Finite Group Databasebeta

← C2×#21457670 #30556381

Subgroups — C2×#21457670 #30556381

Order 15616.

2350 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×#16840456C211yesmaximal, characteristic, complemented
2C2×#16840400C211yesmaximal, characteristic, complemented
3#21457670C2116yesmaximal, direct product factor
4C2×#16840118C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840086C211yesmaximal, characteristic, complemented
7C2×#16840060C211yesmaximal, characteristic, complemented
8C2×#16839998C211yesmaximal, characteristic, complemented
9C2×#16839994C211yesmaximal, characteristic, complemented
10C2×#16839980C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839897C211yesmaximal, characteristic, complemented
13C2×#16839842C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#416C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758201C2211yescharacteristic, complemented
19C22×D488C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840456—24no—
23#16840456C2218yescomplemented
24#16840400—24no—
25#16840400C2218yescomplemented
26C2×#14519771—21no—
27C2×#14519768C2211yescharacteristic, complemented
28C2×#14519766C2211yescharacteristic
29C2×#14519760—21no—
30C2×#14519759—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519752C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519751C2211yescharacteristic, complemented
35C2×#14519750—21no—
36C2×#14519749—21no—
37C2×#14519745—21no—
38C2×C4×D244—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic, complemented
41C2×C4×C22⋊D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43C22×#11758198—21no—
44#16840118C2218yescomplemented
45#16840096C2218yescomplemented
46#16840086C2218yescomplemented
47#16840060C2218yescomplemented
48#16839998C2218yescomplemented
49#16839994C2218yescomplemented
50#16839980C2218yescomplemented
51#16839907C2218yescomplemented
52#16839897C2218yescomplemented
53#16839842C2218yescomplemented
54C8×C22⋊D61C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#102×D61C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic, complemented
71C2×#117×C61C2211yescharacteristic, complemented
72C61×#416C2218yescomplemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61D411yescharacteristic
85C2×D4×D61—24no—
86C2×D4×D61—22no—
87C2×D4×D61—42no—
88C2×D4×D61C2314yes—
89C23×Dic61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C2×#11758201—42no—
94C2×#11758201C2314yescomplemented
95C2×D488—42no—
96C2×D488C2314yes—
97C2×#11758199—24no—
98C2×#11758199C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—42no—
102C2×C8×D61C2314yes—
103#14519771—28no—
104#14519768—22no—
105#14519768C2314yescomplemented
106#14519766—22no—
107#14519766C2314yes—
108#14519760—28no—
109#14519759—28no—
110#14519753—22no—
111#14519753C2314yes—
112#14519752—22no—
113#14519752C2314yes—
114#14519751—22no—
115#14519751—22no—
116#14519751C2314yes—
117#14519751C2314yescomplemented
118#14519750—28no—
119#14519749—28no—
120#14519745—28no—
121C4×D244—28no—
122D4×Dic61—22no—
123D4×Dic61C2314yes—
124#14519739—22no—
125#14519739C2314yescomplemented
126C4×C22⋊D61D414yes—
127C4×C22⋊D61C2314yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C4⋊C4×D61—22no—
136C4⋊C4×D61C2314yes—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61D411yescharacteristic
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—28no—
147C2×#11758198D411yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yescomplemented
150#14519710C2314yescomplemented
151#14519708C2314yescomplemented
152#14519706C2314yescomplemented
153#14519701C2314yescomplemented
154#14519699C2314yes—
155#14519699C2314yescomplemented
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yescomplemented
160#14519689C2314yes—
161C8×Dic61C2314yescomplemented
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61C2311yescharacteristic
171C22×C8×C61—42no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yescomplemented
175#117×C61—22no—
176#117×C61C2314yescomplemented
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181#103×C61C2314yescomplemented
182#103×C61C2314yescomplemented
183#102×C61C2314yes—
184#102×C61C2314yes—
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
194#41×C61—28no—
195#41×C61—44no—
196#41×C61—48no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—44no—
205C2×D4×C61#4114yes—
206C2×D4×C61C2412yes—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—44no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61C2×D414yes—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—24no—
229C22×Dic61—82no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233D4×D61—28no—
234D4×D61—44no—
235D4×D61—48no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—22no—
240C2×D244—24no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244—44no—
244C2×D244C2412yes—
245C2×D244C2412yes—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—82no—
