414yes—
319C2×C4×D11C22×C414yescomplemented
320C2×C4×D11C22×C414yescomplemented
321C2×C4×D11C2×D418yes—
322C2×C4×D11C2×D418yescomplemented
323C11×C4⋊C4—24no—
324C11×C22⋊C4—24no—
325C11×C22⋊C4—28no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—28no—
328C11×C22⋊C4—44no—
329C11×C22⋊C4C2×D414yescomplemented
330C42×C11—24no—
331C22⋊Dic11—28no—
332C22⋊Dic11—24no—
333C22⋊Dic11—28no—
334C22⋊Dic11—22no—
335C22⋊Dic11—44no—
336C22⋊Dic11C2×D414yescomplemented
337(C2×D11)⋊C4—28no—
338(C2×D11)⋊C4—28no—
339(C2×D11)⋊C4—28no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—24no—
342(C2×D11)⋊C4—28no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4C2×D418yescomplemented
346C4⋊Dic11—24no—
347Dic11⋊C4—28no—
348C4×Dic11—24no—
349C4×Dic11—24no—
350C4×Dic11—24no—
351C24×D4—111no—
352C22×C4×D4—112no—
353C23×C22⋊C4—112no—
354D4×C22⋊C4—112no—
355D4×C22⋊C4—114no—
356D4×C22⋊C4—111no—
357D4×C22⋊C4—112no—
358D4×C22⋊C4—111no—
359D4×C22⋊C4—111no—
360D4×C22⋊C4—112no—
361D4×C22⋊C4—112no—
362D4×C22⋊C4D1111yescharacteristic, direct product factor
363C2×#390—112no—
364C2×#386—114no—
365C2×#380—111no—
366C2×#379—112no—
367C2×C4×C22⋊C4—111no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—24no—
372C23×C11—22no—
373C23×C11—216no—
374C23×C11—216no—
375C23×C11—22no—
376C23×C11—24no—
377C23×C11—22no—
378C23×C11—24no—
379C23×C11—48no—
380C23×C11—416no—
381C23×C11—416no—
382C23×C11C23×C414yes—
383C23×C11C23×C414yes—
384C23×C11C23×C412yes—
385C23×C11C22×D418yes—
386C23×C11C22×D412yes—
387C23×C11C2×#4112yes—
388C23×C11C2511yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—24no—
393C22×D11—22no—
394C22×D11—28no—
395C22×D11—216no—
396C22×D11—28no—
397C22×D11—216no—
398C22×D11—232no—
399C22×D11—216no—
400C22×D11—216no—
401C22×D11—232no—
402C22×D11—216no—
403C22×D11—216no—
404C22×D11—22no—
405C22×D11—24no—
406C22×D11—22no—
407C22×D11—24no—
408C22×D11—216no—
409C22×D11—216no—
410C22×D11—216no—
411C22×D11—216no—
412C22×D11—216no—
413C22×D11—216no—
414C22×D11—216no—
415C22×D11—48no—
416C22×D11—48no—
417C22×D11—48no—
418C22×D11—416no—
419C22×D11—416no—
420C22×D11—4256no—
421C22×D11—416no—
422C22×D11—416no—
423C22×D11—416no—
424C22×D11—416no—
425C22×D11—416no—
426C22×D11—416no—
427C22×D11C2×C22⋊C4132yescomplemented
428C22×D11C4×D4116yescomplemented
429C22×D11C23×C414yes—
430C22×D11C23×C414yes—
431C22×D11C23×C412yes—
432C22×D11C23×C412yes—
433C22×D11C22×D418yes—
434C22×D11C22×D412yes—
435C22×D11C22×D414yes—
436C22×D11C22×D412yes—
437C22×D11C2×#4112yes—
438C22×D11C2×#4112yes—
439C22×D11H(5,𝔽2)14yes—
440D4×C11—216no—
441D4×C11—28no—
442D4×C11C2×C22⋊C4116yescomplemented
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—28no—
447C2×C4×C11—22no—
448C2×C4×C11—24no—
449C2×C4×C11—24no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—24no—
453C2×C4×C11—416no—
454C2×C4×C11C23×C412yes—
