Finite Group Databasebeta

← #14916578

Subgroups — #14916578

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2#13071772C212yesmaximal, complemented
3#13071769C212yesmaximal, complemented
4#13071655C212yesmaximal, complemented
5#13071649C212yesmaximal, complemented
6#13071486C211yesmaximal, characteristic, complemented
7#13071480C211yesmaximal, characteristic, complemented
8#13071468C211yesmaximal, characteristic, complemented
9#13071465C211yesmaximal, characteristic, complemented
10#13071462C211yesmaximal, characteristic, complemented
11C22⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
12#13071432C211yesmaximal, characteristic, complemented
13#13071379C212yesmaximal, complemented
14#13071376C212yesmaximal, complemented
15#13071308C212yesmaximal, complemented
16#13071304C212yesmaximal, complemented
17#13071197C211yesmaximal, characteristic, complemented
18#13071196C211yesmaximal, characteristic, complemented
19#13071193C211yesmaximal, characteristic, complemented
20#13071191C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C11×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2212yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C2×#66945C2212yescomplemented
37C2×#66937C4116yescomplemented
38C2×#66937C2211yescharacteristic
39C2×#66937C2211yescharacteristic
40C2×#66937C2211yescharacteristic
41C2×#66937C2211yescharacteristic
42C2×#66937C2211yescharacteristic
43C2×#66937C2211yescharacteristic
44C2×#66937C2211yescharacteristic
45C2×#66937C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×#66930C2211yescharacteristic
50C2×#66930C2211yescharacteristic
51C2×#66925C2212yescomplemented
52C11×#388C2212yescomplemented
53C11×#388C2212yescomplemented
54C11×#385C2212yescomplemented
55C11×#381C2211yescharacteristic
56C11×#380C2211yescharacteristic
57C11×#379C2211yescharacteristic
58C4×C11×C22⋊C4C2211yescharacteristic
59C4×C11×C22⋊C4C2212yescomplemented
60#10622860C2211yescharacteristic
61#10622826C2212yescomplemented
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic
65#10622824C2211yescharacteristic
66C4×C22⋊Dic11C2211yescharacteristic
67#10622603C2212yescomplemented
68#10622602C2212yescomplemented
69#10622601C2212yescomplemented
70#10622601C2212yescomplemented
71#10622600C2212yescomplemented
72#10622591C2212yescomplemented
73#10622585C2212yescomplemented
74#10622571C2212yescomplemented
75#10622571C2212yescomplemented
76#10622571C2212yescomplemented
77#10622570C2212yescomplemented
78#10622570C2212yescomplemented
79#10622570C2212yescomplemented
80#10622570C2212yescomplemented
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622569C2212yescomplemented
84#10622569C2212yescomplemented
85#10622568C2211yescharacteristic
86#10622568C2211yescharacteristic
87#10622568C2211yescharacteristic
88#10622568C2211yescharacteristic
89#10622568C2211yescharacteristic
90#10622568C2211yescharacteristic
91#10622564C2212yescomplemented
92#10622564C2212yescomplemented
93#10622563C2212yescomplemented
94#10622556C2211yescharacteristic
95#10622556C2211yescharacteristic
96#10622555C2211yescharacteristic
97#10622555C2211yescharacteristic
98C22⋊C4×Dic11C2211yescharacteristic
99C22⋊C4×Dic11C2211yescharacteristic
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yescomplemented
102#10622552C2212yescomplemented
103#10622552C2212yescomplemented
104C4×(C2×D11)⋊C4C2212yescomplemented
105C4×(C2×D11)⋊C4C2212yescomplemented
106#10622546C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108#10622283C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2212yescomplemented
