Finite Group Databasebeta

← C4×#10623187 #14912230

Subgroups — C4×#10623187 #14912230

Order 2816.

3902 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623187C211yesmaximal, characteristic
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3C22×C42×D11C211yesmaximal, characteristic, complemented
4#13071150C212yesmaximal, complemented
5C4×#66949C212yesmaximal, complemented
6#123×Dic11C211yesmaximal, characteristic, complemented
7C4×#66982C211yesmaximal, characteristic, complemented
8#13071133C211yesmaximal, characteristic, complemented
9#13071128C212yesmaximal, complemented
10C4×#66937C212yesmaximal, complemented
11#13071121C211yesmaximal, characteristic, complemented
12C4×#66935C211yesmaximal, characteristic, complemented
13#13071117C211yesmaximal, characteristic, complemented
14C4×#66990C211yesmaximal, characteristic, complemented
15#13071101C211yesmaximal, characteristic, complemented
16#13071095C211yesmaximal, characteristic, complemented
17#13071058C212yesmaximal, complemented
18#13071054C212yesmaximal, complemented
19#13070996C211yesmaximal, characteristic, complemented
20C4×#66946C212yesmaximal, complemented
21C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C4×C11×#123C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#123C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#66990C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×#66982C2211yescharacteristic
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic, complemented
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic, complemented
41#10623187C4116yesdirect product factor
42C4×#4341—28no—
43C2×#66949C2212yes—
44C2×#66946C2212yes—
45C2×#66946C2212yes—
46C2×#66945C2211yescharacteristic, complemented
47C2×#66940C2211yescharacteristic, complemented
48C2×#66937C2212yes—
49C2×#66935C2211yescharacteristic
50C2×(C22⋊D11)⋊C4C2211yescharacteristic
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
54C2×#66930C2211yescharacteristic
55C2×#66930C2211yescharacteristic
56C2×#66930C2211yescharacteristic
57C2×#66930C2211yescharacteristic, complemented
58C2×C4×D44C2212yes—
59C2×C42×D11—28no—
60C2×C42×D11C2212yes—
61C2×C42×D11C2212yes—
62C2×C42×D11C2212yes—
63C2×C42×D11C2212yes—
64C2×C42×D11C2211yescharacteristic, complemented
65C2×C4×Dic22C2211yescharacteristic, complemented
66C11×#388C2212yescomplemented
67C11×#387C2212yescomplemented
68C11×#386C2211yescharacteristic
69C11×#385C2211yescharacteristic
70C11×#381C2211yescharacteristic
71C4×C11×C4⋊C4C2212yescomplemented
72C4×C11×C22⋊C4C2211yescharacteristic
73C4×C11×C22⋊C4C2212yescomplemented
74#10622833C2211yescharacteristic
75#10622826C2211yescharacteristic
76#10622824C2211yescharacteristic
77#10622823C2211yescharacteristic
78C4×C22⋊Dic11C2211yescharacteristic
79#10622602C2212yes—
80#10622602C2212yes—
81#10622594C2212yescomplemented
82C4⋊C4×Dic11C2212yescomplemented
83C4⋊C4×Dic11C2212yescomplemented
84#10622585C2212yescomplemented
85#10622571C2211yescharacteristic
86#10622570C2212yescomplemented
87#10622569C2212yes—
88#10622569C2212yes—
89#10622568C2211yescharacteristic
90#10622568C2211yescharacteristic
91#10622564C2212yescomplemented
92#10622563C2211yescharacteristic
93#10622559C2211yescharacteristic
94C22⋊C4×Dic11C2211yescharacteristic
95C22⋊C4×Dic11C2211yescharacteristic
96C22⋊C4×Dic11C2212yescomplemented
97C22⋊C4×Dic11C2212yescomplemented
98#10622553C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yes—
100C4×(C2×D11)⋊C4C2212yes—
101C4×(C2×D11)⋊C4C2212yescomplemented
102#10622546C2212yescomplemented
103C4×Dic11⋊C4C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105C42×Dic11C2212yescomplemented
106#10622282C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yes—
109#10622280C2212yes—
