Finite Group Databasebeta

← #30625491

Subgroups — #30625491

Order 15616.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840842C211yesmaximal, characteristic, complemented
2D61⋊#568C211yesmaximal, characteristic, complemented
3#21462599C214yesmaximal, complemented
4#21462597C214yesmaximal, complemented
5#21462594C218yesmaximal, complemented
6#21462592C218yesmaximal, complemented
7D61⋊#430C211yesmaximal, characteristic, complemented
8C2×#16840761C211yesmaximal, characteristic, complemented
9D61⋊#421C211yesmaximal, characteristic, complemented
10#21462382C211yesmaximal, characteristic, complemented
11C2×#16840561C211yesmaximal, characteristic
12#16840842—22no—
13#16840842—22no—
14#16840842C2212yescomplemented
15#16840842C2214yescomplemented
16#16840842C2214yescomplemented
17#16840841—22no—
18#16840841C2214yescomplemented
19#16840840—22no—
20#16840840C2212yescomplemented
21C2×#14519865—22no—
22C2×#14519865C2214yescomplemented
23D61⋊#131—22no—
24D61⋊#131C2214yescomplemented
25C2×D61⋊M16—22no—
26C2×D61⋊M16—22no—
27C2×D61⋊M16C2211yescharacteristic
28C2×D61⋊M16C2211yescharacteristic
29C2×D61⋊M16C2211yescharacteristic
30C2×#14519856C2211yescharacteristic
31#16840808C22116yescomplemented
32#16840807C22116yescomplemented
33#16840806C22116yescomplemented
34#16840805C22116yescomplemented
35#16840777C2214yescomplemented
36#16840777C2214yescomplemented
37D61⋊#108C2214yescomplemented
38#16840761C2214yescomplemented
39#16840761C2214yescomplemented
40#16840761C2212yescomplemented
41#16840760C2212yescomplemented
42#16840759C2214yescomplemented
43C2×#14519842C2214yescomplemented
44D61⋊#104C2214yescomplemented
45#16840728C2214yescomplemented
46#16840725C2214yescomplemented
47M16×#6923C2214yescomplemented
48C22×#11758226C2211yescharacteristic
49C2×#41×D61C2211yescharacteristic
50#16840561C414yescomplemented
51#16840561C414yescomplemented
52#16840561C2214yes—
53#16840561C2214yes—
54C2×#14519809C412yescomplemented
55C2×#14519808C411yescharacteristic, complemented
56C2×#14519805C411yescharacteristic, complemented
57C2×#14519804C412yescomplemented
58C2×#14519802C411yescharacteristic, complemented
59C2×#14519800C2212yes—
60C2×#14519798C2212yes—
61C2×M16×D61C2211yescharacteristic
62C2×#137×C61C411yescharacteristic, complemented
63#14519865—24no—
64#14519865—28no—
65#14519865—28no—
66#14519865—28no—
67#14519865C23116yescomplemented
68#14519865C2318yescomplemented
69#14519864—28no—
70#14519864—28no—
71#14519864—24no—
72#14519864C2318yescomplemented
73C2×#11758213—24no—
74C2×#11758213—24no—
75C2×#11758213D412yes—
76C2×#11758213C2312yes—
77C2×#11758213C2312yes—
78D61⋊M16—21no—
79D61⋊M16—21no—
80D61⋊M16—21no—
81D61⋊M16—21no—
82D61⋊M16—24no—
83D61⋊M16—28no—
84D61⋊M16—28no—
85D61⋊M16—24no—
86D61⋊M16—24no—
87D61⋊M16D412yes—
88D61⋊M16D412yes—
89D61⋊M16C2312yes—
90D61⋊M16C2312yes—
91D61⋊M16C2312yes—
92D61⋊M16C2312yes—
