Finite Group Databasebeta

← #14925894

Subgroups — #14925894

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×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074201C212yesmaximal, complemented
4#13074200C212yesmaximal, complemented
5#13073965C211yesmaximal, characteristic, complemented
6#13073959C211yesmaximal, characteristic, complemented
7#13073958C212yesmaximal, complemented
8#13073506C211yesmaximal, characteristic, complemented
9#13073501C212yesmaximal, complemented
10#13072895C211yesmaximal, characteristic, complemented
11#13071941C211yesmaximal, characteristic, complemented
12#13071940C211yesmaximal, characteristic, complemented
13#13071927C211yesmaximal, characteristic
14#13071861C212yesmaximal, complemented
15#13071855C212yesmaximal, complemented
16#13071143C212yesmaximal, complemented
17#123×Dic11C211yesmaximal, characteristic, complemented
18#13071133C211yesmaximal, characteristic, complemented
19#13071121C212yesmaximal, complemented
20#120×Dic11C211yesmaximal, characteristic, complemented
21#13071115C211yesmaximal, characteristic, complemented
22#13070998C211yesmaximal, characteristic, complemented
23C11×#2534C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic, complemented
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic, complemented
29C2×C11×#123C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C2×C4×D4×C11C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic, complemented
33C2×#67006C2211yescharacteristic
34C2×#66990C2212yes—
35C2×D4×Dic11C2211yescharacteristic
36C2×D4×Dic11C2212yescomplemented
37C2×#66982C2211yescharacteristic
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic, complemented
42C22×C4×Dic11C2211yescharacteristic, complemented
43C4×D4×D11—28no—
44C2×#66946C2211yescharacteristic, complemented
45C2×#66945C2212yescomplemented
46C2×C4⋊C4×D11C2211yescharacteristic, complemented
47C2×#66936C2212yes—
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yescomplemented
53C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×(C22⋊D11)⋊C4C2212yescomplemented
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic, complemented
58C2×C4×D44C2211yescharacteristic, complemented
59C2×C42×D11C2211yescharacteristic, complemented
60C11×#396C2212yescomplemented
61C11×#394C2212yescomplemented
62C11×#388C2212yescomplemented
63C11×#386C2212yescomplemented
64C11×#381C2211yescharacteristic, complemented
65C11×#380C2211yescharacteristic, complemented
66C11×#379C2211yescharacteristic, complemented
67#10622860C2211yescharacteristic, complemented
68#10622836C2212yes—
69#10622833C2211yescharacteristic
70#10622833C2211yescharacteristic
71#10622833C2212yescomplemented
72#10622825C2211yescharacteristic, complemented
73#10622824C2211yescharacteristic, complemented
74#10622823C2212yescomplemented
75#10622607C2212yescomplemented
76#10622604C2212yescomplemented
77#10622602C2212yescomplemented
78#10622600C2212yescomplemented
79#10622597C2212yescomplemented
80#10622596C2212yescomplemented
81#10622594C2212yescomplemented
82C4⋊C4×Dic11C2212yescomplemented
83#10622574C2212yescomplemented
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622572C2212yescomplemented
87#10622572C2212yescomplemented
88#10622571C2211yescharacteristic
89#10622571C2211yescharacteristic
90#10622571C2212yescomplemented
91#10622569C2212yes—
92#10622569C2212yes—
93#10622569C2212yescomplemented
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622568C2212yescomplemented
97#10622564C2212yescomplemented
98#10622563C2212yescomplemented
99#10622563C2211yescharacteristic, complemented
100#10622563C2211yescharacteristic, complemented
101#10622561C2212yescomplemented
102#10622561C2212yescomplemented
103#10622559C2212yescomplemented
104#10622559C2211yescharacteristic, complemented
105#10622559C2211yescharacteristic, complemented
106#10622557C2212yescomplemented
