Finite Group Databasebeta

← C2×#21456064 #30548309

Subgroups — C2×#21456064 #30548309

Order 15616.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840368C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic, complemented
3#21456064C2116yesmaximal, direct product factor
4C2×#16840089C211yesmaximal, characteristic, complemented
5C2×#16840088C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16839958C211yesmaximal, characteristic, complemented
8C2×#16839957C211yesmaximal, characteristic, complemented
9C2×#16839897C211yesmaximal, characteristic, complemented
10C2×#16839897C211yesmaximal, characteristic, complemented
11C2×#16839873C211yesmaximal, characteristic, complemented
12C2×#16839871C211yesmaximal, characteristic, complemented
13C2×#16839844C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C22×D488C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840368—24no—
23#16840368C2218yescomplemented
24C2×#14519774C2211yescharacteristic, complemented
25C2×#14519762—21no—
26C2×#14519762—21no—
27C2×#14519752—21no—
28C2×#14519752—21no—
29C2×#14519752C2211yescharacteristic
30C2×#14519752C2211yescharacteristic
31#16840234—24no—
32#16840234C2218yescomplemented
33C2×C4×D244C2211yescharacteristic
34C2×D4×Dic61C2211yescharacteristic
35C2×#14519739C2211yescharacteristic
36C2×#14519739C2211yescharacteristic, complemented
37C2×#14519739C2211yescharacteristic, complemented
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42C22×#11758198—21no—
43C2×C22⋊C4×D61—21no—
44#16840089C2218yescomplemented
45#16840088C2218yescomplemented
46#16840059C2218yescomplemented
47#16839958C2218yescomplemented
48#16839957C2218yescomplemented
49#16839897C2218yescomplemented
50#16839897C2218yescomplemented
51#16839873C2218yescomplemented
52#16839871C2218yescomplemented
53#16839844C2218yescomplemented
54#16839842C2218yescomplemented
55#16839822C2218yescomplemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic, complemented
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic, complemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×#125×C61C2211yescharacteristic, complemented
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×D244—21no—
79C22×D244—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C2×D4×D61—24no—
87C2×D4×D61—24no—
88C2×D4×D61—22no—
89C2×D4×D61C2314yes—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96C2×D488—24no—
97C2×D488—24no—
98C2×D488C2314yes—
99C2×D488C2314yes—
100C2×#11758199—24no—
101C2×#11758199—24no—
102C2×#11758199C2314yes—
103C2×#11758199C2314yes—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106#14519774—22no—
107#14519774C2314yescomplemented
108#14519762—28no—
109#14519762—28no—
110#14519752—22no—
111#14519752—22no—
112#14519752—28no—
113#14519752—28no—
114#14519752C2314yes—
115#14519752C2314yes—
116C4×D244—22no—
117C4×D244C2314yes—
118D4×Dic61—22no—
119D4×Dic61C2314yes—
120#14519739—22no—
121#14519739—22no—
122#14519739—22no—
123#14519739C2314yes—
124#14519739C2314yescomplemented
125#14519739C2314yescomplemented
126C4×C22⋊D61—28no—
127#14519737—28no—
128#14519735—22no—
129#14519735C2314yes—
130#14519734D414yes—
131#14519734C2314yes—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—28no—
144C2×#11758198D411yescharacteristic
145C2×#11758198D411yescharacteristic
146C22⋊C4×D61—28no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yescomplemented
150#14519708C2314yescomplemented
151C4⋊#92418C2314yescomplemented
152#14519699C2314yescomplemented
153#14519699C2314yescomplemented
154#14519697C2314yes—
155#14519697C2314yes—
156#14519697C2314yescomplemented
157#14519697C2314yescomplemented
158#14519689C2314yes—
159#14519689C2314yes—
160#14519687C2314yescomplemented
161C8×Dic61C2314yescomplemented
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yescomplemented
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yescomplemented
