Finite Group Databasebeta

← C2×#21458902 #30561038

Subgroups — C2×#21458902 #30561038

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840498C211yesmaximal, characteristic, complemented
2C2×#16840495C211yesmaximal, characteristic, complemented
3#21458902C2116yesmaximal, direct product factor
4C2×#16840150C211yesmaximal, characteristic, complemented
5C2×#16840149C211yesmaximal, characteristic, complemented
6C2×#16840145C211yesmaximal, characteristic, complemented
7C2×#16839985C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839976C211yesmaximal, characteristic, complemented
10C2×#16839975C211yesmaximal, characteristic, complemented
11C2×#16839955C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839859C211yesmaximal, characteristic, complemented
15C2×#16839842C211yesmaximal, characteristic, complemented
16C2×C61×#459C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840498—24no—
25#16840498C2218yescomplemented
26#16840495—24no—
27#16840495C2218yescomplemented
28C2×#14519773C2211yescharacteristic
29C2×#14519765C2211yescharacteristic
30C2×#14519764—21no—
31C2×#14519764C2211yescharacteristic
32C2×#14519764C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519763—21no—
35C2×#14519760—21no—
36C2×#14519759—21no—
37C2×#14519758—21no—
38C2×#14519758—21no—
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×D4×Dic61—21no—
43C2×D4×Dic61C2211yescharacteristic
44C2×D4×Dic61C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×C4×C22⋊D61—21no—
47#16840150C2218yescomplemented
48#16840149C2218yescomplemented
49#16840145C2218yescomplemented
50#16839985C2218yescomplemented
51#16839983C2218yescomplemented
52#16839976C2218yescomplemented
53#16839975C2218yescomplemented
54#16839955C2218yescomplemented
55#16839891C2218yescomplemented
56#16839862C2218yescomplemented
57#16839859C2218yescomplemented
58#16839842C2218yescomplemented
59C2×#14519710C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#459C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×Dic244—42no—
87C2×Dic244C2314yes—
88C2×#11758190—42no—
89C2×#11758190C2314yes—
90C2×#11758200—24no—
91C2×#11758200—24no—
92C2×#11758200—42no—
93C2×#11758200C2314yes—
94C2×#11758200C2314yes—
95C2×#11758200C2314yes—
96C2×#11758199—24no—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519773—22no—
103#14519773C2314yes—
104#14519765—22no—
105#14519765C2314yes—
106#14519764—28no—
107#14519764—22no—
108#14519764—22no—
109#14519764—22no—
110#14519764C2314yes—
111#14519764C2314yes—
112#14519764C2314yes—
113#14519763—28no—
114#14519760—28no—
115#14519759—28no—
116#14519758—28no—
117#14519758—28no—
118C4×Dic122—22no—
119C4×Dic122D414yes—
120C4×Dic122C2314yes—
121C4×Dic122C2314yes—
122#14519742—22no—
123#14519742C2314yes—
124D4×Dic61—28no—
125D4×Dic61—22no—
126D4×Dic61—22no—
127D4×Dic61C2314yes—
128D4×Dic61C2314yes—
129#14519739—22no—
130#14519739C2314yes—
131C4×C22⋊D61—28no—
132C2×C4⋊Dic61D411yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519710C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160#14519688C2314yes—
161#14519687C2314yes—
162C8×Dic61C2314yes—
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C23×C4×C61—21no—
169C2×D8×C61—42no—
170C2×D8×C61—42no—
171C2×D8×C61C2314yes—
172C2×D8×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#127×C61—22no—
176#127×C61C2314yes—
177C4×D4×C61—22no—
178C4×D4×C61C2314yes—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—21no—
188C23×D61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—44no—
201C2×D4×C61—82no—
202C2×D4×C61C2412yes—
203C2×D4×C61C2412yes—
204C2×D4×C61C2412yes—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—82no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2411yescharacteristic
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—82no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—24no—
220C22×Dic61—82no—
221C22×Dic61—82no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C2×D244—22no—
227C2×D244—22no—
228C2×D244—21no—
229C2×D244C2412yes—
230C2×C4×D61—24no—
231C2×C4×D61—82no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—42no—
239C2×Dic122C2×D414yes—
240C2×Dic122C2412yes—
241C2×Dic122C2412yes—
242D8×C61—44no—
243D8×C61—44no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C42×C61C2×D412yes—
252C42×C61C2412yes—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261#11758200—28no—
262#11758200—28no—
263#11758200—44no—
264#11758199—28no—
