Finite Group Databasebeta

← #14914914

Subgroups — #14914914

Order 2816.

3658 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071665C212yesmaximal, complemented
5#13071660C212yesmaximal, complemented
6#13071637C212yesmaximal, complemented
7#13071629C212yesmaximal, complemented
8#13071607C212yesmaximal, complemented
9#13071605C212yesmaximal, complemented
10#13071597C212yesmaximal, complemented
11#13071596C212yesmaximal, complemented
12#13071290C211yesmaximal, characteristic, complemented
13#13071284C211yesmaximal, characteristic, complemented
14#13071274C211yesmaximal, characteristic, complemented
15#13071192C211yesmaximal, characteristic, complemented
16C4×#66939C211yesmaximal, characteristic, complemented
17C4×#66988C211yesmaximal, characteristic, complemented
18#120×Dic11C211yesmaximal, characteristic, complemented
19#13071115C211yesmaximal, characteristic, complemented
20D11×#386C211yesmaximal, characteristic, complemented
21D11×#385C211yesmaximal, characteristic, complemented
22#13070968C211yesmaximal, characteristic, complemented
23C11×#2321C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic, complemented
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic, complemented
31C2×#67006C2211yescharacteristic
32C2×#66991C2212yes—
33C2×#66990C2212yes—
34C2×#66988C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C2×D4×Dic11C2212yescomplemented
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×C4×C22⋊D11C2211yescharacteristic, complemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×Dic11⋊C4C2211yescharacteristic, complemented
42C22×C4×Dic11C2211yescharacteristic, complemented
43#10623120C4116yescomplemented
44#10623076—28no—
45C2×#66946C2211yescharacteristic, complemented
46C2×#66945C2211yescharacteristic, complemented
47C2×C4⋊C4×D11C2212yescomplemented
48C2×#66939C2211yescharacteristic
49C2×#66937C2212yes—
50C2×#66936C2212yes—
51C2×(C22⋊D11)⋊C4—28no—
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yescomplemented
56C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
57C2×(C22⋊D11)⋊C4C2212yescomplemented
58C2×(C22⋊D11)⋊C4C2212yescomplemented
59C2×C22⋊C4×D11C2211yescharacteristic
60C2×C22⋊C4×D11C2211yescharacteristic
61C2×C22⋊C4×D11C2211yescharacteristic
62C2×C22⋊C4×D11C2211yescharacteristic, complemented
63C2×C22⋊C4×D11C2212yescomplemented
64C2×C4×D44C2211yescharacteristic, complemented
65C2×#66925C2211yescharacteristic, complemented
66C11×#390C2212yescomplemented
67C11×#388C2212yescomplemented
68C11×#388C2212yescomplemented
69C11×#386C2211yescharacteristic
70C11×#386C2212yescomplemented
71C11×#385C2211yescharacteristic, complemented
72C11×#379C2211yescharacteristic, complemented
73C4×C11×C22⋊C4C2211yescharacteristic, complemented
74#10622860C2211yescharacteristic, complemented
75#10622833C2211yescharacteristic
76#10622833C2212yescomplemented
77#10622826C2211yescharacteristic
78#10622823C2211yescharacteristic, complemented
79C4×C22⋊Dic11C2212yescomplemented
80C4×C22⋊Dic11C2211yescharacteristic, complemented
81#10622602C2212yescomplemented
82#10622602C2212yescomplemented
83#10622591C2212yescomplemented
84#10622586C2212yescomplemented
85#10622571C2211yescharacteristic
86#10622571C2212yescomplemented
87#10622570C2212yescomplemented
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622563C2212yescomplemented
95#10622563C2211yescharacteristic, complemented
96#10622559C2212yescomplemented
97#10622559C2211yescharacteristic, complemented