107C22⋊C4×Dic11C2211yescharacteristic, complemented
108C22⋊C4×Dic11C2212yescomplemented
109C22⋊C4×Dic11C2211yescharacteristic, complemented
110C22⋊C4×Dic11C2212yescomplemented
111C22⋊C4×Dic11C2212yescomplemented
112#10622546C2212yescomplemented
113#10622288C2212yescomplemented
114#10622287C2212yescomplemented
115#10622282C2212yescomplemented
116#10622281C2212yescomplemented
117#10622281C2212yescomplemented
118#10622279C2212yescomplemented
119#10622279C2212yescomplemented
120#10622277C2212yescomplemented
121#10622277C2212yescomplemented
122#10622266C2212yescomplemented
123#10622265C2212yescomplemented
124#10622262C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11—24no—
134C22×C22⋊D11—28no—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2311yescharacteristic
140C23×Dic11—24no—
141C23×Dic11—44no—
142C23×Dic11C2312yes—
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2312yes—
147C23×Dic11C2311yescharacteristic
148C2×D4×D11—24no—
149C2×D4×D11—24no—
150C2×D4×D11—24no—
151C22×D44C2311yescharacteristic
152C22×C4×D11—24no—
153C22×C4×D11—44no—
154C22×C4×D11—44no—
155C22×C4×D11D418yescomplemented
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C11×#123—24no—
166C11×#120—24no—
167C4×D4×C11—24no—
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C22⋊C4—24no—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C11×C22⋊C4C2312yes—
180C2×C11×C22⋊C4C2312yes—
181C2×C11×C22⋊C4C2312yes—
182C2×C42×C11C2311yescharacteristic
183#67006—24no—
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2312yes—
193#66990—28no—
194D4×Dic11—24no—
195D4×Dic11—44no—
196#66982—24no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—24no—
199C2×(C2×D11)⋊C4—24no—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×Dic11⋊C4—24no—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11—24no—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233#66946—24no—
234#66945—44no—
235C4⋊C4×D11—24no—
236#66936—28no—
237(C22⋊D11)⋊C4—24no—
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—28no—
241(C22⋊D11)⋊C4—28no—
242(C22⋊D11)⋊C4—24no—
243(C22⋊D11)⋊C4—44no—
244C22⋊C4×D11—24no—
245C22⋊C4×D11—24no—
246C4×D44—24no—
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×C11—22no—
266C24×C11—24no—
267C24×C11—22no—
268C24×C11—22no—
269C24×C11—42no—
270C24×C11C2411yescharacteristic
271C24×C11C2412yes—
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—24no—
279C23×D11—24no—
280C23×D11—42no—
281C23×D11—42no—
282C23×D11C2×D414yes—
283C23×D11C2411yescharacteristic
284C23×D11C2411yescharacteristic
285C23×D11C2411yescharacteristic
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—24no—
289C2×D4×C11—24no—
290C2×D4×C11—42no—
291C2×D4×C11#4114yes—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—42no—
297C22×C4×C11—42no—
298C22×C4×C11C2×D414yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—232no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11#4118yes—
322C2×C22⋊D11#4114yes—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—24no—
326C22×Dic11—24no—
327C22×Dic11—22no—
328C22×Dic11—24no—
329C22×Dic11—24no—
330C22×Dic11—24no—
331C22×Dic11—22no—
332C22×Dic11—22no—
333C22×Dic11—42no—
334C22×Dic11—42no—
335C22×Dic11—42no—
336C22×Dic11—416no—
337C22×Dic11C2×D414yes—
338C22×Dic11C2412yes—
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2412yes—
341C22×Dic11C2412yes—
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2412yes—
346C22×Dic11C2411yescharacteristic
347D4×D11—232no—
348C2×D44—22no—
349C2×D44—22no—
350C2×D44—22no—
351C2×C4×D11—22no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—22no—
355C2×C4×D11—24no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—22no—
361C2×C4×D11—22no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—42no—
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—42no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—24no—
