Finite Group Databasebeta

← C4×D11×C22⋊Q8 #14912215

Subgroups — C4×D11×C22⋊Q8 #14912215

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3C22×C42×D11C211yesmaximal, characteristic
4#13071154C211yesmaximal, characteristic, complemented
5C4×#66950C211yesmaximal, characteristic, complemented
6C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
7C4×#66977C211yesmaximal, characteristic, complemented
8#13071150C212yesmaximal, complemented
9C4×#66949C212yesmaximal, complemented
10#13071148C212yesmaximal, complemented
11C4×#66931C212yesmaximal, complemented
12#13071146C211yesmaximal, characteristic, complemented
13C4×#66999C211yesmaximal, characteristic, complemented
14#13071144C211yesmaximal, characteristic, complemented
15D11×#391C211yesmaximal, characteristic, complemented
16D11×#389C211yesmaximal, characteristic, complemented
17D11×#387C212yesmaximal, complemented
18D11×#385C212yesmaximal
19D11×#380C211yesmaximal, characteristic
20C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
21C4×C4⋊C4×D11C212yesmaximal, complemented
22C4×C22⋊C4×D11C212yesmaximal
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic, complemented
30C22×C42×C11C2211yescharacteristic
31C2×#66999C2211yescharacteristic
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C2×#66977C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37D11×C22⋊Q8C4116yesdirect product factor
38C4×Q8×D11—28no—
39C2×#66950C2211yescharacteristic
40C2×#66949C2212yes—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2212yes—
45C2×C4⋊C4×D11C2212yes—
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66940C2211yescharacteristic, complemented
48C2×#66940C2212yescomplemented
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×#66931C2212yes—
52C2×C42×D11—28no—
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2212yes—
58C2×C42×D11C2212yes—
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C42×D11C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C4×Dic22C2212yescomplemented
64C2×C4×Dic22C2211yescharacteristic, complemented
65C11×#391C2211yescharacteristic, complemented
66C11×#389C2211yescharacteristic, complemented
67C11×#387C2212yescomplemented
68C11×#385C2212yes—
69C11×#380C2211yescharacteristic
70C4×C11×C4⋊C4C2212yescomplemented
71C4×C11×C4⋊C4C2211yescharacteristic, complemented
72C4×C11×C22⋊C4C2212yes—
73#10622843C2211yescharacteristic, complemented
74#10622825C2211yescharacteristic
75#10622823C2212yes—
76C4×C22⋊Dic11C2212yes—
77#10622602C2212yes—
78#10622602C2212yes—
79#10622600C2211yescharacteristic
80#10622600C2211yescharacteristic
81#10622598C2211yescharacteristic, complemented
82#10622594C2212yescomplemented
83#10622591C2212yescomplemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85C4⋊C4×Dic11C2212yescomplemented
86C4⋊C4×Dic11C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2212yescomplemented
88#10622587C2211yescharacteristic, complemented
89#10622586C2211yescharacteristic, complemented
90#10622585C2212yescomplemented
91#10622563C2212yes—
92#10622559C2212yes—
93#10622555C2212yes—
94C22⋊C4×Dic11C2212yes—
95C22⋊C4×Dic11C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98C4×C4⋊Dic11C2211yescharacteristic, complemented
99C4×C4⋊Dic11C2212yescomplemented
100#10622546C2212yescomplemented
101C4×Dic11⋊C4C2212yescomplemented
102C4×Dic11⋊C4C2212yescomplemented
