Finite Group Databasebeta

← #14914103

Subgroups — #14914103

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071659C211yesmaximal, characteristic, complemented
5#13071656C211yesmaximal, characteristic, complemented
6#13071653C211yesmaximal, characteristic, complemented
7#13071650C211yesmaximal, characteristic, complemented
8#13071636C211yesmaximal, characteristic, complemented
9#13071632C211yesmaximal, characteristic, complemented
10#13071630C211yesmaximal, characteristic, complemented
11#13071464C212yesmaximal, complemented
12#13071463C212yesmaximal, complemented
13#13071434C212yesmaximal, complemented
14D4×(C2×D11)⋊C4C212yesmaximal, complemented
15#13071308C212yesmaximal, complemented
16#13071304C212yesmaximal, complemented
17#13071231C211yesmaximal, characteristic, complemented
18#13071195C211yesmaximal, characteristic, complemented
19#13071126C212yesmaximal, complemented
20C4×#66992C212yesmaximal, complemented
21#13070997C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2361C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2212yescomplemented
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic, complemented
34C2×D4×Dic11C2212yescomplemented
35C2×#66983C2211yescharacteristic
36C2×C4×C22⋊D11C2212yescomplemented
37C2×C4×C22⋊D11C2212yescomplemented
38C22×(C2×D11)⋊C4C2212yes—
39C22×(C2×D11)⋊C4C2212yes—
40C22×C4⋊Dic11C2211yescharacteristic, complemented
41C22×C4×Dic11C2212yescomplemented
42D11×#121C4116yescomplemented
43#10623076—28no—
44C2×#66948C2211yescharacteristic
45C2×#66946C2211yescharacteristic, complemented
46C2×#66945—28no—
47C2×#66945C2211yescharacteristic
48C2×#66945C2212yes—
49C2×#66945C2211yescharacteristic
50C2×#66945C2211yescharacteristic, complemented
51C2×#66945C2211yescharacteristic, complemented
52C2×#66945C2212yescomplemented
53C2×C4⋊C4×D11C2211yescharacteristic
54C2×#66937C2212yes—
55C2×(C22⋊D11)⋊C4C2212yescomplemented
56C2×(C22⋊D11)⋊C4C2212yescomplemented
57C2×C22⋊C4×D11C2212yes—
58C2×C22⋊C4×D11C2212yes—
59C2×C4×D44C2211yescharacteristic, complemented
60C2×#66925C2211yescharacteristic
61C2×#66925C2211yescharacteristic
62C11×#390C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#388C2212yescomplemented
65C11×#386C2212yescomplemented
66C11×#385C2212yescomplemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C22⋊C4C2211yescharacteristic, complemented
69#10622834C2211yescharacteristic, complemented
70#10622833C2212yescomplemented
71#10622826C2212yescomplemented
72#10622826C2212yescomplemented
73C4×C22⋊Dic11C2211yescharacteristic, complemented
74C4×C22⋊Dic11C2212yescomplemented
75#10622603C2212yescomplemented
76#10622603C2212yescomplemented
77#10622602C2212yescomplemented
78#10622601C2211yescharacteristic, complemented
79#10622601C2212yescomplemented
80#10622600C2212yes—
81#10622598C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622585C2212yescomplemented
86#10622571C2212yescomplemented
87#10622571C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622568C2211yescharacteristic
93#10622568C2212yes—
94#10622568C2211yescharacteristic
95#10622568C2212yes—
96#10622564C2212yescomplemented
97#10622563C2212yescomplemented
98#10622558C2212yescomplemented
99#10622557C2212yescomplemented
100#10622555C2211yescharacteristic, complemented