110#10622280C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622279C2212yes—
115#10622279C2212yescomplemented
116#10622279C2212yescomplemented
117#10622278C2212yes—
118#10622278C2212yes—
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C2×#4341—24no—
141C2×#4341—24no—
142C2×#4341C2×C418yescomplemented
143C22×D44C2312yes—
144C22×C4×D11—24no—
145C22×C4×D11—24no—
146C22×C4×D11—24no—
147C22×C4×D11—24no—
148C22×C4×D11—28no—
149C22×C4×D11—28no—
150C22×C4×D11C2×C418yescomplemented
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2312yes—
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×Dic22C2311yescharacteristic
161C11×#123C2×C418yescomplemented
162C4×D4×C11—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11—24no—
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2312yes—
175C2×C42×C11C2312yes—
176C2×C42×C11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2311yescharacteristic
182#66990C2×C418yescomplemented
183D4×Dic11—24no—
184#66982C2×C418yescomplemented
185C4×C22⋊D11—24no—
186C4×C22⋊D11—28no—
187C4×C22⋊D11—24no—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×C4×Dic11—24no—
211C2×C4×Dic11—24no—
212C2×C4×Dic11—24no—
213C2×C4×Dic11D418yescomplemented
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232#66949C2×C4116yescomplemented
233#66946—28no—
234#66946C2×C4116yescomplemented
235#66945—24no—
236#66940—24no—
237#66937C2×C4116yescomplemented
238#66935C2×C418yescomplemented
239(C22⋊D11)⋊C4—24no—
240(C22⋊D11)⋊C4—28no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4C2×C4116yescomplemented
243#66930—24no—
244#66930—24no—
245#66930—24no—
246#66930C2×C418yescomplemented
247C4×D44—28no—
248C42×D11—28no—
249C42×D11—28no—
250C42×D11—28no—
251C42×D11—28no—
252C42×D11—24no—
253C4×Dic22—24no—
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—
270C4×#525—111nomaximal, Sylow
271C24×C11C2411yescharacteristic
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11C22×C414yes—
278C23×D11C2411yescharacteristic
279C23×D11C2412yes—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11C22×C414yes—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2×D414yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11C22×C418yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yescomplemented
310C22×Dic11—22no—
311C22×Dic11—24no—
312C22×Dic11—24no—
313C22×Dic11—22no—
314C22×Dic11—22no—
315C22×Dic11—24no—
316C22×Dic11—22no—
317C22×Dic11C22×C414yes—
318C22×Dic11C22×C414yescomplemented
319C22×Dic11C2×D414yes—
320C22×Dic11C2×D414yes—
321C22×Dic11#4114yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2412yes—
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2412yes—
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332#4341—232no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44C22×C418yes—
336C2×C4×D11—232no—
337C2×C4×D11—232no—
338C2×C4×D11—232no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—22no—
349C2×C4×D11—22no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—22no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11C22×C418yes—
360C2×C4×D11C22×C418yes—
361C2×C4×D11C22×C414yescomplemented
362C2×C4×D11#4118yescomplemented
363C2×C4×D11#4118yescomplemented
364C2×Dic22—22no—
365C2×Dic22—22no—
366C2×Dic22C22×C414yescomplemented
367C11×C4⋊C4—22no—
368C11×C4⋊C4—24no—
369C11×C4⋊C4C22×C418yescomplemented
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4C22×C414yes—
375C11×C22⋊C4C22×C418yescomplemented
376C42×C11—22no—
377C42×C11—24no—
378C42×C11—24no—
379C42×C11—24no—
380C22⋊Dic11—22no—
381C22⋊Dic11—24no—
382C22⋊Dic11—22no—
383C22⋊Dic11—22no—
384C22⋊Dic11C22×C414yes—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4C22×C418yes—
394(C2×D11)⋊C4C22×C418yes—
395(C2×D11)⋊C4C22×C418yescomplemented
396C4⋊Dic11—22no—
