Finite Group Databasebeta

← C2×#21458836 #30560966

Subgroups — C2×#21458836 #30560966

Order 15616.

2250 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840481C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic, complemented
3#21458836C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16839960C211yesmaximal, characteristic, complemented
7C2×#16839959C211yesmaximal, characteristic, complemented
8C2×#16839975C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839965C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839890C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×#16839863C211yesmaximal, characteristic, complemented
15C2×D8×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#496C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23#16840481—24no—
24#16840481C2218yescomplemented
25#16840432—24no—
26#16840432C2218yescomplemented
27C2×#14519775C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519770—21no—
31C2×#14519770—21no—
32C2×#14519764C2211yescharacteristic
33C2×#14519754—21no—
34C2×#14519749—21no—
35C2×#14519749—21no—
36C2×#14519748—21no—
37C2×Q8×Dic61C2211yescharacteristic
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×D4×Dic61C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519733—21no—
45#16840150C2218yescomplemented
46#16840133C2218yescomplemented
47#16839975C2218yescomplemented
48#16839974C2218yescomplemented
49#16839965C2218yescomplemented
50#16839960C2218yescomplemented
51#16839959C2218yescomplemented
52#16839955C2218yescomplemented
53#16839890C2218yescomplemented
54#16839864C2218yescomplemented
55#16839863C2218yescomplemented
56D8×Dic61C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C22×D8×C61C2211yescharacteristic
73C2×#127×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#496C2218yescomplemented
76C2×#97×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122D411yescharacteristic
80C22×Dic122C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C23×Dic61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C2×#11758190—24no—
91C2×#11758190C2314yes—
92C2×#11758200—42no—
93C2×#11758200—42no—
94C2×#11758200C2314yes—
95C2×#11758200C2314yes—
96C2×#11758201—42no—
97C2×#11758201C2314yes—
98C2×#11758199—42no—
99C2×#11758199C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519775—22no—
103#14519775C2314yes—
104#14519773—22no—
105#14519773—22no—
106#14519773C2314yes—
107#14519773C2314yes—
108#14519770—28no—
109#14519770—28no—
110#14519764—22no—
111#14519764C2314yes—
112#14519754—28no—
113#14519749—28no—
114#14519749—28no—
115#14519748—28no—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118C4×Dic122—22no—
119C4×Dic122D414yes—
120C4×Dic122C2314yes—
121C4×Dic122C2314yes—
122C4×D244—22no—
123C4×D244C2314yes—
124D4×Dic61—22no—
125D4×Dic61—22no—
126D4×Dic61—22no—
127D4×Dic61C2314yes—
128D4×Dic61C2314yes—
129D4×Dic61C2314yes—
130#14519733—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61D411yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196D411yescharacteristic
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150#14519711C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×SD16×C61—24no—
169C2×SD16×C61—42no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C2×D8×C61—24no—
173C2×D8×C61—42no—
174C2×D8×C61C2314yes—
175C2×D8×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#127×C61—22no—
179#127×C61C2314yes—
180#124×C61—22no—
181#124×C61C2314yes—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C42×C61C2311yescharacteristic
185#97×C61C2314yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C23×D61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×D4×C61—24no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—24no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—44no—
206C2×D4×C61—82no—
207C2×D4×C61C2412yes—
208C2×D4×C61C2412yes—
209C2×D4×C61C2412yes—
210C22×C4×C61—21no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—82no—
221C2×C22⋊D61—82no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—24no—
226C22×Dic61—24no—
227C22×Dic61—24no—
228C22×Dic61—44no—
229C22×Dic61—44no—
230C22×Dic61—44no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235#11758224—432no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—21no—
239C2×D244C2412yes—
240C2×C4×D61—24no—
241C2×C4×D61—44no—
242C2×Dic122—24no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—21no—
246C2×Dic122C2×D414yes—
247C2×Dic122C2412yes—
248SD16×C61—28no—
249SD16×C61—44no—
250D8×C61—28no—
251D8×C61—44no—
252C2×C8×C61—22no—
253C2×C8×C61#4114yescomplemented
254C2×C8×C61C2412yes—
255C2×C8×C61C2412yes—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C42×C61C2×D412yes—
259C42×C61C2412yes—
260C22⋊Dic61—24no—
261C22⋊Dic61—24no—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265#11758201—44no—
266#11758200—44no—
