Finite Group Databasebeta

← #14921944

Subgroups — #14921944

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×#10623131C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13072859C212yesmaximal, complemented
4#13072675C212yesmaximal, complemented
5#13072516C212yesmaximal, complemented
6#13072491C211yesmaximal, characteristic, complemented
7#13072401C211yesmaximal, characteristic, complemented
8#13072341C211yesmaximal, characteristic, complemented
9#13072263C211yesmaximal, characteristic, complemented
10#13072195C211yesmaximal, characteristic, complemented
11#13072104C211yesmaximal, characteristic, complemented
12#13072074C212yesmaximal, complemented
13#13072067C211yesmaximal, characteristic, complemented
14#13071872C212yesmaximal, complemented
15#13071851C212yesmaximal, complemented
16#13071163C211yesmaximal, characteristic, complemented
17#13071144C211yesmaximal, characteristic, complemented
18#121×Dic11C211yesmaximal, characteristic, complemented
19#120×Dic11C212yesmaximal, complemented
20#13071078C211yesmaximal, characteristic, complemented
21#13070994C212yesmaximal, complemented
22C4×D4×Dic11C211yesmaximal, characteristic, complemented
23C11×#2408C211yesmaximal, characteristic
24C23×D4×C11C2211yescharacteristic
25C24×Dic11C2212yes—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120C2212yes—
29C2×C4×D4×C11C2211yescharacteristic
30C22×C22⋊Dic11C2212yes—
31C2×#66989C2211yescharacteristic
32C2×#66989C2211yescharacteristic
33C2×#66988C2212yescomplemented
34C2×D4×Dic11—28no—
35C2×D4×Dic11C2212yes—
36C2×D4×Dic11C2211yescharacteristic
37C2×D4×Dic11C2211yescharacteristic
38C2×D4×Dic11C2211yescharacteristic
39C2×D4×Dic11C2212yes—
40C2×D4×Dic11C2211yescharacteristic
41C2×D4×Dic11C2211yescharacteristic
42C2×D4×Dic11C2211yescharacteristic
43C2×D4×Dic11C2212yescomplemented
44C2×D4×Dic11C2212yescomplemented
45C22×C4⋊Dic11C2211yescharacteristic
46C2×#66977C2211yescharacteristic
47C2×#66977C2211yescharacteristic, complemented
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic, complemented
50#10623131—28no—
51C2×#66943C2211yescharacteristic, complemented
52C2×#66940C2211yescharacteristic, complemented
53C2×#66932C2212yescomplemented
54C2×#66930C2212yescomplemented
55C2×#66930C2212yescomplemented
56C11×#394C2212yes—
57C11×#392C2212yes—
58C11×#390C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#380C2211yescharacteristic
61C11×#379C2212yes—
62#10622860C2212yes—
63#10622860C2212yes—
64#10622835C2212yes—
65#10622835C2212yes—
66#10622835C2212yescomplemented
67#10622835C2212yescomplemented
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70#10622833C2212yes—
71#10622833C2212yescomplemented
72#10622833C2212yescomplemented
73#10622833C2212yescomplemented
74#10622825C2211yescharacteristic, complemented
75C4×C22⋊Dic11C2211yescharacteristic
76C4×C22⋊Dic11C2211yescharacteristic, complemented
77#10622598C2211yescharacteristic, complemented
78#10622597C2212yescomplemented
79#10622590C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83#10622587C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622566C2212yescomplemented
87#10622566C2212yescomplemented
88#10622565C2212yescomplemented
89#10622565C2212yescomplemented
90#10622564C2212yescomplemented
91#10622563C2212yes—
92#10622563C2212yescomplemented
93#10622563C2212yescomplemented
94#10622562C2212yescomplemented
95#10622561C2212yescomplemented
96#10622561C2212yescomplemented
97#10622559C2212yes—
98#10622558C2212yescomplemented
99#10622557C2212yescomplemented
100#10622557C2212yescomplemented
101#10622557C2212yescomplemented
102#10622556C2212yescomplemented
103#10622556C2212yescomplemented
104#10622555C2212yes—
105#10622555C2212yes—
106#10622555C2212yescomplemented
107#10622555C2212yescomplemented
108C22⋊C4×Dic11C2212yes—
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2212yescomplemented
112C22⋊C4×Dic11C2212yescomplemented
113C22⋊C4×Dic11C2212yescomplemented
114C22⋊C4×Dic11C2212yescomplemented