98#10622559C2212yescomplemented
99#10622558C2212yescomplemented
100#10622557C2212yescomplemented
101#10622557C2212yescomplemented
102#10622557C2212yescomplemented
103#10622556C2211yescharacteristic, complemented
104#10622556C2211yescharacteristic, complemented
105C22⋊C4×Dic11C2212yescomplemented
106C22⋊C4×Dic11C2211yescharacteristic, complemented
107C22⋊C4×Dic11C2212yescomplemented
108C22⋊C4×Dic11C2211yescharacteristic, complemented
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111C4×(C2×D11)⋊C4C2212yescomplemented
112C4×C4⋊Dic11C2212yescomplemented
113C4×Dic11⋊C4C2212yescomplemented
114#10622283C2212yescomplemented
115#10622282C2212yescomplemented
116#10622281C2212yescomplemented
117#10622279C2212yescomplemented
118#10622279C2212yescomplemented
119#10622278C2212yescomplemented
120D11×#95C2212yescomplemented
121D11×#95C2212yescomplemented
122#10622267C2212yescomplemented
123#10622266C2212yescomplemented
124#10622265C2212yescomplemented
125#10622260C2212yescomplemented
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11—24no—
135C22×C22⋊D11—24no—
136C22×C22⋊D11C2×C418yescomplemented
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2312yes—
142C23×Dic11—24no—
143C23×Dic11—44no—
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2312yes—
146C23×Dic11C2312yes—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C2×D4×D11—24no—
151C2×D4×D11—24no—
152C2×D4×D11C2×C418yescomplemented
153C22×D44C2311yescharacteristic
154C22×C4×D11—24no—
155C22×C4×D11—44no—
156C22×C4×D11C2312yes—
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2312yes—
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2312yes—
165C11×#120C2×C418yescomplemented
166C4×D4×C11—24no—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C22⋊C4—24no—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2312yes—
180C2×C42×C11C2311yescharacteristic
181C2×C42×C11C2312yes—
182#67006C2×C418yescomplemented
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192#66991C2×C4116yescomplemented
193#66990C2×C4116yescomplemented
194#66988C2×C418yescomplemented
195D4×Dic11—24no—
196D4×Dic11—44no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—24no—
199C2×(C2×D11)⋊C4—24no—
200C2×(C2×D11)⋊C4D418yescomplemented
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2311yescharacteristic
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2311yescharacteristic
213C2×(C2×D11)⋊C4C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×Dic11⋊C4—24no—
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11—24no—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234#66946—24no—
235#66945—24no—
236C4⋊C4×D11—44no—
237#66939C2×C418yescomplemented
238#66937C2×C4116yescomplemented
239#66936C2×C4116yescomplemented
240(C22⋊D11)⋊C4—24no—
241(C22⋊D11)⋊C4—28no—
242(C22⋊D11)⋊C4—28no—
243(C22⋊D11)⋊C4—28no—
244(C22⋊D11)⋊C4—28no—
245(C22⋊D11)⋊C4—24no—
246(C22⋊D11)⋊C4—44no—
247C22⋊C4×D11—24no—
248C22⋊C4×D11—24no—
249C22⋊C4×D11—24no—
250C22⋊C4×D11—44no—
251C22⋊C4×D11C2×C418yescomplemented
252C4×D44—24no—
253#66925—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—
270#34264—111nomaximal, Sylow
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—42no—
274C24×C11—42no—
275C24×C11C22×C414yes—
276C24×C11C2411yescharacteristic
277C24×C11C2412yes—
278C24×C11C2411yescharacteristic
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—42no—
282C23×D11—42no—
283C23×D11—42no—
284C23×D11—42no—
285C23×D11C22×C414yes—
