Finite Group Databasebeta

← #30548921

Subgroups — #30548921

Order 15616.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459554C211yesmaximal, characteristic, complemented
2#21456110C212yesmaximal, complemented
3#21456062C212yesmaximal, complemented
4#21456048C212yesmaximal, complemented
5#21456003C212yesmaximal, complemented
6#21455970C212yesmaximal, complemented
7#21455928C212yesmaximal, complemented
8#21455879C212yesmaximal, complemented
9#21455837C212yesmaximal, complemented
10#21455750C211yesmaximal, characteristic, complemented
11C2×#16840086C211yesmaximal, characteristic, complemented
12#21455681C211yesmaximal, characteristic, complemented
13#21455670C211yesmaximal, characteristic, complemented
14#21455358C211yesmaximal, characteristic, complemented
15#21455358C211yesmaximal, characteristic, complemented
16#21455071C211yesmaximal, characteristic, complemented
17#21455037C211yesmaximal, characteristic, complemented
18#21454700C211yesmaximal, characteristic, complemented
19#21454692C211yesmaximal, characteristic, complemented
20#21454647C211yesmaximal, characteristic, complemented
21#21454647C211yesmaximal, characteristic, complemented
22#21454477C211yesmaximal, characteristic, complemented
23C61×#3428C211yesmaximal, characteristic, complemented
24C2×#14519802C2211yescharacteristic
25C2×#14519802C2211yescharacteristic
26C2×#14519797C2211yescharacteristic
27C2×#14519797C2211yescharacteristic
28#16840475—21no—
29#16840460—21no—
30#16840456—21no—
31#16840436—22no—
32#16840413—21no—
33#16840402—22no—
34#16840390C2211yescharacteristic, complemented
35#16840383C2212yes—
36#16840367C2212yes—
37#16840331C2211yescharacteristic, complemented
38#16840312C2212yescomplemented
39#16840296C2212yescomplemented
40#16840273C2211yescharacteristic
41C2×#14519751C2211yescharacteristic
42#16840242C2211yescharacteristic, complemented
43#16840236C2211yescharacteristic, complemented
44#16840103C2212yescomplemented
45#16840103C2212yescomplemented
46#16840086C2212yes—
47#16840086C2212yes—
48#16840086C2212yescomplemented
49#16840086C2212yescomplemented
50#16840086C2212yescomplemented
51#16840086C2212yescomplemented
52#16840069C2212yescomplemented
53#16840069C2212yescomplemented
54#16840062C2212yescomplemented
55#16840062C2212yescomplemented
56#16840057C2212yescomplemented
57#16840052C2212yescomplemented
58#16840047C2212yescomplemented
59#16840042C2212yescomplemented
60#16839984C2212yescomplemented
61#16839984C2212yescomplemented
62#16839977C2212yescomplemented
63#16839977C2212yescomplemented
64#16839962C2212yescomplemented
65#16839962C2212yescomplemented
66#16839957C2212yescomplemented
67#16839957C2212yescomplemented
68#16839924C2211yescharacteristic, complemented
69#16839924C2211yescharacteristic, complemented
70#16839918C2211yescharacteristic, complemented
71#16839913C2211yescharacteristic, complemented
72#16839907C2212yes—
73#16839907C2212yes—
74#16839907C2211yescharacteristic, complemented
75#16839907C2211yescharacteristic, complemented
76#16839901C2212yes—
77#16839901C2211yescharacteristic, complemented
78#16839896C2212yes—
79#16839896C2211yescharacteristic, complemented
80#16839872C2212yescomplemented
81#16839872C2212yescomplemented
82#16839872C2212yescomplemented
83#16839867C2212yescomplemented
84#16839862C2212yescomplemented
85#16839860C2212yescomplemented
86#16839860C2212yescomplemented
87#16839860C2212yescomplemented
88C4×#11758202C2212yescomplemented
89C4×#11758201C2212yescomplemented
90C4×#11758201C2212yescomplemented
91C4×#11758201C2212yescomplemented
92C4×#11758200C2212yescomplemented
93C4×#11758199C2212yescomplemented
94C4×#11758199C2212yescomplemented
95C4×#11758199C2212yescomplemented
96#16839823C2212yescomplemented
97#16839823C2212yescomplemented