101#10622555C2211yescharacteristic, complemented
102C22⋊C4×Dic11C2212yescomplemented
103#10622552C2211yescharacteristic, complemented
104#10622552C2212yescomplemented
105C4×(C2×D11)⋊C4C2212yes—
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110C4×Dic11⋊C4C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yescomplemented
113#10622283C2212yescomplemented
114#10622281C2212yescomplemented
115#10622280C2212yes—
116#10622280C2211yescharacteristic, complemented
117#10622280C2211yescharacteristic, complemented
118#10622279C2212yes—
119#10622279C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622277C2211yescharacteristic
123#10622277C2211yescharacteristic
124#10622262C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2311yescharacteristic
127C24×D11C2312yes—
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C23×C4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2312yes—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—44no—
142C2×D4×D11—44no—
143C2×D4×D11C2×C418yescomplemented
144C2×D4×D11C2×C4116yescomplemented
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×C4×D11—24no—
148C22×C4×D11—24no—
149C22×C4×D11C2×C418yescomplemented
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C11×#121C2×C418yescomplemented
158C4×D4×C11—24no—
159C4×D4×C11—44no—
160C2×C11×C4⋊C4—24no—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181#66992C2×C4116yescomplemented
182#66991C2×C418yescomplemented
183D4×Dic11—24no—
184D4×Dic11—44no—
185#66983C2×C418yescomplemented
186C4×C22⋊D11—28no—
187C4×C22⋊D11—44no—
188C2×(C2×D11)⋊C4—28no—
189C2×(C2×D11)⋊C4—28no—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×C4⋊Dic11—24no—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×C4×Dic11—28no—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233#66948C2×C418yescomplemented
234#66946—24no—
235#66945—24no—
236#66945—24no—
237#66945—28no—
238#66945—24no—
239#66945—28no—
240#66945D418yescomplemented
241C4⋊C4×D11C2×C418yescomplemented
242#66937C2×C4116yescomplemented
243(C22⋊D11)⋊C4—28no—
244(C22⋊D11)⋊C4—44no—
245C22⋊C4×D11—28no—
246C22⋊C4×D11C2×C4116yescomplemented
247C4×D44—24no—
248#66925—24no—
249#66925—24no—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2311yescharacteristic
253C11×#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266#34204—111nomaximal, Sylow
267C24×C11C2412yes—
268C24×C11C2411yescharacteristic
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—41no—
276C23×D11—41no—
277C23×D11—42no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11—42no—
281C23×D11C22×C414yes—
282C23×D11C22×C418yes—
283C23×D11C2411yescharacteristic
284C23×D11C2412yes—
285C23×D11C2411yescharacteristic
286C2×D4×C11—24no—
287C2×D4×C11—24no—
288C2×D4×C11—22no—
289C2×D4×C11—22no—
290C2×D4×C11C22×C414yes—
291C2×D4×C11C22×C418yes—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
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×C11C22×C414yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C22×C4×C11C2411yescharacteristic
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11C22×C418yes—
317C2×C22⋊D11C22×C418yes—
318C2×C22⋊D11C22×C418yes—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—42no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11C22×C414yes—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2412yes—