455C2×C4×C11C23×C412yes—
456C2×C4×C11C22×D414yes—
457C2×C4×C11C22×D414yescomplemented
458C22⋊D11—216no—
459C22⋊D11—216no—
460C22⋊D11—216no—
461C22⋊D11C2×C22⋊C4132yescomplemented
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—28no—
466C2×Dic11—22no—
467C2×Dic11—24no—
468C2×Dic11—24no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—24no—
472C2×Dic11—416no—
473C2×Dic11C23×C412yes—
474C2×Dic11C23×C412yes—
475C2×Dic11C22×D414yes—
476C2×Dic11C22×D414yescomplemented
477D44—216no—
478D44—28no—
479D44C2×C22⋊C4116yescomplemented
480C4×D11—28no—
481C4×D11—216no—
482C4×D11—28no—
483C4×D11—28no—
484C4×D11—416no—
485C4×D11—416no—
486C4×D11—416no—
487C4×D11—48no—
488C4×D11C2×C22⋊C4116yescomplemented
489C26—112no—
490C23×D4—111no—
491C23×D4—112no—
492C23×D4—112no—
493C23×D4—111no—
494C23×D4—111no—
495C23×D4—112no—
496C23×D4—111no—
497C23×D4—1116no—
498C23×D4—111no—
499C23×D4—2216no—
500C23×D4C2×D1111yescharacteristic
501C24×C4—111no—
502C24×C4—114no—
503C2×C4×D4—112no—
504C2×C4×D4—114no—
505C2×C4×D4—112no—
506C2×C4×D4—114no—
507C2×C4×D4—112no—
508C2×C4×D4—2216no—
509C2×C4×D4C2×D1112yescomplemented
510C22×C4⋊C4—112no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—112no—
513C22×C22⋊C4—114no—
514C22×C22⋊C4—112no—
515C22×C22⋊C4—112no—
516C22×C22⋊C4—112no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—114no—
519C22×C22⋊C4—114no—
520C22×C22⋊C4—114no—
521C22×C22⋊C4—114no—
522C22×C22⋊C4—2216no—
523C22×C22⋊C4C2×D1112yescomplemented
524C22×C42—112no—
525#390—112no—
526#390—112no—
527#390—114no—
528#390—114no—
529#390—112no—
530#390C2×D1112yescomplemented
531#386—114no—
532#386—114no—
533#386—114no—
534#386—114no—
535#386—114no—
536#386—114no—
537#386—114no—
538#386C2×D1114yescomplemented
539#380—111no—
540#380—112no—
541#380—112no—
542#380—112no—
543#380C2×D1111yescharacteristic, complemented
544#379—112no—
545#379—112no—
546#379—112no—
547#379—114no—
548#379—114no—
549#379C2×D1112yescomplemented
550C4×C22⋊C4—111no—
551C4×C22⋊C4—111no—
552C4×C22⋊C4—111no—
553C4×C22⋊C4—112no—
554C4×C22⋊C4—112no—
555C4×C22⋊C4C2×D1111yescharacteristic, complemented
556C2×#95—112no—
557C2×#95—112no—
558C22×C11—22no—
559C22×C11—24no—
560C22×C11—22no—
561C22×C11—24no—
562C22×C11—28no—
563C22×C11—24no—
564C22×C11—24no—
565C22×C11—28no—
566C22×C11—24no—
567C22×C11—24no—
568C22×C11—24no—
569C22×C11—432no—
570C22×C11—44no—
571C22×C11—44no—
572C22×C11C22×C22⋊C418yescomplemented
573C22×C11C2×C4×D414yescomplemented
574C22×C11C24×C411yescharacteristic
575C22×C11C23×D412yes—
576C22×C11C23×D411yescharacteristic
577C22×C11C22×#4111yescharacteristic
578C22×C11C2×H(5,𝔽2)12yes—
579C2×D11—22no—
580C2×D11—24no—
581C2×D11—22no—
582C2×D11—24no—
583C2×D11—24no—
584C2×D11—28no—
585C2×D11—24no—
586C2×D11—28no—
587C2×D11—232no—
588C2×D11—264no—
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—432no—
