Finite Group Databasebeta

← #15622168

Subgroups — #15622168

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic, complemented
2#13078772C212yesmaximal, complemented
3#13078761C212yesmaximal, complemented
4#13078719C214yesmaximal, complemented
5#13078681C212yesmaximal, complemented
6#13078670C212yesmaximal, complemented
7#13078628C214yesmaximal, complemented
8#13078545C212yesmaximal, complemented
9#13078417C211yesmaximal, characteristic, complemented
10#13078409C211yesmaximal, characteristic, complemented
11#13078084C211yesmaximal, characteristic, complemented
12#13078076C211yesmaximal, characteristic, complemented
13#13077856C212yesmaximal, complemented
14C4×#67004C212yesmaximal, complemented
15C4×#67002C212yesmaximal, complemented
16#13077249C211yesmaximal, characteristic, complemented
17C11×#3444C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic, complemented
21C11×#533C2211yescharacteristic, complemented
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic, complemented
24C11×#532C2211yescharacteristic, complemented
25C11×#529—21no—
26C11×#529—21no—
27C11×#529—21no—
28C11×#529—21no—
29C11×#529C2212yescomplemented
30C11×#529C2212yescomplemented
31C11×#525—21no—
32C11×#525—21no—
33C11×#525C2212yes—
34C4×C11×#41—21no—
35C4×C11×#41—21no—
36C4×C11×#41C2212yes—
37C22×C42×C11C2211yescharacteristic
38C2×#67004C2212yes—
39C2×#67002C2212yes—
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×#4339C2212yes—
50C4×#4339C2212yes—
51C2×C4×D44C2211yescharacteristic
52C2×C4×D44C2211yescharacteristic
53C2×#66925—21no—
54C2×C42×D11—21no—
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57#10622845C2212yes—
58#10622845C2212yes—
59#10622820C2212yes—
60#10622707C2212yescomplemented
61#10622704C2212yescomplemented
62#10622703C2212yescomplemented
63#10622700C2212yescomplemented
64#10622697C2212yescomplemented
65#10622696C2212yescomplemented
66#10622688C2212yescomplemented
67#10622685C2212yescomplemented
68#10622679C2214yescomplemented
69#10622676C2214yescomplemented
70#10622670C2214yescomplemented
71#10622667C2214yescomplemented
72#10622660C2214yes—
73#10622660C2214yes—
74#10622658C2214yescomplemented
75#10622658C2214yescomplemented
76#10622650C2214yes—
77#10622650C2214yes—
78#10622648C2214yescomplemented
79#10622648C2214yescomplemented
80#10622643C2214yescomplemented
81C4×#4326C2214yescomplemented
82#10622639C2214yescomplemented
83C4×#4325C2214yescomplemented
84#10622631C2214yescomplemented
85C4×#4324C2214yescomplemented
86#10622627C2214yescomplemented
87C4×#4323C2214yescomplemented
88#10622617C2212yes—
89#10622614C2212yes—
90#10622608C2212yes—
91#10622608C2212yes—
92#10622539C2212yescomplemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95#10622538C2212yescomplemented
96#10622537C2211yescharacteristic
97#10622537C2211yescharacteristic
98C4×#4318C2212yes—
99C2×C11×#41—21no—
100C2×C11×#41—21no—
101C2×C11×#41C2312yes—
102C23×C4×C11D411yescharacteristic
103C23×C4×C11D411yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C22×C22⋊D11—21no—
106C2×#4339—21no—
107C2×#4339—21no—
108C2×#4339—24no—
109C2×#4339—24no—
110C2×#4339C2312yes—
111C2×#4339C2312yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic
117C11×C4⋊Q8C2311yescharacteristic
118C11×C4⋊Q8C2311yescharacteristic
119C11×C4⋊Q8C2311yescharacteristic
120C11×#127C2311yescharacteristic
121C11×#126—22no—
122C11×#126—22no—
