Finite Group Databasebeta

← C2×#21458139 #30556939

Subgroups — C2×#21458139 #30556939

Order 15616.

2426 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840431C211yesmaximal, characteristic, complemented
2C2×#16840412C211yesmaximal, characteristic, complemented
3#21458139C2116yesmaximal, direct product factor
4C2×#16840107C211yesmaximal, characteristic, complemented
5C2×#16840081C211yesmaximal, characteristic, complemented
6C2×#16840079C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16840012C211yesmaximal, characteristic, complemented
10C2×#16839955C211yesmaximal, characteristic, complemented
11C2×#16839906C211yesmaximal, characteristic, complemented
12C2×SD16×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C2×#16839762C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224—21no—
19C22×#11758199C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22#16840431—24no—
23#16840431C2218yescomplemented
24#16840412—24no—
25#16840412C2218yescomplemented
26C2×#14519776C2211yescharacteristic
27C2×#14519773—21no—
28C2×#14519773C2211yescharacteristic
29C2×#14519759—21no—
30C2×#14519758—21no—
31C2×#14519754—21no—
32C2×#14519751—21no—
33C2×#14519751C2211yescharacteristic
34C2×#14519748—21no—
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61C2211yescharacteristic
41C22×C4⋊Dic61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840107C2218yescomplemented
44#16840081C2218yescomplemented
45#16840079C2218yescomplemented
46#16840045C2218yescomplemented
47#16840013C2218yescomplemented
48#16840012C2218yescomplemented
49#16839955C2218yescomplemented
50#16839906C2218yescomplemented
51SD16×Dic61C2218yescomplemented
52#16839837C2218yescomplemented
53C2×#14519709C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57#16839763C2218yescomplemented
58#16839762C2218yescomplemented
59C2×#14519701C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C2×#11758224—28no—
82C2×#11758224—48no—
83C22×Dic122—21no—
84C22×D244—21no—
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61D411yescharacteristic
92C23×Dic61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758194—42no—
100C2×#11758194C2314yes—
101C2×#11758189—42no—
102C2×#11758189C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519776—22no—
106#14519776C2314yes—
107#14519773—28no—
108#14519773—22no—
109#14519773C2314yes—
110#14519759—28no—
111#14519758—28no—
112#14519754—28no—
113#14519751—22no—
114#14519751—28no—
115#14519751C2314yes—
116#14519748—22no—
117#14519748—22no—
118#14519748—28no—
119#14519748C2314yes—
120#14519748C2314yes—
121Q8×Dic61—22no—
122Q8×Dic61C2314yes—
123D4×Dic61—22no—
124D4×Dic61C2314yes—
125C4×C22⋊D61—28no—
126C4×C22⋊D61D414yes—
127C4×C22⋊D61C2314yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—22no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2314yes—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C4⋊C4×D61—22no—
139C4⋊C4×D61C2314yes—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61D411yescharacteristic
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148#14519709C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151#14519706C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519697C2314yes—
160#14519689C2314yes—
161C8×Dic61C2314yes—
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C2×SD16×C61—24no—
174C2×SD16×C61C2314yes—
175C2×D8×C61—42no—
176C2×D8×C61C2314yes—
177C22×C8×C61C2311yescharacteristic
178C22×C8×C61C2311yescharacteristic
179#121×C61—22no—
180#121×C61C2314yes—
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C22⋊C4×C61—21no—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C22⋊C8×C61C2314yes—
186C24×C61—21no—
187C24×C61—21no—
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191#41×C61—28no—
192#41×C61—44no—
193#41×C61—48no—
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61#4114yescomplemented
197C2×Q8×C61C2412yes—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61C2412yes—