593C2×D11—432no—
594C2×D11—432no—
595C2×D11—44no—
596C2×D11—44no—
597C2×D11—432no—
598C2×D11C22×C22⋊C414yes—
599C2×D11C22×C22⋊C418yescomplemented
600C2×D11C2×C4×D414yes—
601C2×D11C2×C4×D414yescomplemented
602C2×D11#51814yes—
603C2×D11D4218yes—
604C2×D11#54618yes—
605C4×C11—22no—
606C4×C11—24no—
607C4×C11—44no—
608C4×C11—42no—
609C4×C11C22×C22⋊C414yescomplemented
610Dic11—22no—
611Dic11—24no—
612Dic11—44no—
613Dic11—42no—
614Dic11C22×C22⋊C414yescomplemented
615C25—111no—
616C25—112no—
617C25—112no—
618C25—1116no—
619C25—112no—
620C25—112no—
621C25—112no—
622C25—228no—
623C25—2216no—
624C25—228no—
625C25—448no—
626C25C22×D1112yes—
627C22×D4—28no—
628C22×D4—112no—
629C22×D4—118no—
630C22×D4—1116no—
631C22×D4—1116no—
632C22×D4—112no—
633C22×D4—112no—
634C22×D4—112no—
635C22×D4—118no—
636C22×D4—118no—
637C22×D4—1116no—
638C22×D4—1116no—
639C22×D4—118no—
640C22×D4—118no—
641C22×D4—111no—
642C22×D4—112no—
643C22×D4—111no—
644C22×D4—228no—
645C22×D4—228no—
646C22×D4—2216no—
647C22×D4—22128no—
648C22×D4—228no—
649C22×D4—2216no—
650C22×D4—2216no—
651C22×D4—228no—
652C22×D4C4×D1118yescomplemented
653C22×D4C22×D1112yes—
654C22×D4C22×D1111yescharacteristic
655C22×D4C22×D1111yescharacteristic
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—118no—
659C23×C4—112no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—114no—
664C23×C4—112no—
665C23×C4—114no—
666C23×C4—114no—
667C23×C4—114no—
668C23×C4—228no—
669C23×C4—2216no—
670C23×C4—2216no—
671C23×C4—448no—
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1114yescomplemented
674C4×D4—28no—
675C4×D4—228no—
676C4×D4—2216no—
677C4×D4—228no—
678C4×D4—2216no—
679C4×D4—228no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—228no—
683C2×C4⋊C4C22×D1112yescomplemented
684C2×C22⋊C4—28no—
685C2×C22⋊C4—111no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—118no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—111no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—228no—
702C2×C22⋊C4—2216no—
703C2×C22⋊C4—2216no—
704C2×C22⋊C4—228no—
705C2×C22⋊C4—2216no—
706C2×C22⋊C4—224no—
707C2×C22⋊C4—2216no—
708C2×C22⋊C4—228no—
709C2×C22⋊C4—228no—
710C2×C22⋊C4—448no—
711C2×C22⋊C4C22×D1112yes—
712C2×C22⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4C22×D1111yescharacteristic
714C2×C22⋊C4C22×D1114yescomplemented
715C2×C22⋊C4C22×D1114yescomplemented
716C2×C22⋊C4C22×D1114yescomplemented
717C2×C42—112no—
718C2×C42—112no—
719C2×C42—112no—
720C2×C42—228no—
721C2×C42C22×D1112yescomplemented
722#95—112no—
723#95—112no—
724#95—112no—
725#95—114no—
726#95—112no—
727#95C22×D1112yescomplemented
728#95C22×D1112yescomplemented
729C2×C11—24no—
730C2×C11—28no—
731C2×C11—44no—
732C2×C11C23×C22⋊C411yescharacteristic
733C2×C11C22×C4×D411yescharacteristic
734C2×C11C2×#51811yescharacteristic
735C2×C11C2×D4212yes—
736C2×C11C2×#54612yes—
