Finite Group Databasebeta

← #15624510

Subgroups — #15624510

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic, complemented
2#13079426C214yesmaximal, complemented
3#13079418C212yesmaximal, complemented
4#13079413C212yesmaximal, complemented
5#13079377C214yesmaximal, complemented
6#13079369C212yesmaximal, complemented
7#13079364C212yesmaximal, complemented
8#13078556C212yesmaximal, complemented
9#13078536C212yesmaximal, complemented
10#13078237C214yesmaximal, complemented
11#13077868C212yesmaximal, complemented
12#13077842C212yesmaximal, complemented
13C2×#10622820C211yesmaximal, characteristic, complemented
14C2×C11×#525C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C23×D44C2211yescharacteristic, complemented
19C11×#525—21no—
20C11×#525—21no—
21C11×#525—21no—
22C11×#525—21no—
23C11×#525C2212yes—
24C11×#525C2212yescomplemented
25C11×#525C2212yescomplemented
26C11×#525C2212yescomplemented
27C2×C11×#123—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic, complemented
29C2×C11×C22⋊Q8C2211yescharacteristic, complemented
30C2×C11×#121C2211yescharacteristic, complemented
31C2×C11×#121C2211yescharacteristic, complemented
32C2×C11×#120—21no—
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11—21no—
35C2×C11×#117C2211yescharacteristic, complemented
36C2×#67002C2214yescomplemented
37C2×#66983—21no—
38C2×#66983—21no—
39C2×#66983—21no—
40C2×#66983—21no—
41C2×#66983—21no—
42C2×#66983—21no—
43C2×#66983C2212yes—
44C2×#66983C2212yes—
45C2×#66983C2212yes—
46C2×#66983C2212yescomplemented
47C2×#66983C2212yescomplemented
48C2×#66983C2212yescomplemented
49C22×(C2×D11)⋊C4—21no—
50C22×C4⋊Dic11C2211yescharacteristic, complemented
51C22×#4318C2212yescomplemented
52#10622851C2218yescomplemented
53#10622845C2214yescomplemented
54#10622840C2214yescomplemented
55#10622830C2214yescomplemented
56#10622820C2212yescomplemented
57#10622820C2212yescomplemented
58#10622820C2212yescomplemented
59#10622820C2212yescomplemented
60C2×C22⋊(C11⋊C8)C2212yescomplemented
61C2×C22⋊(C11⋊C8)C2212yescomplemented
62#10622662C2218yescomplemented
63#10622661C2218yescomplemented
64#10622659C2214yescomplemented
65#10622659C2214yescomplemented
66#10622657C2214yescomplemented
67#10622656C2214yescomplemented
68#10622652C2218yescomplemented
69#10622651C2218yescomplemented
70#10622649C2214yescomplemented
71#10622649C2214yescomplemented
72#10622647C2214yescomplemented
73#10622646C2214yescomplemented
74#10622616C2218yescomplemented
75#10622614C2214yescomplemented
76#10622608C2214yescomplemented
77#10622581C2214yescomplemented
78#10622580C2214yescomplemented
79C25×C11D411yescharacteristic
80C24×D11—21no—
81C2×C11×#41—21no—
82C2×C11×#41—21no—
83C2×C11×#41—44no—
84C2×C11×#41C2312yes—
85C2×C11×#41C2312yescomplemented
86C22×Q8×C11C2311yescharacteristic, complemented
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic, complemented
91C23×C4×C11—21no—
92C23×C4×C11—44no—
93C23×C4×C11D411yescharacteristic
94C23×C4×C11D411yescharacteristic
95C23×C4×C11D411yescharacteristic
96C23×C4×C11D411yescharacteristic
97C23×C4×C11D411yescharacteristic
98C23×C4×C11D411yescharacteristic
99C23×C4×C11D411yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C22×C22⋊D11—22no—
108C22×C22⋊D11—22no—
109C22×C22⋊D11—22no—
110C22×C22⋊D11—22no—
111C22×C22⋊D11—22no—
112C22×C22⋊D11—22no—
113C22×C22⋊D11—48no—
114C23×Dic11—21no—
115C22×D44—21no—
116C22×D44—21no—
117C22×D44—21no—
118C22×D44—44no—
