Finite Group Databasebeta

← #14925897

Subgroups — #14925897

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074205C212yesmaximal, complemented
4#13074201C212yesmaximal, complemented
5#13073967C212yesmaximal, complemented
6#13073966C211yesmaximal, characteristic, complemented
7#13073960C211yesmaximal, characteristic, complemented
8#13073511C211yesmaximal, characteristic, complemented
9#13073510C212yesmaximal, complemented
10#13073505C211yesmaximal, characteristic, complemented
11#13072895C211yesmaximal, characteristic, complemented
12#13071945C211yesmaximal, characteristic, complemented
13#13071940C211yesmaximal, characteristic, complemented
14#13071928C211yesmaximal, characteristic
15#13071860C212yesmaximal, complemented
16#13071856C212yesmaximal, complemented
17C4×#66947C212yesmaximal, complemented
18C4×#66982C211yesmaximal, characteristic, complemented
19C4×#66935C212yesmaximal, complemented
20C4×#66935C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C4×C11×#123C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C23×C4×D11C2211yescharacteristic, complemented
29C2×C11×#123C2211yescharacteristic
30C2×C4×D4×C11C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic, complemented
32C2×#66990C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×#66982C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic, complemented
37C2×C4×C22⋊D11C2212yescomplemented
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×C4⋊Dic11C2211yescharacteristic, complemented
41C4×D4×D11—28no—
42C2×#66947C2212yes—
43C2×#66946C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic, complemented
45C2×#66935C2212yes—
46C2×#66935C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic, complemented
51C2×C4×D44—28no—
52C2×C4×D44C2212yes—
53C2×C4×D44C2212yes—
54C2×C4×D44C2212yescomplemented
55C2×C4×D44C2211yescharacteristic, complemented
56C2×C4×D44C2212yescomplemented
57C2×C4×D44C2212yescomplemented
58C2×#66925C2212yescomplemented
59C2×C42×D11C2211yescharacteristic, complemented
60C11×#388C2212yescomplemented
61C11×#387C2212yescomplemented
62C11×#386C2211yescharacteristic
63C11×#385C2211yescharacteristic, complemented
64C11×#381C2211yescharacteristic, complemented
65C4×C11×C4⋊C4C2212yescomplemented
66C4×C11×C22⋊C4C2211yescharacteristic, complemented
67C4×C11×C22⋊C4C2212yescomplemented
68#10622833C2211yescharacteristic
69#10622826C2211yescharacteristic
70#10622824C2211yescharacteristic, complemented
71#10622823C2211yescharacteristic, complemented
72C4×C22⋊Dic11C2211yescharacteristic, complemented
73#10622607C2212yescomplemented
74#10622607C2212yescomplemented
75#10622604C2212yescomplemented
76#10622604C2212yescomplemented
77#10622603C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622594C2212yescomplemented
81#10622573C2212yes—
82#10622572C2212yescomplemented
83#10622572C2212yescomplemented
84#10622571C2211yescharacteristic
85#10622571C2212yescomplemented
86#10622569C2212yescomplemented
87#10622568C2211yescharacteristic
88#10622568C2211yescharacteristic
89#10622568C2211yescharacteristic, complemented
90#10622568C2212yescomplemented
91#10622568C2211yescharacteristic, complemented
92#10622563C2212yescomplemented
93#10622563C2211yescharacteristic, complemented
94#10622561C2212yescomplemented
95#10622559C2211yescharacteristic, complemented
96#10622555C2211yescharacteristic, complemented
97#10622555C2211yescharacteristic, complemented
98#10622553C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×(C2×D11)⋊C4C2212yescomplemented
103#10622546C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105#10622289C2212yescomplemented
106#10622288C2212yescomplemented
107#10622287C2212yescomplemented
108#10622285C2212yescomplemented
109#10622285C2212yescomplemented