103C4×Dic11⋊C4C2212yescomplemented
104#10622542C2211yescharacteristic, complemented
105#10622541C2211yescharacteristic, complemented
106#10622281C2212yes—
107#10622281C2212yes—
108#10622280C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111D11×#95C2212yes—
112D11×#95C2212yes—
113D11×#95C2212yes—
114D11×#95C2212yes—
115D11×#95C2212yes—
116#10622268C2212yescomplemented
117#10622267C2212yescomplemented
118#10622266C2212yescomplemented
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×Q8×D11—24no—
135C2×Q8×D11—24no—
136C2×Q8×D11C2×C418yescomplemented
137C22×C4×D11—24no—
138C22×C4×D11—24no—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11—24no—
144C22×C4×D11C2×C418yes—
145C22×C4×D11Q818yescomplemented
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×Dic22C2312yes—
163C22×Dic22C2311yescharacteristic
164C11×C22⋊Q8C2×C418yescomplemented
165C4×Q8×C11—24no—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11—24no—
175C2×C42×C11C2312yes—
176C2×C42×C11C2311yescharacteristic
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2312yes—
180C2×C42×C11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183#66999C2×C418yescomplemented
184Q8×Dic11—24no—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2312yes—
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195#66977C2×C418yescomplemented
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11—24no—
206C2×C4×Dic11—24no—
207C2×C4×Dic11—24no—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66950C2×C418yescomplemented
227#66949C2×C4116yescomplemented
228C4⋊C4×D11—24no—
229C4⋊C4×D11—28no—
230C4⋊C4×D11—24no—
231C4⋊C4×D11—28no—
232C4⋊C4×D11C2×C418yescomplemented
233C4⋊C4×D11C2×C4116yescomplemented
234#66940—24no—
235#66940—28no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11C2×C4116yes—
238#66931C2×C4116yescomplemented
239C42×D11—24no—
240C42×D11—24no—
241C42×D11—24no—
242C42×D11—28no—
243C42×D11—28no—
244C42×D11—24no—
245C42×D11—24no—
246C42×D11—24no—
247C42×D11—24no—
248C42×D11D418yes—
249C4×Dic22—24no—
250C4×Dic22—28no—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270C11⋊#95C2312yes—
271C2×C4×C22⋊Q8—111nomaximal, Sylow
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11C22×C414yes—
278C23×D11C2×Q814yes—
279C23×D11#4114yes—
280C23×D11C2411yescharacteristic
281C23×D11C2411yescharacteristic
282C2×Q8×C11—22no—
283C2×Q8×C11—22no—
284C2×Q8×C11C22×C414yescomplemented
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11C22×C414yes—
293C22×C4×C11C2×Q814yescomplemented
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11C22×C414yes—
312C22×Dic11C2×Q814yescomplemented
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323Q8×D11—232no—
324C2×C4×D11—232no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—232no—
332C2×C4×D11—232no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11C22×C418yes—
360C2×C4×D11C22×C418yes—
361C2×C4×D11C22×C414yes—
362C2×C4×D11C22×C414yes—
363C2×C4×D11C22×C414yes—
364C2×C4×D11C22×C414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11C2×D414yes—
367C2×C4×D11C2×D414yes—
368C2×C4×D11C2×Q814yes—
369C2×C4×D11C2×Q814yes—
370C2×C4×D11C2×Q814yescomplemented
371C2×C4×D11C2×Q814yescomplemented
372C2×C4×D11#4114yes—
373C2×C4×D11#4114yes—
374C2×C4×D11#4114yes—
375C2×Dic22—24no—
376C2×Dic22—24no—
377C2×Dic22—22no—
378C2×Dic22—22no—
379C2×Dic22C22×C418yescomplemented