119C22×D44C2312yes—
120C22×D44C2312yes—
121C22×D44C2312yes—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×#123—22no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—21no—
128C11×C22⋊Q8—21no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8C2312yes—
131C11×C22⋊Q8C2312yes—
132C11×C22⋊Q8C2312yescomplemented
133C11×C22⋊Q8C2312yescomplemented
134C11×#121—21no—
135C11×#121—21no—
136C11×#121—21no—
137C11×#121—21no—
138C11×#121C2312yes—
139C11×#121C2312yes—
140C11×#121C2312yescomplemented
141C11×#121C2312yescomplemented
142C11×#120—22no—
143C11×#120—22no—
144C11×#120—22no—
145C11×#120—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C4×D4×C11—22no—
151C4×D4×C11—22no—
152C4×D4×C11—22no—
153C4×D4×C11—22no—
154C11×#117—21no—
155C11×#117—21no—
156C11×#117C2312yes—
157C11×#117C2312yescomplemented
158C2×C11×C4⋊C4—21no—
159C2×C11×C4⋊C4—21no—
160C2×C11×C4⋊C4C2311yescharacteristic, complemented
161C2×C11×C4⋊C4C2311yescharacteristic, complemented
162C2×C11×C22⋊C4—21no—
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4—21no—
165C2×C11×C22⋊C4—21no—
166C2×C11×C22⋊C4—21no—
167C2×C42×C11—21no—
168#67002—48no—
169C2×#4325C2318yescomplemented
170C2×#4323C2318yescomplemented
171#66983—22no—
172#66983—22no—
173#66983—22no—
174#66983—22no—
175#66983—22no—
176#66983—22no—
177#66983—22no—
178#66983—22no—
179#66983—22no—
180#66983—22no—
181#66983—22no—
182#66983—22no—
183#66983C2314yes—
184#66983C2314yes—
185#66983C2314yes—
186#66983C2314yes—
187C2×(C2×D11)⋊C4—22no—
188C2×(C2×D11)⋊C4—22no—
189C2×(C2×D11)⋊C4—22no—
190C2×(C2×D11)⋊C4—22no—
191C2×(C2×D11)⋊C4—22no—
192C2×(C2×D11)⋊C4—22no—
193C2×C4⋊Dic11—21no—
194C2×C4⋊Dic11—21no—
195C2×C4⋊Dic11—21no—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×#4318—44no—
200C2×#4318C2314yes—
201C2×#4318C2314yescomplemented
202C22×C11⋊C8C2314yescomplemented
203#66899C2318yescomplemented
204#66896C2318yescomplemented
205C22⋊(C11⋊C8)C2314yes—
206C22⋊(C11⋊C8)C2314yes—
207C22⋊(C11⋊C8)C2314yescomplemented
208C22⋊(C11⋊C8)C2314yescomplemented
209#66873C2318yescomplemented
210#66873C2318yescomplemented
211#66872C2318yescomplemented
212#66871C2318yescomplemented
213#60750—111nomaximal, Sylow
214C24×C11—24no—
215C24×C11—21no—
216C24×C11—42no—
217C24×C11—42no—
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C24×C11C2×D411yescharacteristic
224C24×C11C2×D411yescharacteristic
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—22no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C11×#41—28no—
232C11×#41—44no—
233C11×#41—44no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2412yes—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—21no—
245C2×D4×C11—42no—
246C2×D4×C11—44no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11C2412yes—
250C22×C4×C11—24no—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—42no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—44no—
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—48no—
303C2×C22⋊D11—48no—
304C2×C22⋊D11—48no—
305C2×C22⋊D11—48no—
306C2×C22⋊D11—48no—
307C2×C22⋊D11—48no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11—44no—
312C2×D44—22no—
313C2×D44—22no—
314C2×D44—22no—
315C2×D44—28no—
316C2×D44—44no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44C2414yes—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—21no—
328C11×C4⋊C4C2412yes—
329C11×C4⋊C4C2412yes—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—22no—