178#106×C61C2314yescomplemented
179C4⋊C8×C61C2314yescomplemented
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61—28no—
185C23×D61—24no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—82no—
189C23×D61—82no—
190C23×D61C2×D411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61#4114yes—
194C2×D4×C61C2412yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—24no—
199C22×C4×C61—82no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—28no—
204C2×C22⋊D61—24no—
205C22×Dic61—21no—
206C22×Dic61—24no—
207C22×Dic61—82no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211D4×D61—216no—
212D4×D61—28no—
213D4×D61—28no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—24no—
224C2×D244—24no—
225C2×D244—24no—
226C2×D244—82no—
227C2×D244—82no—
228C2×D244—82no—
229C2×D244—82no—
230C2×D244#4114yes—
231C2×D244C2412yes—
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—82no—
241C2×C4×D61—82no—
242C2×C4×D61—82no—
243C2×C4×D61—82no—
244C2×C4×D61C2×D412yes—
245C2×C4×D61C2412yes—
246C2×C8×C61—22no—
247C2×C8×C61—22no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C42×C61C2×D412yes—
260C42×C61C2412yes—
261C22⋊Dic61—24no—
262#11758199—28no—
263#11758199—28no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198C2×D414yes—
272#11758198C2×D414yes—
273C4⋊Dic61—21no—
274C4⋊Dic61C2412yes—
275#11758196C2×D414yes—
276#11758196C2×D414yes—
277C4×Dic61—24no—
278C4×Dic61C2×D412yes—
279C4×Dic61C2412yes—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284D488—28no—
285D488—28no—
286C23×C61—24no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D411yescharacteristic
291C22×D61—22no—
292C22×D61—24no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—216no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—84no—
308C22×D61—84no—
309C22×D61—816no—
310C22×D61C22×D412yes—
311D4×C61—24no—
312D4×C61—22no—
313D4×C61C2×#4114yes—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—84no—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4112yes—
327C2×C4×C61C2×#4112yes—
328C2×C4×C61C2511yescharacteristic
329C22⋊D61—216no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—42no—
335C2×Dic61—84no—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339D244—24no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—42no—
346D244—42no—
347D244—84no—
348D244—84no—
349D244—84no—
350D244—84no—
351D244C2×#4114yes—
352C4×D61—24no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—84no—
356C4×D61—84no—
357C4×D61—84no—
358C4×D61—84no—
359C8×C61—22no—
360C8×C61—22no—
361#92418—22no—
362#92418—22no—
363C2×#3122—611nomaximal, Sylow
364C22×C61—24no—
365C22×C61—48no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61#52512yes—
369C22×C61#57612yes—
370C22×C61#57612yes—
371C22×C61C23×D411yescharacteristic
372C2×D61—22no—
373C2×D61—24no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—44no—
377C2×D61—48no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—816no—
387C2×D61—84no—
388C2×D61—84no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61#52512yes—
395C4×C61C22×#4111yescharacteristic
396C4×C61C22×#4111yescharacteristic
397Dic61—22no—
398Dic61—22no—
399Dic61—22no—
400Dic61—42no—
401C2×#540—611no—
402C2×#518—611no—
403#3122—6116no—
404C2×#482—611no—
405C2×#482—611no—
406C2×#478—611no—
407C2×#478D6111yescharacteristic, complemented
408C2×#459—611no—
409C2×#459—611no—
410C2×#447—611no—
411C2×#447—611no—
412C2×#442—611no—
413C2×#442—611no—
414C2×C4×D8—611no—
415C2×C4×D8—611no—
416C2×#433—611no—
417C2×C61—44no—
418C2×C61#312214yescomplemented
419C2×C61C2×#52511yescharacteristic
420C2×C61C2×#57611yescharacteristic
421C2×C61C2×#57611yescharacteristic
422D61—42no—
423D61—44no—
424D61—82no—
425D61—82no—
426C23×D4—611no—
427C22×D8—611no—
428C22×D8—611no—
429C22×D8—611no—
430C22×D8—611no—
431#540—618no—
432#540—1224no—
433C2×#127—611no—
434C2×#125C2×D6111yescharacteristic, complemented
435C2×#123—1221no—