98#16839819C2212yescomplemented
99#16839815C2212yescomplemented
100#16839802C2211yescharacteristic, complemented
101#16839802C2211yescharacteristic, complemented
102C2×#14519710C2211yescharacteristic, complemented
103C2×#14519708C2211yescharacteristic, complemented
104#16839789C2211yescharacteristic, complemented
105#16839789C2211yescharacteristic, complemented
106#16839763C2211yescharacteristic
107#16839763C2211yescharacteristic
108#16839761C2211yescharacteristic, complemented
109#16839761C2211yescharacteristic, complemented
110#16839758C2211yescharacteristic
111#16839758C2211yescharacteristic
112C2×#14519697C2211yescharacteristic, complemented
113C2×#14519697C2211yescharacteristic, complemented
114#16839726C2211yescharacteristic
115C2×C22⋊#92418C2211yescharacteristic
116#16839718C2211yescharacteristic, complemented
117#16839718C2211yescharacteristic, complemented
118C22×#41×C61C2211yescharacteristic
119C61×#520—21no—
120C61×#520—21no—
121C61×#520C2211yescharacteristic
122C61×#520C2211yescharacteristic
123C61×#520C2211yescharacteristic
124C61×#520C2211yescharacteristic
125C61×#519C2212yescomplemented
126C61×#518—22no—
127C61×#518C2212yescomplemented
128C4×#41×C61—22no—
129C4×#41×C61C2212yescomplemented
130C4×#41×C61C2212yescomplemented
131C2×#117×C61—21no—
132C2×#117×C61—21no—
133C2×#117×C61C2211yescharacteristic
134C2×#117×C61C2211yescharacteristic
135C2×#11758222—22no—
136C2×#11758222C2311yescharacteristic
137C22×D244C2311yescharacteristic
138C22×C22⋊D61—21no—
139#14519802—24no—
140#14519802—24no—
141#14519797—24no—
142#14519797—24no—
143C2×#11758202C2311yescharacteristic
144C2×#11758202C2311yescharacteristic
145C2×#11758200C2311yescharacteristic
146C2×#11758200C2311yescharacteristic
147C2×#11758201C2311yescharacteristic
148C2×#11758201C2311yescharacteristic
149C2×#11758201C2312yes—
150C2×#11758201C2312yes—
151C2×#11758199C2311yescharacteristic
152C2×#11758199C2311yescharacteristic
153C2×#11758199C2312yes—
154C2×#11758199C2312yes—
155C2×#11758194C2311yescharacteristic
156C2×#11758194C2311yescharacteristic
157C22×#92418C2311yescharacteristic
158C22×#92418C2311yescharacteristic
159#14519777C2312yes—
160#14519776—21no—
161#14519774C2312yes—
162#14519772—22no—
163#14519771—22no—
164#14519769C2312yes—
165#14519768—21no—
166#14519765—22no—
167#14519765C2312yes—
168#14519763—22no—
169#14519762—22no—
170#14519762—22no—
171#14519760—21no—
172#14519760—22no—
173#14519759—22no—
174#14519756C2311yescharacteristic
175#14519756C2311yescharacteristic
176#14519755—22no—
177#14519754—22no—
178#14519752—21no—
179#14519752—21no—
180#14519751—21no—
181#14519751—21no—
182#14519751—22no—
183#14519751C2312yes—
184#14519751C2312yes—
185#14519751C2311yescharacteristic
186#14519751C2311yescharacteristic
187#14519750—22no—
188#14519750—22no—
189#14519747—22no—
190#14519746—21no—
191C4×Dic122C2312yes—
192C4×D244—22no—
193C4×D244C2312yes—
194C4×D244C2312yes—
195C4×D244C2312yes—
196#14519739—21no—
197#14519739—21no—
198C4×C22⋊D61—21no—
199C4×C22⋊D61—21no—
200C4×C22⋊D61—22no—
201#14519737—22no—
202#14519736C2311yescharacteristic
203#14519735—21no—
204#14519734—22no—
205C2×C4⋊Dic61C2311yescharacteristic
206C4⋊C4×D61—21no—
207C2×#11758198—21no—
208C22⋊C4×D61—22no—
209#14519710C2312yes—
210#14519710C2312yes—
211#14519710C2312yes—
212#14519710C2312yes—
213#14519708C2312yes—
214#14519708C2312yes—
215#14519708C2312yes—
216#14519708C2312yes—
217C4⋊#92418C2312yes—
218C4⋊#92418C2312yes—
219C4⋊#92418C2312yes—
220C4⋊#92418C2312yes—
221#14519701C2311yescharacteristic
222#14519701C2311yescharacteristic
223#14519701C2311yescharacteristic
224#14519701C2311yescharacteristic
225#14519701C2312yes—
226#14519701C2312yes—
227#14519700C2312yes—
228#14519700C2312yes—
229#14519698C2311yescharacteristic