397C4⋊Dic11—24no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4C22×C418yescomplemented
406Dic11⋊C4C22×C418yescomplemented
407C4×Dic11—24no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—22no—
419C4×Dic11—24no—
420C4×Dic11C22×C418yescomplemented
421C4×Dic11C2×D414yes—
422C4×Dic11C2×D414yes—
423C4×Dic11C2×D414yes—
424C4×Dic11C2×D414yes—
425C2×#525—111no—
426C2×C4×#41—111no—
427C23×C42—111no—
428C4×C22⋊Q8—112no—
429C4×C22⋊Q8—112no—
430C4×#123—111no—
431C4×#123—111no—
432C4×#123—111no—
433C4×#123D1111yescharacteristic, complemented
434C4×#121—112no—
435C4×#121—112no—
436C4×#120—111no—
437C4×#120—111no—
438C4×#120—111no—
439C4×#120—111no—
440#2297—111no—
441#2296—111no—
442#2290—112no—
443#2290—112no—
444#2280—111no—
445C42×D4—112no—
446C42×D4—112no—
447C4×#117—111no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—21no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—21no—
454C23×C11C23×C412yes—
455C23×C11C23×C412yes—
456C23×C11C22×D412yes—
457C23×C11C2×#4112yes—
458C23×C11C2511yescharacteristic
459C22×D11—28no—
460C22×D11—28no—
461C22×D11—216no—
462C22×D11—28no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—216no—
468C22×D11—21no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—21no—
472C22×D11C23×C412yes—
473C22×D11C23×C414yes—
474C22×D11C2×#4114yes—
475C22×D11C2×#4114yes—
476D4×C11—28no—
477C2×C4×C11—28no—
478C2×C4×C11—28no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—28no—
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—22no—
496C2×C4×C11—44no—
497C2×C4×C11C23×C414yes—
498C2×C4×C11C23×C414yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C2×#4114yes—
503C2×C4×C11C2×#4114yes—
504C22⋊D11—28no—
505C22⋊D11—216no—
506C22⋊D11—28no—
507C2×Dic11—28no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—28no—
516C2×Dic11—28no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—44no—
525C2×Dic11C4×D4116yescomplemented
526C2×Dic11C23×C414yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C412yes—
529C2×Dic11C23×C412yes—
530C2×Dic11C22×D412yes—
531C2×Dic11C22×D412yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C22×D412yes—
534C2×Dic11C2×#4114yes—
535C2×Dic11C2×#4112yes—
536C2×Dic11C2×#4112yes—
537C2×Dic11C2×#4114yes—
538D44—216no—
539C4×D11—216no—
540C4×D11—216no—
541C4×D11—216no—
542C4×D11—216no—
543C4×D11—216no—
544C4×D11—28no—
545C4×D11—216no—
546C4×D11—44no—
547C4×D11—44no—
548Dic22—28no—
549C22×#41—111no—
550C24×C4—111no—
551C24×C4—111no—
552C24×C4—111no—
553#525—1116no—
554C2×#123—111no—
555C2×#123C2×D1111yescharacteristic
556C2×C22⋊Q8—112no—
557C2×#121—112no—
558C2×#120—111no—
559C2×#120—111no—
560C4×#41—228no—
561C2×C4×Q8—111no—
562C2×C4×Q8—111no—
563C2×C4×D4—111no—
564C2×C4×D4—111no—
565C2×C4×D4—112no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4C2×D1111yescharacteristic
575C2×#117—111no—
576C2×#117—111no—
577C2×#117—111no—
578C2×#117—111no—
579C2×#117—111no—
580C22×C42—111no—
581C22×C42—111no—
582C22×C42—111no—
583C22×C42—111no—
584C22×C42—112no—
585C22×C42—112no—
586C22×C42—112no—
587C22×C42—112no—
588C22×C42—111no—
589C22×C42—228no—
590C22×C42C2×D1111yescharacteristic
591#391—112no—
592#390—112no—
593#389—112no—
594#389—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388C2×D1112yescomplemented
599#387—112no—
600#387—112no—
601#387—112no—
602#387C2×D1112yescomplemented
603#386—111no—
604#386—111no—
605#386—112no—
606#386—112no—
607#386—111no—
608#386—112no—
609#386—112no—
610#386C2×D1111yescharacteristic
611#385—111no—
612#385—112no—
613#385—112no—
614#385—111no—
615#385—111no—
616#385—112no—
617#385—112no—
618#385C2×D1111yescharacteristic
619#381—111no—
620#381C2×D1111yescharacteristic
621#380—112no—
622#380—112no—
623#379—111no—
624#379—111no—
625C4×C4⋊C4—112no—
