Finite Group Databasebeta

← C4×#10623083 #14913596

Subgroups — C4×#10623083 #14913596

Order 2816.

3232 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3C22×C4×Dic22C211yesmaximal, characteristic, complemented
4#13071688C212yesmaximal, complemented
5#13071685C211yesmaximal, characteristic, complemented
6#13071644C212yesmaximal, complemented
7#13071641C211yesmaximal, characteristic, complemented
8#13071633C212yesmaximal, complemented
9#13071630C211yesmaximal, characteristic, complemented
10#13071545C211yesmaximal, characteristic, complemented
11#13071539C212yesmaximal, complemented
12#13071536C211yesmaximal, characteristic, complemented
13#13071456C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
15C4×#66928C211yesmaximal, characteristic, complemented
16C4×#66938C212yesmaximal, complemented
17C4×#66977C211yesmaximal, characteristic, complemented
18C4×#66949C212yesmaximal, complemented
19C4×#66983C211yesmaximal, characteristic, complemented
20C4×#66992C212yesmaximal, complemented
21C42×Dic22C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C42×C11C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#66992C2212yes—
32C2×#66983C2211yescharacteristic
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2212yes—
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C22×Dic11⋊C4C2212yes—
40C22×C4×Dic11C2212yes—
41#10623083C4116yesdirect product factor
42C2×#66949C2212yes—
43C2×#66938C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×#66928C2211yescharacteristic
47C4×#4339—28no—
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×#66925C2212yes—
51C2×C42×D11C2212yes—
52C2×C4×Dic22—28no—
53C2×C4×Dic22C2211yescharacteristic
54C2×C4×Dic22C2212yes—
55C2×C4×Dic22C2212yes—
56C2×C4×Dic22C2211yescharacteristic
57C2×C4×Dic22C2211yescharacteristic
58C2×C4×Dic22C2211yescharacteristic
59C2×C4×Dic22C2211yescharacteristic
60C2×C4×Dic22C2211yescharacteristic
61C2×C4×Dic22C2211yescharacteristic
62C4×C11×C4⋊C4C2211yescharacteristic
63C4×C11×C4⋊C4C2211yescharacteristic
64C4×C11×C4⋊C4C2211yescharacteristic
65C4×C11×C22⋊C4C2211yescharacteristic
66C4×C11×C22⋊C4C2211yescharacteristic
67C4×C11×C22⋊C4C2211yescharacteristic
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2211yescharacteristic
70C4×C11×C22⋊C4C2211yescharacteristic
71C43×C11C2211yescharacteristic
72#10622833C2212yes—
73#10622826C2212yes—
74#10622825C2211yescharacteristic
75#10622825C2211yescharacteristic
76#10622823C2212yes—
77C4×C22⋊Dic11C2212yes—
78#10622603C2212yes—
79#10622602C2212yes—
80#10622594C2212yes—
81#10622585C2212yes—
82#10622585C2212yes—
83#10622571C2212yes—
84#10622570C2212yes—
85#10622570C2212yes—
86#10622564C2212yes—
87#10622558C2212yes—
88#10622557C2212yes—
89#10622555C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2212yes—
92#10622553C2212yes—
93#10622553C2212yes—
94#10622553C2212yes—
95#10622552C2211yescharacteristic
96#10622552C2211yescharacteristic
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yes—
99C4×(C2×D11)⋊C4C2212yes—
100#10622549C2211yescharacteristic
101C4×C4⋊Dic11C2211yescharacteristic
102C4×C4⋊Dic11C2211yescharacteristic
103C4×C4⋊Dic11C2211yescharacteristic
104#10622546C2212yes—
105C4×Dic11⋊C4C2212yes—
106C4×Dic11⋊C4C2212yes—
107C4×Dic11⋊C4C2212yes—
108C4×Dic11⋊C4C2212yes—
109C42×Dic11C2212yes—
110#10622542C2211yescharacteristic
111#10622542C2211yescharacteristic
112#10622541C2211yescharacteristic
113#10622541C2211yescharacteristic
114#10622283C2212yes—
