Finite Group Databasebeta

← #30548423

Subgroups — #30548423

Order 15616.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459111C211yesmaximal, characteristic
2C22×Q8×Dic61C211yesmaximal, characteristic, complemented
3#21455991C212yesmaximal, complemented
4#21455985C212yesmaximal, complemented
5#21455944C212yesmaximal, complemented
6#21455936C212yesmaximal, complemented
7#21455900C212yesmaximal, complemented
8#21455894C212yesmaximal, complemented
9#21455853C212yesmaximal, complemented
10#21455845C212yesmaximal, complemented
11#21455744C211yesmaximal, characteristic, complemented
12#21455739C211yesmaximal, characteristic, complemented
13#21455621C212yesmaximal, complemented
14#21455288C212yesmaximal, complemented
15#21455053C211yesmaximal, characteristic, complemented
16#137×Dic61C212yesmaximal, complemented
17#21454634C212yesmaximal, complemented
18#21454448C211yesmaximal, characteristic, complemented
19C61×#3004C211yesmaximal, characteristic, complemented
20C2×#14519808C2212yes—
21#16840315C2211yescharacteristic
22#16840314C2211yescharacteristic
23#16840314C2211yescharacteristic
24#16840308C2211yescharacteristic
25#16840307C2211yescharacteristic
26#16840307C2211yescharacteristic
27#16840298C2211yescharacteristic
28#16840298C2211yescharacteristic
29#16840293C2211yescharacteristic
30#16840293C2211yescharacteristic
31#16840292—21no—
32#16840292—21no—
33#16840289—21no—
34#16840289—21no—
35#16840273C2211yescharacteristic
36#16840268—21no—
37#16840268—21no—
38#41×Dic61C2211yescharacteristic
39#16840230C2211yescharacteristic
40C4×#11758224—21no—
41C4×#11758224—21no—
42C2×Q8×Dic61—21no—
43C2×Q8×Dic61—21no—
44C2×Q8×Dic61—21no—
45C2×Q8×Dic61—21no—
46C2×Q8×Dic61—21no—
47C2×Q8×Dic61—21no—
48C2×Q8×Dic61C2212yes—
49C2×Q8×Dic61C2212yes—
50C2×Q8×Dic61C2212yes—
51C2×Q8×Dic61C2212yes—
52C2×Q8×Dic61C2212yes—
53C2×Q8×Dic61C2212yes—
54C22×C4⋊Dic61—21no—
55C22×C4⋊Dic61C2211yescharacteristic
56C22×C4×Dic61—21no—
57C22×C4×Dic61C2211yescharacteristic
58#16840098C2212yes—
59#16840095C2212yes—
60#16840093C2212yes—
61#16840090C2212yes—
62#16840081C2212yes—
63#16840078C2212yes—
64#16840076C2212yes—
65#16840073C2212yes—
66#16840071C2214yescomplemented
67#16840067C2214yescomplemented
68#16840055C2214yescomplemented
69#16840045C2214yescomplemented
70#16839986C2214yescomplemented
71#16839982C2214yescomplemented
72#16839970C2214yescomplemented
73#16839960C2214yescomplemented
74#16839918C2212yes—
75#16839918C2212yes—
76#16839901C2212yes—
77#16839901C2212yes—
78#16839869C2214yescomplemented
79#16839866C2214yescomplemented
80#16839865C2214yescomplemented
81#16839863C2214yescomplemented
82Q16×Dic61C2214yescomplemented
83#16839854C2214yescomplemented
84SD16×Dic61C2214yescomplemented
85#16839847C2214yescomplemented
86#16839816C2212yes—
87#16839816C2212yes—
88#16839812C2212yes—
89#16839812C2212yes—
90#16839805C2212yes—
91#16839804C2212yes—
92#16839785C2212yes—
93#16839771C2212yes—
94#16839764C2212yes—
95#16839763C2212yes—
96#16839726C2211yescharacteristic
97M16×Dic61C2212yes—