110#10622284C2212yes—
111#10622282C2212yescomplemented
112#10622281C2212yescomplemented
113#10622281C2212yescomplemented
114#10622281C2212yescomplemented
115#10622280C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622277C2212yescomplemented
121#10622277C2212yescomplemented
122#10622274C2212yescomplemented
123#10622270C2212yescomplemented
124#10622268C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C22×D44—24no—
143C22×D44—28no—
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×D44C2312yes—
148C22×C4×D11—24no—
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11—44no—
152C22×C4×D11—44no—
153C22×C4×D11D418yescomplemented
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C11×#123—24no—
166C4×D4×C11—24no—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C42×C11—24no—
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2312yes—
179C2×C42×C11C2312yes—
180C2×C42×C11C2312yes—
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2312yes—
186#66990—24no—
187D4×Dic11—24no—
188#66982—24no—
189C4×C22⋊D11—24no—
190C4×C22⋊D11—24no—
191C4×C22⋊D11—44no—
192C2×(C2×D11)⋊C4—24no—
193C2×(C2×D11)⋊C4—24no—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×C4⋊Dic11—24no—
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2312yes—
218C2×C4⋊Dic11C2311yescharacteristic
219C2×C4⋊Dic11C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2312yes—
231#66947—28no—
232#66946—24no—
233C4⋊C4×D11—24no—
234#66935—24no—
235#66935—28no—
236(C22⋊D11)⋊C4—24no—
237(C22⋊D11)⋊C4—24no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240C4×D44—28no—
241C4×D44—28no—
242C4×D44—28no—
243C4×D44—28no—
244C4×D44—24no—
245C4×D44—44no—
246#66925—44no—
247C42×D11—24no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34956—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—24no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11—42no—
281C23×D11C2×D414yes—
282C23×D11C2411yescharacteristic
283C23×D11C2412yes—
284C23×D11C2411yescharacteristic
285C23×D11C2411yescharacteristic
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11#4114yes—
289C22×C4×C11—22no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—24no—
297C22×C4×C11C2×D414yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11#4114yes—
316C22×Dic11—22no—
317C22×Dic11—22no—
318C22×Dic11—42no—
319C22×Dic11—42no—
320C22×Dic11—42no—
321C22×Dic11C2×D414yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2412yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2412yes—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330D4×D11—232no—
331C2×D44—232no—
332C2×D44—24no—
333C2×D44—24no—
334C2×D44—22no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—22no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—22no—
342C2×D44—42no—
343C2×D44#4118yes—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—416no—
366C2×C4×D11—416no—
367C2×C4×D11—416no—
368C2×C4×D11C2×D414yes—
369C2×C4×D11C2×D414yes—
370C2×C4×D11C2×D414yes—
371C2×C4×D11C2×D414yes—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—24no—
374C11×C4⋊C4—24no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—24no—
379C11×C22⋊C4—22no—
380C11×C22⋊C4—24no—
381C42×C11—22no—
382C42×C11—24no—
383C42×C11—24no—
384C42×C11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388C22⋊Dic11—22no—
389C22⋊Dic11—42no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—22no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—24no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408(C2×D11)⋊C4—42no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411C4⋊Dic11—24no—
412C4⋊Dic11—24no—
413C4⋊Dic11—22no—
414C4⋊Dic11—42no—
415Dic11⋊C4—22no—
416Dic11⋊C4—24no—
417Dic11⋊C4—22no—
418Dic11⋊C4—24no—
419Dic11⋊C4—42no—
420Dic11⋊C4—42no—
421Dic11⋊C4—42no—
422C4×Dic11—22no—
