Finite Group Databasebeta

← C2×#21456867 #30551342

Subgroups — C2×#21456867 #30551342

Order 15616.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840365C211yesmaximal, characteristic, complemented
2C2×#16840326C211yesmaximal, characteristic, complemented
3#21456867C2116yesmaximal, direct product factor
4C2×#16840148C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840118C211yesmaximal, characteristic, complemented
8C2×#16839980C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839956C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic, complemented
13C2×#16839898C211yesmaximal, characteristic, complemented
14C2×#16839895C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C22×#11758201C2211yescharacteristic, complemented
19C22×D488C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic, complemented
24#16840365—24no—
25#16840365C2218yescomplemented
26#16840326—24no—
27#16840326C2218yescomplemented
28C2×#14519773C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519773C2211yescharacteristic, complemented
31C2×#14519768C2211yescharacteristic, complemented
32C2×#14519766C2211yescharacteristic
33C2×#14519766C2211yescharacteristic
34C2×#14519761—21no—
35C2×#14519759—21no—
36C2×#14519751—21no—
37C2×#14519751—21no—
38C2×#14519751C2211yescharacteristic
39C2×#14519749—21no—
40C2×#14519748—21no—
41C2×#14519745—21no—
42C2×#14519745—21no—
43C2×D4×Dic61C2211yescharacteristic, complemented
44C2×#14519739C2211yescharacteristic, complemented
45C2×#14519736C2211yescharacteristic
46#16840148C2218yescomplemented
47#16840137C2218yescomplemented
48#16840125C2218yescomplemented
49#16840118C2218yescomplemented
50#16839980C2218yescomplemented
51#16839979C2218yescomplemented
52#16839956C2218yescomplemented
53#16839955C2218yescomplemented
54#16839907C2218yescomplemented
55#16839898C2218yescomplemented
56#16839895C2218yescomplemented
57#16839820C2218yescomplemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic, complemented
71C22×D8×C61C2211yescharacteristic, complemented
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic
77C24×D61—21no—
78C22×D244—21no—
79C22×D244—22no—
80C22×D244—42no—
81C22×D244—42no—
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×D244C2314yes—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C2×#11758201—42no—
96C2×#11758201C2314yescomplemented
97C2×D488—42no—
98C2×D488—42no—
99C2×D488C2314yes—
100C2×D488C2314yes—
101C2×#11758199—42no—
102C2×#11758199—42no—
103C2×#11758199—42no—
104C2×#11758199C2314yes—
105C2×#11758199C2314yes—
106C2×#11758199C2314yescomplemented
107C22×#92418C2311yescharacteristic
108C22×#92418C2311yescharacteristic
109#14519773—22no—
110#14519773—22no—
111#14519773—22no—
112#14519773C2314yes—
113#14519773C2314yes—
114#14519773C2314yescomplemented
115#14519768—22no—
116#14519768C2314yescomplemented
117#14519766—22no—
118#14519766—22no—
119#14519766C2314yes—
120#14519766C2314yes—
121#14519761—28no—
122#14519759—28no—
123#14519751—22no—
124#14519751—28no—
125#14519751—28no—
126#14519751C2314yes—
127#14519749—28no—
128#14519748—28no—
129#14519745—28no—
130#14519745—28no—
131D4×Dic61—22no—
132D4×Dic61C2314yescomplemented
133#14519739—22no—
134#14519739C2314yescomplemented
135#14519736D414yes—
136#14519736C2314yes—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61D411yescharacteristic
139C2×C4⋊Dic61D411yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61D411yescharacteristic
144C2×C22⋊Dic61D411yescharacteristic
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519706C2314yescomplemented
154#14519706C2314yescomplemented
155#14519701C2314yescomplemented
156#14519699C2314yes—
157#14519699C2314yes—
158#14519698C2314yescomplemented
159#14519697C2314yes—
160#14519697C2314yes—
161C22⋊#92418C2314yes—
162#14519687C2314yescomplemented
163C8×Dic61C2314yescomplemented
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C2×SD16×C61—42no—
176C2×SD16×C61C2314yescomplemented
177C2×D8×C61—42no—
178C2×D8×C61C2314yescomplemented
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—24no—
195C23×D61—44no—
196C23×D61—82no—
197C23×D61—82no—
198#41×C61—44no—
199#41×C61—44no—
