Finite Group Databasebeta

← #14920189

Subgroups — #14920189

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074542C211yesmaximal, characteristic, complemented
4#13074539C211yesmaximal, characteristic, complemented
5#13074508C211yesmaximal, characteristic, complemented
6#13074505C211yesmaximal, characteristic, complemented
7#13074456C212yesmaximal, complemented
8#13074452C212yesmaximal, complemented
9#13074428C211yesmaximal, characteristic, complemented
10#13074420C211yesmaximal, characteristic, complemented
11#13074388C212yesmaximal, complemented
12#13074357C211yesmaximal, characteristic, complemented
13#13074349C211yesmaximal, characteristic, complemented
14#13074327C212yesmaximal, complemented
15#13071876C211yesmaximal, characteristic, complemented
16#13071875C211yesmaximal, characteristic, complemented
17#13071860C212yesmaximal, complemented
18#13071854C212yesmaximal, complemented
19#13071829C211yesmaximal, characteristic, complemented
20C4×#66936C212yesmaximal, complemented
21C4×#66990C212yesmaximal, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C11×#2388C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yescomplemented
30#10623359—28no—
31C2×#66999C2211yescharacteristic
32C2×#66999C2211yescharacteristic, complemented
33C2×#66991C2211yescharacteristic
34C2×#66991C2211yescharacteristic, complemented
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66988C2212yescomplemented
38C2×D4×Dic11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×C4×C22⋊D11C2212yescomplemented
43C2×C4×C22⋊D11C2212yescomplemented
44C2×#66979C2211yescharacteristic, complemented
45C4×D4×D11—28no—
46C2×#66946C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×#66936C2212yes—
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×(C22⋊D11)⋊C4C2211yescharacteristic
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C4×D44C2211yescharacteristic
54C2×#66925C2212yescomplemented
55C2×C42×D11C2211yescharacteristic
56C11×#395C2211yescharacteristic, complemented
57C11×#394C2212yescomplemented
58C11×#394C2211yescharacteristic, complemented
59C11×#393C2211yescharacteristic, complemented
60C11×#392C2212yes—
61C11×#392C2211yescharacteristic, complemented
62C4×C11×C22⋊C4C2211yescharacteristic, complemented
63C4×C11×C22⋊C4C2212yescomplemented
64#10622844C2211yescharacteristic, complemented
65#10622842C2211yescharacteristic, complemented
66#10622836C2212yes—
67#10622836C2212yes—
68#10622836C2211yescharacteristic, complemented
69#10622835C2212yes—
70#10622835C2212yescomplemented
71#10622835C2212yescomplemented
72#10622835C2211yescharacteristic, complemented
73#10622833C2212yescomplemented
74C4×C22⋊Dic11C2212yescomplemented
75C4×C22⋊Dic11C2211yescharacteristic, complemented
76C4×C22⋊Dic11C2212yescomplemented
77#10622606C2212yescomplemented
78#10622602C2212yes—
79#10622602C2212yescomplemented
80#10622599C2211yescharacteristic, complemented
81#10622596C2211yescharacteristic, complemented
82#10622593C2212yescomplemented
83#10622574C2212yes—
84#10622574C2212yes—
85#10622574C2212yescomplemented
86#10622573C2212yes—
87#10622572C2212yescomplemented
88#10622572C2212yescomplemented
89#10622569C2212yes—
90#10622569C2212yes—
91#10622569C2212yescomplemented
92#10622568C2212yes—
93#10622568C2212yes—
94#10622566C2211yescharacteristic, complemented
95#10622566C2212yescomplemented
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622562C2211yescharacteristic, complemented
99#10622561C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622559C2212yescomplemented
103#10622558C2212yescomplemented
104#10622555C2212yescomplemented
105C4×(C2×D11)⋊C4C2212yes—
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×C4⋊Dic11C2212yescomplemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622290C2211yescharacteristic, complemented
110#10622289C2212yescomplemented
111#10622288C2212yescomplemented
112#10622287C2211yescharacteristic, complemented
113#10622285C2212yes—
114#10622281C2212yes—
115#10622280C2211yescharacteristic
116#10622280C2211yescharacteristic
117#10622277C2212yes—
118#10622277C2211yescharacteristic, complemented
119#10622277C2211yescharacteristic, complemented
120#10622274C2211yescharacteristic, complemented
121#10622272C2211yescharacteristic, complemented
122#10622270C2212yescomplemented
123#10622267C2212yescomplemented
124#10622265C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C2×C11×#41—24no—
128C2×C11×#41—44no—
129C22×Q8×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C2×D4×D11—24no—
145C2×D4×D11—24no—
146C2×D4×D11—24no—
147C22×D44C2311yescharacteristic
148C22×C4×D11—24no—
149C22×C4×D11—44no—
150C22×C4×D11—44no—
151C22×C4×D11D418yescomplemented
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C4×D4×C11—24no—