93D61⋊M16C2312yes—
94D61⋊M16C2312yes—
95C2×#11758217—21no—
96C2×#11758217—21no—
97C2×#11758217—24no—
98C2×#11758217D412yes—
99C2×D61⋊C8—21no—
100C2×D61⋊C8—21no—
101C2×D61⋊C8—24no—
102C2×D61⋊C8—24no—
103C2×D61⋊C8C2312yes—
104#14519856—21no—
105#14519856—21no—
106#14519856C2312yes—
107#14519856C2312yes—
108C2×C4⋊#6923—21no—
109C2×C22⋊#6923—21no—
110C2×C4×#6923C2312yes—
111#14519848C2318yescomplemented
112#14519847C2318yescomplemented
113#14519842C2318yescomplemented
114#14519842C23116yescomplemented
115#14519841C2318yescomplemented
116#14519831C2318yescomplemented
117C8×#6923C2318yescomplemented
118C2×#11758226—21no—
119C2×#11758226—21no—
120C2×#11758226—21no—
121C2×#11758226—21no—
122C2×#11758226—21no—
123C2×#11758226—21no—
124C2×#11758226C2×C412yes—
125C2×#11758226C2×C412yes—
126C2×#11758226C2×C412yes—
127C2×#11758226C2312yes—
128C2×#11758226C2312yes—
129C2×#11758226C2311yescharacteristic
130C2×#11758226C2312yes—
131C2×#11758222—21no—
132C2×#11758222C2×C411yescharacteristic
133C2×#11758224—21no—
134C2×#11758224C2311yescharacteristic
135#41×D61—21no—
136#41×D61—21no—
137#41×D61—21no—
138#41×D61—21no—
139#41×D61C2×C412yes—
140#41×D61C2×C412yes—
141#41×D61C2312yes—
142#41×D61C2312yes—
143C2×Q8×D61C2×C411yescharacteristic
144C22×D244—21no—
145C22×D244C2×C411yescharacteristic
146C2×D4×D61—21no—
147C2×D4×D61C2×C411yescharacteristic
148C22×C4×D61—21no—
149C22×C4×D61—21no—
150C22×C4×D61C2311yescharacteristic
151#14519809C2×C418yes—
152#14519809C2×C418yescomplemented
153#14519808C2×C414yes—
154#14519808C2×C414yescomplemented
155#14519805C2×C414yes—
156#14519805C2×C414yescomplemented
157#14519804C2×C418yes—
158#14519804C2×C418yescomplemented
159#14519802C2×C414yes—
160#14519802C2×C414yescomplemented
161#14519800C2×C418yescomplemented
162#14519800C2318yes—
163#14519798C2×C418yescomplemented
164#14519798C2318yes—
165C2×#11758202C2×C412yescomplemented
166C2×#11758190C2×C412yescomplemented
167C2×#11758201C2×C412yescomplemented
168C2×#11758201C2×C412yescomplemented
169C2×D488C2×C412yescomplemented
170C2×#11758199C2×C412yescomplemented
171C2×#11758194C2×C411yescharacteristic
172C2×#11758189C2×C412yes—
173M16×D61C2×C412yes—
174M16×D61C2×C412yes—
175M16×D61C2312yes—
176M16×D61C2312yes—
177C2×C8×D61C2312yes—
178C2×#41×C61C2×C411yescharacteristic
179C22×Q8×C61C2×C411yescharacteristic
180#137×C61C2×C414yes—
181#137×C61C2×C414yescomplemented
182C2×Q16×C61C2×C412yescomplemented
183C2×SD16×C61C2×C412yescomplemented
184C2×M16×C61C2×C411yescharacteristic
185C23×D61—21no—
186C23×D61—21no—
187C23×D61#4111yescharacteristic
188C22×#6923—22no—
189#41×C61—21no—
190#41×C61—21no—
191#41×C61C22×C412yes—
192#41×C61C22×C412yes—
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61C22×C412yes—
197C2×Q8×C61C22×C412yes—
198C2×Q8×C61C22×C411yescharacteristic
199C2×Q8×C61C22×C412yes—
200C2×D4×C61—21no—
