Finite Group Databasebeta

← #30551456

Subgroups — #30551456

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#21456848C211yesmaximal, characteristic, complemented
4#21456847C212yesmaximal, complemented
5#21456846C211yesmaximal, characteristic, complemented
6#21456843C211yesmaximal, characteristic, complemented
7#21456842C212yesmaximal, complemented
8#21456766C212yesmaximal, complemented
9#21456765C212yesmaximal, complemented
10#21456743C212yesmaximal, complemented
11#21456742C212yesmaximal, complemented
12#21456275C212yesmaximal, complemented
13#21456198C212yesmaximal, complemented
14#21455303C212yesmaximal, complemented
15#21455301C212yesmaximal, complemented
16#21455054C212yesmaximal, complemented
17#21455050C212yesmaximal, complemented
18#21454449C211yesmaximal, characteristic, complemented
19C61×#3218C211yesmaximal, characteristic, complemented
20C22×Q8×D61C2212yes—
21C2×#14519809C2214yes—
22C2×#14519806C2214yes—
23#16840318C2211yescharacteristic
24#16840316C2211yescharacteristic
25#16840314C2211yescharacteristic
26#16840311C2211yescharacteristic
27#16840309C2211yescharacteristic
28#16840307C2211yescharacteristic
29C2×#14519777C2211yescharacteristic
30C2×#14519776—21no—
31C2×#14519776—21no—
32C2×#14519775C2212yes—
33C4⋊Q8×D61—21no—
34C4⋊Q8×D61—21no—
35C4⋊Q8×D61—21no—
36C4⋊Q8×D61—21no—
37C4⋊Q8×D61C2212yes—
38C4⋊Q8×D61C2212yes—
39C4⋊Q8×D61C2212yes—
40C4⋊Q8×D61C2212yes—
41#16840297C2211yescharacteristic
42#16840296C2211yescharacteristic
43#16840295—21no—
44#16840295—21no—
45#16840291C2211yescharacteristic
46#16840290—21no—
47#16840289—21no—
48#16840275C2211yescharacteristic
49#16840272C2211yescharacteristic
50#16840271—21no—
51#16840270—21no—
52C4×#11758226C2211yescharacteristic
53#16840230—21no—
54C4×#11758224—21no—
55C4×#11758224C2211yescharacteristic
56C2×C4⋊C4×D61—21no—
57C2×C4⋊C4×D61—21no—
58C2×C42×D61C2211yescharacteristic
59#16840157C2212yescomplemented
60#16840156C2212yescomplemented
61#16840154C2212yescomplemented
62#16840140C2214yescomplemented
63#16840133C2214yescomplemented
64#16840132C2212yescomplemented
65#16840131C2212yescomplemented
66#16840130C2212yescomplemented
67#16840111C2214yescomplemented
68#16840111C2214yescomplemented
69#16839973C2212yescomplemented
70#16839972C2212yescomplemented
71#16839971C2214yescomplemented
72#16839970C2214yescomplemented
73#16839969C2212yescomplemented
74#16839968C2212yescomplemented
75#16839967C2212yescomplemented
76#16839966C2214yescomplemented
77#16839965C2214yescomplemented
78#16839964C2212yescomplemented
79#16839920C2212yes—
80#16839919C2214yes—
81#16839918C2212yes—
82#16839917C2212yes—
83#16839916C2214yes—
84#16839903C2212yes—
85#16839902C2214yes—
86#16839901C2212yes—
87#16839900C2212yes—
88#16839899C2214yes—
89#16839819C2211yescharacteristic
90#16839817C2212yes—
91#16839814C2212yes—
92#16839812C2212yes—
93#16839784C2212yes—
94#16839769C2214yes—
95#16839769C2214yes—
96#16839724C2212yes—
97#16839714C2212yes—
98C2×C4⋊Q8×C61C2211yescharacteristic
99C61×#529C2211yescharacteristic
100C61×#497C2212yescomplemented
101C61×#491C2212yescomplemented