286C23×D11C22×C414yescomplemented
287C23×D11C2×D414yes—
288C23×D11#4114yes—
289C23×D11C2411yescharacteristic
290C23×D11C2411yescharacteristic
291C23×D11C2411yescharacteristic
292C2×D4×C11—22no—
293C2×D4×C11—22no—
294C2×D4×C11—42no—
295C2×D4×C11—42no—
296C2×D4×C11C22×C414yes—
297C2×D4×C11C22×C418yescomplemented
298C22×C4×C11—22no—
299C22×C4×C11—22no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11—42no—
303C22×C4×C11C2×D414yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2412yes—
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—232no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11C22×C418yes—
324C2×C22⋊D11C22×C418yes—
325C2×C22⋊D11C22×C414yes—
326C2×C22⋊D11C22×C414yescomplemented
327C2×C22⋊D11C22×C418yescomplemented
328C22×Dic11—24no—
329C22×Dic11—24no—
330C22×Dic11—24no—
331C22×Dic11—24no—
332C22×Dic11—24no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—22no—
336C22×Dic11—22no—
337C22×Dic11—42no—
338C22×Dic11—42no—
339C22×Dic11—42no—
340C22×Dic11—42no—
341C22×Dic11—416no—
342C22×Dic11C22×C414yes—
343C22×Dic11C2×D414yes—
344C22×Dic11C2412yes—
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2412yes—
348C22×Dic11C2412yes—
349C22×Dic11C2411yescharacteristic
350C22×Dic11C2411yescharacteristic
351C22×Dic11C2411yescharacteristic
352C22×Dic11C2412yes—
353D4×D11—232no—
354C2×D44—22no—
355C2×D44—22no—
356C2×D44C22×C414yescomplemented
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—24no—
362C2×C4×D11—24no—
363C2×C4×D11—22no—
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—24no—
367C2×C4×D11—22no—
368C2×C4×D11—42no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11—42no—
374C2×C4×D11—42no—
375C2×C4×D11—42no—
376C2×C4×D11—42no—
377C2×C4×D11—42no—
378C2×C4×D11—416no—
379C2×C4×D11C22×C414yescomplemented
380C2×C4×D11C22×C418yescomplemented
381C11×C4⋊C4—22no—
382C11×C4⋊C4—42no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—24no—
388C11×C22⋊C4—42no—
389C11×C22⋊C4—42no—
390C11×C22⋊C4—42no—
391C11×C22⋊C4C22×C414yes—
392C11×C22⋊C4C22×C418yescomplemented
393C42×C11—22no—
394C42×C11—42no—
395C22⋊Dic11—22no—
396C22⋊Dic11—24no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399C22⋊Dic11—42no—
400C22⋊Dic11—42no—
401C22⋊Dic11C22×C414yes—
402C22⋊Dic11C22×C418yescomplemented
403C22⋊Dic11C22×C418yescomplemented
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—24no—
406(C2×D11)⋊C4—22no—
407(C2×D11)⋊C4—22no—
408(C2×D11)⋊C4—24no—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4C22×C418yescomplemented
412(C2×D11)⋊C4C22×C418yescomplemented
413(C2×D11)⋊C4C2×D414yes—
414(C2×D11)⋊C4C2×D414yes—
415(C2×D11)⋊C4C2×D414yes—
416(C2×D11)⋊C4C2×D414yes—
417C4⋊Dic11—22no—
418C4⋊Dic11—24no—
419C4⋊Dic11C22×C418yescomplemented
420Dic11⋊C4—22no—
421Dic11⋊C4—24no—
422Dic11⋊C4—24no—
423Dic11⋊C4—24no—
424Dic11⋊C4—22no—
425Dic11⋊C4—42no—
426Dic11⋊C4C22×C418yescomplemented
427C4×Dic11—22no—
428C4×Dic11—22no—
429C4×Dic11—24no—
430C4×Dic11—24no—
431C4×Dic11—22no—
432C4×Dic11—42no—
433C4×Dic11—42no—
434C4×Dic11—42no—
435C2×#534—111no—
436C2×#518—111no—
437C22×C4×D4—111no—
438#2364—112no—
439#2364—112no—
440#2361—112no—
441#2361—112no—
442#2359—112no—
443#2359—112no—
444#2358—112no—
445#2358—112no—
446#2322—111no—
447#2322—111no—
448#2321—111no—
449#2321D1111yescharacteristic, complemented
450#2308—111no—
451C4×#123—111no—
452C4×#123—111no—
453C4×#120—111no—
454C4×#120—111no—
455C2×#386—111no—
456C2×#385—111no—
457#2273—111no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—28no—
