Finite Group Databasebeta

← C2×#21456868 #30551343

Subgroups — C2×#21456868 #30551343

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×#16840363C211yesmaximal, characteristic, complemented
2C2×#16840325C211yesmaximal, characteristic, complemented
3#21456868C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840137C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839978C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839954C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic, complemented
12C2×#16839904C211yesmaximal, characteristic, complemented
13C2×#16839897C211yesmaximal, characteristic, complemented
14C2×#16839894C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#459C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758190C2211yescharacteristic, complemented
20C22×#11758200C2211yescharacteristic, complemented
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758199C2211yescharacteristic, complemented
25#16840363—24no—
26#16840363C2218yescomplemented
27#16840325—24no—
28#16840325C2218yescomplemented
29C2×#14519773C2211yescharacteristic
30C2×#14519773C2211yescharacteristic, complemented
31C2×#14519768C2211yescharacteristic, complemented
32C2×#14519765C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519760—21no—
35C2×#14519759—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519751—21no—
38C2×#14519750—21no—
39C2×#14519749—21no—
40C2×#14519749—21no—
41C2×#14519748C2211yescharacteristic
42C2×#14519745—21no—
43C2×#14519745—21no—
44C2×C4×D244C2211yescharacteristic, complemented
45C2×#14519734C2211yescharacteristic
46#16840150C2218yescomplemented
47#16840137C2218yescomplemented
48#16840125C2218yescomplemented
49#16840115C2218yescomplemented
50#16839978C2218yescomplemented
51#16839977C2218yescomplemented
52#16839954C2218yescomplemented
53#16839908C2218yescomplemented
54#16839904C2218yescomplemented
55#16839897C2218yescomplemented
56#16839894C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×D8×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic, complemented
71C2×#127×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic, complemented
73C61×#459C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758224—22no—
79C2×#11758224—42no—
80C2×#11758224—42no—
81C2×#11758224C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
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—
93C2×D4×D61—22no—
94C2×D4×D61—42no—
95C2×D4×D61—42no—
96C2×D4×D61C2314yes—
97C23×Dic61—21no—
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C2×#11758190—42no—
101C2×#11758190C2314yescomplemented
102C2×#11758200—42no—
103C2×#11758200C2314yescomplemented
104C2×D488—42no—
105C2×D488C2314yes—
106C2×#11758199—42no—
107C2×#11758199—42no—
108C2×#11758199—42no—
109C2×#11758199C2314yes—
110C2×#11758199C2314yes—
111C2×#11758199C2314yescomplemented
112C22×#92418C2311yescharacteristic
113C22×#92418C2311yescharacteristic
114#14519773—22no—
115#14519773—22no—
116#14519773C2314yes—
117#14519773C2314yescomplemented
118#14519768—22no—
119#14519768C2314yescomplemented
120#14519765—22no—
121#14519765C2314yes—
122#14519764—22no—
123#14519764C2314yes—
124#14519760—28no—
125#14519759—28no—
126#14519752—22no—
127#14519752C2314yes—
128#14519751—28no—
129#14519750—28no—
130#14519749—28no—
131#14519749—28no—
132#14519748—22no—
133#14519748C2314yes—
134#14519745—28no—
135#14519745—28no—
136C4×D244—22no—
137C4×D244C2314yescomplemented
138#14519734D414yes—
139#14519734C2314yes—
140C2×C4⋊Dic61—21no—
141C2×C4⋊Dic61C2311yescharacteristic
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C2×#11758196D411yescharacteristic
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198D411yescharacteristic
153C2×#11758198D411yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yescomplemented
156#14519702C2314yescomplemented
157#14519700C2314yescomplemented
158#14519699C2314yes—
159#14519698C2314yes—
160#14519698C2314yescomplemented
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yescomplemented
165C8×Dic61C2314yescomplemented
