Finite Group Databasebeta

← C4×#10623127 #14912297

Subgroups — C4×#10623127 #14912297

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C2×C4×#4341C212yesmaximal, complemented
3#13071187C211yesmaximal, characteristic, complemented
4C4×#66941C211yesmaximal, characteristic, complemented
5#13071180C211yesmaximal, characteristic, complemented
6C4×#66993C211yesmaximal, characteristic, complemented
7#13071157C212yesmaximal, complemented
8C4×#66938C212yesmaximal, complemented
9#121×Dic11C211yesmaximal, characteristic, complemented
10C4×#66983C211yesmaximal, characteristic, complemented
11#13071126C212yesmaximal, complemented
12C4×#66992C212yesmaximal, complemented
13#13071122C211yesmaximal, characteristic, complemented
14#13071101C212yesmaximal, complemented
15#13071078C211yesmaximal, characteristic, complemented
16#13071076C212yesmaximal, complemented
17#13071074C211yesmaximal, characteristic, complemented
18#13071018C211yesmaximal, characteristic, complemented
19C4×D4×Dic11C211yesmaximal, characteristic, complemented
20C4×#66946C211yesmaximal, characteristic, complemented
21C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
22C2×C42×Dic11C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C22×#4341C2212yes—
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C2×#66993C2211yescharacteristic
30C2×#66992C2212yes—
31C2×D4×Dic11C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11C2212yes—
36C2×C4×C22⋊D11C2212yes—
37C2×C4×C22⋊D11C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2212yes—
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45#10623127C4116yesdirect product factor
46C4×#4341—216no—
47C2×#66946C2211yescharacteristic
48C2×#66946C2211yescharacteristic
49C2×#66945C2212yes—
50C2×#66941C2211yescharacteristic
51C2×#66940C2212yes—
52C2×#66938C2212yes—
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×(C22⋊D11)⋊C4C2212yes—
57C2×#66930C2212yes—
58C2×#66930C2212yes—
59C2×C4×D44C2211yescharacteristic
60C2×C42×D11C2212yes—
61C2×C4×Dic22C2212yes—
62C11×#390C2211yescharacteristic
63C11×#389C2211yescharacteristic
64C11×#388C2212yes—
65C11×#386C2212yes—
66C11×#380C2211yescharacteristic
67C4×C11×C4⋊C4C2211yescharacteristic
68C4×C11×C22⋊C4C2212yes—
69#10622834C2211yescharacteristic
70#10622833C2212yes—
71#10622826C2212yes—
72#10622825C2211yescharacteristic
73C4×C22⋊Dic11C2212yes—
74#10622603C2212yes—
75#10622601C2211yescharacteristic
76#10622598C2211yescharacteristic
77#10622589C2211yescharacteristic
78#10622589C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic
81C4⋊C4×Dic11C2211yescharacteristic
82C4⋊C4×Dic11C2211yescharacteristic
83#10622586C2211yescharacteristic
84#10622585C2212yes—
85#10622571C2212yes—
86#10622570C2212yes—
87#10622570C2212yes—
88#10622570C2212yes—
89#10622570C2212yes—
90#10622564C2212yes—
91#10622558C2212yes—
92#10622557C2212yes—
93#10622555C2212yes—
94C22⋊C4×Dic11C2212yes—
95C22⋊C4×Dic11C2212yes—
96C22⋊C4×Dic11C2212yes—
97C22⋊C4×Dic11C2212yes—
98#10622553C2212yes—
99#10622552C2211yescharacteristic
100C4×(C2×D11)⋊C4C2212yes—
101C4×(C2×D11)⋊C4C2212yes—
102C4×C4⋊Dic11C2211yescharacteristic
103C4×Dic11⋊C4C2212yes—
104C42×Dic11C2211yescharacteristic
105C42×Dic11C2211yescharacteristic
106C42×Dic11C2211yescharacteristic
107C42×Dic11C2211yescharacteristic
108C42×Dic11C2211yescharacteristic
109C42×Dic11C2211yescharacteristic
110C42×Dic11C2211yescharacteristic
111C42×Dic11C2211yescharacteristic
112#10622541C2211yescharacteristic
113#10622283C2212yes—