382C11×C22⋊C4—24no—
383C11×C22⋊C4—24no—
384C11×C22⋊C4—42no—
385C42×C11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—24no—
389C22⋊Dic11—22no—
390C22⋊Dic11—24no—
391C22⋊Dic11—22no—
392C22⋊Dic11—22no—
393C22⋊Dic11—42no—
394C22⋊Dic11—42no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—22no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408C4⋊Dic11—22no—
409C4⋊Dic11—24no—
410C4⋊Dic11—42no—
411C4⋊Dic11—42no—
412Dic11⋊C4—22no—
413Dic11⋊C4—24no—
414Dic11⋊C4—24no—
415Dic11⋊C4—24no—
416Dic11⋊C4—24no—
417Dic11⋊C4—22no—
418Dic11⋊C4—42no—
419C4×Dic11—22no—
420C4×Dic11—22no—
421C4×Dic11—24no—
422C4×Dic11—24no—
423C4×Dic11—24no—
424C4×Dic11—24no—
425C4×Dic11—22no—
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#2534D1111yescharacteristic, complemented
436#2483—111no—
437#2405—111no—
438#2405—111no—
439#2403—111no—
440#2392—112no—
441#2392—112no—
442C4×#123—112no—
443C4×#123—111no—
444C4×#123—111no—
445C4×#120—112no—
446C4×#120—111no—
447C4×#120—111no—
448#2280—111no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—28no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—21no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—48no—
463C23×C11—48no—
464C23×C11—44no—
465C23×C11—44no—
466C23×C11C22×D412yes—
467C23×C11C2×#4112yes—
468C23×C11C2×#4112yes—
469C23×C11C2×#4114yes—
470C23×C11C2×#4112yes—
471C23×C11C2511yescharacteristic
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—22no—
475C22×D11—28no—
476C22×D11—28no—
477C22×D11—21no—
478C22×D11—22no—
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—21no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—28no—
486C22×D11—44no—
487C22×D11—48no—
488C22×D11—48no—
489C22×D11—48no—
490C22×D11—48no—
491C22×D11—44no—
492C22×D11—44no—
493C22×D11C22×D412yes—
494C22×D11C22×D412yes—
495C22×D11C2×#4112yes—
496C22×D11C2×#4114yes—
497D4×C11—28no—
498D4×C11—48no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
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—44no—
517C2×C4×C11—44no—
518C2×C4×C11—44no—
519C2×C4×C11C22×D412yes—
520C2×C4×C11C22×D412yes—
521C2×C4×C11C2×#4112yes—
522C22⋊D11—28no—
523C22⋊D11—216no—
524C22⋊D11—28no—
525C22⋊D11—216no—
526C22⋊D11—48no—
527C2×Dic11—28no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—28no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—21no—
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—22no—
546C2×Dic11—22no—
547C2×Dic11—48no—
548C2×Dic11—44no—
549C2×Dic11—44no—
550C2×Dic11—48no—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C2×#4112yes—
554C2×Dic11C2×#4114yes—
555C2×Dic11H(5,𝔽2)14yes—
556D44—28no—
557C4×D11—28no—
558C4×D11—28no—
559C4×D11—28no—
560C4×D11—44no—
561C4×D11—44no—
562C4×D11—44no—
563C4×D11—44no—
564C4×D11—44no—
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×#120C2×D1111yescharacteristic
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—112no—
581C2×C4×D4—111no—
582C2×C4×D4—112no—
583C2×C4×D4—112no—
584C2×C4×D4—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—112no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
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⋊C4C2×D1111yescharacteristic, complemented
600C22×C42—111no—
601C22×C42—111no—
602#398—112no—
603#398—112no—
604#397—112no—
605#397—112no—
606#396—112no—
607#396—112no—
608#396—112no—
609#396C2×D1112yescomplemented
610#394—112no—
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#394C2×D1112yescomplemented
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#387—112no—
626#386—111no—
627#386—111no—
628#386—112no—
629#386—112no—
630#386—111no—
631#386—112no—
632#386—111no—
633#386—112no—
634#386—112no—
635#386C2×D1112yescomplemented
636#385—112no—
637#385—112no—
638#385—112no—
639#385—112no—
640#385—111no—
641#385—111no—
642#385—111no—
643#385—111no—
644#385—112no—
645#385—112no—
646#381—111no—
647#381—112no—
648#381—112no—
