Finite Group Databasebeta

← #30555950

Subgroups — #30555950

Order 15616.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840578C211yesmaximal, characteristic, complemented
2C2×#16840570C211yesmaximal, characteristic, complemented
3#21459608C211yesmaximal, characteristic, complemented
4#21459600C211yesmaximal, characteristic, complemented
5#21457392C214yesmaximal, complemented
6#21457378C214yesmaximal, complemented
7#21457347C214yesmaximal, complemented
8#21457322C214yesmaximal, complemented
9C2×#16840155C211yesmaximal, characteristic, complemented
10#21455471C211yesmaximal, characteristic, complemented
11#21455461C211yesmaximal, characteristic, complemented
12#21455315C211yesmaximal, characteristic, complemented
13#21455305C211yesmaximal, characteristic, complemented
14#21455110C211yesmaximal, characteristic, complemented
15#21455108C211yesmaximal, characteristic, complemented
16#21455098C211yesmaximal, characteristic, complemented
17#21454615C211yesmaximal, characteristic, complemented
18#21454534C211yesmaximal, characteristic, complemented
19C61×#3011C211yesmaximal, characteristic, complemented
20C2×#14519825C2211yescharacteristic
21C2×#14519824C2211yescharacteristic, complemented
22C2×#14519823C2211yescharacteristic
23#16840578—28no—
24#16840570—28no—
25C2×#14519810C2211yescharacteristic
26C2×#14519809C2212yescomplemented
27C2×#14519808C2211yescharacteristic
28C2×#14519808C2212yes—
29C2×#14519806C2212yescomplemented
30C2×#14519802C2211yescharacteristic
31C2×#14519802C2212yes—
32C2×#14519798C2212yescomplemented
33C2×#14519797C2212yes—
34C2×#14519797C2211yescharacteristic
35C22×#11758202C2211yescharacteristic, complemented
36C2×Q16×D61C2212yescomplemented
37C22×#11758190C2211yescharacteristic
38C22×#11758201C2211yescharacteristic
39C22×#11758201C2212yes—
40C2×#14519785C2211yescharacteristic, complemented
41C2×#14519784C2211yescharacteristic
42Q8×C22⋊D61C2214yescomplemented
43#16840422C2214yes—
44#16840411—24no—
45#16840411C2214yescomplemented
46#16840404—24no—
47#16840403C2214yes—
48#16840337—21no—
49#16840336—21no—
50#16840336C2211yescharacteristic, complemented
51#16840333—21no—
52#16840333C2211yescharacteristic
53#16840331C2211yescharacteristic
54#16840330—21no—
55#16840313—21no—
56#16840308—21no—
57#16840308C2211yescharacteristic
58C2×#14519775—21no—
59C2×#14519775C2211yescharacteristic, complemented
60C2×#14519766C2211yescharacteristic
61#124×D61—21no—
62#41×Dic61C2211yescharacteristic, complemented
63#16840230C2211yescharacteristic
64#16840155C2214yescomplemented
65#16840155C2214yescomplemented
66#16840018C2214yescomplemented
67#16840011C2214yescomplemented
68#16840001C2214yescomplemented
69#16839994C2214yescomplemented
70#16839986C2214yescomplemented
71#16839979C2214yescomplemented
72#16839971C2214yescomplemented
73#16839966C2214yescomplemented
74#16839926C2214yes—
75#16839923C2214yescomplemented
76#16839916C2214yescomplemented
77#16839915C2214yes—
78#16839908C2214yescomplemented
79#16839902C2214yescomplemented
80#16839871C2212yescomplemented
81#16839866C2212yescomplemented
82#16839865C2212yescomplemented