115#10622282C2212yes—
116#10622281C2212yes—
117#10622280C2212yes—
118#10622279C2212yes—
119#10622279C2212yes—
120#10622265C2212yes—
121#10622263C2212yes—
122#10622262C2212yes—
123#10622262C2212yes—
124#10622259C2212yes—
125#10622259C2212yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137C2×#4339—24no—
138C2×#4339—24no—
139C2×#4339C2×C418yescomplemented
140C22×D44C2311yescharacteristic
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×Dic22—24no—
145C22×Dic22—24no—
146C22×Dic22C2×C418yescomplemented
147C22×Dic22C2311yescharacteristic
148C22×Dic22C2312yes—
149C22×Dic22C2311yescharacteristic
150C4×D4×C11—24no—
151C4×D4×C11—24no—
152C4×D4×C11C2×C418yescomplemented
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C42×C11—24no—
163C2×C42×C11—24no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181#66992C2×C4116yescomplemented
182#66983C2×C418yescomplemented
183C4×C22⋊D11—28no—
184C4×C22⋊D11—28no—
185C4×C22⋊D11—28no—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195#66979—24no—
196C2×C4⋊Dic11—24no—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203#66977C2×C418yescomplemented
204C2×Dic11⋊C4—28no—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11—28no—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227#66949C2×C4116yescomplemented
228#66938C2×C4116yescomplemented
229(C22⋊D11)⋊C4—28no—
230(C22⋊D11)⋊C4C2×C4116yescomplemented
231#66928C2×C418yescomplemented
232C4×D44—24no—
233C4×D44—24no—
234#66925—28no—
235C42×D11—28no—
236C4×Dic22—24no—
237C4×Dic22—24no—
238C4×Dic22—24no—
239C4×Dic22—24no—
240C4×Dic22—24no—
241C4×Dic22—28no—
242C4×Dic22—28no—
243C4×Dic22C2×C418yescomplemented
244C4×Dic22D418yescomplemented
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11×#95C2311yescharacteristic
249C11×#95C2311yescharacteristic
250C11×#95C2311yescharacteristic
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—
264C4×#548—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11C2412yes—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11C22×C414yes—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—41no—
285C22×C4×C11—41no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C22×C414yes—
288C22×C4×C11#4114yescomplemented
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11C22×C418yes—
307C2×C22⋊D11C22×C418yes—
308C22×Dic11—24no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—42no—
313C22×Dic11C22×C418yes—
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321#4339—232no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44C22×C414yes—
325C2×C4×D11—24no—
326C2×C4×D11—24no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—42no—
333C2×C4×D11C22×C418yes—
334C2×Dic22—24no—
335C2×Dic22—24no—
336C2×Dic22—232no—
337C2×Dic22—22no—
338C2×Dic22—22no—
339C2×Dic22C22×C414yes—
340C2×Dic22C22×C418yes—
341C2×Dic22C22×C414yes—
342C2×Dic22C2×D414yes—
343C2×Dic22#4114yes—
344C11×C4⋊C4—22no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4C22×C414yes—
347C11×C22⋊C4—22no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4C22×C414yes—
351C11×C22⋊C4C22×C414yes—
352C11×C22⋊C4#4114yescomplemented
353C42×C11—22no—
354C42×C11—22no—
355C42×C11—22no—
356C42×C11—22no—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—22no—
361C42×C11—22no—
362C42×C11—22no—
363C42×C11—41no—
364C42×C11C22×C414yes—
365C42×C11C2×D414yes—
366C22⋊Dic11—24no—
367C22⋊Dic11—24no—
368C22⋊Dic11—42no—