333C11×C22⋊C4—22no—
334C11×C22⋊C4—22no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—22no—
340C42×C11—22no—
341C42×C11—22no—
342#4325—48no—
343#4323—48no—
344(C2×D11)⋊C4—24no—
345(C2×D11)⋊C4—24no—
346(C2×D11)⋊C4—24no—
347(C2×D11)⋊C4—24no—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11—22no—
351C4⋊Dic11C2414yes—
352#4318—28no—
353#4318—44no—
354C2×C11⋊C8—44no—
355C2×C11⋊C8C2418yes—
356C2×#525D1111yescharacteristic, complemented
357C22×#121—111no—
358#3194—114no—
359#3193—112no—
360#3192—112no—
361#3188—114no—
362#3187—112no—
363#3186—112no—
364#3094—112no—
365#3092—112no—
366#3055—114no—
367#3006—112no—
368#3003—112no—
369C2×#407—111no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—416no—
392C23×C11—42no—
393C23×C11—42no—
394C23×C11—42no—
395C23×C11AGL(1,ℤ/8)14yescomplemented
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C22×D411yescharacteristic
399C23×C11C22×D411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C22×D11—24no—
404C22×D11—44no—
405C22×D11—44no—
406C22×D11—44no—
407C22×D11—44no—
408C22×D11—44no—
409C22×D11—44no—
410C22×D11—44no—
411C22×D11—44no—
412C22×D11—44no—
413C22×D11—816no—
414Q8×C11—24no—
415Q8×C11—42no—
416D4×C11—24no—
417D4×C11—42no—
418D4×C11—44no—
419D4×C11—44no—
420D4×C11—44no—
421D4×C11—44no—
422D4×C11—44no—
423D4×C11—44no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—44no—
455C2×C4×C11—42no—
456C2×C4×C11—42no—
457C2×C4×C11—42no—
458C2×C4×C11—44no—
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C22×D411yescharacteristic
462C2×C4×C11C22×D411yescharacteristic
463C2×C4×C11C22×D411yescharacteristic
464C2×C4×C11C22×D411yescharacteristic
465C2×C4×C11C22×D411yescharacteristic
466C2×C4×C11H(5,𝔽2)14yes—
467C2×C4×C11C2511yescharacteristic
468C22⋊D11—48no—
469C22⋊D11—48no—
470C22⋊D11—48no—
471C22⋊D11—48no—
472C2×Dic11—24no—
473C2×Dic11—44no—
474C2×Dic11—44no—
475C2×Dic11—44no—
476D44—28no—
477D44—44no—
478D44—44no—
479D44—44no—
480C11⋊C8—28no—
481C22×#41C2×D1111yescharacteristic, complemented
482C23×D4—111no—
483C23×D4—221no—
484C24×C4C2×D1111yescharacteristic
485C2×AGL(1,ℤ/8)—114no—
486C22×M16—112no—
487#525—21no—
488#525—21no—
489#525—21no—
490#525—21no—
491#525C2×D1112yes—
492#525C2×D1112yescomplemented
493#525C2×D1112yescomplemented
494#525C2×D1112yescomplemented
495C2×#123—21no—
496C2×C22⋊Q8C2×D1111yescharacteristic, complemented
497C2×C22⋊Q8C2×D1111yescharacteristic, complemented
498C2×#121—112no—
499C2×#121—112no—
500C2×#121—112no—
501C2×#121—112no—
502C2×#121—112no—
503C2×#121—112no—
504C2×#121—221no—
505C2×#121—221no—
506C2×#121—221no—
507C2×#121—221no—
508C2×#121—221no—
509C2×#121—221no—
510C2×#121C2×D1111yescharacteristic, complemented
511C2×#121C2×D1111yescharacteristic, complemented
512C2×#120—21no—
513C2×C4×D4—21no—
514C2×C4×D4—21no—
515C2×#117C2×D1111yescharacteristic, complemented
516C22×C4⋊C4—111no—
517C22×C22⋊C4—221no—
518#484—114no—
519#483—114no—
520#482—118no—
521#481—114no—
522#481—114no—
523#480—114no—
524#480—114no—
525#469—118no—
526#468—118no—
527#466—118no—
528#465—118no—
529#450—114no—
530#450—114no—
531#449—118no—
532#448—114no—
533#447—114no—
534#447—114no—
535#447—114no—
536#428—114no—
537#418—114no—
538#417—114no—
539#407—112no—
540#407—112no—
541#407—112no—
542#407—112no—
543C2×C22⋊C8—112no—
544C2×C22⋊C8—112no—
545C22×C11—28no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11—21no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—44no—
