Finite Group Databasebeta

← C2×#21456865 #30551340

Subgroups — C2×#21456865 #30551340

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×#16840329C211yesmaximal, characteristic, complemented
3#21456865C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839976C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839956C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839909C211yesmaximal, characteristic, complemented
13C2×#16839905C211yesmaximal, characteristic, complemented
14C2×#16839896C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#447C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758190C2211yescharacteristic, complemented
19C22×#11758200C2211yescharacteristic, complemented
20C22×D488C2211yescharacteristic, complemented
21C22×#11758199C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic, complemented
24#16840365—24no—
25#16840365C2218yescomplemented
26#16840329—24no—
27#16840329C2218yescomplemented
28C2×#14519773C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519773C2211yescharacteristic, complemented
31C2×#14519768C2211yescharacteristic, complemented
32C2×#14519764C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519761—21no—
35C2×#14519759—21no—
36C2×#14519751C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519748—21no—
39C2×#14519748—21no—
40C2×#14519748—21no—
41C2×#14519746—21no—
42C2×#14519746—21no—
43C2×D4×Dic61C2211yescharacteristic, complemented
44C2×#14519739C2211yescharacteristic, complemented
45C2×#14519736C2211yescharacteristic
46#16840150C2218yescomplemented
47#16840137C2218yescomplemented
48#16840125C2218yescomplemented
49#16840115C2218yescomplemented
50#16839976C2218yescomplemented
51#16839975C2218yescomplemented
52#16839956C2218yescomplemented
53#16839955C2218yescomplemented
54#16839909C2218yescomplemented
55#16839905C2218yescomplemented
56#16839896C2218yescomplemented
57#16839820C2218yescomplemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519700C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic, complemented
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic, complemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C23×D4×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#447C2218yescomplemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C2×#11758190—42no—
96C2×#11758190C2314yescomplemented
97C2×#11758200—42no—
98C2×#11758200C2314yescomplemented
99C2×D488—42no—
100C2×D488C2314yescomplemented
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#14519764—22no—
118#14519764—22no—
119#14519764C2314yes—
120#14519764C2314yes—
121#14519761—28no—
122#14519759—28no—
123#14519751—22no—
124#14519751C2314yes—
125#14519749—28no—
126#14519748—28no—
127#14519748—28no—
128#14519748—28no—
129#14519746—28no—
130#14519746—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⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61D411yescharacteristic
148C2×C22⋊Dic61D411yescharacteristic
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519706C2314yescomplemented
154#14519706C2314yescomplemented
155#14519702C2314yescomplemented
156#14519700C2314yescomplemented
157#14519699C2314yescomplemented
158#14519698C2314yes—
159#14519698C2314yes—
160#14519697C2314yescomplemented
161C22⋊#92418C2314yes—
162#14519687C2314yescomplemented
163C8×Dic61C2314yescomplemented
164C25×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61—21no—
167C22×D4×C61—22no—
168C22×D4×C61—42no—
169C22×D4×C61—42no—
170C22×D4×C61C2311yescharacteristic
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C22×D4×C61C2314yes—
174C23×C4×C61C2311yescharacteristic
175C2×D8×C61—42no—
176C2×D8×C61—42no—
177C2×D8×C61C2314yes—
178C2×D8×C61C2314yes—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#102×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C24×C61—24no—
192C24×C61—44no—
193C24×C61—82no—
194C24×C61—82no—
195C24×C61C2×D411yescharacteristic
196C23×D61—21no—
197C23×D61—21no—
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—48no—
213C2×D4×C61—82no—
214C2×D4×C61C2412yes—
215C2×D4×C61C2412yes—
216C2×D4×C61C2412yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61—82no—
234C2×C22⋊D61—82no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61—82no—
239C2×C22⋊D61—82no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—24no—
243C22×Dic61—82no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758222—44no—