98C23×Q8×C61C2211yescharacteristic
99C2×#137×C61C2212yes—
100C61×#525C2211yescharacteristic
101C61×#451C2212yes—
102C61×#451C2212yes—
103C61×#448C2212yes—
104C61×#448C2212yes—
105C61×#419C2212yes—
106C61×#407C2211yescharacteristic
107C2×#11758222C2311yescharacteristic
108C2×#11758224—21no—
109C2×#11758224—21no—
110C23×Dic61—21no—
111C23×Dic61D411yescharacteristic
112C23×Dic61D411yescharacteristic
113#14519808—28no—
114C2×#11758202C2314yes—
115C2×#11758201C2314yes—
116C2×#11758194C2312yes—
117#14519776C2311yescharacteristic
118#14519776C2311yescharacteristic
119#14519775C2311yescharacteristic
120#14519773C2311yescharacteristic
121#14519772—21no—
122#14519772—21no—
123#14519770—21no—
124#14519770—21no—
125#14519768C2311yescharacteristic
126#14519768C2311yescharacteristic
127#14519767—21no—
128#14519767—21no—
129#14519766C2311yescharacteristic
130#14519764C2311yescharacteristic
131#14519763—21no—
132#14519763—21no—
133#14519761—21no—
134#14519761—21no—
135#14519760—21no—
136#14519758—21no—
137#14519758—21no—
138#14519756C2311yescharacteristic
139#14519756C2311yescharacteristic
140#14519754—21no—
141#14519754—21no—
142#14519754—21no—
143#14519754—21no—
144#14519751C2311yescharacteristic
145#14519751C2311yescharacteristic
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519749—21no—
150#14519746—21no—
151Q8×Dic61—22no—
152Q8×Dic61—22no—
153Q8×Dic61—22no—
154Q8×Dic61—22no—
155Q8×Dic61—22no—
156Q8×Dic61—22no—
157Q8×Dic61—22no—
158Q8×Dic61—22no—
159Q8×Dic61—22no—
160Q8×Dic61—22no—
161Q8×Dic61—22no—
162Q8×Dic61—22no—
163Q8×Dic61C2314yes—
164Q8×Dic61C2314yes—
165Q8×Dic61C2314yes—
166Q8×Dic61C2314yes—
167Q8×Dic61C2311yescharacteristic
168Q8×Dic61C2311yescharacteristic
169C4×Dic122—21no—
170C4×Dic122—21no—
171#14519742—21no—
172#14519742—21no—
173#14519742C2311yescharacteristic
174#14519742C2311yescharacteristic
175D4×Dic61—21no—
176D4×Dic61—21no—
177D4×Dic61—21no—
178D4×Dic61—21no—
179D4×Dic61C2311yescharacteristic
180D4×Dic61C2311yescharacteristic
181#14519739C2311yescharacteristic
182#14519739C2311yescharacteristic
183C4×C22⋊D61—21no—
184C4×C22⋊D61—21no—
185C4×C22⋊D61—21no—
186C4×C22⋊D61—21no—
187#14519737—21no—
188#14519737—21no—
189#14519737—21no—
190#14519737—21no—
191#14519737—21no—
192#14519737—21no—
193#14519736—21no—
194#14519736C2311yescharacteristic
195#14519735—21no—
196#14519735—21no—
197#14519734—21no—
198#14519733—21no—
199#14519733—21no—
200#14519733—21no—
201#14519733—21no—
202C2×C4⋊Dic61—21no—
203C2×C4⋊Dic61—21no—
204C2×C4⋊Dic61—21no—
205C2×C4⋊Dic61—22no—
206C2×C4⋊Dic61—22no—
207C2×C4⋊Dic61—22no—
208C2×C4⋊Dic61—22no—
209C2×C4⋊Dic61—22no—
210C2×C4⋊Dic61—22no—
211C2×C4⋊Dic61C2312yes—
212C2×C4⋊Dic61C2312yes—
213C2×C4⋊Dic61C2312yes—
214C2×C4×Dic61—22no—
215C2×C4×Dic61—22no—
216C2×C4×Dic61—22no—
217C2×C4×Dic61—22no—
218C2×C4×Dic61—22no—
219C2×C4×Dic61—22no—
220C2×C4×Dic61—21no—
221C2×C4×Dic61D411yescharacteristic
222C2×C4×Dic61D411yescharacteristic
223C2×C4×Dic61D411yescharacteristic
224C2×C4×Dic61D411yescharacteristic
225C2×C4×Dic61D411yescharacteristic