563C22×C11—44no—
564C22×C11—44no—
565C22×C11—44no—
566C22×C11—44no—
567C22×C11—44no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—84no—
572C22×C11#53412yes—
573C22×C11C2×AGL(1,ℤ/8)12yes—
574C22×C11C2×AGL(1,ℤ/8)12yes—
575C22×C11C2×AGL(1,ℤ/8)12yes—
576C22×C11#57512yes—
577C22×C11C23×D411yescharacteristic
578C2×D11—44no—
579C2×D11—44no—
580C2×D11—44no—
581C2×D11—88no—
582C2×D11—88no—
583C2×D11—88no—
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11#53412yes—
594C4×C11C2×H(5,𝔽2)12yes—
595Dic11—44no—
596C25—221no—
597C25C22⋊D1111yescharacteristic
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—44no—
601C2×#41C22×D1112yes—
602C2×#41C22×D1112yescomplemented
603C22×Q8C22×D1111yescharacteristic, complemented
604C22×D4—21no—
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—112no—
608C22×D4—112no—
609C22×D4—112no—
610C22×D4—222no—
611C22×D4—222no—
612C22×D4—222no—
613C22×D4—222no—
614C22×D4—222no—
615C22×D4—222no—
616C22×D4—221no—
617C22×D4—221no—
618C22×D4—221no—
619C22×D4—444no—
620C22×D4—448no—
621C22×D4C22×D1111yescharacteristic, complemented
622C23×C4—21no—
623C23×C4—44no—
624C23×C4—221no—
625C23×C4C22⋊D1111yescharacteristic
626C23×C4C22⋊D1111yescharacteristic
627C23×C4C22⋊D1111yescharacteristic
628C23×C4C22⋊D1111yescharacteristic
629C23×C4C22⋊D1111yescharacteristic
630C23×C4C22⋊D1111yescharacteristic
631C23×C4C22⋊D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639AGL(1,ℤ/8)—448no—
640C2×SD16—118no—
641C2×D8—118no—
642C2×M16—114no—
643C2×M16—114no—
644C2×M16—444no—
645C22×C8—114no—
646#123—22no—
647#123—22no—
648#123—22no—
649#123—22no—
650C22⋊Q8—21no—
651C22⋊Q8—21no—
652C22⋊Q8—21no—
653C22⋊Q8—21no—
654C22⋊Q8C22×D1112yes—
655C22⋊Q8C22×D1112yes—
656C22⋊Q8C22×D1112yescomplemented
657C22⋊Q8C22×D1112yescomplemented
658#121—21no—
659#121—21no—
660#121—21no—
661#121—21no—
662#121—114no—
663#121—114no—
664#121—114no—
665#121—114no—
666#121—222no—
667#121—222no—
668#121—222no—
669#121—222no—
670#121—222no—
671#121—222no—
672#121—222no—
673#121—222no—
674#121—222no—
675#121—222no—
676#121—222no—
677#121—222no—
678#121C22×D1112yes—
679#121C22×D1112yes—
680#121C22×D1112yescomplemented
681#121C22×D1112yescomplemented
682#120—22no—
683#120—22no—
684#120—22no—
685#120—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694#117—21no—
695#117—21no—
696#117C22×D1112yes—
697#117C22×D1112yescomplemented
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—221no—
704C2×C4⋊C4—221no—
705C2×C4⋊C4—221no—
706C2×C4⋊C4C22×D1111yescharacteristic, complemented
707C2×C4⋊C4C22×D1111yescharacteristic, complemented
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C42—21no—
720#107—118no—
721#106—118no—
722#103—118no—
723#102—118no—
724#102—118no—
725#102—118no—
726C22⋊C8—114no—
727C22⋊C8—114no—
728C22⋊C8—114no—
729C22⋊C8—114no—
730C2×C11—22no—
731C2×C11—22no—
732C2×C11—22no—
733C2×C11—22no—
734C2×C11—22no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11—82no—
738C2×C11C2×#53411yescharacteristic
739C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
740C2×C11C2×#57511yescharacteristic
741D11—84no—
742C24—24no—
743C24—21no—
744C24—42no—
745C24—42no—
746C24—222no—
747C24—222no—
748C24—222no—
749C24—444no—
750C24—444no—
751C24—444no—
752C24C2×C22⋊D1111yescharacteristic
753C24C2×C22⋊D1111yescharacteristic
754C24C2×C22⋊D1111yescharacteristic
755C24C2×C22⋊D1111yescharacteristic
756C24C2×C22⋊D1111yescharacteristic