115C22⋊C4×Dic11C2211yescharacteristic, complemented
116C22⋊C4×Dic11C2211yescharacteristic, complemented
117C4×C4⋊Dic11C2211yescharacteristic, complemented
118C42×Dic11C2211yescharacteristic, complemented
119#10622542C2211yescharacteristic, complemented
120#10622541C2211yescharacteristic, complemented
121#10622274C2212yescomplemented
122#10622273C2212yescomplemented
123#10622265C2212yescomplemented
124#10622262C2212yescomplemented
125C25×C11C2312yes—
126C22×D4×C11—24no—
127C22×D4×C11—24no—
128C22×D4×C11—24no—
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C22×D4×C11C2312yes—
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×Dic11—28no—
138C23×Dic11—28no—
139C23×Dic11—44no—
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2312yes—
145C23×Dic11C2312yes—
146C23×Dic11C2312yes—
147C23×Dic11C2312yes—
148C23×Dic11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C11×#121—24no—
151C11×#121—24no—
152C11×#120—28no—
153C4×D4×C11—24no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C22⋊Dic11—28no—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187#66989—24no—
188#66989—24no—
189#66988—28no—
190D4×Dic11—24no—
191D4×Dic11—24no—
192D4×Dic11—28no—
193D4×Dic11—28no—
194D4×Dic11—24no—
195D4×Dic11—28no—
196D4×Dic11—24no—
197D4×Dic11—24no—
198D4×Dic11—44no—
199D4×Dic11D418yescomplemented
200C2×C4⋊Dic11—24no—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209#66977—24no—
210#66977—24no—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×C4×Dic11—24no—
219C2×C4×Dic11—24no—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
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
234#66943—24no—
235#66940—24no—
236#66932—28no—
237#66930—28no—
238#66930—44no—
239C11×#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
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
269C24×C11C2411yescharacteristic
270C2×D4×C11—232no—
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—24no—
277C2×D4×C11—24no—
278C2×D4×C11—24no—
279C2×D4×C11—22no—
280C2×D4×C11—24no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11C2×D414yes—
287C2×D4×C11#4114yes—
288C2×D4×C11#4114yes—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11#4114yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×Dic11—22no—
303C22×Dic11—24no—
304C22×Dic11—24no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—22no—
313C22×Dic11—24no—
314C22×Dic11—24no—
315C22×Dic11—24no—
316C22×Dic11—22no—
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—24no—
322C22×Dic11—42no—
323C22×Dic11—42no—
324C22×Dic11—42no—
325C22×Dic11—41no—
326C22×Dic11—41no—
327C22×Dic11—432no—
328C22×Dic11C2×D418yes—
329C22×Dic11#4114yes—
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2412yes—
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2412yes—
336C22×Dic11C2412yes—
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2412yes—
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2411yescharacteristic
342C2×Dic22—22no—
343C2×Dic22—22no—
344C2×Dic22—22no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—24no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C42×C11—22no—
358C22⋊Dic11—24no—
359C22⋊Dic11—24no—
360C22⋊Dic11—24no—
361C22⋊Dic11—22no—
362C22⋊Dic11—24no—
363C22⋊Dic11—24no—
364C22⋊Dic11—24no—
365C22⋊Dic11—24no—
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368C22⋊Dic11—22no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—42no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376C22⋊Dic11C2×D418yes—
377C4⋊Dic11—24no—
378C4⋊Dic11—24no—
379C4⋊Dic11—22no—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—22no—
383C4⋊Dic11—42no—
384C4⋊Dic11C2×D414yes—
385Dic11⋊C4—24no—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388Dic11⋊C4—24no—
389Dic11⋊C4—42no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392C4×Dic11—22no—
393C4×Dic11—24no—
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×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#2435—111no—
