Finite Group Databasebeta

← #14921952

Subgroups — #14921952

Order 2816.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13072861C212yesmaximal, complemented
4#13072677C212yesmaximal, complemented
5#13072518C212yesmaximal, complemented
6#13072490C211yesmaximal, characteristic, complemented
7#13072399C211yesmaximal, characteristic, complemented
8#13072340C211yesmaximal, characteristic, complemented
9#13072196C211yesmaximal, characteristic, complemented
10#13072106C211yesmaximal, characteristic, complemented
11#13072082C212yesmaximal, complemented
12#13072068C211yesmaximal, characteristic, complemented
13#13071966C211yesmaximal, characteristic
14#13071872C212yesmaximal, complemented
15#13071859C212yesmaximal, complemented
16#124×Dic11C211yesmaximal, characteristic, complemented
17C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
18#13071132C211yesmaximal, characteristic, complemented
19#13071115C212yesmaximal, complemented
20#13071078C211yesmaximal, characteristic, complemented
21#13070994C212yesmaximal, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2435C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C24×Dic11C2212yes—
26C2×C11×#124C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×#67006C2212yes—
30C22×C22⋊Dic11C2212yes—
31C2×#66999C2211yescharacteristic, complemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C2×#66991C2211yescharacteristic
34C2×#66991C2211yescharacteristic
35C2×D4×Dic11—28no—
36C2×D4×Dic11C2212yes—
37C2×D4×Dic11C2211yescharacteristic
38C2×D4×Dic11C2211yescharacteristic
39C2×D4×Dic11C2212yes—
40C2×D4×Dic11C2211yescharacteristic
41C2×D4×Dic11C2211yescharacteristic
42C2×C4×C22⋊D11C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45#10623211—28no—
46C2×#66936C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2212yescomplemented
50C2×(C22⋊D11)⋊C4C2212yescomplemented
51C2×#66932C2212yescomplemented
52C2×#66930C2212yescomplemented
53C2×#66930C2212yescomplemented
54C2×C42×D11C2211yescharacteristic, complemented
55C2×#66923C2211yescharacteristic, complemented
56C11×#394C2212yes—
57C11×#394C2212yes—
58C11×#390C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#379C2212yes—
61C11×#379C2212yes—
62C4×C11×C22⋊C4C2211yescharacteristic
63#10622860C2212yes—
64#10622843C2211yescharacteristic, complemented
65#10622843C2211yescharacteristic, complemented
66#10622836C2212yes—
67#10622835C2212yes—
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70#10622825C2211yescharacteristic
71#10622607C2212yescomplemented
72#10622600C2211yescharacteristic, complemented
73#10622598C2211yescharacteristic, complemented
74#10622597C2212yescomplemented
75#10622594C2212yescomplemented
76C4⋊C4×Dic11C2212yescomplemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78#10622586C2211yescharacteristic, complemented
79#10622574C2212yescomplemented
80#10622572C2212yescomplemented
81#10622571C2212yes—
82#10622571C2212yescomplemented
83#10622571C2212yescomplemented
84#10622569C2212yescomplemented
85#10622566C2212yescomplemented
86#10622565C2212yescomplemented
87#10622565C2212yescomplemented
88#10622565C2212yescomplemented
89#10622564C2212yescomplemented
90#10622564C2212yescomplemented
91#10622563C2212yes—
92#10622562C2212yescomplemented
93#10622561C2212yescomplemented
94#10622559C2212yes—
95#10622559C2212yescomplemented
96#10622559C2212yescomplemented
97#10622558C2212yescomplemented
98#10622558C2212yescomplemented
99#10622557C2212yescomplemented
100#10622556C2212yescomplemented
101#10622556C2212yescomplemented
102#10622555C2212yes—
103#10622555C2212yes—
104#10622555C2212yescomplemented
105#10622555C2212yescomplemented
106C22⋊C4×Dic11C2212yes—
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2212yescomplemented
110C22⋊C4×Dic11C2212yescomplemented
111C22⋊C4×Dic11C2212yescomplemented
112C22⋊C4×Dic11C2212yescomplemented
113C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
114#10622549C2211yescharacteristic, complemented
115C4×Dic11⋊C4C2211yescharacteristic, complemented
116C42×Dic11C2211yescharacteristic, complemented
117#10622541C2211yescharacteristic, complemented
118#10622541C2211yescharacteristic, complemented
119#10622279C2211yescharacteristic, complemented
120#10622279C2211yescharacteristic, complemented
121#10622273C2212yescomplemented
122#10622270C2212yescomplemented