209C2×D4×C61C2412yes—
210C22×C4×C61—21no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—44no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—82no—
229C2×C22⋊D61—82no—
230C2×C22⋊D61—82no—
231C2×C22⋊D61C2×D414yes—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—21no—
236C22×Dic61—24no—
237C22×Dic61—44no—
238C22×Dic61—44no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242#11758226—28no—
243#11758226—44no—
244#11758226—48no—
245#11758224—432no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244—24no—
249C2×D244—21no—
250C2×D244—44no—
251C2×D244C2412yes—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×C4×D61—24no—
255C2×C4×D61—24no—
256C2×C4×D61—44no—
257C2×C4×D61—44no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2412yes—
260C2×Dic122—24no—
261C2×Dic122—44no—
262SD16×C61—28no—
263D8×C61—44no—
264C2×C8×C61—22no—
265C2×C8×C61—22no—
266C2×C8×C61C2412yes—
267C2×C8×C61C2412yes—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C2412yes—
270C22⋊C4×C61—24no—
271C22⋊Dic61—24no—
272C22⋊Dic61—24no—
273C22⋊Dic61—24no—
274C22⋊Dic61C2×D414yes—
275#11758199—44no—
276#11758198—24no—
277#11758198C2×D414yes—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—24no—
283C4⋊Dic61C2412yes—
284C4⋊Dic61C2412yes—
285C4⋊Dic61C2412yes—
286#11758196—24no—
287#11758196—24no—
288#11758196C2×D414yes—
289C4×Dic61—24no—
290C4×Dic61C2×D412yes—
291C4×Dic61C2412yes—
292#11758194—44no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297#11758189—44no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61C22×D412yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61C22×D412yes—
319Q8×C61—24no—
320Q8×C61—22no—
321Q8×C61C2×#4114yescomplemented
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—48no—
327D4×C61—48no—
328D4×C61—42no—
329D4×C61—42no—
330C2×C4×C61—24no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—24no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—48no—
338C2×C4×C61—42no—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4112yes—
342C2×C4×C61H(5,𝔽2)12yes—
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—28no—
345C22⋊D61—48no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C22⋊D61—84no—
349C22⋊D61—84no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—48no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—42no—
359C2×Dic61—48no—
360C2×Dic61AGL(1,ℤ/8)14yes—
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363C2×Dic61C22×D412yes—
364D244—22no—
365D244—22no—
366D244—48no—
367D244—42no—
368C4×D61—24no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—48no—
372C4×D61—48no—
373Dic122—48no—
374C8×C61—22no—
375C8×C61—22no—
376#92418—22no—
377#92418—22no—
378C2×#3332—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—44no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—84no—
390C22×C61—84no—
391C22×C61#54612yes—
392C22×C61C2×AGL(1,ℤ/8)12yes—
393C22×C61#57712yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—22no—
398C2×D61—44no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—84no—
403C4×C61—24no—
404C4×C61—22no—
405C4×C61—42no—
406C4×C61#54612yes—
407C4×C61C22×#4111yescharacteristic
408C4×C61C2×H(5,𝔽2)11yescharacteristic
409Dic61—22no—
410Dic61—22no—
411Dic61—42no—
412Dic61—42no—
413Dic61—42no—
414Dic61C2×AGL(1,ℤ/8)14yes—
415C2×#550—611no—
416C2×#547—611no—
417#3332—6116no—
418C2×#486—611no—
419C2×#481—611no—
420C2×#481—611no—
421C2×#475—611no—
422C2×#469—611no—
423C2×#469—611no—
424C2×#459—611no—
425C2×#449—611no—
426C2×#449D6111yescharacteristic, complemented
427C2×C4×SD16—611no—
428C2×#436—611no—
429C2×#417—611no—
430C2×#417—611no—
431C2×C61—42no—
432C2×C61—82no—
433C2×C61—82no—
434C2×C61#333214yescomplemented
435C2×C61C2×#54611yescharacteristic
436C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C61C2×#57711yescharacteristic
438D61—42no—
439D61—82no—
440C22×#41—611no—
441C22×#41—1221no—
442C22×#41C2×D6111yescharacteristic
