Finite Group Databasebeta

← #30547436

Subgroups — #30547436

Order 15616.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic, complemented
2C2×#16840560C211yesmaximal, characteristic, complemented
3C2×#16840560C211yesmaximal, characteristic, complemented
4C2×#16840528C211yesmaximal, characteristic, complemented
5#21455559C214yesmaximal, complemented
6#21455555C214yesmaximal, complemented
7#21455550C214yesmaximal, complemented
8#21455546C214yesmaximal, complemented
9#21455538C218yesmaximal, complemented
10C2×#16839810C211yesmaximal, characteristic, complemented
11C2×#16839744C211yesmaximal, characteristic, complemented
12C2×C61×#413C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C22×#11758222C2211yescharacteristic
15#16840562—22no—
16#16840562—22no—
17#16840562C2214yes—
18#16840562C2214yescomplemented
19#16840560—22no—
20#16840560—22no—
21#16840560—22no—
22#16840560—22no—
23#16840560—22no—
24#16840560—22no—
25#16840560C2214yes—
26#16840560C2214yescomplemented
27C2×#14519810—21no—
28C2×#14519810C2212yescomplemented
29C2×#14519808C2212yescomplemented
30C2×#14519808C2212yescomplemented
31C2×#14519807—21no—
32C2×#14519807C2212yescomplemented
33C2×#14519805—21no—
34C2×#14519805C2212yescomplemented
35C2×#14519803C2212yescomplemented
36C2×#14519803C2212yescomplemented
37C2×#14519802—21no—
38C2×#14519802C2212yescomplemented
39C2×#14519799—22no—
40C2×#14519797—22no—
41C2×#14519797C2214yescomplemented
42#16840528—22no—
43#16840528—22no—
44#16840528C2214yescomplemented
45#16840528C2214yescomplemented
46C2×#14519785C2214yescomplemented
47C2×#14519783—22no—
48C22×#11758194C2211yescharacteristic
49C22×#11758194C2211yescharacteristic
50C2×M16×D61—22no—
51#16840036C22116yescomplemented
52#16840031C22116yescomplemented
53#16840028C22116yescomplemented
54#16840024C22116yescomplemented
55#16839810C2214yescomplemented
56#16839810C2214yescomplemented
57C2×#14519712C2214yescomplemented
58#16839744C2214yescomplemented
59#16839744C2214yescomplemented
60C2×#14519695C2212yescomplemented
61C2×#14519693C2212yescomplemented
62C22×#41×C61C2211yescharacteristic
63C22×M16×C61C2211yescharacteristic
64C22×M16×C61C2211yescharacteristic
65C61×#413C2214yescomplemented
66C61×#413C2214yescomplemented
67C2×#101×C61C2212yescomplemented
68C2×#100×C61C2212yescomplemented
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—21no—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—21no—
82C2×#11758222—21no—
83C2×#11758222—21no—
84C2×#11758222—21no—
85C2×#11758222D412yes—
86C2×#11758222D412yes—
87C2×#11758222D412yes—
88C2×#11758222C2312yes—
89C2×#11758222C2312yes—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C2×#11758222C2312yes—
93C22×Dic122D411yescharacteristic
94C22×Dic122C2311yescharacteristic
95C22×D244D411yescharacteristic
96C22×D244C2311yescharacteristic
97C22×C22⋊D61—21no—
98C22×C22⋊D61—21no—
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101#14519810—24no—
102#14519810—24no—
103#14519810—24no—