461C23×C11—21no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—21no—
465C23×C11—22no—
466C23×C11—22no—
467C23×C11—22no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—48no—
472C23×C11—44no—
473C23×C11—44no—
474C23×C11—48no—
475C23×C11C23×C412yes—
476C23×C11C23×C414yes—
477C23×C11C23×C412yes—
478C23×C11C22×D412yes—
479C23×C11C2×#4112yes—
480C23×C11C2511yescharacteristic
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—21no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—28no—
490C22×D11—44no—
491C22×D11—48no—
492C22×D11—44no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—82no—
496C22×D11—82no—
497C22×D11—84no—
498C22×D11C4×D4116yescomplemented
499C22×D11C23×C412yes—
500C22×D11C23×C412yes—
501C22×D11C23×C412yes—
502C22×D11C22×D412yes—
503C22×D11C22×D412yes—
504C22×D11C2×#4112yes—
505C22×D11C2×#4112yes—
506D4×C11—28no—
507D4×C11—48no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—21no—
515C2×C4×C11—22no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—44no—
525C2×C4×C11—44no—
526C2×C4×C11—82no—
527C2×C4×C11C23×C412yes—
528C2×C4×C11C23×C414yes—
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D412yes—
531C22⋊D11—28no—
532C22⋊D11—28no—
533C22⋊D11—216no—
534C22⋊D11—216no—
535C22⋊D11—48no—
536C2×Dic11—28no—
537C2×Dic11—28no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—21no—
549C2×Dic11—21no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—44no—
556C2×Dic11—48no—
557C2×Dic11—48no—
558C2×Dic11—82no—
559C2×Dic11C23×C414yes—
560C2×Dic11C23×C414yes—
561C2×Dic11C23×C412yes—
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D412yes—
564C2×Dic11H(5,𝔽2)14yes—
565D44—28no—
566C4×D11—28no—
567C4×D11—48no—
568C4×D11—48no—
569C4×D11—48no—
570C4×D11—82no—
571C4×D11—82no—
572C4×D11—82no—
573C4×D11—82no—
574C4×D11—84no—
575C23×D4—111no—
576C23×D4—111no—
577C24×C4—111no—
578C24×C4—111no—
579#534—1116no—
580C2×#123—111no—
581C2×#123—111no—
582C2×#123—112no—
583C2×#121—112no—
584C2×#121—112no—
585C2×#120—111no—
586C2×#120—112no—
587C2×#120C2×D1111yescharacteristic
588#518—228no—
589C2×C4×D4—111no—
590C2×C4×D4—111no—
591C2×C4×D4—111no—
592C2×C4×D4—112no—
593C2×C4×D4—111no—
594C2×C4×D4—111no—
595C2×C4×D4—112no—
596C2×C4×D4—112no—
597C2×C4×D4—111no—
598C2×C4×D4—112no—
599C2×C4×D4—112no—
600C2×C4×D4—112no—
601C2×C4×D4—111no—
602C2×C4×D4—228no—
603C2×C4×D4C2×D1111yescharacteristic
604C2×#117—111no—
605C2×#117—111no—
606C22×C4⋊C4—111no—
607C22×C4⋊C4—112no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—111no—
611C22×C22⋊C4—111no—
612C22×C22⋊C4—111no—
613C22×C22⋊C4—111no—
614C22×C22⋊C4—112no—
615C22×C22⋊C4C2×D1111yescharacteristic, complemented
616C22×C42—111no—
617#390—112no—
618#390C2×D1112yescomplemented
619#389—112no—
620#389—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#388—112no—
625#388—112no—
626#388—112no—
627#388C2×D1112yescomplemented
628#388C2×D1112yescomplemented
629#387—112no—
630#387—112no—
631#387—112no—
632#387—112no—
633#386—112no—
634#386—111no—
635#386—111no—
636#386—112no—
637#386—112no—
638#386—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—111no—
644#386—112no—
645#386C2×D1111yescharacteristic
646#386C2×D1112yescomplemented
647#385—111no—
648#385—112no—
649#385—112no—
650#385—112no—
651#385—112no—
652#385—112no—
653#385—111no—
654#385—111no—
655#385—112no—
656#385C2×D1111yescharacteristic, complemented
657#381—111no—
658#381—111no—
659#379—111no—
