Finite Group Databasebeta

← #14921951

Subgroups — #14921951

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×#10623088C211yesmaximal, characteristic, complemented
2#13072856C212yesmaximal, complemented
3#13072676C212yesmaximal, complemented
4#13072517C212yesmaximal, complemented
5#13072482C211yesmaximal, characteristic, complemented
6#13072397C211yesmaximal, characteristic, complemented
7#13072334C211yesmaximal, characteristic, complemented
8#13072263C211yesmaximal, characteristic, complemented
9#13072187C211yesmaximal, characteristic, complemented
10#13072102C211yesmaximal, characteristic, complemented
11#13072078C212yesmaximal, complemented
12#13072061C211yesmaximal, characteristic, complemented
13#13071966C211yesmaximal, characteristic
14#13071875C212yesmaximal, complemented
15#13071858C212yesmaximal, complemented
16C4×#66989C211yesmaximal, characteristic, complemented
17C4×#66977C211yesmaximal, characteristic, complemented
18C4×#66991C211yesmaximal, characteristic, complemented
19C4×#67006C212yesmaximal, complemented
20#13071081C211yesmaximal, characteristic, complemented
21#13070999C212yesmaximal, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C22×C4×D4×C11C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C24×C4×C11C2212yes—
26C2×C4×D4×C11—28no—
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C22×C11×C4⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2212yes—
35C22×C42×C11C2211yescharacteristic
36C2×#67006C2212yes—
37C2×#66991C2211yescharacteristic
38C2×#66991C2211yescharacteristic
39C2×#66989C2211yescharacteristic
40C2×#66989C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×C4×C22⋊D11C2211yescharacteristic
43C2×C4×C22⋊D11C2211yescharacteristic
44C2×C4×C22⋊D11C2212yescomplemented
45C2×C4×C22⋊D11C2212yescomplemented
46C2×#66979C2212yescomplemented
47C2×#66979C2212yescomplemented
48C2×#66977C2211yescharacteristic
49#10623088—28no—
50C2×#66950C2211yescharacteristic, complemented
51C2×#66943C2211yescharacteristic, complemented
52C2×#66936C2212yescomplemented
53C2×#66932C2212yescomplemented
54C2×C42×D11C2211yescharacteristic, complemented
55C2×C4×Dic22C2211yescharacteristic, complemented
56#10622860C2212yes—
57#10622860C2212yes—
58#10622860C2212yes—
59#10622836C2212yes—
60#10622835C2212yes—
61#10622835C2212yes—
62#10622835C2212yes—
63#10622834C2211yescharacteristic
64#10622834C2211yescharacteristic
65#10622834C2211yescharacteristic
66#10622834C2211yescharacteristic
67#10622826C2212yes—
68#10622826C2212yescomplemented
69#10622826C2212yescomplemented
70#10622825C2211yescharacteristic
71#10622825C2212yes—
72#10622825C2212yes—
73#10622825C2212yescomplemented
74#10622825C2212yescomplemented
75#10622824C2212yescomplemented
76#10622824C2212yescomplemented
77#10622823C2212yes—
78#10622823C2212yes—
79#10622823C2212yescomplemented
80#10622823C2212yescomplemented
81C4×C22⋊Dic11C2212yes—
82C4×C22⋊Dic11C2211yescharacteristic
83C4×C22⋊Dic11C2211yescharacteristic
84C4×C22⋊Dic11C2211yescharacteristic
85C4×C22⋊Dic11C2212yescomplemented
86C4×C22⋊Dic11C2212yescomplemented
87C4×C22⋊Dic11C2212yescomplemented
88C4×C22⋊Dic11C2212yescomplemented
89#10622607C2212yescomplemented
90#10622600C2211yescharacteristic, complemented
91#10622599C2212yescomplemented
92#10622598C2211yescharacteristic, complemented
93#10622598C2211yescharacteristic, complemented
94#10622597C2212yescomplemented
95#10622596C2212yescomplemented
96#10622590C2211yescharacteristic, complemented
97#10622587C2211yescharacteristic, complemented
98#10622586C2211yescharacteristic, complemented
99#10622574C2212yescomplemented
100#10622572C2212yescomplemented
101#10622569C2212yescomplemented