102C61×#462C2212yescomplemented
103C61×#461C2212yescomplemented
104C61×#451C2212yes—
105C61×#448C2212yes—
106C61×#432C2211yescharacteristic
107C2×#11758226C2311yescharacteristic
108C2×#11758222—21no—
109C2×#11758224—21no—
110C2×#11758224C2311yescharacteristic
111C22×Dic122—22no—
112C22×Dic122C2312yes—
113C2×Q8×D61—22no—
114C2×Q8×D61—22no—
115C2×Q8×D61—48no—
116C2×Q8×D61C2314yes—
117C2×Q8×D61C2314yes—
118C22×C4×D61—22no—
119C22×C4×D61D411yescharacteristic
120C22×C4×D61D411yescharacteristic
121C22×C4×D61C2311yescharacteristic
122#14519809—48no—
123#14519806—48no—
124C2×Dic244C2314yes—
125C2×#11758202C2314yes—
126C2×#11758202C2314yes—
127C2×#11758190C2314yes—
128C2×#11758200C2314yes—
129C2×#11758201C2314yes—
130C2×#11758189C2314yes—
131#14519777—21no—
132#14519777—21no—
133#14519777C2312yes—
134#14519777C2312yes—
135#14519776—22no—
136#14519776—22no—
137#14519776—22no—
138#14519776—22no—
139#14519776—22no—
140#14519776—22no—
141#14519776—22no—
142#14519776—22no—
143#14519776C2311yescharacteristic
144#14519776C2311yescharacteristic
145#14519775—22no—
146#14519775—22no—
147#14519775C2314yes—
148#14519775C2314yes—
149#14519775C2311yescharacteristic
150#14519773C2311yescharacteristic
151#14519772—21no—
152#14519771—21no—
153#14519770—21no—
154#14519769C2311yescharacteristic
155#14519767—21no—
156#14519767—21no—
157#14519765C2311yescharacteristic
158#14519763—21no—
159#14519763—21no—
160#14519762—21no—
161#14519762—21no—
162#14519760—21no—
163#14519759—21no—
164#14519759—21no—
165#14519757C2311yescharacteristic
166#14519756C2311yescharacteristic
167#14519755—21no—
168#14519755—21no—
169#14519755—21no—
170#14519754—21no—
171#14519753C2311yescharacteristic
172#14519752C2311yescharacteristic
173#14519751C2311yescharacteristic
174#14519750—21no—
175#14519750—21no—
176#14519750—21no—
177#14519749—21no—
178#14519748C2311yescharacteristic
179#14519747—21no—
180#14519745—21no—
181Q8×Dic61C2311yescharacteristic
182C4×Dic122—21no—
183C4×Dic122C2311yescharacteristic
184#14519742—21no—
185#14519742—21no—
186#14519742—21no—
187#14519742C2311yescharacteristic
188C4×D244—21no—
189C4×D244C2311yescharacteristic
190D4×Dic61—21no—
191D4×Dic61C2311yescharacteristic
192#14519739—21no—
193#14519739—21no—
194#14519739—21no—
195#14519739C2311yescharacteristic
196C4×C22⋊D61—21no—
197C4×C22⋊D61—21no—
198C4×C22⋊D61—21no—
199#14519737—21no—
200#14519737—21no—
201#14519737—21no—
202#14519737—21no—
203#14519737—21no—
204#14519737—21no—
205#14519737—21no—
206#14519735—21no—
207#14519735—21no—
208#14519735C2311yescharacteristic
209#14519735C2311yescharacteristic
210#14519734—21no—
211#14519734—21no—
212#14519733—21no—
213#14519733—21no—
214#14519733—21no—
215C2×C4⋊Dic61—21no—
216C2×C4⋊Dic61—21no—
217C2×#11758196—22no—
218C2×#11758196—22no—
219C4⋊C4×D61—22no—
220C4⋊C4×D61—22no—
221C4⋊C4×D61—22no—
222C4⋊C4×D61—22no—
223C4⋊C4×D61—22no—
224C4⋊C4×D61—22no—
225C4⋊C4×D61—22no—
226C4⋊C4×D61—22no—
227C2×C4×Dic61—21no—
228C2×C4×Dic61D411yescharacteristic
229C2×C4×Dic61D411yescharacteristic
230C2×C4×Dic61C2311yescharacteristic
231C42×D61—21no—