660#379C2×D1111yescharacteristic, complemented
661C4×C4⋊C4—112no—
662C4×C4⋊C4—112no—
663C4×C22⋊C4—111no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—111no—
666C4×C22⋊C4—111no—
667C4×C22⋊C4—112no—
668C4×C22⋊C4—112no—
669C4×C22⋊C4—112no—
670C4×C22⋊C4—112no—
671C4×C22⋊C4—112no—
672C4×C22⋊C4—112no—
673C4×C22⋊C4—112no—
674C4×C22⋊C4C2×D1111yescharacteristic, complemented
675C2×#95—112no—
676C2×#95—112no—
677C22×C11—24no—
678C22×C11—22no—
679C22×C11—22no—
680C22×C11—24no—
681C22×C11—22no—
682C22×C11—24no—
683C22×C11—24no—
684C22×C11—24no—
685C22×C11—24no—
686C22×C11—416no—
687C22×C11—41no—
688C22×C11—42no—
689C22×C11—41no—
690C22×C11—42no—
691C22×C11—42no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11C2×C4×D414yes—
695C22×C11C24×C411yescharacteristic
696C22×C11C23×D411yescharacteristic
697C22×C11C22×#4111yescharacteristic
698C22×C11C2×H(5,𝔽2)12yes—
699C22×C11#58512yes—
700C2×D11—24no—
701C2×D11—24no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—22no—
706C2×D11—24no—
707C2×D11—24no—
708C2×D11—22no—
709C2×D11—24no—
710C2×D11—416no—
711C2×D11—41no—
712C2×D11—41no—
713C2×D11—42no—
714C2×D11—88no—
715C2×D11C2×C4×D414yes—
716C2×D11C2×C4×D414yes—
717C4×C11—22no—
718C4×C11—24no—
719C4×C11—22no—
720C4×C11—22no—
721C4×C11—42no—
722C4×C11—41no—
723C4×C11—41no—
724C4×C11—42no—
725Dic11—22no—
726Dic11—24no—
727Dic11—24no—
728Dic11—24no—
729Dic11—22no—
730Dic11—22no—
731Dic11—41no—
732Dic11—41no—
733Dic11—42no—
734C25—111no—
735C25—111no—
736C25C22×D1111yescharacteristic
737C22×D4—118no—
738C22×D4—112no—
739C22×D4—111no—
740C22×D4—112no—
741C22×D4—111no—
742C22×D4—112no—
743C22×D4—118no—
744C22×D4—111no—
745C22×D4—224no—
746C22×D4—224no—
747C22×D4—224no—
748C22×D4—224no—
749C22×D4C22×D1111yescharacteristic
750C22×D4C22×D1112yes—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—112no—
755C23×C4—111no—
756C23×C4—112no—
757C23×C4—112no—
758C23×C4—111no—
759C23×C4—112no—
760C23×C4—112no—
761C23×C4—112no—
762C23×C4—111no—
763C23×C4—111no—
764C23×C4—111no—
765C23×C4—111no—
766C23×C4—224no—
767C23×C4—224no—
768C23×C4—444no—
769C23×C4—444no—
770C23×C4C22×D1111yescharacteristic
771C23×C4C22×D1111yescharacteristic
772C23×C4C22×D1111yescharacteristic
773#123—118no—
774#123—118no—
775#123—1116no—
776#121—1116no—
777#121—1116no—
778#120—118no—
779#120—1116no—
780#120C4×D1118yescomplemented
781C4×D4—24no—
782C4×D4—224no—
783C4×D4—228no—
784C4×D4—228no—
785C4×D4—228no—
786C4×D4—228no—
787C4×D4—224no—
788C4×D4—224no—
789C4×D4—224no—
790C4×D4—224no—
791C4×D4—224no—
792C4×D4—224no—
793C4×D4—444no—
794C4×D4—444no—
795#117—224no—
796#117—224no—
797C2×C4⋊C4—112no—
798C2×C4⋊C4—112no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—112no—
803C2×C4⋊C4—111no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—111no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—224no—
808C2×C4⋊C4—444no—
809C2×C4⋊C4C22×D1111yescharacteristic
810C2×C4⋊C4C22×D1112yes—
811C2×C22⋊C4—24no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—118no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—111no—
818C2×C22⋊C4—111no—
819C2×C22⋊C4—111no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—118no—
823C2×C22⋊C4—111no—
824C2×C22⋊C4—111no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—224no—
837C2×C22⋊C4—224no—
838C2×C22⋊C4—224no—
839C2×C22⋊C4—224no—
840C2×C22⋊C4—444no—
841C2×C22⋊C4C22×D1111yescharacteristic
842C2×C22⋊C4C22×D1111yescharacteristic
843C2×C22⋊C4C22×D1111yescharacteristic