83#16839859C2212yescomplemented
84#16839836C2214yescomplemented
85#16839830C2214yescomplemented
86#16839798C2211yescharacteristic, complemented
87#16839785C2211yescharacteristic, complemented
88#16839771C2211yescharacteristic, complemented
89#16839770C2211yescharacteristic, complemented
90#16839768C2211yescharacteristic
91#16839759C2211yescharacteristic
92#16839728C2211yescharacteristic, complemented
93C2×#14519687C2211yescharacteristic, complemented
94C2×2−1+4×C61C2211yescharacteristic
95C2×#137×C61C2211yescharacteristic, complemented
96C22×Q16×C61C2211yescharacteristic, complemented
97C61×#536C2211yescharacteristic
98C61×#452C2214yescomplemented
99C61×#451C2214yescomplemented
100C61×#419C2211yescharacteristic, complemented
101C61×#416C2211yescharacteristic, complemented
102C61×#408C2211yescharacteristic
103#14519825—24no—
104#14519825—42no—
105#14519824—24no—
106#14519824—42no—
107#14519823—24no—
108#14519823—42no—
109C2×#11758226—21no—
110C2×#11758226—21no—
111C2×#11758226C2312yes—
112C2×#11758222—22no—
113C2×#11758222—21no—
114C2×#11758222C2311yescharacteristic
115C2×#11758222C2312yes—
116C2×#11758222C2311yescharacteristic
117C2×#11758224—22no—
118C2×#11758224C2312yes—
119C22×Dic122—21no—
120C22×Dic122C2311yescharacteristic
121C2×Q8×D61—21no—
122C2×Q8×D61C2312yes—
123C2×Q8×D61C2312yes—
124C22×D244C2311yescharacteristic
125C22×D244C2312yes—
126C2×D4×D61—21no—
127C2×D4×D61—22no—
128#14519810—24no—
129#14519809—28no—
130#14519808—24no—
131#14519808—28no—
132#14519806—28no—
133#14519802—24no—
134#14519802—28no—
135#14519798—28no—
136#14519797—28no—
137#14519797D418yescomplemented
138C2×Dic244C2312yes—
139C2×#11758202—24no—
140C2×#11758202C2312yes—
141C2×#11758202C2312yes—
142C2×#11758202C2312yes—
143C2×#11758202C2311yescharacteristic
144Q16×D61—28no—
145C2×#11758190—42no—
146C2×#11758190C2312yes—
147C2×#11758190C2314yes—
148C2×#11758200C2311yescharacteristic
149C2×#11758201—28no—
150C2×#11758201—24no—
151C2×#11758201C2312yes—
152C2×#11758201C2312yes—
153C2×#11758201C2312yes—
154C2×#11758201C2312yes—
155C2×#11758201C2311yescharacteristic
156C2×#11758199C2312yes—
157C2×#11758199C2311yescharacteristic
158#14519785—24no—
159#14519784—24no—
160C2×#11758194C2311yescharacteristic
161C2×#11758194C2312yes—
162C2×#11758189C2312yes—
163C22×#92418C2312yes—
164C22×#92418C2311yescharacteristic
165C2×C8×D61C2312yes—
166#14519775—21no—
167#14519775—21no—
168#14519775—24no—
169#14519775—21no—
170#14519775—21no—
171#14519775D411yescharacteristic
172#14519775C2314yes—
173#14519774—21no—
174#14519773D411yescharacteristic
175#14519766—21no—
176#14519766—21no—
177#14519766—21no—
178#14519766D411yescharacteristic
179#14519766C2314yes—
180#14519765—21no—
181#14519764—21no—
182#14519764D411yescharacteristic
183#14519763—24no—
184#14519762—24no—
185#14519760—22no—
186#14519760—24no—
187#14519758—22no—
188#14519758—24no—
189#14519756—24no—
190#14519756C2314yes—
191#14519755—24no—
192#14519753—24no—
193#14519753C2314yes—
194#14519752—24no—
195#14519752C2314yes—
196#14519750—24no—
197#14519749—24no—
198#14519749D414yes—
199#14519747—24no—
200#14519747—22no—