123C11×#125—21no—
124C11×#125—21no—
125C11×#125C2312yes—
126C11×#124—21no—
127C11×#124—21no—
128C11×#124C2312yes—
129C11×#123—22no—
130C11×#123—22no—
131C11×#123—22no—
132C11×C22⋊Q8—21no—
133C11×C22⋊Q8—21no—
134C11×C22⋊Q8—21no—
135C11×C22⋊Q8—21no—
136C11×C22⋊Q8C2312yes—
137C11×C22⋊Q8C2312yes—
138C11×#121—21no—
139C11×#121—21no—
140C11×#121—21no—
141C11×#121—21no—
142C11×#121C2312yes—
143C11×#121C2312yes—
144C11×#120—22no—
145C4×Q8×C11—21no—
146C4×Q8×C11—21no—
147C4×Q8×C11—21no—
148C4×Q8×C11—21no—
149C4×Q8×C11C2312yes—
150C4×Q8×C11C2312yes—
151C4×D4×C11—22no—
152C4×D4×C11—22no—
153C4×D4×C11—22no—
154C4×D4×C11—22no—
155C4×D4×C11—22no—
156C4×D4×C11—22no—
157C4×D4×C11—21no—
158C4×D4×C11—21no—
159C4×D4×C11—21no—
160C4×D4×C11—21no—
161C4×D4×C11C2312yes—
162C4×D4×C11C2312yes—
163C11×#117—21no—
164C11×#117—21no—
165C11×#117—22no—
166C11×#117—22no—
167C11×#117—22no—
168C11×#117C2312yes—
169C2×C42×C11—22no—
170C2×C42×C11D411yescharacteristic
171C2×C42×C11D411yescharacteristic
172C2×C42×C11D411yescharacteristic
173C2×C42×C11D411yescharacteristic
174C2×C42×C11D411yescharacteristic
175C2×C42×C11D411yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C42×C11C2311yescharacteristic
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2311yescharacteristic
180C2×C42×C11C2311yescharacteristic
181C2×C42×C11C2311yescharacteristic
182C2×C22⋊Dic11—21no—
183#67004—28no—
184#67002—28no—
185C2×#4326C2314yes—
186C2×#4325C2314yes—
187C2×#4324C2314yes—
188C2×#4323C2314yes—
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—
196C4×C22⋊D11—22no—
197C2×(C2×D11)⋊C4—21no—
198C2×(C2×D11)⋊C4—21no—
199#66979—21no—
200#66979—21no—
201#66979C2312yes—
202#66979C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4—21no—
206C2×Dic11⋊C4—21no—
207C2×C4×Dic11—21no—
208C2×C4×Dic11—21no—
209C2×C4×Dic11—21no—
210C2×#4318C2312yes—
211C2×#4318C2312yes—
212C4×D44—21no—
213C4×D44—21no—
214C4×D44—21no—
215C4×D44—21no—
216C4×D44C2312yes—
217C4×D44C2312yes—
218C4×D44C2312yes—
219C4×D44C2312yes—
220#66925—22no—
221#66925—22no—
222#66925—22no—
223#66925—22no—
224C42×D11—22no—
225C42×D11—22no—
226C42×D11—22no—
227C42×D11—22no—
228C4×Dic22—21no—
229C4×Dic22—21no—
230C4×Dic22—21no—
231C4×Dic22—21no—
232C4×Dic22C2312yes—
233C4×Dic22C2312yes—
234C4×Dic22C2312yes—
235C4×Dic22C2312yes—
236#66899C2314yes—
237#66899C2314yes—
238#66896C2314yes—
239#66896C2314yes—
240C22⋊(C11⋊C8)C2314yes—
241C22⋊(C11⋊C8)C2314yes—
242#66874C2314yes—
243#66874C2314yes—
244#66873C2314yes—
245#66873C2314yes—
246#66872C2314yes—
247#66872C2314yes—
248#66871C2314yes—
249#66871C2314yes—
250C4⋊(C11⋊C8)C2312yes—
251C4⋊(C11⋊C8)C2312yes—
252C4⋊(C11⋊C8)C2312yes—
253C4⋊(C11⋊C8)C2312yes—
254#66867C2314yes—
255C4×C11⋊C8C2314yes—
256#60559—111nomaximal, Sylow
257C24×C11C2×D411yescharacteristic
258C23×D11—21no—
259C11×#41—24no—
260C11×#41—24no—
261C11×#41—44no—
262C11×#41—44no—
263C2×Q8×C11—21no—
264C2×Q8×C11—21no—
265C2×Q8×C11C2412yes—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—21no—
270C2×D4×C11—21no—
271C2×D4×C11C2412yes—
272C22×C4×C11—22no—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
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×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—28no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303#4339—28no—
304#4339—28no—
305#4339—24no—
306#4339—24no—
307#4339—24no—
308#4339—24no—
309C2×D44—21no—
310C2×D44—22no—