114#10622282C2212yes—
115#10622279C2212yes—
116#10622279C2212yes—
117#10622279C2212yes—
118#10622279C2212yes—
119#10622263C2212yes—
120#10622262C2212yes—
121#10622262C2212yes—
122#10622260C2212yes—
123#10622259C2212yes—
124#10622259C2212yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C2×#4341—28no—
141C2×#4341—28no—
142C2×#4341C2×C4116yescomplemented
143C22×D44C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×Dic22C2312yes—
148C11×#121C2×C418yescomplemented
149C4×D4×C11—28no—
150C4×D4×C11—24no—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C42×C11—24no—
161C2×C42×C11C2312yes—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171#66993C2×C418yescomplemented
172#66992C2×C4116yescomplemented
173D4×Dic11—28no—
174D4×Dic11—24no—
175D4×Dic11C2×C418yescomplemented
176#66983C2×C418yescomplemented
177C4×C22⋊D11—28no—
178C4×C22⋊D11—28no—
179C4×C22⋊D11—28no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×C4×Dic11—24no—
200C2×C4×Dic11—28no—
201C2×C4×Dic11—24no—
202C2×C4×Dic11—24no—
203C2×C4×Dic11—24no—
204C2×C4×Dic11C2×C418yescomplemented
205C2×C4×Dic11D418yescomplemented
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2311yescharacteristic
235#66946—24no—
236#66946C2×C418yescomplemented
237#66945—28no—
238#66941C2×C418yescomplemented
239#66940—28no—
240#66938C2×C4116yescomplemented
241(C22⋊D11)⋊C4—28no—
242(C22⋊D11)⋊C4—28no—
243(C22⋊D11)⋊C4—28no—
244(C22⋊D11)⋊C4C2×C4116yescomplemented
245#66930—28no—
246#66930—28no—
247C4×D44—24no—
248C42×D11—28no—
249C4×Dic22—28no—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C4×#532—111nomaximal, Sylow
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C23×D11C2412yes—
266C2×D4×C11—24no—
267C2×D4×C11—24no—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11C22×C414yes—
271C2×D4×C11C22×C418yes—
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—24no—
280C22×C4×C11—24no—
281C22×C4×C11—24no—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C2×D414yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—24no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11C22×C418yes—
300C2×C22⋊D11C22×C418yes—
301C2×C22⋊D11C22×C418yes—
302C22×Dic11—24no—
303C22×Dic11—22no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—24no—
313C22×Dic11—22no—
314C22×Dic11C22×C418yes—
315C22×Dic11C22×C414yes—
316C22×Dic11C22×C414yes—
317C22×Dic11C2×D414yes—
318C22×Dic11C2×D414yes—
319C22×Dic11#4114yes—
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2412yes—
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331#4341—264no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44C22×C414yes—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11C22×C418yes—
344C2×Dic22—24no—
345C2×Dic22—24no—
346C2×Dic22C22×C418yes—
347C11×C4⋊C4—24no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4C22×C414yes—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4C22×C418yes—
356C42×C11—24no—
357C42×C11—22no—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11#4114yescomplemented
361C22⋊Dic11—24no—
362C22⋊Dic11—24no—
363C22⋊Dic11—24no—
364C22⋊Dic11—24no—
365C22⋊Dic11C22×C418yes—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—24no—
372(C2×D11)⋊C4C22×C418yes—
373(C2×D11)⋊C4C22×C418yes—
374C4⋊Dic11—24no—
375C4⋊Dic11—22no—
376C4⋊Dic11—22no—
377C4⋊Dic11C22×C414yes—
378Dic11⋊C4—24no—
379Dic11⋊C4—24no—
380Dic11⋊C4—24no—
381Dic11⋊C4—24no—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4C22×C418yes—
385C4×Dic11—24no—
386C4×Dic11—24no—
387C4×Dic11—24no—