369C22⋊Dic11C22×C418yes—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—24no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—24no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4C22×C418yes—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379C4⋊Dic11—24no—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—22no—
383C4⋊Dic11C22×C414yes—
384C4⋊Dic11C2×D414yes—
385Dic11⋊C4—24no—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388Dic11⋊C4—24no—
389Dic11⋊C4—24no—
390Dic11⋊C4—24no—
391Dic11⋊C4—24no—
392Dic11⋊C4C22×C418yes—
393Dic11⋊C4C22×C418yes—
394Dic11⋊C4C2×D418yes—
395C4×Dic11—24no—
396C4×Dic11—24no—
397C4×Dic11—24no—
398C4×Dic11—24no—
399C4×Dic11—24no—
400C4×Dic11—24no—
401C4×Dic11—24no—
402C4×Dic11—24no—
403C4×Dic11—42no—
404C4×Dic11C22×C418yes—
405C4×Dic11C2×D418yes—
406C2×#548—111no—
407C2×C4×#41—111no—
408C22×C4×Q8—111no—
409#2367—111no—
410#2367—112no—
411#2362—112no—
412#2362—111no—
413#2361—111no—
414#2361—112no—
415#2352—112no—
416#2352—111no—
417#2351—111no—
418#2341—111no—
419Q8×C22⋊C4—111no—
420C4×#124—112no—
421C4×#124—111no—
422C4×C22⋊Q8—111no—
423C4×C22⋊Q8—112no—
424C4×#121—111no—
425C4×#121—112no—
426C42×Q8—111no—
427C42×D4—112no—
428C42×D4D1111yescharacteristic, complemented
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11C23×C412yes—
440C23×C11C23×C412yes—
441C23×C11C2×#4112yes—
442C23×C11C2×#4112yes—
443C23×C11C2511yescharacteristic
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11C23×C414yes—
451D4×C11—28no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—28no—
469C2×C4×C11—28no—
470C2×C4×C11—28no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—44no—
481C2×C4×C11—44no—
482C2×C4×C11—44no—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C23×C412yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C22×D412yes—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C22×D412yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C11C2×#4112yes—
496C2×C4×C112−1+412yes—
497C22⋊D11—216no—
498C22⋊D11—216no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—216no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—48no—
516C2×Dic11C23×C414yes—
517C2×Dic11C23×C414yes—
518C2×Dic11C23×C414yes—
519C2×Dic11C22×D414yes—
520C2×Dic11C22×D414yes—
521C2×Dic11C2×#4114yes—
522D44—28no—
523C4×D11—216no—
524C4×D11—48no—
525C4×D11—48no—
526Dic22—28no—
527Dic22—216no—
528Dic22C4×D4116yescomplemented
529C22×#41—111no—
530C23×Q8—111no—
531#548—1116no—
532C2×#124—112no—
533C2×#124—111no—
534C2×C22⋊Q8—111no—
535C2×C22⋊Q8—112no—
536C2×#121—112no—
537C2×#121—111no—
538C4×#41—228no—
539C2×C4×Q8—111no—
540C2×C4×Q8—111no—
541C2×C4×Q8—111no—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×Q8—111no—
545C2×C4×Q8—112no—
546C2×C4×Q8—112no—
547C2×C4×Q8—111no—
548C2×C4×Q8—228no—
549C2×C4×D4—112no—
550C2×C4×D4—112no—
551C2×C4×D4—112no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—111no—
555C2×C4×D4—111no—
556C2×C4×D4C2×D1111yescharacteristic
557C2×C4×D4C2×D1111yescharacteristic
558C2×C4×D4C2×D1111yescharacteristic
559C2×#117—111no—
560C2×#117—112no—
561C22×C4⋊C4—112no—
562C22×C4⋊C4—111no—
563C22×C42—112no—
564C22×C42—112no—
565C22×C42C2×D1111yescharacteristic
566C22×C42C2×D1111yescharacteristic
567#391—111no—
568#391—111no—
569#391—112no—
570#391—112no—
571#390—112no—
572#390—112no—
573#390—111no—
574#390—111no—
575#389—112no—
576#389—112no—
577#389—111no—
578#389—111no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#387—112no—
589#387—112no—
590#387—112no—
591#386—112no—
592#386—112no—
593#386—112no—