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337D4×D11—232no—
338D4×D11—432no—
339C2×D44—22no—
340C2×D44—22no—
341C2×D44—42no—
342C2×D44—42no—
343C2×D44C22×C414yes—
344C2×D44C22×C418yes—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—232no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11C22×C414yes—
361C2×C4×D11C22×C414yes—
362C2×C4×D11C22×C414yes—
363C2×C4×D11C22×C418yes—
364C2×C4×D11C22×C414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11#4114yes—
367C11×C4⋊C4—24no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—42no—
370C11×C4⋊C4C22×C414yes—
371C11×C4⋊C4C2×D414yescomplemented
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—42no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4C22×C418yes—
378C42×C11—22no—
379C42×C11—22no—
380C42×C11—42no—
381C22⋊Dic11—24no—
382C22⋊Dic11—22no—
383C22⋊Dic11—22no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386C22⋊Dic11C22×C418yes—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—41no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—41no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—41no—
402(C2×D11)⋊C4—41no—
403(C2×D11)⋊C4—42no—
404(C2×D11)⋊C4C22×C418yes—
405(C2×D11)⋊C4C22×C418yes—
406(C2×D11)⋊C4C2×D418yes—
407C4⋊Dic11—24no—
408C4⋊Dic11—22no—
409C4⋊Dic11—42no—
410C4⋊Dic11C22×C414yes—
411C4⋊Dic11C2×D414yescomplemented
412Dic11⋊C4—22no—
413Dic11⋊C4—22no—
414Dic11⋊C4—22no—
415Dic11⋊C4—22no—
416Dic11⋊C4—42no—
417Dic11⋊C4—42no—
418Dic11⋊C4C22×C418yes—
419C4×Dic11—24no—
420C4×Dic11—24no—
421C4×Dic11—22no—
422C4×Dic11—24no—
423C4×Dic11—22no—
424C4×Dic11—42no—
425C4×Dic11—42no—
426C4×Dic11—42no—
427C4×Dic11C2×D418yescomplemented
428C22×#121—111no—
429C2×#518—111no—
430C22×#117—111no—
431#2363—111no—
432#2363—111no—
433#2363—111no—
434#2363—111no—
435#2361—111no—
436#2361—111no—
437#2361—111no—
438#2361D1111yescharacteristic, complemented
439#2342—112no—
440#2342—112no—
441D4×C22⋊C4—112no—
442D4×C22⋊C4—112no—
443#2324—112no—
444#2324—112no—
445#2316—111no—
446#2309—111no—
447C4×#121—112no—
448C4×#121—112no—
449#2280—111no—
450#2274—111no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11C23×C414yes—
462C23×C11C23×C412yes—
463C23×C11H(5,𝔽2)12yes—
464C23×C11H(5,𝔽2)12yes—
465C23×C11C2511yescharacteristic
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—28no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—21no—
478C22×D11—21no—
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—28no—
484C22×D11—216no—
485C22×D11—44no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11—44no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—44no—
492C22×D11—84no—
493C22×D11—84no—
494C22×D11—84no—
495C22×D11—84no—
496C22×D11C23×C414yes—
497C22×D11C23×C412yes—
498C22×D11C23×C412yes—
499C22×D11C22×D412yes—
500C22×D11C2×#4112yes—
501D4×C11—216no—
502D4×C11—28no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—28no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—22no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—48no—
526C2×C4×C11—84no—
527C2×C4×C11C23×C414yes—
528C2×C4×C11C23×C412yes—
529C2×C4×C11C23×C412yes—
530C2×C4×C11C22×D414yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C2×#4112yes—