230#14519698C2311yescharacteristic
231#14519698C2311yescharacteristic
232#14519698C2311yescharacteristic
233#14519698C2312yes—
234#14519698C2312yes—
235#14519697C2312yes—
236#14519697C2312yes—
237#14519697C2312yes—
238#14519697C2312yes—
239#14519697C2312yes—
240#14519697C2312yes—
241C22⋊#92418C2311yescharacteristic
242C22⋊#92418C2311yescharacteristic
243C22⋊#92418C2311yescharacteristic
244C22⋊#92418C2311yescharacteristic
245C22⋊#92418C2312yes—
246C22⋊#92418C2312yes—
247#14519688C2312yes—
248#14519688C2312yes—
249C4×#92418C2312yes—
250C4×#92418C2312yes—
251C2×#41×C61—24no—
252C2×#41×C61—24no—
253C2×#41×C61—21no—
254C2×#41×C61—21no—
255C2×#41×C61C2311yescharacteristic
256C2×#41×C61C2311yescharacteristic
257C2×#41×C61C2311yescharacteristic
258C2×#41×C61C2311yescharacteristic
259C22×Q8×C61C2311yescharacteristic
260C22×D4×C61—21no—
261C22×D4×C61C2311yescharacteristic
262C23×C4×C61—21no—
263C23×C4×C61C2311yescharacteristic
264C4×Q8×C61—22no—
265C4×Q8×C61—22no—
266C4×Q8×C61C2312yes—
267C4×Q8×C61C2312yes—
268C4×Q8×C61C2312yes—
269C4×Q8×C61C2312yes—
270C4×D4×C61—22no—
271C4×D4×C61—22no—
272C4×D4×C61—22no—
273C4×D4×C61—22no—
274C4×D4×C61—22no—
275C4×D4×C61—22no—
276C4×D4×C61—22no—
277C4×D4×C61—22no—
278C4×D4×C61—22no—
279C4×D4×C61—22no—
280C4×D4×C61C2312yes—
281C4×D4×C61C2312yes—
282C4×D4×C61C2312yes—
283C4×D4×C61C2312yes—
284#117×C61—21no—
285#117×C61—21no—
286#117×C61—21no—
287#117×C61—21no—
288#117×C61—21no—
289#117×C61—21no—
290#117×C61—22no—
291#117×C61—22no—
292#117×C61—22no—
293#117×C61—22no—
294#117×C61D411yescharacteristic
295#117×C61D411yescharacteristic
296#117×C61D412yes—
297#117×C61C2312yes—
298#117×C61C2312yes—
299#117×C61C2311yescharacteristic
300#117×C61C2311yescharacteristic
301#117×C61C2312yes—
302C2×C4⋊C4×C61—21no—
303C2×C4⋊C4×C61—21no—
304C2×C4⋊C4×C61—21no—
305C2×C4⋊C4×C61—21no—
306C2×C4⋊C4×C61D411yescharacteristic
307C2×C4⋊C4×C61D411yescharacteristic
308C2×C4⋊C4×C61C2311yescharacteristic
309C2×C4⋊C4×C61C2311yescharacteristic
310C2×C22⋊C4×C61—21no—
311C2×C22⋊C4×C61—22no—
312C2×C22⋊C4×C61—22no—
313C2×C22⋊C4×C61D412yes—
314C2×C42×C61—21no—
315C2×C42×C61—22no—
316C2×C42×C61—22no—
317C2×C42×C61C2312yes—
318C24×C61—21no—
319C24×C61C2×D411yescharacteristic
320C23×D61—21no—
321#41×C61—28no—
322#41×C61—28no—
323#41×C61—22no—
324#41×C61—22no—
325#41×C61—22no—
326#41×C61—22no—
327#41×C61—22no—
328#41×C61—22no—
329#41×C61#4114yescomplemented
330#41×C61#4114yescomplemented
331C2×Q8×C61—22no—
332C2×Q8×C61—22no—
333C2×Q8×C61—21no—
334C2×Q8×C61C2411yescharacteristic
335C2×Q8×C61C2411yescharacteristic
336C2×D4×C61—28no—
337C2×D4×C61—21no—
338C2×D4×C61—21no—
339C2×D4×C61—21no—
340C2×D4×C61—21no—
341C2×D4×C61—22no—
342C2×D4×C61—22no—
343C2×D4×C61—21no—
344C2×D4×C61C2411yescharacteristic
345C2×D4×C61C2411yescharacteristic
346C22×C4×C61—28no—
347C22×C4×C61—21no—
348C22×C4×C61—21no—
349C22×C4×C61—21no—
350C22×C4×C61—21no—
351C22×C4×C61—21no—
352C22×C4×C61—22no—
353C22×C4×C61—22no—
354C22×C4×C61—21no—
355C22×C4×C61—21no—
356C22×C4×C61—22no—
357C22×C4×C61—22no—
358C22×C4×C61—22no—
359C22×C4×C61—22no—
360C22×C4×C61C2×D411yescharacteristic
361C22×C4×C61C2×D411yescharacteristic
362C22×C4×C61C2×D411yescharacteristic
363C22×C4×C61C2×D412yes—
364C22×C4×C61C2×D412yes—
365C22×C4×C61C2411yescharacteristic
366C22×C4×C61C2411yescharacteristic
367C22×C4×C61C2411yescharacteristic
368C2×C22⋊D61—22no—
369C2×C22⋊D61—21no—
370C2×C22⋊D61—21no—
371C2×C22⋊D61—22no—
372C2×C22⋊D61—21no—
373C2×C22⋊D61—82no—
374C22×Dic61—21no—
375#11758222—22no—
376#11758222—22no—
377#11758222—84no—
378C2×D244—22no—
379C2×D244—22no—
380C2×D244—21no—
381C2×D244—22no—
382C2×D244—22no—
383C2×D244C2412yes—
384C2×D244C2411yescharacteristic
385C2×C4×D61—21no—
386C2×C4×D61—22no—
387C2×C4×D61—22no—
388C2×C4×D61—22no—