201C2×D4×C61C22×C411yescharacteristic
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C22×C411yescharacteristic
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C22×Dic61—21no—
209C22×Dic61C2×D411yescharacteristic
210#11758226—22no—
211#11758226—22no—
212#11758226—22no—
213#11758226—22no—
214#11758226—22no—
215#11758226—22no—
216#11758226—21no—
217#11758226—22no—
218#11758226—22no—
219#11758226—22no—
220#11758226—21no—
221#11758226—22no—
222#11758226—22no—
223#11758226—22no—
224#11758226C22×C414yes—
225#11758226C22×C414yes—
226#11758226C22×C412yes—
227#11758226C22×C414yes—
228#11758226C2412yes—
229#11758226C2414yes—
230Q8×D61—21no—
231Q8×D61—21no—
232Q8×D61C22×C412yes—
233Q8×D61C22×C412yes—
234#11758224—22no—
235#11758224—22no—
236#11758224—22no—
237#11758224—22no—
238#11758224—21no—
239#11758224—21no—
240#11758224C22×C412yes—
241#11758224C2412yes—
242D4×D61—22no—
243D4×D61—22no—
244D4×D61—22no—
245D4×D61—22no—
246D4×D61—21no—
247D4×D61—21no—
248D4×D61C22×C412yes—
249D4×D61C22×C412yes—
250#11758222—21no—
251#11758222—21no—
252#11758222—22no—
253#11758222—22no—
254#11758222—22no—
255#11758222—22no—
256#11758222C22×C412yes—
257#11758222C22×C412yes—
258C2×D244—22no—
259C2×D244—22no—
260C2×D244—22no—
261C2×D244—21no—
262C2×D244—22no—
263C2×D244—22no—
264C2×D244—22no—
265C2×D244—21no—
266C2×D244—21no—
267C2×D244—21no—
268C2×D244C22×C411yescharacteristic
269C2×D244C22×C412yes—
270C2×D244C22×C412yes—
271C2×D244C22×C412yes—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—22no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—21no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—22no—
281C2×C4×D61—22no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61C22×C411yescharacteristic
286C2×C4×D61C22×C411yescharacteristic
287C2×C4×D61C22×C411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61#4111yescharacteristic
292C2×C4×D61#4111yescharacteristic
293C2×C4×D61#4111yescharacteristic
294C2×C4×D61C2411yescharacteristic
295C2×C4×D61C2411yescharacteristic
296C2×C4×D61C2411yescharacteristic
297C2×Dic122—21no—
298C2×Dic122C22×C411yescharacteristic
299C22⋊#6923—22no—
300C22⋊#6923—22no—
301#11758217—22no—
302#11758217—22no—
303#11758217—22no—
304#11758217—22no—
305#11758217—28no—
306#11758217C2×D414yes—
307#11758217C2×D414yes—
308C2×#92420—22no—
309C2×#92420—22no—
310C2×#92420—28no—
311C2×#92420C2×D414yes—
312C4⋊#6923—22no—
313C4⋊#6923—22no—
314C4×#6923—22no—
315C4×#6923C2414yes—
316#11758213—22no—
317#11758213—22no—
318#11758213—28no—
319#11758213—216no—
320#11758213C2×D414yes—
321#11758213C2×D414yes—
322#11758213C2414yes—
323#11758213C2414yes—
324D61⋊C8—22no—
325D61⋊C8—22no—
326D61⋊C8—22no—
327D61⋊C8—22no—
328D61⋊C8—28no—
329D61⋊C8—216no—
330D61⋊C8C2×D414yes—
331D61⋊C8C2414yes—
332Q16×C61C22×C418yes—
333SD16×C61C22×C418yes—
334M16×C61C22×C412yes—
335M16×C61C22×C412yes—
336C2×C8×C61C22×C412yes—