443C22×SD16C2×D6111yescharacteristic
444C22×D8—611no—
445C22×D8C2×D6111yescharacteristic
446C22×M16—611no—
447C22×M16—611no—
448#550—618no—
449#550—1224no—
450#547—618no—
451#547—1224no—
452C2×C4⋊Q8—611no—
453C2×#127—611no—
454C2×#127—1221no—
455C2×#123—1221no—
456C2×#123—1221no—
457C2×C22⋊Q8—1221no—
458C2×#121—611no—
459C2×#121—611no—
460C2×#121—611no—
461C2×#121—1221no—
462C2×#121—1221no—
463C2×#121C2×D6111yescharacteristic
464C2×C4×Q8—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×C4×D4—1221no—
468C22×C4⋊C4—611no—
469C22×C4⋊C4—611no—
470#486—618no—
471#481—618no—
472#481—618no—
473#475—618no—
474#469—618no—
475#469—618no—
476#459—618no—
477#449—618no—
478#449C2×D6118yescomplemented
479C4×SD16—618no—
480#436—618no—
481C2×#106—611no—
482C2×#106—611no—
483C2×#106—611no—
484C2×C4⋊C8—611no—
485#417—618no—
486#417—618no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103C2×D6111yescharacteristic
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102C2×D6111yescharacteristic
497C2×C22⋊C8—611no—
498C2×C22⋊C8C2×D6111yescharacteristic
499C2×C4×C8—611no—
500C61C2×#333211yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—24no—
503C2×#41—42no—
504C2×#41—614no—
505C2×#41—1222no—
506C2×#41—1228no—
507C2×#41—1224no—
508C2×#41—2442no—
509C2×#41—2448no—
510C2×#41C22×D6114yes—
511C22×Q8—1221no—
512C22×Q8C22×D6111yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—611no—
516C22×D4—611no—
517C22×D4—1221no—
518C22×D4—1221no—
519C22×D4—1221no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4C22×D6111yescharacteristic
524C22×D4C22×D6111yescharacteristic
525C23×C4—21no—
526C23×C4—611no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C2×SD16—24no—
533C2×SD16C22×D6114yes—
534C2×D8—42no—
535C2×D8—614no—
536C2×D8—2442no—
537C2×D8C22×D6114yes—
538C2×M16—614no—
539C2×M16—614no—
540C2×M16—2442no—
541C2×M16—2442no—
542C22×C8—611no—
543C22×C8—611no—
544C22×C8C22×D6111yescharacteristic
545C22×C8C22×D6111yescharacteristic
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#127—614no—
549#127—1222no—
550#127—1228no—
551#123—1228no—
552#123—1228no—
553C22⋊Q8—1228no—
554#121—22no—
555#121—614no—
556#121—614no—
557#121—614no—
558#121—1228no—
559#121—1228no—
560#121—1222no—
561#121—1222no—
562#121—1222no—
563#121C22×D6114yes—
564C4×Q8—614no—
565C4×Q8—1222no—
566C4×D4—614no—
567C4×D4—614no—
568C4×D4—614no—
569C4×D4—1222no—
570C4×D4—1228no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—614no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—614no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1222no—
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—611no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C42—611no—
592C2×C42—1221no—
593#106—614no—
594#106—614no—
595#106—614no—
596C4⋊C8—614no—
597#103—614no—
598#103—614no—
599#103C22×D6114yes—
600#102—614no—
601#102—614no—
602#102—614no—
603#102—614no—
604#102—614no—
605#102—614no—
606#102C22×D6114yes—
607C22⋊C8—614no—
608C22⋊C8C22×D6114yes—
609C4×C8—614no—
610C24—21no—
611C24—21no—
612C24—611no—
613C24—1221no—
614C24D4×D6111yescharacteristic
615#41—28no—
616#41—44no—
617#41—48no—
618#41—1228no—
619#41—2444no—
620#41—2448no—
621#41—24432no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—1224no—
625C2×Q8—2444no—
626C2×Q8#1175822414yescomplemented
627C2×Q8C23×D6112yes—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—614no—
639C2×D4—612no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1224no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—1221no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—4882no—
651C2×D4—4882no—
652C2×D4—4882no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4C23×D6112yes—
657C2×D4C23×D6112yes—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—44no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—1224no—
670C22×C4—1224no—