423C4×Dic11—22no—
424C4×Dic11—22no—
425C4×Dic11—24no—
426C22×C4×D4—111no—
427C22×C4×D4—111no—
428#2600—112no—
429#2600—112no—
430#2579—112no—
431#2579—111no—
432#2579—111no—
433#2534—112no—
434#2534—111no—
435#2534—111no—
436#2483—111no—
437#2405—111no—
438#2405—111no—
439#2403—111no—
440#2392—112no—
441#2392—112no—
442C4×#123—111no—
443C4×#123—112no—
444C4×#123D1111yescharacteristic, complemented
445C4×#120—111no—
446C4×#120—112no—
447C4×#120—111no—
448#2280—111no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—21no—
454C23×C11—22no—
455C23×C11C22×D412yes—
456C23×C11C2×#4112yes—
457C23×C11C2×#4112yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—28no—
466C22×D11—22no—
467C22×D11—21no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—21no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—28no—
481C22×D11—44no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—48no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11—44no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—44no—
492C22×D11C22×D412yes—
493C22×D11C22×D412yes—
494C22×D11C2×#4112yes—
495C22×D11C2×#4114yes—
496C22×D11C2×#4114yes—
497D4×C11—28no—
498C2×C4×C11—28no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—28no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—44no—
519C2×C4×C11—44no—
520C2×C4×C11C22×D412yes—
521C2×C4×C11C22×D412yes—
522C2×C4×C11C2×#4112yes—
523C2×C4×C11C2×#4114yes—
524C2×C4×C11H(5,𝔽2)14yes—
525C22⋊D11—28no—
526C22⋊D11—28no—
527C22⋊D11—48no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—44no—
546C2×Dic11—44no—
547C2×Dic11—44no—
548C2×Dic11C22×D412yes—
549C2×Dic11C22×D412yes—
550C2×Dic11C2×#4112yes—
551D44—216no—
552D44—28no—
553D44—216no—
554D44—48no—
555C4×D11—28no—
556C4×D11—28no—
557C4×D11—28no—
558C4×D11—44no—
559C4×D11—44no—
560C4×D11—44no—
561C4×D11—48no—
562C4×D11—44no—
563C4×D11—44no—
564C4×D11—48no—
565C4×D11—44no—
566C23×D4—111no—
567C23×D4—111no—
568C24×C4—111no—
569C24×C4—111no—
570C24×C4—111no—
571C2×#123—111no—
572C2×#123—112no—
573C2×#123C2×D1111yescharacteristic
574C2×#120—111no—
575C2×#120—112no—
576C2×#120—111no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—112no—
581C2×C4×D4—111no—
582C2×C4×D4—111no—
583C2×C4×D4—111no—
584C2×C4×D4—112no—
585C2×C4×D4—112no—
586C2×C4×D4—112no—
587C2×C4×D4—112no—
588C2×C4×D4—111no—
589C2×C4×D4—112no—
590C2×C4×D4—228no—
591C2×C4×D4—228no—
592C2×C4×D4C2×D1111yescharacteristic
593C2×#117—112no—
594C22×C4⋊C4—111no—
595C22×C4⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C42—111no—
601C22×C42C2×D1111yescharacteristic, complemented
602#398—112no—
603#398—112no—
604#397—112no—
605#397—112no—
606#396—112no—
607#396—112no—
608#396—112no—
609#396—112no—
610#394—112no—
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#394—112no—
616#392—112no—
617#392—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388C2×D1112yescomplemented
622#387—112no—
623#387—112no—
624#387—112no—
625#387C2×D1112yescomplemented
626#386—111no—
627#386—111no—
628#386—111no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—112no—
635#386C2×D1111yescharacteristic
636#385—111no—
637#385—112no—
638#385—112no—
639#385—112no—
640#385—111no—
641#385—111no—
642#385—112no—
643#385—112no—
644#385—112no—
645#385C2×D1111yescharacteristic, complemented
646#381—111no—
647#381—112no—
648#381—112no—
649#381C2×D1111yescharacteristic, complemented
650#380—111no—
651#380—111no—
652#380—112no—
653#379—111no—
654#379—111no—
655#379—111no—
656#379—111no—
657#379—112no—
658C4×C4⋊C4—112no—
659C4×C4⋊C4C2×D1112yescomplemented
660C4×C22⋊C4—111no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4—112no—
663C4×C22⋊C4—112no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4C2×D1112yescomplemented