337#11758202C22×C418yes—
338#11758201C22×C418yes—
339#11758201C22×C418yes—
340#11758199C22×C418yes—
341#11758194C22×C412yes—
342#11758194C22×C412yes—
343C2×#92418C22×C412yes—
344D488C22×C418yes—
345#11758190C22×C418yes—
346#11758189C22×C414yes—
347#11758189C22×C414yes—
348C8×D61C22×C414yes—
349C8×D61C2414yes—
350C23×C61—21no—
351C23×C61C4×D411yescharacteristic
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—21no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—81no—
359C22×D61—82no—
360C22×D61—82no—
361C22×D61C4×D411yescharacteristic
362C22×D61C4×D411yescharacteristic
363C22×D61C4×D411yescharacteristic
364C22×D61C2×#4111yescharacteristic
365C22×D61C2×#4111yescharacteristic
366C22×D61C2×#4111yescharacteristic
367C2×#6923—24no—
368C2×#6923—82no—
369Q8×C61—21no—
370Q8×C61—22no—
371Q8×C61—22no—
372Q8×C61—22no—
373Q8×C61C23×C412yes—
374Q8×C61C23×C414yes—
375D4×C61—22no—
376D4×C61—22no—
377D4×C61—21no—
378D4×C61C23×C412yes—
379C2×C4×C61—21no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61C4×D411yescharacteristic
386C2×C4×C61C4×D411yescharacteristic
387C2×C4×C61C4×D411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C2×C4×C61C23×C411yescharacteristic
391C22⋊D61—22no—
392C22⋊D61—22no—
393C22⋊D61—22no—
394C22⋊D61—22no—
395C22⋊D61—22no—
396C22⋊D61—22no—
397C2×Dic61—21no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61C4×D411yescharacteristic
401C2×Dic61C4×D411yescharacteristic
402C2×Dic61C4×D411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405C2×Dic61C22×D411yescharacteristic
406D244—24no—
407D244—24no—
408D244—24no—
409D244—22no—
410D244—24no—
411D244—22no—
412D244—22no—
413D244—22no—
414D244—22no—
415D244—21no—
416D244C23×C414yes—
417D244C23×C412yes—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—24no—
424C4×D61—24no—
425C4×D61—24no—
426C4×D61—22no—
427C4×D61—24no—
428C4×D61C4×D411yescharacteristic
429C4×D61C4×D411yescharacteristic
430C4×D61C4×D411yescharacteristic
431C4×D61C4×D411yescharacteristic
432C4×D61C4×D411yescharacteristic
433C4×D61C4×D411yescharacteristic
434C4×D61C23×C411yescharacteristic
435C4×D61C23×C411yescharacteristic
436C4×D61C23×C411yescharacteristic
437C4×D61C22×D411yescharacteristic
438C4×D61C22×D411yescharacteristic
439C4×D61C22×D411yescharacteristic
440C4×D61C2×#4111yescharacteristic
441C4×D61C2×#4111yescharacteristic
442C4×D61C2×#4111yescharacteristic
443C4×D61C2511yescharacteristic
444Dic122—21no—
445Dic122—22no—
446Dic122—22no—
447Dic122C23×C412yes—
448#92420—24no—
449#92420—24no—
450#92420C22×D418yes—
451C8×C61C23×C414yes—
452#92418C23×C414yes—
453#60182—611nomaximal, Sylow
454C22×C61—22no—
455C22×C61—41no—
456C22×C61—81no—
457C22×C61C2×C4×D411yescharacteristic
458C22×C61C2×C4×D411yescharacteristic
459C22×C61C2×C4×D411yescharacteristic
460C2×D61—24no—
461C2×D61—22no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—44no—