737D11—24no—
738D11—28no—
739D11—44no—
740D11D4×C22⋊C418yesdirect product factor
741C24—24no—
742C24—28no—
743C24—24no—
744C24—44no—
745C24—111no—
746C24—114no—
747C24—118no—
748C24—114no—
749C24—1116no—
750C24—114no—
751C24—111no—
752C24—112no—
753C24—118no—
754C24—112no—
755C24—118no—
756C24—118no—
757C24—118no—
758C24—224no—
759C24—224no—
760C24—228no—
761C24—224no—
762C24—224no—
763C24—224no—
764C24—224no—
765C24—224no—
766C24—228no—
767C24—228no—
768C24—2264no—
769C24—228no—
770C24—228no—
771C24—224no—
772C24—2264no—
773C24—224no—
774C24—224no—
775C24—224no—
776C24—228no—
777C24—224no—
778C24—444no—
779C24—444no—
780C24—444no—
781C24—4432no—
782C24—4464no—
783C24—4464no—
784C24C2×C4×D1118yescomplemented
785C24C23×D1112yes—
786C24C23×D1112yes—
787C24C23×D1111yescharacteristic
788C2×D4—28no—
789C2×D4—232no—
790C2×D4—24no—
791C2×D4—118no—
792C2×D4—1116no—
793C2×D4—1164no—
794C2×D4—118no—
795C2×D4—118no—
796C2×D4—118no—
797C2×D4—114no—
798C2×D4—118no—
799C2×D4—114no—
800C2×D4—118no—
801C2×D4—2232no—
802C2×D4—228no—
803C2×D4—2232no—
804C2×D4—228no—
805C2×D4—2264no—
806C2×D4—2232no—
807C2×D4—2264no—
808C2×D4—2264no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—2232no—
812C2×D4—224no—
813C2×D4C2×C4×D1114yes—
814C2×D4C2×C4×D1118yescomplemented
815C2×D4C2×C4×D1114yescomplemented
816C2×D4D4×D1118yes—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—44no—
821C22×C4—111no—
822C22×C4—114no—
823C22×C4—118no—
824C22×C4—114no—
825C22×C4—111no—
826C22×C4—112no—
827C22×C4—114no—
828C22×C4—114no—
829C22×C4—114no—
830C22×C4—118no—
831C22×C4—112no—
832C22×C4—114no—
833C22×C4—224no—
834C22×C4—2232no—
835C22×C4—228no—
836C22×C4—224no—
837C22×C4—224no—
838C22×C4—224no—
839C22×C4—224no—
840C22×C4—228no—
841C22×C4—228no—
842C22×C4—224no—
843C22×C4—224no—
844C22×C4—228no—
845C22×C4—228no—
846C22×C4—228no—
847C22×C4—224no—
848C22×C4—228no—
849C22×C4—224no—
850C22×C4—228no—
851C22×C4—228no—
852C22×C4—444no—
853C22×C4—444no—
854C22×C4—4464no—
855C22×C4—444no—
856C22×C4C2×C4×D1114yescomplemented
857C22×C4C23×D1112yes—
858C22×C4C23×D1114yes—
859C22×C4C23×D1111yescharacteristic
860C22×C4C23×D1112yes—
861C22×C4C23×D1111yescharacteristic
862C4⋊C4—24no—
863C4⋊C4—228no—
864C4⋊C4—224no—
865C22⋊C4—24no—
866C22⋊C4—28no—
867C22⋊C4—22no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—114no—
871C22⋊C4—118no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—228no—
876C22⋊C4—224no—
877C22⋊C4—228no—
878C22⋊C4—224no—
879C22⋊C4—228no—
880C22⋊C4—222no—
881C22⋊C4—228no—
882C22⋊C4—444no—
883C22⋊C4—444no—
884C22⋊C4—444no—
885C22⋊C4D4×D1114yesdirect product factor
886C42—24no—
887C42—224no—
888C42—224no—
889C42—224no—
890C11C2×D4×C22⋊C411yescharacteristic, complemented, Sylow
891C23—22no—
892C23—22no—
893C23—22no—
894C23—24no—
895C23—22no—
896C23—216no—
897C23—216no—
898C23—22no—