166C22×D4×C61—21no—
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61—21no—
172C2×D8×C61—42no—
173C2×D8×C61—42no—
174C2×D8×C61C2314yes—
175C2×D8×C61C2314yescomplemented
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#127×C61—22no—
179#127×C61C2314yes—
180C4×D4×C61—22no—
181C4×D4×C61C2314yescomplemented
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yescomplemented
186#102×C61C2314yes—
187#102×C61C2314yescomplemented
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—24no—
194C23×D61—44no—
195C23×D61—82no—
196C23×D61—82no—
197C23×D61C2×D411yescharacteristic
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—24no—
202C2×D4×C61—24no—
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—82no—
210C2×D4×C61—82no—
211C2×D4×C61C2412yes—
212C2×D4×C61C2412yes—
213C2×D4×C61C2412yes—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—82no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—82no—
230C2×C22⋊D61—82no—
231C2×C22⋊D61—82no—
232C2×C22⋊D61—82no—
233C2×C22⋊D61—82no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—24no—
237C22×Dic61—44no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241#11758224—44no—
242#11758224—44no—
243#11758224—48no—
244D4×D61—44no—
245D4×D61—44no—
246D4×D61—48no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—24no—
254C2×D244—82no—
255C2×D244C2412yes—
256C2×D244C2412yes—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—24no—
260C2×C4×D61—82no—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2412yes—
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—
276C42×C61C2×D412yes—
277C42×C61C2412yes—
278C22⋊Dic61—24no—
279C22⋊Dic61—24no—
280C22⋊Dic61—24no—
281#11758200—44no—
282#11758199—44no—
283#11758199—44no—
284#11758199—44no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289#11758198C2×D414yes—
290#11758198C2×D414yes—
291C4⋊Dic61—21no—
292C4⋊Dic61—24no—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295#11758196C2×D414yes—
296#11758196C2×D414yes—
297C4×Dic61C2×D412yes—
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—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61C22×D411yescharacteristic
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—48no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—84no—
331C22×D61—84no—
332C22×D61—816no—
333C22×D61C22×D412yes—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—42no—
341D4×C61—42no—
342D4×C61—42no—
343D4×C61—84no—
344D4×C61—84no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—42no—
349C2×C4×C61—84no—
350C2×C4×C61C22×D412yes—
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—48no—
358C22⋊D61—84no—
359C22⋊D61—84no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—48no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61C22×D412yes—
372C2×Dic61C22×D412yes—
373C2×Dic61C22×D412yes—
374D244—22no—
375D244—22no—
376D244—22no—
377D244—22no—
378D244—42no—
379D244—42no—
380D244—84no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
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—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—84no—
403C22×C61—84no—
404C22×C61—84no—
405C22×C61#53512yes—
406C22×C61#57612yes—
407C22×C61#57612yes—
408C22×C61C23×D411yescharacteristic
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—44no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—816no—
420C2×D61—84no—
421C2×D61—84no—
422C4×C61—22no—
423C4×C61—22no—
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—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×#459D6111yescharacteristic, complemented
444C2×#449—611no—
445C2×#449—611no—
446C2×#447—611no—
447C2×#447—611no—
448C2×#433—611no—
449C2×C61—82no—
450C2×C61—82no—
451C2×C61—82no—
452C2×C61#322014yescomplemented
453C2×C61C2×#53511yescharacteristic
454C2×C61C2×#57611yescharacteristic
455C2×C61C2×#57611yescharacteristic
456D61—42no—
457D61—82no—
458D61—82no—
459C22×#41—611no—
460C23×D4—611no—
461C22×SD16—611no—
462C22×SD16—611no—
463C22×D8—611no—
464C22×D8—611no—
465C22×D8—611no—
466C22×D8—611no—
