Finite Group Databasebeta

← C2×#21457500 #30555213

Subgroups — C2×#21457500 #30555213

Order 15616.

3074 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic, complemented
2C23×#11758199C211yesmaximal, characteristic, complemented
3C2×#16840408C211yesmaximal, characteristic, complemented
4#21457500C2116yesmaximal, direct product factor
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840001C211yesmaximal, characteristic, complemented
7C2×#16839996C211yesmaximal, characteristic, complemented
8C2×#16839977C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic, complemented
11C2×#16839905C211yesmaximal, characteristic, complemented
12C2×#16839913C211yesmaximal, characteristic, complemented
13C2×#16839912C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×D4×#92418C211yesmaximal, characteristic, complemented
16C2×C61×#546C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic, complemented
18C23×D244C2211yescharacteristic
19C2×#14519797—28no—
20C2×#14519797C2218yescomplemented
21C22×#11758202C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic, complemented
23C22×#11758200C2211yescharacteristic, complemented
24C22×#11758201C2211yescharacteristic, complemented
25C22×#11758201C2211yescharacteristic, complemented
26C22×#11758199—28no—
27C22×#11758199C2211yescharacteristic
28C22×#11758199C2211yescharacteristic
29C22×#11758199C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2218yescomplemented
32C23×#92418C2211yescharacteristic
33C23×#92418C2211yescharacteristic, complemented
34#16840408—24no—
35#16840408C2218yescomplemented
36C2×#14519765C2211yescharacteristic, complemented
37C2×#14519762—21no—
38C2×#14519756C2211yescharacteristic
39C2×#14519751C2211yescharacteristic, complemented
40C2×#14519750—21no—
41C2×#14519745—21no—
42C2×C4×D244C2211yescharacteristic, complemented
43C2×C22⋊C4×D61—21no—
44#16840144C2218yescomplemented
45#16840001C2218yescomplemented
46#16839996C2218yescomplemented
47#16839977C2218yescomplemented
48#16839974C2218yescomplemented
49#16839913C2218yescomplemented
50#16839912C2218yescomplemented
51#16839907C2218yescomplemented
52#16839905C2218yescomplemented
53C4×#11758199C2218yescomplemented
54D4×#92418C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×C4⋊#92418C2211yescharacteristic, complemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519700C2211yescharacteristic, complemented
59C2×#14519698C2211yescharacteristic, complemented
60C2×#14519698C2211yescharacteristic, complemented
61C2×#14519697C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic, complemented
65C2×C4×#92418C2211yescharacteristic, complemented
66C22×#41×C61C2211yescharacteristic, complemented
67C23×D4×C61C2211yescharacteristic
68C61×#546—24no—
69C61×#546C2218yescomplemented
70C2×#124×C61C2211yescharacteristic, complemented
71C2×#123×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61—21no—
74C2×#121×C61C2211yescharacteristic, complemented
75C2×#120×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C2×C4×D4×C61C2211yescharacteristic, complemented
78C22×C22⋊C4×C61—21no—
79C24×D61—21no—
80C2×#11758222—22no—
81C2×#11758222—24no—
82C2×#11758222—42no—
83C2×#11758222C2314yescomplemented
84C22×Dic122C2311yescharacteristic
85C22×D244—24no—
86C22×D244—21no—
87C22×D244—22no—
88C22×D244—42no—
89C22×D244C2311yescharacteristic
90C22×D244C2314yes—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96#14519797—232no—
97C2×#11758202—24no—
98C2×#11758202C2314yescomplemented
99C2×#11758200—24no—
100C2×#11758200—42no—
101C2×#11758200C2314yescomplemented
102C2×#11758200C2314yescomplemented
103C2×#11758201—24no—
104C2×#11758201—42no—
105C2×#11758201C2314yescomplemented