533C22⋊D11—216no—
534C22⋊D11—216no—
535C22⋊D11—48no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—28no—
543C2×Dic11—22no—
544C2×Dic11—21no—
545C2×Dic11—21no—
546C2×Dic11—21no—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—21no—
550C2×Dic11—21no—
551C2×Dic11—22no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—22no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—48no—
559C2×Dic11—84no—
560C2×Dic11C23×C414yes—
561C2×Dic11C23×C412yes—
562C2×Dic11C23×C412yes—
563C2×Dic11C22×D414yes—
564C2×Dic11C22×D412yes—
565C2×Dic11C2×#4112yes—
566D44—28no—
567D44—48no—
568C4×D11—28no—
569C4×D11—28no—
570C4×D11—28no—
571C4×D11—48no—
572C4×D11—84no—
573C4×D11—84no—
574C4×D11C4×D4116yescomplemented
575C23×D4—111no—
576C23×D4—112no—
577C24×C4—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—111no—
581C2×#121—1116no—
582C2×#121—111no—
583C2×#121—112no—
584C2×#121C2×D1111yescharacteristic
585#518—228no—
586C2×C4×D4—111no—
587C2×C4×D4—112no—
588C2×C4×D4—112no—
589C2×C4×D4—112no—
590C2×C4×D4—111no—
591C2×C4×D4—112no—
592C2×C4×D4—112no—
593C2×C4×D4—111no—
594C2×C4×D4C2×D1111yescharacteristic, complemented
595C2×C4×D4C2×D1112yescomplemented
596C2×#117—111no—
597C2×#117—111no—
598C2×#117—112no—
599C2×#117—112no—
600C2×#117—111no—
601C2×#117—111no—
602C2×#117—111no—
603C2×#117—111no—
604C2×#117—228no—
605C22×C4⋊C4—111no—
606C22×C4⋊C4—111no—
607C22×C4⋊C4C2×D1111yescharacteristic, complemented
608C22×C22⋊C4—112no—
609C22×C22⋊C4—112no—
610C22×C22⋊C4—112no—
611C22×C22⋊C4—112no—
612C22×C42—112no—
613#390—111no—
614#390—111no—
615#390—112no—
616#390—112no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—111no—
621#390—112no—
622#390C2×D1111yescharacteristic, complemented
623#389—112no—
624#389—111no—
625#389—111no—
626#389—111no—
627#389—112no—
628#389C2×D1111yescharacteristic, complemented
629#388—112no—
630#388—112no—
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388C2×D1112yescomplemented
637#386—112no—
638#386—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#386C2×D1112yescomplemented
645#385—112no—
646#385—112no—
647#385—112no—
648#385C2×D1112yescomplemented
649#381—111no—
650#381—111no—
651#380—112no—
652#380—111no—
653#380—111no—
654#380—112no—
655#380—111no—
656#380—111no—
657#379—112no—
658#379—112no—
659#379—111no—
660#379—111no—
661C4×C4⋊C4—111no—
662C4×C4⋊C4—111no—
663C4×C4⋊C4—112no—
664C4×C4⋊C4—111no—
665C4×C4⋊C4—112no—
666C4×C4⋊C4C2×D1111yescharacteristic, complemented
667C4×C22⋊C4—112no—
668C4×C22⋊C4—111no—
669C4×C22⋊C4—112no—
670C4×C22⋊C4—112no—
671C4×C22⋊C4—112no—
672C4×C22⋊C4—111no—
673C4×C22⋊C4—111no—
674C4×C22⋊C4—112no—
675C4×C22⋊C4—112no—
676C4×C22⋊C4C2×D1111yescharacteristic, complemented
677C22×C11—22no—
678C22×C11—22no—
679C22×C11—22no—
680C22×C11—22no—
681C22×C11—22no—
682C22×C11—22no—
683C22×C11—24no—
684C22×C11—24no—
685C22×C11—24no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—42no—
689C22×C11—42no—
690C22×C11#51814yescomplemented
691C22×C11C24×C411yescharacteristic
692C22×C11C23×D411yescharacteristic
693C22×C11C22×#4111yescharacteristic
694C22×C11C2×H(5,𝔽2)11yescharacteristic
695C22×C11C2×H(5,𝔽2)11yescharacteristic
696C22×C11#58511yescharacteristic
697C22×C11#58511yescharacteristic
698C2×D11—22no—