389C2×Dic122—22no—
390C2×Dic122C2411yescharacteristic
391C4⋊C4×C61—21no—
392C4⋊C4×C61—21no—
393C4⋊C4×C61—22no—
394C4⋊C4×C61—22no—
395C4⋊C4×C61—22no—
396C4⋊C4×C61—22no—
397C4⋊C4×C61C2×D411yescharacteristic
398C4⋊C4×C61C2×D411yescharacteristic
399C4⋊C4×C61C2×D411yescharacteristic
400C4⋊C4×C61C2×D411yescharacteristic
401C4⋊C4×C61C2×D412yes—
402C4⋊C4×C61C2×D412yes—
403C4⋊C4×C61C2412yes—
404C4⋊C4×C61C2412yes—
405C22⋊C4×C61—22no—
406C22⋊C4×C61—22no—
407C22⋊C4×C61—22no—
408C22⋊C4×C61—22no—
409C22⋊C4×C61—22no—
410C22⋊C4×C61—22no—
411C22⋊C4×C61C2×D412yes—
412C22⋊C4×C61C2×D412yes—
413C22⋊C4×C61C2×D412yes—
414C22⋊C4×C61C2×D412yes—
415C42×C61—22no—
416C42×C61—22no—
417C42×C61—22no—
418C42×C61—22no—
419C42×C61—22no—
420C42×C61—22no—
421C42×C61C2×D412yes—
422C42×C61C2×D412yes—
423C42×C61C2412yes—
424C42×C61C2412yes—
425C22⋊Dic61—21no—
426C22⋊Dic61—21no—
427C22⋊Dic61—21no—
428#11758202—22no—
429#11758202—22no—
430#11758201—22no—
431#11758201—22no—
432#11758201—24no—
433#11758201—24no—
434#11758200—22no—
435#11758200—22no—
436#11758199—22no—
437#11758199—22no—
438#11758199—24no—
439#11758199—24no—
440#11758198—22no—
441#11758198—22no—
442#11758198—22no—
443#11758198—22no—
444#11758198—22no—
445#11758198—22no—
446#11758198—21no—
447#11758198—22no—
448#11758198—21no—
449C4⋊Dic61—21no—
450C4⋊Dic61—22no—
451C4⋊Dic61C2412yes—
452C4⋊Dic61C2411yescharacteristic
453C4⋊Dic61C2411yescharacteristic
454#11758196—22no—
455#11758196—21no—
456#11758196—22no—
457#11758196—22no—
458#11758196—21no—
459C4×Dic61—22no—
460C4×Dic61—21no—
461#11758194—22no—
462#11758194—22no—
463C2×#92418—22no—
464C2×#92418—22no—
465C2×#92418C2411yescharacteristic
466C2×#92418C2411yescharacteristic
467C2×#92418C2412yes—
468C2×#92418C2412yes—
469C2×#92418C2411yescharacteristic
470C2×#92418C2411yescharacteristic
471C23×C61—24no—
472C23×C61—21no—
473C23×C61—21no—
474C23×C61—22no—
475C23×C61—41no—
476C23×C61—41no—
477C23×C61—81no—
478C23×C61—81no—
479C23×C61C22×D411yescharacteristic
480C23×C61C22×D411yescharacteristic
481C23×C61C22×D411yescharacteristic
482C22×D61—22no—
483C22×D61—21no—
484C22×D61—42no—
485C22×D61—81no—
486C22×D61—81no—
487Q8×C61—24no—
488Q8×C61—21no—
489Q8×C61—21no—
490Q8×C61C2×#4112yes—
491Q8×C61C2×#4112yes—
492D4×C61—24no—
493D4×C61—24no—
494D4×C61—24no—
495D4×C61—24no—
496D4×C61—24no—
497D4×C61—21no—
498D4×C61—21no—
499D4×C61C2×#4112yes—
500D4×C61C2×#4112yes—
501C2×C4×C61—24no—
502C2×C4×C61—24no—
503C2×C4×C61—24no—
504C2×C4×C61—22no—
505C2×C4×C61—21no—
506C2×C4×C61—21no—
507C2×C4×C61—22no—
508C2×C4×C61—24no—
509C2×C4×C61—24no—
510C2×C4×C61—22no—
511C2×C4×C61—21no—
512C2×C4×C61—21no—
513C2×C4×C61—21no—
514C2×C4×C61—21no—
515C2×C4×C61—22no—
516C2×C4×C61—22no—
517C2×C4×C61—42no—
518C2×C4×C61—42no—
519C2×C4×C61—82no—
520C2×C4×C61—82no—
521C2×C4×C61—82no—
522C2×C4×C61—82no—
523C2×C4×C61—81no—
524C2×C4×C61—81no—
525C2×C4×C61C22×D412yes—
526C2×C4×C61C22×D412yes—
527C2×C4×C61C22×D411yescharacteristic
528C2×C4×C61C22×D411yescharacteristic
529C2×C4×C61C22×D412yes—
530C2×C4×C61C22×D412yes—
531C2×C4×C61C22×D411yescharacteristic
532C2×C4×C61C2×#4112yes—
533C2×C4×C61C2×#4112yes—
534C2×C4×C61C2511yescharacteristic
535C22⋊D61—42no—
536C22⋊D61—44no—
537C22⋊D61—42no—
538C22⋊D61—81no—
539C22⋊D61—82no—
540C2×Dic61—21no—
541C2×Dic61—21no—
542C2×Dic61—22no—
543C2×Dic61—21no—
544C2×Dic61—81no—
545D244—22no—
546D244—22no—
547D244—21no—
548D244—21no—
549D244—42no—
550D244—82no—
551D244—82no—
552C4×D61—42no—
553C4×D61—82no—
554C4×D61—82no—
555C4×D61—82no—
556Dic122—21no—
557Dic122—21no—
558Dic122—82no—
559#92418—21no—
560#92418—21no—
561#92418—21no—
562#92418—21no—
563#92418—22no—
564#92418—22no—
565#60587—611nomaximal, Sylow
566C22×C61—21no—
567C22×C61—21no—
568C22×C61—21no—
569C22×C61—21no—
570C22×C61—21no—