226C2×C4×Dic61D411yescharacteristic
227C2×C4×Dic61C2311yescharacteristic
228C2×C4×Dic61C2311yescharacteristic
229C2×C4×Dic61C2311yescharacteristic
230C2×C4×Dic61C2311yescharacteristic
231C2×C4×Dic61C2311yescharacteristic
232C2×C4×Dic61C2311yescharacteristic
233C42×D61—21no—
234#14519711C2314yes—
235#14519710C2314yes—
236#14519709C2314yes—
237#14519708C2314yes—
238#14519706C2314yes—
239#14519706C2314yes—
240#14519702C2314yes—
241#14519701C2314yes—
242#14519701C2314yes—
243#14519701C2314yes—
244#14519699C2314yes—
245#14519698C2314yes—
246C22⋊#92418C2312yes—
247C22⋊#92418C2312yes—
248#14519687C2314yes—
249C8×Dic61C2314yes—
250C2×#41×C61C2311yescharacteristic
251C22×Q8×C61—28no—
252C22×Q8×C61—21no—
253C22×Q8×C61—21no—
254C22×Q8×C61—21no—
255C22×Q8×C61C2312yes—
256C22×Q8×C61C2312yes—
257C22×Q8×C61C2312yes—
258C23×C4×C61—21no—
259C23×C4×C61C2311yescharacteristic
260#137×C61—28no—
261C2×Q16×C61C2314yes—
262C2×SD16×C61C2314yes—
263C2×M16×C61C2312yes—
264#123×C61—21no—
265C22⋊Q8×C61C2311yescharacteristic
266C22⋊Q8×C61C2311yescharacteristic
267#121×C61C2311yescharacteristic
268#121×C61C2311yescharacteristic
269#120×C61—21no—
270C4×D4×C61—21no—
271C4×D4×C61—21no—
272#117×C61C2311yescharacteristic
273#103×C61C2314yes—
274#103×C61C2314yes—
275C22⋊C8×C61C2312yes—
276C22⋊C8×C61C2312yes—
277C24×C61C2×D411yescharacteristic
278#41×C61—24no—
279C2×Q8×C61—28no—
280C2×Q8×C61—28no—
281C2×Q8×C61—28no—
282C2×Q8×C61—28no—
283C2×Q8×C61—28no—
284C2×Q8×C61—22no—
285C2×Q8×C61—22no—
286C2×Q8×C61—22no—
287C2×Q8×C61—24no—
288C2×Q8×C61#4118yescomplemented
289C2×Q8×C61C2411yescharacteristic
290C2×Q8×C61C2414yes—
291C2×D4×C61—21no—
292C2×D4×C61—21no—
293C2×D4×C61—21no—
294C2×D4×C61C2411yescharacteristic
295C22×C4×C61—28no—
296C22×C4×C61—22no—
297C22×C4×C61—22no—
298C22×C4×C61—22no—
299C22×C4×C61—24no—
300C22×C4×C61—21no—
301C22×C4×C61C2×D411yescharacteristic
302C22×C4×C61C2×D411yescharacteristic
303C22×C4×C61C2×D411yescharacteristic
304C22×C4×C61C2411yescharacteristic
305C22×C4×C61C2411yescharacteristic
306C22×C4×C61C2411yescharacteristic
307C2×C22⋊D61—21no—
308C2×C22⋊D61—21no—
309C2×C22⋊D61—21no—
310C2×C22⋊D61—21no—
311C2×C22⋊D61—21no—
312C22×Dic61—24no—
313C22×Dic61—22no—
314C22×Dic61—22no—
315C22×Dic61—22no—
316C22×Dic61—21no—
317C22×Dic61—21no—
318C22×Dic61—42no—
319C22×Dic61—44no—
320C22×Dic61C2×D411yescharacteristic
321C22×Dic61C2×D411yescharacteristic
322C22×Dic61C2×D411yescharacteristic
323C22×Dic61C2×D411yescharacteristic
324C22×Dic61C2×D411yescharacteristic
325C22×Dic61C2×D411yescharacteristic
326C22×Dic61C2×D411yescharacteristic
327C22×Dic61C2×D411yescharacteristic
328C22×Dic61C2×D411yescharacteristic
329C22×Dic61C2×D411yescharacteristic
330C22×Dic61C2×D411yescharacteristic
331C22×Dic61C2×D411yescharacteristic
332#11758224—44no—
333#11758224—44no—
334#11758222—24no—
335C2×D244C2411yescharacteristic
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×Dic122—21no—
340C2×Dic122—21no—
341C2×Dic122C2411yescharacteristic
342Q16×C61—28no—
343SD16×C61—28no—
344M16×C61—24no—