104#14519810C2318yes—
105#14519808—24no—
106#14519808—24no—
107#14519808—24no—
108#14519808C2318yes—
109#14519807—24no—
110#14519807—24no—
111#14519807—24no—
112#14519807—24no—
113#14519805—24no—
114#14519805—24no—
115#14519805—24no—
116#14519805C2318yes—
117#14519803—24no—
118#14519803—24no—
119#14519803—24no—
120#14519803C2318yes—
121#14519802—24no—
122#14519802—24no—
123#14519802—24no—
124#14519802—24no—
125#14519799—28no—
126#14519799—28no—
127#14519797—28no—
128#14519797—28no—
129#14519797—28no—
130#14519797—28no—
131C2×Dic244—22no—
132C2×#11758202—22no—
133C2×#11758202C2314yescomplemented
134C2×#11758190—22no—
135C2×#11758190—22no—
136C2×#11758200—22no—
137C2×#11758200C2314yescomplemented
138C2×#11758201—22no—
139C2×#11758201C2314yescomplemented
140C2×D488—22no—
141C2×#11758199—22no—
142C2×#11758199C2314yescomplemented
143#14519785—28no—
144#14519785C23116yes—
145#14519783—28no—
146#14519783—28no—
147C2×#11758194—21no—
148C2×#11758194—21no—
149C2×#11758194—21no—
150C2×#11758194D412yes—
151C2×#11758194D412yes—
152C2×#11758194D412yes—
153C2×#11758194D412yes—
154C2×#11758194C2312yes—
155C2×#11758194C2312yes—
156C2×#11758194C2312yes—
157C2×#11758194C2312yes—
158C2×#11758194C2312yes—
159C2×#11758189—24no—
160M16×D61—28no—
161M16×D61—28no—
162C22×#92418—21no—
163C22×#92418C2312yes—
164C2×C8×D61—24no—
165#14519712C23116yescomplemented
166#14519695C2318yescomplemented
167#14519693C2318yescomplemented
168C2×#41×C61—21no—
169C2×#41×C61—21no—
170C2×#41×C61—21no—
171C2×#41×C61—21no—
172C2×#41×C61—21no—
173C2×#41×C61—21no—
174C2×#41×C61—21no—
175C2×#41×C61—21no—
176C2×#41×C61—21no—
177C2×#41×C61—21no—
178C2×#41×C61C2312yes—
179C2×#41×C61C2312yes—
180C22×Q8×C61C2311yescharacteristic
181C22×D4×C61—21no—
182C22×D4×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61C2311yescharacteristic
185C2×M16×C61—21no—
186C2×M16×C61—21no—
187C2×M16×C61—21no—
188C2×M16×C61—21no—
189C2×M16×C61—21no—
190C2×M16×C61—21no—
191C2×M16×C61C2312yes—
192C2×M16×C61C2312yes—
193C2×M16×C61C2312yes—
194C2×M16×C61C2312yes—
195C2×M16×C61C2312yes—
196C2×M16×C61C2312yes—
197C22×C8×C61—21no—
198C22×C8×C61—21no—
199#101×C61C2318yescomplemented
200#100×C61C2318yescomplemented
201C24×C61—21no—
202C24×C61#4111yescharacteristic
203C23×D61—21no—
204C23×D61—21no—
205#41×C61—22no—
206#41×C61—22no—
207#41×C61—22no—
208#41×C61—22no—
209#41×C61—22no—
210#41×C61—22no—
211#41×C61—22no—
212#41×C61—22no—
213#41×C61—41no—
214#41×C61—41no—
215#41×C61—41no—
216#41×C61—41no—
217#41×C61—41no—
218#41×C61—41no—
219#41×C61—41no—
220#41×C61—41no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—21no—
226C2×Q8×C61C2412yes—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—41no—
235C2×D4×C61—41no—
236C2×D4×C61—41no—
237C2×D4×C61—41no—
238C2×D4×C61C2412yes—
239C22×C4×C61—21no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—41no—
243C22×C4×C61—41no—
244C22×C4×C61—41no—
245C22×C4×C61—41no—
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61#4111yescharacteristic
