Finite Group Databasebeta

← #15622227

Subgroups — #15622227

Order 2816.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic, complemented
2#13078783C212yesmaximal, complemented
3#13078750C212yesmaximal, complemented
4#13078719C214yesmaximal, complemented
5#13078692C212yesmaximal, complemented
6#13078659C212yesmaximal, complemented
7#13078628C214yesmaximal, complemented
8#13078560C211yesmaximal, characteristic, complemented
9#13078552C211yesmaximal, characteristic, complemented
10#13078434C212yesmaximal, complemented
11#13078106C212yesmaximal, complemented
12#13077874C211yesmaximal, characteristic, complemented
13#13077866C211yesmaximal, characteristic
14C4×#66995C212yesmaximal, complemented
15C4×#66985C212yesmaximal, complemented
16#13077249C211yesmaximal, characteristic, complemented
17C2×C11×#529C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C11×#529—21no—
20C11×#529—21no—
21C11×#529—21no—
22C11×#529—21no—
23C11×#529C2212yes—
24C11×#529C2212yes—
25C11×#529C2212yescomplemented
26C11×#529C2212yescomplemented
27C2×C11×#126—21no—
28C2×C11×#125C2211yescharacteristic, complemented
29C2×C11×#124C2211yescharacteristic, complemented
30C2×C11×#123—21no—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C2×C11×#121C2211yescharacteristic
33C2×C4×Q8×C11C2211yescharacteristic, complemented
34C2×C4×D4×C11—21no—
35C2×C4×D4×C11C2211yescharacteristic, complemented
36C2×C11×#117—21no—
37C22×C42×C11C2211yescharacteristic
38C2×#66995C2212yes—
39C2×#66985C2212yes—
40C2×C4×C22⋊D11—21no—
41C2×C4×C22⋊D11—21no—
42C2×#66979C2211yescharacteristic
43C4×#4339—21no—
44C4×#4339—21no—
45C4×#4339—21no—
46C4×#4339—21no—
47C4×#4339C2212yes—
48C4×#4339C2212yes—
49C4×#4339C2212yescomplemented
50C4×#4339C2212yescomplemented
51C2×C4×D44C2211yescharacteristic, complemented
52C2×C4×D44C2211yescharacteristic, complemented
53C2×#66925—21no—
54C2×C42×D11—21no—
55C2×C4×Dic22C2211yescharacteristic, complemented
56C2×C4×Dic22C2211yescharacteristic, complemented
57#10622838C2212yescomplemented
58#10622828C2212yescomplemented
59#10622820C2211yescharacteristic
60#10622820C2211yescharacteristic
61#10622679C2214yescomplemented
62#10622679C2214yescomplemented
63#10622676C2214yescomplemented
64#10622676C2214yescomplemented
65#10622670C2214yescomplemented
66#10622670C2214yescomplemented
67#10622667C2214yescomplemented
68#10622667C2214yescomplemented
69#10622663C2212yescomplemented
70#10622660C2214yescomplemented
71#10622659C2212yescomplemented
72#10622658C2214yescomplemented
73#10622657C2212yescomplemented
74#10622656C2212yescomplemented
75#10622653C2212yes—
76#10622650C2214yes—
77#10622649C2212yes—
78#10622648C2214yescomplemented
79#10622647C2212yes—
80#10622646C2212yes—
81#10622643C2214yescomplemented
82C4×#4326C2214yescomplemented
83#10622639C2214yescomplemented
84C4×#4325C2214yescomplemented
85#10622631C2214yescomplemented
86C4×#4324C2214yescomplemented
87#10622627C2214yescomplemented
88C4×#4323C2214yescomplemented
89#10622579C2212yes—
90#10622579C2212yes—
91#10622577C2212yescomplemented
92#10622577C2212yescomplemented