251C2×C4×D61—82no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2412yes—
254C2×C8×C61—22no—
255C2×C8×C61—22no—
256C2×C8×C61—44no—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C4⋊C4×C61C2412yes—
263C22⋊C4×C61—24no—
264C42×C61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61C2×D414yes—
267#11758201—44no—
268#11758199—28no—
269#11758198—24no—
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—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196C2×D414yes—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418C2412yes—
291C2×#92418C2412yes—
292D488—44no—
293C8×D61—44no—
294C23×C61—24no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—48no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—48no—
315C22×D61—84no—
316C22×D61—816no—
317C22×D61#13514yes—
318C22×D61C22×D412yes—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61—42no—
322D4×C61—24no—
323D4×C61—22no—
324D4×C61—48no—
325D4×C61C2×#4114yes—
326C2×C4×C61—22no—
327C2×C4×C61—24no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—48no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4112yes—
340C2×C4×C61H(5,𝔽2)12yes—
341C2×C4×C61C2511yescharacteristic
342C22⋊D61—28no—
343C22⋊D61—48no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—84no—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356C2×Dic61C22×D412yes—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—22no—
361D244—48no—
362D244—42no—
363D244—42no—
364C4×D61—24no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—84no—
368C4×D61—84no—
369C8×C61—22no—
370C8×C61—22no—
371#92418—22no—
372#92418—22no—
373C2×#3297—611nomaximal, Sylow
374C22×C61—24no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—48no—
379C22×C61—44no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61#54612yes—
383C22×C61C2×#13512yes—
384C22×C61#57612yes—
385C22×C61C23×D411yescharacteristic
386C2×D61—22no—
387C2×D61—28no—
388C2×D61—22no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—816no—
396C2×D61—84no—
397C2×D61—84no—
398C2×D61C2×#13514yes—
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#3297—6116no—
414C2×#488—611no—
415C2×#484—611no—
416C2×#482—611no—
417C2×#478—611no—
418C2×#466—611no—
419C2×#465—611no—
420C2×#463—611no—
421C2×#449—611no—
422C2×#447—611no—
423C2×C4×D8—611no—
424C2×C8×D4—611no—
425C2×#416D6111yescharacteristic, complemented
426C22×#102—611no—
427C2×C61—44no—
428C2×C61—42no—
429C2×C61#329714yescomplemented
430C2×C61C2×#54611yescharacteristic
431C2×C61C22×#13511yescharacteristic
432C2×C61C2×#57611yescharacteristic
433D61—24no—
434D61—82no—
435D61—82no—
436C22×#41C2×D6111yescharacteristic
437C23×D4—611no—
438C22×SD16—611no—
439C22×D8—611no—
440C22×D8—611no—
441C23×C8—611no—
442C23×C8C2×D6111yescharacteristic, complemented
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—611no—
456C2×#121—1221no—
457C2×#121—1221no—
458C2×#120—1221no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—611no—
462C2×C4×D4—1221no—
463C2×#117C2×D6111yescharacteristic, complemented
464C22×C4⋊C4—611no—
465C22×C22⋊C4—1221no—
466#488—618no—
467#484—618no—
468#482—618no—
469#478—618no—
470#466—618no—
471#465—618no—
472#463—618no—
473#449—618no—
474#447—618no—
475C4×D8—618no—
476C8×D4—618no—
477C2×#107—611no—
478C2×#107—611no—
479C2×#106—611no—
480C2×C4⋊C8—611no—
481#416C2×D6118yescomplemented
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—618no—
491C2×#102C2×D6111yescharacteristic
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×C4×C8—611no—
496C61C2×#329711yescharacteristic, complemented, Sylow
497C25—1221no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D6114yes—
502C22×Q8C22×D6111yescharacteristic
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—
528C22×C8—42no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—614no—
532C22×C8—2442no—
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6114yescomplemented
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—614no—
546#121—614no—
547#121—614no—
548#121—1228no—
549#121—1228no—
550#121—1222no—
551#121—1222no—
552#121—1222no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—1228no—
559C4×D4—1222no—
560C4×D4—1222no—
561#117—22no—
562#117C22×D6114yescomplemented
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—614no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
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—21no—
587C2×C42—611no—
588#107—614no—
589#107—614no—
590#106—614no—
591C4⋊C8—614no—
592#103—614no—
593#103C22×D6114yescomplemented
594#103C22×D6114yescomplemented
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⋊C8—614no—
604C4×C8—614no—
605C24—21no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—1221no—
610C24—4882no—
611C24—2444no—
612C24—2444no—
613C24D4×D6111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D6112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—614no—