232C42×D61D411yescharacteristic
233C42×D61D411yescharacteristic
234C42×D61D411yescharacteristic
235C42×D61D411yescharacteristic
236C42×D61C2311yescharacteristic
237C42×D61C2311yescharacteristic
238C42×D61C2311yescharacteristic
239C42×D61C2311yescharacteristic
240C4⋊#92418C2312yes—
241#14519706C2314yes—
242#14519702C2314yes—
243#14519702C2314yes—
244#14519701C2314yes—
245#14519701C2314yes—
246#14519700C2314yes—
247#14519700C2314yes—
248C22⋊#92418C2312yes—
249#14519689C2314yes—
250#14519688C2312yes—
251C8×Dic61C2314yes—
252C22×Q8×C61C2312yes—
253C2×Q16×C61C2314yes—
254C2×SD16×C61C2314yes—
255C4⋊Q8×C61—21no—
256C4⋊Q8×C61—21no—
257C4⋊Q8×C61C2312yes—
258C4⋊Q8×C61C2312yes—
259#126×C61—21no—
260#125×C61C2311yescharacteristic
261#124×C61C2311yescharacteristic
262#123×C61—21no—
263C22⋊Q8×C61C2311yescharacteristic
264#121×C61C2311yescharacteristic
265C4×Q8×C61C2311yescharacteristic
266C4×D4×C61—21no—
267C4×D4×C61C2311yescharacteristic
268#117×C61—21no—
269C2×C4⋊C4×C61—21no—
270C2×C4⋊C4×C61—21no—
271C2×C42×C61C2311yescharacteristic
272C4⋊C8×C61C2312yes—
273#103×C61C2314yes—
274#103×C61C2314yes—
275C22⋊C8×C61C2312yes—
276#97×C61C2312yes—
277C23×D61C2×D411yescharacteristic
278C2×Q8×C61—22no—
279C2×Q8×C61—44no—
280C2×Q8×C61C2414yes—
281C2×Q8×C61C2411yescharacteristic
282C2×D4×C61—21no—
283C2×D4×C61C2411yescharacteristic
284C22×C4×C61—22no—
285C22×C4×C61—21no—
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2411yescharacteristic
289C2×C22⋊D61—21no—
290C2×C22⋊D61—21no—
291C2×C22⋊D61—21no—
292C2×C22⋊D61—21no—
293C2×C22⋊D61—21no—
294C22×Dic61—22no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61C2×D411yescharacteristic
298C22×Dic61C2×D411yescharacteristic
299C22×Dic61C2×D411yescharacteristic
300#11758226—24no—
301Q8×D61—28no—
302Q8×D61—28no—
303Q8×D61—44no—
304Q8×D61—44no—
305Q8×D61—48no—
306Q8×D61—48no—
307#11758224—24no—
308#11758224—44no—
309#11758222—44no—
310C2×D244—21no—
311C2×D244—21no—
312C2×D244C2411yescharacteristic
313C2×C4×D61—24no—
314C2×C4×D61—24no—
315C2×C4×D61—24no—
316C2×C4×D61—24no—
317C2×C4×D61—24no—
318C2×C4×D61—21no—
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—48no—
322C2×C4×D61C2×D411yescharacteristic
323C2×C4×D61C2×D411yescharacteristic
324C2×C4×D61C2×D411yescharacteristic
325C2×C4×D61C2×D411yescharacteristic
326C2×C4×D61C2×D411yescharacteristic
327C2×C4×D61C2×D411yescharacteristic
328C2×C4×D61C2×D411yescharacteristic
329C2×C4×D61C2×D411yescharacteristic
330C2×C4×D61C2×D411yescharacteristic
331C2×C4×D61C2×D411yescharacteristic
332C2×C4×D61C2411yescharacteristic
333C2×C4×D61C2411yescharacteristic
334C2×Dic122—22no—
335C2×Dic122—24no—
336C2×Dic122—24no—
337C2×Dic122—21no—
338C2×Dic122—21no—
339C2×Dic122—44no—
340C2×Dic122—48no—
341C2×Dic122C2414yes—
342C2×Dic122C2411yescharacteristic
343Q16×C61—44no—
344SD16×C61—44no—
345C2×C8×C61C2414yes—
346C4⋊C4×C61—22no—
347C4⋊C4×C61—22no—
348C4⋊C4×C61—22no—
349C4⋊C4×C61—22no—
350C4⋊C4×C61—21no—
351C4⋊C4×C61—21no—
352C4⋊C4×C61—21no—
353C4⋊C4×C61—21no—
354C4⋊C4×C61C2411yescharacteristic
355C4⋊C4×C61C2411yescharacteristic
356C22⋊C4×C61—21no—