699C2×D11—22no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—24no—
706C2×D11—22no—
707C2×D11—24no—
708C2×D11—22no—
709C2×D11—24no—
710C2×D11—416no—
711C2×D11—41no—
712C2×D11—41no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—41no—
716C2×D11—41no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—816no—
720C2×D11C2×C4×D414yes—
721C4×C11—22no—
722C4×C11—24no—
723C4×C11—24no—
724C4×C11—42no—
725C4×C11—41no—
726C4×C11—41no—
727C4×C11—41no—
728C4×C11—41no—
729C4×C11C2×C4×D414yes—
730Dic11—22no—
731Dic11—24no—
732Dic11—24no—
733Dic11—41no—
734Dic11—42no—
735Dic11—41no—
736Dic11—41no—
737Dic11—41no—
738Dic11C2×C4×D414yes—
739C25—111no—
740C25—112no—
741C22×D4—112no—
742C22×D4—112no—
743C22×D4—112no—
744C22×D4—118no—
745C22×D4—1116no—
746C22×D4—111no—
747C22×D4—112no—
748C22×D4—224no—
749C22×D4—224no—
750C22×D4—444no—
751C22×D4—444no—
752C22×D4C22×D1112yes—
753C22×D4C22×D1111yescharacteristic
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—118no—
757C23×C4—111no—
758C23×C4—111no—
759C23×C4—111no—
760C23×C4—112no—
761C23×C4—112no—
762C23×C4—112no—
763C23×C4—112no—
764C23×C4—112no—
765C23×C4—224no—
766C23×C4—224no—
767C23×C4C22×D1112yes—
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1112yes—
770#121—118no—
771#121—1116no—
772#121—118no—
773#121—118no—
774#121—1116no—
775#121C4×D1118yescomplemented
776C4×D4—24no—
777C4×D4—44no—
778C4×D4—224no—
779C4×D4—228no—
780C4×D4—228no—
781C4×D4—224no—
782C4×D4—224no—
783C4×D4—444no—
784C4×D4—444no—
785C4×D4—444no—
786#117—118no—
787#117—224no—
788#117—224no—
789#117—228no—
790#117—228no—
791#117—224no—
792#117—224no—
793#117—224no—
794C2×C4⋊C4—24no—
795C2×C4⋊C4—111no—
796C2×C4⋊C4—112no—
797C2×C4⋊C4—111no—
798C2×C4⋊C4—118no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—111no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4—224no—
809C2×C4⋊C4C22×D1112yes—
810C2×C4⋊C4C22×D1111yescharacteristic
811C2×C4⋊C4C22×D1112yes—
812C2×C4⋊C4C22×D1111yescharacteristic
813C2×C4⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—1116no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—111no—
821C2×C22⋊C4—111no—
822C2×C22⋊C4—111no—
823C2×C22⋊C4—111no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—111no—
838C2×C22⋊C4—111no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—228no—
842C2×C22⋊C4—228no—
843C2×C22⋊C4—228no—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1111yescharacteristic
846C2×C22⋊C4C22×D1111yescharacteristic
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yes—
849C2×C22⋊C4C22×D1112yes—
850C2×C42—112no—
851C2×C42—112no—
852C2×C42—112no—
853C2×C42—112no—
854C2×C42—111no—
855C2×C42—111no—
856C2×C42—112no—
857C2×C42—112no—
858C2×C42—112no—
859C2×C42—228no—
860C2×C42C22×D1111yescharacteristic
861C2×C42C22×D1111yescharacteristic
862C2×C42C22×D1112yes—
863#95—111no—
864#95—111no—
865#95—111no—
866#95—111no—
867#95—112no—
868#95—112no—
869#95—112no—
870#95—111no—
871#95—111no—
872#95—112no—
873#95—112no—
874#95—112no—
875#95C22×D1112yes—
876#95C22×D1112yes—
877#95C22×D1111yescharacteristic
878#95C22×D1111yescharacteristic
879C2×C11—24no—
880C2×C11—44no—
881C2×C11C22×C4×D411yescharacteristic
882C2×C11C2×#51811yescharacteristic
883C2×C11#342811yescharacteristic
884C2×C11#348811yescharacteristic
885C2×C11#348811yescharacteristic