469C2×D61—44no—
470C2×D61—82no—
471C2×D61—82no—
472C2×D61—81no—
473C2×D61—82no—
474C2×D61C2×C4×D411yescharacteristic
475C2×D61C2×C4×D411yescharacteristic
476C2×D61C2×C4×D411yescharacteristic
477C2×D61C22×#4111yescharacteristic
478#6923—44no—
479C4×C61—22no—
480C4×C61—24no—
481C4×C61C2×C4×D411yescharacteristic
482C4×C61C2×C4×D411yescharacteristic
483C4×C61C2×C4×D411yescharacteristic
484C4×C61C24×C411yescharacteristic
485Dic61—22no—
486Dic61C2×C4×D411yescharacteristic
487Dic61C2×C4×D411yescharacteristic
488Dic61C2×C4×D411yescharacteristic
489Dic61C23×D411yescharacteristic
490C2×#575—611no—
491C2×#568—611no—
492C2×#568—611no—
493#2957—614no—
494#2957—614no—
495#2956—618no—
496#2955—618no—
497C2×#430—611no—
498C2×#421—611no—
499C2×#421—611no—
500#2873—611no—
501C2×C61—21no—
502C2×C61—21no—
503C2×C61—21no—
504C2×C61—42no—
505C2×C61C22×C4×D411yescharacteristic
506D61—21no—
507D61—21no—
508D61—21no—
509D61—21no—
510D61—44no—
511D61—42no—
512C22×#41—611no—
513C22×#41—611no—
514#575—614no—
515#575—614no—
516#575—614no—
517#575—614no—
518C2×#137—611no—
519C2×#137—612no—
520C2×#137#692311yescharacteristic, complemented
521C2×AGL(1,ℤ/8)—611no—
522C2×AGL(1,ℤ/8)—612no—
523C2×AGL(1,ℤ/8)—611no—
524C2×#135—612no—
525C2×#135—612no—
526#568—612no—
527#568—614no—
528#568—614no—
529#568—612no—
530#568—614no—
531#568—1222no—
532#568—1222no—
533#568—1222no—
534#568—1222no—
535C2×#131—614no—
536C2×#131—614no—
537C2×#131—1222no—
538C2×#131—1222no—
539C22×M16—611no—
540C22×M16—611no—
541C22×M16—611no—
542C22×M16—611no—
543C22×M16—1222no—
544C22×M16—1222no—
545C2×#117—611no—
546#444—6116no—
547#444—6116no—
548#443—6116no—
549#443—6116no—
550#430—614no—
551#430—614no—
552C2×#108—614no—
553#421—614no—
554#421—612no—
555#421—614no—
556#421—614no—
557#421—612no—
558C2×#104—614no—
559C2×#104—614no—
560#405—614no—
561#405—614no—
562C4×M16—614no—
563C61#6018211yescharacteristic, complemented, Sylow
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—612no—
567C2×#41—612no—
568C2×#41—612no—
569C2×#41—612no—
570C2×#41—612no—
571C2×#41—612no—
572C2×#41—611no—
573C2×#41—612no—
574C2×#41—612no—
575C2×#41—611no—
576C2×#41—611no—
577C2×#41—1221no—
578C2×#41—1221no—
579C2×#41—1221no—
580C2×#41—1221no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1221no—
585C2×#41—1221no—
586C2×#41—1221no—
587C2×#41—1221no—
588C2×#41—1221no—
589C2×#41C2×#692311yescharacteristic
590C22×Q8—611no—
591C22×Q8C2×#692311yescharacteristic
592C22×D4—611no—
593C22×D4—611no—
594C22×D4—1221no—
595C22×D4—1221no—
596C23×C4—611no—
597C23×C4—1221no—
598C23×C4—1221no—
599#137—614no—
600#137—614no—
601#137—618no—
602#137—618no—
603#137C2×#692314yes—
604#137C2×#692314yescomplemented
605AGL(1,ℤ/8)—614no—
606AGL(1,ℤ/8)—614no—
607AGL(1,ℤ/8)—618no—
608AGL(1,ℤ/8)—618no—
609AGL(1,ℤ/8)—614no—
610AGL(1,ℤ/8)—614no—
611#135—618no—
612#135—618no—