255C22×C4×C61#4111yescharacteristic
256C22×C4×C61#4111yescharacteristic
257C22×C4×C61C2411yescharacteristic
258C22×C4×C61C2411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C2×C22⋊D61—22no—
261C2×C22⋊D61—22no—
262C2×C22⋊D61—22no—
263C2×C22⋊D61—22no—
264C2×C22⋊D61—22no—
265C2×C22⋊D61—22no—
266C2×C22⋊D61—22no—
267C2×C22⋊D61—22no—
268C2×C22⋊D61—41no—
269C2×C22⋊D61—41no—
270C2×C22⋊D61—41no—
271C2×C22⋊D61—41no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274#11758222—22no—
275#11758222—22no—
276#11758222—22no—
277#11758222—22no—
278#11758222—22no—
279#11758222—22no—
280#11758222—22no—
281#11758222—22no—
282#11758222—22no—
283#11758222—22no—
284#11758222—22no—
285#11758222—22no—
286#11758222—22no—
287#11758222—22no—
288#11758222—22no—
289#11758222—22no—
290#11758222—22no—
291#11758222—22no—
292#11758222—22no—
293#11758222—22no—
294#11758222—41no—
295#11758222—41no—
296#11758222—41no—
297#11758222—41no—
298#11758222—41no—
299#11758222—41no—
300#11758222—41no—
301#11758222—41no—
302#11758222C2×D414yes—
303#11758222C2×D414yes—
304#11758222C2×D414yes—
305#11758222C2414yes—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—21no—
311C2×D244—21no—
312C2×D244—21no—
313C2×D244—21no—
314C2×D244C2×D412yes—
315C2×D244C2×D412yes—
316C2×D244C2×D412yes—
317C2×D244C2412yes—
318C2×C4×D61—22no—
319C2×C4×D61—22no—
320C2×C4×D61—22no—
321C2×C4×D61—22no—
322C2×C4×D61—22no—
323C2×C4×D61—22no—
324C2×C4×D61—22no—
325C2×C4×D61—22no—
326C2×C4×D61—41no—
327C2×C4×D61—41no—
328C2×C4×D61—41no—
329C2×C4×D61—41no—
330C2×Dic122—21no—
331C2×Dic122—21no—
332C2×Dic122—21no—
333C2×Dic122—21no—
334C2×Dic122—21no—
335C2×Dic122—21no—
336C2×Dic122—21no—
337C2×Dic122—21no—
338C2×Dic122C2×D412yes—
339C2×Dic122C2×D412yes—
340C2×Dic122C2×D412yes—
341C2×Dic122C2412yes—
342M16×C61—22no—
343M16×C61—22no—
344M16×C61—22no—
345M16×C61—22no—
346M16×C61—22no—
347M16×C61—22no—
348M16×C61C2414yes—
349M16×C61C2414yes—
350C2×C8×C61—22no—
351C2×C8×C61—22no—
352C2×C8×C61—22no—
353C2×C8×C61—22no—
354C2×C8×C61—22no—
355C2×C8×C61—22no—
356#11758202—28no—
357#11758202—28no—
358#11758201—28no—
359#11758201—28no—
360#11758200—28no—
361#11758200—28no—
362#11758199—28no—
363#11758199—28no—
364#11758194—22no—
365#11758194—22no—
366#11758194—22no—
367#11758194C2×D414yes—
368#11758194C2×D414yes—
369#11758194C2×D414yes—
370#11758194C2×D414yes—
371#11758194C2414yes—
372C2×#92418—22no—
373C2×#92418—22no—
374C2×#92418—22no—
375C2×#92418C2×D414yes—
376C2×#92418C2×D414yes—
377C2×#92418C2414yes—
378Dic244—28no—
379D488—28no—
380#11758190—28no—
381#11758190—28no—
382#11758189—216no—
383C8×D61—216no—
384C23×C61—22no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—81no—
388C23×C61—82no—
389C23×C61#12111yescharacteristic
390C23×C61#12111yescharacteristic
391C23×C61#12111yescharacteristic
392C23×C61#12111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61C2×#4111yescharacteristic