886C2×C11#349411yescharacteristic
887C2×C11#349411yescharacteristic
888D11—24no—
889D11—42no—
890D11—44no—
891C24—111no—
892C24—112no—
893C24—111no—
894C24—114no—
895C24—118no—
896C24—222no—
897C24—222no—
898C24—224no—
899C24—224no—
900C24—222no—
901C24—222no—
902C24—441no—
903C24—441no—
904C24—442no—
905C24—442no—
906C24—442no—
907C24—442no—
908C24C23×D1112yes—
909C24C23×D1111yescharacteristic
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—118no—
915C2×D4—118no—
916C2×D4—118no—
917C2×D4—114no—
918C2×D4—118no—
919C2×D4—2232no—
920C2×D4—224no—
921C2×D4—224no—
922C2×D4—224no—
923C2×D4—224no—
924C2×D4—222no—
925C2×D4—222no—
926C2×D4—442no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4—442no—
930C2×D4—4432no—
931C2×D4C2×C4×D1118yes—
932C2×D4C2×C4×D1114yes—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—111no—
942C22×C4—114no—
943C22×C4—114no—
944C22×C4—114no—
945C22×C4—114no—
946C22×C4—111no—
947C22×C4—112no—
948C22×C4—112no—
949C22×C4—114no—
950C22×C4—114no—
951C22×C4—114no—
952C22×C4—118no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—112no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—2232no—
961C22×C4—224no—
962C22×C4—222no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—224no—
967C22×C4—224no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—224no—
971C22×C4—224no—
972C22×C4—442no—
973C22×C4—442no—
974C22×C4—442no—
975C22×C4—442no—
976C22×C4—442no—
977C22×C4—442no—
978C22×C4—442no—
979C22×C4—442no—
980C22×C4—442no—
981C22×C4C2×C4×D1114yes—
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1111yescharacteristic
984C22×C4C23×D1111yescharacteristic
985C22×C4C23×D1111yescharacteristic
986C22×C4C23×D1112yes—
987C22×C4C23×D1112yes—
988C22×C4C23×D1111yescharacteristic
989C22×C4C23×D1112yes—
990C22×C4C23×D1111yescharacteristic
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—42no—
994C4⋊C4—118no—
995C4⋊C4—114no—
996C4⋊C4—114no—
997C4⋊C4—224no—
998C4⋊C4—222no—
999C4⋊C4—222no—
1000C4⋊C4—222no—
1001C4⋊C4—222no—
1002C4⋊C4—222no—
1003C4⋊C4—442no—
1004C4⋊C4—442no—
1005C4⋊C4—442no—
1006C4⋊C4C2×C4×D1114yes—
1007C4⋊C4D4×D1114yescomplemented
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—24no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—118no—
1014C22⋊C4—118no—
1015C22⋊C4—118no—
1016C22⋊C4—118no—
1017C22⋊C4—224no—
1018C22⋊C4—224no—
1019C22⋊C4—222no—
1020C22⋊C4—222no—
1021C22⋊C4—224no—
1022C22⋊C4—222no—
1023C22⋊C4—222no—
1024C22⋊C4—224no—
1025C22⋊C4—222no—
1026C22⋊C4—222no—
1027C22⋊C4—224no—
1028C22⋊C4—224no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C22⋊C4—441no—
1032C22⋊C4—442no—
1033C22⋊C4—441no—
1034C22⋊C4—442no—
1035C22⋊C4—441no—
1036C22⋊C4—441no—
1037C22⋊C4—442no—
1038C22⋊C4—442no—
1039C22⋊C4C2×C4×D1118yes—
1040C42—22no—
1041C42—22no—
1042C42—42no—
1043C42—118no—
1044C42—224no—
1045C42—224no—
1046C42—224no—
1047C42—222no—
1048C42—222no—
1049C42—442no—
1050C42—442no—
1051C42—442no—
1052C11#3420411yescharacteristic, complemented, Sylow
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—112no—
1064C23—112no—
1065C23—112no—
1066C23—114no—
1067C23—112no—
1068C23—228no—
1069C23—2216no—
1070C23—221no—
1071C23—221no—
1072C23—221no—
1073C23—221no—
1074C23—228no—
1075C23—221no—
1076C23—222no—
1077C23—222no—
