Finite Group Databasebeta

← #15622235

Subgroups — #15622235

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×#10623010C211yesmaximal, characteristic, complemented
2#13078787C212yesmaximal, complemented
3#13078754C212yesmaximal, complemented
4#13078725C214yesmaximal, complemented
5#13078696C212yesmaximal, complemented
6#13078663C212yesmaximal, complemented
7#13078634C214yesmaximal, complemented
8#13078564C211yesmaximal, characteristic, complemented
9#13078556C211yesmaximal, characteristic, complemented
10#13078438C212yesmaximal, complemented
11#13078110C212yesmaximal, complemented
12#13077876C211yesmaximal, characteristic, complemented
13#13077868C211yesmaximal, characteristic
14C4×#67004C212yesmaximal, complemented
15C4×#67002C212yesmaximal, complemented
16#13077249C211yesmaximal, characteristic, complemented
17C2×C4×C11×#41C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C4×C11×#41—21no—
20C4×C11×#41—21no—
21C4×C11×#41—21no—
22C4×C11×#41—21no—
23C4×C11×#41C2212yes—
24C4×C11×#41C2212yes—
25C4×C11×#41C2212yescomplemented
26C4×C11×#41C2212yescomplemented
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic, complemented
32C2×C4×D4×C11C2211yescharacteristic, complemented
33C2×C11×#117—21no—
34C2×C11×#117C2211yescharacteristic
35C22×C42×C11—21no—
36C22×C42×C11C2211yescharacteristic
37C2×#67004C2212yes—
38C2×#67002C2212yes—
39C2×#66983C2211yescharacteristic
40C2×#66982—21no—
41C2×C4×C22⋊D11—21no—
42C2×#66977C2211yescharacteristic
43#10623010—21no—
44#10623010—21no—
45#10623010—21no—
46#10623010—21no—
47#10623010C2212yes—
48#10623010C2212yes—
49#10623010C2212yescomplemented
50#10623010C2212yescomplemented
51C2×#66929—21no—
52C2×#66928C2211yescharacteristic, complemented
53C2×C4×D44C2211yescharacteristic, complemented
54C2×#66925—21no—
55C2×#66923C2211yescharacteristic, complemented
56C2×C4×Dic22C2211yescharacteristic, complemented
57#10622852C2214yescomplemented
58#10622851C2214yes—
59#10622845C2212yes—
60#10622845C2212yes—
61#10622841C2212yescomplemented
62#10622840C2212yes—
63#10622831C2212yescomplemented
64#10622830C2212yes—
65#10622820C2211yescharacteristic
66#10622820C2211yescharacteristic
67#10622643C2214yescomplemented
68C4×#4326C2214yescomplemented
69#10622641C2214yescomplemented
70#10622641C2214yescomplemented
71#10622639C2214yescomplemented
72C4×#4325C2214yescomplemented
73#10622635C2214yescomplemented
74#10622635C2214yescomplemented
75#10622631C2214yescomplemented
76C4×#4324C2214yescomplemented
77#10622629C2214yescomplemented
78#10622629C2214yescomplemented
79#10622627C2214yescomplemented
80C4×#4323C2214yescomplemented
81#10622622C2214yescomplemented
82#10622622C2214yescomplemented
83#10622617C2212yescomplemented
84#10622616C2214yescomplemented
85#10622614C2212yescomplemented
86#10622609C2214yescomplemented
87#10622608C2212yescomplemented
88#10622608C2212yescomplemented
89#10622584C2212yescomplemented
90#10622583C2212yescomplemented
91#10622581C2212yes—
92#10622580C2212yes—
93#10622539C2212yescomplemented
94#10622539C2212yescomplemented
95#10622538C2212yescomplemented
96#10622538C2212yescomplemented
97#10622537C2212yescomplemented
98C4×#4318C2212yescomplemented
99C2×C11×#41—28no—
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41C2312yes—
103C2×C11×#41C2312yes—
104C22×Q8×C11C2311yescharacteristic
105C22×D4×C11—21no—