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—82no—
403C22×D61—82no—
404Q8×C61—22no—
405Q8×C61—22no—
406Q8×C61—41no—
407Q8×C61—41no—
408D4×C61—22no—
409D4×C61—22no—
410D4×C61—42no—
411D4×C61—42no—
412D4×C61—42no—
413D4×C61—42no—
414D4×C61—41no—
415D4×C61—41no—
416C2×C4×C61—22no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61#12111yescharacteristic
424C2×C4×C61#12111yescharacteristic
425C2×C4×C61#12111yescharacteristic
426C2×C4×C61#12111yescharacteristic
427C2×C4×C61#12111yescharacteristic
428C2×C4×C61#12111yescharacteristic
429C2×C4×C61#12111yescharacteristic
430C2×C4×C61#12111yescharacteristic
431C2×C4×C61#12111yescharacteristic
432C2×C4×C61#12111yescharacteristic
433C2×C4×C61#12111yescharacteristic
434C2×C4×C61#12111yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C22×D411yescharacteristic
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61C22×D411yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61C2×#4111yescharacteristic
448C2×C4×C61C2×#4111yescharacteristic
449C2×C4×C61C2×#4111yescharacteristic
450C2×C4×C61C2511yescharacteristic
451C22⋊D61—24no—
452C22⋊D61—24no—
453C22⋊D61—24no—
454C22⋊D61—24no—
455C22⋊D61—42no—
456C22⋊D61—42no—
457C22⋊D61—42no—
458C22⋊D61—42no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465D244—22no—
466D244—22no—
467D244—22no—
468D244—22no—
469D244—22no—
470D244—41no—
471D244—41no—
472D244C22×D414yes—
473C4×D61—24no—
474C4×D61—24no—
475C4×D61—24no—
476C4×D61—24no—
477C4×D61—42no—
478C4×D61—42no—
479C4×D61—42no—
480C4×D61—42no—
481Dic122—22no—
482Dic122—22no—
483Dic122—22no—
484Dic122—22no—
485Dic122—22no—
486Dic122—41no—
487Dic122—41no—
488Dic122C22×D414yes—
489C8×C61—24no—
490C8×C61—24no—
491#92418—24no—
492#92418C22×D418yes—
493#60469—611nomaximal, Sylow
494C22×C61—41no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—42no—
502C22×C61—82no—
503C22×C61—82no—
504C22×C61—82no—
505C22×C61C2×#12111yescharacteristic
506C22×C61C2×#12111yescharacteristic
507C22×C61C2×#12111yescharacteristic
508C22×C61C2×#12111yescharacteristic
509C22×C61C2×#12111yescharacteristic
510C22×C61C2×#12111yescharacteristic
511C22×C61C22×#4111yescharacteristic
512C2×D61—24no—
513C2×D61—44no—
514C2×D61—42no—
515C2×D61—82no—
516C2×D61—82no—
517C2×D61—82no—
518C2×D61—82no—
519C2×D61—82no—
520C4×C61—42no—
521C4×C61C2×#12111yescharacteristic
522C4×C61C2×#12111yescharacteristic
523C4×C61C2×#12111yescharacteristic
524C4×C61C2×#12111yescharacteristic
525C4×C61C2×#12111yescharacteristic
526C4×C61C2×#12111yescharacteristic
527C4×C61C23×D411yescharacteristic
528C4×C61C23×D411yescharacteristic
529Dic61—24no—
530Dic61—42no—
531C2×#575—611no—
532C2×#575—611no—
533C2×#575—611no—
534C2×#568—611no—
535#3069—614no—
536#3069—614no—
537#3068—614no—
538#3068—614no—
539#3067—618no—
540C2×#430—611no—
541C2×#413—611no—
542C2×#413D6111yescharacteristic, complemented
543C2×C61—21no—
544C2×C61—21no—
545C2×C61—21no—
546C2×C61—21no—
547C2×C61—21no—
548C2×C61—21no—
549C2×C61—21no—
550C2×C61—82no—