388C4×Dic11—24no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—22no—
392C4×Dic11—22no—
393C4×Dic11—22no—
394C4×Dic11—22no—
395C4×Dic11—22no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—24no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—22no—
403C4×Dic11C22×C414yes—
404C4×Dic11C22×C414yes—
405C4×Dic11C22×C414yes—
406C4×Dic11C22×C414yes—
407C4×Dic11C2×D414yes—
408C4×Dic11C2×D414yes—
409C4×Dic11C2×D414yes—
410C4×Dic11C2×D414yes—
411C4×Dic11#4114yescomplemented
412C4×Dic11#4114yescomplemented
413C4×Dic11#4114yescomplemented
414C2×#532—111no—
415C2×C4×#41—112no—
416C4×C4⋊Q8—111no—
417C4×C4⋊Q8—111no—
418C4×#127—111no—
419C4×#127—111no—
420C4×#124—112no—
421C4×#124—112no—
422C4×#121—111no—
423C4×#121—112no—
424C4×#121—111no—
425C4×#121—111no—
426C4×#121—112no—
427C4×#121D1111yescharacteristic, complemented
428#2297—112no—
429#2293—111no—
430#2293—111no—
431#2293—112no—
432#2285—111no—
433C42×D4—111no—
434C42×D4—112no—
435C42×D4—111no—
436C2×C43—111no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11C23×C414yes—
448C23×C11C23×C412yes—
449C23×C11C22×D412yes—
450C23×C11C2×#4112yes—
451C23×C11C2511yescharacteristic
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11C23×C414yes—
459D4×C11—216no—
460D4×C11—28no—
461C2×C4×C11—28no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—28no—
473C2×C4×C11—28no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—48no—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C414yes—
483C2×C4×C11C23×C412yes—
484C2×C4×C11C22×D412yes—
485C2×C4×C11C22×D412yes—
486C2×C4×C11C2×#4112yes—
487C2×C4×C11C2×#4112yes—
488C2×C4×C11C2×#4112yes—
489C2×C4×C11C2×#4112yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2×#4112yes—
492C22⋊D11—216no—
493C22⋊D11—216no—
494C22⋊D11—216no—
495C2×Dic11—28no—
496C2×Dic11—22no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—216no—
507C2×Dic11—28no—
508C2×Dic11—28no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—48no—
516C2×Dic11C4×D4116yescomplemented
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C414yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C412yes—
522C2×Dic11C22×D412yes—
523C2×Dic11C22×D412yes—
524C2×Dic11C22×D412yes—
525C2×Dic11C22×D412yes—
526C2×Dic11C2×#4112yes—
527C2×Dic11C2×#4112yes—
528C2×Dic11C2×#4112yes—
529C2×Dic11C2×#4112yes—
530C2×Dic11C2×#4112yes—
531C2×Dic11C2×#4112yes—
532C2×Dic11C2×#4112yes—
533C2×Dic11C2×#4112yes—
534D44—28no—
535C4×D11—216no—
536C4×D11—48no—
537C4×D11—48no—
538Dic22—216no—
539C22×#41—112no—
540#532—1116no—
541C2×C4⋊Q8—111no—
542C2×#127—111no—
543C2×#124—112no—
544C2×#121—112no—
545C2×#121—111no—
546C2×#121C2×D1111yescharacteristic
547C4×#41—2216no—
548C2×C4×Q8—112no—
549C2×C4×Q8—112no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—112no—
553C2×C4×D4—112no—
554C2×C4×D4—112no—
555C2×C4×D4—112no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—112no—
559C2×C4×D4—112no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4C2×D1111yescharacteristic
564C2×C4×D4C2×D1112yes—
565C2×#117—112no—
566C2×#117—112no—
567C2×#117—112no—
568C22×C42—111no—
569C22×C42—111no—
570C22×C42—112no—
571C22×C42—111no—
572C22×C42—111no—
573C22×C42—111no—
574C22×C42—111no—
575C22×C42—112no—
576C22×C42C2×D1111yescharacteristic
577#391—112no—
578#391—112no—
579#390—111no—
580#390—111no—
581#390—112no—
582#390—112no—
583#390—112no—
584#390—112no—
585#390—111no—
586#390C2×D1111yescharacteristic
587#389—112no—
588#389—111no—
589#389—111no—
590#389—111no—
591#389—112no—