106C22×D4×C11C2311yescharacteristic
107C23×C4×C11—21no—
108C23×C4×C11—21no—
109C23×C4×C11—21no—
110C23×C4×C11D411yescharacteristic
111C23×C4×C11D411yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C22×C22⋊D11—21no—
114C22×D44C2311yescharacteristic
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11C2312yes—
138C4×D4×C11C2312yes—
139C4×D4×C11C2312yes—
140C4×D4×C11C2312yes—
141C11×#117—21no—
142C11×#117—21no—
143C11×#117—22no—
144C11×#117—22no—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117C2312yes—
148C11×#117C2312yes—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—21no—
155C2×C11×C22⋊C4—21no—
156C2×C42×C11—21no—
157C2×C42×C11—21no—
158C2×C42×C11—21no—
159C2×C42×C11—22no—
160C2×C42×C11—22no—
161C2×C42×C11—22no—
162C2×C42×C11—22no—
163C2×C42×C11D411yescharacteristic
164C2×C42×C11D411yescharacteristic
165C2×C42×C11D411yescharacteristic
166C2×C42×C11D411yescharacteristic
167C2×C42×C11D411yescharacteristic
168C2×C42×C11D411yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11—21no—
176#67004—28no—
177#67002—28no—
178C2×#4326C2314yes—
179C2×#4325C2314yes—
180C2×#4324C2314yes—
181C2×#4323C2314yes—
182#66983—21no—
183#66983—21no—
184#66983C2312yes—
185#66983C2312yes—
186#66982—22no—
187#66982—22no—
188#66982—22no—
189#66982—22no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C2×(C2×D11)⋊C4—21no—
195C2×(C2×D11)⋊C4—21no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—21no—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200#66977—21no—
201#66977—21no—
202#66977C2312yes—
203#66977C2312yes—
204C2×Dic11⋊C4—21no—
205C2×Dic11⋊C4—21no—
206C2×Dic11⋊C4—21no—
207C2×Dic11⋊C4—21no—
208C2×C4×Dic11—21no—
209C2×#4318C2312yes—
210C2×#4318C2312yes—
211#66929—22no—
212#66929—22no—
213#66929—22no—
214#66929—22no—
215#66928—21no—
216#66928—21no—
217#66928C2312yes—
218#66928C2312yes—
219C4×D44—21no—
220C4×D44—21no—
221C4×D44C2312yes—
222C4×D44C2312yes—
223#66925—22no—
224#66925—22no—
225#66925—22no—
226#66925—22no—
227#66923—21no—
228#66923—21no—
229#66923C2312yes—
230#66923C2312yes—
231C4×Dic22—21no—
232C4×Dic22—21no—
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—
259C11×#41—28no—
260C11×#41—28no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—24no—
264C11×#41#4118yes—
265C2×Q8×C11—24no—
266C2×Q8×C11—21no—
267C2×Q8×C11C2412yes—
268C2×D4×C11—28no—
269C2×D4×C11—22no—
270C2×D4×C11—22no—
271C2×D4×C11—24no—
272C2×D4×C11—21no—
273C2×D4×C11C2412yes—
274C22×C4×C11—28no—
275C22×C4×C11—21no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—24no—
279C22×C4×C11—21no—
280C22×C4×C11—21no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—44no—
288C22×C4×C11—44no—
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2×D411yescharacteristic
297C22×C4×C11C2×D411yescharacteristic
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—44no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C2×D44—21no—
314C2×D44—24no—
315C2×D44C2412yes—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—44no—
319C2×Dic22—21no—
320C2×Dic22—24no—
321C2×Dic22C2412yes—
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—
336C42×C11—22no—
337C42×C11—22no—
338C42×C11—22no—
339C42×C11—22no—
340C42×C11—22no—
341C42×C11—22no—
342C42×C11C2×D411yescharacteristic
343C42×C11C2×D411yescharacteristic
344C42×C11C2×D411yescharacteristic
345C42×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