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1112yes—
846C2×C22⋊C4C22×D1112yes—
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yes—
849C2×C22⋊C4C22×D1111yescharacteristic
850C2×C22⋊C4C22×D1112yes—
851C2×C42—111no—
852C2×C42—111no—
853C2×C42—111no—
854C2×C42—112no—
855C2×C42—112no—
856C2×C42—112no—
857C2×C42—112no—
858C2×C42—112no—
859C2×C42—224no—
860C2×C42C22×D1111yescharacteristic
861C2×C42C22×D1112yes—
862#95—112no—
863#95—112no—
864#95—112no—
865#95—112no—
866#95—112no—
867#95—112no—
868#95—112no—
869#95—112no—
870#95—112no—
871#95—112no—
872#95—112no—
873#95—112no—
874#95—112no—
875#95C22×D1112yes—
876#95C22×D1112yes—
877#95C22×D1112yes—
878C2×C11—24no—
879C2×C11—42no—
880C2×C11—44no—
881C2×C11C22×C4×D411yescharacteristic
882C2×C11C4×H(5,𝔽2)12yes—
883C2×C11#348411yescharacteristic
884C2×C11#348511yescharacteristic
885C2×C11#350512yes—
886D11—24no—
887D11—24no—
888D11—42no—
889C24—22no—
890C24—22no—
891C24—42no—
892C24—42no—
893C24—111no—
894C24—111no—
895C24—114no—
896C24—114no—
897C24—114no—
898C24—111no—
899C24—114no—
900C24—222no—
901C24—222no—
902C24—442no—
903C24—442no—
904C24—442no—
905C24—442no—
906C24C2×C4×D1114yes—
907C24C23×D1111yescharacteristic
908C24C23×D1112yes—
909C24C23×D1111yescharacteristic
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—118no—
915C2×D4—114no—
916C2×D4—118no—
917C2×D4—114no—
918C2×D4—118no—
919C2×D4—114no—
920C2×D4—222no—
921C2×D4—222no—
922C2×D4—2232no—
923C2×D4—224no—
924C2×D4—224no—
925C2×D4—222no—
926C2×D4—2232no—
927C2×D4—222no—
928C2×D4—224no—
929C2×D4—224no—
930C2×D4—222no—
931C2×D4—222no—
932C2×D4—442no—
933C2×D4—442no—
934C2×D4C2×C4×D1114yes—
935C2×D4C2×C4×D1118yescomplemented
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—114no—
942C22×C4—112no—
943C22×C4—111no—
944C22×C4—112no—
945C22×C4—112no—
946C22×C4—111no—
947C22×C4—111no—
948C22×C4—114no—
949C22×C4—114no—
950C22×C4—118no—
951C22×C4—112no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—222no—
957C22×C4—222no—
958C22×C4—222no—
959C22×C4—224no—
960C22×C4—224no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—224no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—224no—
967C22×C4—224no—
968C22×C4—224no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—442no—
975C22×C4—442no—
976C22×C4—442no—
977C22×C4—442no—
978C22×C4—442no—
979C22×C4—442no—
980C22×C4—442no—
981C22×C4—442no—
982C22×C4—442no—
983C22×C4—442no—
984C22×C4—4416no—
985C22×C4—442no—
986C22×C4—442no—
987C22×C4—442no—
988C22×C4—442no—
989C22×C4—4416no—
990C22×C4D4×D1114yes—
991C22×C4C23×D1112yes—
992C22×C4C23×D1111yescharacteristic
993C22×C4C23×D1112yes—
994C22×C4C23×D1111yescharacteristic
995C22×C4C23×D1112yes—
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1111yescharacteristic
999C4⋊C4—22no—
1000C4⋊C4—42no—
1001C4⋊C4—118no—
1002C4⋊C4—118no—
1003C4⋊C4—224no—
1004C4⋊C4—224no—
1005C4⋊C4—224no—
1006C4⋊C4—224no—
1007C4⋊C4—222no—
1008C4⋊C4—222no—
1009C4⋊C4—222no—
1010C4⋊C4—442no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—24no—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—114no—
1020C22⋊C4—118no—
1021C22⋊C4—118no—
1022C22⋊C4—118no—
1023C22⋊C4—118no—
1024C22⋊C4—114no—
1025C22⋊C4—114no—
1026C22⋊C4—114no—
1027C22⋊C4—114no—
1028C22⋊C4—222no—
1029C22⋊C4—224no—
1030C22⋊C4—222no—
1031C22⋊C4—222no—
1032C22⋊C4—224no—
1033C22⋊C4—222no—
1034C22⋊C4—224no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—442no—
1039C22⋊C4—442no—
1040C22⋊C4—442no—
1041C22⋊C4C2×C4×D1114yes—