200#41×C61—48no—
201C2×Q8×C61—21no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61C2412yes—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—44no—
214C2×D4×C61—82no—
215C2×D4×C61C2412yes—
216C2×D4×C61C2412yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—44no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2412yes—
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—24no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61—82no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61—82no—
239C2×C22⋊D61—82no—
240C2×C22⋊D61—82no—
241C22×Dic61—21no—
242C22×Dic61—24no—
243C22×Dic61—82no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—24no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—44no—
259C2×D244—44no—
260C2×D244—44no—
261C2×D244—48no—
262C2×D244C2412yes—
263C2×D244C2412yes—
264C2×D244C2412yes—
265C2×C4×D61—24no—
266C2×C4×D61—82no—
267SD16×C61—44no—
268D8×C61—44no—
269C2×C8×C61—22no—
270C2×C8×C61—22no—
271C2×C8×C61C2412yes—
272C2×C8×C61C2412yes—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C2412yes—
275C22⋊C4×C61—24no—
276C22⋊Dic61—24no—
277C22⋊Dic61C2×D414yes—
278C22⋊Dic61C2×D414yes—
279#11758201—44no—
280#11758199—44no—
281#11758199—44no—
282#11758199—44no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289C4⋊Dic61—21no—
290C4⋊Dic61—24no—
291C4⋊Dic61C2×D414yes—
292C4⋊Dic61C2×D414yes—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295C4×Dic61C2×D412yes—
296C4×Dic61C2×D412yes—
297C4×Dic61C2412yes—
298C4×Dic61C2412yes—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303D488—44no—
304D488—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61C22×D412yes—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—48no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—816no—
334Q8×C61—22no—
335Q8×C61—22no—
336Q8×C61—42no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—48no—
342D4×C61—42no—
343D4×C61—42no—
344D4×C61—84no—
345C2×C4×C61—22no—
346C2×C4×C61—24no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—48no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61H(5,𝔽2)12yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—84no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C22⋊D61—84no—
364C22⋊D61—84no—
365C22⋊D61—84no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—84no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C2×Dic61C22×D412yes—
377D244—22no—
378D244—22no—
379D244—22no—
380D244—22no—
381D244—22no—
382D244—22no—
383D244—48no—
384D244—42no—
385D244—42no—
386D244—42no—
387C4×D61—84no—
388C8×C61—22no—
389C8×C61—22no—
390#92418—22no—
391#92418—22no—
392C2×#3220—611nomaximal, Sylow
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—44no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—84no—
404C22×C61—84no—
405C22×C61#53512yes—
406C22×C61#57612yes—
407C22×C61#57612yes—
408C22×C61C23×D411yescharacteristic
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—816no—
419C2×D61—84no—
420C2×D61—84no—
421C2×D61—84no—
422C4×C61—22no—
423C4×C61—42no—
424C4×C61—42no—
425C4×C61#53512yes—
426C4×C61C2×H(5,𝔽2)11yescharacteristic
427C4×C61C2×H(5,𝔽2)11yescharacteristic
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433C2×#540—611no—
434C2×#535—611no—
435#3220—6116no—
436C2×#496—611no—
437C2×#493—611no—
438C2×#490—611no—
439C2×#488—611no—
440C2×#463—611no—
441C2×#463—611no—
442C2×#459—611no—
443C2×#459—611no—
444C2×#449—611no—
445C2×#449D6111yescharacteristic, complemented
446C2×#447—611no—
447C2×#447—611no—
448C2×#433—611no—
449C2×C61—42no—
450C2×C61—82no—
451C2×C61—82no—
452C2×C61#322014yescomplemented
453C2×C61C2×#53511yescharacteristic
454C2×C61C2×#57611yescharacteristic
455C2×C61C2×#57611yescharacteristic
456D61—82no—
457D61—82no—
458D61—82no—
459C22×#41C2×D6111yescharacteristic
460C23×D4—611no—
461C22×SD16—611no—
462C22×SD16C2×D6111yescharacteristic, complemented
463C22×D8—611no—
464C22×D8—611no—
465C22×D8—611no—
466C22×D8—611no—
467C22×D8—611no—
468C22×D8C2×D6111yescharacteristic, complemented
469#540—618no—
470#540—1224no—
471#535—618no—
472#535—1224no—
473C2×#127—611no—
474C2×#127—611no—
475C2×#127—611no—
476C2×#125—611no—