613#135—618no—
614#135—618no—
615C2×Q16—612no—
616C2×Q16C2×#692312yescomplemented
617C2×SD16—612no—
618C2×SD16—612no—
619C2×SD16—612no—
620C2×SD16C2×#692312yescomplemented
621C2×D8—612no—
622C2×D8—612no—
623#131—618no—
624#131—618no—
625#131—6116no—
626#131—1228no—
627#131—1228no—
628#131—1228no—
629#131—1224no—
630#131—1228no—
631#131—1224no—
632#131—1228no—
633C2×M16—612no—
634C2×M16—612no—
635C2×M16—612no—
636C2×M16—612no—
637C2×M16—612no—
638C2×M16—612no—
639C2×M16—611no—
640C2×M16—612no—
641C2×M16—612no—
642C2×M16—612no—
643C2×M16—612no—
644C2×M16—612no—
645C2×M16—612no—
646C2×M16—612no—
647C2×M16—612no—
648C2×M16—612no—
649C2×M16—612no—
650C2×M16—612no—
651C2×M16—1224no—
652C2×M16—1224no—
653C2×M16—1224no—
654C2×M16—1224no—
655C2×M16—1228no—
656C2×M16—1224no—
657C2×M16—1228no—
658C2×M16—1224no—
659C2×M16—1221no—
660C2×M16—1221no—
661C2×M16—1221no—
662C2×M16—1221no—
663C2×M16—1221no—
664C2×M16—1221no—
665C2×M16C2×#692311yescharacteristic
666C22×C8—612no—
667C22×C8—612no—
668C22×C8—1224no—
669C22×C8—1224no—
670C22×C8—1221no—
671C22×C8—1221no—
672#117—612no—
673#117—612no—
674#117—1221no—
675#117—1221no—
676C2×C4⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C42—612no—
679#108—618no—
680#108—618no—
681#104—618no—
682#104—618no—
683#104—6116no—
684#97—618no—
685C4×C8—618no—
686C24—611no—
687C24—1221no—
688C24—1221no—
689#41—21no—
690#41—21no—
691#41—612no—
692#41—614no—
693#41—612no—
694#41—614no—
695#41—614no—
696#41—614no—
697#41—612no—
698#41—612no—
699#41—612no—
700#41—612no—
701#41—1222no—
702#41—1222no—
703#41—1222no—
704#41—1222no—
705#41—1222no—
706#41—1222no—
707#41—1221no—
708#41—1222no—
709#41—1222no—
710#41—1221no—
711#41—1222no—
712#41—1222no—
713#41—1221no—
714#41—1222no—
715#41—1222no—
716#41—1222no—
717#41—1222no—
718#41—1222no—
719#41—1222no—
720#41—1222no—
721#41—1222no—
722#41—1222no—
723#41—1222no—
724#41—1221no—
725#41—1221no—
726#41—1221no—
727#41C22×#692312yes—
728#41C22×#692312yes—
729C2×Q8—21no—
730C2×Q8—21no—
731C2×Q8—21no—
732C2×Q8—612no—
733C2×Q8—612no—
734C2×Q8—611no—
735C2×Q8—1221no—
736C2×Q8—1221no—
737C2×Q8—1221no—
738C2×Q8C22×#692311yescharacteristic
739C2×Q8C22×#692312yes—
740C2×Q8C22×#692312yes—
741C2×Q8C22×#692312yes—
742C2×D4—21no—
743C2×D4—612no—
744C2×D4—612no—
745C2×D4—612no—
746C2×D4—611no—
747C2×D4—612no—
748C2×D4—612no—
749C2×D4—1221no—
750C2×D4—1222no—
751C2×D4—1222no—
752C2×D4—1222no—
753C2×D4—1222no—
754C2×D4—1222no—
755C2×D4—1222no—
756C2×D4—1221no—
757C2×D4—1221no—
758C2×D4—1221no—
759C2×D4—1222no—
760C2×D4—1222no—
761C2×D4—1222no—
762C2×D4—1222no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4C22×#692311yescharacteristic
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—1222no—
785C22×C4—1222no—
786C22×C4—1221no—
787C22×C4—1222no—
788C22×C4—1222no—
789C22×C4—1222no—
790C22×C4—1222no—
791C22×C4—1222no—
792C22×C4—1222no—