201Q8×Dic61C2312yes—
202#14519742C2312yes—
203D4×Dic61—22no—
204D4×Dic61C2312yes—
205#14519739—24no—
206#14519739C2312yes—
207C4×C22⋊D61—24no—
208C4×C22⋊D61C2314yes—
209#14519737—22no—
210#14519736—21no—
211#14519736C2311yescharacteristic
212#14519734—21no—
213C2×#11758196—22no—
214C2×#11758196—24no—
215C2×#11758198—22no—
216C22⋊C4×D61—24no—
217C2×C4×Dic61—21no—
218C2×C4×Dic61C2311yescharacteristic
219C42×D61—21no—
220#14519710C2312yes—
221#14519708C2312yes—
222#14519706C2314yes—
223#14519702C2312yes—
224#14519701C2314yes—
225#14519700C2314yes—
226#14519699C2314yes—
227#14519699C2312yes—
228#14519689C2314yes—
229#14519687C2312yes—
230#14519687C2312yes—
2312−1+4×C61—24no—
2322−1+4×C61—42no—
233C2×#41×C61—21no—
234C2×#41×C61—22no—
235C2×#41×C61C2312yes—
236C2×#41×C61C2311yescharacteristic
237C2×#41×C61C2311yescharacteristic
238C22×Q8×C61—21no—
239C22×Q8×C61C2311yescharacteristic
240C22×Q8×C61C2311yescharacteristic
241C22×Q8×C61C2312yes—
242#137×C61—24no—
243C2×Q16×C61—42no—
244C2×Q16×C61C2312yes—
245C2×Q16×C61C2314yes—
246C2×SD16×C61C2312yes—
247C2×M16×C61C2311yescharacteristic
248C22×C8×C61C2311yescharacteristic
249C4⋊Q8×C61—21no—
250#124×C61—21no—
251#123×C61—22no—
252C22⋊Q8×C61C2314yes—
253#117×C61C2311yescharacteristic
254#103×C61C2314yes—
255#103×C61C2312yes—
256#102×C61C2312yes—
257C22⋊C8×C61C2314yes—
258C23×D61—22no—
259C23×D61—21no—
260#41×C61—22no—
261#41×C61—22no—
262#41×C61—22no—
263#41×C61—24no—
264#41×C61—42no—
265#41×C61—44no—
266#41×C61—48no—
267#41×C61C2×D414yes—
268C2×Q8×C61—21no—
269C2×Q8×C61—22no—
270C2×Q8×C61—21no—
271C2×Q8×C61—24no—
272C2×Q8×C61—22no—
273C2×Q8×C61—22no—
274C2×Q8×C61—22no—
275C2×Q8×C61—22no—
276C2×Q8×C61—42no—
277C2×Q8×C61—44no—
278C2×Q8×C61C2×D411yescharacteristic
279C2×Q8×C61C2412yes—
280C2×Q8×C61C2412yes—
281C2×Q8×C61C2411yescharacteristic
282C2×D4×C61—21no—
283C2×D4×C61—22no—
284C2×D4×C61C2×D412yes—
285C2×D4×C61C2×D411yescharacteristic
286C2×D4×C61C2411yescharacteristic
287C22×C4×C61—21no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—22no—
291C22×C4×C61—22no—
292C22×C4×C61C2412yes—
293C22×C4×C61C2411yescharacteristic
294C2×C22⋊D61—21no—
295C2×C22⋊D61—22no—
296C2×C22⋊D61—22no—
297C2×C22⋊D61C2×D412yes—
298C2×C22⋊D61C2×D414yes—
299C22×Dic61—21no—
300C22×Dic61—22no—
301C22×Dic61—22no—
302C22×Dic61C2×D412yes—
303#11758226—24no—
304#11758226—42no—
305#11758226—44no—
306#11758226—44no—
307Q8×D61—24no—
308Q8×D61—24no—
309Q8×D61—42no—
310Q8×D61—42no—
311Q8×D61—44no—
312#11758224—24no—
313#11758224—42no—
314#11758224—48no—
315D4×D61—44no—
316D4×D61—48no—
317#11758222—22no—
318#11758222—22no—
319#11758222—22no—
320#11758222—24no—
321#11758222—42no—
322#11758222—44no—
323#11758222—48no—
324#11758222C2×D414yes—
325C2×D244—22no—
326C2×D244—22no—
327C2×D244—24no—
328C2×D244—22no—
329C2×D244—22no—
330C2×D244—21no—
331C2×D244—24no—
332C2×D244—42no—
333C2×D244C2×D411yescharacteristic
334C2×D244C2412yes—
335C2×D244C2411yescharacteristic
336C2×C4×D61—21no—
337C2×C4×D61—22no—
338C2×C4×D61—22no—
339C2×C4×D61—22no—
340C2×C4×D61—22no—
341C2×C4×D61—22no—
342C2×C4×D61C2412yes—
343C2×Dic122—22no—
344C2×Dic122—22no—