106C2×#11758201C2314yescomplemented
107C2×#11758199—24no—
108C2×#11758199—24no—
109C2×#11758199—232no—
110C2×#11758199—24no—
111C2×#11758199D418yescomplemented
112C2×#11758199C2314yes—
113C2×#11758199C2314yes—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C22×#92418—24no—
117C22×#92418—24no—
118C22×#92418C2311yescharacteristic
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C22×#92418C2314yes—
122C22×#92418C2311yescharacteristic
123C22×#92418C2314yescomplemented
124#14519765—22no—
125#14519765C2314yescomplemented
126#14519762—28no—
127#14519756—22no—
128#14519756C2314yes—
129#14519751—22no—
130#14519751C2314yescomplemented
131#14519750—28no—
132#14519745—28no—
133C4×D244—22no—
134C4×D244C2314yescomplemented
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C22⋊C4×D61—28no—
143#14519710C2314yescomplemented
144C4⋊#92418C2314yescomplemented
145#14519701C2314yescomplemented
146#14519700C2314yescomplemented
147#14519698C2314yescomplemented
148#14519698C2314yescomplemented
149#14519697C2314yescomplemented
150#14519697C2314yescomplemented
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yescomplemented
153C4×#92418C2314yescomplemented
154C25×C61—21no—
155C2×#41×C61—22no—
156C2×#41×C61—24no—
157C2×#41×C61—42no—
158C2×#41×C61C2314yescomplemented
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61—24no—
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61—22no—
164C22×D4×C61—21no—
165C22×D4×C61—42no—
166C22×D4×C61D411yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2314yes—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
174#124×C61—22no—
175#124×C61C2314yescomplemented
176#123×C61—28no—
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yes—
179#121×C61—22no—
180#121×C61—28no—
181#121×C61C2314yescomplemented
182#120×C61—28no—
183C4×D4×C61—22no—
184C4×D4×C61D414yes—
185C4×D4×C61C2314yes—
186C4×D4×C61C2314yescomplemented
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61D411yescharacteristic
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61—28no—
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C22⋊C4×C61D411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—24no—
202C24×C61—44no—
203C24×C61—44no—
204C24×C61—82no—
205C24×C61C2×D411yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—24no—
210C23×D61—44no—
211C23×D61—44no—
212C23×D61—82no—
213#41×C61—28no—
214#41×C61—44no—
215#41×C61—48no—
216C2×Q8×C61—21no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61C2412yes—
220C2×D4×C61—24no—
221C2×D4×C61—28no—
222C2×D4×C61—24no—
223C2×D4×C61—24no—
224C2×D4×C61—21no—
225C2×D4×C61—22no—
226C2×D4×C61—24no—
227C2×D4×C61—21no—
228C2×D4×C61—22no—
229C2×D4×C61—22no—
230C2×D4×C61—44no—
231C2×D4×C61—48no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—82no—
235C2×D4×C61C2×D414yes—
236C2×D4×C61C2×D414yes—
237C2×D4×C61C2412yes—
238C2×D4×C61C2412yes—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—24no—
246C22×C4×C61—24no—
247C22×C4×C61—44no—
248C22×C4×C61—82no—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2412yes—
256C22×C4×C61C2412yes—
257C22×C4×C61C2411yescharacteristic
258C2×C22⋊D61—24no—
259C2×C22⋊D61—24no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—82no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264#11758222—28no—
265#11758222—44no—
266#11758222—48no—
267C2×D244—21no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—22no—
271C2×D244—28no—
272C2×D244—24no—
273C2×D244—21no—
274C2×D244—44no—
275C2×D244—48no—
276C2×D244—44no—
277C2×D244C2×D414yes—
278C2×D244C2412yes—
279C2×D244C2412yes—
280C2×C4×D61—24no—
281C2×C4×D61—24no—
282C2×C4×D61—44no—
283C2×C4×D61—82no—
284C2×Dic122—22no—
285C2×Dic122—22no—
286C2×Dic122—21no—