793C22×C4—1222no—
794C22×C4—1222no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1222no—
799C22×C4C22×#692311yescharacteristic
800Q16—618no—
801Q16C22×#692318yes—
802SD16—618no—
803SD16—618no—
804SD16—618no—
805SD16C22×#692318yes—
806D8—618no—
807D8—618no—
808M16—614no—
809M16—614no—
810M16—614no—
811M16—614no—
812M16—612no—
813M16—612no—
814M16—614no—
815M16—614no—
816M16—614no—
817M16—614no—
818M16—1228no—
819M16—12216no—
820M16—1228no—
821M16—1222no—
822M16—1222no—
823M16—1222no—
824M16—1222no—
825M16—1222no—
826M16—1222no—
827M16C22×#692312yes—
828M16C22×#692312yes—
829C2×C8—614no—
830C2×C8—614no—
831C2×C8—614no—
832C2×C8—612no—
833C2×C8—614no—
834C2×C8—614no—
835C2×C8—1228no—
836C2×C8—12216no—
837C2×C8—1228no—
838C2×C8—1222no—
839C2×C8—1222no—
840C2×C8—1222no—
841C2×C8—1222no—
842C2×C8—1222no—
843C2×C8—1222no—
844C2×C8C22×#692312yes—
845C4⋊C4—1222no—
846C4⋊C4—1222no—
847C22⋊C4—1222no—
848C22⋊C4—1222no—
849C42—614no—
850C42—1222no—
851C23—21no—
852C23—611no—
853C23—611no—
854C23—611no—
855C23—611no—
856C23—611no—
857C23—611no—
858C23—1222no—
859C23—1222no—
860C23—1222no—
861C23—1221no—
862C23—1222no—
863C23—1222no—
864C23—4882no—
865C23—4881no—
866C23—4882no—
867C23D4×#692311yescharacteristic
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—21no—
872Q8—612no—
873Q8—1222no—
874Q8—1222no—
875Q8—1221no—
876Q8C23×#692312yes—
877Q8C23×#692314yes—
878D4—22no—
879D4—22no—
880D4—21no—
881D4—614no—
882D4—612no—
883D4—1222no—
884D4—1222no—
885D4—1224no—
886D4—1224no—
887D4—1224no—
888D4—1224no—
889D4—1222no—
890D4—1222no—
891D4—1222no—
892D4—1222no—
893D4—1222no—
894D4—1222no—
895D4—1222no—
896D4—1222no—
897D4—1222no—
898D4—1221no—
899D4C23×#692312yes—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—611no—
919C2×C4—611no—
920C2×C4—611no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—611no—
927C2×C4—611no—
928C2×C4—1222no—
929C2×C4—1224no—
930C2×C4—1222no—
931C2×C4—1224no—
932C2×C4—1224no—
933C2×C4—1224no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1221no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1224no—
942C2×C4—4882no—
943C2×C4D4×#692311yescharacteristic
944C2×C4D4×#692311yescharacteristic
945C2×C4D4×#692311yescharacteristic
946C2×C4C23×#692311yescharacteristic
947C2×C4C23×#692311yescharacteristic
948C2×C4C23×#692311yescharacteristic
949C8—618no—
950C8—614no—
951C8—1224no—
952C8—1224no—
953C8C23×#692314yes—
954C22—22no—
955C22—41no—
956C22—81no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—1224no—
962C22—1222no—
963C22—4882no—
964C22—4881no—
965C22—4882no—
966C22—4882no—
967C22—2441no—
968C22—2441no—
969C22—2441no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2444no—
974C22—2444no—
975C22C2×D4×#692311yescharacteristic
976C22C2×D4×#692311yescharacteristic
977C22C2×D4×#692311yescharacteristic
978C4—22no—
979C4—24no—
980C4—611no—