571C22×C61—21no—
572C22×C61—21no—
573C22×C61—21no—
574C22×C61—22no—
575C22×C61—22no—
576C22×C61—41no—
577C22×C61—41no—
578C22×C61—41no—
579C22×C61—41no—
580C22×C61—82no—
581C22×C61—84no—
582C22×C61#52512yes—
583C22×C61C23×D411yescharacteristic
584C2×D61—42no—
585C2×D61—41no—
586C2×D61—41no—
587C2×D61—42no—
588C2×D61—41no—
589C2×D61—42no—
590C2×D61—162no—
591C4×C61—22no—
592C4×C61—22no—
593C4×C61—22no—
594C4×C61—22no—
595C4×C61—21no—
596C4×C61—22no—
597C4×C61—22no—
598C4×C61—21no—
599C4×C61—42no—
600C4×C61—42no—
601C4×C61#52512yes—
602C4×C61C22×#4111yescharacteristic
603C4×C61C22×#4111yescharacteristic
604Dic61—41no—
605Dic61—41no—
606Dic61—42no—
607Dic61—41no—
608#3494—611no—
609#3428D6111yescharacteristic, complemented
610#3126—612no—
611#3122—612no—
612#3121—612no—
613#3118—612no—
614#3115—612no—
615#3111—612no—
616#3106—612no—
617#3102—612no—
618#3093—611no—
619C2×#482—611no—
620#3084—611no—
621#3083—611no—
622#3045—611no—
623#3045—611no—
624#3006—611no—
625#3002—611no—
626#2952—611no—
627#2951—611no—
628#2946—611no—
629#2946—611no—
630#2924—611no—
631C2×C61—22no—
632C2×C61—41no—
633C2×C61—41no—
634C2×C61—42no—
635C2×C61—42no—
636C2×C61C2×#52511yescharacteristic
637C2×C61#358411yescharacteristic
638C2×C61#358511yescharacteristic
639D61—81no—
640D61—82no—
641C22×#41C2×D6111yescharacteristic
642C2×AGL(1,ℤ/8)—611no—
643C2×AGL(1,ℤ/8)—611no—
644C2×#135—611no—
645C2×#135—611no—
646#555—1221no—
647#553—1221no—
648#553—1221no—
649#551—1222no—
650#547—1221no—
651#546—1222no—
652#544—611no—
653#542—612no—
654#540—612no—
655#535—611no—
656#532—612no—
657#529—612no—
658#525—611no—
659C2×#121—611no—
660#520—21no—
661#520—21no—
662#520—611no—
663#520C2×D6111yescharacteristic
664#520C2×D6111yescharacteristic
665#520C2×D6111yescharacteristic
666#520C2×D6111yescharacteristic
667#519C2×D6112yescomplemented
668#518—22no—
669#518—611no—
670#518C2×D6112yescomplemented
671C4×#41—22no—
672C4×#41C2×D6112yescomplemented
673C4×#41C2×D6112yescomplemented
674C2×#117—21no—
675C2×#117—21no—
676C2×#117C2×D6111yescharacteristic
677C2×#117C2×D6111yescharacteristic
678#485—612no—
679#485—612no—
680#482—612no—
681#482—612no—
682#482—612no—
683#482—612no—
684#482—612no—
685#482—612no—
686#479—612no—
687#479—612no—
688#478—612no—
689#478—612no—
690#477—612no—
691#476—612no—
692#475—612no—
693#474—612no—
694#464—612no—
695#464—612no—
696#463—612no—
697#463—612no—
698#460—612no—
699#460—612no—
700#459—612no—
701#459—612no—
702#452—611no—
703#452—611no—
704#451—611no—
705#450—611no—
706#449—612no—
707#449—611no—
708#449—612no—
709#449—611no—
710#448—612no—
711#448—611no—
712#447—612no—
713#447—611no—
714#442—612no—
715#442—612no—
716#442—612no—
717#441—612no—
718#440—612no—
719#440—612no—
720#440—612no—
721#440—612no—
722C4×Q16—612no—
723C4×SD16—612no—
724C4×SD16—612no—
725C4×SD16—612no—
726C4×SD16—612no—
727C4×D8—612no—
728C4×D8—612no—
729C4×D8—612no—
730#433—612no—
731#433—612no—
732#432—612no—
733#431—612no—
734#428—611no—
735#428—611no—
736C2×#107—611no—
737C2×#106—611no—
738#424—611no—
739#424—611no—
740#417—611no—
741#417—611no—
742#417—611no—
743#417—611no—
744#416—611no—
745#416—611no—
746C2×#102—611no—
747C2×#102—611no—
748#407—611no—
749C2×C22⋊C8—611no—
750#405—611no—
751#405—611no—
752C61#6058711yescharacteristic, complemented, Sylow
753C2×#41—24no—
754C2×#41—24no—
755C2×#41—21no—
756C2×#41—21no—
757C2×#41—611no—
758C2×#41—1222no—
759C2×#41C22×D6111yescharacteristic
760C2×#41C22×D6111yescharacteristic
761C2×#41C22×D6111yescharacteristic
762C2×#41C22×D6111yescharacteristic
763C22×Q8C22×D6111yescharacteristic
764C22×D4—21no—
765C22×D4—611no—
766C22×D4—1221no—
767C22×D4C22×D6111yescharacteristic
768C23×C4—21no—
769C23×C4C22×D6111yescharacteristic
770AGL(1,ℤ/8)—1224no—