649#381C2×D1111yescharacteristic, complemented
650#380—111no—
651#380—112no—
652#380C2×D1111yescharacteristic, complemented
653#379—111no—
654#379—111no—
655#379—111no—
656#379—112no—
657#379C2×D1111yescharacteristic, complemented
658C4×C4⋊C4—112no—
659C4×C4⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4—112no—
663C4×C22⋊C4—111no—
664C4×C22⋊C4—111no—
665C4×C22⋊C4—112no—
666C4×C22⋊C4—112no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—24no—
670C22×C11—24no—
671C22×C11—22no—
672C22×C11—24no—
673C22×C11—24no—
674C22×C11—24no—
675C22×C11—24no—
676C22×C11—416no—
677C22×C11—41no—
678C22×C11—42no—
679C22×C11—41no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11#52514yes—
685C22×C11C23×D411yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C22×#4111yescharacteristic
688C22×C11C22×#4112yes—
689C22×C11C2×H(5,𝔽2)12yes—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—24no—
693C2×D11—24no—
694C2×D11—22no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—22no—
698C2×D11—24no—
699C2×D11—416no—
700C2×D11—416no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11#52514yes—
707C4×C11—22no—
708C4×C11—22no—
709C4×C11—22no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—42no—
714C4×C11—42no—
715Dic11—22no—
716Dic11—24no—
717Dic11—22no—
718Dic11—41no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722Dic11—42no—
723Dic11#53414yes—
724C25—111no—
725C25—111no—
726C25C22×D1111yescharacteristic
727C22×D4—112no—
728C22×D4—111no—
729C22×D4—111no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—111no—
733C22×D4—224no—
734C22×D4—224no—
735C22×D4—228no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4C22×D1112yes—
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—112no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—224no—
757C23×C4—224no—
758C23×C4—444no—
759C23×C4—444no—
760C23×C4—444no—
761C23×C4C22×D1111yescharacteristic
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764#123—24no—
765#123—228no—
766#123—224no—
767#120—24no—
768#120—228no—
769#120—224no—
770C4×D4—24no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—228no—
774C4×D4—228no—
775C4×D4—228no—
776C4×D4—228no—
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—112no—
789C2×C4⋊C4—111no—
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—24no—
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—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—111no—
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—224no—
825C2×C22⋊C4—224no—
826C2×C22⋊C4—224no—
827C2×C22⋊C4C22×D1111yescharacteristic
828C2×C22⋊C4C22×D1111yescharacteristic
829C2×C22⋊C4C22×D1112yes—
830C2×C22⋊C4C22×D1112yes—
831C2×C22⋊C4C22×D1111yescharacteristic
832C2×C22⋊C4C22×D1112yes—
833C2×C22⋊C4C22×D1112yes—
834C2×C22⋊C4C22×D1111yescharacteristic
835C2×C22⋊C4C22×D1112yes—
836C2×C22⋊C4C22×D1112yes—
837C2×C42—112no—
838C2×C42—112no—
839C2×C42—112no—
840C2×C42—111no—
841C2×C42—111no—
842C2×C42—112no—
843C2×C42—111no—
844C2×C42—224no—
845C2×C42—224no—
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#95—112no—
859#95—112no—
860#95C22×D1112yes—
861#95C22×D1112yes—
862#95C22×D1112yes—
863C2×C11—24no—
864C2×C11—42no—
865C2×C11—44no—
866C2×C11C2×#52511yescharacteristic
867C2×C11C2×#52511yescharacteristic
868C2×C11C2×#53411yescharacteristic
869C2×C11#348112yes—
870C2×C11#348112yes—
871D11—24no—
872D11—42no—
873D11—42no—
874C24—22no—
875C24—24no—
876C24—22no—
877C24—22no—
878C24—42no—
879C24—111no—
880C24—111no—
881C24—111no—
882C24—114no—
883C24—222no—
884C24—224no—
885C24—222no—
886C24—224no—
887C24—222no—
888C24—222no—
889C24—222no—
890C24—442no—
891C24—442no—
892C24C23×D1111yescharacteristic
893C24C23×D1112yes—
894C24C23×D1111yescharacteristic
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—42no—
900C2×D4—118no—
901C2×D4—114no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—224no—