477C2×#124—611no—
478C2×#124—611no—
479C2×#123—1221no—
480C2×#123—1221no—
481C2×#121—611no—
482C2×#121—1221no—
483C2×#121—1221no—
484C2×#121—1221no—
485C2×#121—1221no—
486C2×#121C2×D6111yescharacteristic
487C2×#120—1221no—
488C2×#120—1221no—
489C2×C4×D4—611no—
490C2×C4×D4—611no—
491C2×#117—611no—
492#496—618no—
493#493—618no—
494#490—618no—
495#488—618no—
496#463—618no—
497#463—618no—
498#459—618no—
499#459—618no—
500#449—618no—
501#449C2×D6118yescomplemented
502#447—618no—
503#447—618no—
504#433—618no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8—611no—
507C2×#103—611no—
508C2×#103C2×D6111yescharacteristic, complemented
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102C2×D6111yescharacteristic, complemented
515C2×C22⋊C8—611no—
516C2×C22⋊C8C2×D6111yescharacteristic
517C2×#97—611no—
518C2×C4×C8—611no—
519C61C2×#322011yescharacteristic, complemented, Sylow
520C25—1221no—
521C2×#41—22no—
522C2×#41—42no—
523C2×#41—42no—
524C2×#41C22×D6114yes—
525C22×Q8C22×D6111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—611no—
531C22×D4—614no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—1221no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—1222no—
541C22×D4—2442no—
542C22×D4—2442no—
543C22×D4C22×D6111yescharacteristic
544C22×D4C22×D6111yescharacteristic
545C23×C4—21no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4C22×D6111yescharacteristic
549C2×SD16—42no—
550C2×SD16—614no—
551C2×SD16—2442no—
552C2×SD16C22×D6114yescomplemented
553C2×D8—42no—
554C2×D8—614no—
555C2×D8—614no—
556C2×D8—614no—
557C2×D8—614no—
558C2×D8—614no—
559C2×D8—2442no—
560C2×D8—2442no—
561C2×D8—2442no—
562C2×D8—2442no—
563C2×D8—2442no—
564C2×D8C22×D6114yescomplemented
565C22×C8—611no—
566C22×C8—611no—
567C22×C8C22×D6111yescharacteristic
568C22×C8C22×D6111yescharacteristic
569#127—614no—
570#127—614no—
571#127—614no—
572#127—1222no—
573#127—1222no—
574#127—1222no—
575#125—614no—
576#125—1222no—
577#124—614no—
578#124—614no—
579#124—1222no—
580#124—1222no—
581#123—1228no—
582#123—1228no—
583#121—22no—
584#121—614no—
585#121—1228no—
586#121—1228no—
587#121—1228no—
588#121—1228no—
589#121—1222no—
590#121C22×D6114yes—
591#120—1228no—
592#120—1228no—
593C4×D4—614no—
594C4×D4—614no—
595C4×D4—1222no—
596C4×D4—1222no—
597#117—614no—
598#117—614no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C42—611no—
616C2×C42—611no—
617C4⋊C8—614no—
618C4⋊C8—614no—
619#103—614no—
620#103C22×D6114yescomplemented
621#102—614no—
622#102—614no—
623#102—614no—
624#102—614no—
625#102—614no—
626#102C22×D6114yescomplemented
627C22⋊C8—614no—
628C22⋊C8C22×D6114yes—
629#97—614no—
630C4×C8—614no—
631C24—21no—
632C24—21no—
633C24—1224no—
634C24—1221no—
635C24—1221no—
636C24—1221no—
637C24—4882no—
638C24—4882no—
639C24—2444no—
640C24D4×D6111yescharacteristic
641#41—44no—
642#41—44no—
643#41—48no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D6112yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—44no—
657C2×D4—82no—
658C2×D4—612no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1221no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—4882no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—4882no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4—2448no—
689C2×D4C23×D6112yes—
690C2×D4C23×D6112yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—24no—
696C22×C4—44no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—1224no—
702C22×C4—1224no—
703C22×C4—1221no—
704C22×C4—4882no—
705C22×C4—4882no—
706C22×C4D4×D6112yes—
707C22×C4D4×D6111yescharacteristic
708C22×C4C23×D6112yes—
709C22×C4C23×D6111yescharacteristic
710SD16—44no—
711SD16—2444no—
712D8—44no—
713D8—2444no—
714D8—2444no—
715D8—2444no—
716D8—2444no—
717D8—2444no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—612no—
721C2×C8—612no—
722C2×C8—1222no—
723C2×C8—1222no—
724C2×C8C23×D6112yes—
725C2×C8C23×D6112yes—
726C4⋊C4—21no—
727C4⋊C4—614no—
728C4⋊C4—614no—
729C4⋊C4—612no—
730C4⋊C4—1224no—
731C4⋊C4—1224no—
732C4⋊C4—1221no—
733C4⋊C4C23×D6112yes—
734C22⋊C4—24no—
735C22⋊C4—614no—
736C22⋊C4—614no—
737C22⋊C4—1224no—
738C22⋊C4—1224no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C22⋊C4—1224no—