551C2×C61C22×#12111yescharacteristic
552D61—44no—
553D61—82no—
554C22×#41—611no—
555C22×#41—611no—
556C22×#41C2×D6111yescharacteristic
557#575—614no—
558#575—614no—
559#575—614no—
560#575—614no—
561#575—1222no—
562#575—1222no—
563#575—1222no—
564#575—1222no—
565#575—1222no—
566#575—1222no—
567#575—1222no—
568#575—1222no—
569C2×#137—612no—
570C2×#137—612no—
571C2×#137—612no—
572C2×#137—612no—
573C2×#137—1221no—
574C2×#137—1221no—
575C2×AGL(1,ℤ/8)—612no—
576C2×AGL(1,ℤ/8)—612no—
577C2×AGL(1,ℤ/8)—612no—
578C2×AGL(1,ℤ/8)—612no—
579C2×AGL(1,ℤ/8)—1221no—
580C2×AGL(1,ℤ/8)—1221no—
581C2×#135—614no—
582C2×#135—1222no—
583C2×#135—1222no—
584#568—614no—
585#568—614no—
586#568—1222no—
587#568—1222no—
588C2×#131—614no—
589C2×#131—1222no—
590C22×M16—611no—
591C22×M16—611no—
592C22×M16—1222no—
593C22×M16C2×D6111yescharacteristic
594C22×M16C2×D6111yescharacteristic
595#473—6116no—
596#472—6116no—
597#471—6116no—
598#471—6116no—
599#430—614no—
600#430—614no—
601C2×#108—614no—
602#413—614no—
603#413—614no—
604#413C2×D6114yescomplemented
605#413C2×D6114yescomplemented
606C2×#101—612no—
607C2×#101C2×D6112yescomplemented
608C2×#100—612no—
609C2×#100C2×D6112yescomplemented
610C61#6046911yescharacteristic, complemented, Sylow
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—21no—
619C2×#41—21no—
620C2×#41—21no—
621C2×#41—612no—
622C2×#41—612no—
623C2×#41—612no—
624C2×#41—612no—
625C2×#41—612no—
626C2×#41—612no—
627C2×#41—612no—
628C2×#41—612no—
629C2×#41—1221no—
630C2×#41—1221no—
631C2×#41—1221no—
632C2×#41—1221no—
633C2×#41—1221no—
634C2×#41—1221no—
635C2×#41—1221no—
636C2×#41—1221no—
637C2×#41—1221no—
638C2×#41—1221no—
639C2×#41—1221no—
640C2×#41—1221no—
641C2×#41—1221no—
642C2×#41—1221no—
643C2×#41—1221no—
644C2×#41—1221no—
645C2×#41C22×D6112yes—
646C2×#41C22×D6112yes—
647C22×Q8—611no—
648C22×Q8—611no—
649C22×Q8C22×D6111yescharacteristic
650C22×D4—21no—
651C22×D4—611no—
652C22×D4—611no—
653C22×D4—1221no—
654C22×D4—1221no—
655C22×D4C22×D6111yescharacteristic
656C23×C4—21no—
657C23×C4—1221no—
658C23×C4—1221no—
659C23×C4C22×D6111yescharacteristic
660#137—618no—
661#137—618no—
662#137—1224no—
663#137—1224no—
664#137—1224no—
665#137—1224no—
666#137—1224no—
667#137—1224no—
668#137—1224no—
669#137—1224no—
670#137—1224no—
671#137—1224no—
672AGL(1,ℤ/8)—618no—
673AGL(1,ℤ/8)—618no—
674AGL(1,ℤ/8)—1224no—
675AGL(1,ℤ/8)—1224no—
676AGL(1,ℤ/8)—1224no—
677AGL(1,ℤ/8)—1224no—
678AGL(1,ℤ/8)—1224no—
679AGL(1,ℤ/8)—1224no—
680AGL(1,ℤ/8)—1224no—
681AGL(1,ℤ/8)—1224no—
682AGL(1,ℤ/8)—1224no—
683AGL(1,ℤ/8)—1224no—
684#135—1228no—
685#135—1228no—
686#135—1228no—
687#135—1228no—
688#135—1228no—
689#135—1228no—
690C2×Q16—614no—
691C2×Q16—1222no—
692C2×Q16—1222no—
693C2×SD16—614no—
694C2×SD16—614no—
695C2×SD16—1222no—
696C2×SD16—1222no—
697C2×SD16—1222no—
698C2×SD16—1222no—
699C2×D8—614no—
700C2×D8—1222no—
701C2×D8—1222no—
702#131—6116no—
703#131—1228no—
704#131—1228no—
705#131—1228no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—21no—