467C22×D8C2×D6111yescharacteristic
468C22×D8C2×D6111yescharacteristic, complemented
469#540—618no—
470#540—1224no—
471#535—618no—
472#535—1224no—
473C2×#127—611no—
474C2×#127—611no—
475C2×#127C2×D6111yescharacteristic
476C2×#125—611no—
477C2×#124—611no—
478C2×#124—611no—
479C2×#123—1221no—
480C2×#123—1221no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—1221no—
484C2×#121—1221no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#120—1221no—
488C2×#120—1221no—
489C2×C4×D4—611no—
490C2×C4×D4C2×D6111yescharacteristic, complemented
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#459C2×D6118yescomplemented
500#449—618no—
501#449—618no—
502#447—618no—
503#447—618no—
504#433—618no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8C2×D6111yescharacteristic, complemented
507C2×#103—611no—
508C2×#103—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102C2×D6111yescharacteristic
514C2×#102C2×D6111yescharacteristic, complemented
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517C2×#97—611no—
518C2×C4×C8—611no—
519C61C2×#322011yescharacteristic, complemented, Sylow
520C25—1221no—
521C2×#41—614no—
522C2×#41—1222no—
523C2×#41—2442no—
524C2×#41—2442no—
525C22×Q8—611no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—614no—
529C22×D4—611no—
530C22×D4—611no—
531C22×D4—1221no—
532C22×D4—1222no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—1221no—
536C22×D4—1221no—
537C22×D4—1221no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—2442no—
541C22×D4—2442no—
542C22×D4C22×D6111yescharacteristic
543C22×D4C22×D6111yescharacteristic
544C22×D4C22×D6111yescharacteristic
545C23×C4—21no—
546C23×C4—611no—
547C23×C4—1221no—
548C23×C4—1221no—
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×D6114yescomplemented
565C22×C8—611no—
566C22×C8—611no—
567C22×C8C22×D6111yescharacteristic
568C22×C8C22×D6111yescharacteristic
569#127—22no—
570#127—614no—
571#127—614no—
572#127—1222no—
573#127—1222no—
574#127C22×D6114yes—
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—614no—
584#121—614no—
585#121—1228no—
586#121—1228no—
587#121—1222no—
588#121—1228no—
589#121—1228no—
590#121—1222no—
591#120—1228no—
592#120—1228no—
593C4×D4—22no—
594C4×D4—614no—
595C4×D4—1222no—
596C4×D4C22×D6114yescomplemented
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×C42C22×D6111yescharacteristic
617C4⋊C8—614no—
618C4⋊C8C22×D6114yescomplemented
619#103—614no—
620#103—614no—
621#102—614no—
622#102—614no—
623#102—614no—
624#102—614no—
625#102C22×D6114yes—
626#102C22×D6114yescomplemented
627C22⋊C8—614no—
628C22⋊C8—614no—
629#97—614no—
630C4×C8—614no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—611no—
635C24—1224no—
636C24—1221no—
637C24—1221no—
638C24—4882no—
639C24—4882no—
640C24—2444no—
641#41—2444no—
642#41—2444no—
643#41—2448no—
644C2×Q8—612no—
645C2×Q8—1221no—
646C2×Q8—1222no—
647C2×Q8—1222no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—82no—
660C2×D4—82no—
661C2×D4—612no—
662C2×D4—612no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—4882no—
678C2×D4—4882no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—2444no—
684C2×D4—2444no—
685C2×D4—2448no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4C23×D6112yes—
689C2×D4C23×D6112yes—
690C2×D4C23×D6112yes—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—82no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—1224no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1224no—
705C22×C4—4882no—
706C22×C4—2444no—
707C22×C4D4×D6111yescharacteristic
708C22×C4D4×D6111yescharacteristic
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—
746C42D4×D6112yes—
747C42C23×D6112yes—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—612no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—4884no—
767C23—4884no—
768C23—48816no—
769C23—2448no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23—2442no—
776C23C2×D4×D6111yescharacteristic
777Q8—1222no—
778Q8—1222no—
779Q8—2442no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—42no—