162C4×D4×C11—44no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185#66999—24no—
186#66999—24no—
187#66991—24no—
188#66991—24no—
189#66990—28no—
190#66990—28no—
191#66988—28no—
192D4×Dic11—24no—
193C4×C22⋊D11—24no—
194C4×C22⋊D11—24no—
195C4×C22⋊D11—28no—
196C4×C22⋊D11—28no—
197C4×C22⋊D11—44no—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211#66979—24no—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231#66946—24no—
232C4⋊C4×D11—24no—
233#66936—28no—
234(C22⋊D11)⋊C4—24no—
235(C22⋊D11)⋊C4—24no—
236C22⋊C4×D11—24no—
237C22⋊C4×D11—24no—
238C4×D44—24no—
239#66925—44no—
240C42×D11—24no—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34562—111nomaximal, Sylow
260C24×C11C2412yes—
261C24×C11C2411yescharacteristic
262C24×C11C2411yescharacteristic
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11C2×D414yes—
272C23×D11#4114yescomplemented
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C11×#41—416no—
277C2×Q8×C11—22no—
278C2×Q8×C11—42no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C2×D4×C11—42no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—22no—
293C22×C4×C11—24no—
294C22×C4×C11—24no—
295C22×C4×C11—24no—
296C22×C4×C11C2×D414yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C22×Dic11—22no—
321C22×Dic11—42no—
322C22×Dic11—42no—
323C22×Dic11C2×D414yes—
324C22×Dic11C2412yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2412yes—
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333D4×D11—232no—
334C2×D44—22no—
335C2×D44—22no—
336C2×D44—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11—416no—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11C2×D414yes—
357C2×C4×D11#4114yescomplemented
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C42×C11—22no—
368C42×C11—24no—
369C22⋊Dic11—22no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393C4⋊Dic11—22no—
394C4⋊Dic11—24no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407C4×Dic11—22no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C2×#525—111no—
413C22×C4×D4—111no—
414#2638—111no—
415#2638—111no—
416#2635—111no—
417#2635—111no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—112no—
423#2618—111no—
424#2617—111no—
425#2613—112no—
426#2395—111no—
427#2395—111no—
428#2392—112no—
429#2392—112no—
430#2388—111no—
431#2388D1111yescharacteristic, complemented
432C4×#123—112no—
433C4×#120—112no—
434#2280—111no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11C22×D412yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—48no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478Q8×C11—44no—
479D4×C11—28no—
480D4×C11—44no—
481D4×C11—48no—
482D4×C11—48no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—28no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—44no—
501C2×C4×C11—48no—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11H(5,𝔽2)14yes—
506C22⋊D11—28no—
507C22⋊D11—28no—
508C22⋊D11—48no—
509C22⋊D11—48no—
510C22⋊D11—48no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—44no—
532C2×Dic11—44no—
533C2×Dic11C22×D412yes—
534C2×Dic11C22×D412yes—
535C2×Dic11C2×#4112yes—
536D44—28no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—28no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—44no—
545C4×D11—44no—
546C22×#41C2×D1111yescharacteristic, complemented
547C23×D4—111no—
548C24×C4—111no—
549C24×C4—111no—
550#525—228no—
551C2×#123—112no—
552C2×#123—112no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8—111no—
555C2×#121—111no—
556C2×#121—111no—
557C2×#120—112no—
558C2×#120—112no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—112no—
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—111no—
568C2×C4×D4—111no—
569C2×C4×D4—228no—
570C2×C4×D4C2×D1111yescharacteristic
571C2×C4×D4C2×D1112yescomplemented
572C2×#117—111no—
573C2×#117—112no—
574C22×C4⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C42—111no—
578#400—111no—
579#400—111no—
580#399—111no—
581#399—111no—
582#398—111no—
583#398—112no—
584#398—111no—
585#398—112no—
586#397—112no—
587#397—111no—
588#397—112no—
589#397—112no—
590#397—111no—
591#397—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—111no—
597#395C2×D1111yescharacteristic, complemented
598#394—112no—
599#394—112no—
600#394—111no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—112no—
608#394C2×D1111yescharacteristic, complemented
609#394C2×D1112yescomplemented
610#393—111no—
611#393C2×D1111yescharacteristic, complemented
612#392—112no—
613#392—112no—
614#392—111no—
615#392—112no—
616#392C2×D1112yes—
617#392C2×D1111yescharacteristic, complemented
618#388—112no—
619#388—112no—
620#387—112no—
621#387—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#381—112no—
631#381—111no—
632#381—111no—
633#380—112no—
634#380—111no—
635#380—111no—