415#2427—111no—
416#2420—111no—
417#2418—112no—
418#2417—111no—
419#2408D1111yescharacteristic
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—21no—
435C23×C11—22no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—21no—
452C23×C11—48no—
453C23×C11—48no—
454C23×C11—48no—
455C23×C11—48no—
456C23×C11—48no—
457C23×C11—48no—
458C23×C11C22×D414yes—
459C23×C11C2×#4114yes—
460C23×C11C2×#4112yes—
461C23×C11C2×#4112yes—
462C23×C11C2×#4112yes—
463C23×C11C2×#4112yes—
464C23×C11C2511yescharacteristic
465D4×C11—216no—
466D4×C11—28no—
467D4×C11—28no—
468D4×C11—28no—
469D4×C11—48no—
470D4×C11—48no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—28no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—44no—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C2×#4112yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—28no—
501C2×Dic11—216no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—48no—
527C2×Dic11—44no—
528C2×Dic11—44no—
529C2×Dic11—48no—
530C2×Dic11—48no—
531C2×Dic11—44no—
532C2×Dic11—48no—
533C2×Dic11C22×D412yes—
534C2×Dic11C22×D414yes—
535C2×Dic11C22×D412yes—
536C2×Dic11C2×#4112yes—
537C2×Dic11C2×#4112yes—
538C2×Dic11H(5,𝔽2)12yes—
539Dic22—44no—
540C23×D4C2×D1111yescharacteristic
541C24×C4—112no—
542#529—228no—
543C2×#126—112no—
544C2×#125—111no—
545C2×#124—111no—
546C2×#124—111no—
547C2×#123—112no—
548C2×C22⋊Q8—111no—
549C2×C22⋊Q8—111no—
550C2×#121C2×D1111yescharacteristic
551C2×#121C2×D1111yescharacteristic
552C2×#120C2×D1112yes—
553C2×C4×Q8—111no—
554C2×C4×D4—111no—
555C2×C4×D4—112no—
556C2×C4×D4—112no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—112no—
564C2×C4×D4—228no—
565C2×C4×D4C2×D1111yescharacteristic
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#394—112no—
586#394C2×D1112yes—
587#392C2×D1112yes—
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—112no—
617#380—112no—
618#380—112no—
619#380—112no—
620#380C2×D1111yescharacteristic
621#379—112no—
622#379—112no—
623#379C2×D1112yes—
624C4×C4⋊C4—111no—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—112no—
629C4×C22⋊C4—111no—
630C4×C22⋊C4—111no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—112no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—111no—
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—22no—
650C22×C11—24no—
651C22×C11—22no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—22no—
655C22×C11—24no—
656C22×C11—432no—
657C22×C11—41no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—41no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—41no—
665C22×C11—42no—
666C22×C11—41no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11#52914yescomplemented
670C22×C11C23×D411yescharacteristic
671C22×C11C22×#4111yescharacteristic
672C22×C11C22×#4111yescharacteristic
673C22×C11C22×#4111yescharacteristic
674C22×C11C22×#4111yescharacteristic
675C22×C11C2×H(5,𝔽2)11yescharacteristic
676C22×C11#58511yescharacteristic
677C4×C11—22no—
678C4×C11—22no—
679C4×C11—41no—
680C4×C11—41no—
681C4×C11—42no—
682C4×C11—42no—
683C4×C11#52514yes—
684Dic11—22no—
685Dic11—24no—
686Dic11—22no—
687Dic11—42no—
688Dic11—42no—
689Dic11—41no—
690Dic11—42no—
691Dic11—41no—
692Dic11—41no—
693Dic11—41no—
694Dic11—41no—
695Dic11#54614yes—
696C25C22×D1112yes—
697C22×Q8—111no—
698C22×D4—24no—
699C22×D4—24no—
700C22×D4—24no—
701C22×D4C22×D1112yes—
702C22×D4C22×D1112yes—
703C22×D4C22×D1112yes—
704C22×D4C22×D1111yescharacteristic
705C22×D4C22×D1111yescharacteristic
706C22×D4C22×D1111yescharacteristic
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—112no—
715C23×C4—111no—
716C23×C4—228no—
717C23×C4—228no—
718C23×C4—444no—
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1111yescharacteristic
721#126—228no—
722#125—224no—
723#124—224no—
724#124—224no—
725#123—228no—
726C22⋊Q8—224no—
727C22⋊Q8—224no—
728#121—24no—
729#121—24no—
730#120—28no—
731C4×Q8—224no—
732C4×D4—24no—
733C4×D4—118no—
734C4×D4—224no—
735C4×D4—228no—
736C4×D4—224no—
737C4×D4—228no—