436C2×#123—1221no—
437C2×#121—611no—
438C2×#121—611no—
439C2×#121—1221no—
440C2×#121—1221no—
441#518—618no—
442#518—1224no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×C4×D4—1221no—
450C2×C4×D4C2×D6111yescharacteristic
451C2×#117—611no—
452C2×#117—611no—
453C22×C22⋊C4—1221no—
454C22×C22⋊C4—1221no—
455#482—618no—
456#482—618no—
457#478—618no—
458#478C2×D6118yescomplemented
459#459—618no—
460#459—618no—
461#447—618no—
462#447—618no—
463#442—618no—
464#442—618no—
465C4×D8—618no—
466C4×D8—618no—
467#433—618no—
468C2×#107—611no—
469C2×#107C2×D6111yescharacteristic, complemented
470C2×#106—611no—
471C2×#106C2×D6111yescharacteristic, complemented
472C2×C4⋊C8—611no—
473C2×C4⋊C8C2×D6111yescharacteristic, complemented
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102C2×D6111yescharacteristic
481C2×#102C2×D6111yescharacteristic
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×#97—611no—
485C2×C4×C8—611no—
486C61C2×#312211yescharacteristic, complemented, Sylow
487C25—1221no—
488C22×D4—614no—
489C22×D4—611no—
490C22×D4—611no—
491C22×D4—611no—
492C22×D4—1221no—
493C22×D4—1221no—
494C22×D4—1222no—
495C22×D4—1221no—
496C22×D4—1224no—
497C22×D4—1224no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C23×C4—21no—
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4—1221no—
508C2×D8—614no—
509C2×D8—614no—
510C2×D8—614no—
511C2×D8—614no—
512C2×D8—1224no—
513C2×D8—1224no—
514C2×D8—1224no—
515C2×D8—1224no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6111yescharacteristic
520#127—614no—
521#127—1222no—
522#125—22no—
523#125C22×D6114yescomplemented
524#123—1228no—
525#123—1228no—
526#121—614no—
527#121—614no—
528#121—1228no—
529#121—1228no—
530#121—1222no—
531#121—1222no—
532C4×D4—22no—
533C4×D4—614no—
534C4×D4—614no—
535C4×D4—614no—
536C4×D4—614no—
537C4×D4—614no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—1222no—
542C4×D4—1228no—
543C4×D4—1228no—
544C4×D4—1222no—
545C4×D4C22×D6114yes—
546#117—614no—
547#117—614no—
548#117—614no—
549#117—1222no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C4⋊C4C22×D6111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—611no—
561C2×C22⋊C4—1228no—
562C2×C22⋊C4—1228no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C42—611no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#107C22×D6114yescomplemented
576#106—614no—
577#106C22×D6114yescomplemented
578C4⋊C8—614no—
579C4⋊C8C22×D6114yescomplemented
580#102—614no—
581#102—614no—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102C22×D6114yes—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97—614no—
591C4×C8—614no—
592C24—21no—
593C24—611no—
594C24—1224no—
595C24—1228no—
596C24—1221no—
597C24—1221no—
598C24—1221no—
599C24—4882no—
600C24—4882no—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—614no—
604C2×D4—612no—
605C2×D4—612no—
606C2×D4—612no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—1228no—
611C2×D4—12216no—
612C2×D4—1228no—
613C2×D4—1228no—
614C2×D4—1221no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—4882no—
627C2×D4—4882no—
628C2×D4#1175822614yes—
629C2×D4C23×D6112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1221no—
647C22×C4—1224no—
648C22×C4—4882no—
649C22×C4—4882no—
650C22×C4—4882no—
651C22×C4—4882no—
652C22×C4—4882no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656D8—1228no—
657D8—1228no—
658D8—1228no—
659D8—1228no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8C23×D6112yes—
667C2×C8C23×D6112yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—614no—
674C4⋊C4—614no—
675C4⋊C4—612no—
676C4⋊C4—1221no—
677C4⋊C4C23×D6112yes—
678C4⋊C4C23×D6112yes—
679C4⋊C4C23×D6112yes—
680C22⋊C4—24no—
681C22⋊C4—614no—
682C22⋊C4—614no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C42—612no—
692C42—612no—
693C42—1224no—
694C42D4×D6112yes—
695C42C23×D6112yes—
696C23—24no—
697C23—22no—
698C23—42no—
699C23—42no—
700C23—612no—
701C23—12216no—