380C2×Dic22C22×C414yescomplemented
381C11×C4⋊C4—24no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—24no—
384C11×C4⋊C4—22no—
385C11×C4⋊C4C22×C418yescomplemented
386C11×C4⋊C4C22×C414yescomplemented
387C11×C22⋊C4—24no—
388C11×C22⋊C4C22×C418yes—
389C42×C11—24no—
390C42×C11—22no—
391C42×C11—22no—
392C42×C11—22no—
393C42×C11—24no—
394C42×C11C2×D414yes—
395C22⋊Dic11—24no—
396C22⋊Dic11C22×C418yes—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4C22×C418yes—
400(C2×D11)⋊C4C22×C418yes—
401C4⋊Dic11—24no—
402C4⋊Dic11—24no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11C22×C418yescomplemented
406C4⋊Dic11C22×C414yescomplemented
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—24no—
413Dic11⋊C4C22×C418yescomplemented
414Dic11⋊C4C22×C418yescomplemented
415Dic11⋊C4C22×C418yescomplemented
416C4×Dic11—22no—
417C4×Dic11—22no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—22no—
421C4×Dic11—22no—
422C4×Dic11—24no—
423C4×Dic11—24no—
424C4×Dic11—24no—
425C4×Dic11—24no—
426C4×Dic11—24no—
427C4×Dic11—22no—
428C4×Dic11—22no—
429C4×Dic11—22no—
430C4×Dic11—24no—
431C4×Dic11C2×D414yes—
432C4×Dic11C2×D414yes—
433C4×Dic11C2×D414yes—
434C22×C22⋊Q8—111no—
435C22×C4×Q8—111no—
436C23×C42—111no—
437C4×C22⋊Q8—111no—
438C4×C22⋊Q8—111no—
439C4×C22⋊Q8—111no—
440C4×C22⋊Q8—112no—
441C4×C22⋊Q8—112no—
442C4×C22⋊Q8—111no—
443C4×C22⋊Q8—112no—
444C4×C22⋊Q8—111no—
445C4×C22⋊Q8—112no—
446C4×C22⋊Q8—111no—
447C4×C22⋊Q8—111no—
448C4×C22⋊Q8D1111yescharacteristic, direct product factor
449C2×#391—111no—
450C2×#389—111no—
451C2×#387—112no—
452C2×#385—112no—
453C2×#380—111no—
454C2×C4×C4⋊C4—112no—
455C2×C4×C4⋊C4—111no—
456C2×C4×C22⋊C4—112no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—21no—
460C23×C11—21no—
461C23×C11C23×C412yes—
462C23×C11C22×Q812yes—
463C23×C11C2×#4112yes—
464C23×C11C2511yescharacteristic
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—28no—
470C22×D11—28no—
471C22×D11—28no—
472C22×D11—28no—
473C22×D11—28no—
474C22×D11—28no—
475C22×D11C4×Q8116yescomplemented
476C22×D11C23×C412yes—
477C22×D11C23×C412yes—
478C22×D11C22×D412yes—
479C22×D11C22×Q812yes—
480C22×D11C22×Q812yes—
481C22×D11C2×#4112yes—
482C22×D11C2×#4112yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485C22×D11C2×#4112yes—
486Q8×C11—28no—
487C2×C4×C11—28no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—28no—
501C2×C4×C11—28no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C414yes—
510C2×C4×C11C23×C414yes—
511C2×C4×C11C23×C412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C22×D412yes—
515C2×C4×C11C22×Q812yes—
516C2×C4×C11C22×Q812yes—
517C2×C4×C11C2×#4112yes—
518C2×C4×C11C2×#4112yes—
519C2×C4×C11C2×#4112yes—
520C2×Dic11—28no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—28no—
534C2×Dic11—28no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11C23×C414yes—
542C2×Dic11C23×C412yes—
543C2×Dic11C23×C414yes—
544C2×Dic11C23×C412yes—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×Q812yes—
549C2×Dic11C22×Q812yes—
550C2×Dic11C2×#4112yes—
551C2×Dic11C2×#4112yes—
552C2×Dic11C2×#4112yes—
553C4×D11—28no—
554C4×D11—28no—
555C4×D11—28no—
556C4×D11—216no—
557C4×D11—216no—
558C4×D11—28no—
559C4×D11—28no—
560C4×D11—28no—
561C4×D11—28no—
562C4×D11—28no—
563C4×D11—28no—
564C4×D11—28no—
565C4×D11—48no—
566C4×D11—48no—
567C4×D11C4×D4116yes—
568C4×D11C22⋊Q8116yesdirect product factor