355C42×C11C2411yescharacteristic
356C42×C11C2411yescharacteristic
357C42×C11C2411yescharacteristic
358C22⋊Dic11—22no—
359C22⋊Dic11—22no—
360#4326—28no—
361#4325—28no—
362#4324—28no—
363#4323—28no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366(C2×D11)⋊C4—22no—
367(C2×D11)⋊C4—22no—
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—
380Dic11⋊C4—22no—
381Dic11⋊C4—22no—
382Dic11⋊C4—22no—
383Dic11⋊C4—22no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386#4318—24no—
387#4318—24no—
388C2×C11⋊C8C2414yes—
389C2×C11⋊C8C2414yes—
390C2×#529—111no—
391C2×C4×#41D1111yescharacteristic, complemented
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—24no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—41no—
412C23×C11—42no—
413C23×C11—42no—
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C22×D11—22no—
418C22×D11—42no—
419C22×D11—42no—
420C22×D11—42no—
421Q8×C11—24no—
422Q8×C11—22no—
423Q8×C11C2×#4114yes—
424D4×C11—28no—
425D4×C11—24no—
426D4×C11—28no—
427D4×C11—22no—
428D4×C11C2×#4114yes—
429C2×C4×C11—24no—
430C2×C4×C11—28no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—28no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
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—44no—
453C2×C4×C11—44no—
454C2×C4×C11—44no—
455C2×C4×C11—42no—
456C2×C4×C11—42no—
457C2×C4×C11—44no—
458C2×C4×C11C22×D411yescharacteristic
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×C11C22×D411yescharacteristic
467C2×C4×C11C22×D411yescharacteristic
468C2×C4×C11C22×D411yescharacteristic
469C2×C4×C11C2×#4114yes—
470C2×C4×C11C2511yescharacteristic
471C22⋊D11—44no—
472C22⋊D11—44no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—42no—
477C2×Dic11—42no—
478C2×Dic11—42no—
479D44—24no—
480D44—42no—
481C4×D11—44no—
482C4×D11—44no—
483Dic22—24no—
484Dic22—42no—
485C11⋊C8—24no—
486C11⋊C8—24no—
487C22×#41C2×D1111yescharacteristic
488C2×#137—112no—
489C2×AGL(1,ℤ/8)—112no—
490#529—112no—
491#529—112no—
492#529—112no—
493#529—112no—
494#529—221no—
495#529—221no—
496#529—221no—
497#529—221no—
498C2×#126—221no—
499C2×#125—111no—
500C2×#124—111no—
501C2×#123—221no—
502C2×C22⋊Q8—111no—
503C2×#121—111no—
504C4×#41—21no—
505C4×#41—21no—
506C4×#41—21no—
507C4×#41—21no—
508C4×#41C2×D1112yes—
509C4×#41C2×D1112yes—
510C4×#41C2×D1112yescomplemented
511C4×#41C2×D1112yescomplemented
512C2×C4×Q8—111no—
513C2×C4×Q8C2×D1111yescharacteristic, complemented
514C2×C4×Q8C2×D1111yescharacteristic, complemented
515C2×C4×D4—21no—
516C2×C4×D4—21no—
517C2×C4×D4—111no—
518C2×C4×D4—221no—
519C2×C4×D4C2×D1111yescharacteristic, complemented
520C2×C4×D4C2×D1111yescharacteristic, complemented
521C2×#117—21no—
522C2×#117—221no—
523C2×#117C2×D1111yescharacteristic
524C22×C42—21no—
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—24no—
574C22×C11—21no—
575C22×C11—21no—
576C22×C11—44no—
577C22×C11—48no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11#52512yes—
581C22×C11#57512yes—
582C22×C11C23×D411yescharacteristic
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—84no—
587C4×C11—21no—
588C4×C11—24no—
589C4×C11—21no—
590C4×C11—21no—
591C4×C11—21no—
592C4×C11—21no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—21no—
596C4×C11—21no—
597C4×C11—42no—
598C4×C11—42no—
599C4×C11#52512yes—
600C4×C11#57512yes—
601C4×C11C22×#4112yes—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605C2×#41—28no—