899C23—24no—
900C23—22no—
901C23—24no—
902C23—48no—
903C23—416no—
904C23—416no—
905C23—112no—
906C23—112no—
907C23—114no—
908C23—112no—
909C23—114no—
910C23—1132no—
911C23—1116no—
912C23—112no—
913C23—114no—
914C23—112no—
915C23—118no—
916C23—112no—
917C23—114no—
918C23—228no—
919C23—2232no—
920C23—2216no—
921C23—2216no—
922C23—2232no—
923C23—2216no—
924C23—228no—
925C23—2216no—
926C23—2216no—
927C23—2216no—
928C23—2216no—
929C23—2216no—
930C23—2216no—
931C23—2216no—
932C23—2216no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—224no—
937C23—222no—
938C23—2216no—
939C23—2216no—
940C23—222no—
941C23—224no—
942C23—222no—
943C23—224no—
944C23—448no—
945C23—448no—
946C23—448no—
947C23—4416no—
948C23—4416no—
949C23—4416no—
950C23—4416no—
951C23—4416no—
952C23—4416no—
953C23—44256no—
954C23—4416no—
955C23—4416no—
956C23C22×C4×D1114yes—
957C23C22×C4×D1114yes—
958C23C22×C4×D1112yes—
959C23C2×D4×D1118yes—
960C23C2×D4×D1112yes—
961C23#41×D1112yes—
962C23C24×D1111yescharacteristic
963D4—216no—
964D4—28no—
965D4—1132no—
966D4—1116no—
967D4—2216no—
968D4—2216no—
969D4—2216no—
970D4—2216no—
971D4—228no—
972D4C22⋊C4×D11116yesdirect product factor
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—416no—
984C2×C4—112no—
985C2×C4—114no—
986C2×C4—1116no—
987C2×C4—112no—
988C2×C4—114no—
989C2×C4—228no—
990C2×C4—228no—
991C2×C4—2216no—
992C2×C4—228no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—228no—
997C2×C4—222no—
998C2×C4—224no—
999C2×C4—224no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—224no—
1003C2×C4—4416no—
1004C2×C4—4416no—
1005C2×C4—4416no—
1006C2×C4—448no—
1007C2×C4—4416no—
1008C2×C4C22×C4×D1112yes—
1009C2×C4C22×C4×D1112yes—
1010C2×C4C2×D4×D1114yes—
1011C2×C4C2×D4×D1114yescomplemented
1012C22—22no—
1013C22—24no—
1014C22—28no—
1015C22—24no—
1016C22—22no—
1017C22—24no—
1018C22—24no—
1019C22—28no—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—432no—
1024C22—44no—
1025C22—44no—
1026C22—114no—
1027C22—114no—
1028C22—118no—
1029C22—114no—
1030C22—118no—
1031C22—118no—
1032C22—114no—
1033C22—2232no—
1034C22—2264no—
1035C22—222no—
1036C22—224no—
1037C22—228no—
1038C22—224no—
1039C22—222no—
1040C22—224no—
1041C22—224no—
1042C22—228no—
1043C22—224no—
1044C22—224no—
1045C22—224no—
1046C22—4432no—
1047C22—4432no—
1048C22—4432no—
1049C22—4432no—
1050C22—444no—
1051C22—444no—
1052C22C2×C22⋊C4×D1118yescomplemented
1053C22C4×D4×D1114yescomplemented
1054C22C23×C4×D1111yescharacteristic
1055C22C22×D4×D1112yes—
1056C22C22×D4×D1111yescharacteristic
1057C22C2×#41×D1111yescharacteristic
1058C22D11×H(5,𝔽2)12yes—
1059C4—22no—
1060C4—24no—
1061C4—44no—
1062C4—42no—
1063C4—114no—
1064C4—222no—
1065C4—224no—
1066C4—444no—
1067C4—442no—
1068C4C2×C22⋊C4×D1114yescomplemented
1069C2—24no—
1070C2—28no—
1071C2—44no—
1072C2—118no—
1073C2—224no—
1074C2—228no—
1075C2—444no—