345C2×Dic122—21no—
346C2×Dic122—22no—
347C2×Dic122—22no—
348C2×Dic122—44no—
349C2×Dic122C2×D411yescharacteristic
350C2×Dic122C2412yes—
351C2×Dic122C2411yescharacteristic
352Q16×C61—24no—
353Q16×C61—44no—
354SD16×C61—24no—
355M16×C61—22no—
356C2×C8×C61—22no—
357C2×C8×C61C2412yes—
358C2×C8×C61C2412yes—
359C4⋊C4×C61—24no—
360C4⋊C4×C61C2412yes—
361C22⋊C4×C61—21no—
362C22⋊C4×C61—24no—
363C42×C61—21no—
364C22⋊Dic61—21no—
365C22⋊Dic61—24no—
366C22⋊Dic61—22no—
367C22⋊Dic61C2×D414yes—
368#11758202—24no—
369#11758202—24no—
370#11758202—24no—
371#11758202C2×D414yes—
372#11758201—24no—
373#11758201—24no—
374#11758201—24no—
375#11758201—24no—
376#11758201C2×D414yes—
377#11758200C2×D414yes—
378#11758199—24no—
379#11758199C2×D414yes—
380#11758198—24no—
381#11758198—24no—
382#11758198—24no—
383#11758198—24no—
384#11758198—22no—
385#11758198C2×D414yes—
386C4⋊Dic61—22no—
387C4⋊Dic61C2412yes—
388#11758196—24no—
389#11758196—24no—
390#11758196—24no—
391#11758196—24no—
392#11758196—22no—
393#11758196C2×D414yes—
394C4×Dic61—21no—
395C4×Dic61—22no—
396C4×Dic61—22no—
397C4×Dic61C2×D411yescharacteristic
398C4×Dic61C2×D411yescharacteristic
399C4×Dic61C2412yes—
400#11758194—22no—
401#11758194—24no—
402C2×#92418—24no—
403C2×#92418C2×D414yes—
404C2×#92418C2412yes—
405C2×#92418C2411yescharacteristic
406C2×#92418C2411yescharacteristic
407Dic244—24no—
408#11758190—24no—
409#11758190—44no—
410#11758189—24no—
411C8×D61—24no—
412C23×C61—21no—
413C23×C61C22×D412yes—
414C23×C61C22×D411yescharacteristic
415C22×D61—21no—
416C22×D61—22no—
417C22×D61—44no—
418C22×D61—42no—
419C22×D61—84no—
420C22×D61—82no—
421C22×D61C22×D412yes—
422Q8×C61—22no—
423Q8×C61—21no—
424Q8×C61—22no—
425Q8×C61—22no—
426Q8×C61—22no—
427Q8×C61—22no—
428Q8×C61—44no—
429Q8×C61—42no—
430Q8×C61—42no—
431Q8×C61C22×D412yes—
432D4×C61—24no—
433D4×C61—24no—
434D4×C61—22no—
435D4×C61—21no—
436D4×C61—44no—
437D4×C61C22×D412yes—
438C2×C4×C61—21no—
439C2×C4×C61—24no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—22no—
444C2×C4×C61—22no—
445C2×C4×C61—44no—
446C2×C4×C61—44no—
447C2×C4×C61—42no—
448C2×C4×C61—42no—
449C2×C4×C61C22×D412yes—
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61C22×D412yes—
452C2×C4×C61H(5,𝔽2)12yes—
453C2×C4×C61C2511yescharacteristic
454C22⋊D61—24no—
455C22⋊D61—24no—
456C22⋊D61—44no—
457C22⋊D61—44no—
458C22⋊D61—44no—
459C2×Dic61—21no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—42no—
463C2×Dic61—44no—
464C2×Dic61—44no—
465C2×Dic61—42no—
466C2×Dic61C22×D412yes—
467C2×Dic61C22×D412yes—
468C2×Dic61C22×D412yes—
469D244—22no—
470D244—22no—
471D244—21no—
472D244—22no—
473D244—44no—
474D244—44no—
475D244—42no—
476D244—84no—
477D244C22×D412yes—
478C4×D61—24no—
479C4×D61—22no—
480C4×D61—22no—
481C4×D61—44no—
482C4×D61—44no—
483C4×D61—44no—
484C4×D61—44no—
485C4×D61—82no—
486Dic122—22no—
487Dic122—21no—
488Dic122—22no—
489Dic122—22no—
490Dic122—44no—
491Dic122—44no—
492Dic122—42no—
493Dic122C22×D412yes—
494C8×C61—22no—
495C8×C61—22no—
496#92418—22no—
497#92418C22×D412yes—
498#92418C22×D412yes—
499#61083—611nomaximal, Sylow
500C22×C61—22no—
501C22×C61—24no—
502C22×C61—22no—