345C2×C8×C61C2414yes—
346C4⋊C4×C61—21no—
347C4⋊C4×C61—21no—
348C4⋊C4×C61C2411yescharacteristic
349C4⋊C4×C61C2411yescharacteristic
350C22⋊C4×C61—21no—
351C22⋊C4×C61—21no—
352C22⋊C4×C61—21no—
353C22⋊C4×C61—21no—
354C22⋊C4×C61—21no—
355C42×C61—21no—
356C22⋊Dic61—21no—
357C22⋊Dic61—21no—
358C22⋊Dic61—21no—
359C22⋊Dic61—21no—
360C22⋊Dic61—21no—
361C22⋊Dic61—21no—
362C22⋊Dic61—21no—
363#11758202—28no—
364#11758201—28no—
365#11758198—21no—
366#11758198—21no—
367#11758198—21no—
368#11758198—21no—
369#11758198—21no—
370#11758198—21no—
371C4⋊Dic61—22no—
372C4⋊Dic61—22no—
373C4⋊Dic61—22no—
374C4⋊Dic61—24no—
375C4⋊Dic61—24no—
376C4⋊Dic61—24no—
377C4⋊Dic61—24no—
378C4⋊Dic61—21no—
379C4⋊Dic61—21no—
380C4⋊Dic61—21no—
381C4⋊Dic61—21no—
382C4⋊Dic61C2414yes—
383C4⋊Dic61C2411yescharacteristic
384C4⋊Dic61C2411yescharacteristic
385#11758196—21no—
386#11758196—21no—
387#11758196—21no—
388#11758196—21no—
389#11758196—21no—
390#11758196—21no—
391#11758196—21no—
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395C4×Dic61—21no—
396C4×Dic61—21no—
397C4×Dic61—21no—
398C4×Dic61—24no—
399C4×Dic61—24no—
400C4×Dic61—24no—
401C4×Dic61—24no—
402C4×Dic61—21no—
403C4×Dic61—21no—
404C4×Dic61C2×D411yescharacteristic
405C4×Dic61C2×D411yescharacteristic
406C4×Dic61C2×D411yescharacteristic
407C4×Dic61C2×D411yescharacteristic
408C4×Dic61C2×D411yescharacteristic
409C4×Dic61C2×D411yescharacteristic
410C4×Dic61C2×D411yescharacteristic
411C4×Dic61C2×D411yescharacteristic
412C4×Dic61C2×D411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416C4×Dic61C2411yescharacteristic
417C4×Dic61C2411yescharacteristic
418C4×Dic61C2411yescharacteristic
419C4×Dic61C2411yescharacteristic
420#11758194—24no—
421C2×#92418C2414yes—
422C23×C61—22no—
423C23×C61—22no—
424C23×C61—22no—
425C23×C61—21no—
426C23×C61C22×D411yescharacteristic
427C23×C61C22×D411yescharacteristic
428C23×C61C22×D411yescharacteristic
429C22×D61—21no—
430Q8×C61—28no—
431Q8×C61—28no—
432Q8×C61—28no—
433Q8×C61—24no—
434Q8×C61—22no—
435Q8×C61C2×#4118yes—
436D4×C61—22no—
437D4×C61—42no—
438D4×C61—42no—
439D4×C61—42no—
440C2×C4×C61—28no—
441C2×C4×C61—28no—
442C2×C4×C61—28no—
443C2×C4×C61—22no—
444C2×C4×C61—24no—
445C2×C4×C61—22no—
446C2×C4×C61—22no—
447C2×C4×C61—22no—
448C2×C4×C61—22no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—21no—
452C2×C4×C61—42no—
453C2×C4×C61C22×D411yescharacteristic
454C2×C4×C61C22×D411yescharacteristic
455C2×C4×C61C22×D411yescharacteristic
456C2×C4×C61C2×#4114yes—
457C2×C4×C61C2511yescharacteristic
458C22⋊D61—42no—
459C22⋊D61—42no—
460C22⋊D61—42no—
461C22⋊D61—42no—
462C22⋊D61—42no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—24no—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—42no—
479C2×Dic61—44no—
480C2×Dic61—44no—
481C2×Dic61—44no—
482C2×Dic61—42no—
483C2×Dic61#13714yescomplemented
484C2×Dic61C22×D411yescharacteristic
485C2×Dic61C22×D411yescharacteristic
486C2×Dic61C22×D411yescharacteristic
487C2×Dic61C22×D411yescharacteristic
488C2×Dic61C22×D411yescharacteristic
489C2×Dic61C22×D411yescharacteristic