1076C2C22×C22⋊C4×D1111yescharacteristic
1077C2C2×C4×D4×D1111yescharacteristic
1078C2D11×#51811yescharacteristic
1079C2D42×D1112yes—
1080C2D11×#54612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D4×D11C2
hypercenterD4×C22⋊C4D11
hypocenterC11C2×D4×C22⋊C4
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D11C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. C22⋊C4×D44C2semidirect
5. D4×C22⋊Dic11C2semidirect
6. #13071437C2semidirect
7. #13071436C2semidirect
8. C22⋊C4×C22⋊D11C2semidirect
9. #13071434C2semidirect
10. D4×(C2×D11)⋊C4C2semidirect
11. #13071432C2semidirect
12. D11×#390C2semidirect
13. D11×#386C2semidirect
14. D11×#380C2semidirect
15. D11×#379C2semidirect
16. C4×C22⋊C4×D11C2semidirect
17. D4×C11×C22⋊C4C2semidirect
22. C22×D4×D11C4semidirect
31. C23×C4×D11C22semidirect
32. C2×C4×D4×C11C22semidirect
33. C22×C11×C22⋊C4C22semidirect
34. C22×C22⋊Dic11C22semidirect
35. C2×D4×Dic11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C22×(C2×D11)⋊C4C22semidirect
39. C2×#66946C22semidirect
40. C2×C4⋊C4×D11C22semidirect
41. C2×(C22⋊D11)⋊C4C22semidirect
46. C2×C22⋊C4×D11C22semidirect
47. C2×C22⋊C4×D11C22semidirect
48. C2×C22⋊C4×D11C22semidirect
49. C2×C22⋊C4×D11C22semidirect
50. C2×C22⋊C4×D11C22semidirect
51. C2×C22⋊C4×D11C22semidirect
52. C2×C4×D44C22semidirect
53. C2×C42×D11C22semidirect
54. C11×#390C22semidirect
55. C11×#386C22semidirect
56. C11×#380C22semidirect
57. C11×#379C22semidirect
58. C4×C11×C22⋊C4C22semidirect
59. #10622860C22semidirect
60. #10622834C22semidirect
61. #10622833C22semidirect
62. #10622826C22semidirect
63. #10622825C22semidirect
64. C4×C22⋊Dic11C22semidirect
65. #10622601C22semidirect
66. #10622600C22semidirect
67. #10622571C22semidirect
68. #10622570C22semidirect
69. #10622570C22semidirect
70. #10622569C22semidirect
71. #10622569C22semidirect
72. #10622568C22semidirect
73. #10622568C22semidirect
74. #10622568C22semidirect
75. #10622568C22semidirect
76. #10622555C22semidirect
77. C22⋊C4×Dic11C22semidirect
78. C22⋊C4×Dic11C22semidirect
79. #10622552C22semidirect
80. C4×(C2×D11)⋊C4C22semidirect
81. #10622280C22semidirect
82. #10622279C22semidirect
83. #10622278C22semidirect
84. #10622278C22semidirect
85. D11×#95C22semidirect
86. D11×#95C22semidirect
92. C24×D11C2×C4semidirect
100. C22×D4×C11C2×C4semidirect
105. C23×C4×C11C23semidirect
107. C22×C22⋊D11C2×C4semidirect
113. C23×Dic11C23semidirect
121. C2×D4×D11C2×C4semidirect
122. C2×D4×D11C2×C4semidirect
123. C2×D4×D11C2×C4semidirect
124. C2×D4×D11C2×C4semidirect
125. C2×D4×D11C2×C4semidirect
128. C22×D44C2×C4semidirect
136. C22×C4×D11C2×C4semidirect
144. C22×C4×D11C23semidirect
145. C22×C4×D11C23semidirect
147. C2×C11×C4⋊C4C23semidirect
152. C2×C11×C22⋊C4C23semidirect
153. C2×C11×C22⋊C4C23semidirect
154. C2×C11×C22⋊C4C23semidirect
155. C2×C42×C11C23semidirect