787D4—42no—
788D4—42no—
789D4—84no—
790D4—84no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—1222no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—2448no—
802D4—2448no—
803D4—2442no—
804D4—2442no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—612no—
811C2×C4—612no—
812C2×C4—612no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1224no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—4884no—
822C2×C4—2448no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4C2×D4×D6112yes—
826C2×C4C2×D4×D6112yes—
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#1451982212yes—
829C2×C4#1451982312yes—
830C2×C4C24×D6111yescharacteristic
831C8—22no—
832C8—22no—
833C8—1222no—
834C8—1222no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—84no—
845C22—84no—
846C22—84no—
847C22—1222no—
848C22—1222no—
849C22—1222no—
850C22—48816no—
851C22—4884no—
852C22—4884no—
853C22—2442no—
854C22—2442no—
855C22—2442no—
856C22—2442no—
857C22—2442no—
858C22—2442no—
859C22—2444no—
860C22#1684032812yes—
861C22#1684056312yes—
862C22#1684056612yes—
863C22C22×D4×D6111yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—1222no—
868C4—1222no—
869C4—1222no—
870C4—2442no—
871C4—2442no—
872C4#1684032812yes—
873C4C2×#1451982211yescharacteristic
874C4C2×#1451982311yescharacteristic
875C2—82no—
876C2—82no—
877C2—82no—
878C2—4882no—
879C2—4882no—
880C2—2442no—
881C2#2145686814yesdirect product factor
882C2C2×#1684032811yescharacteristic
883C2C2×#1684056311yescharacteristic
884C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#459C2
socleC23×C61C22×D4
hypercenterC2×#459D61
hypocenterC61C2×#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16840363C2semidirect
2. C2×#16840325C2semidirect
3. #21456868C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840137C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839978C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839954C2semidirect
11. C2×#16839908C2semidirect
12. C2×#16839904C2semidirect
13. C2×#16839897C2semidirect
14. C2×#16839894C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#459C2semidirect
19. C22×#11758190C22semidirect
20. C22×#11758200C22semidirect
24. C22×#11758199C22semidirect
26. #16840363C22semidirect
28. #16840325C22semidirect
30. C2×#14519773C22semidirect
31. C2×#14519768C22semidirect
44. C2×C4×D244C22semidirect
46. #16840150C22semidirect
47. #16840137C22semidirect
48. #16840125C22semidirect
49. #16840115C22semidirect
50. #16839978C22semidirect
51. #16839977C22semidirect
52. #16839954C22semidirect
53. #16839908C22semidirect
54. #16839904C22semidirect
55. #16839897C22semidirect
56. #16839894C22semidirect
57. #16839822C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
63. C2×#14519698C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
70. C22×D8×C61C22semidirect
72. C2×C4×D4×C61C22semidirect
73. C61×#459C22semidirect
74. C2×C4⋊C8×C61C22semidirect
76. C2×#102×C61C22semidirect
101. C2×#11758190C23semidirect
103. C2×#11758200C23semidirect
111. C2×#11758199C23semidirect
117. #14519773C23semidirect
119. #14519768C23semidirect
137. C4×D244C23semidirect
155. C4⋊#92418C23semidirect
156. #14519702C23semidirect
157. #14519700C23semidirect
160. #14519698C23semidirect
164. #14519687C23semidirect
165. C8×Dic61C23semidirect
175. C2×D8×C61C23semidirect
181. C4×D4×C61C23semidirect
185. C4⋊C8×C61C23semidirect
187. #102×C61C23semidirect
443. C2×#459D61semidirect
452. C2×C61#3220semidirect
468. C22×D8C2×D61semidirect
490. C2×C4×D4C2×D61semidirect
499. #459C2×D61semidirect
506. C2×C4⋊C8C2×D61semidirect
514. C2×#102C2×D61semidirect
519. C61C2×#3220semidirect
564. C2×D8C22×D61semidirect
596. C4×D4C22×D61semidirect
618. C4⋊C8C22×D61semidirect
626. #102C22×D61semidirect
881. C2#21456868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403632
C2×#168403252
#214568682
C2×#168401502
C2×#168401372
C2×#168401252
C2×#168401152
C2×#168399782
C2×#168399772
C2×#168399542
C2×#168399082
C2×#168399042
C2×#168398972
C2×#168398942
C2×#168398222
C2×C61×#4592
C2×#322061