771AGL(1,ℤ/8)—1224no—
772#135—1224no—
773#135—1224no—
774C2×Q16—611no—
775C2×Q16—611no—
776C2×SD16—611no—
777C2×SD16—611no—
778C2×SD16—612no—
779C2×SD16—612no—
780C2×SD16—611no—
781C2×SD16—611no—
782C2×D8—611no—
783C2×D8—611no—
784C2×D8—612no—
785C2×D8—612no—
786C2×M16—611no—
787C2×M16—611no—
788C22×C8—611no—
789C22×C8—611no—
790C4⋊Q8—612no—
791C4⋊Q8—1221no—
792#127—612no—
793#126—1222no—
794#126—1222no—
795#125—612no—
796#125—1221no—
797#124—612no—
798#124—1222no—
799#124—1222no—
800#123—1221no—
801#123—1222no—
802#123—1222no—
803#123—1222no—
804#123—1222no—
805C22⋊Q8—611no—
806C22⋊Q8—611no—
807C22⋊Q8—1222no—
808C22⋊Q8—1222no—
809#121—612no—
810#121—612no—
811#121—611no—
812#121—611no—
813#121—1221no—
814#121—1221no—
815#121—1222no—
816#121—1221no—
817#121—1221no—
818#121—1222no—
819#121—1222no—
820#120—1221no—
821#120—1222no—
822C4×Q8—22no—
823C4×Q8—22no—
824C4×Q8—612no—
825C4×Q8C22×D6112yes—
826C4×Q8C22×D6112yes—
827C4×Q8C22×D6112yes—
828C4×Q8C22×D6112yes—
829C4×D4—22no—
830C4×D4—22no—
831C4×D4—22no—
832C4×D4—22no—
833C4×D4—22no—
834C4×D4—22no—
835C4×D4—22no—
836C4×D4—22no—
837C4×D4—22no—
838C4×D4—22no—
839C4×D4—612no—
840C4×D4—612no—
841C4×D4—612no—
842C4×D4—1221no—
843C4×D4—1221no—
844C4×D4—1222no—
845C4×D4—1221no—
846C4×D4—1221no—
847C4×D4—1222no—
848C4×D4—1222no—
849C4×D4C22×D6112yes—
850C4×D4C22×D6112yes—
851C4×D4C22×D6112yes—
852C4×D4C22×D6112yes—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—22no—
860#117—22no—
861#117—22no—
862#117—22no—
863#117—611no—
864#117—1221no—
865#117—1222no—
866#117C22⋊D6111yescharacteristic
867#117C22⋊D6111yescharacteristic
868#117C22⋊D6112yes—
869#117C22×D6112yes—
870#117C22×D6112yes—
871#117C22×D6111yescharacteristic
872#117C22×D6112yes—
873#117C22×D6111yescharacteristic
874C2×C4⋊C4—21no—
875C2×C4⋊C4—21no—
876C2×C4⋊C4—21no—
877C2×C4⋊C4—21no—
878C2×C4⋊C4—611no—
879C2×C4⋊C4—1221no—
880C2×C4⋊C4C22⋊D6111yescharacteristic
881C2×C4⋊C4C22⋊D6111yescharacteristic
882C2×C4⋊C4C22×D6111yescharacteristic
883C2×C4⋊C4C22×D6111yescharacteristic
884C2×C22⋊C4—21no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—1221no—
888C2×C22⋊C4—1222no—
889C2×C22⋊C4C22⋊D6112yes—
890C2×C42—21no—
891C2×C42—22no—
892C2×C42—22no—
893C2×C42C22×D6112yes—
894#107—612no—
895#107—612no—
896#107—612no—
897#107—612no—
898#106—612no—
899#106—612no—
900#106—612no—
901#106—612no—
902C4⋊C8—612no—
903C4⋊C8—612no—
904C4⋊C8—612no—
905C4⋊C8—612no—
906#103—611no—
907#103—611no—
908#103—611no—
909#103—611no—
910#103—612no—
911#103—612no—
912#103—612no—
913#103—612no—
914#102—611no—
915#102—611no—
916#102—611no—
917#102—611no—
918#102—612no—
919#102—612no—
920#102—612no—
921#102—612no—
922#102—612no—
923#102—612no—
924#102—612no—
925#102—612no—
926C22⋊C8—611no—
927C22⋊C8—611no—
928C22⋊C8—611no—
929C22⋊C8—611no—
930C22⋊C8—612no—
931C22⋊C8—612no—
932#97—612no—
933#97—612no—
934C4×C8—612no—
935C4×C8—612no—
936C24—21no—
937C24—1221no—
938C24C2×C22⋊D6111yescharacteristic
939#41—28no—
940#41—28no—
941#41—22no—
942#41—22no—
943#41—22no—
944#41—22no—
945#41—22no—
946#41—22no—
947#41—1222no—
948#41—1222no—
949#41—4884no—
950#41#1175822214yescomplemented
951#41#1175822214yescomplemented
952C2×Q8—22no—
953C2×Q8—22no—
954C2×Q8—21no—
955C2×Q8—611no—
956C2×Q8—1222no—
957C2×Q8C23×D6111yescharacteristic
958C2×Q8C23×D6111yescharacteristic
959C2×D4—28no—
960C2×D4—21no—
961C2×D4—21no—
962C2×D4—21no—
963C2×D4—21no—
964C2×D4—22no—
965C2×D4—22no—
966C2×D4—21no—
967C2×D4—612no—
968C2×D4—611no—
969C2×D4—1221no—
970C2×D4—1222no—
971C2×D4—1221no—
972C2×D4—1221no—
973C2×D4—1222no—
974C2×D4—1222no—
975C2×D4—1222no—
976C2×D4—1221no—
977C2×D4—1222no—
978C2×D4—1222no—
979C2×D4—4882no—
980C2×D4C23×D6111yescharacteristic
981C2×D4C23×D6111yescharacteristic