666C4×C22⋊C4C2×D1111yescharacteristic, complemented
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—24no—
670C22×C11—24no—
671C22×C11—22no—
672C22×C11—24no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11#52514yes—
677C22×C11C23×D411yescharacteristic
678C22×C11C22×#4111yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C22×#4112yes—
681C22×C11C2×H(5,𝔽2)12yes—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—24no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—24no—
694C2×D11—416no—
695C2×D11—416no—
696C2×D11—416no—
697C2×D11—42no—
698C2×D11—41no—
699C2×D11—42no—
700C2×D11—41no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11#52514yes—
707C4×C11—24no—
708C4×C11—22no—
709C4×C11—22no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11#53414yes—
716Dic11—22no—
717Dic11—22no—
718Dic11—22no—
719Dic11—41no—
720Dic11—42no—
721Dic11—41no—
722Dic11—42no—
723Dic11—42no—
724C25—111no—
725C25—111no—
726C25—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—228no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—224no—
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—118no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—112no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—112no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4—444no—
758C23×C4—444no—
759C23×C4—444no—
760C23×C4C22×D1111yescharacteristic
761C23×C4C22×D1111yescharacteristic
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764#123—24no—
765#123—228no—
766#123—224no—
767#120—224no—
768#120—228no—
769#120—224no—
770C4×D4—24no—
771C4×D4—228no—
772C4×D4—228no—
773C4×D4—228no—
774C4×D4—228no—
775C4×D4—224no—
776C4×D4—224no—
777C4×D4—224no—
778C4×D4—224no—
779C4×D4—224no—
780C4×D4—224no—
781C4×D4—224no—
782C4×D4—444no—
783C4×D4—444no—
784#117—444no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—224no—
797C2×C4⋊C4—224no—
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C4⋊C4C22×D1112yes—
800C2×C4⋊C4C22×D1112yes—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—224no—
828C2×C22⋊C4—224no—
829C2×C22⋊C4—224no—
830C2×C22⋊C4—224no—
831C2×C22⋊C4C22×D1111yescharacteristic
832C2×C22⋊C4C22×D1111yescharacteristic
833C2×C22⋊C4C22×D1111yescharacteristic
834C2×C22⋊C4C22×D1112yes—
835C2×C22⋊C4C22×D1111yescharacteristic
836C2×C22⋊C4C22×D1112yes—
837C2×C42—24no—
838C2×C42—111no—
839C2×C42—111no—
840C2×C42—112no—
841C2×C42—111no—
842C2×C42—224no—
843C2×C42C22×D1112yes—
844C2×C42C22×D1112yes—
845C2×C42C22×D1112yes—
846C2×C42C22×D1111yescharacteristic
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95C22×D1112yes—
859#95C22×D1112yes—
860#95C22×D1112yes—
861#95C22×D1112yes—
862#95C22×D1112yes—
863C2×C11—24no—
864C2×C11—42no—
865C2×C11C2×#52511yescharacteristic
866C2×C11C2×#52511yescharacteristic
867C2×C11C2×#53411yescharacteristic
868C2×C11#348112yes—
869C2×C11#348112yes—
870D11—24no—
871D11—42no—
872D11—44no—
873D11—42no—
874C24—111no—
875C24—111no—
876C24—112no—
877C24—111no—
878C24—114no—
879C24—222no—
880C24—224no—
881C24—224no—
882C24—222no—
883C24—224no—
884C24—222no—
885C24—222no—
886C24—222no—
887C24—222no—
888C24—222no—
889C24—222no—
890C24—442no—
891C24—442no—
892C24—442no—
893C24C23×D1111yescharacteristic
894C24C23×D1111yescharacteristic
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—114no—
898C2×D4—118no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—222no—
905C2×D4—2232no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—222no—
909C2×D4—2232no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—224no—
915C2×D4—224no—
916C2×D4—222no—
917C2×D4—224no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4#433914yes—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—24no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—114no—