503C22×C61—22no—
504C22×C61—42no—
505C22×C61D4212yes—
506C22×C61C23×D411yescharacteristic
507C2×D61—24no—
508C2×D61—22no—
509C2×D61—22no—
510C2×D61—42no—
511C2×D61—44no—
512C2×D61—42no—
513C2×D61—164no—
514C2×D61—162no—
515C4×C61—22no—
516C4×C61—22no—
517C4×C61—42no—
518C4×C61—42no—
519C4×C61—42no—
520C4×C61D4212yes—
521C4×C61C23×D411yescharacteristic
522C4×C61C2×H(5,𝔽2)11yescharacteristic
523Dic61—22no—
524Dic61—22no—
525Dic61—22no—
526Dic61—22no—
527Dic61—42no—
528Dic61—42no—
529C2×#578—611no—
530C2×#577—611no—
531#3500—611no—
532#3499—611no—
533#3270—614no—
534#3269—614no—
535#3267—614no—
536#3266—614no—
537C2×#497—611no—
538#3059—611no—
539#3057—611no—
540#3040—611no—
541#3039—611no—
542#3011—611no—
543#3011D6111yescharacteristic, complemented
544#3010—611no—
545#3009—611no—
546#2943—611no—
547#2932—611no—
548C2×C61—22no—
549C2×C61—42no—
550C2×C61—42no—
551C2×C61C2×D4211yescharacteristic
552C2×C61#358612yes—
553D61—42no—
554D61—42no—
555D61—82no—
556C2×2−1+4—611no—
557C2×2−1+4—611no—
558C2×2−1+4C2×D6111yescharacteristic
559C2×H(5,𝔽2)—611no—
560#578—1228no—
561#577—1228no—
562C2×#137—611no—
563C2×#137—612no—
564C2×#137—612no—
565C2×#137—612no—
566C2×#137—611no—
567C2×#137C2×D6111yescharacteristic, complemented
568C2×AGL(1,ℤ/8)—611no—
569C2×AGL(1,ℤ/8)—612no—
570C2×#135—611no—
571C2×#135—612no—
572C2×#135—612no—
573C22×Q16—611no—
574C22×Q16—612no—
575C22×Q16C2×D6111yescharacteristic, complemented
576C22×SD16—611no—
577C22×SD16—612no—
578C22×SD16—611no—
579C2×#131—611no—
580C2×#131—611no—
581D4×Q8—614no—
582#548—614no—
583#547—614no—
584#547—1224no—
585#546—614no—
586#546—1224no—
587#536—611no—
588#536—611no—
589#536—1221no—
590#536—1221no—
591#536—1221no—
592#536C2×D6111yescharacteristic
593#535—611no—
594#535—1221no—
595#532—611no—
596#532—1221no—
597#532—1221no—
598C2×C4⋊Q8—611no—
599C2×C4⋊Q8—1221no—
600C2×#124—611no—
601C2×#124—1221no—
602C4×#41—611no—
603C4×#41—611no—
604#497—614no—
605#497—614no—
606#470—614no—
607#468—614no—
608#467—614no—
609#465—614no—
610#464—614no—
611#463—614no—
612#462—614no—
613#461—614no—
614#452—614no—
615#452—614no—
616#452C2×D6114yescomplemented
617#451—614no—
618#451C2×D6114yescomplemented
619#450—614no—
620#449—614no—
621#448—614no—
622#442—612no—
623#441—612no—
624#440—612no—
625#440—612no—
626#435—614no—
627#435—614no—
628#427—611no—
629#423—611no—
630#419—611no—
631#419—611no—
632#419C2×D6111yescharacteristic, complemented
633#418—611no—
634#416—611no—
635#416C2×D6111yescharacteristic, complemented
636#408—611no—
637#408C2×D6111yescharacteristic
638C2×#97—611no—
639C61#6108311yescharacteristic, complemented, Sylow
6402−1+4—24no—
6412−1+4—42no—
6422−1+4—1224no—
6432−1+4—1224no—
6442−1+4—2442no—
6452−1+4—2442no—
646H(5,𝔽2)—1224no—
647H(5,𝔽2)—2442no—
648C2×#41—21no—
649C2×#41—22no—
650C2×#41—611no—
651C2×#41—612no—
652C2×#41—612no—
653C2×#41—611no—
654C2×#41—612no—
655C2×#41—1221no—
656C2×#41—1222no—
657C2×#41—1222no—
658C2×#41—1221no—
659C2×#41—1221no—
660C2×#41C22×D6112yes—
661C2×#41C22×D6111yescharacteristic
662C2×#41C22×D6111yescharacteristic
663C22×Q8—21no—
664C22×Q8—612no—
665C22×Q8—612no—