702C23—1222no—
703C23—1224no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—4884no—
710C23—4884no—
711C23—48816no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23—2442no—
719C23—2442no—
720C23C2×D4×D6111yescharacteristic
721D4—24no—
722D4—22no—
723D4—614no—
724D4—12216no—
725D4—1224no—
726D4—1222no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—4884no—
732D4—4884no—
733D4—4884no—
734D4—4884no—
735D4—2442no—
736D4—2442no—
737D4C2×#1175822614yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1224no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—4884no—
758C2×C4—4884no—
759C2×C4—4884no—
760C2×C4—4884no—
761C2×C4—4884no—
762C2×C4—2442no—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6112yes—
767C2×C4C2×#1175822612yes—
768C2×C4C24×D6111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1222no—
772C8—1222no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—1224no—
781C22—48816no—
782C22—4884no—
783C22—4884no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22—2442no—
791C22—2442no—
792C22—2444no—
793C22—2448no—
794C22#1684027512yes—
795C22#1684056412yes—
796C22#1684056612yes—
797C22C22×D4×D6111yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—1222no—
804C4—1222no—
805C4—1222no—
806C4—2442no—
807C4#1684027512yes—
808C4C2×#41×D6111yescharacteristic
809C4C22×#1175822611yescharacteristic
810C2—44no—
811C2—4882no—
812C2—4882no—
813C2—2442no—
814C2—2444no—
815C2#2145606414yesdirect product factor
816C2C2×#1684027511yescharacteristic
817C2C2×#1684056411yescharacteristic
818C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
hypercenterC2×#478D61
hypocenterC61C2×#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840368C2semidirect
2. C2×#16840234C2semidirect
3. #21456064C2direct (N × H)
4. C2×#16840089C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16839958C2semidirect
8. C2×#16839957C2semidirect
9. C2×#16839897C2semidirect
10. C2×#16839897C2semidirect
11. C2×#16839873C2semidirect
12. C2×#16839871C2semidirect
13. C2×#16839844C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#478C2semidirect
23. #16840368C22semidirect
24. C2×#14519774C22semidirect
32. #16840234C22semidirect
36. C2×#14519739C22semidirect
37. C2×#14519739C22semidirect
44. #16840089C22semidirect
45. #16840088C22semidirect
46. #16840059C22semidirect
47. #16839958C22semidirect
48. #16839957C22semidirect
49. #16839897C22semidirect
50. #16839897C22semidirect
51. #16839873C22semidirect
52. #16839871C22semidirect
53. #16839844C22semidirect
54. #16839842C22semidirect
55. #16839822C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519699C22semidirect
60. C2×#14519699C22semidirect
63. C2×#14519697C22semidirect
64. C2×#14519697C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#478C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
107. #14519774C23semidirect
124. #14519739C23semidirect
125. #14519739C23semidirect
149. #14519710C23semidirect
150. #14519708C23semidirect
151. C4⋊#92418C23semidirect
152. #14519699C23semidirect
153. #14519699C23semidirect
156. #14519697C23semidirect
157. #14519697C23semidirect
160. #14519687C23semidirect
161. C8×Dic61C23semidirect
167. #125×C61C23semidirect
177. #107×C61C23semidirect
178. #106×C61C23semidirect
179. C4⋊C8×C61C23semidirect
407. C2×#478D61semidirect
418. C2×C61#3122semidirect
434. C2×#125C2×D61semidirect
458. #478C2×D61semidirect
469. C2×#107C2×D61semidirect
471. C2×#106C2×D61semidirect
473. C2×C4⋊C8C2×D61semidirect
486. C61C2×#3122semidirect
523. #125C22×D61semidirect
575. #107C22×D61semidirect
577. #106C22×D61semidirect
579. C4⋊C8C22×D61semidirect
815. C2#21456064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403682
C2×#168402342
#214560642
C2×#168400892
C2×#168400882
C2×#168400592
C2×#168399582
C2×#168399572
C2×#168398972
C2×#168398732
C2×#168398712
C2×#168398442
C2×#168398422
C2×#168398222
C2×C61×#4782
C2×#312261