710C2×M16—21no—
711C2×M16—21no—
712C2×M16—612no—
713C2×M16—612no—
714C2×M16—612no—
715C2×M16—612no—
716C2×M16—612no—
717C2×M16—612no—
718C2×M16—612no—
719C2×M16—612no—
720C2×M16—612no—
721C2×M16—1224no—
722C2×M16—1228no—
723C2×M16—1228no—
724C2×M16—1221no—
725C2×M16—1221no—
726C2×M16—1221no—
727C2×M16C22×D6112yes—
728C2×M16C22×D6112yes—
729C2×M16C22×D6112yes—
730C2×M16C22×D6112yes—
731C2×M16C22×D6112yes—
732C2×M16C22×D6112yes—
733C22×C8—21no—
734C22×C8—21no—
735C22×C8—612no—
736C22×C8—1224no—
737C22×C8—1221no—
738#108—6116no—
739#101—618no—
740#101C22×D6118yescomplemented
741#100—618no—
742#100C22×D6118yescomplemented
743C24—21no—
744C24—1221no—
745C24—1221no—
746C24#1175822211yescharacteristic
747#41—22no—
748#41—22no—
749#41—22no—
750#41—22no—
751#41—22no—
752#41—22no—
753#41—22no—
754#41—22no—
755#41—41no—
756#41—41no—
757#41—41no—
758#41—41no—
759#41—41no—
760#41—41no—
761#41—41no—
762#41—41no—
763#41—614no—
764#41—614no—
765#41—614no—
766#41—614no—
767#41—1222no—
768#41—1222no—
769#41—1222no—
770#41—1222no—
771#41—1222no—
772#41—1222no—
773#41—1222no—
774#41—1222no—
775#41—1222no—
776#41—1222no—
777#41—1222no—
778#41—1222no—
779#41—1222no—
780#41—1222no—
781#41—1222no—
782#41—1222no—
783#41—1222no—
784#41—1222no—
785#41—1222no—
786#41—1222no—
787#41—2441no—
788#41—2441no—
789#41—2441no—
790#41—2441no—
791#41—2441no—
792#41—2441no—
793#41—2441no—
794#41—2441no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—612no—
801C2×Q8—612no—
802C2×Q8—612no—
803C2×Q8—612no—
804C2×Q8—1221no—
805C2×Q8—1221no—
806C2×Q8—1221no—
807C2×Q8—1221no—
808C2×Q8—1221no—
809C2×Q8—1221no—
810C2×Q8—1221no—
811C2×Q8—1221no—
812C2×Q8C23×D6112yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—612no—
825C2×D4—612no—
826C2×D4—612no—
827C2×D4—612no—
828C2×D4—1222no—
829C2×D4—1222no—
830C2×D4—1222no—
831C2×D4—1222no—
832C2×D4—1222no—
833C2×D4—1222no—
834C2×D4—1222no—
835C2×D4—1222no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—1221no—
841C2×D4—1221no—
842C2×D4—1221no—
843C2×D4—1221no—
844C2×D4—2441no—
845C2×D4—2441no—
846C2×D4—2441no—
847C2×D4—2441no—
848C2×D4C23×D6112yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—1221no—
857C22×C4—1222no—
858C22×C4—1222no—
859C22×C4—1222no—
860C22×C4—1222no—
861C22×C4—1222no—
862C22×C4—1222no—
863C22×C4—1221no—
864C22×C4—1222no—
865C22×C4—1222no—
866C22×C4—2441no—
867C22×C4—2441no—
868C22×C4—2441no—
869C22×C4—2441no—
870C22×C4#1175822211yescharacteristic
871C22×C4#1175822211yescharacteristic
872C22×C4#1175822211yescharacteristic
873C22×C4D4×D6111yescharacteristic
874C22×C4D4×D6111yescharacteristic
875C22×C4D4×D6111yescharacteristic
876C22×C4D4×D6111yescharacteristic
877C22×C4D4×D6111yescharacteristic
878C22×C4D4×D6111yescharacteristic
879C22×C4D4×D6111yescharacteristic
880C22×C4D4×D6111yescharacteristic
881C22×C4C23×D6111yescharacteristic
882C22×C4C23×D6111yescharacteristic
883C22×C4C23×D6111yescharacteristic
884Q16—1228no—
885Q16—1228no—