102#10622566C2212yescomplemented
103#10622565C2212yescomplemented
104#10622565C2212yescomplemented
105#10622565C2212yescomplemented
106#10622564C2212yescomplemented
107#10622564C2212yescomplemented
108#10622562C2212yescomplemented
109#10622561C2212yescomplemented
110#10622558C2212yescomplemented
111#10622558C2212yescomplemented
112#10622557C2212yescomplemented
113C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
114C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
115C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
116C4×C4⋊Dic11C2211yescharacteristic, complemented
117#10622546C2212yescomplemented
118C4×Dic11⋊C4C2211yescharacteristic, complemented
119C4×Dic11⋊C4C2212yescomplemented
120C4×Dic11⋊C4C2211yescharacteristic, complemented
121C4×Dic11⋊C4C2211yescharacteristic, complemented
122C42×Dic11C2211yescharacteristic, complemented
123#10622542C2211yescharacteristic, complemented
124#10622541C2211yescharacteristic, complemented
125C25×C11C2312yes—
126C22×D4×C11—24no—
127C22×D4×C11—24no—
128C22×D4×C11—24no—
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C23×C4×C11—28no—
133C23×C4×C11—28no—
134C23×C4×C11—44no—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2312yes—
138C23×C4×C11C2312yes—
139C23×C4×C11C2312yes—
140C23×C4×C11C2312yes—
141C23×C4×C11C2311yescharacteristic
142C23×C4×C11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C4×D4×C11—24no—
151C4×D4×C11—28no—
152C4×D4×C11—24no—
153C4×D4×C11—28no—
154C4×D4×C11—24no—
155C4×D4×C11D418yescomplemented
156C2×C11×C4⋊C4—24no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4—28no—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11—24no—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170#67006—28no—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
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—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190#66991—24no—
191#66991—24no—
192#66989—24no—
193#66989—24no—
194C4×C22⋊D11—28no—
195C4×C22⋊D11—24no—
196C4×C22⋊D11—24no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—44no—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2312yes—
204#66979—28no—
205#66979—44no—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213#66977—24no—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2311yescharacteristic
233#66950—24no—
234#66943—24no—
235#66936—28no—
236#66932—28no—
237C42×D11—24no—
238C4×Dic22—24no—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
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×D4×C11—232no—
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11C2×D414yes—
279C2×D4×C11#4114yes—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—24no—
289C22×C4×C11—22no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11—24no—
294C22×C4×C11—24no—
295C22×C4×C11—24no—
296C22×C4×C11—24no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—41no—
301C22×C4×C11—432no—
302C22×C4×C11C2×D418yes—
303C22×C4×C11#4114yes—
304C22×C4×C11#4114yes—
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C2×C22⋊D11—24no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11#4114yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2412yes—
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—41no—
342C2×Dic22—22no—
343C2×Dic22—22no—
344C2×Dic22—22no—
345C11×C4⋊C4—24no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4C2×D414yes—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4C2×D418yes—
352C42×C11—22no—
353C42×C11—22no—
354C42×C11—22no—
355C42×C11C2×D414yes—
356C22⋊Dic11—24no—
357C22⋊Dic11—24no—
358C22⋊Dic11—24no—
359C22⋊Dic11—24no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—22no—