93#10622539C2212yescomplemented
94#10622539C2212yescomplemented
95#10622538C2212yescomplemented
96#10622538C2212yescomplemented
97#10622537C2212yescomplemented
98C4×#4318C2212yescomplemented
99C22×Q8×C11C2311yescharacteristic
100C22×D4×C11—21no—
101C22×D4×C11C2311yescharacteristic
102C23×C4×C11—21no—
103C23×C4×C11D411yescharacteristic
104C23×C4×C11D411yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—21no—
107C2×#4339—21no—
108C2×#4339—21no—
109C2×#4339—28no—
110C2×#4339C2312yes—
111C2×#4339C2312yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic
117C11×#126—22no—
118C11×#126—22no—
119C11×#126—22no—
120C11×#126—22no—
121C11×#125—21no—
122C11×#125—21no—
123C11×#125C2312yes—
124C11×#125C2312yes—
125C11×#124—21no—
126C11×#124—21no—
127C11×#124C2312yes—
128C11×#124C2312yes—
129C11×#123—22no—
130C11×#123—22no—
131C11×#123—22no—
132C11×#123—22no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8C2312yes—
136C11×C22⋊Q8C2312yes—
137C11×#121—21no—
138C11×#121—21no—
139C11×#121C2312yes—
140C11×#121C2312yes—
141C4×Q8×C11—21no—
142C4×Q8×C11—21no—
143C4×Q8×C11C2312yes—
144C4×Q8×C11C2312yes—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—21no—
150C4×D4×C11—21no—
151C4×D4×C11C2312yes—
152C4×D4×C11C2312yes—
153C11×#117—22no—
154C11×#117—22no—
155C11×#117—22no—
156C11×#117—22no—
157C2×C11×C4⋊C4—21no—
158C2×C11×C4⋊C4—21no—
159C2×C11×C4⋊C4—21no—
160C2×C11×C4⋊C4—21no—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4—21no—
165C2×C11×C22⋊C4—21no—
166C2×C11×C22⋊C4—21no—
167C2×C11×C22⋊C4—21no—
168C2×C42×C11—21no—
169C2×C42×C11D411yescharacteristic
170C2×C42×C11D411yescharacteristic
171C2×C42×C11D411yescharacteristic
172C2×C42×C11D411yescharacteristic
173C2×C42×C11D411yescharacteristic
174C2×C42×C11D411yescharacteristic
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2311yescharacteristic
180C2×C42×C11C2311yescharacteristic
181C2×C22⋊Dic11—21no—
182C2×#4326C2314yes—
183#66995—28no—
184C2×#4325C2314yes—
185C2×#4324C2314yes—
186#66985—28no—
187C2×#4323C2314yes—
188C4×C22⋊D11—22no—
189C4×C22⋊D11—22no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—21no—
198#66979—21no—
199#66979—21no—
200#66979C2312yes—
201#66979C2312yes—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4—21no—
205C2×Dic11⋊C4—21no—
206C2×C4×Dic11—21no—
207C2×C4×Dic11—21no—
208C2×C4×Dic11—21no—
209C2×#4318C2312yes—
210C2×#4318C2312yes—
211C4×D44—21no—
212C4×D44—21no—
213C4×D44—21no—
214C4×D44—21no—
215C4×D44C2312yes—
216C4×D44C2312yes—
217C4×D44C2312yes—
218C4×D44C2312yes—
219#66925—22no—
220#66925—22no—
221#66925—22no—
222#66925—22no—
223C42×D11—22no—
224C42×D11—22no—
225C42×D11—22no—
226C42×D11—22no—
227C4×Dic22—21no—
228C4×Dic22—21no—
229C4×Dic22—21no—
230C4×Dic22—21no—
231C4×Dic22C2312yes—
232C4×Dic22C2312yes—
233C4×Dic22C2312yes—
234C4×Dic22C2312yes—
235#66899C2314yes—
236#66899C2314yes—
237#66896C2314yes—
238#66896C2314yes—
239C22⋊(C11⋊C8)C2312yes—
240C22⋊(C11⋊C8)C2312yes—
241C22⋊(C11⋊C8)C2312yes—
242C22⋊(C11⋊C8)C2312yes—
243#66874C2314yes—
244#66874C2314yes—
245#66873C2314yes—
246#66873C2314yes—
247#66872C2314yes—
248#66872C2314yes—