626C4×C4⋊C4—112no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4—112no—
629C4×C4⋊C4—112no—
630C4×C4⋊C4—112no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4C2×D1112yescomplemented
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1111yescharacteristic
648C4×C22⋊C4C2×D1112yescomplemented
649#376—112no—
650C43—112no—
651C22×C11—24no—
652C22×C11—22no—
653C22×C11—22no—
654C22×C11—24no—
655C22×C11—22no—
656C22×C11—24no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11C2×C4×D414yes—
661C22×C11C24×C411yescharacteristic
662C22×C11C23×D411yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C22×#4112yes—
665C22×C11C22×#4112yes—
666C2×D11—232no—
667C2×D11—24no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—24no—
672C2×D11—24no—
673C2×D11—22no—
674C2×D11—24no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—42no—
678C2×D11C4×#4118yescomplemented
679C4×C11—24no—
680C4×C11—22no—
681C4×C11—24no—
682C4×C11—22no—
683C4×C11—24no—
684C4×C11—41no—
685C4×C11—41no—
686C4×C11—42no—
687C4×C11#52514yescomplemented
688Dic11—22no—
689Dic11—24no—
690Dic11—22no—
691Dic11—24no—
692Dic11—41no—
693Dic11—41no—
694Dic11—42no—
695Dic11C2×C4×D414yes—
696Dic11C2×C4×D414yes—
697Dic11#52514yescomplemented
698C25—111no—
699C2×#41—118no—
700C2×#41—224no—
701C2×#41—224no—
702C22×Q8—111no—
703C22×D4—112no—
704C22×D4—111no—
705C22×D4—111no—
706C22×D4—112no—
707C22×D4C22×D1111yescharacteristic
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—118no—
712C23×C4—111no—
713C23×C4—112no—
714C23×C4—112no—
715C23×C4—112no—
716C23×C4—112no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—112no—
721C23×C4—112no—
722C23×C4—111no—
723C23×C4—224no—
724C23×C4—228no—
725C23×C4—228no—
726C23×C4—224no—
727C23×C4—224no—
728C23×C4—224no—
729C23×C4C22×D1111yescharacteristic
730C23×C4C22×D1111yescharacteristic
731C23×C4C22×D1111yescharacteristic
732C23×C4C22×D1111yescharacteristic
733#123—118no—
734#123C4×D1118yescomplemented
735C22⋊Q8—1116no—
736#121—1116no—
737#120—118no—
738#120—118no—
739C4×Q8—224no—
740C4×Q8—224no—
741C4×D4—24no—
742C4×D4—1116no—
743C4×D4—1116no—
744C4×D4—228no—
745C4×D4—224no—
746C4×D4—224no—
747C4×D4—224no—
748C4×D4—228no—
749C4×D4—228no—
750C4×D4—228no—
751C4×D4—224no—
752C4×D4—224no—
753#117—118no—
754#117—224no—
755#117—224no—
756#117—224no—
757#117—224no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1112yes—
771C2×C4⋊C4C22×D1112yes—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4C22×D1111yescharacteristic
790C2×C22⋊C4C22×D1111yescharacteristic
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1111yescharacteristic
793C2×C22⋊C4C22×D1112yes—
794C2×C42—24no—
795C2×C42—118no—
796C2×C42—111no—
797C2×C42—112no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—111no—
802C2×C42—111no—
803C2×C42—112no—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—111no—
813C2×C42—112no—
814C2×C42—224no—
815C2×C42—228no—
816C2×C42—228no—
817C2×C42—228no—
818C2×C42—228no—
819C2×C42—224no—
820C2×C42—224no—
821C2×C42—224no—
822C2×C42C22×D1112yes—
823C2×C42C22×D1112yes—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1112yes—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95C22×D1112yes—
838#95C22×D1112yes—
839#95C22×D1112yes—
840#95C22×D1112yes—
841#95C22×D1112yes—
842C2×C11—24no—
843C2×C11—42no—
844C2×C11C22×C4×D411yescharacteristic
845C2×C11C2×C4×#4112yes—
846C2×C11C2×#52511yescharacteristic
847C2×C11C2×#52511yescharacteristic
848C2×C11#344412yes—
849D11—28no—
850D11—42no—
851C24—112no—
852C24—114no—
853C24—111no—
854C24—224no—
855C24—224no—
856C24—222no—
857C24—222no—
858C24C23×D1111yescharacteristic
859C24C23×D1111yescharacteristic
860#41—2232no—
861C2×Q8—114no—
862C2×Q8—222no—
863C2×Q8—222no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—118no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—118no—