363C22⋊Dic11—22no—
364C22⋊Dic11—22no—
365C22⋊Dic11—24no—
366C22⋊Dic11—24no—
367C22⋊Dic11—24no—
368C22⋊Dic11—24no—
369C22⋊Dic11—42no—
370C22⋊Dic11—42no—
371C22⋊Dic11—42no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—42no—
380C4⋊Dic11—22no—
381C4⋊Dic11—24no—
382C4⋊Dic11—24no—
383C4⋊Dic11—22no—
384C4⋊Dic11—22no—
385C4⋊Dic11—42no—
386C4⋊Dic11—42no—
387Dic11⋊C4—22no—
388Dic11⋊C4—24no—
389Dic11⋊C4—24no—
390Dic11⋊C4—24no—
391Dic11⋊C4—22no—
392Dic11⋊C4—22no—
393Dic11⋊C4—42no—
394Dic11⋊C4—42no—
395C4×Dic11—22no—
396C4×Dic11—24no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—24no—
405C4×Dic11—41no—
406C2×#529—111no—
407C22×C4×D4D1111yescharacteristic, complemented
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#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—
465D4×C11—216no—
466D4×C11—28no—
467D4×C11—28no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—28no—
477C2×C4×C11—28no—
478C2×C4×C11—216no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—21no—
485C2×C4×C11—48no—
486C2×C4×C11—44no—
487C2×C4×C11—48no—
488C2×C4×C11—48no—
489C2×C4×C11—48no—
490C2×C4×C11C22×D412yes—
491C2×C4×C11C22×D414yes—
492C2×C4×C11C22×D412yes—
493C2×C4×C11C22×D412yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C11C2×#4112yes—
496C2×C4×C11C2×#4112yes—
497C2×C4×C11C2×#4112yes—
498C2×C4×C11C2×#4112yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C22⋊D11—28no—
501C22⋊D11—48no—
502C22⋊D11—48no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11C2×#4112yes—
536C4×D11—44no—
537C4×D11—44no—
538C4×D11—44no—
539Dic22—44no—
540C23×D4C2×D1111yescharacteristic
541C24×C4C2×D1112yes—
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×#121—111no—
551C2×#121—111no—
552C2×#120—112no—
553C2×C4×Q8—111no—
554C2×C4×D4—28no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—112no—
559C2×C4×D4—112no—
560C2×C4×D4C2×D1112yes—
561C2×C4×D4C2×D1111yescharacteristic
562C2×C4×D4C2×D1111yescharacteristic
563C2×C4×D4C2×D1112yes—
564C2×C4×D4C2×D1111yescharacteristic
565C2×C4×D4C2×D1111yescharacteristic
566C2×#117—112no—
567C2×#117—112no—
568C22×C4⋊C4C2×D1111yescharacteristic
569C22×C22⋊C4C2×D1112yes—
570C22×C42—111no—
571C22×C42C2×D1111yescharacteristic
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#394—112no—
587#392—112no—
588#391—111no—
589#391—111no—
590#390—111no—
591#390—111no—
592#390—111no—
593#390—111no—
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#380—111no—
621#379—112no—
622#379—112no—
623#379—112no—
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—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—111no—
638C4×C22⋊C4—111no—
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—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—22no—
679C4×C11—24no—
680C4×C11—22no—
681C4×C11—42no—
682C4×C11—41no—
683C4×C11#52514yes—
684C4×C11#54614yes—
685Dic11—22no—
686Dic11—42no—
687Dic11—41no—
688Dic11—41no—
689Dic11—42no—
690Dic11—41no—
691Dic11—41no—
692Dic11—42no—
693Dic11—41no—
694Dic11—41no—
695Dic11—42no—
696C25C22×D1112yes—
697C22×Q8—111no—
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—28no—
708C23×C4—28no—
709C23×C4—44no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—111no—
713C23×C4C22×D1112yes—
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1112yes—
716C23×C4C22×D1112yes—
717C23×C4C22×D1112yes—
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1112yes—
721#126—228no—
722#125—224no—
723#124—224no—
724#124—224no—
725#123—228no—
726C22⋊Q8—224no—
727C22⋊Q8—224no—
728#121—224no—
729#121—224no—
730#120—228no—
731C4×Q8—224no—
732C4×D4—24no—
733C4×D4—28no—
734C4×D4—24no—
735C4×D4—28no—
736C4×D4—24no—
737C4×D4—224no—