569Dic22—28no—
570Dic22—216no—
571C23×Q8—111no—
572C24×C4—111no—
573C24×C4—111no—
574C24×C4—111no—
575C2×C22⋊Q8—111no—
576C2×C22⋊Q8—111no—
577C2×C22⋊Q8—1116no—
578C2×C22⋊Q8—112no—
579C2×C22⋊Q8—111no—
580C2×C22⋊Q8—112no—
581C2×C22⋊Q8C2×D1111yescharacteristic
582C2×C4×Q8—111no—
583C2×C4×Q8—112no—
584C2×C4×Q8—111no—
585C2×C4×Q8—112no—
586C2×C4×Q8—111no—
587C2×C4×Q8—228no—
588C2×C4×Q8C2×D1111yescharacteristic, complemented
589C22×C4⋊C4—112no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C4⋊C4—112no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4—112no—
595C22×C22⋊C4—112no—
596C22×C22⋊C4—112no—
597C22×C42—111no—
598C22×C42—111no—
599C22×C42—111no—
600C22×C42—111no—
601C22×C42—111no—
602C22×C42—111no—
603C22×C42—111no—
604C22×C42—111no—
605C22×C42—111no—
606C22×C42—111no—
607C22×C42—111no—
608C22×C42—112no—
609C22×C42—112no—
610C22×C42—228no—
611C22×C42C2×D1111yescharacteristic
612#391—111no—
613#391—111no—
614#391—111no—
615#391—112no—
616#391—112no—
617#391C2×D1111yescharacteristic, complemented
618#389—112no—
619#389—111no—
620#389—111no—
621#389—111no—
622#389—112no—
623#389C2×D1111yescharacteristic, complemented
624#387—112no—
625#387—112no—
626#387—112no—
627#387—112no—
628#387—112no—
629#387—112no—
630#387—112no—
631#387C2×D1112yescomplemented
632#385—112no—
633#385—112no—
634#385—112no—
635#385—112no—
636#385—112no—
637#385—112no—
638#385—112no—
639#385C2×D1112yes—
640#380—111no—
641#380—111no—
642#380—111no—
643#380—112no—
644#380—112no—
645#380C2×D1111yescharacteristic
646C4×C4⋊C4—112no—
647C4×C4⋊C4—112no—
648C4×C4⋊C4—111no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—112no—
651C4×C4⋊C4—112no—
652C4×C4⋊C4—112no—
653C4×C4⋊C4—112no—
654C4×C4⋊C4—111no—
655C4×C4⋊C4—112no—
656C4×C4⋊C4—112no—
657C4×C4⋊C4—112no—
658C4×C4⋊C4C2×D1112yescomplemented
659C4×C4⋊C4C2×D1111yescharacteristic, complemented
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4—112no—
663C4×C22⋊C4—112no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—112no—
666C4×C22⋊C4—112no—
667C4×C22⋊C4C2×D1112yes—
668C2×#95—112no—
669C2×#95—112no—
670C2×#95—112no—
671C2×#95—112no—
672C2×#95—112no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—22no—
677C22×C11—22no—
678C22×C11—22no—
679C22×C11C2×C4×Q814yescomplemented
680C22×C11C24×C411yescharacteristic
681C22×C11C23×D411yescharacteristic
682C22×C11C23×Q811yescharacteristic
683C22×C11C22×#4111yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C22×#4111yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—232no—
694C2×D11C2×C4×D414yes—
695C2×D11C2×C4×Q814yes—
696C2×D11C2×C4×Q814yescomplemented
697C2×D11C4×#4114yes—
698C2×D11C2×C22⋊Q814yes—
699C2×D11#52514yes—
700C2×D11#52914yes—
701C2×D11#53314yes—
702C4×C11—22no—
703C4×C11—24no—
704C4×C11—24no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11C2×C4×D414yes—
711C4×C11C2×C22⋊Q814yescomplemented
712Dic11—24no—
713Dic11—22no—
714Dic11—24no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—42no—
719Dic11—42no—
720Dic11C2×C4×D414yes—
721Dic11C2×C22⋊Q814yescomplemented
722C25—111no—
723C22×Q8—118no—
724C22×Q8—112no—
725C22×Q8—111no—
726C22×Q8—224no—
727C22×Q8—224no—
728C22×Q8C22×D1111yescharacteristic
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—118no—
734C23×C4—118no—
735C23×C4—112no—
736C23×C4—112no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—224no—