287C2×Dic122C2412yes—
288C4⋊C4×C61—24no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C2×D414yes—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—24no—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—24no—
297C22⋊C4×C61C2×D414yes—
298C22⋊C4×C61C2×D414yes—
299C42×C61C2×D412yes—
300C42×C61C2412yes—
301C22⋊Dic61—24no—
302#11758202—28no—
303#11758201—28no—
304#11758201—44no—
305#11758200—28no—
306#11758200—44no—
307#11758199—28no—
308#11758199—28no—
309#11758199—28no—
310#11758199C2×D4116yescomplemented
311#11758198—24no—
312#11758198—24no—
313#11758198—24no—
314#11758198—24no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317#11758196—24no—
318C2×#92418—22no—
319C2×#92418—22no—
320C2×#92418—22no—
321C2×#92418—28no—
322C2×#92418—28no—
323C2×#92418C2×D414yes—
324C2×#92418C2412yes—
325C2×#92418C2412yes—
326C2×#92418C2412yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—24no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—48no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—48no—
342C23×C61—42no—
343C23×C61—84no—
344C23×C61—816no—
345C23×C61#13514yescomplemented
346C23×C61C22×D412yes—
347C23×C61C22×D412yes—
348C23×C61C22×D411yescharacteristic
349C22×D61—24no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—48no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—48no—
358C22×D61—42no—
359C22×D61—84no—
360C22×D61—816no—
361Q8×C61—22no—
362Q8×C61—22no—
363Q8×C61—42no—
364D4×C61—28no—
365D4×C61—24no—
366D4×C61—22no—
367D4×C61—22no—
368D4×C61—22no—
369D4×C61—48no—
370D4×C61—48no—
371D4×C61—42no—
372D4×C61—84no—
373D4×C61C22×D414yes—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—24no—
379C2×C4×C61—24no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—48no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—84no—
390C2×C4×C61C22×D412yes—
391C2×C4×C61C22×D412yes—
392C2×C4×C61C22×D412yes—
393C2×C4×C61C22×D412yes—
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D412yes—
396C2×C4×C61H(5,𝔽2)12yes—
397C2×C4×C61C2511yescharacteristic
398C22⋊D61—48no—
399C22⋊D61—84no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404D244—24no—
405D244—22no—
406D244—22no—
407D244—22no—
408D244—48no—
409D244—42no—
410D244C22×D414yes—
411C4×D61—48no—
412C4×D61—84no—
413Dic122—22no—
414Dic122—22no—
415Dic122—42no—
416#92418—22no—
417#92418—22no—
418#92418—22no—
419#92418C22×D414yes—
420C2×#3280—611nomaximal, Sylow
421C22×C61—22no—
422C22×C61—28no—
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—24no—
426C22×C61—22no—
427C22×C61—22no—
428C22×C61—44no—
429C22×C61—48no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—816no—
436C22×C61—84no—
437C22×C61D4212yes—
438C22×C61C2×#13512yes—
439C22×C61C2×#13514yescomplemented
440C22×C61#57612yes—
441C22×C61C23×D411yescharacteristic
442C2×D61—24no—
443C2×D61—48no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—84no—
451C4×C61—22no—
452C4×C61—22no—
453C4×C61—22no—
454C4×C61—22no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61D4212yes—
458C4×C61C23×D411yescharacteristic
459C4×C61C2×H(5,𝔽2)11yescharacteristic
460Dic61—42no—
461Dic61—42no—
462C22×#135—611no—
463C23×D8—611no—
464C2×#546—611no—
465C2×#546D6111yescharacteristic, complemented
466#3280—6116no—
467C2×#495—611no—
468C2×#467—611no—
469C2×#466—611no—
470C2×#463—611no—
471C2×#463—611no—
472C2×#449—611no—
473C2×#449—611no—
474C2×#450—611no—
475C2×#450—611no—
476C2×C4×D8—611no—
477C2×C8×D4—611no—
478C2×C61—24no—
479C2×C61—42no—
480C2×C61—44no—
481C2×C61—82no—
482C2×C61#328014yescomplemented
483C2×C61C2×D4211yescharacteristic
484C2×C61C22×#13511yescharacteristic
485C2×C61C2×#57611yescharacteristic
486D61—44no—
487D61—82no—
488C22×#41—611no—