666C22×Q8—611no—
667C22×Q8—1221no—
668C22×Q8—1221no—
669C22×Q8C22×D6111yescharacteristic
670C22×Q8C22×D6111yescharacteristic
671C22×Q8C22×D6112yes—
672C22×D4—611no—
673C22×D4—612no—
674C22×D4—1221no—
675C22×D4—1222no—
676#137—24no—
677#137—1224no—
678#137—1228no—
679#137—1228no—
680#137—1228no—
681#137—1224no—
682AGL(1,ℤ/8)—1228no—
683AGL(1,ℤ/8)—1224no—
684#135—618no—
685#135—1228no—
686#135—1228no—
687C2×Q16—42no—
688C2×Q16—611no—
689C2×Q16—612no—
690C2×Q16—612no—
691C2×Q16—612no—
692C2×Q16—612no—
693C2×Q16—1224no—
694C2×Q16—1228no—
695C2×Q16C22×D6112yes—
696C2×Q16C22×D6114yes—
697C2×SD16—611no—
698C2×SD16—611no—
699C2×SD16—612no—
700C2×SD16—612no—
701C2×SD16—612no—
702C2×SD16—612no—
703C2×SD16—612no—
704C2×SD16—614no—
705C2×SD16—1224no—
706C2×SD16—1228no—
707C2×SD16—2442no—
708C2×SD16C22×D6112yes—
709C2×D8—611no—
710C2×D8—612no—
711#131—1224no—
712#131—1224no—
713C2×M16—611no—
714C2×M16—612no—
715C2×M16—612no—
716C2×M16C22×D6111yescharacteristic
717C22×C8—611no—
718C22×C8—612no—
719C22×C8—612no—
720C22×C8C22×D6111yescharacteristic
721C4⋊Q8—21no—
722C4⋊Q8—611no—
723C4⋊Q8—614no—
724C4⋊Q8—1221no—
725C4⋊Q8—1221no—
726C4⋊Q8—1224no—
727C4⋊Q8—1221no—
728C4⋊Q8—1221no—
729#127—611no—
730#127—1221no—
731#124—21no—
732#124—611no—
733#124—611no—
734#124—614no—
735#124—1221no—
736#124—1221no—
737#124—1221no—
738#124—1224no—
739#124—1221no—
740#124—1221no—
741#123—22no—
742#123—1224no—
743#123—1224no—
744#123—1224no—
745#123—1222no—
746#123—1222no—
747C22⋊Q8—614no—
748C22⋊Q8—614no—
749C22⋊Q8—1224no—
750C22⋊Q8—1224no—
751C22⋊Q8—1224no—
752C22⋊Q8C22×D6114yes—
753#121—614no—
754#121—614no—
755#121—1224no—
756#121—1224no—
757#121—1224no—
758#120—1222no—
759#120—1224no—
760C4×Q8—612no—
761C4×Q8—612no—
762C4×D4—614no—
763C4×D4—612no—
764C4×D4—612no—
765C4×D4—1222no—
766C4×D4—1224no—
767C4×D4—1224no—
768C4×D4—1222no—
769#117—611no—
770#117—1221no—
771#117—1221no—
772#117C22×D6111yescharacteristic
773C2×C4⋊C4—1224no—
774C2×C4⋊C4—1222no—
775C2×C22⋊C4—1224no—
776C2×C22⋊C4—1222no—
777C2×C42—611no—
778C2×C42—1221no—
779C2×C42—1221no—
780#107—612no—
781#106—612no—
782C4⋊C8—614no—
783#103—614no—
784#103—612no—
785#103—614no—
786#103C22×D6112yes—
787#103C22×D6114yes—
788#102—612no—
789#102—614no—
790#102C22×D6112yes—
791C22⋊C8—614no—
792C22⋊C8C22×D6114yes—
793#97—612no—
794#97—612no—
795C24—1222no—
796C24—1221no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—24no—
801#41—42no—
802#41—44no—
803#41—48no—
804#41—614no—
805#41—1224no—
806#41—1222no—
807#41—1222no—
808#41—1222no—
809#41—1224no—
810#41—1224no—
811#41—2442no—
812#41—2444no—
813#41—2448no—
814#41—2442no—
815#41—2442no—
816#41—2444no—
817#41—2444no—
818#41—2448no—
819#41D4×D6114yes—
820C2×Q8—22no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—24no—
824C2×Q8—22no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—42no—
829C2×Q8—44no—
830C2×Q8—611no—
831C2×Q8—611no—
832C2×Q8—612no—
833C2×Q8—1222no—
834C2×Q8—1222no—
835C2×Q8—1221no—
836C2×Q8—1224no—
837C2×Q8—1224no—
838C2×Q8—1222no—
839C2×Q8—1222no—
840C2×Q8—2444no—
841C2×Q8—2442no—
842C2×Q8—2442no—
843C2×Q8—2444no—
