Finite Group Databasebeta

← C2×#21458023 #30556813

Subgroups — C2×#21458023 #30556813

Order 15616.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic, complemented
2C2×#16840409C211yesmaximal, characteristic, complemented
3#21458023C2116yesmaximal, direct product factor
4C2×#16840115C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840065C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839909C211yesmaximal, characteristic, complemented
11C2×#16839897C211yesmaximal, characteristic, complemented
12C2×#16839844C211yesmaximal, characteristic, complemented
13C2×#16839837C211yesmaximal, characteristic, complemented
14C2×#16839761C211yesmaximal, characteristic, complemented
15C2×#16839765C211yesmaximal, characteristic, complemented
16C2×C61×#480C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758190C2211yescharacteristic, complemented
20C22×D488C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758194C2211yescharacteristic, complemented
23C22×#11758189C2211yescharacteristic
24#16840460—24no—
25#16840460C2218yescomplemented
26#16840409—24no—
27#16840409C2218yescomplemented
28C2×#14519772—21no—
29C2×#14519768C2211yescharacteristic, complemented
30C2×#14519764C2211yescharacteristic
31C2×#14519762—21no—
32C2×#14519759—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×#14519751—21no—
36C2×#14519751C2211yescharacteristic, complemented
37C2×#14519748—21no—
38C2×#14519745—21no—
39C2×#14519739C2211yescharacteristic
40C2×#14519739C2211yescharacteristic, complemented
41C2×C4×C22⋊D61—21no—
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×#14519735C2211yescharacteristic
44C2×C22⋊C4×D61—21no—
45#16840115C2218yescomplemented
46#16840105C2218yescomplemented
47#16840065C2218yescomplemented
48#16840013C2218yescomplemented
49#16840009C2218yescomplemented
50#16839976C2218yescomplemented
51#16839909C2218yescomplemented
52#16839897C2218yescomplemented
53#16839844C2218yescomplemented
54#16839837C2218yescomplemented
55C2×#14519708C2211yescharacteristic, complemented
56C2×#14519706C2211yescharacteristic, complemented
57#16839765C2218yescomplemented
58#16839761C2218yescomplemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519700C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#480C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#107×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61D411yescharacteristic
90C2×D4×D61—24no—
91C2×D4×D61—22no—
92C2×D4×D61—42no—
93C2×D4×D61C2314yes—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758190—42no—
99C2×#11758190C2314yescomplemented
100C2×D488—24no—
101C2×D488C2314yes—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C2×#11758194—42no—
105C2×#11758194C2314yescomplemented
106C2×#11758189—42no—
107C2×#11758189C2314yes—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110#14519772—28no—
111#14519768—22no—
112#14519768C2314yescomplemented
113#14519764—22no—
114#14519764C2314yes—
115#14519762—28no—
116#14519759—28no—
117#14519757—22no—
118#14519757C2314yes—
119#14519752—22no—
120#14519752C2314yes—
121#14519751—22no—
122#14519751—28no—
123#14519751C2314yescomplemented
124#14519748—28no—
125#14519745—28no—
126#14519739—22no—
127#14519739—22no—
128#14519739C2314yes—
129#14519739C2314yescomplemented
130C4×C22⋊D61—28no—
131C4×C22⋊D61D414yes—
132C4×C22⋊D61C2314yes—
133#14519735—22no—
134#14519735C2314yes—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61D411yescharacteristic
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198D411yescharacteristic
150C22⋊C4×D61—28no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61C2311yescharacteristic
153#14519708C2314yescomplemented
154#14519706C2314yescomplemented
155#14519702C2314yescomplemented
156#14519700C2314yescomplemented
157#14519700C2314yescomplemented
158#14519699C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161#14519697C2314yes—
162#14519697C2314yescomplemented
163#14519689C2314yes—
164C8×Dic61C2314yescomplemented
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171#121×C61—22no—
172#121×C61C2314yes—
173C2×C4⋊C4×C61—22no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2314yescomplemented