594#385—112no—
595#385—112no—
596#385—112no—
597#382—111no—
598#382—112no—
599#380—111no—
600#380—111no—
601#380—112no—
602#380—112no—
603C4×C4⋊C4—112no—
604C4×C4⋊C4—111no—
605C4×C4⋊C4—112no—
606C4×C4⋊C4—111no—
607C4×C4⋊C4—112no—
608C4×C4⋊C4—112no—
609C4×C4⋊C4—111no—
610C4×C4⋊C4—112no—
611C4×C4⋊C4—112no—
612C4×C4⋊C4C2×D1111yescharacteristic
613C4×C4⋊C4C2×D1111yescharacteristic
614C4×C4⋊C4C2×D1111yescharacteristic
615C4×C22⋊C4—112no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4C2×D1111yescharacteristic
624C4×C22⋊C4C2×D1111yescharacteristic
625C4×C22⋊C4C2×D1111yescharacteristic
626C4×C22⋊C4C2×D1111yescharacteristic
627C4×C22⋊C4C2×D1111yescharacteristic
628C4×C22⋊C4C2×D1111yescharacteristic
629C43—112no—
630C43C2×D1111yescharacteristic
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—22no—
634C22×C11—22no—
635C22×C11—22no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—41no—
641C22×C11—41no—
642C22×C11—41no—
643C22×C11—41no—
644C22×C11C4×#4114yescomplemented
645C22×C11C24×C411yescharacteristic
646C22×C11C23×D411yescharacteristic
647C22×C11C22×#4111yescharacteristic
648C22×C11C22×#4111yescharacteristic
649C22×C11C22×#4111yescharacteristic
650C22×C11C2×2−1+411yescharacteristic
651C22×C11#58511yescharacteristic
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C4×C11—22no—
660C4×C11—22no—
661C4×C11—22no—
662C4×C11—22no—
663C4×C11—22no—
664C4×C11—22no—
665C4×C11—22no—
666C4×C11—22no—
667C4×C11—41no—
668C4×C11—41no—
669C4×C11—41no—
670C4×C11C2×C4×D414yes—
671C4×C11#54814yescomplemented
672Dic11—24no—
673Dic11—24no—
674Dic11—24no—
675Dic11—42no—
676Dic11—42no—
677Dic11—42no—
678Dic11C2×C4×D418yes—
679C2×#41—118no—
680C2×#41—224no—
681C2×#41—224no—
682C22×Q8—118no—
683C22×Q8—111no—
684C22×Q8—112no—
685C22×Q8—111no—
686C22×Q8—224no—
687C22×Q8—224no—
688C22×D4—112no—
689C22×D4—112no—
690C22×D4—111no—
691C22×D4C22×D1111yescharacteristic
692C23×C4—112no—
693C23×C4—112no—
694C23×C4—112no—
695C23×C4—112no—
696C23×C4—112no—
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C23×C4C22×D1111yescharacteristic
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703#124—1116no—
704#124—118no—
705C22⋊Q8—118no—
706C22⋊Q8—1116no—
707#121—1116no—
708#121—118no—
709C4×Q8—118no—
710C4×Q8—118no—
711C4×Q8—228no—
712C4×Q8—228no—
713C4×Q8—224no—
714C4×Q8—224no—
715C4×Q8—224no—
716C4×Q8—224no—
717C4×Q8—224no—
718C4×D4—24no—
719C4×D4—24no—
720C4×D4—1116no—
721C4×D4—224no—
722C4×D4—228no—
723C4×D4—228no—
724C4×D4—228no—
725C4×D4—228no—
726C4×D4—224no—
727C4×D4C4×D1118yescomplemented
728#117—228no—
729#117—224no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—111no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—112no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—228no—
747C2×C4⋊C4—224no—
748C2×C4⋊C4C22×D1111yescharacteristic
749C2×C4⋊C4C22×D1111yescharacteristic
750C2×C4⋊C4C22×D1111yescharacteristic
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4C22×D1111yescharacteristic
765C2×C22⋊C4C22×D1111yescharacteristic
766C2×C22⋊C4C22×D1111yescharacteristic
767C2×C22⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4C22×D1111yescharacteristic
769C2×C22⋊C4C22×D1111yescharacteristic
770C2×C42—24no—
771C2×C42—24no—
772C2×C42—112no—
773C2×C42—112no—
774C2×C42—112no—
775C2×C42—112no—
776C2×C42—112no—
777C2×C42—112no—
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—112no—
783C2×C42—228no—
784C2×C42—228no—
785C2×C42C22×D1111yescharacteristic
