Finite Group Databasebeta

← C2×#21457520 #30555235

Subgroups — C2×#21457520 #30555235

Order 15616.

2934 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D61C211yesmaximal, characteristic, complemented
2C2×#16840419C211yesmaximal, characteristic, complemented
3C2×#16840400C211yesmaximal, characteristic, complemented
4#21457520C2116yesmaximal, direct product factor
5C2×#16840143C211yesmaximal, characteristic, complemented
6C2×#16839991C211yesmaximal, characteristic, complemented
7C2×#16839988C211yesmaximal, characteristic, complemented
8C2×#16839986C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839916C211yesmaximal, characteristic, complemented
13C2×#16839894C211yesmaximal, characteristic, complemented
14C2×SD16×Dic61C211yesmaximal, characteristic, complemented
15C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
16C22×#135×C61C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C2×SD16×D61—28no—
24C2×SD16×D61C2218yescomplemented
25C22×#11758199C2211yescharacteristic
26C22×C8×D61C2211yescharacteristic
27#16840419—24no—
28#16840419C2218yescomplemented
29#16840400—24no—
30#16840400C2218yescomplemented
31C2×#14519766C2211yescharacteristic
32C2×#14519764—21no—
33C2×#14519764C2211yescharacteristic, complemented
34C2×#14519760—21no—
35C2×#14519756—21no—
36C2×#14519756C2211yescharacteristic, complemented
37C2×#14519753C2211yescharacteristic
38C2×#14519751C2211yescharacteristic
39C2×#14519749—21no—
40C2×#14519748—21no—
41C2×#14519748C2211yescharacteristic
42C2×#14519745—21no—
43C2×Q8×Dic61C2211yescharacteristic, complemented
44C2×D4×Dic61C2211yescharacteristic
45C2×C4×C22⋊D61—21no—
46C2×C4×C22⋊D61C2211yescharacteristic
47C22×#11758198—21no—
48#16840143C2218yescomplemented
49#16839991C2218yescomplemented
50#16839988C2218yescomplemented
51#16839986C2218yescomplemented
52#16839975C2218yescomplemented
53#16839924C2218yescomplemented
54#16839916C2218yescomplemented
55#16839907C2218yescomplemented
56#16839894C2218yescomplemented
57SD16×Dic61C2218yescomplemented
58C8×C22⋊D61C2218yescomplemented
59C2×#14519709C2211yescharacteristic, complemented
60C2×#14519706C2211yescharacteristic, complemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519701C2211yescharacteristic, complemented
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519698C2211yescharacteristic, complemented
67C2×C22⋊#92418C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic
69C2×C8×Dic61C2211yescharacteristic, complemented
70C22×#41×C61C2211yescharacteristic
71C22×#41×C61C2211yescharacteristic, complemented
72C2×#135×C61—28no—
73C2×#135×C61C2218yescomplemented
74C22×Q16×C61C2211yescharacteristic, complemented
75C22×SD16×C61C2211yescharacteristic
76C22×SD16×C61C2211yescharacteristic, complemented
77C22×D8×C61C2211yescharacteristic
78C23×C8×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C2×Q8×D61—22no—
83C2×Q8×D61—24no—
84C2×Q8×D61—42no—
85C2×Q8×D61C2314yes—
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61D411yescharacteristic
91C2×D4×D61—24no—
92C2×D4×D61—22no—
93C2×D4×D61—42no—
94C2×D4×D61C2314yes—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61C2311yescharacteristic
98C2×#11758202—42no—
99C2×#11758202C2314yescomplemented
100C2×#11758190—24no—
101C2×#11758190C2314yes—
102C2×#11758200—24no—
103C2×#11758200C2314yes—
104C2×#11758201—24no—
105C2×#11758201C2314yes—
106SD16×D61—232no—
107C2×#11758199—42no—
108C2×#11758199C2314yes—
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111C2×C8×D61—24no—
112C2×C8×D61C2314yes—
113#14519766—22no—
114#14519766C2314yes—
115#14519764—28no—
116#14519764—22no—
117#14519764C2314yescomplemented
118#14519760—28no—
119#14519756—22no—
120#14519756—28no—
121#14519756C2314yescomplemented
122#14519753—22no—
123#14519753C2314yes—
124#14519751—22no—
125#14519751C2314yes—
126#14519749—28no—
127#14519748—28no—
128#14519748—22no—
129#14519748C2314yes—
130#14519745—28no—
131Q8×Dic61—22no—