357C22⋊C4×C61—21no—
358C22⋊C4×C61—21no—
359C22⋊C4×C61—21no—
360C22⋊C4×C61—21no—
361C42×C61—21no—
362C42×C61C2×D411yescharacteristic
363C42×C61C2×D411yescharacteristic
364C42×C61C2411yescharacteristic
365C42×C61C2411yescharacteristic
366C22⋊Dic61—21no—
367C22⋊Dic61—21no—
368C22⋊Dic61—21no—
369#11758202—44no—
370#11758202—44no—
371#11758201—44no—
372#11758200—44no—
373#11758198—21no—
374#11758198—21no—
375#11758198—21no—
376#11758198—21no—
377#11758198—21no—
378#11758198—21no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383C4⋊Dic61—22no—
384C4⋊Dic61—22no—
385C4⋊Dic61—22no—
386C4⋊Dic61—22no—
387C4⋊Dic61—21no—
388C4⋊Dic61—21no—
389C4⋊Dic61C2411yescharacteristic
390C4⋊Dic61C2411yescharacteristic
391#11758196—21no—
392#11758196—21no—
393#11758196—21no—
394#11758196—21no—
395#11758196—24no—
396#11758196—24no—
397#11758196—24no—
398#11758196—24no—
399#11758196—21no—
400#11758196—21no—
401#11758196—21no—
402#11758196—21no—
403#11758196—21no—
404#11758196—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61C2×D411yescharacteristic
411C4×Dic61C2×D411yescharacteristic
412C4×Dic61C2×D411yescharacteristic
413C4×Dic61C2×D411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416C4×Dic61C2×D411yescharacteristic
417C4×Dic61C2×D411yescharacteristic
418C4×Dic61C2×D411yescharacteristic
419C4×Dic61C2×D411yescharacteristic
420C4×Dic61C2411yescharacteristic
421C4×Dic61C2411yescharacteristic
422C2×#92418C2414yes—
423Dic244—44no—
424#11758190—44no—
425#11758189—28no—
426C23×C61—21no—
427C23×C61C22×D411yescharacteristic
428C22×D61—22no—
429C22×D61—22no—
430C22×D61—22no—
431C22×D61—21no—
432C22×D61C22×D411yescharacteristic
433C22×D61C22×D411yescharacteristic
434Q8×C61—24no—
435Q8×C61—22no—
436Q8×C61—24no—
437Q8×C61—44no—
438D4×C61—22no—
439D4×C61—42no—
440C2×C4×C61—22no—
441C2×C4×C61—22no—
442C2×C4×C61—22no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—24no—
447C2×C4×C61—44no—
448C2×C4×C61—42no—
449C2×C4×C61C22×D411yescharacteristic
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D411yescharacteristic
453C2×C4×C61C22×D411yescharacteristic
454C2×C4×C61C2511yescharacteristic
455C22⋊D61—42no—
456C22⋊D61—42no—
457C22⋊D61—42no—
458C22⋊D61—42no—
459C22⋊D61—42no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—24no—
466C2×Dic61—44no—
467C2×Dic61—42no—
468C2×Dic61—42no—
469C2×Dic61#13714yescomplemented
470C2×Dic61C22×D411yescharacteristic
471C2×Dic61C22×D411yescharacteristic
472C2×Dic61C22×D411yescharacteristic
473C2×Dic61C22×D411yescharacteristic
474C2×Dic61C22×D411yescharacteristic
475C2×Dic61C22×D411yescharacteristic
476D244—22no—
477D244—42no—
478D244—42no—
479C4×D61—22no—
480C4×D61—22no—
481C4×D61—22no—
482C4×D61—22no—
483C4×D61—22no—
484C4×D61—22no—
485C4×D61—22no—
486C4×D61—22no—
487C4×D61—22no—
488C4×D61—22no—
489C4×D61—48no—
490C4×D61—48no—
491C4×D61—42no—
492C4×D61—42no—
493C4×D61—42no—
494C4×D61#13714yescomplemented
495C4×D61H(5,𝔽2)14yes—
496Dic122—24no—
497Dic122—22no—
498Dic122—24no—
499Dic122—48no—
500Dic122—44no—
501Dic122—48no—
502Dic122—42no—
503Dic122—42no—
504C8×C61—24no—
505#92418—24no—