123#10622262C2211yescharacteristic, complemented
124#10622262C2211yescharacteristic, complemented
125C25×C11C2312yes—
126C22×Q8×C11C2311yescharacteristic
127C22×D4×C11—24no—
128C22×D4×C11—24no—
129C22×D4×C11—24no—
130C22×D4×C11C2312yes—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C23×Dic11—28no—
138C23×Dic11—28no—
139C23×Dic11—44no—
140C23×Dic11C2312yes—
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2312yes—
143C23×Dic11C2312yes—
144C23×Dic11C2312yes—
145C23×Dic11C2312yes—
146C23×Dic11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C11×#124—24no—
151C11×#124—24no—
152C11×C22⋊Q8—24no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168#67006—28no—
169C2×C22⋊Dic11—28no—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182#66999—24no—
183Q8×Dic11—24no—
184#66991—24no—
185#66991—24no—
186D4×Dic11—24no—
187D4×Dic11—28no—
188D4×Dic11—28no—
189D4×Dic11—24no—
190D4×Dic11—24no—
191D4×Dic11D418yescomplemented
192C4×C22⋊D11—24no—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×C4⋊Dic11—24no—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11—24no—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229#66936—28no—
230(C22⋊D11)⋊C4—24no—
231(C22⋊D11)⋊C4—28no—
232(C22⋊D11)⋊C4—24no—
233(C22⋊D11)⋊C4—44no—
234#66932—28no—
235#66930—28no—
236#66930—44no—
237C42×D11—24no—
238#66923—24no—
239C11×#95C2311yescharacteristic
240C11×#95C2311yescharacteristic
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#34700—111nomaximal, Sylow
259C24×C11—24no—
260C24×C11—24no—
261C24×C11—24no—
262C24×C11—24no—
263C24×C11—24no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11C2412yes—
267C24×C11C2412yes—
268C24×C11C2411yescharacteristic
269C23×D11C2411yescharacteristic
270C2×Q8×C11—22no—
271C2×Q8×C11—22no—
272C2×Q8×C11—22no—
273C2×D4×C11—232no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—24no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11C2×D414yes—
282C2×D4×C11#4114yes—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11#4114yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—24no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11#4114yes—
303C22×Dic11—22no—
304C22×Dic11—24no—
305C22×Dic11—24no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—24no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—24no—
313C22×Dic11—24no—
314C22×Dic11—24no—
315C22×Dic11—24no—
316C22×Dic11—22no—
317C22×Dic11—24no—
318C22×Dic11—42no—
319C22×Dic11—42no—
320C22×Dic11—42no—
321C22×Dic11—41no—
322C22×Dic11—432no—
323C22×Dic11C2×D418yes—
324C22×Dic11#4114yes—
325C22×Dic11C2412yes—
326C22×Dic11C2412yes—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C2×C4×D11—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—22no—
344C2×C4×D11—41no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—22no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4—42no—
358C42×C11—22no—
359C42×C11—22no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—24no—
363C22⋊Dic11—24no—
364C22⋊Dic11—24no—
365C22⋊Dic11—24no—
366C22⋊Dic11—22no—
367C22⋊Dic11—24no—
368C22⋊Dic11—24no—
369C22⋊Dic11—42no—
370C22⋊Dic11—42no—
371C22⋊Dic11C2×D418yes—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—22no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—42no—
377C4⋊Dic11—24no—
378C4⋊Dic11—24no—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—42no—
383C4⋊Dic11C2×D414yes—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386Dic11⋊C4—24no—
387Dic11⋊C4—22no—
388Dic11⋊C4—22no—
389Dic11⋊C4—22no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393C4×Dic11—22no—
394C4×Dic11—22no—
395C4×Dic11—24no—
396C4×Dic11—22no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—24no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—41no—
405C4×Dic11C2×D414yes—
406C2×#529—111no—
407C22×C4×D4—111no—
408#2480—112no—
409#2468—112no—
410#2457—112no—
411#2454—111no—
412#2447—111no—
413#2442—111no—
414#2435D1111yescharacteristic, complemented
415#2427—111no—
416#2420—111no—
417#2418—112no—
418#2417—111no—
419#2408—111no—
420#2395—112no—
421#2392—112no—
422C4×#124—111no—
423C4×C22⋊Q8—111no—
424C4×#121—111no—
425C4×#120—112no—
426#2293—111no—
427#2280—112no—
428C42×D4—111no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—216no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—48no—
447C23×C11—48no—
448C23×C11—48no—
449C23×C11—48no—