489C22×#41C2×D6111yescharacteristic, complemented
490C23×D4—611no—
491C23×D4C2×D6111yescharacteristic
492C2×#135—618no—
493C2×#135—1228no—
494C22×Q16—611no—
495C22×SD16—611no—
496C22×SD16—611no—
497C22×SD16—611no—
498C22×SD16—611no—
499C22×D8—611no—
500C22×D8—611no—
501C22×D8—611no—
502C22×D8—611no—
503C22×D8—618no—
504C22×D8—1228no—
505C23×C8—611no—
506C23×C8—611no—
507#546—24no—
508#546—618no—
509#546—1224no—
510#546C2×D6118yescomplemented
511C2×#124—611no—
512C2×#124C2×D6111yescharacteristic, complemented
513C2×#123—21no—
514C2×#123—1221no—
515C2×C22⋊Q8—611no—
516C2×C22⋊Q8C2×D6111yescharacteristic
517C2×#121—21no—
518C2×#121—611no—
519C2×#121—1221no—
520C2×#121C2×D6111yescharacteristic, complemented
521C2×#120—21no—
522C2×#120—1221no—
523C2×C4×D4—611no—
524C2×C4×D4C2×D6111yescharacteristic
525C2×C4×D4C2×D6111yescharacteristic, complemented
526C22×C22⋊C4—21no—
527C22×C22⋊C4—1221no—
528#495—618no—
529#467—618no—
530#466—618no—
531#463—618no—
532#463—618no—
533#450—618no—
534#450—618no—
535#449—618no—
536#449—618no—
537C4×D8—618no—
538C8×D4—618no—
539C2×#107—611no—
540C2×C4⋊C8—611no—
541C2×#103—611no—
542C2×#103—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×#102—611no—
546C2×#102—611no—
547C2×C22⋊C8—611no—
548C2×C22⋊C8—611no—
549C2×C4×C8—611no—
550C61C2×#328011yescharacteristic, complemented, Sylow
551C25—21no—
552C25—1221no—
553C2×#41—22no—
554C2×#41—24no—
555C2×#41—42no—
556C2×#41—614no—
557C2×#41—1224no—
558C2×#41—1222no—
559C2×#41—2442no—
560C2×#41C22×D6114yescomplemented
561C22×Q8—611no—
562C22×Q8C22×D6111yescharacteristic
563C22×D4—24no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—22no—
568C22×D4—42no—
569C22×D4—611no—
570C22×D4—611no—
571C22×D4—614no—
572C22×D4—1224no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1222no—
577C22×D4—2442no—
578C22×D4C22⋊D6111yescharacteristic
579C22×D4C22×D6111yescharacteristic
580C22×D4C22×D6114yes—
581C22×D4C22×D6111yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588#135—12232no—
589C2×Q16—614no—
590C2×Q16—1224no—
591C2×SD16—614no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×SD16—1224no—
596C2×SD16—1224no—
597C2×SD16—2442no—
598C2×SD16—2442no—
599C2×D8—618no—
600C2×D8—614no—
601C2×D8—614no—
602C2×D8—614no—
603C2×D8—614no—
604C2×D8—1224no—
605C2×D8—12232no—
606C2×D8—1224no—
607C2×D8—1224no—
608C22×C8—611no—
609C22×C8—611no—
610C22×C8—614no—
611C22×C8—611no—
612C22×C8—614no—
613C22×C8—611no—
614C22×C8—1224no—
615C22×C8—1224no—
616#124—22no—
617#124—614no—
618#124—1222no—
619#124C22×D6114yescomplemented
620#123—28no—
621#123—1228no—
622C22⋊Q8—22no—
623C22⋊Q8—614no—
624C22⋊Q8—1222no—
625C22⋊Q8C22×D6114yes—
626#121—22no—
627#121—28no—
628#121—614no—
629#121—1222no—
630#121—1228no—
631#121C22×D6114yescomplemented
632#120—28no—
633#120—1228no—
634C4×D4—22no—
635C4×D4—614no—
636C4×D4—1222no—
637C4×D4C22⋊D6114yes—
638C4×D4C22×D6114yes—
639C4×D4C22×D6114yescomplemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4C22⋊D6111yescharacteristic
644C2×C4⋊C4C22×D6111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—28no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1228no—
657C2×C22⋊C4C22⋊D6111yescharacteristic
658C2×C22⋊C4C22⋊D6111yescharacteristic
659C2×C42C22×D6111yescharacteristic
660#107—614no—
661C4⋊C8—614no—
662#103—614no—
663#103—614no—
664#102—614no—
665#102—614no—
666#102—614no—
667#102—614no—
668C22⋊C8—614no—
669C22⋊C8—614no—
670C4×C8—614no—
671C24—21no—
672C24—21no—
673C24—24no—
674C24—44no—
675C24—44no—
676C24—82no—
677C24—1221no—
678C24—1224no—
679C24—1221no—
680C24—4882no—
681C24—2444no—
682C24—2444no—
683C24C2×C22⋊D6111yescharacteristic
684C24C2×C22⋊D6111yescharacteristic
685#41—28no—