311C2×D44#4114yescomplemented
312C2×D44C2412yes—
313C2×C4×D11—28no—
314C2×C4×D11—22no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×Dic22—21no—
323C2×Dic22—22no—
324C2×Dic22#4114yescomplemented
325C2×Dic22C2412yes—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—21no—
328C11×C4⋊C4—21no—
329C11×C4⋊C4—21no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—22no—
336C11×C4⋊C4C2412yes—
337C11×C4⋊C4C2412yes—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—22no—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—22no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C42×C11—22no—
348C42×C11—22no—
349C42×C11—22no—
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×C11C2×D411yescharacteristic
359C42×C11C2×D411yescharacteristic
360C42×C11C2×D411yescharacteristic
361C42×C11C2×D411yescharacteristic
362C42×C11C2411yescharacteristic
363C42×C11C2411yescharacteristic
364C42×C11C2411yescharacteristic
365C42×C11C2411yescharacteristic
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368#4326—28no—
369#4325—28no—
370#4324—28no—
371#4323—28no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—22no—
375(C2×D11)⋊C4—22no—
376C4⋊Dic11—21no—
377C4⋊Dic11—21no—
378C4⋊Dic11C2412yes—
379C4⋊Dic11C2412yes—
380Dic11⋊C4—22no—
381Dic11⋊C4—22no—
382Dic11⋊C4—22no—
383Dic11⋊C4—22no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390#4318—24no—
391#4318—24no—
392C2×C11⋊C8C2414yes—
393C2×C11⋊C8C2414yes—
394#3444D1111yescharacteristic, complemented
395C2×C4×#41—111no—
396#3116—112no—
397#3115—112no—
398#3111—114no—
399#3107—112no—
400#3106—112no—
401#3102—114no—
402#3093—112no—
403#3078—111no—
404#3077—111no—
405#3037—111no—
406#3036—111no—
407#3005—112no—
408C4×#137—112no—
409C4×AGL(1,ℤ/8)—112no—
410#2920—111no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C23×C11C22×D411yescharacteristic
418C22×D11—24no—
419C22×D11—22no—
420C22×D11—42no—
421C22×D11—42no—
422Q8×C11—22no—
423Q8×C11—22no—
424Q8×C11—42no—
425Q8×C11—42no—
426D4×C11—22no—
427D4×C11—22no—
428D4×C11—42no—
429D4×C11—44no—
430D4×C11—44no—
431D4×C11—44no—
432D4×C11—42no—
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—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—44no—
456C2×C4×C11—44no—
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×#4112yes—
470C2×C4×C11C2×#4112yes—
471C2×C4×C11C2511yescharacteristic
472C22⋊D11—28no—
473C22⋊D11—28no—
474C2×Dic11—24no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—42no—
479C2×Dic11—42no—
480D44—24no—
481D44—22no—
482D44C2×#4114yes—
483C4×D11—28no—
484C4×D11—28no—
485C4×D11—44no—
486C4×D11—44no—
487C4×D11—44no—
488C4×D11—44no—
489Dic22—24no—
490Dic22—22no—
491Dic22C2×#4114yes—
492C11⋊C8—24no—
493C11⋊C8—24no—
494C22×#41—111no—
495C2×#137—112no—
496C2×AGL(1,ℤ/8)—112no—
497#533C2×D1111yescharacteristic
498#533C2×D1111yescharacteristic, complemented
499#533C2×D1111yescharacteristic, complemented
500#532C2×D1111yescharacteristic
501#532C2×D1111yescharacteristic, complemented
502#532C2×D1111yescharacteristic, complemented
503#529—21no—
504#529—21no—
505#529—21no—
506#529—21no—
507#529C2×D1112yescomplemented
508#529C2×D1112yescomplemented
509#525—21no—
510#525—21no—
511#525C2×D1112yes—
512C4×#41—21no—
513C4×#41—21no—
514C4×#41—112no—
515C4×#41—112no—
516C4×#41—112no—
517C4×#41—112no—
518C4×#41—221no—
519C4×#41—221no—
520C4×#41—221no—
521C4×#41—221no—
522C4×#41C2×D1112yes—