506#60800—611nomaximal, Sylow
507C22×C61—21no—
508C22×C61—21no—
509C22×C61—41no—
510C22×C61—41no—
511C22×C61—41no—
512C22×C61C2×#13712yes—
513C22×C61C23×D411yescharacteristic
514C2×D61—28no—
515C2×D61—21no—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—41no—
520C2×D61—41no—
521C2×D61—41no—
522C2×D61#53512yes—
523C2×D61C2×#13712yes—
524C4×C61—21no—
525C4×C61—21no—
526C4×C61—21no—
527C4×C61—21no—
528C4×C61—44no—
529C4×C61—41no—
530C4×C61—41no—
531C4×C61—41no—
532C4×C61C2×#13712yes—
533C4×C61C2×H(5,𝔽2)12yes—
534Dic61—21no—
535Dic61—21no—
536Dic61—44no—
537Dic61—41no—
538Dic61—41no—
539Dic61—41no—
540Dic61#53512yes—
541Dic61C2×#13712yes—
542Dic61C2×#13712yes—
543Dic61C2×#13712yes—
544#3444—611no—
545C22×C4⋊Q8—611no—
546#3218—612no—
547#3218—612no—
548#3218—611no—
549#3218—611no—
550#3218—611no—
551#3218D6111yescharacteristic, complemented
552#3209—612no—
553#3209—612no—
554#3206—612no—
555#3206—612no—
556#3152—612no—
557#3139—612no—
558#3039—612no—
559#3039—612no—
560#3004—612no—
561#3004—612no—
562#2920—611no—
563C2×C61—22no—
564C2×C61—81no—
565C2×C61C2×#53511yescharacteristic
566C2×C61C22×#13711yescharacteristic
567C2×C61C22×#13711yescharacteristic
568D61—22no—
569D61—22no—
570D61—81no—
571C23×Q8—612no—
572C2×#137—614no—
573C2×#137—614no—
574#533—611no—
575#533—611no—
576#533—611no—
577#532—611no—
578#532—611no—
579#532—611no—
580C2×C4⋊Q8—612no—
581C2×C4⋊Q8—612no—
582C2×C4⋊Q8—612no—
583C2×C4⋊Q8—612no—
584C2×C4⋊Q8—612no—
585C2×C4⋊Q8—611no—
586C2×C4⋊Q8—1221no—
587C2×C4⋊Q8—1221no—
588C2×C4⋊Q8—1221no—
589C2×C4⋊Q8—1221no—
590C2×C4⋊Q8—1221no—
591C2×C4⋊Q8—1221no—
592C2×C4⋊Q8C2×D6111yescharacteristic
593#529—611no—
594#529—611no—
595#529—611no—
596#529—1221no—
597#529—1221no—
598#529—1221no—
599#529—1221no—
600#529C2×D6111yescharacteristic
601#525—611no—
602#525—611no—
603#525—1221no—
604#525—1221no—
605C4×#41—611no—
606C4×#41—611no—
607C4×#41—1221no—
608C4×#41—1221no—
609C22×C4⋊C4—1221no—
610C22×C4⋊C4—1221no—
611C22×C42—611no—
612#497—612no—
613#497—612no—
614#497—612no—
615#497C2×D6112yescomplemented
616#494—614no—
617#492—614no—
618#491—612no—
619#491—612no—
620#491—612no—
621#491C2×D6112yescomplemented
622#487—614no—
623#487—614no—
624#462—614no—
625#462—612no—
626#462—612no—
627#462—612no—
628#462—614no—
629#462C2×D6112yescomplemented
630#461—614no—
631#461—612no—
632#461—612no—
633#461—612no—
634#461—614no—
635#461C2×D6112yescomplemented
636#451—612no—
637#451—614no—
638#451—612no—
639#451—614no—
640#451—612no—
641#451C2×D6112yes—
642#448—612no—
643#448—614no—
644#448—612no—
645#448—614no—
646#448—612no—
647#448C2×D6112yes—
648#432—611no—
649#432—612no—
650#432C2×D6111yescharacteristic
651#431—612no—
652#431—612no—
653#423—612no—
654#419—614no—
655#419—614no—
656#407—612no—
657C4×M16—612no—
658C61#6080011yescharacteristic, complemented, Sylow
659C2×#41—611no—
660C2×#41—611no—
661C2×#41—1221no—
662C2×#41—1221no—
663C22×Q8—614no—
664C22×Q8—614no—
665C22×Q8—612no—
666C22×Q8—1222no—
667C22×Q8—1222no—
668C22×Q8—1222no—
669C22×Q8—2448no—
670C22×Q8C22×D6112yes—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—611no—