265#11758199—44no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269C4⋊Dic61—21no—
270C4⋊Dic61C2×D414yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196C2×D414yes—
275#11758196C2×D414yes—
276C4×Dic61—24no—
277C4×Dic61—24no—
278C4×Dic61C2×D412yes—
279C4×Dic61C2×D412yes—
280C4×Dic61C2412yes—
281C4×Dic61C2412yes—
282C2×#92418—22no—
283C2×#92418#4114yes—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286Dic244—44no—
287#11758190—44no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—48no—
312D4×C61—42no—
313D4×C61—42no—
314D4×C61—42no—
315D4×C61—84no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61—84no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—84no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—84no—
340C2×Dic61—84no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
345D244—22no—
346D244—22no—
347D244—42no—
348C4×D61—84no—
349Dic122—22no—
350Dic122—22no—
351Dic122—22no—
352Dic122—22no—
353Dic122—44no—
354Dic122—42no—
355Dic122—42no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418C2×#4114yes—
360C2×#3403—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—84no—
371C22×C61—84no—
372C22×C61—84no—
373C22×C61#55012yes—
374C22×C61#57512yes—
375C22×C61#57612yes—
376C22×C61C23×D411yescharacteristic
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—84no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—42no—
384C4×C61#55012yes—
385C4×C61C22×#4111yescharacteristic
386C4×C61C2×H(5,𝔽2)11yescharacteristic
387Dic61—22no—
388Dic61—22no—
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394C2×#559—611no—
395C2×#559—611no—
396#3403—6116no—
397C2×#496—611no—
398C2×#496—611no—
399C2×#495—611no—
400C2×#464—611no—
401C2×#464—611no—
402C2×#463—611no—
403C2×#463—611no—
404C2×#459—611no—
405C2×#459D6111yescharacteristic, complemented
406C2×#446—611no—
407C2×#440—611no—
408C2×#440—611no—
409C2×C4×D8—611no—
410C2×C61—82no—
411C2×C61—82no—
412C2×C61—82no—
413C2×C61#340314yescomplemented
414C2×C61C2×#55011yescharacteristic
415C2×C61C2×#57511yescharacteristic
416C2×C61C2×#57611yescharacteristic
417D61—82no—
418C22×Q16—611no—
419C22×SD16—611no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×SD16—611no—
423C22×D8—611no—
424C22×D8—611no—
425C22×D8C2×D6111yescharacteristic
426C22×D8C2×D6111yescharacteristic
427#559—618no—
428#559—618no—
429#559—1224no—
430#559—1224no—
431C2×#127—611no—
432C2×#127C2×D6111yescharacteristic
433C2×#124—611no—
434C2×#124—611no—
435C2×#124—611no—
436C2×#124—611no—
437C2×#124—1221no—
438C2×#124—1221no—
439C2×#123—1221no—
440C2×#123—1221no—
441C2×#123—1221no—
442C2×#123—1221no—
443C2×C4×Q8—611no—
444C2×C4×Q8—611no—
445C2×C4×Q8—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—1221no—
450C2×C4×D4—1221no—
451C2×C4×D4C2×D6111yescharacteristic
452#496—618no—
453#496—618no—
454#495—618no—
455#464—618no—
456#464—618no—
457#463—618no—
458#463—618no—
459#459—618no—
460#459C2×D6118yescomplemented
461#446—618no—
462#440—618no—
463#440—618no—
464C4×D8—618no—
465C2×#107—611no—
466C2×C4⋊C8—611no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8C2×D6111yescharacteristic
469C2×#103—611no—
470C2×#103—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102C2×D6111yescharacteristic
474C2×#102C2×D6111yescharacteristic
475C2×#97—611no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C61C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—611no—
480C22×Q8—611no—
481C22×Q8—611no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4C22×D6111yescharacteristic
488C22×D4C22×D6111yescharacteristic
489C22×D4C22×D6111yescharacteristic
490C23×C4—21no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×Q16—614no—
495C2×Q16—2442no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×SD16—614no—
500C2×SD16—1224no—
501C2×SD16—1224no—
502C2×SD16—2442no—
503C2×SD16—2442no—
504C2×D8—42no—
505C2×D8—42no—
506C2×D8—614no—
507C2×D8—614no—
508C2×D8—1224no—
509C2×D8—2442no—
510C2×D8C22×D6114yes—
511C2×D8C22×D6114yes—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8C22×D6111yescharacteristic
515C22×C8C22×D6111yescharacteristic
516#127—22no—
517#127—614no—
518#127—1222no—
519#127C22×D6114yes—
520#124—614no—
521#124—614no—
522#124—614no—
523#124—614no—
524#124—1222no—
525#124—1222no—
526#124—1222no—
527#124—1228no—
528#124—1228no—
529#124—1222no—
530#123—1228no—
531#123—1228no—
532#123—1228no—
533#123—1228no—
534C4×Q8—614no—
535C4×Q8—614no—
536C4×Q8—614no—
537C4×Q8—614no—
538C4×Q8—1222no—
539C4×Q8—1222no—