111#10622280C2212yescomplemented
112#10622279C2212yescomplemented
113#10622279C2212yescomplemented
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622277C2212yescomplemented
119#10622277C2212yescomplemented
120#10622268C2212yescomplemented
121#10622265C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124C25×C11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11—44no—
131C22×C22⋊D11—42no—
132C22×C22⋊D11—42no—
133C22×C22⋊D11C2×C418yes—
134C22×C22⋊D11C2×C418yescomplemented
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2312yes—
146C22×D44—42no—
147C22×D44—42no—
148C22×D44C2×C418yescomplemented
149C22×D44C2311yescharacteristic
150C22×D44C2311yescharacteristic
151C22×D44C2311yescharacteristic
152C22×D44C2311yescharacteristic
153C22×C4×D11—44no—
154C22×C4×D11C2×C418yescomplemented
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2312yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C11×#117—42no—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C22⋊C4—42no—
165C2×C11×C22⋊C4C2×C418yescomplemented
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C42×C11C2312yes—
178C2×C42×C11C2312yes—
179C2×C22⋊Dic11—42no—
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C4×C22⋊D11—44no—
188C2×(C2×D11)⋊C4C2×C418yescomplemented
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
207#66979—42no—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×Dic11⋊C4C2×C418yescomplemented
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225#66945—44no—
226#66937C2×C418yescomplemented
227#66937C2×C418yescomplemented
228#66937C2×C418yescomplemented
229#66937C2×C418yescomplemented
230#66937C2×C418yescomplemented
231#66937C2×C418yescomplemented
232#66937C2×C418yescomplemented
233#66937C2×C418yescomplemented
234(C22⋊D11)⋊C4—44no—
235C22⋊C4×D11—42no—
236C22⋊C4×D11—42no—
237#66930—42no—
238#66930—42no—
239#66925—44no—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256#34363—111nomaximal, Sylow
257C24×C11—22no—
258C24×C11—22no—
259C24×C11—42no—
260C24×C11—42no—
261C24×C11C22×C414yes—
262C24×C11C2411yescharacteristic
263C24×C11C2411yescharacteristic
264C24×C11C2411yescharacteristic
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11C22×C414yes—
274C23×D11C22×C414yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11C22×C414yes—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—416no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—41no—
301C2×C22⋊D11—41no—
302C2×C22⋊D11—41no—
303C2×C22⋊D11—41no—
304C2×C22⋊D11—41no—
305C2×C22⋊D11—41no—
306C2×C22⋊D11—41no—
307C2×C22⋊D11—41no—
308C2×C22⋊D11—416no—
309C2×C22⋊D11C22×C414yes—
310C2×C22⋊D11C22×C414yes—
311C2×C22⋊D11C22×C414yes—
312C2×C22⋊D11C22×C414yes—
313C2×C22⋊D11C22×C414yes—
314C2×C22⋊D11C22×C414yes—
315C2×C22⋊D11C22×C414yes—
316C2×C22⋊D11C22×C414yes—
317C22×Dic11—24no—
318C22×Dic11—22no—
319C22×Dic11—22no—
320C22×Dic11—42no—
321C22×Dic11—42no—
322C22×Dic11—42no—
323C22×Dic11C22×C414yes—
324C22×Dic11C22×C414yes—
325C22×Dic11C2412yes—
326C22×Dic11C2412yes—
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C2×D44—416no—
334C2×D44—41no—
335C2×D44—41no—
336C2×D44—41no—
337C2×D44—41no—
338C2×D44—41no—
339C2×D44—41no—
340C2×D44—41no—
341C2×D44—41no—
342C2×D44C22×C414yes—
343C2×D44C22×C414yes—
344C2×D44C22×C414yes—
345C2×D44C22×C414yes—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—416no—
357C2×C4×D11C22×C414yes—
358C2×C4×D11C22×C414yes—
359C2×C4×D11C22×C414yes—
360C2×C4×D11C22×C414yes—