751C23×C4—224no—
752C23×C4—224no—
753C23×C4—224no—
754C23×C4—224no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C22⋊Q8—118no—
761C22⋊Q8—118no—
762C22⋊Q8—1116no—
763C22⋊Q8—118no—
764C22⋊Q8—1116no—
765C22⋊Q8C4×D1118yesdirect product factor
766C4×Q8—24no—
767C4×Q8—228no—
768C4×Q8—224no—
769C4×Q8—228no—
770C4×Q8—224no—
771C4×Q8—224no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—118no—
778C2×C4⋊C4—1116no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4—228no—
791C2×C4⋊C4—224no—
792C2×C4⋊C4—228no—
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1112yes—
797C2×C4⋊C4C22×D1112yes—
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—1116no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—228no—
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C42—24no—
810C2×C42—111no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—118no—
814C2×C42—112no—
815C2×C42—112no—
816C2×C42—112no—
817C2×C42—112no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—111no—
825C2×C42—111no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—224no—
830C2×C42—224no—
831C2×C42—224no—
832C2×C42—228no—
833C2×C42—228no—
834C2×C42—224no—
835C2×C42—224no—
836C2×C42—224no—
837C2×C42—224no—
838C2×C42—224no—
839C2×C42—224no—
840C2×C42—224no—
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843C2×C42C22×D1112yes—
844C2×C42C22×D1112yes—
845C2×C42C22×D1111yescharacteristic
846C2×C42C22×D1111yescharacteristic
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95C22×D1112yes—
863#95C22×D1112yes—
864#95C22×D1112yes—
865#95C22×D1112yes—
866#95C22×D1112yes—
867C2×C11—24no—
868C2×C11C22×C4×D411yescharacteristic
869C2×C11C22×C4×Q811yescharacteristic
870C2×C11C2×C4×#4111yescharacteristic
871C2×C11C22×C22⋊Q811yescharacteristic
872C2×C11C2×#52511yescharacteristic
873C2×C11C2×#52911yescharacteristic
874C2×C11C2×#53311yescharacteristic
875D11—24no—
876D11C4×C22⋊Q818yesdirect product factor
877C24—111no—
878C24—114no—
879C24—114no—
880C24—114no—
881C24—111no—
882C24—222no—
883C24—222no—
884C24—222no—
885C24—222no—
886C24C23×D1111yescharacteristic
887C2×Q8—22no—
888C2×Q8—22no—
889C2×Q8—118no—
890C2×Q8—114no—
891C2×Q8—224no—
892C2×Q8—224no—
893C2×Q8—2232no—
894C2×Q8—222no—
895C2×Q8—222no—
896C2×Q8C2×C4×D1114yescomplemented
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—118no—
921C22×C4—118no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—114no—
925C22×C4—114no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—112no—
931C22×C4—112no—
932C22×C4—222no—
933C22×C4—222no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—2232no—
939C22×C4—2232no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—222no—
950C22×C4—222no—
951C22×C4—222no—
952C22×C4—222no—
953C22×C4—224no—
954C22×C4—2232no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—224no—
959C22×C4—224no—
960C22×C4—224no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4C2×C4×D1114yes—
975C22×C4Q8×D1114yescomplemented
976C22×C4C23×D1112yes—
977C22×C4C23×D1112yes—
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1112yes—
980C22×C4C23×D1112yes—
981C22×C4C23×D1111yescharacteristic
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1111yescharacteristic
984C22×C4C23×D1111yescharacteristic
985C22×C4C23×D1111yescharacteristic
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—118no—