179C2×C22⋊C4×C61—21no—
180#107×C61C2314yescomplemented
181#107×C61C2314yescomplemented
182#102×C61C2314yes—
183#102×C61C2314yes—
184C22⋊C8×C61C2314yescomplemented
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—82no—
193C23×D61C2×D411yescharacteristic
194C2×D4×C61—24no—
195C2×D4×C61—21no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—82no—
199C2×D4×C61C2412yes—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—24no—
206C22×C4×C61—82no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2411yescharacteristic
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—44no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61C2×D414yes—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224D4×D61—28no—
225D4×D61—44no—
226D4×D61—48no—
227#11758222—28no—
228#11758222—44no—
229#11758222—48no—
230C2×D244—21no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—21no—
235C2×D244—24no—
236C2×D244—82no—
237C2×D244#4114yes—
238C2×D244C2412yes—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—24no—
245C2×C4×D61—44no—
246C2×C4×D61—82no—
247C2×C4×D61—82no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2412yes—
250C2×Dic122—22no—
251C2×Dic122—22no—
252C2×Dic122—21no—
253C2×Dic122C2412yes—
254C2×C8×C61—22no—
255C2×C8×C61—22no—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C2412yes—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61C2×D414yes—
269#11758199—44no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198C2×D414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—24no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196C2×D414yes—
283C4×Dic61—24no—
284C4×Dic61C2×D412yes—
285C4×Dic61C2412yes—
286#11758194—44no—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291D488—28no—
292#11758190—44no—
293#11758189—44no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—24no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—48no—
310C22×D61—48no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—84no—
317C22×D61—816no—
318C22×D61C22×D412yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—42no—
322D4×C61—84no—
323C2×C4×C61—22no—
324C2×C4×C61—24no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—84no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4112yes—
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61C2511yescharacteristic
339C22⋊D61—44no—
340C22⋊D61—48no—
341C22⋊D61—48no—
342C22⋊D61—48no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353D244—24no—
354D244—22no—
355D244—22no—
356D244—22no—
357D244—42no—
358D244—84no—
359D244C2×#4114yes—
360C4×D61—24no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—48no—
364C4×D61—84no—
365C4×D61—84no—
366Dic122—22no—
367Dic122—22no—
368Dic122—42no—
369C8×C61—22no—
370C8×C61—22no—
371#92418—22no—
372#92418—22no—
373C2×#3322—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—44no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—84no—
382C22×C61#54612yes—
383C22×C61#57512yes—
384C22×C61#57612yes—
385C22×C61C23×D411yescharacteristic
386C2×D61—22no—
387C2×D61—24no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—44no—
391C2×D61—48no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—816no—
398C2×D61—84no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#54612yes—
404C4×C61C22×#4111yescharacteristic
405C4×C61C2×H(5,𝔽2)11yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—22no—
409Dic61—42no—
410Dic61—42no—
411C2×#553—611no—
412C2×#546—611no—
413#3322—6116no—
414C2×#488—611no—
415C2×#485—611no—
416C2×#480D6111yescharacteristic, complemented
417C2×#478—611no—
418C2×#469—611no—
419C2×#468—611no—
420C2×#463—611no—
421C2×#449—611no—
422C2×#447—611no—
423C2×C4×D8—611no—
424C2×#436—611no—
425C2×#417—611no—
426C2×#418—611no—
427C2×C61—42no—
428C2×C61—82no—
429C2×C61#332214yescomplemented
430C2×C61C2×#54611yescharacteristic
431C2×C61C2×#57511yescharacteristic
432C2×C61C2×#57611yescharacteristic
433D61—42no—
434D61—44no—
435D61—82no—
436C22×#41—611no—
437C23×D4—611no—
438C22×SD16—611no—
439C22×D8—611no—
440C22×D8—611no—
441C22×M16—611no—
442C22×M16—611no—
443#553—618no—
444#553—1224no—