249#66871C2314yes—
250#66871C2314yes—
251C4⋊(C11⋊C8)C2314yes—
252C4⋊(C11⋊C8)C2314yes—
253#66867C2314yes—
254C4×C11⋊C8C2314yes—
255#60563—111nomaximal, Sylow
256C24×C11—21no—
257C24×C11C2×D411yescharacteristic
258C23×D11—21no—
259C2×Q8×C11—21no—
260C2×Q8×C11—24no—
261C2×Q8×C11C2412yes—
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—21no—
265C2×D4×C11—24no—
266C2×D4×C11—44no—
267C2×D4×C11C2412yes—
268C22×C4×C11—24no—
269C22×C4×C11—21no—
270C22×C4×C11—21no—
271C22×C4×C11—21no—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—44no—
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×C11C2×D411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—28no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301#4339—28no—
302#4339—28no—
303#4339—24no—
304#4339—24no—
305#4339—24no—
306#4339#4118yes—
307C2×D44—24no—
308C2×D44—21no—
309C2×D44C2412yes—
310C2×C4×D11—28no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×Dic22—24no—
320C2×Dic22—21no—
321C2×Dic22C2412yes—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—21no—
331C11×C4⋊C4—21no—
332C11×C4⋊C4C2412yes—
333C11×C4⋊C4C2412yes—
334C11×C22⋊C4—22no—
335C11×C22⋊C4—22no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—22no—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C42×C11—22no—
345C42×C11—22no—
346C42×C11C2×D411yescharacteristic
347C42×C11C2×D411yescharacteristic
348C42×C11C2×D411yescharacteristic
349C42×C11C2×D411yescharacteristic
350C42×C11C2×D411yescharacteristic
351C42×C11C2×D411yescharacteristic
352C42×C11C2×D411yescharacteristic
353C42×C11C2×D411yescharacteristic
354C42×C11C2×D411yescharacteristic
355C42×C11C2×D411yescharacteristic
356C42×C11C2×D411yescharacteristic
357C42×C11C2×D411yescharacteristic
358C42×C11C2411yescharacteristic
359C42×C11C2411yescharacteristic
360C42×C11C2411yescharacteristic
361C42×C11C2411yescharacteristic
362C22⋊Dic11—22no—
363C22⋊Dic11—22no—
364#4326—28no—
365#4325—28no—
366#4324—28no—
367#4323—28no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372C4⋊Dic11—21no—
373C4⋊Dic11—21no—
374C4⋊Dic11C2412yes—
375C4⋊Dic11C2412yes—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379Dic11⋊C4—22no—
380C4×Dic11—22no—
381C4×Dic11—22no—
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386#4318—24no—
387#4318—24no—
388C2×C11⋊C8C2414yes—
389C2×C11⋊C8C2414yes—
390C2×#529D1111yescharacteristic, complemented
391C2×C4×#41—111no—
392#3117—112no—
393#3114—112no—
394#3111—114no—
395#3108—112no—
396#3105—112no—
397#3102—114no—
398#3095—111no—
399#3094—111no—
400#3080—112no—
401#3040—112no—
402#3007—111no—
403#3006—111no—
404C4×#137—112no—
405C4×AGL(1,ℤ/8)—112no—
406#2920—111no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—41no—
411C23×C11—42no—
412C23×C11—42no—
413C23×C11—42no—
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C22×D11—24no—
418C22×D11—22no—
419C22×D11—42no—
420C22×D11—42no—
421Q8×C11—24no—
422Q8×C11—42no—
423D4×C11—24no—
424D4×C11—44no—
425D4×C11—44no—
426D4×C11—42no—
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—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—44no—