592#389C2×D1111yescharacteristic
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388—112no—
600#388C2×D1112yes—
601#386—112no—
602#386—112no—
603#386—112no—
604#386C2×D1112yes—
605#384—111no—
606#384—111no—
607#382—112no—
608#380—111no—
609#380—112no—
610#380C2×D1111yescharacteristic
611C4×C4⋊C4—111no—
612C4×C4⋊C4—111no—
613C4×C4⋊C4—111no—
614C4×C4⋊C4—111no—
615C4×C4⋊C4—112no—
616C4×C4⋊C4—111no—
617C4×C4⋊C4—112no—
618C4×C4⋊C4—112no—
619C4×C4⋊C4C2×D1111yescharacteristic
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4—112no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4C2×D1112yes—
632C43—111no—
633C43—111no—
634C43—111no—
635C43—111no—
636C43—111no—
637C43—111no—
638C43—111no—
639C43—111no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11—22no—
643C22×C11—22no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11C2×C4×D414yes—
654C22×C11C24×C411yescharacteristic
655C22×C11C23×D411yescharacteristic
656C22×C11C22×#4111yescharacteristic
657C22×C11C22×#4111yescharacteristic
658C22×C11C22×#4111yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C22×#4111yescharacteristic
661C2×D11—24no—
662C2×D11—24no—
663C2×D11—24no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C4×C11—24no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—22no—
672C4×C11—22no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11C4×#4114yescomplemented
676C4×C11#53214yescomplemented
677Dic11—24no—
678Dic11—22no—
679Dic11—22no—
680Dic11—22no—
681Dic11—22no—
682Dic11—42no—
683Dic11—42no—
684Dic11C2×C4×D414yes—
685Dic11C2×C4×D414yes—
686Dic11C4×#4114yescomplemented
687Dic11#53214yescomplemented
688C2×#41—1116no—
689C2×#41—228no—
690C2×#41—228no—
691C22×Q8—112no—
692C22×D4—112no—
693C22×D4—112no—
694C22×D4—112no—
695C22×D4—111no—
696C22×D4C22×D1111yescharacteristic
697C22×D4C22×D1112yes—
698C23×C4—111no—
699C23×C4—112no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—112no—
703C23×C4—112no—
704C23×C4—111no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1112yes—
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1111yescharacteristic
711C4⋊Q8—118no—
712#127—118no—
713#124—1116no—
714#121—1116no—
715#121—118no—
716#121C4×D1118yescomplemented
717C4×Q8—228no—
718C4×Q8—228no—
719C4×D4—28no—
720C4×D4—24no—
721C4×D4—118no—
722C4×D4—118no—
723C4×D4—1116no—
724C4×D4—228no—
725C4×D4—228no—
726C4×D4—224no—
727C4×D4—228no—
728C4×D4—228no—
729C4×D4—224no—
730C4×D4—228no—
731C4×D4—228no—
732C4×D4—228no—
733C4×D4—224no—
734#117—228no—
735#117—228no—
736#117—228no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4C22×D1112yes—
749C2×C4⋊C4C22×D1111yescharacteristic
750C2×C4⋊C4C22×D1111yescharacteristic
751C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4—112no—
765C2×C22⋊C4C22×D1112yes—
766C2×C22⋊C4C22×D1112yes—
767C2×C22⋊C4C22×D1112yes—
768C2×C22⋊C4C22×D1112yes—
769C2×C22⋊C4C22×D1112yes—
770C2×C42—24no—
771C2×C42—118no—
772C2×C42—118no—
773C2×C42—111no—
774C2×C42—111no—
775C2×C42—111no—
776C2×C42—111no—
777C2×C42—111no—
778C2×C42—111no—
779C2×C42—111no—
780C2×C42—111no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42—111no—
791C2×C42—111no—
792C2×C42—111no—
793C2×C42—111no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—111no—
797C2×C42—111no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—112no—
801C2×C42—111no—
802C2×C42—228no—
803C2×C42—228no—
804C2×C42—224no—
805C2×C42—224no—
806C2×C42—224no—
807C2×C42—224no—
808C2×C42C22×D1111yescharacteristic
809C2×C42C22×D1111yescharacteristic