844C2×Q8D4×D6111yescharacteristic
845C2×Q8C23×D6112yes—
846C2×Q8C23×D6112yes—
847C2×Q8C23×D6111yescharacteristic
848C2×D4—21no—
849C2×D4—22no—
850C2×D4—612no—
851C2×D4—614no—
852C2×D4—611no—
853C2×D4—611no—
854C2×D4—612no—
855C2×D4—1224no—
856C2×D4—1224no—
857C2×D4—1222no—
858C2×D4—1221no—
859C2×D4—1222no—
860C2×D4—1222no—
861C2×D4—1222no—
862C2×D4—1222no—
863C2×D4—1221no—
864C2×D4—1222no—
865C2×D4—2442no—
866C2×D4—2444no—
867C2×D4—2448no—
868C2×D4D4×D6112yes—
869C2×D4D4×D6111yescharacteristic
870C2×D4C23×D6111yescharacteristic
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—612no—
877C22×C4—612no—
878C22×C4—1222no—
879C22×C4—1222no—
880C22×C4—1222no—
881C22×C4—1222no—
882C22×C4—1222no—
883C22×C4—1222no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1222no—
887C22×C4C23×D6112yes—
888C22×C4C23×D6111yescharacteristic
889Q16—24no—
890Q16—44no—
891Q16—614no—
892Q16—1224no—
893Q16—1224no—
894Q16—1224no—
895Q16—1224no—
896SD16—24no—
897SD16—614no—
898SD16—614no—
899SD16—1224no—
900SD16—1224no—
901SD16—1224no—
902SD16—1224no—
903SD16—1224no—
904SD16—2444no—
905D8—614no—
906D8—1224no—
907M16—22no—
908M16—1224no—
909M16—1224no—
910M16—1222no—
911C2×C8—22no—
912C2×C8—614no—
913C2×C8—611no—
914C2×C8—611no—
915C2×C8—612no—
916C2×C8—1224no—
917C2×C8—1224no—
918C2×C8C23×D6112yes—
919C2×C8C23×D6112yes—
920C4⋊C4—24no—
921C4⋊C4—614no—
922C4⋊C4—612no—
923C4⋊C4—1224no—
924C4⋊C4—1224no—
925C4⋊C4—1224no—
926C4⋊C4—1222no—
927C4⋊C4—1222no—
928C4⋊C4—1224no—
929C4⋊C4C23×D6112yes—
930C22⋊C4—24no—
931C22⋊C4—21no—
932C22⋊C4—614no—
933C22⋊C4—614no—
934C22⋊C4—1224no—
935C22⋊C4—1224no—
936C22⋊C4—1224no—
937C22⋊C4—1222no—
938C22⋊C4—1224no—
939C22⋊C4—1222no—
940C22⋊C4—1221no—
941C22⋊C4—1224no—
942C42—21no—
943C42—611no—
944C42—611no—
945C42—612no—
946C42—1222no—
947C42—1222no—
948C42—1221no—
949C23—21no—
950C23—612no—
951C23—1221no—
952C23—1222no—
953C23—4882no—
954C23—4884no—
955C23—2444no—
956C23—2442no—
957C23C2×D4×D6112yes—
958C23C2×D4×D6111yescharacteristic
959Q8—21no—
960Q8—22no—
961Q8—22no—
962Q8—22no—
963Q8—22no—
964Q8—22no—
965Q8—44no—
966Q8—42no—
967Q8—42no—
968Q8—612no—
969Q8—1221no—
970Q8—1222no—
971Q8—1222no—
972Q8—1222no—
973Q8—2444no—
974Q8—2444no—
975Q8—2442no—
976Q8C2×D4×D6112yes—
977D4—24no—
978D4—24no—
979D4—21no—
980D4—22no—
981D4—44no—
982D4—612no—
983D4—1224no—
984D4—1224no—
985D4—1222no—
986D4—1221no—
987D4—1222no—
988D4—1222no—
989D4—4884no—
990D4—2444no—
991D4—2444no—
992D4—2444no—
993D4—2444no—
994D4—2444no—
995D4—2442no—
996D4C2×D4×D6112yes—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—612no—
1009C2×C4—612no—
1010C2×C4—612no—
1011C2×C4—1221no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1224no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—4882no—
1018C2×C4—2444no—
1019C2×C4—2444no—
1020C2×C4—2444no—
1021C2×C4—2444no—
1022C2×C4—2442no—
1023C2×C4—2444no—
1024C2×C4—2444no—
1025C2×C4—2442no—
1026C2×C4C2×D4×D6112yes—
1027C2×C4C2×D4×D6112yes—
1028C2×C4C2×D4×D6111yescharacteristic
1029C2×C4#1451982212yes—
1030C2×C4C24×D6111yescharacteristic
1031C8—22no—
1032C8—22no—
1033C8—612no—
1034C8—612no—