935C22×C4—114no—
936C22×C4—114no—
937C22×C4—112no—
938C22×C4—111no—
939C22×C4—112no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—224no—
948C22×C4—222no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—222no—
953C22×C4—224no—
954C22×C4—224no—
955C22×C4—222no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—224no—
959C22×C4—4416no—
960C22×C4—442no—
961C22×C4—442no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—4416no—
967C22×C4—4416no—
968C22×C4—442no—
969C22×C4—442no—
970C22×C4—442no—
971C22×C4D4×D1114yes—
972C22×C4C23×D1112yes—
973C22×C4C23×D1111yescharacteristic
974C22×C4C23×D1112yes—
975C22×C4C23×D1112yes—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1112yes—
980C22×C4C23×D1111yescharacteristic
981C4⋊C4—24no—
982C4⋊C4—22no—
983C4⋊C4—24no—
984C4⋊C4—222no—
985C4⋊C4—224no—
986C4⋊C4—224no—
987C4⋊C4—222no—
988C4⋊C4—224no—
989C4⋊C4—222no—
990C4⋊C4—224no—
991C4⋊C4—442no—
992C4⋊C4—442no—
993C4⋊C4—442no—
994C4⋊C4—442no—
995C22⋊C4—22no—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—24no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—222no—
1008C22⋊C4—222no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—224no—
1012C22⋊C4—224no—
1013C22⋊C4—224no—
1014C22⋊C4—222no—
1015C22⋊C4—222no—
1016C22⋊C4—222no—
1017C22⋊C4—222no—
1018C22⋊C4—224no—
1019C22⋊C4—222no—
1020C22⋊C4—224no—
1021C22⋊C4—442no—
1022C22⋊C4—442no—
1023C22⋊C4—442no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C42—24no—
1028C42—24no—
1029C42—22no—
1030C42—24no—
1031C42—222no—
1032C42—222no—
1033C42—222no—
1034C42—224no—
1035C11#3495611yescharacteristic, complemented, Sylow
1036C23—22no—
1037C23—22no—
1038C23—21no—
1039C23—22no—
1040C23—21no—
1041C23—22no—
1042C23—112no—
1043C23—114no—
1044C23—112no—
1045C23—112no—
1046C23—114no—
1047C23—228no—
1048C23—228no—
1049C23—228no—
1050C23—221no—
1051C23—221no—
1052C23—222no—
1053C23—228no—
1054C23—222no—
1055C23—221no—
1056C23—221no—
1057C23—221no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—221no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—444no—
1069C23—448no—
1070C23—448no—
1071C23—448no—
1072C23—448no—
1073C23—448no—
1074C23—444no—
1075C23—444no—
1076C23—448no—
1077C23—444no—
1078C23—444no—
1079C23C2×#433912yes—
1080C23C2×#433912yes—
1081C23C2×D4×D1112yes—
1082C23#41×D1112yes—
1083C23C24×D1111yescharacteristic
1084D4—28no—
1085D4—2216no—
1086D4—228no—
1087D4—2216no—
1088D4—228no—
1089D4—228no—
1090D4—448no—
1091D4—448no—
1092C2×C4—28no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—112no—
1115C2×C4—112no—
1116C2×C4—112no—
1117C2×C4—228no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—228no—
1123C2×C4—228no—
1124C2×C4—222no—
1125C2×C4—221no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—448no—
1140C2×C4—444no—
1141C2×C4—444no—
1142C2×C4—444no—
1143C2×C4—444no—
1144C2×C4—444no—
1145C2×C4—444no—
1146C2×C4—448no—
1147C2×C4—444no—
1148C2×C4C2×#433912yes—
1149C2×C4C2×D4×D1112yes—
1150C2×C4C2×D4×D1112yes—
1151C2×C4#41×D1114yes—
1152C2×C4#6704214yes—
1153C22—22no—
1154C22—24no—
1155C22—24no—
1156C22—22no—
1157C22—22no—
1158C22—24no—
1159C22—41no—
1160C22—42no—
1161C22—41no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—224no—
1166C22—224no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—224no—
1171C22—224no—
1172C22—224no—
1173C22—224no—
1174C22—222no—
1175C22—4416no—
1176C22—4416no—
1177C22—4416no—
1178C22—442no—
1179C22—442no—
1180C22—441no—
1181C22—442no—
1182C22—442no—
1183C22—442no—
1184C22—442no—
1185C22—442no—
1186C22—441no—
1187C22#1062307814yes—
1188C22C22×#433911yescharacteristic
1189C22C22×D4×D1111yescharacteristic
1190C22C2×#41×D1111yescharacteristic
1191C22C2×#41×D1112yes—
1192C22C2×#6704212yes—
1193C4—22no—
1194C4—22no—