810C2×C42C22×D1112yes—
811C2×C42C22×D1111yescharacteristic
812C2×C42C22×D1111yescharacteristic
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95C22×D1112yes—
823#95C22×D1112yes—
824#95C22×D1112yes—
825C2×C11—24no—
826C2×C11—44no—
827C2×C11C22×C4×D411yescharacteristic
828C2×C11C2×C4×#4111yescharacteristic
829C2×C11C2×C4×#4111yescharacteristic
830C2×C11C2×#53211yescharacteristic
831C2×C11C2×#53211yescharacteristic
832C2×C11#344411yescharacteristic
833C2×C11#344411yescharacteristic
834D11—44no—
835C24—112no—
836C24C23×D1112yes—
837C24C23×D1111yescharacteristic
838#41—2264no—
839C2×Q8—118no—
840C2×Q8—224no—
841C2×Q8—224no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—118no—
849C2×D4—114no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—224no—
855C2×D4—224no—
856C2×D4—222no—
857C2×D4—222no—
858C2×D4C2×C4×D1114yes—
859C2×D4C2×C4×D1118yes—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—114no—
871C22×C4—114no—
872C22×C4—114no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—111no—
877C22×C4—114no—
878C22×C4—118no—
879C22×C4—114no—
880C22×C4—111no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—118no—
886C22×C4—112no—
887C22×C4—112no—
888C22×C4—224no—
889C22×C4—224no—
890C22×C4—224no—
891C22×C4—224no—
892C22×C4—224no—
893C22×C4—224no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—222no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—222no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4C2×C4×D1114yes—
909C22×C4D4×D1114yes—
910C22×C4C23×D1112yes—
911C22×C4C23×D1112yes—
912C22×C4C23×D1111yescharacteristic
913C22×C4C23×D1112yes—
914C22×C4C23×D1111yescharacteristic
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1111yescharacteristic
919C4⋊C4—24no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—118no—
923C4⋊C4—114no—
924C4⋊C4—224no—
925C4⋊C4—224no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—224no—
929C4⋊C4—224no—
930C4⋊C4—224no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4C2×C4×D1114yes—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—118no—
939C22⋊C4—118no—
940C22⋊C4—118no—
941C22⋊C4—224no—
942C22⋊C4—224no—
943C22⋊C4—224no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—224no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—224no—
951C22⋊C4C2×C4×D1118yes—
952C42—24no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—114no—
957C42—114no—
958C42—114no—
959C42—114no—
960C42—114no—
961C42—114no—
962C42—114no—
963C42—114no—
964C42—114no—
965C42—114no—
966C42—114no—
967C42—224no—
968C42—224no—
969C42—224no—
970C42—224no—
971C42—222no—
972C42—222no—
973C42—222no—
974C42—222no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—222no—
979C42—222no—
980C42—222no—
981C42—224no—
982C42—222no—
983C42—222no—
984C42—222no—
985C42#434114yescomplemented
986C11C4×#53211yescharacteristic, complemented, Sylow
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—114no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23C22×C4×D1114yes—
1005C23C22×C4×D1112yes—
1006C23C2×D4×D1112yes—
1007C23#41×D1112yes—
1008C23C24×D1111yescharacteristic
1009Q8—2216no—
1010D4—216no—
1011D4—28no—
1012D4—2216no—
1013D4—2216no—
1014D4—2216no—
1015D4—228no—
1016C2×C4—28no—
1017C2×C4—22no—
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—22no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—48no—
1036C2×C4—1116no—
1037C2×C4—112no—
1038C2×C4—112no—
1039C2×C4—112no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—112no—