361C11×C4⋊C4—42no—
362C11×C4⋊C4—42no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4C22×C414yes—
371C11×C22⋊C4C22×C414yes—
372C11×C22⋊C4C22×C414yes—
373C11×C22⋊C4C22×C414yes—
374C42×C11—42no—
375C42×C11—42no—
376C22⋊Dic11—22no—
377C22⋊Dic11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—22no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4C22×C414yes—
398(C2×D11)⋊C4C22×C414yes—
399(C2×D11)⋊C4C22×C414yes—
400(C2×D11)⋊C4C22×C414yes—
401C4⋊Dic11—42no—
402C4⋊Dic11—42no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4C22×C414yes—
408Dic11⋊C4C22×C414yes—
409Dic11⋊C4C22×C414yes—
410Dic11⋊C4C22×C414yes—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—42no—
414C4×Dic11—42no—
415C4×Dic11—42no—
416C4×Dic11—42no—
417C22×#121—111no—
418#2377—112no—
419#2377—112no—
420#2363—112no—
421#2363—112no—
422#2344—111no—
423#2344—111no—
424#2342—111no—
425#2342—111no—
426#2342—111no—
427#2342D1111yescharacteristic, complemented
428D4×C22⋊C4—111no—
429D4×C22⋊C4—111no—
430#2333—112no—
431#2333—112no—
432#2324—112no—
433#2324—112no—
434#2309—111no—
435#2309—111no—
436#2308—111no—
437#2308—111no—
438#2280—111no—
439#2280—111no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—28no—
451C23×C11—44no—
452C23×C11—44no—
453C23×C11—84no—
454C23×C11—84no—
455C23×C11C23×C412yes—
456C23×C11C23×C412yes—
457C23×C11C23×C412yes—
458C23×C11H(5,𝔽2)12yes—
459C23×C11H(5,𝔽2)12yes—
460C23×C11C2511yescharacteristic
461C22×D11—28no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—28no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11—44no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—84no—
486C22×D11—84no—
487C22×D11C23×C412yes—
488C22×D11C23×C412yes—
489C22×D11C23×C412yes—
490C22×D11C23×C412yes—
491C2×C4×C11—28no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—44no—
511C2×C4×C11—84no—
512C2×C4×C11C23×C412yes—
513C2×C4×C11C23×C412yes—
514C2×C4×C11C23×C412yes—
515C2×C4×C11C23×C412yes—
516C22⋊D11—28no—
517C22⋊D11—28no—
518C22⋊D11—44no—
519C22⋊D11—44no—
520C22⋊D11—44no—
521C22⋊D11—44no—
522C22⋊D11—44no—
523C22⋊D11—44no—
524C2×Dic11—28no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—28no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
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—84no—
544C2×Dic11C23×C412yes—
545C2×Dic11C23×C412yes—
546C2×Dic11C23×C412yes—
547C2×Dic11C23×C412yes—
548C2×Dic11H(5,𝔽2)14yes—
549D44—44no—
550D44—44no—
551D44—44no—
552D44—44no—
553C4×D11—28no—
554C4×D11—28no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—84no—
558C4×D11—84no—
559C23×D4—111no—
560C23×D4—111no—
561C23×D4—111no—
562C24×C4—111no—
563C2×#121—111no—
564C2×#121—111no—
565C2×#121—111no—
566C2×#121—111no—
567C2×#121—111no—
568C2×#121—111no—
569C2×#121—111no—
570C2×#121—111no—
571C2×#121—1116no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×#117—111no—
575C2×#117—112no—
576C2×#117—111no—
577C2×#117—111no—
578C2×#117—112no—
579C2×#117C2×D1111yescharacteristic
580C22×C4⋊C4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4C2×D1111yescharacteristic
586C22×C22⋊C4C2×D1111yescharacteristic
587#390—112no—
588#390—112no—
589#390—112no—
590#390—112no—
591#390—112no—
592#390—112no—
593#390—112no—
594#390—112no—
595#390—112no—
596#390—112no—
597#389—112no—
598#389—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388C2×D1112yescomplemented
606#388C2×D1112yescomplemented
607#387—112no—
608#387—112no—
609#387—112no—
610#387—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