267#11758200—44no—
268#11758199—44no—
269#11758198—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2×D414yes—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196C2×D414yes—
280#11758196C2×D414yes—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2×D412yes—
285C4×Dic61C2412yes—
286C4×Dic61C2412yes—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291#11758190—28no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61C22×D411yescharacteristic
305C22×D61—22no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—42no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—48no—
319D4×C61—42no—
320D4×C61—42no—
321D4×C61—42no—
322D4×C61—84no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—42no—
327C2×C4×C61C22×D412yes—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61H(5,𝔽2)12yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—48no—
334C22⋊D61—48no—
335C22⋊D61—84no—
336C22⋊D61—84no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—48no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—48no—
348C2×Dic61—48no—
349C2×Dic61AGL(1,ℤ/8)14yes—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354D244—22no—
355D244—22no—
356D244—42no—
357C4×D61—48no—
358Dic122—28no—
359Dic122—22no—
360Dic122—22no—
361Dic122—42no—
362C8×C61—22no—
363C8×C61C2×#4114yescomplemented
364#92418—22no—
365#92418—22no—
366C2×#3397—611nomaximal, Sylow
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—84no—
377C22×C61—84no—
378C22×C61—84no—
379C22×C61#55012yes—
380C22×C61C2×AGL(1,ℤ/8)12yes—
381C22×C61#57712yes—
382C22×C61C23×D411yescharacteristic
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—84no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61#55012yes—
391C4×C61C22×#4111yescharacteristic
392C4×C61C2×H(5,𝔽2)11yescharacteristic
393Dic61—22no—
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61C2×AGL(1,ℤ/8)14yes—
400C2×#556—611no—
401C2×#550—611no—
402#3397—6116no—
403C2×#496—611no—
404C2×#496D6111yescharacteristic, complemented
405C2×#492—611no—
406C2×#460—611no—
407C2×#460—611no—
408C2×#463—611no—
409C2×#463—611no—
410C2×#461—611no—
411C2×#459—611no—
412C2×#446—611no—
413C2×#440—611no—
414C2×#440—611no—
415C2×C4×D8—611no—
416C2×C61—82no—
417C2×C61—82no—
418C2×C61—82no—
419C2×C61#339714yescomplemented
420C2×C61C2×#55011yescharacteristic
421C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C61C2×#57711yescharacteristic
423D61—82no—
424C22×#41—1221no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16C2×D6111yescharacteristic
430C22×SD16C2×D6111yescharacteristic
431C22×D8—611no—
432C22×D8C2×D6111yescharacteristic
433C22×D8C2×D6111yescharacteristic
434#556—618no—
435#556—1224no—
436#550—618no—
437#550—1224no—
438C2×C4⋊Q8—611no—
439C2×#127—611no—
440C2×#127—611no—
441C2×#127C2×D6111yescharacteristic
442C2×#126—1221no—
443C2×#126—1221no—
444C2×#124—611no—
445C2×#124C2×D6111yescharacteristic
446C2×C22⋊Q8—1221no—
447C2×#121—1221no—
448C2×#121—1221no—
449C2×#121—1221no—
450C2×C4×Q8—611no—
451C2×C4×Q8—611no—
452C2×C4×Q8—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×#117—1221no—
458#496—618no—
459#496C2×D6118yescomplemented
460#492—618no—
461#463—618no—
462#463—618no—
463#461—618no—
464#460—618no—
465#460—618no—
466#459—618no—
467#446—618no—
468#440—618no—
469#440—618no—
470C4×D8—618no—
471C2×#107—611no—
472C2×C4⋊C8—611no—
473C2×C4⋊C8—611no—
474C2×C4⋊C8—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#97—611no—
482C2×#97C2×D6111yescharacteristic
483C2×C4×C8—611no—
484C61C2×#339711yescharacteristic, complemented, Sylow
485C2×#41—1228no—
486C2×#41—2448no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8C22×D6111yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—611no—
493C22×D4—1221no—
494C22×D4—1221no—
495C22×D4—1221no—
496C22×D4—1221no—
497C22×D4C22×D6111yescharacteristic
498C22×D4C22×D6111yescharacteristic
499C22×D4C22×D6111yescharacteristic
500C23×C4—1221no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×SD16—24no—
505C2×SD16—42no—
506C2×SD16—614no—
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—614no—
510C2×SD16—1224no—
511C2×SD16—2442no—
512C2×SD16—2442no—
513C2×SD16—2442no—
514C2×SD16C22×D6114yes—
515C2×SD16C22×D6114yes—
516C2×D8—24no—
517C2×D8—42no—
518C2×D8—614no—
519C2×D8—2442no—
520C2×D8C22×D6114yes—
521C2×D8C22×D6114yes—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8C22×D6111yescharacteristic
525C22×C8C22×D6111yescharacteristic
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528#127—22no—
529#127—614no—
530#127—614no—
531#127—1222no—
532#127—1222no—
533#127C22×D6114yes—
534#126—1228no—
535#126—1228no—
536#124—22no—
537#124—614no—
538#124—1222no—
539#124C22×D6114yes—
540C22⋊Q8—1228no—
541#121—1228no—
542#121—1228no—
543#121—1228no—
544C4×Q8—614no—
545C4×Q8—614no—
546C4×Q8—614no—
547C4×Q8—614no—