671C22×C4—1224no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1224no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—2444no—
679C22×C4—2444no—
680C22×C4—2444no—
681C22×C4—2444no—
682C22×C4D4×D6112yes—
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686SD16—28no—
687D8—44no—
688D8—2444no—
689M16—2444no—
690M16—2444no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—612no—
694C2×C8—612no—
695C2×C8—1222no—
696C2×C8—1222no—
697C2×C8C23×D6112yes—
698C2×C8C23×D6112yes—
699C4⋊C4—21no—
700C4⋊C4—614no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1224no—
710C4⋊C4—1221no—
711C4⋊C4C23×D6112yes—
712C22⋊C4—24no—
713C22⋊C4—614no—
714C22⋊C4—614no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C42—612no—
720C42—612no—
721C42—1224no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—612no—
734C23—1222no—
735C23—1222no—
736C23—1222no—
737C23—1222no—
738C23—2442no—
739C23—2442no—
740C23—2442no—
741C23C2×D4×D6112yes—
742C23C2×D4×D6111yescharacteristic
743Q8—22no—
744Q8—24no—
745Q8—2448no—
746Q8C2×#1175822414yescomplemented
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—48no—
753D4—42no—
754D4—42no—
755D4—1228no—
756D4—1222no—
757D4—1222no—
758D4—4884no—
759D4—4884no—
760D4—4884no—
761D4—2448no—
762D4—2448no—
763D4—2448no—
764D4—2442no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—614no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1224no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—2448no—
787C2×C4—2448no—
788C2×C4—2448no—
789C2×C4—2448no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4C2×D4×D6112yes—
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4C2×#1175822412yes—
796C2×C4#1451982212yes—
797C2×C4C24×D6111yescharacteristic
798C8—22no—
799C8—22no—
800C8—1222no—
801C8—1222no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—84no—
813C22—84no—
814C22—1222no—
815C22—1222no—
816C22—1222no—
817C22—4884no—
818C22—2442no—
819C22—2442no—
820C22—2442no—
821C22—2444no—
822C22#1684039912yes—
823C22AGL(1,ℤ/8)×D6112yes—
824C22#1684056912yes—
825C22C22×D4×D6111yescharacteristic
826C4—22no—
827C4—24no—
828C4—42no—
829C4—614no—
830C4—1222no—
831C4—1222no—
832C4—2442no—
833C4—2442no—
834C4—2442no—
835C4#1684039912yes—
836C4C22×#1175822411yescharacteristic
837C4C2×#1451982211yescharacteristic
838C2—42no—
839C2—82no—
840C2—82no—
841C2—4882no—
842C2—2442no—
843C2#2145813914yesdirect product factor
844C2C2×#1684039911yescharacteristic
845C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
846C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3332
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840431C2semidirect
2. C2×#16840412C2semidirect
3. #21458139C2direct (N × H)
4. C2×#16840107C2semidirect
5. C2×#16840081C2semidirect
6. C2×#16840079C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16840012C2semidirect
10. C2×#16839955C2semidirect
11. C2×#16839906C2semidirect
12. C2×SD16×Dic61C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839763C2semidirect
15. C2×#16839762C2semidirect
16. C2×C61×#449C2semidirect
23. #16840431C22semidirect
25. #16840412C22semidirect
43. #16840107C22semidirect
44. #16840081C22semidirect
45. #16840079C22semidirect
46. #16840045C22semidirect
47. #16840013C22semidirect
48. #16840012C22semidirect
49. #16839955C22semidirect
50. #16839906C22semidirect
51. SD16×Dic61C22semidirect
52. #16839837C22semidirect
57. #16839763C22semidirect
58. #16839762C22semidirect
73. C61×#449C22semidirect
196. C2×Q8×C61#41semidirect
321. Q8×C61C2×#41semidirect
426. C2×#449D61semidirect
434. C2×C61#3332semidirect
478. #449C2×D61semidirect
500. C61C2×#3332semidirect
626. C2×Q8#11758224semidirect
746. Q8C2×#11758224semidirect
843. C2#21458139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404312
C2×#168404122
#214581392
C2×#168401072
C2×#168400812
C2×#168400792
C2×#168400452
C2×#168400132
C2×#168400122
C2×#168399552
C2×#168399062
C2×SD16×Dic612
C2×#168398372
C2×#168397632
C2×#168397622
C2×C61×#4492
C2×#333261