1078C23—221no—
1079C23—221no—
1080C23—222no—
1081C23—222no—
1082C23—221no—
1083C23—221no—
1084C23—222no—
1085C23—221no—
1086C23—222no—
1087C23—444no—
1088C23—448no—
1089C23—448no—
1090C23—444no—
1091C23—444no—
1092C23—444no—
1093C23—444no—
1094C23—884no—
1095C23—884no—
1096C23—884no—
1097C23—884no—
1098C23C22×C4×D1114yes—
1099C23C22×C4×D1112yes—
1100C23#6703712yes—
1101C23#6704212yes—
1102C23C24×D1111yescharacteristic
1103D4—216no—
1104D4—28no—
1105D4—2216no—
1106D4—2216no—
1107D4—228no—
1108D4—448no—
1109D4—448no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—28no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—48no—
1133C2×C4—84no—
1134C2×C4—112no—
1135C2×C4—112no—
1136C2×C4—112no—
1137C2×C4—1116no—
1138C2×C4—112no—
1139C2×C4—114no—
1140C2×C4—114no—
1141C2×C4—228no—
1142C2×C4—228no—
1143C2×C4—228no—
1144C2×C4—221no—
1145C2×C4—222no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—228no—
1151C2×C4—222no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—221no—
1155C2×C4—221no—
1156C2×C4—221no—
1157C2×C4—221no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—222no—
1161C2×C4—221no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—222no—
1165C2×C4—221no—
1166C2×C4—448no—
1167C2×C4—448no—
1168C2×C4—884no—
1169C2×C4—884no—
1170C2×C4—884no—
1171C2×C4C22×C4×D1112yes—
1172C2×C4C22×C4×D1114yes—
1173C2×C4C22×C4×D1112yes—
1174C2×C4C2×D4×D1114yes—
1175C2×C4C2×D4×D1112yes—
1176C2×C4#41×D1112yes—
1177C22—22no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—24no—
1184C22—24no—
1185C22—24no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—114no—
1191C22—222no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—222no—
1197C22—222no—
1198C22—224no—
1199C22—224no—
1200C22—222no—
1201C22—222no—
1202C22—224no—
1203C22—4416no—
1204C22—442no—
1205C22—441no—
1206C22—442no—
1207C22—441no—
1208C22—441no—
1209C22—442no—
1210C22—441no—
1211C22—442no—
1212C22—8816no—
1213C22#1062307614yescomplemented
1214C22C23×C4×D1111yescharacteristic
1215C22C22×D4×D1111yescharacteristic
1216C22C2×#6703711yescharacteristic
1217C22C2×#41×D1111yescharacteristic
1218C22C2×#6704211yescharacteristic
1219C22#1062345511yescharacteristic
1220C22#1062345711yescharacteristic
1221C4—24no—
1222C4—22no—
1223C4—24no—
1224C4—42no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—114no—
1230C4—224no—
1231C4—222no—
1232C4—224no—
1233C4—441no—
1234C4—442no—
1235C4—441no—
1236C4—441no—
1237C4—441no—
1238C4C4×D4×D1114yes—
1239C2—24no—
1240C2—44no—
1241C2—224no—
1242C2—442no—
1243C2—444no—
1244C2C2×C4×D4×D1111yescharacteristic
1245C2C2×#1062307611yescharacteristic
1246C2#1308181611yescharacteristic
1247C2#1308227611yescharacteristic
1248C2#1308228211yescharacteristic
1249C2#1308234011yescharacteristic
1250C2#1308234711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2361C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2361D11
hypocenterC11#34204
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. C22×#66945C2semidirect
4. #13071659C2semidirect
5. #13071656C2semidirect
6. #13071653C2semidirect
7. #13071650C2semidirect
8. #13071636C2semidirect
9. #13071632C2semidirect
10. #13071630C2semidirect
11. #13071464C2semidirect
12. #13071463C2semidirect
13. #13071434C2semidirect
14. D4×(C2×D11)⋊C4C2semidirect