490C2×Dic61C22×D411yescharacteristic
491C2×Dic61C22×D411yescharacteristic
492D244—22no—
493C4×D61—42no—
494C4×D61—42no—
495C4×D61—42no—
496Dic122—22no—
497Dic122—42no—
498Dic122—42no—
499C8×C61—24no—
500#92418—24no—
501#60560—611nomaximal, Sylow
502C22×C61—28no—
503C22×C61—21no—
504C22×C61—21no—
505C22×C61—21no—
506C22×C61—21no—
507C22×C61—21no—
508C22×C61—21no—
509C22×C61—41no—
510C22×C61—41no—
511C22×C61—41no—
512C22×C61#52512yes—
513C22×C61C2×#13712yes—
514C22×C61#57512yes—
515C22×C61C23×D411yescharacteristic
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C4×C61—28no—
520C4×C61—21no—
521C4×C61—21no—
522C4×C61—41no—
523C4×C61—41no—
524C4×C61—41no—
525C4×C61#52512yes—
526C4×C61C22×#4112yes—
527Dic61—21no—
528Dic61—21no—
529Dic61—21no—
530Dic61—21no—
531Dic61—21no—
532Dic61—21no—
533Dic61—41no—
534Dic61—41no—
535Dic61—41no—
536Dic61—44no—
537Dic61C2×#13712yes—
538Dic61C2×#13712yes—
539#3444—611no—
540C22×C4×Q8—611no—
541#3117—612no—
542#3117—612no—
543#3113—612no—
544#3112—612no—
545#3108—612no—
546#3108—612no—
547#3104—612no—
548#3103—612no—
549#3092—611no—
550#3092—611no—
551#3078—612no—
552#3037—612no—
553#3004—611no—
554#3004D6111yescharacteristic, complemented
555C4×#137—612no—
556C4×#137—612no—
557#2920—611no—
558C2×C61—22no—
559C2×C61—22no—
560C2×C61—22no—
561C2×C61—81no—
562C2×C61C2×#52511yescharacteristic
563C2×C61C22×#13711yescharacteristic
564C2×C61C2×#57511yescharacteristic
565D61—81no—
566C23×Q8C2×D6111yescharacteristic
567C2×#137—612no—
568C2×#137C2×D6112yes—
569#533—611no—
570#533—611no—
571#533—611no—
572#532—611no—
573#532—611no—
574#532—611no—
575#529—611no—
576#529—611no—
577#529—611no—
578#529—611no—
579#529—1221no—
580#529—1221no—
581#529—1221no—
582#529—1221no—
583#525—611no—
584#525—1221no—
585#525—1221no—
586#525C2×D6111yescharacteristic
587C4×#41—611no—
588C4×#41—611no—
589C4×#41—1221no—
590C4×#41—1221no—
591C2×C4×Q8—612no—
592C2×C4×Q8—612no—
593C2×C4×Q8—612no—
594C2×C4×Q8—612no—
595C2×C4×Q8—612no—
596C2×C4×Q8—612no—
597C2×C4×Q8—1221no—
598C2×C4×Q8—1221no—
599C2×C4×Q8—1221no—
600C2×C4×Q8—1221no—
601C2×C4×Q8—1221no—
602C2×C4×Q8—1221no—
603C22×C4⋊C4—611no—
604C22×C4⋊C4—1221no—
605C22×C42—611no—
606C22×C42—1221no—
607#484—612no—
608#484—612no—
609#483—612no—
610#483—612no—
611#481—612no—
612#481—612no—
613#480—612no—
614#480—612no—
615#479—614no—
616#479—614no—
617#477—614no—
618#475—614no—
619#464—614no—
620#464—614no—
621#462—614no—
622#460—614no—
623#451—612no—
624#451—612no—
625#451C2×D6112yes—
626#451C2×D6112yes—
627#448—612no—
628#448—612no—
629#448C2×D6112yes—
630#448C2×D6112yes—
631#441—614no—
632#441—614no—
633#440—614no—
634#440—614no—
635C4×Q16—614no—
636C4×Q16—614no—
637C4×SD16—614no—
638C4×SD16—614no—
639#432—612no—
640#432—612no—
641#431—612no—
642#431—612no—
643#428—612no—
644#428—612no—
645#423—612no—
646#419—612no—
647#419C2×D6112yes—
648#417—612no—
649#417—612no—
650#407—611no—
651#407C2×D6111yescharacteristic
652C4×M16—612no—
653C61#6056011yescharacteristic, complemented, Sylow
654C2×#41—611no—
655C2×#41—1221no—