618#386—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#385—112no—
624#385—112no—
625#385—112no—
626#385C2×D1112yescomplemented
627#381—111no—
628#381—111no—
629#381—111no—
630#381—112no—
631#381—112no—
632#381C2×D1111yescharacteristic
633#380—111no—
634#380—112no—
635#380—111no—
636#380—111no—
637#380—112no—
638#380C2×D1111yescharacteristic
639#379—111no—
640#379—111no—
641#379—111no—
642#379—111no—
643#379—111no—
644#379—111no—
645#379—111no—
646#379C2×D1111yescharacteristic
647C4×C4⋊C4—112no—
648C4×C4⋊C4—112no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—111no—
652C4×C22⋊C4—111no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4C2×D1111yescharacteristic
658C4×C22⋊C4C2×D1112yescomplemented
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—24no—
662C22×C11—24no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—88no—
674C22×C11#51814yes—
675C22×C11C24×C411yescharacteristic
676C22×C11C2×H(5,𝔽2)11yescharacteristic
677C22×C11C2×H(5,𝔽2)11yescharacteristic
678C22×C11C2×H(5,𝔽2)12yes—
679C22×C11#58512yes—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—416no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—88no—
702C4×C11—22no—
703C4×C11—22no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—42no—
707C4×C11—42no—
708C4×C11—42no—
709C4×C11—42no—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713Dic11—42no—
714Dic11—42no—
715Dic11—42no—
716Dic11—42no—
717Dic11#51814yes—
718C25—111no—
719C25—111no—
720C25C22×D1111yescharacteristic
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—118no—
724C22×D4—118no—
725C22×D4—111no—
726C22×D4—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—111no—
730C22×D4—111no—
731C22×D4—118no—
732C22×D4—111no—
733C22×D4—111no—
734C22×D4—111no—
735C22×D4—111no—
736C22×D4—442no—
737C22×D4—442no—
738C22×D4—444no—
739C22×D4—442no—
740C22×D4—442no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—118no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—112no—
749C23×C4—112no—
750C23×C4—112no—
751C23×C4—444no—
752C23×C4C22×D1111yescharacteristic
753C23×C4C22×D1112yes—
754C23×C4C22×D1111yescharacteristic
755#121—118no—
756#121—118no—
757#121—118no—
758#121—118no—
759#121—118no—
760#121—118no—
761#121—118no—
762#121—118no—
763C4×D4—444no—
764C4×D4—444no—
765#117—42no—
766#117—444no—
767#117—444no—
768#117—442no—
769#117—442no—
770#117—442no—
771C2×C4⋊C4—118no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4C22×D1112yes—
783C2×C4⋊C4C22×D1112yes—
784C2×C22⋊C4—42no—
785C2×C22⋊C4—118no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—442no—
812C2×C22⋊C4—442no—
813C2×C22⋊C4—442no—
814C2×C22⋊C4C4×D1118yescomplemented
815C2×C22⋊C4C22×D1111yescharacteristic
816C2×C22⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C22⋊C4C22×D1111yescharacteristic
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1111yescharacteristic
823C2×C22⋊C4C22×D1111yescharacteristic
824C2×C22⋊C4C22×D1111yescharacteristic
825C2×C22⋊C4C22×D1111yescharacteristic
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42C22×D1112yes—
833C2×C42C22×D1112yes—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95C22×D1112yes—
847#95C22×D1112yes—
848#95C22×D1112yes—
849#95C22×D1112yes—
850C2×C11—24no—
851C2×C11—42no—
852C2×C11—42no—
853C2×C11C2×#51811yescharacteristic
854C2×C11C2×#51811yescharacteristic
855C2×C11#342811yescharacteristic
856C2×C11#354212yes—
857C2×C11#354212yes—
858D11—42no—
859D11—42no—
860D11—42no—
861D11—42no—
862C24—22no—
863C24—22no—
864C24—42no—
865C24—42no—