249#11758222—44no—
250#11758222—48no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244C2412yes—
258C2×D244C2412yes—
259C2×C4×D61—24no—
260C2×C4×D61—24no—
261C2×C4×D61—44no—
262C2×C4×D61—82no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—21no—
266C2×Dic122C2412yes—
267D8×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⋊Dic61—24no—
278C22⋊Dic61—24no—
279C22⋊Dic61—24no—
280C22⋊Dic61—24no—
281C22⋊Dic61C2×D414yes—
282C22⋊Dic61C2×D414yes—
283#11758200—44no—
284#11758199—44no—
285#11758199—44no—
286#11758199—44no—
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—
304#11758190—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—48no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—84no—
322C23×C61—84no—
323C23×C61—816no—
324C23×C61C22×D412yes—
325C23×C61C22×D411yescharacteristic
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—48no—
341D4×C61—42no—
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—42no—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—48no—
357C22⋊D61—84no—
358C22⋊D61—84no—
359C22⋊D61—84no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C22⋊D61—84no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—42no—
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—42no—
382D244—42no—
383C4×D61—48no—
384C4×D61—84no—
385Dic122—22no—
386Dic122—22no—
387Dic122—42no—
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—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—816no—
407C22×C61—84no—
408C22×C61—84no—
409C22×C61—84no—
410C22×C61#53512yes—
411C22×C61#57612yes—
412C22×C61#57612yes—
413C22×C61C23×D411yescharacteristic
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—84no—
421C2×D61—84no—
422C4×C61—22no—
423C4×C61—42no—
424C4×C61#53512yes—
425C4×C61C2×H(5,𝔽2)11yescharacteristic
426C4×C61C2×H(5,𝔽2)11yescharacteristic
427Dic61—22no—
428Dic61—22no—
429Dic61—22no—
430Dic61—22no—
431Dic61—42no—
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×#449—611no—
446C2×#447—611no—
447C2×#447D6111yescharacteristic, complemented
448C2×#433—611no—
449C2×C61—42no—
450C2×C61—82no—
451C2×C61—82no—
452C2×C61—82no—
453C2×C61#322014yescomplemented
454C2×C61C2×#53511yescharacteristic
455C2×C61C2×#57611yescharacteristic
456C2×C61C2×#57611yescharacteristic
457D61—82no—
458D61—82no—
459C22×#41—611no—
460C23×D4C2×D6111yescharacteristic
461C22×SD16—611no—
462C22×SD16—611no—
463C22×D8—611no—
464C22×D8—611no—
465C22×D8—611no—
466C22×D8—611no—
467C22×D8C2×D6111yescharacteristic
468C22×D8C2×D6111yescharacteristic
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#449—618no—
502#447—618no—
503#447C2×D6118yescomplemented
504#433—618no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8—611no—
507C2×#103—611no—
508C2×#103—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102C2×D6111yescharacteristic
514C2×#102C2×D6111yescharacteristic
515C2×C22⋊C8—611no—
516C2×C22⋊C8C2×D6111yescharacteristic
517C2×#97—611no—
518C2×C4×C8—611no—
519C61C2×#322011yescharacteristic, complemented, Sylow
520C25—21no—
521C2×#41—614no—
522C2×#41—1222no—
523C2×#41—2442no—
524C2×#41—2442no—
525C22×Q8—611no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—611no—
532C22×D4—611no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—1221no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4C22×D6111yescharacteristic
542C22×D4C22×D6111yescharacteristic
543C22×D4C22×D6111yescharacteristic
544C22×D4C22×D6114yes—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4C22×D6111yescharacteristic
549C2×SD16—614no—
550C2×SD16—614no—
551C2×SD16—2442no—
552C2×SD16—2442no—
553C2×D8—42no—
554C2×D8—42no—
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×D8C22×D6114yes—
564C2×D8C22×D6114yes—
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#103—614no—
621#102—614no—
622#102—614no—
623#102—614no—
624#102—614no—
625#102C22×D6114yes—
626#102C22×D6114yes—
627C22⋊C8—614no—
628C22⋊C8C22×D6114yes—
629#97—614no—
630C4×C8—614no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—24no—
635C24—44no—
636C24—82no—
637C24—82no—
638C24—1221no—
639C24—1221no—
640C24D4×D6111yescharacteristic
641#41—2444no—
642#41—2444no—
643#41—2448no—
644C2×Q8—612no—
645C2×Q8—1221no—
646C2×Q8—1222no—
647C2×Q8—1222no—
648C2×D4—24no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—44no—
660C2×D4—44no—
661C2×D4—44no—
662C2×D4—48no—