448C2×C4×C11—42no—
449C2×C4×C11—42no—
450C2×C4×C11—42no—
451C2×C4×C11—44no—
452C2×C4×C11C22×D411yescharacteristic
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11C22×D411yescharacteristic
457C2×C4×C11C22×D411yescharacteristic
458C2×C4×C11C22×D411yescharacteristic
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C22×D411yescharacteristic
462C2×C4×C11C22×D411yescharacteristic
463C2×C4×C11C2×#4114yes—
464C2×C4×C11C2511yescharacteristic
465C22⋊D11—28no—
466C22⋊D11—28no—
467C2×Dic11—24no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—42no—
472C2×Dic11—42no—
473D44—24no—
474D44—22no—
475D44C2×#4114yes—
476C4×D11—28no—
477C4×D11—28no—
478C4×D11—44no—
479C4×D11—44no—
480C4×D11—44no—
481C4×D11—44no—
482Dic22—24no—
483Dic22—22no—
484Dic22C2×#4114yes—
485C11⋊C8—24no—
486C11⋊C8—24no—
487C22×#41—111no—
488C2×#137—112no—
489C2×AGL(1,ℤ/8)—112no—
490#529—21no—
491#529—21no—
492#529—21no—
493#529—21no—
494#529C2×D1112yes—
495#529C2×D1112yes—
496#529C2×D1112yescomplemented
497#529C2×D1112yescomplemented
498C2×#126—21no—
499C2×#125C2×D1111yescharacteristic, complemented
500C2×#124C2×D1111yescharacteristic, complemented
501C2×#123—21no—
502C2×C22⋊Q8C2×D1111yescharacteristic
503C2×#121C2×D1111yescharacteristic
504C4×#41—112no—
505C4×#41—112no—
506C4×#41—112no—
507C4×#41—112no—
508C4×#41—221no—
509C4×#41—221no—
510C4×#41—221no—
511C4×#41—221no—
512C2×C4×Q8—111no—
513C2×C4×Q8—111no—
514C2×C4×Q8C2×D1111yescharacteristic, complemented
515C2×C4×D4—21no—
516C2×C4×D4—111no—
517C2×C4×D4—111no—
518C2×C4×D4—221no—
519C2×C4×D4—221no—
520C2×C4×D4C2×D1111yescharacteristic, complemented
521C2×#117—21no—
522C2×#117—111no—
523C2×#117—221no—
524C22×C42—221no—
525C22×C42C2×D1111yescharacteristic
526#485—114no—
527#484—112no—
528#483—112no—
529#482—114no—
530#481—112no—
531#480—112no—
532#479—114no—
533#479—114no—
534#478—114no—
535#478—114no—
536#464—114no—
537#464—114no—
538#463—114no—
539#463—114no—
540#452—114no—
541#451—112no—
542#450—112no—
543#449—114no—
544#448—112no—
545#447—112no—
546#442—114no—
547#441—114no—
548#440—114no—
549#440—114no—
550C4×Q16—114no—
551C4×SD16—114no—
552C4×SD16—114no—
553C4×D8—114no—
554#432—112no—
555#432—112no—
556#431—112no—
557#431—112no—
558#428—112no—
559#428—112no—
560#423—112no—
561#419—112no—
562#418—112no—
563#417—112no—
564#417—112no—
565#407—111no—
566#407—111no—
567C4×M16—112no—
568C22×C11—21no—
569C22×C11—21no—
570C22×C11—21no—
571C22×C11—21no—
572C22×C11—21no—
573C22×C11—21no—
574C22×C11—21no—
575C22×C11—44no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—84no—
580C22×C11#52512yes—
581C22×C11#57512yes—
582C22×C11C23×D411yescharacteristic
583C2×D11—24no—
584C2×D11—48no—
585C2×D11—42no—
586C2×D11—42no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—21no—
591C4×C11—21no—
592C4×C11—21no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—21no—
596C4×C11—42no—
597C4×C11—42no—
598C4×C11—42no—
599C4×C11#52512yes—
600C4×C11#57512yes—
601C4×C11C22×#4112yes—
602Dic11—24no—
603Dic11—42no—
604Dic11—42no—
605C2×#41—112no—
606C2×#41—112no—
607C2×#41—228no—
608C2×#41—221no—