866C24—111no—
867C24—111no—
868C24—111no—
869C24—111no—
870C24—114no—
871C24—114no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24—442no—
877C24—442no—
878C24—442no—
879C24—442no—
880C24C2×C4×D1114yes—
881C24C23×D1111yescharacteristic
882C24C23×D1111yescharacteristic
883C24C23×D1111yescharacteristic
884C2×D4—114no—
885C2×D4—114no—
886C2×D4—114no—
887C2×D4—114no—
888C2×D4—114no—
889C2×D4—114no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—114no—
893C2×D4—114no—
894C2×D4—114no—
895C2×D4—114no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—4416no—
899C2×D4—441no—
900C2×D4—441no—
901C2×D4—441no—
902C2×D4—441no—
903C2×D4—441no—
904C2×D4—441no—
905C2×D4—441no—
906C2×D4—441no—
907C2×D4—4416no—
908C2×D4—4416no—
909C2×D4—441no—
910C2×D4—441no—
911C2×D4—441no—
912C2×D4—441no—
913C2×D4—441no—
914C2×D4—441no—
915C2×D4—441no—
916C2×D4—441no—
917C2×D4—442no—
918C2×D4—442no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—111no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—114no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—114no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—4416no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4C2×C4×D1114yes—
957C22×C4C2×C4×D1114yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1112yes—
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1111yescharacteristic
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—114no—
969C4⋊C4—114no—
970C4⋊C4—114no—
971C4⋊C4—114no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C4⋊C4—442no—
977C4⋊C4—442no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—114no—
986C22⋊C4—114no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4C2×C4×D1114yes—
1011C22⋊C4C2×C4×D1114yes—
1012C22⋊C4C2×C4×D1114yes—
1013C22⋊C4C2×C4×D1114yes—
1014C42—42no—
1015C42—42no—
1016C42—224no—
1017C42—224no—
1018C42—442no—
1019C42—442no—
1020C42—442no—
1021C42—442no—
1022C11#3436311yescharacteristic, complemented, Sylow
1023C23—22no—
1024C23—22no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—28no—
1034C23—44no—
1035C23—44no—
1036C23—84no—
1037C23—84no—
1038C23—112no—
1039C23—112no—
1040C23—112no—
1041C23—112no—
1042C23—228no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—228no—
1060C23—444no—
1061C23—444no—
1062C23—444no—
1063C23—444no—
1064C23—448no—
1065C23—448no—
1066C23—884no—
1067C23—884no—
1068C23C22×C4×D1112yes—
1069C23C22×C4×D1112yes—
1070C23C22×C4×D1112yes—
1071C23#6703712yes—
1072C23#6704212yes—
1073C23C24×D1111yescharacteristic
1074D4—228no—
1075D4—228no—
1076D4—444no—
1077D4—444no—
1078D4—444no—
1079D4—444no—
1080D4—444no—
1081D4—444no—
1082D4—444no—
1083D4—444no—
1084D4—444no—
1085D4—444no—
1086C2×C4—28no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—44no—
1106C2×C4—84no—
1107C2×C4—112no—
1108C2×C4—114no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—228no—
1113C2×C4—228no—
1114C2×C4—228no—
1115C2×C4—228no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4—884no—
1136C2×C4—884no—
1137C2×C4—884no—
1138C2×C4C22×C4×D1112yes—
1139C2×C4C22×C4×D1112yes—
1140C2×C4C22×C4×D1112yes—
1141C2×C4C22×C4×D1112yes—
1142C22—24no—
1143C22—24no—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—88no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—4416no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—888no—
1179C22#1062307614yes—
1180C22C23×C4×D1111yescharacteristic
1181C22C2×#6703711yescharacteristic
1182C22C2×#6704211yescharacteristic
1183C22#1062345312yes—
1184C22D11×H(5,𝔽2)12yes—