906C2×D4—2232no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—222no—
910C2×D4—224no—
911C2×D4—2232no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—222no—
915C2×D4—224no—
916C2×D4—224no—
917C2×D4—224no—
918C2×D4—222no—
919C2×D4—442no—
920C2×D4#434114yes—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—111no—
928C22×C4—114no—
929C22×C4—111no—
930C22×C4—112no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—114no—
935C22×C4—114no—
936C22×C4—112no—
937C22×C4—111no—
938C22×C4—112no—
939C22×C4—111no—
940C22×C4—112no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—224no—
953C22×C4—222no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—222no—
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×C4—4416no—
972C22×C4D4×D1114yes—
973C22×C4C23×D1112yes—
974C22×C4C23×D1112yes—
975C22×C4C23×D1112yes—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1111yescharacteristic
981C4⋊C4—22no—
982C4⋊C4—24no—
983C4⋊C4—42no—
984C4⋊C4—222no—
985C4⋊C4—222no—
986C4⋊C4—224no—
987C4⋊C4—224no—
988C4⋊C4—224no—
989C4⋊C4—224no—
990C4⋊C4—222no—
991C4⋊C4—224no—
992C4⋊C4—442no—
993C4⋊C4—442no—
994C4⋊C4—442no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—24no—
1001C22⋊C4—24no—
1002C22⋊C4—22no—
1003C22⋊C4—24no—
1004C22⋊C4—42no—
1005C22⋊C4—222no—
1006C22⋊C4—224no—
1007C22⋊C4—222no—
1008C22⋊C4—224no—
1009C22⋊C4—224no—
1010C22⋊C4—222no—
1011C22⋊C4—224no—
1012C22⋊C4—224no—
1013C22⋊C4—224no—
1014C22⋊C4—222no—
1015C22⋊C4—224no—
1016C22⋊C4—224no—
1017C22⋊C4—222no—
1018C22⋊C4—222no—
1019C22⋊C4—222no—
1020C22⋊C4—224no—
1021C22⋊C4—222no—
1022C22⋊C4—442no—
1023C22⋊C4—442no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C42—22no—
1028C42—222no—
1029C42—222no—
1030C42—224no—
1031C42—224no—
1032C42—224no—
1033C42—224no—
1034C42—222no—
1035C11#3495611yescharacteristic, complemented, Sylow
1036C23—22no—
1037C23—22no—
1038C23—28no—
1039C23—22no—
1040C23—21no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—21no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—48no—
1050C23—48no—
1051C23—44no—
1052C23—44no—
1053C23—112no—
1054C23—114no—
1055C23—112no—
1056C23—112no—
1057C23—228no—
1058C23—228no—
1059C23—221no—
1060C23—221no—
1061C23—222no—
1062C23—228no—
1063C23—221no—
1064C23—221no—
1065C23—221no—
1066C23—222no—
1067C23—221no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—444no—
1072C23—448no—
1073C23—448no—
1074C23—448no—
1075C23—444no—
1076C23—448no—
1077C23—444no—
1078C23C2×D4×D1112yes—
1079C23C2×#434112yes—
1080C23C2×#434112yes—
1081C23#41×D1114yes—
1082C23#41×D1112yes—
1083C23C24×D1111yescharacteristic
1084D4—28no—
1085D4—48no—
1086D4—228no—
1087D4—2216no—
1088D4—228no—
1089D4—2216no—
1090D4—228no—
1091D4—448no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—112no—
1113C2×C4—114no—
1114C2×C4—112no—
1115C2×C4—112no—
1116C2×C4—114no—
1117C2×C4—228no—
1118C2×C4—228no—
1119C2×C4—228no—
1120C2×C4—228no—
1121C2×C4—228no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—221no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—444no—
1141C2×C4—444no—
1142C2×C4—444no—
1143C2×C4—444no—
1144C2×C4—444no—
1145C2×C4—444no—
1146C2×C4—444no—
1147C2×C4—448no—
1148C2×C4—448no—
1149C2×C4—444no—
1150C2×C4C2×D4×D1112yes—
1151C2×C4C2×D4×D1112yes—
1152C2×C4C2×#434112yes—
1153C22—22no—
1154C22—24no—
1155C22—24no—
1156C22—22no—
1157C22—22no—
1158C22—24no—
1159C22—24no—
1160C22—24no—
1161C22—24no—
1162C22—416no—
1163C22—42no—
1164C22—41no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—41no—
1170C22—114no—
1171C22—222no—
1172C22—222no—
1173C22—224no—
1174C22—224no—
1175C22—222no—
1176C22—222no—
1177C22—222no—
1178C22—224no—
1179C22—222no—
1180C22—4416no—
1181C22—4416no—
1182C22—441no—
1183C22—442no—
1184C22—442no—
1185C22—442no—
1186C22—441no—
1187C22#1062313714yes—
1188C22C22×D4×D1111yescharacteristic
1189C22C22×#434111yescharacteristic
1190C22C2×#41×D1111yescharacteristic