450C23×C11—48no—
451C23×C11—48no—
452C23×C11C22×D414yes—
453C23×C11C2×#4114yes—
454C23×C11C2×#4112yes—
455C23×C11C2×#4112yes—
456C23×C11C2×#4112yes—
457C23×C11C2511yescharacteristic
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11C2×#4112yes—
465Q8×C11—44no—
466D4×C11—216no—
467D4×C11—28no—
468D4×C11—28no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—28no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11C22×D412yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C22⋊D11—28no—
495C22⋊D11—48no—
496C22⋊D11—48no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—28no—
506C2×Dic11—216no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—48no—
526C2×Dic11—44no—
527C2×Dic11—48no—
528C2×Dic11—48no—
529C2×Dic11—48no—
530C2×Dic11C22×D412yes—
531C2×Dic11C22×D414yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C2×#4112yes—
534C2×Dic11C2×#4112yes—
535C2×Dic11C2×#4112yes—
536C2×Dic11H(5,𝔽2)12yes—
537C4×D11—44no—
538C4×D11—44no—
539C4×D11—44no—
540C23×D4C2×D1111yescharacteristic
541C24×C4—112no—
542#529—228no—
543C2×#126—112no—
544C2×#125—111no—
545C2×#124C2×D1111yescharacteristic
546C2×#124C2×D1111yescharacteristic
547C2×#123—112no—
548C2×C22⋊Q8—111no—
549C2×C22⋊Q8C2×D1111yescharacteristic
550C2×#121—111no—
551C2×#121—111no—
552C2×#120—112no—
553C2×C4×Q8—111no—
554C2×C4×D4—111no—
555C2×C4×D4—112no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—112no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—228no—
566C2×#117—112no—
567C2×#117—112no—
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C42—111no—
571C22×C42—111no—
572#400—112no—
573#399—112no—
574#398—112no—
575#398—112no—
576#397—112no—
577#397—112no—
578#397—112no—
579#397—112no—
580#396—112no—
581#396—112no—
582#394—112no—
583#394—112no—
584#394—112no—
585#394C2×D1112yes—
586#394C2×D1112yes—
587#392—112no—
588#391—111no—
589#391—111no—
590#390—111no—
591#390—111no—
592#390C2×D1111yescharacteristic
593#390C2×D1111yescharacteristic
594#389—111no—
595#389—111no—
596#389—111no—
597#389—111no—
598#388—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#387—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#385—112no—
612#382—111no—
613#381—112no—
614#381—112no—
615#380—111no—
616#380—111no—
617#380—112no—
618#380—112no—
619#380—112no—
620#380—112no—
621#379—112no—
622#379C2×D1112yes—
623#379C2×D1112yes—
624C4×C4⋊C4—112no—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—111no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—111no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—112no—
636C4×C22⋊C4—111no—
637C4×C22⋊C4—111no—
638C4×C22⋊C4—111no—
639C4×C22⋊C4C2×D1111yescharacteristic
640C43—111no—
641C22×C11—22no—
642C22×C11—22no—
643C22×C11—22no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—432no—
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#52914yescomplemented
663C22×C11C23×D411yescharacteristic
664C22×C11C22×#4111yescharacteristic
665C22×C11C22×#4111yescharacteristic
666C22×C11C22×#4111yescharacteristic
667C22×C11C22×#4111yescharacteristic
668C22×C11C2×H(5,𝔽2)11yescharacteristic
669C22×C11#58511yescharacteristic
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—41no—
674C2×D11—41no—
675C2×D11—41no—
676C2×D11—41no—
677C4×C11—22no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11—41no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—41no—
684C4×C11#52514yes—
685Dic11—22no—
686Dic11—22no—
687Dic11—24no—
688Dic11—22no—
689Dic11—41no—
690Dic11—41no—
691Dic11—42no—
692Dic11—41no—
693Dic11—42no—
694Dic11—42no—
695Dic11#54614yes—
696C25C22×D1112yes—
697C22×Q8C22×D1111yescharacteristic
698C22×D4—24no—
699C22×D4—24no—
700C22×D4—24no—
701C22×D4—111no—
702C22×D4—112no—
703C22×D4—112no—
704C22×D4C22×D1112yes—
705C22×D4C22×D1111yescharacteristic
706C22×D4C22×D1111yescharacteristic
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—111no—
711C23×C4—112no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—111no—
717C23×C4—228no—
718C23×C4—228no—
719C23×C4—444no—
720C23×C4C22×D1111yescharacteristic
721#126—228no—
722#125—224no—
723#124—24no—
724#124—24no—
725#123—228no—
726C22⋊Q8—24no—
727C22⋊Q8—224no—
728#121—224no—
729#121—224no—
730#120—228no—
731C4×Q8—224no—
732C4×D4—118no—
733C4×D4—224no—
734C4×D4—228no—
735C4×D4—224no—
736C4×D4—224no—
737C4×D4—228no—
738C4×D4—224no—
739C4×D4—228no—