982C22×C4—28no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—1221no—
997C22×C4—1222no—
998C22×C4—1222no—
999C22×C4—1222no—
1000C22×C4—1221no—
1001C22×C4C2×C22⋊D6111yescharacteristic
1002C22×C4C2×C22⋊D6111yescharacteristic
1003C22×C4C2×C22⋊D6111yescharacteristic
1004C22×C4C2×C22⋊D6112yes—
1005C22×C4C2×C22⋊D6112yes—
1006C22×C4C23×D6111yescharacteristic
1007C22×C4C23×D6111yescharacteristic
1008C22×C4C23×D6111yescharacteristic
1009Q16—1222no—
1010Q16—1222no—
1011SD16—1222no—
1012SD16—1222no—
1013SD16—1224no—
1014SD16—1224no—
1015SD16—1222no—
1016SD16—1222no—
1017D8—1222no—
1018D8—1222no—
1019D8—1224no—
1020D8—1224no—
1021M16—1222no—
1022M16—1222no—
1023C2×C8—611no—
1024C2×C8—611no—
1025C2×C8—612no—
1026C2×C8—612no—
1027C2×C8—611no—
1028C2×C8—611no—
1029C2×C8—1222no—
1030C2×C8—1222no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—612no—
1038C4⋊C4—611no—
1039C4⋊C4—611no—
1040C4⋊C4—1221no—
1041C4⋊C4—1222no—
1042C4⋊C4—1221no—
1043C4⋊C4—1222no—
1044C4⋊C4—1222no—
1045C4⋊C4—1221no—
1046C4⋊C4—1222no—
1047C4⋊C4C2×C22⋊D6111yescharacteristic
1048C4⋊C4C2×C22⋊D6111yescharacteristic
1049C4⋊C4C2×C22⋊D6111yescharacteristic
1050C4⋊C4C2×C22⋊D6111yescharacteristic
1051C4⋊C4C2×C22⋊D6112yes—
1052C4⋊C4C2×C22⋊D6112yes—
1053C4⋊C4C23×D6112yes—
1054C4⋊C4C23×D6112yes—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—1221no—
1062C22⋊C4—1221no—
1063C22⋊C4—1221no—
1064C22⋊C4—1222no—
1065C22⋊C4—1222no—
1066C22⋊C4—1222no—
1067C22⋊C4—1222no—
1068C22⋊C4—1222no—
1069C22⋊C4—1222no—
1070C22⋊C4—1221no—
1071C22⋊C4—1222no—
1072C22⋊C4—1221no—
1073C22⋊C4C2×C22⋊D6112yes—
1074C22⋊C4C2×C22⋊D6112yes—
1075C22⋊C4C2×C22⋊D6112yes—
1076C22⋊C4C2×C22⋊D6112yes—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—22no—
1083C42—1221no—
1084C42—1222no—
1085C42C2×C22⋊D6112yes—
1086C42C2×C22⋊D6112yes—
1087C42C23×D6112yes—
1088C42C23×D6112yes—
1089C23—24no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—41no—
1094C23—41no—
1095C23—81no—
1096C23—81no—
1097C23—1222no—
1098C23—1221no—
1099C23—4881no—
1100C23—4881no—
1101C23—2442no—
1102C23C22×C22⋊D6111yescharacteristic
1103C23C22×C22⋊D6111yescharacteristic
1104C23C22×C22⋊D6111yescharacteristic
1105Q8—24no—
1106Q8—21no—
1107Q8—21no—
1108Q8—1221no—
1109Q8—1221no—
1110Q8—4882no—
1111Q8C2×#1175822212yes—
1112Q8C2×#1175822212yes—
1113D4—24no—
1114D4—24no—
1115D4—24no—
1116D4—24no—
1117D4—24no—
1118D4—21no—
1119D4—21no—
1120D4—1222no—
1121D4—1222no—
1122D4—1221no—
1123D4—1221no—
1124D4—4882no—
1125D4—4882no—
1126D4—4881no—
1127D4—4882no—
1128D4—2444no—
1129D4—2442no—
1130D4—2442no—
1131D4—2442no—
1132D4C2×#1175822212yes—
1133D4C2×#1175822212yes—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—82no—
1153C2×C4—82no—
1154C2×C4—82no—
1155C2×C4—82no—
1156C2×C4—81no—
1157C2×C4—81no—
1158C2×C4—1221no—
1159C2×C4—1221no—
1160C2×C4—1221no—
1161C2×C4—1222no—
1162C2×C4—4882no—
1163C2×C4—4882no—
1164C2×C4—4882no—
1165C2×C4—4881no—
1166C2×C4—2442no—
1167C2×C4C22×C22⋊D6111yescharacteristic
1168C2×C4C22×C22⋊D6111yescharacteristic
1169C2×C4C22×C22⋊D6112yes—
1170C2×C4C22×C22⋊D6112yes—
1171C2×C4C22×C22⋊D6112yes—
1172C2×C4C22×C22⋊D6112yes—
1173C2×C4C22×C22⋊D6111yescharacteristic
1174C2×C4C2×#1175822212yes—
1175C2×C4C2×#1175822212yes—
1176C2×C4C24×D6111yescharacteristic
1177C8—1221no—
1178C8—1221no—
1179C8—1221no—
1180C8—1221no—
1181C8—1222no—
1182C8—1222no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—22no—
1190C22—22no—
1191C22—21no—
1192C22—21no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—82no—
1198C22—84no—
1199C22—9762no—
1200C22—2442no—
1201C22—2441no—
1202C22—2441no—
1203C22—2442no—
1204C22—2441no—
1205C22—2442no—
1206C22#1684027312yes—
1207C22C23×C22⋊D6111yescharacteristic
1208C4—22no—
1209C4—22no—
1210C4—21no—
1211C4—22no—
1212C4—22no—
1213C4—21no—
1214C4—22no—
1215C4—22no—