636#379—112no—
637#379—112no—
638C4×C4⋊C4—112no—
639C4×C4⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4C2×D1112yescomplemented
646C4×C22⋊C4C2×D1111yescharacteristic, complemented
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11C23×D411yescharacteristic
665C22×C11C22×#4111yescharacteristic
666C22×C11C22×#4111yescharacteristic
667C22×C11C2×H(5,𝔽2)12yes—
668C22×C11#58512yes—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—24no—
672C2×D11—24no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—24no—
678C2×D11—416no—
679C2×D11—416no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11#52514yes—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—42no—
689C4×C11—41no—
690C4×C11—41no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11#53414yes—
694Dic11—22no—
695Dic11—22no—
696Dic11—22no—
697Dic11—42no—
698Dic11—41no—
699Dic11—41no—
700Dic11—42no—
701Dic11—42no—
702Dic11—42no—
703C25—111no—
704C25—111no—
705C2×#41—24no—
706C2×#41—44no—
707C22×Q8C22×D1111yescharacteristic
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—112no—
713C22×D4—111no—
714C22×D4—224no—
715C22×D4—224no—
716C22×D4—224no—
717C22×D4C22×D1111yescharacteristic
718C22×D4C22×D1112yes—
719C22×D4C22×D1112yes—
720C22×D4C22×D1111yescharacteristic
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—118no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—224no—
734C23×C4—444no—
735C23×C4—444no—
736C23×C4C22×D1112yes—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739#123—228no—
740#123—228no—
741C22⋊Q8—224no—
742C22⋊Q8—224no—
743#121—224no—
744#121—224no—
745#120—228no—
746#120—228no—
747C4×D4—24no—
748C4×D4—44no—
749C4×D4—224no—
750C4×D4—224no—
751C4×D4—224no—
752C4×D4—224no—
753C4×D4—224no—
754C4×D4—228no—
755C4×D4—228no—
756C4×D4—224no—
757C4×D4—224no—
758C4×D4—444no—
759#117—224no—
760#117—444no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—224no—
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—224no—
803C2×C22⋊C4—224no—
804C2×C22⋊C4C22×D1111yescharacteristic
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1112yes—
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—112no—
814C2×C42—112no—
815C2×C42—111no—
816C2×C42—224no—
817C2×C42C22×D1112yes—
818C2×C42C22×D1111yescharacteristic
819#95—112no—
820#95—112no—
821#95—111no—
822#95—111no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95C22×D1111yescharacteristic
834#95C22×D1111yescharacteristic
835#95C22×D1112yes—
836#95C22×D1112yes—
837C2×C11—42no—
838C2×C11—42no—
839C2×C11—82no—
840C2×C11C2×#52511yescharacteristic
841C2×C11C2×#53411yescharacteristic
842C2×C11#344911yescharacteristic
843C2×C11#345912yes—
844C2×C11#346012yes—
845D11—24no—
846D11—42no—
847D11—42no—
848C24—111no—
849C24—111no—
850C24—111no—
851C24—114no—
852C24—114no—
853C24—222no—
854C24—222no—
855C24—222no—
856C24—222no—
857C24—442no—
858C24—442no—
859C24—442no—
860C24—442no—
861C24C23×D1112yes—
862C24C23×D1111yescharacteristic
863C24C23×D1111yescharacteristic
864#41—416no—
865C2×Q8—22no—
866C2×Q8—42no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—222no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—2232no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—222no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C22×C4—24no—
898C22×C4—22no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—111no—
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—112no—
913C22×C4—111no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—112no—
917C22×C4—111no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—4416no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4416no—
935C22×C4—442no—
936C22×C4—442no—
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×D1111yescharacteristic
946C4⋊C4—22no—
947C4⋊C4—42no—
948C4⋊C4—222no—
949C4⋊C4—222no—
950C4⋊C4—224no—
951C4⋊C4—224no—
952C4⋊C4—224no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—224no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—222no—
970C22⋊C4—222no—
971C22⋊C4—222no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—222no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—224no—
983C22⋊C4—224no—
984C22⋊C4—222no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C42—22no—
994C42—24no—
995C42—222no—
996C42—222no—
997C42—222no—
998C42—224no—
999C42—224no—
1000C11#3456211yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—22no—
1003C23—22no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—112no—
1017C23—112no—
1018C23—112no—
1019C23—112no—
1020C23—112no—
1021C23—228no—
1022C23—228no—
1023C23—222no—
1024C23—222no—
1025C23—221no—
1026C23—222no—
1027C23—222no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—222no—
1032C23—222no—
1033C23—444no—
1034C23—444no—
1035C23—448no—