740C4×D4—224no—
741C4×D4—224no—
742C4×D4—444no—
743#117—228no—
744#117—444no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—224no—
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1112yes—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—228no—
782C2×C22⋊C4C22×D1112yes—
783C2×C22⋊C4C22×D1112yes—
784C2×C22⋊C4C22×D1111yescharacteristic
785C2×C22⋊C4C22×D1111yescharacteristic
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1112yes—
788C2×C22⋊C4C22×D1112yes—
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1112yes—
793C2×C42—111no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—112no—
797C2×C42—112no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—111no—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—224no—
807C2×C42—224no—
808C2×C42C22×D1111yescharacteristic
809C2×C42C22×D1111yescharacteristic
810#95—111no—
811#95—111no—
812#95—111no—
813#95—111no—
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#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95C22×D1111yescharacteristic
828#95C22×D1111yescharacteristic
829C2×C11—24no—
830C2×C11—44no—
831C2×C11—44no—
832C2×C11C2×#52511yescharacteristic
833C2×C11C2×#52911yescharacteristic
834C2×C11#346011yescharacteristic
835C2×C11C2×#54611yescharacteristic
836C2×C11D4×#4111yescharacteristic
837C2×C11#347511yescharacteristic
838C2×C11#348111yescharacteristic
839D11—42no—
840C24—24no—
841C24—24no—
842C24—24no—
843C24—24no—
844C24—24no—
845C24—42no—
846C24—42no—
847C24—111no—
848C24C23×D1112yes—
849C24C23×D1112yes—
850C24C23×D1111yescharacteristic
851C2×Q8—22no—
852C2×Q8—22no—
853C2×Q8—22no—
854C2×D4—232no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—22no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—114no—
863C2×D4—222no—
864C2×D4—222no—
865C2×D4—224no—
866C2×D4—224no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—442no—
870C2×D4—442no—
871C2×D4D4×D1114yes—
872C2×D4#434114yes—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—111no—
876C22×C4—118no—
877C22×C4—114no—
878C22×C4—111no—
879C22×C4—111no—
880C22×C4—111no—
881C22×C4—112no—
882C22×C4—112no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—111no—
886C22×C4—111no—
887C22×C4—112no—
888C22×C4—222no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—224no—
895C22×C4—224no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—222no—
907C22×C4—224no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—441no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—442no—
915C22×C4—441no—
916C22×C4—4432no—
917C22×C4#434114yes—
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1112yes—
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—22no—
927C4⋊C4—24no—
928C4⋊C4—114no—
929C4⋊C4—224no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—224no—
933C4⋊C4—222no—
934C4⋊C4—222no—
935C4⋊C4—224no—
936C4⋊C4—222no—
937C4⋊C4—222no—
938C4⋊C4—222no—
939C4⋊C4—222no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—118no—
956C22⋊C4—224no—
957C22⋊C4—222no—
958C22⋊C4—222no—
959C22⋊C4—224no—
960C22⋊C4—224no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—224no—
964C22⋊C4—224no—
965C22⋊C4—222no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—222no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C42—22no—
973C42—22no—
974C42—114no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—222no—
979C42—224no—
980C42—222no—
981C42—224no—
982C42—222no—
983C42—222no—
984C42—222no—
985C42—222no—
986C42—441no—
987C11#3470011yescharacteristic, complemented, Sylow
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—216no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—48no—
1006C23—48no—
1007C23—48no—
1008C23—48no—
1009C23—48no—
1010C23—48no—
1011C23—112no—
1012C23—221no—
1013C23—221no—
1014C23—221no—
1015C23—221no—
1016C23—221no—
1017C23—221no—
1018C23C2×D4×D1114yes—
1019C23C2×#434114yes—
1020C23C2×#434112yes—
1021C23#41×D1112yes—
1022C23#41×D1112yes—
1023C23C24×D1111yescharacteristic
1024Q8—44no—
1025D4—216no—
1026D4—28no—
1027D4—28no—
1028D4—228no—
1029D4—448no—
1030D4—448no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—28no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—112no—
1053C2×C4—112no—
1054C2×C4—112no—
1055C2×C4—112no—
1056C2×C4—114no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—228no—