757C24C2×C22⋊D1111yescharacteristic
758C24C2×C22⋊D1111yescharacteristic
759#41—28no—
760#41—44no—
761#41—44no—
762#41—44no—
763C2×Q8—21no—
764C2×Q8—42no—
765C2×Q8C23×D1112yes—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—21no—
773C2×D4—42no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—114no—
778C2×D4—224no—
779C2×D4—224no—
780C2×D4—224no—
781C2×D4—224no—
782C2×D4—228no—
783C2×D4—222no—
784C2×D4—222no—
785C2×D4—222no—
786C2×D4—444no—
787C2×D4—444no—
788C2×D4—444no—
789C2×D4—444no—
790C2×D4—444no—
791C2×D4—448no—
792C2×D4—448no—
793C2×D4—448no—
794C2×D4—448no—
795C2×D4—448no—
796C2×D4—448no—
797C2×D4C23×D1112yes—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—222no—
821C22×C4—444no—
822C22×C4C2×C22⋊D1111yescharacteristic
823C22×C4C2×C22⋊D1111yescharacteristic
824C22×C4C2×C22⋊D1111yescharacteristic
825C22×C4C2×C22⋊D1111yescharacteristic
826C22×C4C2×C22⋊D1111yescharacteristic
827C22×C4C2×C22⋊D1111yescharacteristic
828C22×C4C2×C22⋊D1111yescharacteristic
829C22×C4C2×C22⋊D1111yescharacteristic
830C22×C4C2×C22⋊D1111yescharacteristic
831C22×C4C2×C22⋊D1111yescharacteristic
832C22×C4C2×C22⋊D1111yescharacteristic
833C22×C4C2×C22⋊D1111yescharacteristic
834C22×C4C2×C22⋊D1111yescharacteristic
835C22×C4C2×C22⋊D1111yescharacteristic
836C22×C4C2×C22⋊D1111yescharacteristic
837C22×C4C2×C22⋊D1111yescharacteristic
838C22×C4C2×C22⋊D1111yescharacteristic
839C22×C4C2×C22⋊D1111yescharacteristic
840C22×C4C2×C22⋊D1111yescharacteristic
841C22×C4C2×C22⋊D1111yescharacteristic
842C22×C4C2×C22⋊D1111yescharacteristic
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1111yescharacteristic
850SD16—448no—
851D8—448no—
852M16—228no—
853M16—444no—
854C2×C8—118no—
855C2×C8—444no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—114no—
863C4⋊C4—222no—
864C4⋊C4—222no—
865C4⋊C4—222no—
866C4⋊C4C23×D1112yes—
867C4⋊C4C23×D1112yes—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—224no—
879C22⋊C4—224no—
880C22⋊C4—224no—
881C22⋊C4—224no—
882C42—22no—
883C42—22no—
884C11#6075011yescharacteristic, complemented, Sylow
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—224no—
911C23—444no—
912C23—444no—
913C23—444no—
914C23—444no—
915C23—444no—
916C23—444no—
917C23—444no—
918C23—444no—
919C23—444no—
920C23—8816no—
921C23#6700214yescomplemented
922C23C22×C22⋊D1111yescharacteristic
923C23C22×C22⋊D1111yescharacteristic
924C23C22×C22⋊D1111yescharacteristic
925C23C22×C22⋊D1111yescharacteristic
926C23C22×C22⋊D1111yescharacteristic
927C23C22×C22⋊D1111yescharacteristic
928C23C22×C22⋊D1111yescharacteristic
929Q8—24no—
930Q8—42no—
931D4—24no—
932D4—42no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—228no—
940D4—444no—
941D4—444no—
942D4—448no—
943D4—448no—
944D4—448no—
945D4—448no—
946D4—444no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—44no—
982C2×C4—224no—
983C2×C4—444no—
984C2×C4—444no—
985C2×C4—444no—
986C2×C4#6703714yes—
987C2×C4C22×C22⋊D1111yescharacteristic
988C2×C4C22×C22⋊D1111yescharacteristic
989C2×C4C22×C22⋊D1111yescharacteristic
990C2×C4C22×C22⋊D1111yescharacteristic
991C2×C4C22×C22⋊D1111yescharacteristic
992C2×C4C22×C22⋊D1111yescharacteristic
993C2×C4C22×C22⋊D1111yescharacteristic
994C2×C4C24×D1111yescharacteristic
995C8—228no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—84no—
1023C22—444no—
1024C22—444no—
1025C22—444no—
1026C22—888no—
1027C22—888no—
1028C22—888no—
1029C22#1062333512yes—
1030C22C2×#6700212yes—