1042C22⋊C4C2×C4×D1118yescomplemented
1043C42—22no—
1044C42—42no—
1045C42—222no—
1046C42—222no—
1047C42—224no—
1048C42—224no—
1049C42—222no—
1050C42—442no—
1051C42—442no—
1052C42—442no—
1053C11#3426411yescharacteristic, complemented, Sylow
1054C23—22no—
1055C23—22no—
1056C23—28no—
1057C23—22no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—48no—
1068C23—44no—
1069C23—48no—
1070C23—44no—
1071C23—112no—
1072C23—112no—
1073C23—112no—
1074C23—112no—
1075C23—112no—
1076C23—112no—
1077C23—1116no—
1078C23—112no—
1079C23—228no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—221no—
1085C23—221no—
1086C23—222no—
1087C23—222no—
1088C23—444no—
1089C23—448no—
1090C23—444no—
1091C23—448no—
1092C23—448no—
1093C23—884no—
1094C23—882no—
1095C23—882no—
1096C23C22×C4×D1112yes—
1097C23C22×C4×D1114yes—
1098C23C22×C4×D1112yes—
1099C23C2×D4×D1112yes—
1100C23#41×D1112yes—
1101C23C24×D1111yescharacteristic
1102D4—28no—
1103D4—48no—
1104D4—228no—
1105D4—228no—
1106D4—2216no—
1107D4—2216no—
1108D4—228no—
1109D4—448no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—82no—
1129C2×C4—114no—
1130C2×C4—112no—
1131C2×C4—114no—
1132C2×C4—112no—
1133C2×C4—112no—
1134C2×C4—114no—
1135C2×C4—228no—
1136C2×C4—228no—
1137C2×C4—228no—
1138C2×C4—221no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—221no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—221no—
1149C2×C4—221no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—448no—
1156C2×C4—448no—
1157C2×C4—448no—
1158C2×C4—444no—
1159C2×C4—448no—
1160C2×C4—448no—
1161C2×C4—882no—
1162C2×C4—882no—
1163C2×C4—884no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4C22×C4×D1114yes—
1168C2×C4C22×C4×D1112yes—
1169C2×C4C2×D4×D1112yes—
1170C2×C4C2×D4×D1112yes—
1171C22—24no—
1172C22—22no—
1173C22—22no—
1174C22—24no—
1175C22—22no—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—416no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—41no—
1186C22—41no—
1187C22—42no—
1188C22—114no—
1189C22—114no—
1190C22—224no—
1191C22—224no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—224no—
1197C22—224no—
1198C22—222no—
1199C22—224no—
1200C22—4416no—
1201C22—442no—
1202C22—441no—
1203C22—441no—
1204C22—888no—
1205C22C4×D4×D1114yes—
1206C22C23×C4×D1111yescharacteristic
1207C22C22×D4×D1111yescharacteristic
1208C22C2×#41×D1111yescharacteristic
1209C22D11×H(5,𝔽2)12yes—
1210C22#1062345512yes—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—24no—
1215C4—42no—
1216C4—42no—
1217C4—41no—
1218C4—41no—
1219C4—224no—
1220C4—222no—
1221C4—222no—
1222C4—222no—
1223C4—224no—
1224C4—224no—
1225C4—442no—
1226C4—441no—
1227C4—441no—
1228C2—24no—
1229C2—44no—
1230C2—42no—
1231C2—224no—
1232C2—224no—
1233C2—442no—
1234C2C2×C4×D4×D1111yescharacteristic
1235C2#1308182012yes—
1236C2#1308225011yescharacteristic
1237C2#1308225711yescharacteristic
1238C2#1308245412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2321C2
socle, cosocleC23×C11C25
prime radicalC2×#10623120C2
hypercenter#2321D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13071665C2semidirect
5. #13071660C2semidirect
6. #13071637C2semidirect
7. #13071629C2semidirect
8. #13071607C2semidirect
9. #13071605C2semidirect
10. #13071597C2semidirect
11. #13071596C2semidirect
12. #13071290C2semidirect
13. #13071284C2semidirect
14. #13071274C2semidirect
15. #13071192C2semidirect
16. C4×#66939C2semidirect
17. C4×#66988C2semidirect
18. #120×Dic11C2semidirect
19. #13071115C2semidirect