686#41—44no—
687#41—48no—
688#41—1228no—
689#41—2444no—
690#41—2448no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—612no—
695C2×Q8—1221no—
696C2×Q8—1222no—
697C2×Q8—1222no—
698C2×Q8C23×D6112yes—
699C2×D4—24no—
700C2×D4—28no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—21no—
705C2×D4—24no—
706C2×D4—21no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—44no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—614no—
715C2×D4—612no—
716C2×D4—612no—
717C2×D4—1228no—
718C2×D4—1224no—
719C2×D4—1224no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1224no—
723C2×D4—1221no—
724C2×D4—1222no—
725C2×D4—1222no—
726C2×D4—4882no—
727C2×D4—2444no—
728C2×D4—2448no—
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4D4×D6114yes—
732C2×D4C2×C22⋊D6114yes—
733C2×D4C23×D6112yes—
734C2×D4C23×D6112yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—44no—
744C22×C4—82no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—4882no—
750C22×C4—2444no—
751C22×C4C2×C22⋊D6112yes—
752C22×C4C2×C22⋊D6112yes—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6111yescharacteristic
756C22×C4C2×C22⋊D6111yescharacteristic
757C22×C4C23×D6112yes—
758C22×C4C23×D6112yes—
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761SD16—1228no—
762SD16—1228no—
763SD16—2444no—
764SD16—2444no—
765D8—6116no—
766D8—1228no—
767D8—1228no—
768D8—1228no—
769C2×C8—614no—
770C2×C8—612no—
771C2×C8—612no—
772C2×C8—612no—
773C2×C8—612no—
774C2×C8—1228no—
775C2×C8—1228no—
776C2×C8—1222no—
777C2×C8—1222no—
778C2×C8—1222no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—612no—
782C4⋊C4—1221no—
783C4⋊C4—1224no—
784C4⋊C4C2×C22⋊D6114yes—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4—1224no—
794C22⋊C4—1224no—
795C22⋊C4—1224no—
796C22⋊C4C2×C22⋊D6114yes—
797C22⋊C4C2×C22⋊D6114yes—
798C42C2×C22⋊D6112yes—
799C42C23×D6112yes—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—24no—
807C23—22no—
808C23—48no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—48no—
813C23—42no—
814C23—42no—
815C23—84no—
816C23—816no—
817C23—1222no—
818C23—1224no—
819C23—1222no—
820C23—48816no—
821C23—4884no—
822C23—2448no—
823C23—2442no—
824C23—2448no—
825C23—2442no—
826C23—2442no—
827C23—2442no—
828C23—2442no—
829C23#1451979714yescomplemented
830C23C22×C22⋊D6112yes—
831C23C22×C22⋊D6112yes—
832C23C22×C22⋊D6111yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—42no—
836Q8—1222no—
837Q8—1222no—
838Q8—2442no—
839D4—28no—
840D4—22no—
841D4—22no—
842D4—22no—
843D4—24no—
844D4—48no—
845D4—48no—
846D4—42no—
847D4—84no—
848D4—614no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—1224no—
853D4—4884no—
854D4—2448no—
855D4—2448no—
856D4—2442no—
857D4C2×D4×D6114yes—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—48no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—84no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—4884no—
877C2×C4—2448no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4C2×D4×D6112yes—
881C2×C4C22×C22⋊D6112yes—
882C2×C4C22×C22⋊D6112yes—
883C2×C4C22×C22⋊D6112yes—
884C2×C4C22×C22⋊D6112yes—
885C2×C4C22×C22⋊D6111yescharacteristic
886C2×C4#1451982212yes—
887C2×C4C24×D6111yescharacteristic
888C8—614no—
889C8—1222no—
890C8—1222no—
891C8—1222no—
892C22—22no—
893C22—22no—
894C22—28no—
895C22—22no—
896C22—24no—
897C22—22no—
898C22—22no—
899C22—42no—
900C22—42no—
901C22—44no—
902C22—48no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—816no—
907C22—84no—
908C22—1224no—
909C22—48816no—
910C22—4884no—
911C22—2442no—
912C22—2442no—
913C22—2442no—
914C22—2442no—
915C22—2442no—
916C22—2448no—
917C22D4×C22⋊D6112yes—
918C22C2×#1451979712yes—
919C22C2×#1451979714yescomplemented
920C22#1684056512yes—