15. #13071308C2semidirect
16. #13071304C2semidirect
17. #13071231C2semidirect
18. #13071195C2semidirect
19. #13071126C2semidirect
20. C4×#66992C2semidirect
21. #13070997C2semidirect
22. #13070970C2semidirect
23. C11×#2361C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C4×D4×C11C22semidirect
30. C22×C11×C4⋊C4C22semidirect
33. C2×D4×Dic11C22semidirect
34. C2×D4×Dic11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C2×C4×C22⋊D11C22semidirect
40. C22×C4⋊Dic11C22semidirect
41. C22×C4×Dic11C22semidirect
42. D11×#121C4semidirect
45. C2×#66946C22semidirect
50. C2×#66945C22semidirect
51. C2×#66945C22semidirect
52. C2×#66945C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×(C22⋊D11)⋊C4C22semidirect
59. C2×C4×D44C22semidirect
62. C11×#390C22semidirect
63. C11×#389C22semidirect
64. C11×#388C22semidirect
65. C11×#386C22semidirect
66. C11×#385C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. C4×C11×C22⋊C4C22semidirect
69. #10622834C22semidirect
70. #10622833C22semidirect
71. #10622826C22semidirect
72. #10622826C22semidirect
73. C4×C22⋊Dic11C22semidirect
74. C4×C22⋊Dic11C22semidirect
75. #10622603C22semidirect
76. #10622603C22semidirect
77. #10622602C22semidirect
78. #10622601C22semidirect
79. #10622601C22semidirect
81. #10622598C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
85. #10622585C22semidirect
86. #10622571C22semidirect
87. #10622571C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
96. #10622564C22semidirect
97. #10622563C22semidirect
98. #10622558C22semidirect
99. #10622557C22semidirect
100. #10622555C22semidirect
101. #10622555C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. #10622552C22semidirect
104. #10622552C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. #10622541C22semidirect
112. #10622283C22semidirect
113. #10622283C22semidirect
114. #10622281C22semidirect
116. #10622280C22semidirect
117. #10622280C22semidirect
119. #10622279C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
124. #10622262C22semidirect
125. #10622260C22semidirect
143. C2×D4×D11C2×C4semidirect
144. C2×D4×D11C2×C4semidirect
149. C22×C4×D11C2×C4semidirect
157. C11×#121C2×C4semidirect
181. #66992C2×C4semidirect
182. #66991C2×C4semidirect
185. #66983C2×C4semidirect
233. #66948C2×C4semidirect
240. #66945D4semidirect
241. C4⋊C4×D11C2×C4semidirect
242. #66937C2×C4semidirect
246. C22⋊C4×D11C2×C4semidirect
371. C11×C4⋊C4C2×D4semidirect
411. C4⋊Dic11C2×D4semidirect
427. C4×Dic11C2×D4semidirect
438. #2361D11semidirect
574. C4×D11C4×D4semidirect
594. C2×C4×D4C2×D11semidirect
595. C2×C4×D4C2×D11semidirect
607. C22×C4⋊C4C2×D11semidirect
622. #390C2×D11semidirect
628. #389C2×D11semidirect
636. #388C2×D11semidirect
644. #386C2×D11semidirect
648. #385C2×D11semidirect
666. C4×C4⋊C4C2×D11semidirect
676. C4×C22⋊C4C2×D11semidirect
690. C22×C11#518semidirect
775. #121C4×D11semidirect
1007. C4⋊C4D4×D11semidirect
1052. C11#34204semidirect
1213. C22#10623076semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×#106230762
C22×#669452
#130716592
#130716562
#130716532
#130716502
#130716362
#130716322
#130716302
#130714642
#130714632
#130714342
D4×(C2×D11)⋊C42
#130713082
#130713042
#130712312
#130711952
#130711262
C4×#669922
#130709972
#130709702
C11×#23612
#3420411