991C4⋊C4—118no—
992C4⋊C4—118no—
993C4⋊C4—114no—
994C4⋊C4—118no—
995C4⋊C4—224no—
996C4⋊C4—224no—
997C4⋊C4—224no—
998C4⋊C4—224no—
999C4⋊C4—224no—
1000C4⋊C4—224no—
1001C4⋊C4—224no—
1002C4⋊C4—222no—
1003C4⋊C4—224no—
1004C4⋊C4—222no—
1005C4⋊C4C2×C4×D1114yescomplemented
1006C4⋊C4C2×C4×D1118yescomplemented
1007C22⋊C4—24no—
1008C22⋊C4—118no—
1009C22⋊C4—118no—
1010C22⋊C4—118no—
1011C22⋊C4—224no—
1012C22⋊C4—224no—
1013C22⋊C4—224no—
1014C22⋊C4C2×C4×D1118yes—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—24no—
1019C42—24no—
1020C42—114no—
1021C42—114no—
1022C42—114no—
1023C42—222no—
1024C42—222no—
1025C42—222no—
1026C42—222no—
1027C42—222no—
1028C42—222no—
1029C42—224no—
1030C42—224no—
1031C42—224no—
1032C42—224no—
1033C42—222no—
1034C42—222no—
1035C42—222no—
1036C42—224no—
1037C42—224no—
1038C42D4×D1114yes—
1039C11C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—112no—
1045C23—112no—
1046C23—112no—
1047C23—112no—
1048C23—112no—
1049C23—112no—
1050C23—112no—
1051C23—1116no—
1052C23—112no—
1053C23—112no—
1054C23—112no—
1055C23—228no—
1056C23—228no—
1057C23—228no—
1058C23—228no—
1059C23—228no—
1060C23—228no—
1061C23—221no—
1062C23—221no—
1063C23—221no—
1064C23—221no—
1065C23C22×C4×D1112yes—
1066C23C2×Q8×D1112yes—
1067C23#41×D1112yes—
1068C23C24×D1111yescharacteristic
1069Q8—28no—
1070Q8—2216no—
1071Q8—228no—
1072C2×C4—28no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—28no—
1086C2×C4—28no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—112no—
1098C2×C4—112no—
1099C2×C4—1116no—
1100C2×C4—1116no—
1101C2×C4—114no—
1102C2×C4—114no—
1103C2×C4—112no—
1104C2×C4—112no—
1105C2×C4—112no—
1106C2×C4—112no—
1107C2×C4—228no—
1108C2×C4—228no—
1109C2×C4—228no—
1110C2×C4—228no—
1111C2×C4—228no—
1112C2×C4—228no—
1113C2×C4—2216no—
1114C2×C4—2216no—
1115C2×C4—228no—
1116C2×C4—228no—
1117C2×C4—228no—
1118C2×C4—228no—
1119C2×C4—228no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—228no—
1133C2×C4—228no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—448no—
1141C2×C4—448no—
1142C2×C4C22×C4×D1114yes—
1143C2×C4C22×C4×D1114yes—
1144C2×C4C22×C4×D1112yes—
1145C2×C4C22×C4×D1112yes—
1146C2×C4C2×D4×D1112yes—
1147C2×C4C2×D4×D1112yes—
1148C2×C4C2×D4×D1112yes—
1149C2×C4C2×Q8×D1112yes—
1150C2×C4C2×Q8×D1112yes—
1151C2×C4#41×D1112yes—
1152C2×C4#41×D1112yes—
1153C2×C4#41×D1112yes—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—114no—
1161C22—114no—
1162C22—114no—
1163C22—114no—
1164C22—114no—
1165C22—114no—
1166C22—114no—
1167C22—114no—
1168C22—2232no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—222no—
1174C22—222no—
1175C22C4×Q8×D1114yescomplemented
1176C22C23×C4×D1111yescharacteristic
1177C22C22×D4×D1111yescharacteristic
1178C22C22×Q8×D1111yescharacteristic
1179C22C2×#41×D1111yescharacteristic
1180C22C2×#41×D1111yescharacteristic
1181C22C2×#41×D1111yescharacteristic
1182C22C2×#41×D1111yescharacteristic
1183C4—22no—
1184C4—24no—
1185C4—24no—
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—42no—
1190C4—42no—
1191C4—114no—
1192C4—114no—
1193C4—222no—
1194C4—224no—
1195C4—224no—
1196C4—222no—
1197C4—222no—
1198C4—222no—
1199C4—442no—
1200C4—442no—
1201C4C4×D4×D1114yes—
1202C4D11×C22⋊Q814yesdirect product factor
1203C2—24no—
1204C2—118no—
1205C2—224no—
1206C2C2×C4×D4×D1111yescharacteristic
1207C2C2×C4×Q8×D1111yescharacteristic