674C23×C4—1222no—
675#137—2448no—
676#137—2448no—
677C2×Q16—614no—
678C2×Q16—614no—
679C2×Q16—614no—
680C2×Q16C22×D6114yes—
681C2×SD16—614no—
682C2×SD16—614no—
683C2×SD16—614no—
684C2×SD16C22×D6114yes—
685C2×M16—614no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—611no—
689C4⋊Q8—611no—
690C4⋊Q8—614no—
691C4⋊Q8—614no—
692C4⋊Q8—611no—
693C4⋊Q8—612no—
694C4⋊Q8—612no—
695C4⋊Q8—1222no—
696C4⋊Q8—1222no—
697C4⋊Q8—1222no—
698C4⋊Q8—1222no—
699C4⋊Q8—1222no—
700C4⋊Q8—1222no—
701C4⋊Q8—1222no—
702C4⋊Q8—1222no—
703C4⋊Q8—1222no—
704C4⋊Q8—1222no—
705C4⋊Q8—1221no—
706C4⋊Q8—1221no—
707C4⋊Q8C22×D6112yes—
708C4⋊Q8C22×D6112yes—
709#127—611no—
710#126—21no—
711#126—1221no—
712#126—1221no—
713#126—1221no—
714#125—611no—
715#125—1221no—
716#125—1221no—
717#125C22×D6111yescharacteristic
718#124—611no—
719#124—1221no—
720#124—1221no—
721#124C22×D6111yescharacteristic
722#123—21no—
723#123—1221no—
724#123—1221no—
725#123—1221no—
726#123—1221no—
727#123—1221no—
728C22⋊Q8—611no—
729C22⋊Q8—611no—
730C22⋊Q8—611no—
731C22⋊Q8—1221no—
732C22⋊Q8—1221no—
733C22⋊Q8—1221no—
734C22⋊Q8—1221no—
735C22⋊Q8C22×D6111yescharacteristic
736#121—611no—
737#121—611no—
738#121—611no—
739#121—1221no—
740#121—1221no—
741#121—1221no—
742#121—1221no—
743#121C22×D6111yescharacteristic
744#120—1221no—
745#120—1221no—
746C4×Q8—611no—
747C4×Q8—611no—
748C4×Q8—611no—
749C4×Q8—1221no—
750C4×Q8—1221no—
751C4×Q8—1221no—
752C4×Q8—1221no—
753C4×Q8C22×D6111yescharacteristic
754C4×D4—21no—
755C4×D4—611no—
756C4×D4—611no—
757C4×D4—611no—
758C4×D4—1221no—
759C4×D4—1221no—
760C4×D4—1221no—
761C4×D4—1221no—
762C4×D4—1221no—
763C4×D4—1221no—
764C4×D4—1221no—
765C4×D4—1221no—
766C4×D4—1221no—
767C4×D4—1221no—
768C4×D4—1221no—
769C4×D4—1221no—
770C4×D4—1221no—
771C4×D4—1221no—
772C4×D4—1221no—
773C4×D4C22×D6111yescharacteristic
774#117—21no—
775#117—611no—
776#117—611no—
777#117—1221no—
778#117—1221no—
779#117—1221no—
780#117—1221no—
781#117—1221no—
782#117—1221no—
783#117—1221no—
784C2×C4⋊C4—21no—
785C2×C4⋊C4—21no—
786C2×C4⋊C4—1222no—
787C2×C4⋊C4—1222no—
788C2×C4⋊C4—1222no—
789C2×C4⋊C4—1222no—
790C2×C4⋊C4—1222no—
791C2×C4⋊C4—1222no—
792C2×C4⋊C4—1222no—
793C2×C4⋊C4—1222no—
794C2×C4⋊C4—1222no—
795C2×C4⋊C4—1222no—
796C2×C4⋊C4—1221no—
797C2×C4⋊C4—1221no—
798C2×C42—611no—
799C2×C42—611no—
800C2×C42—611no—
801C2×C42—611no—
802C2×C42—611no—
803C2×C42—611no—
804C2×C42—611no—
805C2×C42—611no—
806C2×C42—611no—
807C2×C42—611no—
808C2×C42—611no—
809C2×C42—1221no—
810C2×C42—1221no—
811C2×C42C22×D6111yescharacteristic
812C4⋊C8—614no—
813C4⋊C8—612no—
814C4⋊C8C22×D6112yes—
815#103—614no—
816#103—614no—
817#103—614no—
818#103—614no—
819#103—614no—
820#103—614no—
821#103C22×D6114yes—
822#103C22×D6114yes—
823C22⋊C8—612no—
824C22⋊C8—614no—
825C22⋊C8C22×D6112yes—
826#97—612no—
827#97C22×D6112yes—
828C4×C8—614no—
829C24—611no—
830#41—1224no—
831#41—1224no—
832#41—2444no—
833#41—2444no—
834C2×Q8—22no—
835C2×Q8—44no—
836C2×Q8—614no—
837C2×Q8—611no—
838C2×Q8—1221no—
839C2×Q8—1221no—
840C2×Q8—1224no—
841C2×Q8—1224no—
842C2×Q8—1228no—
843C2×Q8—1228no—
844C2×Q8—1222no—