626C2×D4—612no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1228no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1222no—
637C2×D4—1222no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—4882no—
641C2×D4—4882no—
642C2×D4—2444no—
643C2×D4—2444no—
644C2×D4—2448no—
645C2×D4—2444no—
646C2×D4#1175822214yes—
647C2×D4C23×D6112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4882no—
668C22×C4—4882no—
669C22×C4—4882no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—2444no—
675D8—1228no—
676D8—2444no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—44no—
680C2×C8—612no—
681C2×C8—612no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—2444no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—614no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
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—24no—
712C42—612no—
713C42—612no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—42no—
720C23—42no—
721C23—614no—
722C23—612no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—48816no—
728C23—4884no—
729C23—2448no—
730C23—2448no—
731C23—2442no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23C2×D4×D6112yes—
738C23C2×D4×D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—24no—
744D4—48no—
745D4—1228no—
746D4—1222no—
747D4—1222no—
748D4—1222no—
749D4—1222no—
750D4—4884no—
751D4—4884no—
752D4—2448no—
753D4—2448no—
754D4—2442no—
755D4—2442no—
756D4C2×#1175822214yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
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—4884no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4C2×D4×D6112yes—
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4C2×#1175822212yes—
787C2×C4#1451982212yes—
788C2×C4C24×D6111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1222no—
792C8—1222no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—614no—
802C22—1228no—
803C22—1222no—
804C22—1222no—
805C22—48816no—
806C22—4884no—
807C22—4884no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#1684040212yes—
815C22#135×D6112yes—
816C22#1684056412yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1222no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2442no—
827C4#1684040212yes—
828C4C22×#1175822211yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—42no—
831C2—44no—
832C2—1224no—
833C2—4882no—
834C2—4882no—
835C2#2145767014yesdirect product factor
836C2C2×#1684040211yescharacteristic
837C2C2×#135×D6111yescharacteristic
838C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
hypercenterC2×#416D61
hypocenterC61C2×#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16840456C2semidirect
2. C2×#16840400C2semidirect
3. #21457670C2direct (N × H)
4. C2×#16840118C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840086C2semidirect
7. C2×#16840060C2semidirect
8. C2×#16839998C2semidirect
9. C2×#16839994C2semidirect
10. C2×#16839980C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839897C2semidirect
13. C2×#16839842C2semidirect
14. C2×C8×C22⋊D61C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#416C2semidirect
18. C22×#11758201C22semidirect
23. #16840456C22semidirect
25. #16840400C22semidirect
27. C2×#14519768C22semidirect
34. C2×#14519751C22semidirect
40. C2×#14519739C22semidirect
44. #16840118C22semidirect
45. #16840096C22semidirect
46. #16840086C22semidirect
47. #16840060C22semidirect
48. #16839998C22semidirect
49. #16839994C22semidirect
50. #16839980C22semidirect
51. #16839907C22semidirect
52. #16839897C22semidirect
53. #16839842C22semidirect
54. C8×C22⋊D61C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
65. #102×D61C22semidirect
66. C2×C22⋊#92418C22semidirect
68. C2×C8×Dic61C22semidirect
70. C23×C8×C61C22semidirect
71. C2×#117×C61C22semidirect
72. C61×#416C22semidirect
73. C2×#103×C61C22semidirect
74. C2×#103×C61C22semidirect
94. C2×#11758201C23semidirect
105. #14519768C23semidirect
117. #14519751C23semidirect
125. #14519739C23semidirect
149. #14519711C23semidirect
150. #14519710C23semidirect
151. #14519708C23semidirect
152. #14519706C23semidirect
153. #14519701C23semidirect
155. #14519699C23semidirect
159. C22⋊#92418C23semidirect
161. C8×Dic61C23semidirect
174. C22×C8×C61C23semidirect
176. #117×C61C23semidirect
181. #103×C61C23semidirect
182. #103×C61C23semidirect
425. C2×#416D61semidirect
429. C2×C61#3297semidirect
442. C23×C8C2×D61semidirect
463. C2×#117C2×D61semidirect
481. #416C2×D61semidirect
483. C2×#103C2×D61semidirect
484. C2×#103C2×D61semidirect
496. C61C2×#3297semidirect
535. C22×C8C22×D61semidirect
562. #117C22×D61semidirect
593. #103C22×D61semidirect
594. #103C22×D61semidirect
835. C2#21457670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404562
C2×#168404002
#214576702
C2×#168401182
C2×#168400962
C2×#168400862
C2×#168400602
C2×#168399982
C2×#168399942
C2×#168399802
C2×#168399072
C2×#168398972
C2×#168398422
C2×C8×C22⋊D612
C2×#102×D612
C2×C61×#4162
C2×#329761