1044C2×C4—112no—
1045C2×C4—112no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—112no—
1049C2×C4—112no—
1050C2×C4—114no—
1051C2×C4—112no—
1052C2×C4—112no—
1053C2×C4—112no—
1054C2×C4—2216no—
1055C2×C4—2216no—
1056C2×C4—228no—
1057C2×C4—228no—
1058C2×C4—228no—
1059C2×C4—222no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—448no—
1076C2×C4—448no—
1077C2×C4—448no—
1078C2×C4C22×C4×D1112yes—
1079C2×C4C22×C4×D1114yes—
1080C2×C4C22×C4×D1112yes—
1081C2×C4C2×D4×D1112yes—
1082C2×C4C2×D4×D1112yes—
1083C2×C4C2×#434112yes—
1084C2×C4C2×#434112yes—
1085C2×C4C2×#434112yes—
1086C2×C4#41×D1112yes—
1087C2×C4#41×D1112yes—
1088C2×C4#41×D1112yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—224no—
1103C22—224no—
1104C22—224no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22C4×D4×D1114yes—
1110C22C23×C4×D1111yescharacteristic
1111C22C22×D4×D1111yescharacteristic
1112C22C22×#434111yescharacteristic
1113C22C2×#41×D1111yescharacteristic
1114C22C2×#41×D1111yescharacteristic
1115C22C2×#41×D1111yescharacteristic
1116C22C2×#41×D1111yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—24no—
1121C4—22no—
1122C4—42no—
1123C4—42no—
1124C4—114no—
1125C4—114no—
1126C4—114no—
1127C4—114no—
1128C4—222no—
1129C4—222no—
1130C4—222no—
1131C4—224no—
1132C4—222no—
1133C4—442no—
1134C4—442no—
1135C4C4×#434114yescomplemented
1136C4#1062312714yesdirect product factor
1137C2—24no—
1138C2—44no—
1139C2—444no—
1140C2C2×C4×D4×D1111yescharacteristic
1141C2C4×#41×D1111yescharacteristic
1142C2C2×C4×#434111yescharacteristic
1143C2D11×#53211yescharacteristic
1144C2C2×#1062312711yescharacteristic
1145C2#1308190811yescharacteristic
1146C2#1308191011yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623127C2
hypercenterC4×#121D11
hypocenterC11C4×#532
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4341C2semidirect
3. #13071187C2semidirect
4. C4×#66941C2semidirect
5. #13071180C2semidirect
6. C4×#66993C2semidirect
7. #13071157C2semidirect
8. C4×#66938C2semidirect
9. #121×Dic11C2semidirect
10. C4×#66983C2semidirect
11. #13071126C2semidirect
12. C4×#66992C2semidirect
13. #13071122C2semidirect
14. #13071101C2semidirect
15. #13071078C2semidirect
16. #13071076C2semidirect
17. #13071074C2semidirect
18. #13071018C2semidirect
19. C4×D4×Dic11C2semidirect
20. C4×#66946C2semidirect
21. C4×(C22⋊D11)⋊C4C2semidirect
22. C2×C42×Dic11C2semidirect
23. C4×C11×#121C2semidirect
45. #10623127C4direct (N × H)
142. C2×#4341C2×C4semidirect
148. C11×#121C2×C4semidirect
171. #66993C2×C4semidirect
172. #66992C2×C4semidirect
175. D4×Dic11C2×C4semidirect
176. #66983C2×C4semidirect
204. C2×C4×Dic11C2×C4semidirect
205. C2×C4×Dic11D4semidirect
236. #66946C2×C4semidirect
238. #66941C2×C4semidirect
240. #66938C2×C4semidirect
244. (C22⋊D11)⋊C4C2×C4semidirect
360. C42×C11#41semidirect
411. C4×Dic11#41semidirect
412. C4×Dic11#41semidirect
413. C4×Dic11#41semidirect
427. C4×#121D11semidirect
516. C2×Dic11C4×D4semidirect
675. C4×C11C4×#41semidirect
676. C4×C11#532semidirect
686. Dic11C4×#41semidirect
687. Dic11#532semidirect
716. #121C4×D11semidirect
985. C42#4341semidirect
986. C11C4×#532semidirect
1135. C4C4×#4341semidirect
1136. C4#10623127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×C4×#43412
#130711872
C4×#669412
#130711802
C4×#669932
#130711572
C4×#669382
#121×Dic112
C4×#669832
#130711262
C4×#669922
#130711222
#130711012
#130710782
#130710762
#130710742
#130710182
C4×D4×Dic112
C4×#669462
C4×(C22⋊D11)⋊C42
C2×C42×Dic112
C4×C11×#1212
C4×#53211