445#546—618no—
446#546—1224no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#124—611no—
450C2×#123—1221no—
451C2×#123—1221no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×#121—611no—
455C2×#121—1221no—
456C2×#121—1221no—
457C2×#121C2×D6111yescharacteristic
458C2×#120—1221no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—611no—
462C2×C4×D4—1221no—
463C2×#117—611no—
464C22×C4⋊C4C2×D6111yescharacteristic, complemented
465C22×C22⋊C4—1221no—
466#488—618no—
467#485—618no—
468#480C2×D6118yescomplemented
469#478—618no—
470#469—618no—
471#468—618no—
472#463—618no—
473#449—618no—
474#447—618no—
475C4×D8—618no—
476#436—618no—
477C2×#107C2×D6111yescharacteristic, complemented
478C2×#107C2×D6111yescharacteristic, complemented
479C2×#106—611no—
480C2×C4⋊C8—611no—
481#418—618no—
482#417—618no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8C2×D6111yescharacteristic, complemented
495C2×C4×C8—611no—
496C61C2×#332211yescharacteristic, complemented, Sylow
497C25—1221no—
498C2×#41—614no—
499C2×#41—1224no—
500C2×#41—1222no—
501C2×#41—2442no—
502C22×Q8—611no—
503C22×D4—21no—
504C22×D4—611no—
505C22×D4—614no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1222no—
510C22×D4—1221no—
511C22×D4—1224no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—2442no—
515C22×D4C22×D6111yescharacteristic
516C23×C4—21no—
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522C2×SD16—614no—
523C2×SD16—2442no—
524C2×D8—614no—
525C2×D8—614no—
526C2×D8—1224no—
527C2×D8—2442no—
528C2×M16—614no—
529C2×M16—614no—
530C2×M16—2442no—
531C2×M16—2442no—
532C22×C8—611no—
533C22×C8—611no—
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#126—1228no—
537#125—614no—
538#125—1222no—
539#124—614no—
540#124—1222no—
541#123—1228no—
542#123—1228no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545#121—22no—
546#121—614no—
547#121—614no—
548#121—1228no—
549#121—1222no—
550#121—1228no—
551#121—1222no—
552#121C22×D6114yes—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—1222no—
559C4×D4—1222no—
560C4×D4—1228no—
561#117—614no—
562#117—1222no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6114yescomplemented
574C2×C22⋊C4—21no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—1228no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C42—611no—
587C2×C42—1221no—
588#107C22×D6114yescomplemented
589#107C22×D6114yescomplemented
590#106—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103—614no—
595#102—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600#102C22×D6114yes—
601#102C22×D6114yes—
602C22⋊C8—614no—
603C22⋊C8C22×D6114yescomplemented
604C4×C8—614no—
605C24—21no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—1221no—
610C24—4882no—
611C24—2444no—
612C24—2444no—
613C24D4×D6111yescharacteristic
614#41—1228no—
615#41—2444no—
616#41—2448no—
617C2×Q8—612no—
618C2×Q8—1221no—
619C2×Q8—1222no—
620C2×Q8—1222no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—82no—
626C2×D4—614no—
627C2×D4—614no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1228no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—4882no—
641C2×D4—2444no—
642C2×D4—2448no—
643C2×D4—2442no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4C23×D6112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—82no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1224no—
667C22×C4—4882no—
668C22×C4—4882no—
669C22×C4—2444no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—2444no—
675D8—1228no—
676D8—2444no—
677M16—2444no—
678M16—2444no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—612no—
682C2×C8—612no—
683C2×C8—1222no—
684C2×C8—1222no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—614no—
692C4⋊C4—612no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1221no—
697C4⋊C4C23×D6112yes—
698C4⋊C4C23×D6112yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—614no—
702C22⋊C4—614no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C42—612no—
712C42—612no—
713C42—1224no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—612no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1224no—
727C23—1222no—
728C23—4884no—