845C2×Q8—2444no—
846C2×Q8—2448no—
847C2×Q8—2444no—
848C2×Q8—2444no—
849C2×Q8—2448no—
850C2×Q8—2448no—
851C2×Q8C23×D6114yes—
852C2×Q8C23×D6111yescharacteristic
853C2×D4—21no—
854C2×D4—611no—
855C2×D4—1221no—
856C2×D4—1221no—
857C2×D4—1221no—
858C2×D4—1221no—
859C2×D4—1221no—
860C2×D4—1221no—
861C2×D4—1221no—
862C2×D4C23×D6111yescharacteristic
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—611no—
866C22×C4—611no—
867C22×C4—611no—
868C22×C4—611no—
869C22×C4—611no—
870C22×C4—611no—
871C22×C4—611no—
872C22×C4—611no—
873C22×C4—611no—
874C22×C4—611no—
875C22×C4—611no—
876C22×C4—611no—
877C22×C4—611no—
878C22×C4—611no—
879C22×C4—611no—
880C22×C4—1224no—
881C22×C4—1224no—
882C22×C4—1224no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1224no—
886C22×C4—1224no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1222no—
890C22×C4—1221no—
891C22×C4—2448no—
892C22×C4D4×D6111yescharacteristic
893C22×C4D4×D6111yescharacteristic
894C22×C4C23×D6111yescharacteristic
895Q16—44no—
896Q16—2444no—
897Q16—2444no—
898Q16—2444no—
899SD16—44no—
900SD16—2444no—
901SD16—2444no—
902SD16—2444no—
903M16—1228no—
904C2×C8—614no—
905C2×C8C23×D6114yes—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—611no—
915C4⋊C4—611no—
916C4⋊C4—1224no—
917C4⋊C4—1224no—
918C4⋊C4—1224no—
919C4⋊C4—1224no—
920C4⋊C4—1221no—
921C4⋊C4—1221no—
922C4⋊C4—1221no—
923C4⋊C4—1221no—
924C4⋊C4—1221no—
925C4⋊C4—1221no—
926C4⋊C4—1221no—
927C4⋊C4—1221no—
928C4⋊C4—1222no—
929C4⋊C4—1222no—
930C4⋊C4—1222no—
931C4⋊C4—1222no—
932C4⋊C4—1221no—
933C4⋊C4—1221no—
934C4⋊C4—1221no—
935C4⋊C4—1221no—
936C4⋊C4C23×D6111yescharacteristic
937C4⋊C4C23×D6111yescharacteristic
938C22⋊C4—21no—
939C22⋊C4—21no—
940C22⋊C4—21no—
941C22⋊C4—21no—
942C22⋊C4—21no—
943C22⋊C4—1221no—
944C22⋊C4—1221no—
945C22⋊C4—1221no—
946C22⋊C4—1221no—
947C22⋊C4—1221no—
948C22⋊C4—1221no—
949C22⋊C4—1221no—
950C22⋊C4—1221no—
951C22⋊C4—1221no—
952C22⋊C4—1221no—
953C22⋊C4—1221no—
954C22⋊C4—1221no—
955C22⋊C4—1221no—
956C42—21no—
957C42—611no—
958C42—611no—
959C42—611no—
960C42—611no—
961C42—611no—
962C42—611no—
963C42—611no—
964C42—611no—
965C42—611no—
966C42—611no—
967C42—611no—
968C42—611no—
969C42—1221no—
970C42—1221no—
971C42—1221no—
972C42—1221no—
973C42—1221no—
974C42D4×D6111yescharacteristic
975C42D4×D6111yescharacteristic
976C42C23×D6111yescharacteristic
977C42C23×D6111yescharacteristic
978C23—21no—
979C23—611no—
980C23—611no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1221no—
985C23C2×D4×D6111yescharacteristic
986Q8—24no—
987Q8—24no—
988Q8—22no—
989Q8—44no—
990Q8—1224no—
991Q8—1224no—
992Q8—1222no—
993Q8—2444no—
994Q8—2448no—
995Q8—2442no—
996Q8—2442no—
997Q8—2448no—
998D4—22no—
999D4—42no—
1000D4—1222no—
1001D4—2442no—
1002D4—2442no—
1003D4—2442no—
1004D4—2442no—
1005D4—2442no—
1006D4—2442no—
1007D4—2442no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—24no—
1015C2×C4—44no—
1016C2×C4—42no—
1017C2×C4—614no—
1018C2×C4—611no—
1019C2×C4—611no—
1020C2×C4—611no—
1021C2×C4—611no—
1022C2×C4—614no—
1023C2×C4—614no—
1024C2×C4—611no—
1025C2×C4—611no—
1026C2×C4—1222no—