981C4—611no—
982C4—611no—
983C4—611no—
984C4—1222no—
985C4—2444no—
986C4C2×D4×#692311yescharacteristic
987C4C2×D4×#692311yescharacteristic
988C4C2×D4×#692311yescharacteristic
989C4C24×#692311yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—42no—
994C2—1221no—
995C2—1221no—
996C2—1221no—
997C2—1221no—
998C2—2444no—
999C2—2442no—
1000C2C22×D4×#692311yescharacteristic
subgroupG/H
centerC2C22×D4×#6923
commutatorC4×C61C24×C4
FrattiniC4C24×#6923
FittingC2×#137×C61C4
socleC2×C61C22×C4×D4
prime radicalC2×#16840561C2
cosocleC4×D61C25
hypercenterC2×#137#6923
hypocenterC61#60182
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#16840842C2semidirect
2. D61⋊#568C2semidirect
3. #21462599C2semidirect
4. #21462597C2semidirect
5. #21462594C2semidirect
6. #21462592C2semidirect
7. D61⋊#430C2semidirect
8. C2×#16840761C2semidirect
9. D61⋊#421C2semidirect
10. #21462382C2semidirect
14. #16840842C22semidirect
15. #16840842C22semidirect
16. #16840842C22semidirect
18. #16840841C22semidirect
20. #16840840C22semidirect
22. C2×#14519865C22semidirect
24. D61⋊#131C22semidirect
31. #16840808C22semidirect
32. #16840807C22semidirect
33. #16840806C22semidirect
34. #16840805C22semidirect
35. #16840777C22semidirect
36. #16840777C22semidirect
37. D61⋊#108C22semidirect
38. #16840761C22semidirect
39. #16840761C22semidirect
40. #16840761C22semidirect
41. #16840760C22semidirect
42. #16840759C22semidirect
43. C2×#14519842C22semidirect
44. D61⋊#104C22semidirect
45. #16840728C22semidirect
46. #16840725C22semidirect
47. M16×#6923C22semidirect
50. #16840561C4semidirect
51. #16840561C4semidirect
54. C2×#14519809C4semidirect
55. C2×#14519808C4semidirect
56. C2×#14519805C4semidirect
57. C2×#14519804C4semidirect
58. C2×#14519802C4semidirect
62. C2×#137×C61C4semidirect
67. #14519865C23semidirect
68. #14519865C23semidirect
72. #14519864C23semidirect
111. #14519848C23semidirect
112. #14519847C23semidirect
113. #14519842C23semidirect
114. #14519842C23semidirect
115. #14519841C23semidirect
116. #14519831C23semidirect
117. C8×#6923C23semidirect
152. #14519809C2×C4semidirect
154. #14519808C2×C4semidirect
156. #14519805C2×C4semidirect
158. #14519804C2×C4semidirect
160. #14519802C2×C4semidirect
161. #14519800C2×C4semidirect
163. #14519798C2×C4semidirect
165. C2×#11758202C2×C4semidirect
166. C2×#11758190C2×C4semidirect
167. C2×#11758201C2×C4semidirect
168. C2×#11758201C2×C4semidirect
169. C2×D488C2×C4semidirect
170. C2×#11758199C2×C4semidirect
181. #137×C61C2×C4semidirect
182. C2×Q16×C61C2×C4semidirect
183. C2×SD16×C61C2×C4semidirect
520. C2×#137#6923semidirect
563. C61#60182semidirect
604. #137C2×#6923semidirect
616. C2×Q16C2×#6923semidirect
620. C2×SD16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408422
D61⋊#5682
#214625992
#214625972
#214625942
#214625922
D61⋊#4302
C2×#168407612
D61⋊#4212
#214623822
C2×#168405612
#6018261