606C2×#41—21no—
607C2×#41—21no—
608C2×#41C22×D1112yes—
609C2×#41C22×D1112yes—
610C22×Q8—111no—
611C22×Q8C22×D1111yescharacteristic
612C22×D4—21no—
613C22×D4—111no—
614C22×D4—221no—
615C22×D4C22×D1111yescharacteristic
616C23×C4—21no—
617C23×C4—21no—
618C23×C4—21no—
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—222no—
632#126—222no—
633#126—222no—
634#126—222no—
635#125—112no—
636#125—112no—
637#125—221no—
638#125—221no—
639#124—112no—
640#124—112no—
641#124—221no—
642#124—221no—
643#123—222no—
644#123—222no—
645#123—222no—
646#123—222no—
647C22⋊Q8—112no—
648C22⋊Q8—112no—
649C22⋊Q8—221no—
650C22⋊Q8—221no—
651#121—112no—
652#121—112no—
653#121—221no—
654#121—221no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—21no—
658C4×Q8—21no—
659C4×Q8—112no—
660C4×Q8—112no—
661C4×Q8—221no—
662C4×Q8—221no—
663C4×Q8C22×D1112yes—
664C4×Q8C22×D1112yes—
665C4×Q8C22×D1112yes—
666C4×Q8C22×D1112yes—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—22no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—21no—
676C4×D4—21no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—112no—
680C4×D4—112no—
681C4×D4—222no—
682C4×D4—222no—
683C4×D4—222no—
684C4×D4—222no—
685C4×D4—221no—
686C4×D4—221no—
687C4×D4C22×D1112yes—
688C4×D4C22×D1112yes—
689C4×D4C22×D1112yes—
690C4×D4C22×D1112yes—
691#117—21no—
692#117—21no—
693#117—22no—
694#117—22no—
695#117—22no—
696#117—22no—
697#117—222no—
698#117—222no—
699#117—222no—
700#117—222no—
701#117C22×D1112yes—
702#117C22×D1112yes—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—111no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—221no—
708C2×C4⋊C4—221no—
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—221no—
717C2×C22⋊C4—221no—
718C2×C22⋊C4—221no—
719C2×C22⋊C4—221no—
720C2×C22⋊C4—221no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—221no—
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—44no—
765C2×C11C2×#52511yescharacteristic
766C2×C11C2×#57511yescharacteristic
767C2×C11C2×#57511yescharacteristic
768D11—82no—
769C24—21no—
770C24—221no—
771C24C2×C22⋊D1111yescharacteristic
772#41—28no—
773#41—28no—
774#41—24no—
775#41—24no—
776#41—24no—
777#41#433918yes—
778C2×Q8—24no—
779C2×Q8—21no—
780C2×Q8—112no—
781C2×Q8—221no—
782C2×Q8—224no—
783C2×Q8C23×D1112yes—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—21no—
789C2×D4—112no—
790C2×D4—222no—
791C2×D4—222no—
792C2×D4—224no—
793C2×D4—221no—
794C2×D4—444no—
795C2×D4C23×D1112yes—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—222no—
815C22×C4—222no—
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—21no—
848C4⋊C4—21no—
849C4⋊C4—112no—
850C4⋊C4—112no—
851C4⋊C4—221no—
852C4⋊C4—221no—
853C4⋊C4—222no—
854C4⋊C4—222no—
855C4⋊C4—222no—
856C4⋊C4—222no—
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—222no—
870C22⋊C4—222no—
871C22⋊C4—222no—
872C22⋊C4—222no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C22⋊C4—222no—
876C22⋊C4—222no—
877C22⋊C4—222no—
878C22⋊C4—222no—
879C42—22no—
880C42—22no—
881C42—22no—
882C42—22no—
883C42—22no—
884C42—22no—
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—24no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—42no—
911C23—222no—
912C23—442no—
913C23—442no—
914C23—442no—
915C23C22×C22⋊D1111yescharacteristic
916C23C22×C22⋊D1111yescharacteristic
917C23C22×C22⋊D1111yescharacteristic