523C2×C4×Q8—111no—
524C2×C4×Q8—111no—
525C2×C4×D4—111no—
526C2×C4×D4—111no—
527C2×C4×D4—221no—
528C2×C4×D4—221no—
529C2×#117—111no—
530C2×#117—221no—
531C22×C42—221no—
532C22×C42C2×D1111yescharacteristic
533#485—114no—
534#485—114no—
535#482—114no—
536#482—114no—
537#479—114no—
538#478—114no—
539#477—112no—
540#476—112no—
541#475—112no—
542#474—112no—
543#464—114no—
544#463—114no—
545#462—112no—
546#461—112no—
547#460—112no—
548#459—112no—
549#452—114no—
550#452—114no—
551#449—114no—
552#449—114no—
553#442—114no—
554#441—114no—
555#440—114no—
556#440—114no—
557C4×Q16—114no—
558C4×SD16—114no—
559C4×SD16—114no—
560C4×D8—114no—
561#432—112no—
562#432—112no—
563#431—112no—
564#431—112no—
565#428—112no—
566#428—112no—
567#423—111no—
568#423—111no—
569#419—112no—
570#418—112no—
571#417—112no—
572#417—112no—
573#407—112no—
574C4×M16—112no—
575C22×C11—21no—
576C22×C11—21no—
577C22×C11—21no—
578C22×C11—21no—
579C22×C11—21no—
580C22×C11—21no—
581C22×C11—21no—
582C22×C11—21no—
583C22×C11—44no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11#52512yes—
588C22×C11C23×D411yescharacteristic
589C2×D11—24no—
590C2×D11—48no—
591C2×D11—42no—
592C2×D11—42no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—21no—
596C4×C11—21no—
597C4×C11—21no—
598C4×C11—21no—
599C4×C11—21no—
600C4×C11—21no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11—42no—
604C4×C11#52512yes—
605C4×C11#57512yes—
606C4×C11#57512yes—
607C4×C11C22×#4111yescharacteristic
608C4×C11C22×#4111yescharacteristic
609Dic11—24no—
610Dic11—42no—
611Dic11—42no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—112no—
615C2×#41—112no—
616C2×#41—224no—
617C2×#41—224no—
618C2×#41—221no—
619C2×#41—221no—
620C2×#41C22×D1112yes—
621C22×Q8—111no—
622C22×D4—111no—
623C22×D4—221no—
624C23×C4—221no—
625C23×C4—221no—
626C23×C4—221no—
627C23×C4C22⋊D1111yescharacteristic
628C23×C4C22⋊D1111yescharacteristic
629C23×C4C22×D1111yescharacteristic
630#137—228no—
631AGL(1,ℤ/8)—228no—
632C2×Q16—114no—
633C2×SD16—114no—
634C2×SD16—114no—
635C2×D8—114no—
636C2×M16—112no—
637C2×M16—112no—
638C4⋊Q8C22×D1111yescharacteristic
639C4⋊Q8C22×D1111yescharacteristic
640C4⋊Q8C22×D1111yescharacteristic
641#127C22×D1111yescharacteristic
642#126—22no—
643#126—22no—
644#125—21no—
645#125—21no—
646#125C22×D1112yes—
647#124—21no—
648#124—21no—
649#124C22×D1112yes—
650#123—22no—
651#123—22no—
652#123—22no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8C22×D1112yes—
658C22⋊Q8C22×D1112yes—
659#121—21no—
660#121—21no—
661#121—21no—
662#121—21no—
663#121C22×D1112yes—
664#121C22×D1112yes—
665#120—22no—
666C4×Q8—21no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—21no—
670C4×Q8—112no—
671C4×Q8—112no—
672C4×Q8—112no—
673C4×Q8—112no—
674C4×Q8—221no—
675C4×Q8—221no—
676C4×Q8—221no—
677C4×Q8—221no—
678C4×Q8C22×D1112yes—
679C4×Q8C22×D1112yes—
680C4×D4—22no—
681C4×D4—22no—
682C4×D4—22no—
683C4×D4—22no—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—112no—
691C4×D4—112no—
692C4×D4—112no—
693C4×D4—112no—
694C4×D4—222no—
695C4×D4—222no—
696C4×D4—222no—
697C4×D4—222no—
698C4×D4—222no—
699C4×D4—222no—
700C4×D4—222no—
701C4×D4—222no—
702C4×D4—221no—
703C4×D4—221no—
704C4×D4—221no—
705C4×D4—221no—
706C4×D4C22×D1112yes—
707C4×D4C22×D1112yes—
708#117—21no—
709#117—21no—
710#117—22no—
711#117—22no—
712#117—22no—
713#117—112no—
714#117—112no—
715#117—221no—
716#117—221no—
717#117—222no—