609C2×#41—221no—
610C22×Q8—111no—
611C22×Q8C22×D1111yescharacteristic
612C22×D4—21no—
613C22×D4—111no—
614C22×D4—221no—
615C22×D4C22×D1111yescharacteristic
616C23×C4—21no—
617C23×C4—221no—
618C23×C4—221no—
619C23×C4—221no—
620C23×C4C22⋊D1111yescharacteristic
621C23×C4C22⋊D1111yescharacteristic
622C23×C4C22×D1111yescharacteristic
623#137—228no—
624AGL(1,ℤ/8)—228no—
625C2×Q16—114no—
626C2×SD16—114no—
627C2×SD16—114no—
628C2×D8—114no—
629C2×M16—112no—
630C2×M16—112no—
631#126—22no—
632#126—22no—
633#126—22no—
634#126—22no—
635#125—21no—
636#125—21no—
637#125C22×D1112yes—
638#125C22×D1112yes—
639#124—21no—
640#124—21no—
641#124C22×D1112yes—
642#124C22×D1112yes—
643#123—22no—
644#123—22no—
645#123—22no—
646#123—22no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8C22×D1112yes—
650C22⋊Q8C22×D1112yes—
651#121—21no—
652#121—21no—
653#121C22×D1112yes—
654#121C22×D1112yes—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—112no—
658C4×Q8—112no—
659C4×Q8—112no—
660C4×Q8—112no—
661C4×Q8—221no—
662C4×Q8—221no—
663C4×Q8—221no—
664C4×Q8—221no—
665C4×Q8C22×D1112yes—
666C4×Q8C22×D1112yes—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4—112no—
674C4×D4—112no—
675C4×D4—112no—
676C4×D4—112no—
677C4×D4—222no—
678C4×D4—222no—
679C4×D4—222no—
680C4×D4—222no—
681C4×D4—222no—
682C4×D4—222no—
683C4×D4—222no—
684C4×D4—222no—
685C4×D4—221no—
686C4×D4—221no—
687C4×D4—221no—
688C4×D4—221no—
689C4×D4C22×D1112yes—
690C4×D4C22×D1112yes—
691#117—22no—
692#117—22no—
693#117—22no—
694#117—22no—
695#117—112no—
696#117—112no—
697#117—221no—
698#117—221no—
699#117—222no—
700#117—222no—
701#117—222no—
702#117—222no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—111no—
708C2×C4⋊C4—111no—
709C2×C4⋊C4—221no—
710C2×C4⋊C4—221no—
711C2×C4⋊C4C22×D1111yescharacteristic
712C2×C4⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—221no—
719C2×C22⋊C4—221no—
720C2×C22⋊C4—221no—
721C2×C42—21no—
722C2×C42—221no—
723C2×C42—221no—
724C2×C42—221no—
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42C22⋊D1111yescharacteristic
730C2×C42C22⋊D1111yescharacteristic
731C2×C42C22⋊D1111yescharacteristic
732C2×C42C22⋊D1111yescharacteristic
733C2×C42C22⋊D1111yescharacteristic
734C2×C42C22⋊D1111yescharacteristic
735C2×C42C22×D1111yescharacteristic
736C2×C42C22×D1111yescharacteristic
737C2×C42C22×D1111yescharacteristic
738C2×C42C22×D1111yescharacteristic
739C2×C42C22×D1111yescharacteristic
740C2×C42C22×D1111yescharacteristic
741#107—114no—
742#107—114no—
743#106—114no—
744#106—114no—
745C4⋊C8—114no—
746C4⋊C8—114no—
747#103—114no—
748#103—114no—
749#103—114no—
750#103—114no—
751#102—114no—
752#102—114no—
753#102—114no—
754#102—114no—
755C22⋊C8—112no—
756C22⋊C8—112no—
757C22⋊C8—112no—
758C22⋊C8—112no—
759#97—114no—
760C4×C8—114no—
761C2×C11—22no—
762C2×C11—22no—
763C2×C11—41no—
764C2×C11—82no—
765C2×C11C2×#52511yescharacteristic
766C2×C11C2×#57511yescharacteristic
767C2×C11C2×#57511yescharacteristic
768D11—44no—
769C24—21no—
770C24—221no—
771C24C2×C22⋊D1111yescharacteristic
772#41—118no—
773#41—224no—
774#41—224no—
775#41—228no—
776#41—228no—