786C2×C42C22×D1111yescharacteristic
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1111yescharacteristic
791C2×C42C22×D1111yescharacteristic
792C2×C42C22×D1111yescharacteristic
793C2×C42C22×D1111yescharacteristic
794C2×C42C22×D1111yescharacteristic
795C2×C42C22×D1111yescharacteristic
796C2×C42C22×D1111yescharacteristic
797C2×C42C22×D1111yescharacteristic
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95C22×D1111yescharacteristic
812#95C22×D1111yescharacteristic
813#95C22×D1111yescharacteristic
814#95C22×D1111yescharacteristic
815#95C22×D1111yescharacteristic
816#95C22×D1111yescharacteristic
817C2×C11—24no—
818C2×C11—42no—
819C2×C11C22×C4×D411yescharacteristic
820C2×C11C2×C4×#4111yescharacteristic
821C2×C11C4×2−1+411yescharacteristic
822C2×C11C2×#54811yescharacteristic
823C2×C11D4×#4111yescharacteristic
824C2×C11#348011yescharacteristic
825C2×C11#348211yescharacteristic
826D11—44no—
827C24—112no—
828C24C23×D1111yescharacteristic
829C24C23×D1111yescharacteristic
830#41—2232no—
831C2×Q8—114no—
832C2×Q8—118no—
833C2×Q8—114no—
834C2×Q8—114no—
835C2×Q8—114no—
836C2×Q8—224no—
837C2×Q8—224no—
838C2×Q8—2232no—
839C2×Q8—222no—
840C2×Q8—222no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—118no—
844C2×D4—118no—
845C2×D4—114no—
846C2×D4—224no—
847C2×D4—224no—
848C2×D4—224no—
849C2×D4—224no—
850C2×D4—222no—
851C2×D4—222no—
852C2×D4C2×C4×D1114yes—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—112no—
869C22×C4—118no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—118no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—224no—
878C22×C4—224no—
879C22×C4—224no—
880C22×C4—224no—
881C22×C4—224no—
882C22×C4—224no—
883C22×C4—224no—
884C22×C4—224no—
885C22×C4—224no—
886C22×C4—224no—
887C22×C4—224no—
888C22×C4—442no—
889C22×C4—442no—
890C22×C4C2×C4×D1114yes—
891C22×C4C2×C4×D1114yes—
892C22×C4#433914yescomplemented
893C22×C4C23×D1111yescharacteristic
894C22×C4C23×D1111yescharacteristic
895C22×C4C23×D1111yescharacteristic
896C22×C4C23×D1111yescharacteristic
897C22×C4C23×D1111yescharacteristic
898C22×C4C23×D1111yescharacteristic
899C22×C4C23×D1111yescharacteristic
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1111yescharacteristic
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—118no—
909C4⋊C4—118no—
910C4⋊C4—114no—
911C4⋊C4—118no—
912C4⋊C4—114no—
913C4⋊C4—224no—
914C4⋊C4—224no—
915C4⋊C4—224no—
916C4⋊C4—224no—
917C4⋊C4—224no—
918C4⋊C4—224no—
919C4⋊C4—224no—
920C4⋊C4—224no—
921C4⋊C4—222no—
922C4⋊C4—222no—
923C4⋊C4—222no—
924C4⋊C4C2×C4×D1114yes—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—118no—
929C22⋊C4—118no—
930C22⋊C4—118no—
931C22⋊C4—118no—
932C22⋊C4—224no—
933C22⋊C4—224no—
934C22⋊C4—224no—
935C22⋊C4—224no—
936C22⋊C4—224no—
937C22⋊C4—224no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4C2×C4×D1114yes—
942C22⋊C4C2×C4×D1114yes—
943C22⋊C4#433914yescomplemented
944C42—22no—
945C42—22no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—41no—
955C42—118no—
956C42—118no—
957C42—224no—
958C42—224no—
959C42—224no—
960C42—224no—
961C42—224no—
962C42—224no—
963C42—224no—
964C42—224no—
965C42—442no—
966C42C2×C4×D1114yes—
967C42D4×D1114yes—
968C11C4×#54811yescharacteristic, complemented, Sylow
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—114no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23C22×C4×D1112yes—
987C23C22×C4×D1112yes—
988C23C2×#433912yes—
989C23C2×#433912yes—
990C23C24×D1111yescharacteristic
991Q8—1116no—
992Q8—2216no—