1195C4—24no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—41no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—441no—
1206C4—442no—
1207C4—442no—
1208C4—441no—
1209C4#1062318414yes—
1210C2—24no—
1211C2—42no—
1212C2—224no—
1213C2—442no—
1214C2—442no—
1215C2—444no—
1216C2D11×#52511yescharacteristic
1217C2C2×#1062307811yescharacteristic
1218C2C2×#1062318411yescharacteristic
1219C2#1308222212yes—
1220C2#1308222612yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#123C2
prime radical#13071928C2
hypercenterC4×#123D11
hypocenterC11#34956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4×D44C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074205C2semidirect
4. #13074201C2semidirect
5. #13073967C2semidirect
6. #13073966C2semidirect
7. #13073960C2semidirect
8. #13073511C2semidirect
9. #13073510C2semidirect
10. #13073505C2semidirect
11. #13072895C2semidirect
12. #13071945C2semidirect
13. #13071940C2semidirect
15. #13071860C2semidirect
16. #13071856C2semidirect
17. C4×#66947C2semidirect
18. C4×#66982C2semidirect
19. C4×#66935C2semidirect
20. C4×#66935C2semidirect
21. C4×#66990C2semidirect
22. #13070997C2semidirect
23. C4×C11×#123C2semidirect
27. C23×C4×D11C22semidirect
28. C23×C4×D11C22semidirect
31. C22×C42×C11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C2×C4×C22⋊D11C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×C4⋊Dic11C22semidirect
43. C2×#66946C22semidirect
44. C2×C4⋊C4×D11C22semidirect
48. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×C22⋊C4×D11C22semidirect
54. C2×C4×D44C22semidirect
55. C2×C4×D44C22semidirect
56. C2×C4×D44C22semidirect
57. C2×C4×D44C22semidirect
58. C2×#66925C22semidirect
59. C2×C42×D11C22semidirect
60. C11×#388C22semidirect
61. C11×#387C22semidirect
63. C11×#385C22semidirect
64. C11×#381C22semidirect
65. C4×C11×C4⋊C4C22semidirect
66. C4×C11×C22⋊C4C22semidirect
67. C4×C11×C22⋊C4C22semidirect
70. #10622824C22semidirect
71. #10622823C22semidirect
72. C4×C22⋊Dic11C22semidirect
73. #10622607C22semidirect
74. #10622607C22semidirect
75. #10622604C22semidirect
76. #10622604C22semidirect
77. #10622603C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622594C22semidirect
82. #10622572C22semidirect
83. #10622572C22semidirect
85. #10622571C22semidirect
86. #10622569C22semidirect
89. #10622568C22semidirect
90. #10622568C22semidirect
91. #10622568C22semidirect
92. #10622563C22semidirect
93. #10622563C22semidirect
94. #10622561C22semidirect
95. #10622559C22semidirect
96. #10622555C22semidirect
97. #10622555C22semidirect
98. #10622553C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×(C2×D11)⋊C4C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. #10622546C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. #10622289C22semidirect
106. #10622288C22semidirect
107. #10622287C22semidirect
108. #10622285C22semidirect
109. #10622285C22semidirect
111. #10622282C22semidirect
112. #10622281C22semidirect
113. #10622281C22semidirect
114. #10622281C22semidirect
115. #10622280C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622277C22semidirect
121. #10622277C22semidirect
122. #10622274C22semidirect
123. #10622270C22semidirect
124. #10622268C22semidirect
153. C22×C4×D11D4semidirect
444. C4×#123D11semidirect
601. C22×C42C2×D11semidirect
621. #388C2×D11semidirect
625. #387C2×D11semidirect
645. #385C2×D11semidirect
649. #381C2×D11semidirect
659. C4×C4⋊C4C2×D11semidirect
665. C4×C22⋊C4C2×D11semidirect
666. C4×C22⋊C4C2×D11semidirect
1035. C11#34956semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×C4×D4×D112
#130742052
#130742012
#130739672
#130739662
#130739602
#130735112
#130735102
#130735052
#130728952
#130719452
#130719402
#130719282
#130718602
#130718562
C4×#669472
C4×#669822
C4×#669352
C4×#669902
#130709972
C4×C11×#1232
#3495611