20. D11×#386C2semidirect
21. D11×#385C2semidirect
22. #13070968C2semidirect
23. C11×#2321C2semidirect
25. C24×Dic11C22semidirect
30. C22×C11×C22⋊C4C22semidirect
36. C2×D4×Dic11C22semidirect
38. C2×C4×C22⋊D11C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×C4×Dic11C22semidirect
43. #10623120C4semidirect
45. C2×#66946C22semidirect
46. C2×#66945C22semidirect
47. C2×C4⋊C4×D11C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
58. C2×(C22⋊D11)⋊C4C22semidirect
62. C2×C22⋊C4×D11C22semidirect
63. C2×C22⋊C4×D11C22semidirect
64. C2×C4×D44C22semidirect
65. C2×#66925C22semidirect
66. C11×#390C22semidirect
67. C11×#388C22semidirect
68. C11×#388C22semidirect
70. C11×#386C22semidirect
71. C11×#385C22semidirect
72. C11×#379C22semidirect
73. C4×C11×C22⋊C4C22semidirect
74. #10622860C22semidirect
76. #10622833C22semidirect
78. #10622823C22semidirect
79. C4×C22⋊Dic11C22semidirect
80. C4×C22⋊Dic11C22semidirect
81. #10622602C22semidirect
82. #10622602C22semidirect
83. #10622591C22semidirect
84. #10622586C22semidirect
86. #10622571C22semidirect
87. #10622570C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
94. #10622563C22semidirect
95. #10622563C22semidirect
96. #10622559C22semidirect
97. #10622559C22semidirect
98. #10622559C22semidirect
99. #10622558C22semidirect
100. #10622557C22semidirect
101. #10622557C22semidirect
102. #10622557C22semidirect
103. #10622556C22semidirect
104. #10622556C22semidirect
105. C22⋊C4×Dic11C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C22⋊C4×Dic11C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. C4×(C2×D11)⋊C4C22semidirect
112. C4×C4⋊Dic11C22semidirect
113. C4×Dic11⋊C4C22semidirect
114. #10622283C22semidirect
115. #10622282C22semidirect
116. #10622281C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
119. #10622278C22semidirect
120. D11×#95C22semidirect
121. D11×#95C22semidirect
122. #10622267C22semidirect
123. #10622266C22semidirect
124. #10622265C22semidirect
125. #10622260C22semidirect
136. C22×C22⋊D11C2×C4semidirect
152. C2×D4×D11C2×C4semidirect
165. C11×#120C2×C4semidirect
182. #67006C2×C4semidirect
192. #66991C2×C4semidirect
193. #66990C2×C4semidirect
194. #66988C2×C4semidirect
200. C2×(C2×D11)⋊C4D4semidirect
237. #66939C2×C4semidirect
238. #66937C2×C4semidirect
239. #66936C2×C4semidirect
251. C22⋊C4×D11C2×C4semidirect
286. C23×D11C22×C4semidirect
297. C2×D4×C11C22×C4semidirect
326. C2×C22⋊D11C22×C4semidirect
327. C2×C22⋊D11C22×C4semidirect
356. C2×D44C22×C4semidirect
379. C2×C4×D11C22×C4semidirect
380. C2×C4×D11C22×C4semidirect
392. C11×C22⋊C4C22×C4semidirect
402. C22⋊Dic11C22×C4semidirect
403. C22⋊Dic11C22×C4semidirect
411. (C2×D11)⋊C4C22×C4semidirect
412. (C2×D11)⋊C4C22×C4semidirect
419. C4⋊Dic11C22×C4semidirect
426. Dic11⋊C4C22×C4semidirect
449. #2321D11semidirect
498. C22×D11C4×D4semidirect
615. C22×C22⋊C4C2×D11semidirect
618. #390C2×D11semidirect
627. #388C2×D11semidirect
628. #388C2×D11semidirect
646. #386C2×D11semidirect
656. #385C2×D11semidirect
660. #379C2×D11semidirect
674. C4×C22⋊C4C2×D11semidirect
780. #120C4×D11semidirect
935. C2×D4C2×C4×D11semidirect
1042. C22⋊C4C2×C4×D11semidirect
1053. C11#34264semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C2×#106230762
C22×(C22⋊D11)⋊C42
#130716652
#130716602
#130716372
#130716292
#130716072
#130716052
#130715972
#130715962
#130712902
#130712842
#130712742
#130711922
C4×#669392
C4×#669882
#120×Dic112
#130711152
D11×#3862
D11×#3852
#130709682
C11×#23212
#3426411