132Q8×Dic61C2314yescomplemented
133D4×Dic61—22no—
134D4×Dic61C2314yes—
135C4×C22⋊D61—28no—
136C4×C22⋊D61D414yes—
137C4×C22⋊D61C2314yes—
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196D411yescharacteristic
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×C22⋊Dic61D411yescharacteristic
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—28no—
155C2×#11758198D411yescharacteristic
156C2×C4×Dic61—21no—
157C2×C4×Dic61C2311yescharacteristic
158#14519709C2314yescomplemented
159#14519706C2314yescomplemented
160#14519702C2314yescomplemented
161#14519701C2314yescomplemented
162#14519701C2314yescomplemented
163#14519699C2314yes—
164#14519698C2314yes—
165#14519698C2314yescomplemented
166C22⋊#92418C2314yescomplemented
167#14519689C2314yes—
168C8×Dic61C2314yescomplemented
169C2×#41×C61—22no—
170C2×#41×C61—22no—
171C2×#41×C61—24no—
172C2×#41×C61—24no—
173C2×#41×C61—42no—
174C2×#41×C61—42no—
175C2×#41×C61C2314yes—
176C2×#41×C61C2314yescomplemented
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61—21no—
180C22×D4×C61—21no—
181C22×D4×C61C2311yescharacteristic
182C22×D4×C61C2311yescharacteristic
183C23×C4×C61—21no—
184C23×C4×C61—21no—
185C23×C4×C61C2311yescharacteristic
186#135×C61—232no—
187C2×Q16×C61—24no—
188C2×Q16×C61C2314yescomplemented
189C2×SD16×C61—24no—
190C2×SD16×C61D418yescomplemented
191C2×SD16×C61C2314yes—
192C2×SD16×C61C2314yescomplemented
193C2×D8×C61—24no—
194C2×D8×C61C2314yes—
195C22×C8×C61—24no—
196C22×C8×C61C2311yescharacteristic
197C22×C8×C61C2311yescharacteristic
198C22×C8×C61C2314yescomplemented
199C24×C61—21no—
200C24×C61—21no—
201C24×C61C2×D411yescharacteristic
202C23×D61—21no—
203C23×D61—24no—
204C23×D61—44no—
205C23×D61—44no—
206C23×D61—82no—
207C23×D61C2×D411yescharacteristic
208#41×C61—28no—
209#41×C61—28no—
210#41×C61—44no—
211#41×C61—44no—
212#41×C61—48no—
213#41×C61—48no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61C2×D414yes—
220C2×Q8×C61C2412yes—
221C2×Q8×C61C2412yes—
222C2×D4×C61—24no—
223C2×D4×C61—24no—
224C2×D4×C61—21no—
225C2×D4×C61—22no—
226C2×D4×C61—21no—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—44no—
230C2×D4×C61—44no—
231C2×D4×C61C2×D414yes—
232C2×D4×C61C2412yes—
233C2×D4×C61C2412yes—
234C22×C4×C61—21no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—21no—
238C22×C4×C61—24no—
239C22×C4×C61—24no—
240C22×C4×C61—44no—
241C22×C4×C61—44no—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2412yes—
245C22×C4×C61C2411yescharacteristic
246C2×C22⋊D61—24no—
247C2×C22⋊D61—24no—
248C2×C22⋊D61—24no—
249C2×C22⋊D61—24no—
250C2×C22⋊D61—44no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—82no—
253C2×C22⋊D61C2×D414yes—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—24no—
258C22×Dic61—82no—
259C22×Dic61C2×D411yescharacteristic
260C22×Dic61C2×D411yescharacteristic
261C22×Dic61C2×D411yescharacteristic
262Q8×D61—28no—
263Q8×D61—44no—
264Q8×D61—48no—
265D4×D61—28no—
266D4×D61—44no—
267D4×D61—48no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—21no—
271C2×D244C2412yes—
272C2×C4×D61—22no—
273C2×C4×D61—22no—
274C2×C4×D61—24no—
275C2×C4×D61—44no—
276C2×C4×D61C2×D412yes—
277C2×C4×D61C2412yes—
278C2×Dic122—22no—
279C2×Dic122—22no—
280C2×Dic122—21no—
281C2×Dic122—24no—
282C2×Dic122—44no—
283C2×Dic122C2412yes—
284Q16×C61—28no—
285SD16×C61—28no—
286SD16×C61C2×D4116yescomplemented
287D8×C61—28no—
288C2×C8×C61—22no—
289C2×C8×C61—28no—
290C2×C8×C61C2×D414yes—
291C2×C8×C61C2412yes—
292C2×C8×C61C2412yes—
293C22⋊Dic61—24no—
294C22⋊Dic61—24no—
295C22⋊Dic61—24no—
296C22⋊Dic61—24no—
297C22⋊Dic61—24no—
298C22⋊Dic61C2×D414yes—
299#11758202—44no—
300#11758201—28no—
301#11758200—28no—
302#11758199—44no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306#11758198—24no—
307#11758198C2×D414yes—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—24no—
311C4⋊Dic61C2412yes—
312C4⋊Dic61C2412yes—
313#11758196—24no—
314#11758196—24no—
315#11758196C2×D414yes—
316C4×Dic61—24no—