548C4×Q8—1222no—
549C4×Q8—1222no—
550C4×D4—614no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—1222no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558#117—1228no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—1221no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581#107—614no—
582C4⋊C8—614no—
583C4⋊C8—614no—
584C4⋊C8—614no—
585#103—614no—
586#103—614no—
587#102—614no—
588#102—614no—
589#102—614no—
590#102—614no—
591#97—614no—
592#97C22×D6114yes—
593C4×C8—614no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—1221no—
598#41—24432no—
599C2×Q8—21no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—614no—
603C2×Q8—612no—
604C2×Q8—1224no—
605C2×Q8—1221no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8C23×D6112yes—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—82no—
622C2×D4—612no—
623C2×D4—1224no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1224no—
627C2×D4—1221no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—4882no—
631C2×D4—4882no—
632C2×D4—2444no—
633C2×D4—2444no—
634C2×D4C23×D6112yes—
635C2×D4C23×D6112yes—
636C2×D4C23×D6112yes—
637C22×C4—21no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1224no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656SD16—28no—
657SD16—44no—
658SD16—1228no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662D8—28no—
663D8—44no—
664D8—2444no—
665C2×C8—22no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8#1175822414yescomplemented
671C2×C8C23×D6112yes—
672C2×C8C23×D6112yes—
673C4⋊C4—614no—
674C4⋊C4—614no—
675C4⋊C4—614no—
676C4⋊C4—612no—
677C4⋊C4—612no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1224no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—612no—
693C42—612no—
694C42—612no—
695C42—612no—
696C42—1224no—
697C42—1224no—
698C42D4×D6112yes—
699C42C23×D6112yes—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—1222no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—42no—
720Q8—1228no—
721Q8—1222no—
722Q8—1222no—
723Q8—2442no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—84no—
735D4—1222no—
736D4—1222no—
737D4—4884no—
738D4—4884no—
739D4—2448no—
740D4—2448no—
741D4—2442no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—614no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—2448no—
758C2×C4—2448no—
759C2×C4—2448no—
760C2×C4—2448no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6112yes—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C2×#1175822412yes—
768C2×C4#1451982212yes—
769C2×C4C24×D6111yescharacteristic
770C8—22no—
771C8—1222no—
772C8—1222no—
773C8C2×#1175822414yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—84no—
784C22—84no—
785C22—84no—
786C22—4884no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22#1684043212yes—
791C22AGL(1,ℤ/8)×D6112yes—
792C22#1684057212yes—
793C22C22×D4×D6111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—614no—
798C4—1222no—
799C4—1222no—
800C4—1222no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4#1684043212yes—
805C4C22×#1175822411yescharacteristic
806C4C2×#1451982211yescharacteristic
807C2—82no—
808C2—82no—
809C2—82no—
810C2—4882no—
811C2#2145883614yesdirect product factor
812C2C2×#1684043211yescharacteristic
813C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
814C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#496C2
socleC23×C61C22×D4
hypercenterC2×#496D61
hypocenterC61C2×#3397
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#16840481C2semidirect
2. C2×#16840432C2semidirect
3. #21458836C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16839960C2semidirect
7. C2×#16839959C2semidirect
8. C2×#16839975C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839965C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839890C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839863C2semidirect
15. C2×D8×Dic61C2semidirect
16. C2×C61×#496C2semidirect
24. #16840481C22semidirect
26. #16840432C22semidirect
45. #16840150C22semidirect
46. #16840133C22semidirect
47. #16839975C22semidirect
48. #16839974C22semidirect
49. #16839965C22semidirect
50. #16839960C22semidirect
51. #16839959C22semidirect
52. #16839955C22semidirect
53. #16839890C22semidirect
54. #16839864C22semidirect
55. #16839863C22semidirect
56. D8×Dic61C22semidirect
75. C61×#496C22semidirect
253. C2×C8×C61#41semidirect
363. C8×C61C2×#41semidirect
404. C2×#496D61semidirect
419. C2×C61#3397semidirect
459. #496C2×D61semidirect
484. C61C2×#3397semidirect
670. C2×C8#11758224semidirect
773. C8C2×#11758224semidirect
811. C2#21458836direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404812
C2×#168404322
#214588362
C2×#168401502
C2×#168401332
C2×#168399602
C2×#168399592
C2×#168399752
C2×#168399742
C2×#168399652
C2×#168399552
C2×#168398902
C2×#168398642
C2×#168398632
C2×D8×Dic612
C2×C61×#4962
C2×#339761