742C22⋊C4—1224no—
743C22⋊C4—1224no—
744C42—612no—
745C42—612no—
746C42—612no—
747C42—612no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—1222no—
760C23—1222no—
761C23—1222no—
762C23—4884no—
763C23—4884no—
764C23—48816no—
765C23—2448no—
766C23—2442no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23C2×D4×D6112yes—
776C23C2×D4×D6111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—42no—
786D4—42no—
787D4—84no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—2448no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—48no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—612no—
817C2×C4—612no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—4884no—
824C2×C4—4884no—
825C2×C4—2442no—
826C2×C4C2×D4×D6112yes—
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#1451982212yes—
829C2×C4#1451982212yes—
830C2×C4C24×D6111yescharacteristic
831C8—22no—
832C8—22no—
833C8—1222no—
834C8—1222no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—84no—
846C22—84no—
847C22—48816no—
848C22—4884no—
849C22—4884no—
850C22—4884no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22#1684032712yes—
861C22#1684056412yes—
862C22#1684056612yes—
863C22C22×D4×D6111yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—1222no—
868C4—1222no—
869C4—1222no—
870C4—1222no—
871C4—2442no—
872C4#1684032712yes—
873C4C2×#1451982211yescharacteristic
874C4C2×#1451982211yescharacteristic
875C2—42no—
876C2—82no—
877C2—82no—
878C2—4882no—
879C2—4882no—
880C2—4882no—
881C2#2145686714yesdirect product factor
882C2C2×#1684032711yescharacteristic
883C2C2×#1684056411yescharacteristic
884C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3220
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×#16840365C2semidirect
2. C2×#16840326C2semidirect
3. #21456867C2direct (N × H)
4. C2×#16840148C2semidirect
5. C2×#16840137C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840118C2semidirect
8. C2×#16839980C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839956C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839907C2semidirect
13. C2×#16839898C2semidirect
14. C2×#16839895C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#449C2semidirect
18. C22×#11758201C22semidirect
23. C22×#11758199C22semidirect
25. #16840365C22semidirect
27. #16840326C22semidirect
30. C2×#14519773C22semidirect
31. C2×#14519768C22semidirect
43. C2×D4×Dic61C22semidirect
44. C2×#14519739C22semidirect
46. #16840148C22semidirect
47. #16840137C22semidirect
48. #16840125C22semidirect
49. #16840118C22semidirect
50. #16839980C22semidirect
51. #16839979C22semidirect
52. #16839956C22semidirect
53. #16839955C22semidirect
54. #16839907C22semidirect
55. #16839898C22semidirect
56. #16839895C22semidirect
57. #16839820C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519701C22semidirect
63. C2×#14519698C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
70. C22×SD16×C61C22semidirect
71. C22×D8×C61C22semidirect
73. C61×#449C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#102×C61C22semidirect
96. C2×#11758201C23semidirect
106. C2×#11758199C23semidirect
114. #14519773C23semidirect
116. #14519768C23semidirect
132. D4×Dic61C23semidirect
134. #14519739C23semidirect
153. #14519706C23semidirect
154. #14519706C23semidirect
155. #14519701C23semidirect
158. #14519698C23semidirect
162. #14519687C23semidirect
163. C8×Dic61C23semidirect
176. C2×SD16×C61C23semidirect
178. C2×D8×C61C23semidirect
185. #103×C61C23semidirect
186. #102×C61C23semidirect
445. C2×#449D61semidirect
452. C2×C61#3220semidirect
462. C22×SD16C2×D61semidirect
468. C22×D8C2×D61semidirect
501. #449C2×D61semidirect
508. C2×#103C2×D61semidirect
514. C2×#102C2×D61semidirect
519. C61C2×#3220semidirect
552. C2×SD16C22×D61semidirect
564. C2×D8C22×D61semidirect
620. #103C22×D61semidirect
626. #102C22×D61semidirect
881. C2#21456867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403652
C2×#168403262
#214568672
C2×#168401482
C2×#168401372
C2×#168401252
C2×#168401182
C2×#168399802
C2×#168399792
C2×#168399562
C2×#168399552
C2×#168399072
C2×#168398982
C2×#168398952
C2×#168398202
C2×C61×#4492
C2×#322061