738C4×D4—228no—
739C4×D4—224no—
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—112no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—224no—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—228no—
784C2×C22⋊C4C22×D1112yes—
785C2×C22⋊C4C22×D1111yescharacteristic
786C2×C22⋊C4C22×D1111yescharacteristic
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—111no—
807C2×C42—224no—
808C2×C42—224no—
809C2×C42C22×D1111yescharacteristic
810#95—111no—
811#95—111no—
812#95—111no—
813#95—111no—
814#95—111no—
815#95—111no—
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#95—112no—
828#95C22×D1112yes—
829C2×C11—24no—
830C2×C11—42no—
831C2×C11—44no—
832C2×C11—44no—
833C2×C11C2×#52511yescharacteristic
834C2×C11C2×#52911yescharacteristic
835C2×C11#346011yescharacteristic
836C2×C11C2×#54611yescharacteristic
837C2×C11D4×#4111yescharacteristic
838C2×C11#347511yescharacteristic
839C2×C11#348111yescharacteristic
840C24—24no—
841C24—24no—
842C24—24no—
843C24—24no—
844C24—24no—
845C24—42no—
846C24—42no—
847C24C23×D1112yes—
848C24C23×D1112yes—
849C24C23×D1111yescharacteristic
850C24C23×D1111yescharacteristic
851C2×Q8—222no—
852C2×Q8—222no—
853C2×Q8—222no—
854C2×D4—232no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—22no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—22no—
864C2×D4—24no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4D4×D1114yes—
871C2×D4#434114yes—
872C2×D4#434114yes—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—111no—
879C22×C4—118no—
880C22×C4—114no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—112no—
886C22×C4—111no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—112no—
890C22×C4—112no—
891C22×C4—111no—
892C22×C4—222no—
893C22×C4—224no—
894C22×C4—224no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—224no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—442no—
915C22×C4—441no—
916C22×C4—441no—
917C22×C4—4432no—
918C22×C4#434114yes—
919C22×C4C23×D1112yes—
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1112yes—
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—114no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—224no—
933C4⋊C4—224no—
934C4⋊C4—222no—
935C4⋊C4—224no—
936C4⋊C4—222no—
937C4⋊C4—222no—
938C4⋊C4—224no—
939C4⋊C4—222no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C22⋊C4—24no—
945C22⋊C4—22no—
946C22⋊C4—24no—
947C22⋊C4—24no—
948C22⋊C4—22no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—118no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—224no—
957C22⋊C4—222no—
958C22⋊C4—224no—
959C22⋊C4—224no—
960C22⋊C4—224no—
961C22⋊C4—222no—
962C22⋊C4—222no—
963C22⋊C4—224no—
964C22⋊C4—224no—
965C22⋊C4—224no—
966C22⋊C4—222no—
967C22⋊C4—442no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C42—22no—
973C42—114no—
974C42—222no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—224no—
979C42—222no—
980C42—224no—
981C42—222no—
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—21no—
994C23—22no—
995C23—21no—
996C23—22no—
997C23—22no—
998C23—21no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—21no—
1011C23—48no—
1012C23—48no—
1013C23—48no—
1014C23—48no—
1015C23—48no—
1016C23—48no—
1017C23C2×D4×D1114yes—
1018C23C2×#434114yes—
1019C23C2×#434112yes—
1020C23C2×#434112yes—
1021C23C2×#434112yes—
1022C23#41×D1112yes—
1023C23C24×D1111yescharacteristic
1024Q8—444no—
1025D4—216no—
1026D4—28no—
1027D4—28no—
1028D4—28no—
1029D4—48no—
1030D4—48no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—28no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—44no—
1049C2×C4—112no—
1050C2×C4—112no—
1051C2×C4—112no—
1052C2×C4—112no—
1053C2×C4—114no—
1054C2×C4—112no—
1055C2×C4—228no—
1056C2×C4—2216no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—221no—
1074C2×C4—221no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—448no—
1088C2×C4—444no—
1089C2×C4—448no—
1090C2×C4—448no—
1091C2×C4—448no—
1092C2×C4—444no—
1093C2×C4—444no—
1094C2×C4C2×D4×D1112yes—
1095C2×C4C2×#434112yes—