1031C22C2×#6700212yes—
1032C22C2×#6700212yes—
1033C22#1062335312yes—
1034C22C23×C22⋊D1111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—444no—
1045C4#1062333512yes—
1046C4C2×#6703712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—82no—
1055C2—884no—
1056C2C2×#1062333511yescharacteristic
1057C2C22×#6700211yescharacteristic
1058C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. #13079426C2semidirect
3. #13079418C2semidirect
4. #13079413C2semidirect
5. #13079377C2semidirect
6. #13079369C2semidirect
7. #13079364C2semidirect
8. #13078556C2semidirect
9. #13078536C2semidirect
10. #13078237C2semidirect
11. #13077868C2semidirect
12. #13077842C2semidirect
13. C2×#10622820C2semidirect
14. C2×C11×#525C2semidirect
15. C22×C11×#41C22semidirect
18. C23×D44C22semidirect
24. C11×#525C22semidirect
25. C11×#525C22semidirect
26. C11×#525C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×C22⋊Q8C22semidirect
30. C2×C11×#121C22semidirect
31. C2×C11×#121C22semidirect
35. C2×C11×#117C22semidirect
36. C2×#67002C22semidirect
46. C2×#66983C22semidirect
47. C2×#66983C22semidirect
48. C2×#66983C22semidirect
50. C22×C4⋊Dic11C22semidirect
51. C22×#4318C22semidirect
52. #10622851C22semidirect
53. #10622845C22semidirect
54. #10622840C22semidirect
55. #10622830C22semidirect
56. #10622820C22semidirect
57. #10622820C22semidirect
58. #10622820C22semidirect
59. #10622820C22semidirect
60. C2×C22⋊(C11⋊C8)C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622662C22semidirect
63. #10622661C22semidirect
64. #10622659C22semidirect
65. #10622659C22semidirect
66. #10622657C22semidirect
67. #10622656C22semidirect
68. #10622652C22semidirect
69. #10622651C22semidirect
70. #10622649C22semidirect
71. #10622649C22semidirect
72. #10622647C22semidirect
73. #10622646C22semidirect
74. #10622616C22semidirect
75. #10622614C22semidirect
76. #10622608C22semidirect
77. #10622581C22semidirect
78. #10622580C22semidirect
85. C2×C11×#41C23semidirect
86. C22×Q8×C11C23semidirect
90. C22×D4×C11C23semidirect
132. C11×C22⋊Q8C23semidirect
133. C11×C22⋊Q8C23semidirect
140. C11×#121C23semidirect
141. C11×#121C23semidirect
157. C11×#117C23semidirect
160. C2×C11×C4⋊C4C23semidirect
161. C2×C11×C4⋊C4C23semidirect
169. C2×#4325C23semidirect
170. C2×#4323C23semidirect
201. C2×#4318C23semidirect
202. C22×C11⋊C8C23semidirect
203. #66899C23semidirect
204. #66896C23semidirect
207. C22⋊(C11⋊C8)C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
209. #66873C23semidirect
210. #66873C23semidirect
211. #66872C23semidirect
212. #66871C23semidirect
356. C2×#525D11semidirect
395. C23×C11AGL(1,ℤ/8)semidirect
481. C22×#41C2×D11semidirect
492. #525C2×D11semidirect
493. #525C2×D11semidirect
494. #525C2×D11semidirect
496. C2×C22⋊Q8C2×D11semidirect
497. C2×C22⋊Q8C2×D11semidirect
510. C2×#121C2×D11semidirect
511. C2×#121C2×D11semidirect
515. C2×#117C2×D11semidirect
602. C2×#41C22×D11semidirect
603. C22×Q8C22×D11semidirect
621. C22×D4C22×D11semidirect
656. C22⋊Q8C22×D11semidirect
657. C22⋊Q8C22×D11semidirect
680. #121C22×D11semidirect
681. #121C22×D11semidirect
697. #117C22×D11semidirect
706. C2×C4⋊C4C22×D11semidirect
707. C2×C4⋊C4C22×D11semidirect
884. C11#60750semidirect
921. C23#67002semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
#130794262
#130794182
#130794132
#130793772
#130793692
#130793642
#130785562
#130785362
#130782372
#130778682
#130778422
C2×#106228202
C2×C11×#5252
#6075011