1191C22C2×#41×D1112yes—
1192C22D11×H(5,𝔽2)12yes—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—41no—
1201C4—114no—
1202C4—222no—
1203C4—222no—
1204C4—224no—
1205C4—441no—
1206C4—442no—
1207C4—442no—
1208C4—442no—
1209C4—441no—
1210C2—24no—
1211C2—44no—
1212C2—42no—
1213C2—224no—
1214C2—442no—
1215C2—442no—
1216C2D11×#52511yescharacteristic
1217C2C2×#1062313711yescharacteristic
1218C2D11×#53411yescharacteristic
1219C2#1308221912yes—
1220C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2534C2
prime radical#13071927C2
hypercenter#2534D11
hypocenterC11#34956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2534

Complements

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

NH ≅ G/Ntype
1. C22×(C22⋊D11)⋊C4C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074201C2semidirect
4. #13074200C2semidirect
5. #13073965C2semidirect
6. #13073959C2semidirect
7. #13073958C2semidirect
8. #13073506C2semidirect
9. #13073501C2semidirect
10. #13072895C2semidirect
11. #13071941C2semidirect
12. #13071940C2semidirect
14. #13071861C2semidirect
15. #13071855C2semidirect
16. #13071143C2semidirect
17. #123×Dic11C2semidirect
18. #13071133C2semidirect
19. #13071121C2semidirect
20. #120×Dic11C2semidirect
21. #13071115C2semidirect
22. #13070998C2semidirect
23. C11×#2534C2semidirect
25. C24×Dic11C22semidirect
28. C23×C4×D11C22semidirect
32. C22×C11×C22⋊C4C22semidirect
36. C2×D4×Dic11C22semidirect
39. C2×C4×C22⋊D11C22semidirect
41. C22×Dic11⋊C4C22semidirect
42. C22×C4×Dic11C22semidirect
44. C2×#66946C22semidirect
45. C2×#66945C22semidirect
46. C2×C4⋊C4×D11C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×C22⋊C4×D11C22semidirect
58. C2×C4×D44C22semidirect
59. C2×C42×D11C22semidirect
60. C11×#396C22semidirect
61. C11×#394C22semidirect
62. C11×#388C22semidirect
63. C11×#386C22semidirect
64. C11×#381C22semidirect
65. C11×#380C22semidirect
66. C11×#379C22semidirect
67. #10622860C22semidirect
71. #10622833C22semidirect
72. #10622825C22semidirect
73. #10622824C22semidirect
74. #10622823C22semidirect
75. #10622607C22semidirect
76. #10622604C22semidirect
77. #10622602C22semidirect
78. #10622600C22semidirect
79. #10622597C22semidirect
80. #10622596C22semidirect
81. #10622594C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. #10622574C22semidirect
84. #10622574C22semidirect
86. #10622572C22semidirect
87. #10622572C22semidirect
90. #10622571C22semidirect
93. #10622569C22semidirect
96. #10622568C22semidirect
97. #10622564C22semidirect
98. #10622563C22semidirect
99. #10622563C22semidirect
100. #10622563C22semidirect
101. #10622561C22semidirect
102. #10622561C22semidirect
103. #10622559C22semidirect
104. #10622559C22semidirect
105. #10622559C22semidirect
106. #10622557C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C22⋊C4×Dic11C22semidirect
109. C22⋊C4×Dic11C22semidirect
110. C22⋊C4×Dic11C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. #10622546C22semidirect
113. #10622288C22semidirect
114. #10622287C22semidirect
115. #10622282C22semidirect
116. #10622281C22semidirect
117. #10622281C22semidirect
118. #10622279C22semidirect
119. #10622279C22semidirect
120. #10622277C22semidirect
121. #10622277C22semidirect
122. #10622266C22semidirect
123. #10622265C22semidirect
124. #10622262C22semidirect
155. C22×C4×D11D4semidirect
435. #2534D11semidirect
599. C22×C22⋊C4C2×D11semidirect
609. #396C2×D11semidirect
615. #394C2×D11semidirect
621. #388C2×D11semidirect
635. #386C2×D11semidirect
649. #381C2×D11semidirect
652. #380C2×D11semidirect
657. #379C2×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×(C22⋊D11)⋊C42
C2×C4×D4×D112
#130742012
#130742002
#130739652
#130739592
#130739582
#130735062
#130735012
#130728952
#130719412
#130719402
#130719272
#130718612
#130718552
#130711432
#123×Dic112
#130711332
#130711212
#120×Dic112
#130711152
#130709982
C11×#25342
#3495611