1027C2×C4—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1221no—
1039C2×C4—1221no—
1040C2×C4—1221no—
1041C2×C4—1224no—
1042C2×C4—2442no—
1043C2×C4—2442no—
1044C2×C4—2448no—
1045C2×C4—2448no—
1046C2×C4—2442no—
1047C2×C4—2442no—
1048C2×C4—2444no—
1049C2×C4—2442no—
1050C2×C4C2×D4×D6111yescharacteristic
1051C2×C4C2×D4×D6111yescharacteristic
1052C2×C4C2×D4×D6111yescharacteristic
1053C2×C4C2×D4×D6111yescharacteristic
1054C2×C4C2×D4×D6111yescharacteristic
1055C2×C4C24×D6111yescharacteristic
1056C8—24no—
1057C8—1224no—
1058C22—21no—
1059C22—21no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—612no—
1064C22—612no—
1065C22—1228no—
1066C22—1221no—
1067C22—1221no—
1068C22—1221no—
1069C22—1221no—
1070C22—2441no—
1071C22—2441no—
1072C22—2441no—
1073C22#137×D6112yes—
1074C22C22×D4×D6111yescharacteristic
1075C4—21no—
1076C4—21no—
1077C4—21no—
1078C4—21no—
1079C4—41no—
1080C4—41no—
1081C4—44no—
1082C4—41no—
1083C4—612no—
1084C4—612no—
1085C4—612no—
1086C4—612no—
1087C4—1221no—
1088C4—1221no—
1089C4—2441no—
1090C4—2441no—
1091C4—2444no—
1092C4—2441no—
1093C4#137×D6112yes—
1094C4H(5,𝔽2)×D6112yes—
1095C2—22no—
1096C2—81no—
1097C2—1222no—
1098C2—1222no—
1099C2—4881no—
1100C2#535×D6111yescharacteristic
1101C2C2×#137×D6111yescharacteristic
1102C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3218C2
socleC22×C61C23×D4
prime radical#21459113C2
hypercenter#3218D61
hypocenterC61#60800
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D61C2semidirect
3. #21456848C2semidirect
4. #21456847C2semidirect
5. #21456846C2semidirect
6. #21456843C2semidirect
7. #21456842C2semidirect
8. #21456766C2semidirect
9. #21456765C2semidirect
10. #21456743C2semidirect
11. #21456742C2semidirect
12. #21456275C2semidirect
13. #21456198C2semidirect
14. #21455303C2semidirect
15. #21455301C2semidirect
16. #21455054C2semidirect
17. #21455050C2semidirect
18. #21454449C2semidirect
19. C61×#3218C2semidirect
59. #16840157C22semidirect
60. #16840156C22semidirect
61. #16840154C22semidirect
62. #16840140C22semidirect
63. #16840133C22semidirect
64. #16840132C22semidirect
65. #16840131C22semidirect
66. #16840130C22semidirect
67. #16840111C22semidirect
68. #16840111C22semidirect
69. #16839973C22semidirect
70. #16839972C22semidirect
71. #16839971C22semidirect
72. #16839970C22semidirect
73. #16839969C22semidirect
74. #16839968C22semidirect
75. #16839967C22semidirect
76. #16839966C22semidirect
77. #16839965C22semidirect
78. #16839964C22semidirect
100. C61×#497C22semidirect
101. C61×#491C22semidirect
102. C61×#462C22semidirect
103. C61×#461C22semidirect
469. C2×Dic61#137semidirect
494. C4×D61#137semidirect
551. #3218D61semidirect
615. #497C2×D61semidirect
621. #491C2×D61semidirect
629. #462C2×D61semidirect
635. #461C2×D61semidirect
658. C61#60800semidirect

Maximal subgroups

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

subgroupindex
#214591132
C2×C4⋊Q8×D612
#214568482
#214568472
#214568462
#214568432
#214568422
#214567662
#214567652
#214567432
#214567422
#214562752
#214561982
#214553032
#214553012
#214550542
#214550502
#214544492
C61×#32182
#6080061