1185C4—22no—
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—114no—
1194C4—222no—
1195C4—222no—
1196C4—222no—
1197C4—442no—
1198C4—442no—
1199C4—442no—
1200C4—442no—
1201C2—24no—
1202C2—42no—
1203C2—42no—
1204C2—442no—
1205C2—442no—
1206C2—442no—
1207C2—442no—
1208C2D11×#51811yescharacteristic
1209C2C2×#1062307611yescharacteristic
1210C2#1308181711yescharacteristic
1211C2#1308291712yes—
1212C2#1308292512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2342C2
socle, cosocleC23×C11C25
prime radicalC22×#66937C2
hypercenter#2342D11
hypocenterC11#34363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #13071772C2semidirect
3. #13071769C2semidirect
4. #13071655C2semidirect
5. #13071649C2semidirect
6. #13071486C2semidirect
7. #13071480C2semidirect
8. #13071468C2semidirect
9. #13071465C2semidirect
10. #13071462C2semidirect
11. C22⋊C4×C22⋊D11C2semidirect
12. #13071432C2semidirect
13. #13071379C2semidirect
14. #13071376C2semidirect
15. #13071308C2semidirect
16. #13071304C2semidirect
17. #13071197C2semidirect
18. #13071196C2semidirect
19. #13071193C2semidirect
20. #13071191C2semidirect
21. #13070998C2semidirect
22. #13070997C2semidirect
23. C11×#2342C2semidirect
32. C2×C4×C22⋊D11C22semidirect
36. C2×#66945C22semidirect
37. C2×#66937C4semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
51. C2×#66925C22semidirect
52. C11×#388C22semidirect
53. C11×#388C22semidirect
54. C11×#385C22semidirect
59. C4×C11×C22⋊C4C22semidirect
61. #10622826C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
67. #10622603C22semidirect
68. #10622602C22semidirect
69. #10622601C22semidirect
70. #10622601C22semidirect
71. #10622600C22semidirect
72. #10622591C22semidirect
73. #10622585C22semidirect
74. #10622571C22semidirect
75. #10622571C22semidirect
76. #10622571C22semidirect
77. #10622570C22semidirect
78. #10622570C22semidirect
79. #10622570C22semidirect
80. #10622570C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
91. #10622564C22semidirect
92. #10622564C22semidirect
93. #10622563C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. #10622553C22semidirect
102. #10622552C22semidirect
103. #10622552C22semidirect
104. C4×(C2×D11)⋊C4C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. #10622546C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622283C22semidirect
109. #10622282C22semidirect
110. #10622281C22semidirect
111. #10622280C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622277C22semidirect
119. #10622277C22semidirect
120. #10622268C22semidirect
121. #10622265C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
134. C22×C22⋊D11C2×C4semidirect
148. C22×D44C2×C4semidirect
154. C22×C4×D11C2×C4semidirect
165. C2×C11×C22⋊C4C2×C4semidirect
188. C2×(C2×D11)⋊C4C2×C4semidirect
210. C2×Dic11⋊C4C2×C4semidirect
226. #66937C2×C4semidirect
227. #66937C2×C4semidirect
228. #66937C2×C4semidirect
229. #66937C2×C4semidirect
230. #66937C2×C4semidirect
231. #66937C2×C4semidirect
232. #66937C2×C4semidirect
233. #66937C2×C4semidirect
427. #2342D11semidirect
605. #388C2×D11semidirect
606. #388C2×D11semidirect
626. #385C2×D11semidirect
658. C4×C22⋊C4C2×D11semidirect
814. C2×C22⋊C4C4×D11semidirect
1022. C11#34363semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
#130717722
#130717692
#130716552
#130716492
#130714862
#130714802
#130714682
#130714652
#130714622
C22⋊C4×C22⋊D112
#130714322
#130713792
#130713762
#130713082
#130713042
#130711972
#130711962
#130711932
#130711912
#130709982
#130709972
C11×#23422
#3436311