777#41—224no—
778C2×Q8—21no—
779C2×Q8—24no—
780C2×Q8—112no—
781C2×Q8—224no—
782C2×Q8—221no—
783C2×Q8C23×D1112yes—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—21no—
788C2×D4—44no—
789C2×D4—112no—
790C2×D4—224no—
791C2×D4—228no—
792C2×D4—222no—
793C2×D4—222no—
794C2×D4—221no—
795C2×D4C23×D1112yes—
796C22×C4—24no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—44no—
805C22×C4—228no—
806C22×C4—221no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—222no—
812C22×C4—222no—
813C22×C4—222no—
814C22×C4—222no—
815C22×C4—444no—
816C22×C4—444no—
817C22×C4C2×C22⋊D1111yescharacteristic
818C22×C4C2×C22⋊D1111yescharacteristic
819C22×C4C2×C22⋊D1111yescharacteristic
820C22×C4C2×C22⋊D1111yescharacteristic
821C22×C4C2×C22⋊D1111yescharacteristic
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×C4C23×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834C22×C4C23×D1111yescharacteristic
835Q16—228no—
836SD16—228no—
837SD16—228no—
838D8—228no—
839M16—224no—
840M16—224no—
841C2×C8—114no—
842C2×C8—114no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—112no—
854C4⋊C4—112no—
855C4⋊C4—221no—
856C4⋊C4—221no—
857C4⋊C4—222no—
858C4⋊C4—222no—
859C4⋊C4—222no—
860C4⋊C4—222no—
861C4⋊C4C23×D1112yes—
862C4⋊C4C23×D1112yes—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C22⋊C4—222no—
876C22⋊C4—222no—
877C22⋊C4—222no—
878C22⋊C4—222no—
879C42—22no—
880C42—22no—
881C42—222no—
882C42—222no—
883C42—222no—
884C42—222no—
885C42—222no—
886C42—222no—
887C42C2×C22⋊D1111yescharacteristic
888C42C2×C22⋊D1111yescharacteristic
889C42C2×C22⋊D1111yescharacteristic
890C42C2×C22⋊D1111yescharacteristic
891C42C2×C22⋊D1111yescharacteristic
892C42C2×C22⋊D1111yescharacteristic
893C42C2×C22⋊D1111yescharacteristic
894C42C2×C22⋊D1111yescharacteristic
895C42C2×C22⋊D1111yescharacteristic
896C42C2×C22⋊D1111yescharacteristic
897C42C2×C22⋊D1111yescharacteristic
898C42C2×C22⋊D1111yescharacteristic
899C42C23×D1111yescharacteristic
900C42C23×D1111yescharacteristic
901C42C23×D1111yescharacteristic
902C42C23×D1111yescharacteristic
903C11#6056311yescharacteristic, complemented, Sylow
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—224no—
912C23—222no—
913C23—442no—
914C23—442no—
915C23C22×C22⋊D1111yescharacteristic
916C23C22×C22⋊D1111yescharacteristic
917C23C22×C22⋊D1111yescharacteristic
918Q8—24no—
919Q8—42no—
920Q8—114no—
921Q8—224no—
922Q8—222no—
923D4—24no—
924D4—44no—
925D4—44no—
926D4—42no—
927D4—114no—
928D4—224no—
929D4—228no—
930D4—228no—
931D4—222no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—44no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—44no—
957C2×C4—228no—
958C2×C4—224no—
959C2×C4—222no—
960C2×C4—228no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—444no—
964C2×C4—444no—
965C2×C4—444no—
966C2×C4—442no—
967C2×C4—442no—
968C2×C4—444no—
969C2×C4#41×D1114yes—
970C2×C4C22×C22⋊D1111yescharacteristic
971C2×C4C22×C22⋊D1111yescharacteristic
972C2×C4C22×C22⋊D1111yescharacteristic
973C2×C4C22×C22⋊D1111yescharacteristic
974C2×C4C22×C22⋊D1111yescharacteristic
975C2×C4C22×C22⋊D1111yescharacteristic