718#117—222no—
719#117—222no—
720#117—222no—
721#117C22×D1112yes—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—111no—
724C2×C4⋊C4—221no—
725C2×C4⋊C4—221no—
726C2×C22⋊C4—221no—
727C2×C22⋊C4—221no—
728C2×C22⋊C4—221no—
729C2×C42—22no—
730C2×C42—221no—
731C2×C42—221no—
732C2×C42—221no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737C2×C42C22⋊D1111yescharacteristic
738C2×C42C22⋊D1111yescharacteristic
739C2×C42C22⋊D1111yescharacteristic
740C2×C42C22⋊D1111yescharacteristic
741C2×C42C22⋊D1111yescharacteristic
742C2×C42C22⋊D1111yescharacteristic
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1111yescharacteristic
746C2×C42C22×D1111yescharacteristic
747C2×C42C22×D1111yescharacteristic
748C2×C42C22×D1111yescharacteristic
749#107—114no—
750#107—114no—
751#106—114no—
752#106—114no—
753C4⋊C8—112no—
754C4⋊C8—112no—
755C4⋊C8—112no—
756C4⋊C8—112no—
757#103—114no—
758#103—114no—
759#103—114no—
760#103—114no—
761#102—114no—
762#102—114no—
763#102—114no—
764#102—114no—
765C22⋊C8—114no—
766C22⋊C8—114no—
767#97—114no—
768C4×C8—114no—
769C2×C11—22no—
770C2×C11—41no—
771C2×C11—41no—
772C2×C11—82no—
773C2×C11C2×#52511yescharacteristic
774C2×C11C2×#57511yescharacteristic
775C2×C11C2×#57511yescharacteristic
776D11—44no—
777C24—221no—
778C24C2×C22⋊D1111yescharacteristic
779#41—24no—
780#41—24no—
781#41—44no—
782#41—44no—
783#41—224no—
784#41—224no—
785#41—224no—
786#41—224no—
787#41—228no—
788#41—228no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—114no—
792C2×Q8—112no—
793C2×Q8—222no—
794C2×Q8—221no—
795C2×Q8C23×D1112yes—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—114no—
802C2×D4—112no—
803C2×D4—228no—
804C2×D4—222no—
805C2×D4—222no—
806C2×D4—222no—
807C2×D4—221no—
808C2×D4C23×D1112yes—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—228no—
817C22×C4—221no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—222no—
823C22×C4—222no—
824C22×C4—222no—
825C22×C4—222no—
826C22×C4—444no—
827C22×C4—444no—
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
846Q16—228no—
847SD16—228no—
848SD16—228no—
849D8—228no—
850M16—224no—
851M16—224no—
852C2×C8—114no—
853C2×C8—114no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—112no—
865C4⋊C4—112no—
866C4⋊C4—221no—
867C4⋊C4—221no—
868C4⋊C4—222no—
869C4⋊C4—222no—
870C4⋊C4—222no—
871C4⋊C4—222no—
872C4⋊C4C23×D1112yes—
873C4⋊C4C23×D1112yes—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—22no—
883C22⋊C4—222no—
884C22⋊C4—222no—
885C22⋊C4—222no—
886C22⋊C4—222no—
887C22⋊C4—222no—
888C22⋊C4—222no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—222no—
893C42—222no—
894C42—222no—
895C42—222no—
896C42—222no—
897C42—222no—
898C42C2×C22⋊D1111yescharacteristic
899C42C2×C22⋊D1111yescharacteristic
900C42C2×C22⋊D1111yescharacteristic
901C42C2×C22⋊D1111yescharacteristic
902C42C2×C22⋊D1111yescharacteristic
903C42C2×C22⋊D1111yescharacteristic
904C42C2×C22⋊D1111yescharacteristic
905C42C2×C22⋊D1111yescharacteristic
906C42C2×C22⋊D1111yescharacteristic
907C42C2×C22⋊D1111yescharacteristic
908C42C2×C22⋊D1111yescharacteristic
909C42C2×C22⋊D1111yescharacteristic
910C42C23×D1111yescharacteristic
911C42C23×D1111yescharacteristic
912C42C23×D1111yescharacteristic
913C42C23×D1111yescharacteristic
914C11#6055911yescharacteristic, complemented, Sylow
915C23—22no—
916C23—22no—
917C23—41no—
918C23—41no—
919C23—224no—
920C23—222no—
921C23—442no—
922C23—442no—