729C23—48816no—
730C23—2448no—
731C23—2448no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23C2×D4×D6112yes—
738C23C2×D4×D6111yescharacteristic
739Q8—1222no—
740Q8—1222no—
741Q8—2442no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—84no—
746D4—614no—
747D4—1222no—
748D4—1222no—
749D4—1222no—
750D4—1224no—
751D4—4884no—
752D4—2444no—
753D4—2448no—
754D4—2448no—
755D4—2448no—
756D4—2442no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—84no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1224no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—4884no—
780C2×C4—4884no—
781C2×C4—2448no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4C2×D4×D6112yes—
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4#41×D6112yes—
787C2×C4#1451982312yes—
788C2×C4C24×D6111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1222no—
792C8—1222no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—1222no—
802C22—1224no—
803C22—1222no—
804C22—1222no—
805C22—48816no—
806C22—4884no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2444no—
813C22—2448no—
814C22#1684040412yes—
815C22#1684056112yes—
816C22#1684056312yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1222no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2442no—
827C4#1684040412yes—
828C4C2×#41×D6111yescharacteristic
829C4C2×#1451982311yescharacteristic
830C2—42no—
831C2—82no—
832C2—4882no—
833C2—2442no—
834C2—2444no—
835C2#2145802314yesdirect product factor
836C2C2×#1684040411yescharacteristic
837C2C2×#1684056111yescharacteristic
838C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#480C2
socleC23×C61C22×D4
hypercenterC2×#480D61
hypocenterC61C2×#3322
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16840460C2semidirect
2. C2×#16840409C2semidirect
3. #21458023C2direct (N × H)
4. C2×#16840115C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840065C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839909C2semidirect
11. C2×#16839897C2semidirect
12. C2×#16839844C2semidirect
13. C2×#16839837C2semidirect
14. C2×#16839761C2semidirect
15. C2×#16839765C2semidirect
16. C2×C61×#480C2semidirect
19. C22×#11758190C22semidirect
22. C22×#11758194C22semidirect
25. #16840460C22semidirect
27. #16840409C22semidirect
29. C2×#14519768C22semidirect
36. C2×#14519751C22semidirect
40. C2×#14519739C22semidirect
45. #16840115C22semidirect
46. #16840105C22semidirect
47. #16840065C22semidirect
48. #16840013C22semidirect
49. #16840009C22semidirect
50. #16839976C22semidirect
51. #16839909C22semidirect
52. #16839897C22semidirect
53. #16839844C22semidirect
54. #16839837C22semidirect
55. C2×#14519708C22semidirect
56. C2×#14519706C22semidirect
57. #16839765C22semidirect
58. #16839761C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
61. C2×#14519700C22semidirect
66. C2×#14519697C22semidirect
68. C2×C8×Dic61C22semidirect
70. C22×C4⋊C4×C61C22semidirect
71. C61×#480C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#107×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
99. C2×#11758190C23semidirect
105. C2×#11758194C23semidirect
112. #14519768C23semidirect
123. #14519751C23semidirect
129. #14519739C23semidirect
153. #14519708C23semidirect
154. #14519706C23semidirect
155. #14519702C23semidirect
156. #14519700C23semidirect
157. #14519700C23semidirect
162. #14519697C23semidirect
164. C8×Dic61C23semidirect
178. C2×C4⋊C4×C61C23semidirect
180. #107×C61C23semidirect
181. #107×C61C23semidirect
184. C22⋊C8×C61C23semidirect
416. C2×#480D61semidirect
429. C2×C61#3322semidirect
464. C22×C4⋊C4C2×D61semidirect
468. #480C2×D61semidirect
477. C2×#107C2×D61semidirect
478. C2×#107C2×D61semidirect
494. C2×C22⋊C8C2×D61semidirect
496. C61C2×#3322semidirect
573. C2×C4⋊C4C22×D61semidirect
588. #107C22×D61semidirect
589. #107C22×D61semidirect
603. C22⋊C8C22×D61semidirect
835. C2#21458023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404602
C2×#168404092
#214580232
C2×#168401152
C2×#168401052
C2×#168400652
C2×#168400132
C2×#168400092
C2×#168399762
C2×#168399092
C2×#168398972
C2×#168398442
C2×#168398372
C2×#168397612
C2×#168397652
C2×C61×#4802
C2×#332261