540C4×D4—22no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—1228no—
548C4×D4—1228no—
549C4×D4C22×D6114yes—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
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×C42—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575C4⋊C8—614no—
576C4⋊C8—614no—
577C4⋊C8C22×D6114yes—
578#103—614no—
579#103—614no—
580#102—614no—
581#102—614no—
582#102C22×D6114yes—
583#102C22×D6114yes—
584#97—614no—
585#97—614no—
586C4×C8—614no—
587C24—21no—
588C24—21no—
589C24—21no—
590C24—1221no—
591C2×Q8—614no—
592C2×Q8—612no—
593C2×Q8—612no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8—2442no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—82no—
614C2×D4—612no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—4882no—
621C2×D4—2444no—
622C2×D4C23×D6112yes—
623C2×D4C23×D6112yes—
624C2×D4C23×D6112yes—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—82no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—4882no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644Q16—2444no—
645SD16—1228no—
646SD16—1228no—
647SD16—2444no—
648SD16—2444no—
649D8—44no—
650D8—44no—
651D8—1228no—
652D8—2444no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—614no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—1222no—
659C2×C8C23×D6112yes—
660C2×C8C23×D6112yes—
661C4⋊C4—21no—
662C4⋊C4—614no—
663C4⋊C4—614no—
664C4⋊C4—614no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1221no—
668C4⋊C4—1224no—
669C4⋊C4C23×D6112yes—
670C22⋊C4—24no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C42—612no—
683C42—612no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42—1224no—
688C42D4×D6112yes—
689C42C23×D6112yes—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—1222no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23C2×D4×D6111yescharacteristic
707Q8—1222no—
708Q8—1222no—
709Q8—1222no—
710Q8—1222no—
711Q8—2444no—
712Q8—2442no—
713Q8—2442no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—84no—
725D4—1222no—
726D4—1222no—
727D4—4884no—
728D4—2448no—
729D4—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—84no—
735C2×C4—612no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4C2×D4×D6112yes—
753C2×C4C2×D4×D6112yes—
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4#41×D6112yes—
756C2×C4#1451982212yes—
757C2×C4C24×D6111yescharacteristic
758C8—22no—
759C8—22no—
760C8—614no—
761C8—1222no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—84no—
772C22—84no—
773C22—84no—
774C22—4884no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22#1684043012yes—
779C22#1684055812yes—
780C22#1684056312yes—
781C22C22×D4×D6111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—1222no—
786C4—1222no—
787C4—1222no—
788C4—1222no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4#1684043012yes—
793C4C2×#41×D6111yescharacteristic
794C4C2×#1451982211yescharacteristic
795C2—82no—
796C2—82no—
797C2—82no—
798C2—4882no—
799C2#2145890214yesdirect product factor
800C2C2×#1684043011yescharacteristic
801C2C2×#1684055811yescharacteristic
802C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#459C2
socleC23×C61C22×D4
hypercenterC2×#459D61
hypocenterC61C2×#3403
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×#16840498C2semidirect
2. C2×#16840495C2semidirect
3. #21458902C2direct (N × H)
4. C2×#16840150C2semidirect
5. C2×#16840149C2semidirect
6. C2×#16840145C2semidirect
7. C2×#16839985C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839976C2semidirect
10. C2×#16839975C2semidirect
11. C2×#16839955C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839859C2semidirect
15. C2×#16839842C2semidirect
16. C2×C61×#459C2semidirect
25. #16840498C22semidirect
27. #16840495C22semidirect
47. #16840150C22semidirect
48. #16840149C22semidirect
49. #16840145C22semidirect
50. #16839985C22semidirect
51. #16839983C22semidirect
52. #16839976C22semidirect
53. #16839975C22semidirect
54. #16839955C22semidirect
55. #16839891C22semidirect
56. #16839862C22semidirect
57. #16839859C22semidirect
58. #16839842C22semidirect
73. C61×#459C22semidirect
405. C2×#459D61semidirect
413. C2×C61#3403semidirect
460. #459C2×D61semidirect
478. C61C2×#3403semidirect
799. C2#21458902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404982
C2×#168404952
#214589022
C2×#168401502
C2×#168401492
C2×#168401452
C2×#168399852
C2×#168399832
C2×#168399762
C2×#168399752
C2×#168399552
C2×#168398912
C2×#168398622
C2×#168398592
C2×#168398422
C2×C61×#4592
C2×#340361