160. C2×C22⋊Dic11C23semidirect
161. C2×C22⋊Dic11C23semidirect
162. C2×C22⋊Dic11C23semidirect
169. C2×(C2×D11)⋊C4C23semidirect
170. C2×(C2×D11)⋊C4C23semidirect
171. C2×(C2×D11)⋊C4C23semidirect
172. C2×(C2×D11)⋊C4C23semidirect
173. C2×(C2×D11)⋊C4C23semidirect
174. C2×(C2×D11)⋊C4C23semidirect
175. C2×C4⋊Dic11C23semidirect
176. C2×Dic11⋊C4C23semidirect
177. C2×C4×Dic11C23semidirect
178. C2×C4×Dic11C23semidirect
179. C2×C4×Dic11C23semidirect
191. C22⋊C4×D11D4direct (N × H)
194. C11×#95C23semidirect
195. C11×#95C23semidirect
196. C11⋊#95C23semidirect
197. C11⋊#95C23semidirect
198. C11⋊#95C23semidirect
199. C11⋊#95C23semidirect
200. C11⋊#95C23semidirect
206. C24×C11C22×C4semidirect
239. C23×D11C22×C4semidirect
240. C23×D11C22×C4semidirect
241. C23×D11C22×C4semidirect
253. C2×D4×C11C22×C4semidirect
254. C2×D4×C11C22×C4semidirect
260. C22×C4×C11C22×C4semidirect
271. C2×C22⋊D11C22×C4semidirect
272. C2×C22⋊D11C22×C4semidirect
273. C2×C22⋊D11C22×C4semidirect
279. C22×Dic11C22×C4semidirect
290. D4×D11C22⋊C4direct (N × H)
295. C2×D44C22×C4semidirect
296. C2×D44C22×C4semidirect
319. C2×C4×D11C22×C4semidirect
320. C2×C4×D11C22×C4semidirect
322. C2×C4×D11C2×D4semidirect
329. C11×C22⋊C4C2×D4semidirect
336. C22⋊Dic11C2×D4semidirect
345. (C2×D11)⋊C4C2×D4semidirect
362. D4×C22⋊C4D11direct (N × H)
427. C22×D11C2×C22⋊C4semidirect
428. C22×D11C4×D4semidirect
442. D4×C11C2×C22⋊C4semidirect
457. C2×C4×C11C22×D4semidirect
461. C22⋊D11C2×C22⋊C4semidirect
476. C2×Dic11C22×D4semidirect
479. D44C2×C22⋊C4semidirect
488. C4×D11C2×C22⋊C4semidirect
509. C2×C4×D4C2×D11semidirect
523. C22×C22⋊C4C2×D11semidirect
530. #390C2×D11semidirect
538. #386C2×D11semidirect
543. #380C2×D11semidirect
549. #379C2×D11semidirect
555. C4×C22⋊C4C2×D11semidirect
572. C22×C11C22×C22⋊C4semidirect
573. C22×C11C2×C4×D4semidirect
599. C2×D11C22×C22⋊C4semidirect
601. C2×D11C2×C4×D4semidirect
609. C4×C11C22×C22⋊C4semidirect
614. Dic11C22×C22⋊C4semidirect
652. C22×D4C4×D11semidirect
673. C23×C4C22×D11semidirect
683. C2×C4⋊C4C22×D11semidirect
714. C2×C22⋊C4C22×D11semidirect
715. C2×C22⋊C4C22×D11semidirect
716. C2×C22⋊C4C22×D11semidirect
721. C2×C42C22×D11semidirect
727. #95C22×D11semidirect
728. #95C22×D11semidirect
740. D11D4×C22⋊C4direct (N × H)
784. C24C2×C4×D11semidirect
814. C2×D4C2×C4×D11semidirect
815. C2×D4C2×C4×D11semidirect
856. C22×C4C2×C4×D11semidirect
885. C22⋊C4D4×D11direct (N × H)
890. C11C2×D4×C22⋊C4semidirect
972. D4C22⋊C4×D11direct (N × H)
1011. C2×C4C2×D4×D11semidirect
1052. C22C2×C22⋊C4×D11semidirect
1053. C22C4×D4×D11semidirect
1068. C4C2×C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D112
C2×C4×D4×D112
C22×C22⋊C4×D112
C22⋊C4×D442
D4×C22⋊Dic112
#130714372
#130714362
C22⋊C4×C22⋊D112
#130714342
D4×(C2×D11)⋊C42
#130714322
D11×#3902
D11×#3862
D11×#3802
D11×#3792
C4×C22⋊C4×D112
D4×C11×C22⋊C42
C2×D4×C22⋊C411