663C2×D4—82no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—4882no—
685C2×D4—4882no—
686C2×D4—4882no—
687C2×D4—2444no—
688C2×D4C23×D6112yes—
689C2×D4C23×D6112yes—
690C2×D4C23×D6112yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1224no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1224no—
703C22×C4—4882no—
704C22×C4—4882no—
705C22×C4—2444no—
706C22×C4D4×D6112yes—
707C22×C4D4×D6111yescharacteristic
708C22×C4C23×D6112yes—
709C22×C4C23×D6111yescharacteristic
710SD16—2444no—
711SD16—2444no—
712D8—44no—
713D8—44no—
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—22no—
754C23—48no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—84no—
765C23—84no—
766C23—816no—
767C23—1222no—
768C23—1222no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23C2×D4×D6112yes—
776C23C2×D4×D6111yescharacteristic
777Q8—1222no—
778Q8—1222no—
779Q8—2442no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—48no—
787D4—42no—
788D4—42no—
789D4—42no—
790D4—84no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—1222no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—4884no—
802D4—2448no—
803D4—2442no—
804D4—2442no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—42no—
811C2×C4—612no—
812C2×C4—612no—
813C2×C4—612no—
814C2×C4—612no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—4884no—
822C2×C4—4884no—
823C2×C4—2448no—
824C2×C4—2442no—
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—42no—
846C22—42no—
847C22—42no—
848C22—816no—
849C22—84no—
850C22—84no—
851C22—84no—
852C22—4884no—
853C22—4884no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22#1684032712yes—
861C22#1684056312yes—
862C22#1684056612yes—
863C22C22×D4×D6111yescharacteristic
864C4—22no—
865C4—42no—
866C4—1222no—
867C4—1222no—
868C4—1222no—
869C4—1222no—
870C4—2442no—
871C4—2442no—
872C4#1684032712yes—
873C4C2×#1451982211yescharacteristic
874C4C2×#1451982211yescharacteristic
875C2—42no—
876C2—82no—
877C2—82no—
878C2—82no—
879C2—4882no—
880C2—4882no—
881C2#2145686514yesdirect product factor
882C2C2×#1684032711yescharacteristic
883C2C2×#1684056311yescharacteristic
884C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#447C2
socleC23×C61C22×D4
hypercenterC2×#447D61
hypocenterC61C2×#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16840365C2semidirect
2. C2×#16840329C2semidirect
3. #21456865C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840137C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839976C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839956C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839909C2semidirect
13. C2×#16839905C2semidirect
14. C2×#16839896C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#447C2semidirect
18. C22×#11758190C22semidirect
19. C22×#11758200C22semidirect
20. C22×D488C22semidirect
23. C22×#11758199C22semidirect
25. #16840365C22semidirect
27. #16840329C22semidirect
30. C2×#14519773C22semidirect
31. C2×#14519768C22semidirect
43. C2×D4×Dic61C22semidirect
44. C2×#14519739C22semidirect
46. #16840150C22semidirect
47. #16840137C22semidirect
48. #16840125C22semidirect
49. #16840115C22semidirect
50. #16839976C22semidirect
51. #16839975C22semidirect
52. #16839956C22semidirect
53. #16839955C22semidirect
54. #16839909C22semidirect
55. #16839905C22semidirect
56. #16839896C22semidirect
57. #16839820C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519700C22semidirect
62. C2×#14519699C22semidirect
65. C2×#14519697C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
73. C61×#447C22semidirect
96. C2×#11758190C23semidirect
98. C2×#11758200C23semidirect
100. C2×D488C23semidirect
106. C2×#11758199C23semidirect
114. #14519773C23semidirect
116. #14519768C23semidirect
132. D4×Dic61C23semidirect
134. #14519739C23semidirect
153. #14519706C23semidirect
154. #14519706C23semidirect
155. #14519702C23semidirect
156. #14519700C23semidirect
157. #14519699C23semidirect
160. #14519697C23semidirect
162. #14519687C23semidirect
163. C8×Dic61C23semidirect
447. C2×#447D61semidirect
453. C2×C61#3220semidirect
503. #447C2×D61semidirect
519. C61C2×#3220semidirect
881. C2#21456865direct (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×#168403292
#214568652
C2×#168401502
C2×#168401372
C2×#168401252
C2×#168401152
C2×#168399762
C2×#168399752
C2×#168399562
C2×#168399552
C2×#168399092
C2×#168399052
C2×#168398962
C2×#168398202
C2×C61×#4472
C2×#322061