886Q16—1228no—
887SD16—1228no—
888SD16—1228no—
889SD16—1228no—
890SD16—1228no—
891SD16—1228no—
892SD16—1228no—
893D8—1228no—
894D8—1228no—
895D8—1228no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—22no—
900M16—22no—
901M16—22no—
902M16—614no—
903M16—614no—
904M16—614no—
905M16—614no—
906M16—614no—
907M16—12216no—
908M16—1222no—
909M16—1222no—
910M16—1222no—
911M16C23×D6114yes—
912M16C23×D6114yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—22no—
917C2×C8—22no—
918C2×C8—22no—
919C2×C8—614no—
920C2×C8—614no—
921C2×C8—614no—
922C2×C8—12216no—
923C2×C8—1222no—
924C2×C8—1222no—
925C2×C8—1222no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—81no—
930C23—82no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—4882no—
936C23—4882no—
937C23—2441no—
938C23—2441no—
939C23#1451975011yescharacteristic
940C23#1451975011yescharacteristic
941C23#1451975011yescharacteristic
942C23#1451975011yescharacteristic
943C23C2×#1175822211yescharacteristic
944C23C2×#1175822211yescharacteristic
945C23C2×#1175822211yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—41no—
949Q8—41no—
950Q8—614no—
951Q8—1222no—
952Q8—1222no—
953Q8—1222no—
954Q8—1222no—
955Q8—1222no—
956Q8—2441no—
957Q8—2441no—
958D4—22no—
959D4—22no—
960D4—42no—
961D4—42no—
962D4—42no—
963D4—42no—
964D4—41no—
965D4—41no—
966D4—614no—
967D4—1224no—
968D4—1224no—
969D4—1224no—
970D4—1224no—
971D4—1222no—
972D4—1222no—
973D4—1222no—
974D4—1222no—
975D4—1222no—
976D4—2442no—
977D4—2442no—
978D4—2442no—
979D4—2442no—
980D4—2441no—
981D4—2441no—
982C2×C4—22no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1224no—
993C2×C4—1224no—
994C2×C4—1224no—
995C2×C4—1224no—
996C2×C4—1222no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2442no—
1000C2×C4—2442no—
1001C2×C4—2442no—
1002C2×C4—2442no—
1003C2×C4#1451975011yescharacteristic
1004C2×C4#1451975011yescharacteristic
1005C2×C4#1451975011yescharacteristic
1006C2×C4#1451975011yescharacteristic
1007C2×C4#1451975011yescharacteristic
1008C2×C4#1451975011yescharacteristic
1009C2×C4#1451975011yescharacteristic
1010C2×C4#1451975011yescharacteristic
1011C2×C4#1451975011yescharacteristic
1012C2×C4#1451975011yescharacteristic
1013C2×C4#1451975011yescharacteristic
1014C2×C4#1451975011yescharacteristic
1015C2×C4C2×D4×D6111yescharacteristic
1016C2×C4C2×D4×D6111yescharacteristic
1017C2×C4C2×D4×D6111yescharacteristic
1018C2×C4C2×D4×D6111yescharacteristic
1019C2×C4C2×D4×D6111yescharacteristic
1020C2×C4C2×D4×D6111yescharacteristic
1021C2×C4C2×D4×D6111yescharacteristic
1022C2×C4C2×D4×D6111yescharacteristic
1023C2×C4C2×D4×D6111yescharacteristic
1024C2×C4C2×D4×D6111yescharacteristic
1025C2×C4C2×D4×D6111yescharacteristic
1026C2×C4C2×D4×D6111yescharacteristic
1027C2×C4C2×#1175822211yescharacteristic
1028C2×C4C2×#1175822211yescharacteristic
1029C2×C4C2×#1175822211yescharacteristic
1030C2×C4C24×D6111yescharacteristic
1031C8—24no—
1032C8—24no—
1033C8—618no—
1034C8—1224no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—42no—