738C4×D4—224no—
739C4×D4—224no—
740C4×D4—228no—
741C4×D4—444no—
742C4×D4C22⋊D1118yescomplemented
743#117—228no—
744#117—444no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—111no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C22⋊C4—28no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1112yes—
793C2×C42—24no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—111no—
797C2×C42—111no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—112no—
802C2×C42—112no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—224no—
806C2×C42C22×D1111yescharacteristic
807C2×C42C22×D1111yescharacteristic
808C2×C42C22×D1111yescharacteristic
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#95—112no—
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—222no—
852C2×Q8—222no—
853C2×Q8—222no—
854C2×D4—232no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—22no—
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×D4#433914yes—
872C2×D4C2×C22⋊D1114yes—
873C22×C4—22no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—41no—
894C22×C4—432no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—112no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—112no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—111no—
906C22×C4—222no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—441no—
915C22×C4#433914yes—
916C22×C4#434114yes—
917C22×C4C2×C22⋊D1118yes—
918C22×C4C23×D1112yes—
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1112yes—
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—222no—
929C4⋊C4—222no—
930C4⋊C4—222no—
931C4⋊C4—224no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—224no—
935C4⋊C4—224no—
936C4⋊C4—224no—
937C4⋊C4—222no—
938C4⋊C4—224no—
939C4⋊C4—442no—
940C4⋊C4—442no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4C2×C22⋊D1114yes—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—222no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—222no—
951C22⋊C4—224no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—222no—
956C22⋊C4—222no—
957C22⋊C4—224no—
958C22⋊C4—224no—
959C22⋊C4—224no—
960C22⋊C4—224no—
961C22⋊C4—222no—
962C22⋊C4—222no—
963C22⋊C4—224no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4—442no—
967C22⋊C4—442no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4C2×C22⋊D1118yes—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—222no—
979C42—222no—
980C42—224no—
981C42—222no—
982C42—222no—
983C42—222no—
984C42—224no—
985C42—441no—
986C42C2×C22⋊D1114yes—
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×#433914yes—
1019C23C2×#433912yes—
1020C23C2×#434112yes—
1021C23#41×D1112yes—
1022C23C22×C22⋊D1114yes—
1023C23C24×D1111yescharacteristic
1024Q8—444no—
1025D4—216no—
1026D4—28no—
1027D4—28no—
1028D4—228no—
1029D4—448no—
1030D4—448no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—216no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—48no—
1049C2×C4—44no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—112no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—221no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—222no—
1071C2×C4—221no—
1072C2×C4—221no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—222no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—444no—
1087C2×C4—444no—
1088C2×C4—444no—
1089C2×C4C2×#433912yes—
1090C2×C4C2×#433912yes—
1091C2×C4C2×#433912yes—
1092C2×C4C2×#434112yes—
1093C2×C4C2×#434112yes—
1094C2×C4#6703712yes—
1095C2×C4C22×C22⋊D1112yes—
1096C2×C4C22×C22⋊D1114yes—
1097C2×C4C22×C22⋊D1112yes—
1098C2×C4C22×C22⋊D1112yes—
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#1062308814yescomplemented
1128C22C22×#433911yescharacteristic