1208C2C4×#41×D1111yescharacteristic
1209C2C2×D11×C22⋊Q811yescharacteristic
1210C2D11×#52511yescharacteristic
1211C2D11×#52911yescharacteristic
1212C2D11×#53311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11C2×C4×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
4. #13071154C2semidirect
5. C4×#66950C2semidirect
6. C22⋊Q8×Dic11C2semidirect
7. C4×#66977C2semidirect
8. #13071150C2semidirect
9. C4×#66949C2semidirect
10. #13071148C2semidirect
11. C4×#66931C2semidirect
12. #13071146C2semidirect
13. C4×#66999C2semidirect
14. #13071144C2semidirect
15. D11×#391C2semidirect
16. D11×#389C2semidirect
17. D11×#387C2semidirect
20. C4×C4⋊C4×D11C2semidirect
21. C4×C4⋊C4×D11C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
29. C2×C4×Q8×C11C22semidirect
32. C2×Q8×Dic11C22semidirect
37. D11×C22⋊Q8C4direct (N × H)
47. C2×#66940C22semidirect
48. C2×#66940C22semidirect
63. C2×C4×Dic22C22semidirect
64. C2×C4×Dic22C22semidirect
65. C11×#391C22semidirect
66. C11×#389C22semidirect
67. C11×#387C22semidirect
70. C4×C11×C4⋊C4C22semidirect
71. C4×C11×C4⋊C4C22semidirect
73. #10622843C22semidirect
81. #10622598C22semidirect
82. #10622594C22semidirect
83. #10622591C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. #10622587C22semidirect
89. #10622586C22semidirect
90. #10622585C22semidirect
98. C4×C4⋊Dic11C22semidirect
99. C4×C4⋊Dic11C22semidirect
100. #10622546C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. C4×Dic11⋊C4C22semidirect
104. #10622542C22semidirect
105. #10622541C22semidirect
116. #10622268C22semidirect
117. #10622267C22semidirect
118. #10622266C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
136. C2×Q8×D11C2×C4semidirect
145. C22×C4×D11Q8semidirect
164. C11×C22⋊Q8C2×C4semidirect
183. #66999C2×C4semidirect
195. #66977C2×C4semidirect
226. #66950C2×C4semidirect
227. #66949C2×C4semidirect
232. C4⋊C4×D11C2×C4semidirect
233. C4⋊C4×D11C2×C4semidirect
238. #66931C2×C4semidirect
284. C2×Q8×C11C22×C4semidirect
293. C22×C4×C11C2×Q8semidirect
312. C22×Dic11C2×Q8semidirect
370. C2×C4×D11C2×Q8semidirect
371. C2×C4×D11C2×Q8semidirect
379. C2×Dic22C22×C4semidirect
380. C2×Dic22C22×C4semidirect
385. C11×C4⋊C4C22×C4semidirect
386. C11×C4⋊C4C22×C4semidirect
405. C4⋊Dic11C22×C4semidirect
406. C4⋊Dic11C22×C4semidirect
413. Dic11⋊C4C22×C4semidirect
414. Dic11⋊C4C22×C4semidirect
415. Dic11⋊C4C22×C4semidirect
448. C4×C22⋊Q8D11direct (N × H)
475. C22×D11C4×Q8semidirect
568. C4×D11C22⋊Q8direct (N × H)
588. C2×C4×Q8C2×D11semidirect
617. #391C2×D11semidirect
623. #389C2×D11semidirect
631. #387C2×D11semidirect
658. C4×C4⋊C4C2×D11semidirect
659. C4×C4⋊C4C2×D11semidirect
679. C22×C11C2×C4×Q8semidirect
696. C2×D11C2×C4×Q8semidirect
711. C4×C11C2×C22⋊Q8semidirect
721. Dic11C2×C22⋊Q8semidirect
765. C22⋊Q8C4×D11direct (N × H)
876. D11C4×C22⋊Q8direct (N × H)
896. C2×Q8C2×C4×D11semidirect
975. C22×C4Q8×D11semidirect
1005. C4⋊C4C2×C4×D11semidirect
1006. C4⋊C4C2×C4×D11semidirect
1039. C11C2×C4×C22⋊Q8semidirect
1175. C22C4×Q8×D11semidirect
1202. C4D11×C22⋊Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×C4×Q8×D112
C22×C42×D112
#130711542
C4×#669502
C22⋊Q8×Dic112
C4×#669772
#130711502
C4×#669492
#130711482
C4×#669312
#130711462
C4×#669992
#130711442
D11×#3912
D11×#3892
D11×#3872
D11×#3852
D11×#3802
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C4×C11×C22⋊Q82
C2×C4×C22⋊Q811