1060C2×C4—2216no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—221no—
1074C2×C4—221no—
1075C2×C4—221no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—222no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—221no—
1087C2×C4—444no—
1088C2×C4—444no—
1089C2×C4—448no—
1090C2×C4—448no—
1091C2×C4—448no—
1092C2×C4—448no—
1093C2×C4—444no—
1094C2×C4—444no—
1095C2×C4C2×D4×D1112yes—
1096C2×C4C2×#434112yes—
1097C2×C4C2×#434112yes—
1098C2×C4C2×#434112yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—432no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—222no—
1121C22—222no—
1122C22—222no—
1123C22—441no—
1124C22—441no—
1125C22—441no—
1126C22—441no—
1127C22#1062321114yescomplemented
1128C22C22×D4×D1111yescharacteristic
1129C22C22×#434111yescharacteristic
1130C22C22×#434111yescharacteristic
1131C22C2×#41×D1111yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22D11×H(5,𝔽2)11yescharacteristic
1134C22#1062345511yescharacteristic
1135C4—22no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—41no—
1140C4—41no—
1141C4—42no—
1142C4—114no—
1143C4—222no—
1144C4—222no—
1145C4—224no—
1146C4—222no—
1147C4—442no—
1148C4—441no—
1149C4—442no—
1150C4—441no—
1151C4—442no—
1152C4—441no—
1153C4#1062311714yes—
1154C2—24no—
1155C2—44no—
1156C2—44no—
1157C2—442no—
1158C2C2×#1062311711yescharacteristic
1159C2C2×#1062321111yescharacteristic
1160C2#1308202911yescharacteristic
1161C2D11×#54611yescharacteristic
1162C2#1308210011yescharacteristic
1163C2#1308216711yescharacteristic
1164C2#1308222111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2435C2
prime radical#13071966C2
hypercenter#2435D11
hypocenterC11#34700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. C2×#10623211C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13072861C2semidirect
4. #13072677C2semidirect
5. #13072518C2semidirect
6. #13072490C2semidirect
7. #13072399C2semidirect
8. #13072340C2semidirect
9. #13072196C2semidirect
10. #13072106C2semidirect
11. #13072082C2semidirect
12. #13072068C2semidirect
14. #13071872C2semidirect
15. #13071859C2semidirect
16. #124×Dic11C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. #13071132C2semidirect
19. #13071115C2semidirect
20. #13071078C2semidirect
21. #13070994C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2435C2semidirect
31. C2×#66999C22semidirect
32. C2×Q8×Dic11C22semidirect
46. C2×#66936C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66932C22semidirect
52. C2×#66930C22semidirect
53. C2×#66930C22semidirect
54. C2×C42×D11C22semidirect
55. C2×#66923C22semidirect
64. #10622843C22semidirect
65. #10622843C22semidirect
71. #10622607C22semidirect
72. #10622600C22semidirect
73. #10622598C22semidirect
74. #10622597C22semidirect
75. #10622594C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. #10622586C22semidirect
79. #10622574C22semidirect
80. #10622572C22semidirect
82. #10622571C22semidirect
83. #10622571C22semidirect
84. #10622569C22semidirect
85. #10622566C22semidirect
86. #10622565C22semidirect
87. #10622565C22semidirect
88. #10622565C22semidirect
89. #10622564C22semidirect
90. #10622564C22semidirect
92. #10622562C22semidirect
93. #10622561C22semidirect
95. #10622559C22semidirect
96. #10622559C22semidirect
97. #10622558C22semidirect
98. #10622558C22semidirect
99. #10622557C22semidirect
100. #10622556C22semidirect
101. #10622556C22semidirect
104. #10622555C22semidirect
105. #10622555C22semidirect
109. C22⋊C4×Dic11C22semidirect
110. C22⋊C4×Dic11C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. C4×(C2×D11)⋊C4C22semidirect
114. #10622549C22semidirect
115. C4×Dic11⋊C4C22semidirect
116. C42×Dic11C22semidirect
117. #10622541C22semidirect
118. #10622541C22semidirect
119. #10622279C22semidirect
120. #10622279C22semidirect
121. #10622273C22semidirect
122. #10622270C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
191. D4×Dic11D4semidirect
414. #2435D11semidirect
662. C22×C11#529semidirect
987. C11#34700semidirect
1127. C22#10623211semidirect

Maximal subgroups

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

subgroupindex
C2×#106232112
C22×D4×Dic112
#130728612
#130726772
#130725182
#130724902
#130723992
#130723402
#130721962
#130721062
#130720822
#130720682
#130719662
#130718722
#130718592
#124×Dic112
C22⋊Q8×Dic112
#130711322
#130711152
#130710782
#130709942
C4×(C22⋊D11)⋊C42
C11×#24352
#3470011