1035C8—1222no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—24no—
1040C22—42no—
1041C22—1222no—
1042C22—1222no—
1043C22—1224no—
1044C22—9762no—
1045C22—9764no—
1046C22—2442no—
1047C22—2444no—
1048C22—2442no—
1049C22#1684039412yes—
1050C22C22×D4×D6111yescharacteristic
1051C4—22no—
1052C4—22no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—1222no—
1057C4—1222no—
1058C4—1222no—
1059C4—1222no—
1060C4—2442no—
1061C4—2442no—
1062C4#1684039412yes—
1063C4C22×D4×D6111yescharacteristic
1064C4C2×#1451982211yescharacteristic
1065C2—22no—
1066C2—42no—
1067C2—42no—
1068C2—4882no—
1069C2—2442no—
1070C2—2442no—
1071C2C2×#1684039411yescharacteristic
1072C2#2146060412yes—
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3011C2
socleC22×C61C23×D4
hypercenter#3011D61
hypocenterC61#61083
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. C2×#16840578C2semidirect
2. C2×#16840570C2semidirect
3. #21459608C2semidirect
4. #21459600C2semidirect
5. #21457392C2semidirect
6. #21457378C2semidirect
7. #21457347C2semidirect
8. #21457322C2semidirect
9. C2×#16840155C2semidirect
10. #21455471C2semidirect
11. #21455461C2semidirect
12. #21455315C2semidirect
13. #21455305C2semidirect
14. #21455110C2semidirect
15. #21455108C2semidirect
16. #21455098C2semidirect
17. #21454615C2semidirect
18. #21454534C2semidirect
19. C61×#3011C2semidirect
21. C2×#14519824C22semidirect
26. C2×#14519809C22semidirect
29. C2×#14519806C22semidirect
32. C2×#14519798C22semidirect
35. C22×#11758202C22semidirect
36. C2×Q16×D61C22semidirect
40. C2×#14519785C22semidirect
42. Q8×C22⋊D61C22semidirect
45. #16840411C22semidirect
50. #16840336C22semidirect
59. C2×#14519775C22semidirect
62. #41×Dic61C22semidirect
64. #16840155C22semidirect
65. #16840155C22semidirect
66. #16840018C22semidirect
67. #16840011C22semidirect
68. #16840001C22semidirect
69. #16839994C22semidirect
70. #16839986C22semidirect
71. #16839979C22semidirect
72. #16839971C22semidirect
73. #16839966C22semidirect
75. #16839923C22semidirect
76. #16839916C22semidirect
78. #16839908C22semidirect
79. #16839902C22semidirect
80. #16839871C22semidirect
81. #16839866C22semidirect
82. #16839865C22semidirect
83. #16839859C22semidirect
84. #16839836C22semidirect
85. #16839830C22semidirect
86. #16839798C22semidirect
87. #16839785C22semidirect
88. #16839771C22semidirect
89. #16839770C22semidirect
92. #16839728C22semidirect
93. C2×#14519687C22semidirect
95. C2×#137×C61C22semidirect
96. C22×Q16×C61C22semidirect
98. C61×#452C22semidirect
99. C61×#451C22semidirect
100. C61×#419C22semidirect
101. C61×#416C22semidirect
137. #14519797D4semidirect
543. #3011D61semidirect
567. C2×#137C2×D61semidirect
575. C22×Q16C2×D61semidirect
616. #452C2×D61semidirect
618. #451C2×D61semidirect
632. #419C2×D61semidirect
635. #416C2×D61semidirect
639. C61#61083semidirect

Maximal subgroups

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

subgroupindex
C2×#168405782
C2×#168405702
#214596082
#214596002
#214573922
#214573782
#214573472
#214573222
C2×#168401552
#214554712
#214554612
#214553152
#214553052
#214551102
#214551082
#214550982
#214546152
#214545342
C61×#30112
#6108361