656C2×#41—1221no—
657C2×#41C22×D6111yescharacteristic
658C22×Q8—28no—
659C22×Q8—21no—
660C22×Q8—21no—
661C22×Q8—21no—
662C22×Q8C22×D6112yes—
663C22×Q8C22×D6112yes—
664C22×Q8C22×D6112yes—
665C23×C4—21no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—1221no—
669C23×C4C22×D6111yescharacteristic
670#137—28no—
671#137—1228no—
672C2×Q16—614no—
673C2×Q16C22×D6114yes—
674C2×SD16—614no—
675C2×SD16C22×D6114yes—
676C2×M16—612no—
677C2×M16C22×D6112yes—
678C4⋊Q8—611no—
679C4⋊Q8—611no—
680C4⋊Q8—611no—
681#127—611no—
682#126—1221no—
683#126—1221no—
684#126—1221no—
685#126—1221no—
686#125—611no—
687#125—611no—
688#125—1221no—
689#125—1221no—
690#124—611no—
691#124—611no—
692#124—1221no—
693#124—1221no—
694#123—21no—
695#123—1221no—
696#123—1221no—
697#123—1221no—
698#123—1221no—
699#123—1221no—
700C22⋊Q8—611no—
701C22⋊Q8—611no—
702C22⋊Q8—1221no—
703C22⋊Q8—1221no—
704C22⋊Q8—1221no—
705C22⋊Q8—1221no—
706C22⋊Q8C22×D6111yescharacteristic
707C22⋊Q8C22×D6111yescharacteristic
708#121—611no—
709#121—611no—
710#121—1221no—
711#121—1221no—
712#121—1221no—
713#121—1221no—
714#121C22×D6111yescharacteristic
715#121C22×D6111yescharacteristic
716#120—21no—
717#120—1221no—
718C4×Q8—614no—
719C4×Q8—614no—
720C4×Q8—614no—
721C4×Q8—614no—
722C4×Q8—611no—
723C4×Q8—611no—
724C4×Q8—611no—
725C4×Q8—611no—
726C4×Q8—1221no—
727C4×Q8—1221no—
728C4×Q8—1221no—
729C4×Q8—1221no—
730C4×Q8—1222no—
731C4×Q8—1222no—
732C4×Q8—1222no—
733C4×Q8—1222no—
734C4×Q8—1222no—
735C4×Q8—1222no—
736C4×Q8—1222no—
737C4×Q8—1222no—
738C4×Q8—1222no—
739C4×Q8—1222no—
740C4×Q8—1222no—
741C4×Q8—1222no—
742C4×D4—21no—
743C4×D4—21no—
744C4×D4—611no—
745C4×D4—611no—
746C4×D4—611no—
747C4×D4—611no—
748C4×D4—1221no—
749C4×D4—1221no—
750C4×D4—1221no—
751C4×D4—1221no—
752C4×D4—1221no—
753C4×D4—1221no—
754C4×D4—1221no—
755C4×D4—1221no—
756C4×D4—1221no—
757C4×D4—1221no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4—1221no—
762#117—611no—
763#117—1221no—
764#117—1221no—
765#117—1221no—
766#117—1221no—
767#117—1221no—
768#117—1221no—
769#117—1221no—
770#117—1221no—
771#117C22×D6111yescharacteristic
772C2×C4⋊C4—612no—
773C2×C4⋊C4—612no—
774C2×C4⋊C4—612no—
775C2×C4⋊C4—1222no—
776C2×C4⋊C4—1222no—
777C2×C4⋊C4—1222no—
778C2×C4⋊C4—1222no—
779C2×C4⋊C4—1222no—
780C2×C4⋊C4—1222no—
781C2×C4⋊C4—1221no—
782C2×C4⋊C4—1221no—
783C2×C4⋊C4—1221no—
784C2×C42—611no—
785C2×C42—611no—
786C2×C42—611no—
787C2×C42—611no—
788C2×C42—611no—
789C2×C42—611no—
790C2×C42—611no—
791C2×C42—611no—
792C2×C42—611no—
793C2×C42—611no—
794C2×C42—611no—
795C2×C42—611no—
796C2×C42—1221no—
797C2×C42—1221no—
798C2×C42—1222no—
799C2×C42—1222no—
800C2×C42—1222no—
801C2×C42—1222no—
802C2×C42—1222no—
803C2×C42—1222no—
804#107—614no—
805#107—614no—
806#106—614no—
807#106—614no—
808C4⋊C8—614no—
809C4⋊C8—614no—
810#103—614no—
811#103—614no—
812#103—614no—
813#103—614no—
814#103C22×D6114yes—
815#103C22×D6114yes—
816#102—614no—
817#102—614no—
818C22⋊C8—612no—
819C22⋊C8—612no—
820C22⋊C8C22×D6112yes—
821C22⋊C8C22×D6112yes—
822#97—614no—
823C4×C8—614no—
824C24D4×D6111yescharacteristic