1096C2×C4C2×#434112yes—
1097C2×C4C2×#434112yes—
1098C2×C4C2×#434112yes—
1099C22—22no—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—24no—
1107C22—22no—
1108C22—24no—
1109C22—24no—
1110C22—22no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—432no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—41no—
1123C22—42no—
1124C22—41no—
1125C22—42no—
1126C22—41no—
1127C22#1062313114yescomplemented
1128C22C22×D4×D1111yescharacteristic
1129C22C22×#434111yescharacteristic
1130C22C22×#434111yescharacteristic
1131C22C22×#434111yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22D11×H(5,𝔽2)11yescharacteristic
1134C22#1062345511yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—42no—
1138C4—41no—
1139C4—42no—
1140C4—41no—
1141C4—114no—
1142C4—222no—
1143C4—224no—
1144C4—222no—
1145C4—441no—
1146C4—441no—
1147C4—442no—
1148C4—442no—
1149C4—441no—
1150C4—441no—
1151C4—441no—
1152C4—442no—
1153C4#1062311714yes—
1154C2—24no—
1155C2—44no—
1156C2—44no—
1157C2—42no—
1158C2C2×#1062311711yescharacteristic
1159C2C2×#1062313111yescharacteristic
1160C2#1308202911yescharacteristic
1161C2D11×#54611yescharacteristic
1162C2D4×#434111yescharacteristic
1163C2#1308216711yescharacteristic
1164C2#1308221711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC11×#2408C2
hypercenter#2408D11
hypocenterC11#34700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10623131C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13072859C2semidirect
4. #13072675C2semidirect
5. #13072516C2semidirect
6. #13072491C2semidirect
7. #13072401C2semidirect
8. #13072341C2semidirect
9. #13072263C2semidirect
10. #13072195C2semidirect
11. #13072104C2semidirect
12. #13072074C2semidirect
13. #13072067C2semidirect
14. #13071872C2semidirect
15. #13071851C2semidirect
16. #13071163C2semidirect
17. #13071144C2semidirect
18. #121×Dic11C2semidirect
19. #120×Dic11C2semidirect
20. #13071078C2semidirect
21. #13070994C2semidirect
22. C4×D4×Dic11C2semidirect
33. C2×#66988C22semidirect
43. C2×D4×Dic11C22semidirect
44. C2×D4×Dic11C22semidirect
47. C2×#66977C22semidirect
49. C22×C4×Dic11C22semidirect
51. C2×#66943C22semidirect
52. C2×#66940C22semidirect
53. C2×#66932C22semidirect
54. C2×#66930C22semidirect
55. C2×#66930C22semidirect
66. #10622835C22semidirect
67. #10622835C22semidirect
71. #10622833C22semidirect
72. #10622833C22semidirect
73. #10622833C22semidirect
74. #10622825C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. #10622598C22semidirect
78. #10622597C22semidirect
79. #10622590C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. #10622587C22semidirect
84. #10622586C22semidirect
85. #10622586C22semidirect
86. #10622566C22semidirect
87. #10622566C22semidirect
88. #10622565C22semidirect
89. #10622565C22semidirect
90. #10622564C22semidirect
92. #10622563C22semidirect
93. #10622563C22semidirect
94. #10622562C22semidirect
95. #10622561C22semidirect
96. #10622561C22semidirect
98. #10622558C22semidirect
99. #10622557C22semidirect
100. #10622557C22semidirect
101. #10622557C22semidirect
102. #10622556C22semidirect
103. #10622556C22semidirect
106. #10622555C22semidirect
107. #10622555C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. C22⋊C4×Dic11C22semidirect
114. C22⋊C4×Dic11C22semidirect
115. C22⋊C4×Dic11C22semidirect
116. C22⋊C4×Dic11C22semidirect
117. C4×C4⋊Dic11C22semidirect
118. C42×Dic11C22semidirect
119. #10622542C22semidirect
120. #10622541C22semidirect
121. #10622274C22semidirect
122. #10622273C22semidirect
123. #10622265C22semidirect
124. #10622262C22semidirect
199. D4×Dic11D4semidirect
669. C22×C11#529semidirect
987. C11#34700semidirect
1127. C22#10623131semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
C22×D4×Dic112
#130728592
#130726752
#130725162
#130724912
#130724012
#130723412
#130722632
#130721952
#130721042
#130720742
#130720672
#130718722
#130718512
#130711632
#130711442
#121×Dic112
#120×Dic112
#130710782
#130709942
C4×D4×Dic112
C11×#24082
#3470011