993Q8—228no—
994D4—28no—
995D4—2216no—
996D4—2216no—
997D4—228no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—114no—
1030C2×C4—114no—
1031C2×C4—114no—
1032C2×C4—114no—
1033C2×C4—114no—
1034C2×C4—114no—
1035C2×C4—2216no—
1036C2×C4—2216no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—448no—
1053C2×C4—448no—
1054C2×C4—448no—
1055C2×C4C22×C4×D1112yes—
1056C2×C4C22×C4×D1112yes—
1057C2×C4C22×C4×D1112yes—
1058C2×C4C22×C4×D1112yes—
1059C2×C4C22×C4×D1112yes—
1060C2×C4C2×#433912yes—
1061C2×C4C2×#433912yes—
1062C2×C4C2×#433912yes—
1063C2×C4C2×#433912yes—
1064C2×C4C2×D4×D1112yes—
1065C2×C4C2×D4×D1112yes—
1066C2×C4C2×D4×D1112yes—
1067C2×C4#41×D1112yes—
1068C2×C4#6704312yes—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—224no—
1083C22—224no—
1084C22—224no—
1085C22—442no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22C4×#433914yescomplemented
1090C22C23×C4×D1111yescharacteristic
1091C22C22×#433911yescharacteristic
1092C22C22×#433911yescharacteristic
1093C22C22×D4×D1111yescharacteristic
1094C22C2×#41×D1111yescharacteristic
1095C22C2×#6704311yescharacteristic
1096C22#1062345311yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—41no—
1106C4—41no—
1107C4—41no—
1108C4—118no—
1109C4—224no—
1110C4—224no—
1111C4—224no—
1112C4—442no—
1113C4—442no—
1114C4—442no—
1115C4C4×D4×D1114yes—
1116C4#1062308314yesdirect product factor
1117C2—24no—
1118C2—42no—
1119C2—444no—
1120C2C2×C4×D4×D1111yescharacteristic
1121C2C2×C4×#433911yescharacteristic
1122C2C4×#6704311yescharacteristic
1123C2C2×#1062308311yescharacteristic
1124C2D4×#433911yescharacteristic
1125C2#1308220911yescharacteristic
1126C2#1308223111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC42×D4×C11C2
socle, cosocleC23×C11C25
prime radicalC2×#10623083C2
hypercenterC42×D4D11
hypocenterC11C4×#548
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4339C2semidirect
3. C22×C4×Dic22C2semidirect
4. #13071688C2semidirect
5. #13071685C2semidirect
6. #13071644C2semidirect
7. #13071641C2semidirect
8. #13071633C2semidirect
9. #13071630C2semidirect
10. #13071545C2semidirect
11. #13071539C2semidirect
12. #13071536C2semidirect
13. #13071456C2semidirect
14. C22⋊C4×Dic22C2semidirect
15. C4×#66928C2semidirect
16. C4×#66938C2semidirect
17. C4×#66977C2semidirect
18. C4×#66949C2semidirect
19. C4×#66983C2semidirect
20. C4×#66992C2semidirect
21. C42×Dic22C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C42×D4×C11C2semidirect
41. #10623083C4direct (N × H)
139. C2×#4339C2×C4semidirect
146. C22×Dic22C2×C4semidirect
152. C4×D4×C11C2×C4semidirect
181. #66992C2×C4semidirect
182. #66983C2×C4semidirect
203. #66977C2×C4semidirect
227. #66949C2×C4semidirect
228. #66938C2×C4semidirect
230. (C22⋊D11)⋊C4C2×C4semidirect
231. #66928C2×C4semidirect
243. C4×Dic22C2×C4semidirect
244. C4×Dic22D4semidirect
288. C22×C4×C11#41semidirect
352. C11×C22⋊C4#41semidirect
428. C42×D4D11semidirect
528. Dic22C4×D4semidirect
644. C22×C11C4×#41semidirect
671. C4×C11#548semidirect
727. C4×D4C4×D11semidirect
892. C22×C4#4339semidirect
943. C22⋊C4#4339semidirect
968. C11C4×#548semidirect
1089. C22C4×#4339semidirect
1116. C4#10623083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230832
C2×C4×#43392
C22×C4×Dic222
#130716882
#130716852
#130716442
#130716412
#130716332
#130716302
#130715452
#130715392
#130715362
#130714562
C22⋊C4×Dic222
C4×#669282
C4×#669382
C4×#669772
C4×#669492
C4×#669832
C4×#669922
C42×Dic222
C4×(C22⋊D11)⋊C42
C42×D4×C112
C4×#54811