825#41—24no—
826#41—1224no—
827#41—2444no—
828#41—2444no—
829C2×Q8—28no—
830C2×Q8—28no—
831C2×Q8—28no—
832C2×Q8—28no—
833C2×Q8—28no—
834C2×Q8—22no—
835C2×Q8—22no—
836C2×Q8—22no—
837C2×Q8—24no—
838C2×Q8—611no—
839C2×Q8—1221no—
840C2×Q8—1221no—
841C2×Q8#1175822418yescomplemented
842C2×Q8C23×D6111yescharacteristic
843C2×Q8C23×D6114yes—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—611no—
848C2×D4—1221no—
849C2×D4—1221no—
850C2×D4—1221no—
851C2×D4—1221no—
852C2×D4—1221no—
853C2×D4C23×D6111yescharacteristic
854C22×C4—28no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—24no—
859C22×C4—21no—
860C22×C4—611no—
861C22×C4—611no—
862C22×C4—611no—
863C22×C4—611no—
864C22×C4—611no—
865C22×C4—611no—
866C22×C4—611no—
867C22×C4—611no—
868C22×C4—611no—
869C22×C4—611no—
870C22×C4—611no—
871C22×C4—611no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1224no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1222no—
878C22×C4—1222no—
879C22×C4—1222no—
880C22×C4—1221no—
881C22×C4—2442no—
882C22×C4—2444no—
883C22×C4D4×D6111yescharacteristic
884C22×C4D4×D6111yescharacteristic
885C22×C4D4×D6111yescharacteristic
886C22×C4C23×D6111yescharacteristic
887C22×C4C23×D6111yescharacteristic
888C22×C4C23×D6111yescharacteristic
889Q16—28no—
890Q16—1228no—
891SD16—28no—
892SD16—1228no—
893M16—24no—
894M16—1224no—
895C2×C8—614no—
896C2×C8C23×D6114yes—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—614no—
900C4⋊C4—611no—
901C4⋊C4—611no—
902C4⋊C4—1224no—
903C4⋊C4—1224no—
904C4⋊C4—1224no—
905C4⋊C4—1224no—
906C4⋊C4—1221no—
907C4⋊C4—1221no—
908C4⋊C4—1221no—
909C4⋊C4—1221no—
910C4⋊C4—1221no—
911C4⋊C4—1221no—
912C4⋊C4—1221no—
913C4⋊C4—1221no—
914C4⋊C4—1221no—
915C4⋊C4—1221no—
916C4⋊C4—1221no—
917C4⋊C4—1221no—
918C4⋊C4—1222no—
919C4⋊C4—1222no—
920C4⋊C4—1222no—
921C4⋊C4—1221no—
922C4⋊C4—1221no—
923C4⋊C4C23×D6111yescharacteristic
924C4⋊C4C23×D6111yescharacteristic
925C22⋊C4—21no—
926C22⋊C4—21no—
927C22⋊C4—21no—
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—1221no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C22⋊C4—1221no—
934C22⋊C4—1221no—
935C22⋊C4—1221no—
936C22⋊C4—1221no—
937C22⋊C4—1221no—
938C22⋊C4—1221no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—1221no—
942C22⋊C4—1221no—
943C42—21no—
944C42—611no—
945C42—611no—
946C42—611no—
947C42—611no—
948C42—611no—
949C42—611no—
950C42—611no—
951C42—611no—
952C42—611no—
953C42—611no—
954C42—611no—
955C42—611no—
956C42—611no—
957C42—611no—
958C42—611no—
959C42—611no—
960C42—1224no—
961C42—1224no—
962C42—1224no—
963C42—1224no—
964C42—1221no—
965C42—1221no—
966C42—1221no—
967C42—1221no—
968C42—1221no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—21no—
973C23—1221no—
974C23C2×D4×D6111yescharacteristic
975C23C2×D4×D6111yescharacteristic
976C23C2×D4×D6111yescharacteristic
977Q8—28no—
978Q8—28no—
979Q8—28no—
980Q8—24no—
981Q8—22no—
982Q8—1222no—
983Q8—2442no—
984Q8—2442no—
985Q8C2×#1175822418yes—
986D4—22no—
987D4—42no—
988D4—42no—
989D4—42no—
990D4—1222no—
991D4—2442no—
992D4—2442no—
993D4—2442no—