976C2×C4C22×C22⋊D1111yescharacteristic
977C2×C4C22×C22⋊D1111yescharacteristic
978C2×C4C22×C22⋊D1111yescharacteristic
979C2×C4C22×C22⋊D1111yescharacteristic
980C2×C4C22×C22⋊D1111yescharacteristic
981C2×C4C24×D1111yescharacteristic
982C8—224no—
983C8—224no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—44no—
992C22—42no—
993C22—42no—
994C22—42no—
995C22—84no—
996C22—224no—
997C22—448no—
998C22—442no—
999C22—442no—
1000C22#1062335312yes—
1001C22#1062335912yes—
1002C22C23×C22⋊D1111yescharacteristic
1003C4—21no—
1004C4—21no—
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—224no—
1016C4—442no—
1017C4—442no—
1018C4#1062335312yes—
1019C4#1062335912yes—
1020C4C2×#41×D1112yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—82no—
1025C2—444no—
1026C2C2×#1062335911yescharacteristic
1027C2C2×#1062335311yescharacteristic
1028C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC22×C11C23×D4
prime radical#13077866C2
hypercenterC2×#529D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4339C2semidirect
2. #13078783C2semidirect
3. #13078750C2semidirect
4. #13078719C2semidirect
5. #13078692C2semidirect
6. #13078659C2semidirect
7. #13078628C2semidirect
8. #13078560C2semidirect
9. #13078552C2semidirect
10. #13078434C2semidirect
11. #13078106C2semidirect
12. #13077874C2semidirect
14. C4×#66995C2semidirect
15. C4×#66985C2semidirect
16. #13077249C2semidirect
17. C2×C11×#529C2semidirect
25. C11×#529C22semidirect
26. C11×#529C22semidirect
28. C2×C11×#125C22semidirect
29. C2×C11×#124C22semidirect
33. C2×C4×Q8×C11C22semidirect
35. C2×C4×D4×C11C22semidirect
49. C4×#4339C22semidirect
50. C4×#4339C22semidirect
51. C2×C4×D44C22semidirect
52. C2×C4×D44C22semidirect
55. C2×C4×Dic22C22semidirect
56. C2×C4×Dic22C22semidirect
57. #10622838C22semidirect
58. #10622828C22semidirect
61. #10622679C22semidirect
62. #10622679C22semidirect
63. #10622676C22semidirect
64. #10622676C22semidirect
65. #10622670C22semidirect
66. #10622670C22semidirect
67. #10622667C22semidirect
68. #10622667C22semidirect
69. #10622663C22semidirect
70. #10622660C22semidirect
71. #10622659C22semidirect
72. #10622658C22semidirect
73. #10622657C22semidirect
74. #10622656C22semidirect
78. #10622648C22semidirect
81. #10622643C22semidirect
82. C4×#4326C22semidirect
83. #10622639C22semidirect
84. C4×#4325C22semidirect
85. #10622631C22semidirect
86. C4×#4324C22semidirect
87. #10622627C22semidirect
88. C4×#4323C22semidirect
91. #10622577C22semidirect
92. #10622577C22semidirect
93. #10622539C22semidirect
94. #10622539C22semidirect
95. #10622538C22semidirect
96. #10622538C22semidirect
97. #10622537C22semidirect
98. C4×#4318C22semidirect
390. C2×#529D11semidirect
496. #529C2×D11semidirect
497. #529C2×D11semidirect
499. C2×#125C2×D11semidirect
500. C2×#124C2×D11semidirect
514. C2×C4×Q8C2×D11semidirect
520. C2×C4×D4C2×D11semidirect
903. C11#60563semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787832
#130787502
#130787192
#130786922
#130786592
#130786282
#130785602
#130785522
#130784342
#130781062
#130778742
#130778662
C4×#669952
C4×#669852
#130772492
C2×C11×#5292
#6056311