1036C23—444no—
1037C23—444no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23C2×D4×D1112yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—44no—
1045D4—28no—
1046D4—44no—
1047D4—48no—
1048D4—48no—
1049D4—228no—
1050D4—228no—
1051D4—228no—
1052D4—448no—
1053D4—448no—
1054D4—448no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—44no—
1073C2×C4—48no—
1074C2×C4—112no—
1075C2×C4—112no—
1076C2×C4—112no—
1077C2×C4—228no—
1078C2×C4—221no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—221no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—444no—
1101C2×C4—444no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—444no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4C2×D4×D1112yes—
1109C2×C4C2×D4×D1112yes—
1110C2×C4#6703714yes—
1111C2×C4#41×D1112yes—
1112C22—22no—
1113C22—22no—
1114C22—24no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—114no—
1130C22—222no—
1131C22—222no—
1132C22—224no—
1133C22—224no—
1134C22—222no—
1135C22—222no—
1136C22—224no—
1137C22—222no—
1138C22—222no—
1139C22—4416no—
1140C22—4416no—
1141C22—441no—
1142C22—441no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22C22×D4×D1111yescharacteristic
1147C22C2×#6703712yes—
1148C22C2×#41×D1111yescharacteristic
1149C22C2×#41×D1111yescharacteristic
1150C22#1062345312yes—
1151C4—22no—
1152C4—22no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—42no—
1158C4—222no—
1159C4—222no—
1160C4—222no—
1161C4—441no—
1162C4—441no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4#1062312014yes—
1168C2—42no—
1169C2—42no—
1170C2—82no—
1171C2—224no—
1172C2—442no—
1173C2—442no—
1174C2D11×#52511yescharacteristic
1175C2C2×#1062312011yescharacteristic
1176C2#1308194311yescharacteristic
1177C2#1308202312yes—
1178C2#1308203012yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2388C2
hypercenter#2388D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#10623359C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074542C2semidirect
4. #13074539C2semidirect
5. #13074508C2semidirect
6. #13074505C2semidirect
7. #13074456C2semidirect
8. #13074452C2semidirect
9. #13074428C2semidirect
10. #13074420C2semidirect
11. #13074388C2semidirect
12. #13074357C2semidirect
13. #13074349C2semidirect
14. #13074327C2semidirect
15. #13071876C2semidirect
16. #13071875C2semidirect
17. #13071860C2semidirect
18. #13071854C2semidirect
19. #13071829C2semidirect
20. C4×#66936C2semidirect
21. C4×#66990C2semidirect
22. #13070997C2semidirect
23. C11×#2388C2semidirect
24. C22×C11×#41C22semidirect
29. C2×C4×D4×C11C22semidirect
32. C2×#66999C22semidirect
34. C2×#66991C22semidirect
37. C2×#66988C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×#66979C22semidirect
54. C2×#66925C22semidirect
56. C11×#395C22semidirect
57. C11×#394C22semidirect
58. C11×#394C22semidirect
59. C11×#393C22semidirect
61. C11×#392C22semidirect
62. C4×C11×C22⋊C4C22semidirect
63. C4×C11×C22⋊C4C22semidirect
64. #10622844C22semidirect
65. #10622842C22semidirect
68. #10622836C22semidirect
70. #10622835C22semidirect
71. #10622835C22semidirect
72. #10622835C22semidirect
73. #10622833C22semidirect
74. C4×C22⋊Dic11C22semidirect
75. C4×C22⋊Dic11C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. #10622606C22semidirect
79. #10622602C22semidirect
80. #10622599C22semidirect
81. #10622596C22semidirect
82. #10622593C22semidirect
85. #10622574C22semidirect
87. #10622572C22semidirect
88. #10622572C22semidirect
91. #10622569C22semidirect
94. #10622566C22semidirect
95. #10622566C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
98. #10622562C22semidirect
99. #10622561C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622559C22semidirect
103. #10622558C22semidirect
104. #10622555C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622290C22semidirect
110. #10622289C22semidirect
111. #10622288C22semidirect
112. #10622287C22semidirect
118. #10622277C22semidirect
119. #10622277C22semidirect
120. #10622274C22semidirect
121. #10622272C22semidirect
122. #10622270C22semidirect
123. #10622267C22semidirect
124. #10622265C22semidirect
151. C22×C4×D11D4semidirect
272. C23×D11#41semidirect
357. C2×C4×D11#41semidirect
431. #2388D11semidirect
546. C22×#41C2×D11semidirect
571. C2×C4×D4C2×D11semidirect
597. #395C2×D11semidirect
608. #394C2×D11semidirect
609. #394C2×D11semidirect
611. #393C2×D11semidirect
617. #392C2×D11semidirect
645. C4×C22⋊C4C2×D11semidirect
646. C4×C22⋊C4C2×D11semidirect
1000. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×C4×D4×D112
#130745422
#130745392
#130745082
#130745052
#130744562
#130744522
#130744282
#130744202
#130743882
#130743572
#130743492
#130743272
#130718762
#130718752
#130718602
#130718542
#130718292
C4×#669362
C4×#669902
#130709972
C11×#23882
#3456211