870C2×D4—224no—
871C2×D4—224no—
872C2×D4—222no—
873C2×D4—222no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—222no—
877C2×D4—222no—
878C2×D4C2×C4×D1114yes—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—22no—
885C22×C4—24no—
886C22×C4—114no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—111no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—111no—
895C22×C4—112no—
896C22×C4—112no—
897C22×C4—111no—
898C22×C4—118no—
899C22×C4—114no—
900C22×C4—118no—
901C22×C4—118no—
902C22×C4—118no—
903C22×C4—112no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—224no—
910C22×C4—222no—
911C22×C4—2232no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—224no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—2232no—
922C22×C4—2232no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—222no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4C2×C4×D1114yes—
937C22×C4D4×D1114yes—
938C22×C4C23×D1112yes—
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1112yes—
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C4⋊C4—22no—
948C4⋊C4—24no—
949C4⋊C4—118no—
950C4⋊C4—118no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—224no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—222no—
959C4⋊C4—224no—
960C4⋊C4C2×C4×D1118yescomplemented
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—114no—
966C22⋊C4—118no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—222no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—222no—
976C22⋊C4—224no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—224no—
981C22⋊C4C2×C4×D1114yes—
982C22⋊C4C2×C4×D1118yescomplemented
983C42—24no—
984C42—24no—
985C42—22no—
986C42—24no—
987C42—118no—
988C42—114no—
989C42—114no—
990C42—114no—
991C42—114no—
992C42—224no—
993C42—224no—
994C42—224no—
995C42—224no—
996C42—222no—
997C42—222no—
998C42—222no—
999C42—222no—
1000C42—224no—
1001C42—224no—
1002C42—224no—
1003C42—222no—
1004C42—224no—
1005C11C4×#52511yescharacteristic, complemented, Sylow
1006C23—22no—
1007C23—22no—
1008C23—21no—
1009C23—22no—
1010C23—22no—
1011C23—21no—
1012C23—114no—
1013C23—114no—
1014C23—114no—
1015C23—112no—
1016C23—2216no—
1017C23—228no—
1018C23—228no—
1019C23—2216no—
1020C23—228no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—221no—
1026C23—222no—
1027C23—222no—
1028C23—221no—
1029C23C22×C4×D1112yes—
1030C23C22×C4×D1112yes—
1031C23C2×D4×D1112yes—
1032C23#41×D1112yes—
1033C23C24×D1111yescharacteristic
1034Q8—228no—
1035D4—28no—
1036D4—2216no—
1037D4—228no—
1038D4—2216no—
1039D4—228no—
1040C2×C4—28no—
1041C2×C4—28no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—28no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—44no—
1060C2×C4—1116no—
1061C2×C4—112no—
1062C2×C4—112no—
1063C2×C4—112no—
1064C2×C4—112no—
1065C2×C4—112no—
1066C2×C4—112no—
1067C2×C4—114no—
1068C2×C4—112no—
1069C2×C4—114no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—114no—
1073C2×C4—2216no—
1074C2×C4—2216no—
1075C2×C4—2216no—
1076C2×C4—228no—
1077C2×C4—2216no—
1078C2×C4—2216no—
1079C2×C4—228no—
1080C2×C4—228no—
1081C2×C4—228no—
1082C2×C4—222no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—2216no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—444no—
1098C2×C4—444no—
1099C2×C4—444no—
1100C2×C4C22×C4×D1114yes—
1101C2×C4C22×C4×D1112yes—
1102C2×C4C22×C4×D1114yes—
1103C2×C4C2×D4×D1112yes—
1104C2×C4C2×D4×D1112yes—
1105C2×C4#41×D1114yes—
1106C2×C4#41×D1114yes—
1107C22—24no—
1108C22—24no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—24no—
1113C22—42no—
1114C22—41no—
1115C22—41no—
1116C22—118no—
1117C22—2232no—
1118C22—224no—
1119C22—224no—
1120C22—224no—
1121C22—224no—
1122C22—224no—
1123C22—224no—
1124C22—222no—
1125C22—224no—
1126C22—442no—