921C22C23×C22⋊D6111yescharacteristic
922C4—22no—
923C4—22no—
924C4—22no—
925C4—22no—
926C4—42no—
927C4—42no—
928C4—2442no—
929C4—2442no—
930C4D4×C22⋊D6112yes—
931C4C22×D4×D6111yescharacteristic
932C4C2×#1451982211yescharacteristic
933C2—24no—
934C2—42no—
935C2—44no—
936C2—82no—
937C2—4882no—
938C2—2444no—
939C2#2145750014yesdirect product factor
940C2C2×D4×C22⋊D6111yescharacteristic
941C2C22×#1451979711yescharacteristic
942C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61C2×#3280
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#14519797C2semidirect
2. C23×#11758199C2semidirect
3. C2×#16840408C2semidirect
4. #21457500C2direct (N × H)
5. C2×#16840144C2semidirect
6. C2×#16840001C2semidirect
7. C2×#16839996C2semidirect
8. C2×#16839977C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839907C2semidirect
11. C2×#16839905C2semidirect
12. C2×#16839913C2semidirect
13. C2×#16839912C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×D4×#92418C2semidirect
16. C2×C61×#546C2semidirect
17. C22×#11758222C22semidirect
20. C2×#14519797C22semidirect
21. C22×#11758202C22semidirect
22. C22×#11758200C22semidirect
23. C22×#11758200C22semidirect
24. C22×#11758201C22semidirect
25. C22×#11758201C22semidirect
31. C22×#11758199C22semidirect
33. C23×#92418C22semidirect
35. #16840408C22semidirect
36. C2×#14519765C22semidirect
39. C2×#14519751C22semidirect
42. C2×C4×D244C22semidirect
44. #16840144C22semidirect
45. #16840001C22semidirect
46. #16839996C22semidirect
47. #16839977C22semidirect
48. #16839974C22semidirect
49. #16839913C22semidirect
50. #16839912C22semidirect
51. #16839907C22semidirect
52. #16839905C22semidirect
53. C4×#11758199C22semidirect
54. D4×#92418C22semidirect
55. C2×#14519710C22semidirect
56. C2×C4⋊#92418C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519700C22semidirect
59. C2×#14519698C22semidirect
60. C2×#14519698C22semidirect
61. C2×#14519697C22semidirect
62. C2×#14519697C22semidirect
64. C2×C22⋊#92418C22semidirect
65. C2×C4×#92418C22semidirect
66. C22×#41×C61C22semidirect
69. C61×#546C22semidirect
70. C2×#124×C61C22semidirect
74. C2×#121×C61C22semidirect
77. C2×C4×D4×C61C22semidirect
83. C2×#11758222C23semidirect
98. C2×#11758202C23semidirect
101. C2×#11758200C23semidirect
102. C2×#11758200C23semidirect
105. C2×#11758201C23semidirect
106. C2×#11758201C23semidirect
111. C2×#11758199D4semidirect
123. C22×#92418C23semidirect
125. #14519765C23semidirect
130. #14519751C23semidirect
134. C4×D244C23semidirect
143. #14519710C23semidirect
144. C4⋊#92418C23semidirect
145. #14519701C23semidirect
146. #14519700C23semidirect
147. #14519698C23semidirect
148. #14519698C23semidirect
149. #14519697C23semidirect
150. #14519697C23semidirect
152. C22⋊#92418C23semidirect
153. C4×#92418C23semidirect
158. C2×#41×C61C23semidirect
175. #124×C61C23semidirect
181. #121×C61C23semidirect
186. C4×D4×C61C23semidirect
310. #11758199C2×D4semidirect
345. C23×C61#135semidirect
439. C22×C61C2×#135semidirect
465. C2×#546D61semidirect
482. C2×C61#3280semidirect
489. C22×#41C2×D61semidirect
510. #546C2×D61semidirect
512. C2×#124C2×D61semidirect
520. C2×#121C2×D61semidirect
525. C2×C4×D4C2×D61semidirect
550. C61C2×#3280semidirect
560. C2×#41C22×D61semidirect
619. #124C22×D61semidirect
631. #121C22×D61semidirect
639. C4×D4C22×D61semidirect
829. C23#14519797semidirect
919. C22C2×#14519797semidirect
939. C2#21457500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197972
C23×#117581992
C2×#168404082
#214575002
C2×#168401442
C2×#168400012
C2×#168399962
C2×#168399772
C2×#168399742
C2×#168399072
C2×#168399052
C2×#168399132
C2×#168399122
C2×C4×#117581992
C2×D4×#924182
C2×C61×#5462
C2×#328061