1043C22—82no—
1044C22—82no—
1045C22—82no—
1046C22—1224no—
1047C22—4882no—
1048C22—4882no—
1049C22—4882no—
1050C22—4882no—
1051C22—4882no—
1052C22—2444no—
1053C22—2442no—
1054C22C2×#1451975011yescharacteristic
1055C22C2×#1451975011yescharacteristic
1056C22C2×#1451975011yescharacteristic
1057C22C2×#1451975011yescharacteristic
1058C22C2×#1451975011yescharacteristic
1059C22C2×#1451975011yescharacteristic
1060C22C22×#1175822211yescharacteristic
1061C4—42no—
1062C4—1224no—
1063C4—2442no—
1064C4C2×#1451975011yescharacteristic
1065C4C2×#1451975011yescharacteristic
1066C4C2×#1451975011yescharacteristic
1067C4C2×#1451975011yescharacteristic
1068C4C2×#1451975011yescharacteristic
1069C4C2×#1451975011yescharacteristic
1070C4C22×D4×D6111yescharacteristic
1071C4C22×D4×D6111yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—82no—
1080C2—4882no—
1081C2—2444no—
1082C2C22×#1451975011yescharacteristic
subgroupG/H
centerC4C2×#14519750
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#413C2
socleC2×C61C22×#121
hypercenterC2×#413D61
hypocenterC61#60469
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#16840562C2semidirect
2. C2×#16840560C2semidirect
3. C2×#16840560C2semidirect
4. C2×#16840528C2semidirect
5. #21455559C2semidirect
6. #21455555C2semidirect
7. #21455550C2semidirect
8. #21455546C2semidirect
9. #21455538C2semidirect
10. C2×#16839810C2semidirect
11. C2×#16839744C2semidirect
12. C2×C61×#413C2semidirect
18. #16840562C22semidirect
26. #16840560C22semidirect
28. C2×#14519810C22semidirect
29. C2×#14519808C22semidirect
30. C2×#14519808C22semidirect
32. C2×#14519807C22semidirect
34. C2×#14519805C22semidirect
35. C2×#14519803C22semidirect
36. C2×#14519803C22semidirect
38. C2×#14519802C22semidirect
41. C2×#14519797C22semidirect
44. #16840528C22semidirect
45. #16840528C22semidirect
46. C2×#14519785C22semidirect
51. #16840036C22semidirect
52. #16840031C22semidirect
53. #16840028C22semidirect
54. #16840024C22semidirect
55. #16839810C22semidirect
56. #16839810C22semidirect
57. C2×#14519712C22semidirect
58. #16839744C22semidirect
59. #16839744C22semidirect
60. C2×#14519695C22semidirect
61. C2×#14519693C22semidirect
65. C61×#413C22semidirect
66. C61×#413C22semidirect
67. C2×#101×C61C22semidirect
68. C2×#100×C61C22semidirect
133. C2×#11758202C23semidirect
137. C2×#11758200C23semidirect
139. C2×#11758201C23semidirect
142. C2×#11758199C23semidirect
165. #14519712C23semidirect
166. #14519695C23semidirect
167. #14519693C23semidirect
199. #101×C61C23semidirect
200. #100×C61C23semidirect
542. C2×#413D61semidirect
604. #413C2×D61semidirect
605. #413C2×D61semidirect
607. C2×#101C2×D61semidirect
609. C2×#100C2×D61semidirect
610. C61#60469semidirect
740. #101C22×D61semidirect
742. #100C22×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405622
C2×#168405602
C2×#168405282
#214555592
#214555552
#214555502
#214555462
#214555382
C2×#168398102
C2×#168397442
C2×C61×#4132
#6046961