1127C22—441no—
1128C22—441no—
1129C22C4×D4×D1114yes—
1130C22C23×C4×D1111yescharacteristic
1131C22C22×D4×D1111yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22C2×#41×D1112yes—
1134C22C2×#41×D1112yes—
1135C4—24no—
1136C4—22no—
1137C4—24no—
1138C4—24no—
1139C4—22no—
1140C4—42no—
1141C4—41no—
1142C4—41no—
1143C4—114no—
1144C4—114no—
1145C4—114no—
1146C4—222no—
1147C4—224no—
1148C4—222no—
1149C4—224no—
1150C4—442no—
1151C4—441no—
1152C4—441no—
1153C4#1062318714yesdirect product factor
1154C2—24no—
1155C2—42no—
1156C2—228no—
1157C2—442no—
1158C2C2×C4×D4×D1111yescharacteristic
1159C2C4×#41×D1112yes—
1160C2D11×#52511yescharacteristic
1161C2C2×#1062318711yescharacteristic
1162C2#1308191012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#123C2
socle, cosocleC23×C11C25
prime radicalC2×#10623187C2
hypercenterC4×#123D11
hypocenterC11C4×#525
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4341C2semidirect
3. C22×C42×D11C2semidirect
4. #13071150C2semidirect
5. C4×#66949C2semidirect
6. #123×Dic11C2semidirect
7. C4×#66982C2semidirect
8. #13071133C2semidirect
9. #13071128C2semidirect
10. C4×#66937C2semidirect
11. #13071121C2semidirect
12. C4×#66935C2semidirect
13. #13071117C2semidirect
14. C4×#66990C2semidirect
15. #13071101C2semidirect
16. #13071095C2semidirect
17. #13071058C2semidirect
18. #13071054C2semidirect
19. #13070996C2semidirect
20. C4×#66946C2semidirect
21. C4×(C22⋊D11)⋊C4C2semidirect
22. C4×#66930C2semidirect
23. C4×C11×#123C2semidirect
36. C2×C4×C22⋊D11C22semidirect
40. C22×C4×Dic11C22semidirect
41. #10623187C4direct (N × H)
46. C2×#66945C22semidirect
47. C2×#66940C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×#66930C22semidirect
64. C2×C42×D11C22semidirect
65. C2×C4×Dic22C22semidirect
66. C11×#388C22semidirect
67. C11×#387C22semidirect
71. C4×C11×C4⋊C4C22semidirect
73. C4×C11×C22⋊C4C22semidirect
81. #10622594C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622585C22semidirect
86. #10622570C22semidirect
91. #10622564C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. C22⋊C4×Dic11C22semidirect
98. #10622553C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. #10622546C22semidirect
103. C4×Dic11⋊C4C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. C42×Dic11C22semidirect
106. #10622282C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
142. C2×#4341C2×C4semidirect
150. C22×C4×D11C2×C4semidirect
161. C11×#123C2×C4semidirect
182. #66990C2×C4semidirect
184. #66982C2×C4semidirect
213. C2×C4×Dic11D4semidirect
232. #66949C2×C4semidirect
234. #66946C2×C4semidirect
237. #66937C2×C4semidirect
238. #66935C2×C4semidirect
242. (C22⋊D11)⋊C4C2×C4semidirect
246. #66930C2×C4semidirect
309. C2×C22⋊D11C22×C4semidirect
318. C22×Dic11C22×C4semidirect
361. C2×C4×D11C22×C4semidirect
362. C2×C4×D11#41semidirect
363. C2×C4×D11#41semidirect
366. C2×Dic22C22×C4semidirect
369. C11×C4⋊C4C22×C4semidirect
375. C11×C22⋊C4C22×C4semidirect
395. (C2×D11)⋊C4C22×C4semidirect
405. Dic11⋊C4C22×C4semidirect
406. Dic11⋊C4C22×C4semidirect
420. C4×Dic11C22×C4semidirect
433. C4×#123D11semidirect
525. C2×Dic11C4×D4semidirect
598. #388C2×D11semidirect
602. #387C2×D11semidirect
632. C4×C4⋊C4C2×D11semidirect
648. C4×C22⋊C4C2×D11semidirect
678. C2×D11C4×#41semidirect
687. C4×C11#525semidirect
697. Dic11#525semidirect
734. #123C4×D11semidirect
960. C4⋊C4C2×C4×D11semidirect
982. C22⋊C4C2×C4×D11semidirect
1005. C11C4×#525semidirect
1153. C4#10623187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231872
C2×C4×#43412
C22×C42×D112
#130711502
C4×#669492
#123×Dic112
C4×#669822
#130711332
#130711282
C4×#669372
#130711212
C4×#669352
#130711172
C4×#669902
#130711012
#130710952
#130710582
#130710542
#130709962
C4×#669462
C4×(C22⋊D11)⋊C42
C4×#669302
C4×C11×#1232
C4×#52511