923C23C22×C22⋊D1111yescharacteristic
924C23C22×C22⋊D1111yescharacteristic
925C23C22×C22⋊D1111yescharacteristic
926Q8—22no—
927Q8—22no—
928Q8—42no—
929Q8—42no—
930Q8—114no—
931Q8—224no—
932Q8—222no—
933D4—22no—
934D4—22no—
935D4—42no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—42no—
940D4—114no—
941D4—228no—
942D4—228no—
943D4—224no—
944D4—222no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—44no—
970C2×C4—228no—
971C2×C4—228no—
972C2×C4—224no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—444no—
977C2×C4—444no—
978C2×C4—442no—
979C2×C4—442no—
980C2×C4—444no—
981C2×C4—444no—
982C2×C4#41×D1112yes—
983C2×C4#41×D1112yes—
984C2×C4C22×C22⋊D1111yescharacteristic
985C2×C4C22×C22⋊D1111yescharacteristic
986C2×C4C22×C22⋊D1111yescharacteristic
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×C4C22×C22⋊D1111yescharacteristic
995C2×C4C24×D1111yescharacteristic
996C8—224no—
997C8—224no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—44no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—224no—
1011C22—448no—
1012C22—442no—
1013C22—442no—
1014C22#1062335912yes—
1015C22C23×C22⋊D1111yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—224no—
1028C4—442no—
1029C4—442no—
1030C4#1062335312yes—
1031C4#1062335312yes—
1032C4#1062335912yes—
1033C4C2×#41×D1111yescharacteristic
1034C4C2×#41×D1111yescharacteristic
1035C2—22no—
1036C2—41no—
1037C2—41no—
1038C2—82no—
1039C2—444no—
1040C2C2×#1062335911yescharacteristic
1041C2C2×#1062335311yescharacteristic
1042C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4339C2semidirect
2. #13078772C2semidirect
3. #13078761C2semidirect
4. #13078719C2semidirect
5. #13078681C2semidirect
6. #13078670C2semidirect
7. #13078628C2semidirect
8. #13078545C2semidirect
9. #13078417C2semidirect
10. #13078409C2semidirect
11. #13078084C2semidirect
12. #13078076C2semidirect
13. #13077856C2semidirect
14. C4×#67004C2semidirect
15. C4×#67002C2semidirect
16. #13077249C2semidirect
17. C11×#3444C2semidirect
20. C11×#533C22semidirect
21. C11×#533C22semidirect
23. C11×#532C22semidirect
24. C11×#532C22semidirect
29. C11×#529C22semidirect
30. C11×#529C22semidirect
60. #10622707C22semidirect
61. #10622704C22semidirect
62. #10622703C22semidirect
63. #10622700C22semidirect
64. #10622697C22semidirect
65. #10622696C22semidirect
66. #10622688C22semidirect
67. #10622685C22semidirect
68. #10622679C22semidirect
69. #10622676C22semidirect
70. #10622670C22semidirect
71. #10622667C22semidirect
74. #10622658C22semidirect
75. #10622658C22semidirect
78. #10622648C22semidirect
79. #10622648C22semidirect
80. #10622643C22semidirect
81. C4×#4326C22semidirect
82. #10622639C22semidirect
83. C4×#4325C22semidirect
84. #10622631C22semidirect
85. C4×#4324C22semidirect
86. #10622627C22semidirect
87. C4×#4323C22semidirect
92. #10622539C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
95. #10622538C22semidirect
311. C2×D44#41semidirect
324. C2×Dic22#41semidirect
394. #3444D11semidirect
498. #533C2×D11semidirect
499. #533C2×D11semidirect
501. #532C2×D11semidirect
502. #532C2×D11semidirect
507. #529C2×D11semidirect
508. #529C2×D11semidirect
914. C11#60559semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130787722
#130787612
#130787192
#130786812
#130786702
#130786282
#130785452
#130784172
#130784092
#130780842
#130780762
#130778562
C4×#670042
C4×#670022
#130772492
C11×#34442
#6055911