994D4—2442no—
995D4—2442no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—42no—
1009C2×C4—614no—
1010C2×C4—611no—
1011C2×C4—611no—
1012C2×C4—611no—
1013C2×C4—611no—
1014C2×C4—611no—
1015C2×C4—611no—
1016C2×C4—611no—
1017C2×C4—611no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1224no—
1026C2×C4—1221no—
1027C2×C4—1221no—
1028C2×C4—1221no—
1029C2×C4—2442no—
1030C2×C4—2442no—
1031C2×C4—2442no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2442no—
1037C2×C4—2444no—
1038C2×C4—2444no—
1039C2×C4—2444no—
1040C2×C4—2442no—
1041C2×C4C2×D4×D6111yescharacteristic
1042C2×C4C2×D4×D6111yescharacteristic
1043C2×C4C2×D4×D6111yescharacteristic
1044C2×C4C2×#1175822414yes—
1045C2×C4C24×D6111yescharacteristic
1046C8—24no—
1047C8—1224no—
1048C22—28no—
1049C22—21no—
1050C22—21no—
1051C22—21no—
1052C22—21no—
1053C22—21no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—2441no—
1059C22—2441no—
1060C22—2441no—
1061C22#1684026812yes—
1062C22#137×D6112yes—
1063C22#1684056112yes—
1064C22C22×D4×D6111yescharacteristic
1065C4—28no—
1066C4—21no—
1067C4—21no—
1068C4—41no—
1069C4—41no—
1070C4—41no—
1071C4—612no—
1072C4—612no—
1073C4—1221no—
1074C4—1221no—
1075C4—1221no—
1076C4—1221no—
1077C4—1221no—
1078C4—1221no—
1079C4—2441no—
1080C4—2444no—
1081C4—2441no—
1082C4—2441no—
1083C4#1684026812yes—
1084C4C22×#1175822412yes—
1085C2—22no—
1086C2—22no—
1087C2—22no—
1088C2—81no—
1089C2—4881no—
1090C2C2×#1684026811yescharacteristic
1091C2C2×#137×D6111yescharacteristic
1092C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3004C2
socleC22×C61C23×D4
prime radical#21459111C2
hypercenter#3004D61
hypocenterC61#60560
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic61C2semidirect
3. #21455991C2semidirect
4. #21455985C2semidirect
5. #21455944C2semidirect
6. #21455936C2semidirect
7. #21455900C2semidirect
8. #21455894C2semidirect
9. #21455853C2semidirect
10. #21455845C2semidirect
11. #21455744C2semidirect
12. #21455739C2semidirect
13. #21455621C2semidirect
14. #21455288C2semidirect
15. #21455053C2semidirect
16. #137×Dic61C2semidirect
17. #21454634C2semidirect
18. #21454448C2semidirect
19. C61×#3004C2semidirect
66. #16840071C22semidirect
67. #16840067C22semidirect
68. #16840055C22semidirect
69. #16840045C22semidirect
70. #16839986C22semidirect
71. #16839982C22semidirect
72. #16839970C22semidirect
73. #16839960C22semidirect
78. #16839869C22semidirect
79. #16839866C22semidirect
80. #16839865C22semidirect
81. #16839863C22semidirect
82. Q16×Dic61C22semidirect
83. #16839854C22semidirect
84. SD16×Dic61C22semidirect
85. #16839847C22semidirect
288. C2×Q8×C61#41semidirect
483. C2×Dic61#137semidirect
554. #3004D61semidirect
653. C61#60560semidirect
841. C2×Q8#11758224semidirect

Maximal subgroups

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

subgroupindex
#214591112
C22×Q8×Dic612
#214559912
#214559852
#214559442
#214559362
#214559002
#214558942
#214558532
#214558452
#214557442
#214557392
#214556212
#214552882
#214550532
#137×Dic612
#214546342
#214544482
C61×#30042
#6056061