918Q8—24no—
919Q8—22no—
920Q8—224no—
921Q8—442no—
922Q8C2×#433914yes—
923D4—28no—
924D4—24no—
925D4—28no—
926D4—22no—
927D4—224no—
928D4—444no—
929D4—444no—
930D4—442no—
931D4C2×#433914yes—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—28no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—44no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—444no—
965C2×C4—442no—
966C2×C4—442no—
967C2×C4—442no—
968C2×C4—444no—
969C2×C4C2×#433914yes—
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—24no—
990C22—21no—
991C22—21no—
992C22—44no—
993C22—48no—
994C22—42no—
995C22—42no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—884no—
1000C22#1062332212yes—
1001C22#1062335312yes—
1002C22C23×C22⋊D1111yescharacteristic
1003C4—21no—
1004C4—24no—
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—21no—
1013C4—42no—
1014C4—42no—
1015C4—442no—
1016C4—442no—
1017C4—442no—
1018C4#1062332212yes—
1019C4#1062335312yes—
1020C4C22×#433912yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—44no—
1025C2—882no—
1026C2C2×#1062332211yescharacteristic
1027C2C2×#1062335311yescharacteristic
1028C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
socleC22×C11C23×D4
prime radical#13077868C2
hypercenterC2×C4×#41D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. #13078787C2semidirect
3. #13078754C2semidirect
4. #13078725C2semidirect
5. #13078696C2semidirect
6. #13078663C2semidirect
7. #13078634C2semidirect
8. #13078564C2semidirect
9. #13078556C2semidirect
10. #13078438C2semidirect
11. #13078110C2semidirect
12. #13077876C2semidirect
14. C4×#67004C2semidirect
15. C4×#67002C2semidirect
16. #13077249C2semidirect
17. C2×C4×C11×#41C2semidirect
25. C4×C11×#41C22semidirect
26. C4×C11×#41C22semidirect
27. C2×C4×Q8×C11C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×C4×D4×C11C22semidirect
32. C2×C4×D4×C11C22semidirect
49. #10623010C22semidirect
50. #10623010C22semidirect
52. C2×#66928C22semidirect
53. C2×C4×D44C22semidirect
55. C2×#66923C22semidirect
56. C2×C4×Dic22C22semidirect
57. #10622852C22semidirect
61. #10622841C22semidirect
63. #10622831C22semidirect
67. #10622643C22semidirect
68. C4×#4326C22semidirect
69. #10622641C22semidirect
70. #10622641C22semidirect
71. #10622639C22semidirect
72. C4×#4325C22semidirect
73. #10622635C22semidirect
74. #10622635C22semidirect
75. #10622631C22semidirect
76. C4×#4324C22semidirect
77. #10622629C22semidirect
78. #10622629C22semidirect
79. #10622627C22semidirect
80. C4×#4323C22semidirect
81. #10622622C22semidirect
82. #10622622C22semidirect
83. #10622617C22semidirect
84. #10622616C22semidirect
85. #10622614C22semidirect
86. #10622609C22semidirect
87. #10622608C22semidirect
88. #10622608C22semidirect
89. #10622584C22semidirect
90. #10622583C22semidirect
93. #10622539C22semidirect
94. #10622539C22semidirect
95. #10622538C22semidirect
96. #10622538C22semidirect
97. #10622537C22semidirect
98. C4×#4318C22semidirect
391. C2×C4×#41D11semidirect
510. C4×#41C2×D11semidirect
511. C4×#41C2×D11semidirect
513. C2×C4×Q8C2×D11semidirect
514. C2×C4×Q8C2×D11semidirect
519. C2×C4×D4C2×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×#106230102
#130787872
#130787542
#130787252
#130786962
#130786632
#130786342
#130785642
#130785562
#130784382
#130781102
#130778762
#130778682
C4×#670042
C4×#670022
#130772492
C2×C4×C11×#412
#6056311