1216C4—42no—
1217C4—42no—
1218C4—2441no—
1219C4—2441no—
1220C4—2442no—
1221C4—2441no—
1222C4#1684027312yes—
1223C4C22×#1175822211yescharacteristic
1224C4C22×#1175822211yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—42no—
1229C2—42no—
1230C2—4882no—
1231C2—4881no—
1232C2C2×#1684027311yescharacteristic
1233C2#2146059011yescharacteristic
1234C2#2146059811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3428C2
socleC22×C61C23×D4
hypercenter#3428D61
hypocenterC61#60587
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #21459554C2semidirect
2. #21456110C2semidirect
3. #21456062C2semidirect
4. #21456048C2semidirect
5. #21456003C2semidirect
6. #21455970C2semidirect
7. #21455928C2semidirect
8. #21455879C2semidirect
9. #21455837C2semidirect
10. #21455750C2semidirect
11. C2×#16840086C2semidirect
12. #21455681C2semidirect
13. #21455670C2semidirect
14. #21455358C2semidirect
15. #21455358C2semidirect
16. #21455071C2semidirect
17. #21455037C2semidirect
18. #21454700C2semidirect
19. #21454692C2semidirect
20. #21454647C2semidirect
21. #21454647C2semidirect
22. #21454477C2semidirect
23. C61×#3428C2semidirect
34. #16840390C22semidirect
37. #16840331C22semidirect
38. #16840312C22semidirect
39. #16840296C22semidirect
42. #16840242C22semidirect
43. #16840236C22semidirect
44. #16840103C22semidirect
45. #16840103C22semidirect
48. #16840086C22semidirect
49. #16840086C22semidirect
50. #16840086C22semidirect
51. #16840086C22semidirect
52. #16840069C22semidirect
53. #16840069C22semidirect
54. #16840062C22semidirect
55. #16840062C22semidirect
56. #16840057C22semidirect
57. #16840052C22semidirect
58. #16840047C22semidirect
59. #16840042C22semidirect
60. #16839984C22semidirect
61. #16839984C22semidirect
62. #16839977C22semidirect
63. #16839977C22semidirect
64. #16839962C22semidirect
65. #16839962C22semidirect
66. #16839957C22semidirect
67. #16839957C22semidirect
68. #16839924C22semidirect
69. #16839924C22semidirect
70. #16839918C22semidirect
71. #16839913C22semidirect
74. #16839907C22semidirect
75. #16839907C22semidirect
77. #16839901C22semidirect
79. #16839896C22semidirect
80. #16839872C22semidirect
81. #16839872C22semidirect
82. #16839872C22semidirect
83. #16839867C22semidirect
84. #16839862C22semidirect
85. #16839860C22semidirect
86. #16839860C22semidirect
87. #16839860C22semidirect
88. C4×#11758202C22semidirect
89. C4×#11758201C22semidirect
90. C4×#11758201C22semidirect
91. C4×#11758201C22semidirect
92. C4×#11758200C22semidirect
93. C4×#11758199C22semidirect
94. C4×#11758199C22semidirect
95. C4×#11758199C22semidirect
96. #16839823C22semidirect
97. #16839823C22semidirect
98. #16839819C22semidirect
99. #16839815C22semidirect
100. #16839802C22semidirect
101. #16839802C22semidirect
102. C2×#14519710C22semidirect
103. C2×#14519708C22semidirect
104. #16839789C22semidirect
105. #16839789C22semidirect
108. #16839761C22semidirect
109. #16839761C22semidirect
112. C2×#14519697C22semidirect
113. C2×#14519697C22semidirect
116. #16839718C22semidirect
117. #16839718C22semidirect
125. C61×#519C22semidirect
127. C61×#518C22semidirect
129. C4×#41×C61C22semidirect
130. C4×#41×C61C22semidirect
329. #41×C61#41semidirect
330. #41×C61#41semidirect
609. #3428D61semidirect
667. #519C2×D61semidirect
670. #518C2×D61semidirect
672. C4×#41C2×D61semidirect
673. C4×#41C2×D61semidirect
752. C61#60587semidirect
950. #41#11758222semidirect
951. #41#11758222semidirect

Maximal subgroups

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

subgroupindex
#214595542
#214561102
#214560622
#214560482
#214560032
#214559702
#214559282
#214558792
#214558372
#214557502
C2×#168400862
#214556812
#214556702
#214553582
#214550712
#214550372
#214547002
#214546922
#214546472
#214544772
C61×#34282
#6058761