1129C22C22×#433911yescharacteristic
1130C22C22×#434111yescharacteristic
1131C22C2×#6703711yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22#1062345311yescharacteristic
1134C22C23×C22⋊D1111yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—24no—
1138C4—22no—
1139C4—42no—
1140C4—41no—
1141C4—222no—
1142C4—441no—
1143C4—442no—
1144C4—441no—
1145C4—442no—
1146C4—441no—
1147C4—441no—
1148C4—442no—
1149C4—441no—
1150C4—441no—
1151C4—442no—
1152C4#1062332214yes—
1153C4#1062333714yes—
1154C2—24no—
1155C2—44no—
1156C2—44no—
1157C2—442no—
1158C2C2×#1062332211yescharacteristic
1159C2C2×#1062308811yescharacteristic
1160C2#1308203811yescharacteristic
1161C2C2×#1062333711yescharacteristic
1162C2#41×C22⋊D1111yescharacteristic
1163C2#1308217411yescharacteristic
1164C2#1308222011yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
prime radical#13071966C2
hypercenterC22×C4×D4D11
hypocenterC11#34700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623088C2semidirect
2. #13072856C2semidirect
3. #13072676C2semidirect
4. #13072517C2semidirect
5. #13072482C2semidirect
6. #13072397C2semidirect
7. #13072334C2semidirect
8. #13072263C2semidirect
9. #13072187C2semidirect
10. #13072102C2semidirect
11. #13072078C2semidirect
12. #13072061C2semidirect
14. #13071875C2semidirect
15. #13071858C2semidirect
16. C4×#66989C2semidirect
17. C4×#66977C2semidirect
18. C4×#66991C2semidirect
19. C4×#67006C2semidirect
20. #13071081C2semidirect
21. #13070999C2semidirect
22. C42×C22⋊D11C2semidirect
23. C22×C4×D4×C11C2semidirect
44. C2×C4×C22⋊D11C22semidirect
45. C2×C4×C22⋊D11C22semidirect
46. C2×#66979C22semidirect
47. C2×#66979C22semidirect
50. C2×#66950C22semidirect
51. C2×#66943C22semidirect
52. C2×#66936C22semidirect
53. C2×#66932C22semidirect
54. C2×C42×D11C22semidirect
55. C2×C4×Dic22C22semidirect
68. #10622826C22semidirect
69. #10622826C22semidirect
73. #10622825C22semidirect
74. #10622825C22semidirect
75. #10622824C22semidirect
76. #10622824C22semidirect
79. #10622823C22semidirect
80. #10622823C22semidirect
85. C4×C22⋊Dic11C22semidirect
86. C4×C22⋊Dic11C22semidirect
87. C4×C22⋊Dic11C22semidirect
88. C4×C22⋊Dic11C22semidirect
89. #10622607C22semidirect
90. #10622600C22semidirect
91. #10622599C22semidirect
92. #10622598C22semidirect
93. #10622598C22semidirect
94. #10622597C22semidirect
95. #10622596C22semidirect
96. #10622590C22semidirect
97. #10622587C22semidirect
98. #10622586C22semidirect
99. #10622574C22semidirect
100. #10622572C22semidirect
101. #10622569C22semidirect
102. #10622566C22semidirect
103. #10622565C22semidirect
104. #10622565C22semidirect
105. #10622565C22semidirect
106. #10622564C22semidirect
107. #10622564C22semidirect
108. #10622562C22semidirect
109. #10622561C22semidirect
110. #10622558C22semidirect
111. #10622558C22semidirect
112. #10622557C22semidirect
113. C4×(C2×D11)⋊C4C22semidirect
114. C4×(C2×D11)⋊C4C22semidirect
115. C4×(C2×D11)⋊C4C22semidirect
116. C4×C4⋊Dic11C22semidirect
117. #10622546C22semidirect
118. C4×Dic11⋊C4C22semidirect
119. C4×Dic11⋊C4C22semidirect
120. C4×Dic11⋊C4C22semidirect
121. C4×Dic11⋊C4C22semidirect
122. C42×Dic11C22semidirect
123. #10622542C22semidirect
124. #10622541C22semidirect
155. C4×D4×C11D4semidirect
407. C22×C4×D4D11semidirect
662. C22×C11#529semidirect
742. C4×D4C22⋊D11semidirect
987. C11#34700semidirect
1127. C22#10623088semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130728562
#130726762
#130725172
#130724822
#130723972
#130723342
#130722632
#130721872
#130721022
#130720782
#130720612
#130719662
#130718752
#130718582
C4×#669892
C4×#669772
C4×#669912
C4×#670062
#130710812
#130709992
C42×C22⋊D112
C22×C4×D4×C112
#3470011