317C4×Dic61C2×D412yes—
318C4×Dic61C2412yes—
319C2×#92418—22no—
320C2×#92418—22no—
321C2×#92418C2412yes—
322C2×#92418C2412yes—
323#11758190—28no—
324C8×D61—28no—
325C23×C61—24no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—42no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61C22×D412yes—
337C23×C61C22×D411yescharacteristic
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—48no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—48no—
346C22×D61—84no—
347C22×D61—816no—
348C22×D61#13514yescomplemented
349C22×D61C22×D412yes—
350Q8×C61—24no—
351Q8×C61—22no—
352Q8×C61—22no—
353Q8×C61—22no—
354Q8×C61—42no—
355Q8×C61C22×D414yes—
356D4×C61—24no—
357D4×C61—22no—
358D4×C61—22no—
359D4×C61—22no—
360D4×C61—48no—
361D4×C61—48no—
362D4×C61—42no—
363D4×C61C22×D414yes—
364C2×C4×C61—24no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—24no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—48no—
372C2×C4×C61—48no—
373C2×C4×C61—42no—
374C2×C4×C61C22×D412yes—
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D412yes—
377C2×C4×C61H(5,𝔽2)12yes—
378C2×C4×C61C2511yescharacteristic
379C22⋊D61—28no—
380C22⋊D61—48no—
381C22⋊D61—48no—
382C22⋊D61—84no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61—84no—
393C2×Dic61C22×D412yes—
394C2×Dic61C22×D412yes—
395C2×Dic61C22×D412yes—
396D244—22no—
397D244—22no—
398D244—42no—
399C4×D61—24no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—48no—
403Dic122—22no—
404Dic122—22no—
405Dic122—48no—
406Dic122—42no—
407C8×C61—22no—
408C8×C61C22×D414yes—
409#92418—22no—
410#92418—22no—
411C2×#3282—611nomaximal, Sylow
412C22×C61—24no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—48no—
417C22×C61—44no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—84no—
424C22×C61D4212yes—
425C22×C61C2×#13512yes—
426C22×C61#57712yes—
427C22×C61C23×D411yescharacteristic
428C2×D61—22no—
429C2×D61—28no—
430C2×D61—22no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—816no—
435C2×D61—84no—
436C2×D61C2×#13514yescomplemented
437C4×C61—24no—
438C4×C61—22no—
439C4×C61—42no—
440C4×C61D4212yes—
441C4×C61C23×D411yescharacteristic
442C4×C61C2×H(5,𝔽2)11yescharacteristic
443Dic61—22no—
444Dic61—22no—
445Dic61—22no—
446Dic61—42no—
447Dic61—42no—
448Dic61—42no—
449C22×#135D6111yescharacteristic, complemented
450C23×SD16—611no—
451C2×#548—611no—
452C2×#546—611no—
453#3282—6116no—
454C2×#495—611no—
455C2×#465—611no—
456C2×#465—611no—
457C2×#464—611no—
458C2×#463—611no—
459C2×#452—611no—
460C2×#449—611no—
461C2×#451—611no—
462C2×#447—611no—
463C2×C4×SD16—611no—
464C2×C8×D4—611no—
465C2×C61—44no—
466C2×C61—42no—
467C2×C61—82no—
468C2×C61#328214yescomplemented
469C2×C61C2×D4211yescharacteristic
470C2×C61C22×#13511yescharacteristic
471C2×C61C2×#57711yescharacteristic
472D61—24no—
473D61—82no—
474C22×#41C2×D6111yescharacteristic
475C22×#41C2×D6111yescharacteristic, complemented
476C23×Q8—611no—
477C23×D4—611no—
478C2×#135—28no—
479C2×#135C2×D6118yescomplemented
480C22×Q16—611no—
481C22×Q16C2×D6111yescharacteristic, complemented
482C22×SD16—611no—
483C22×SD16—611no—
484C22×SD16—618no—
485C22×SD16—611no—
486C22×SD16—1228no—
487C22×SD16C2×D6111yescharacteristic
488C22×SD16C2×D6111yescharacteristic, complemented
489C22×D8—611no—
490C22×D8C2×D6111yescharacteristic
491C23×C8—611no—
492C23×C8C2×D6111yescharacteristic, complemented
493#548—618no—
494#548—1224no—
495#546—618no—
496#546—1224no—
497C2×#124—611no—
498C2×#124—611no—
499C2×#124—1221no—
500C2×#123—1221no—
501C2×C22⋊Q8—611no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8—1221no—
504C2×#121—611no—
505C2×#121—611no—
506C2×#121—1221no—
507C2×#121—1221no—
508C2×#120—1221no—
509C2×C4×Q8—611no—
510C2×C4×D4—611no—
511C2×C4×D4—611no—
512C2×C4×D4—1221no—
513C22×C22⋊C4—1221no—
514#495—618no—
515#465—618no—
516#465—618no—
517#464—618no—
518#463—618no—
519#452—618no—
520#451—618no—
521#449—618no—
522#447—618no—
523C4×SD16—618no—
524C8×D4—618no—
525C2×#106—611no—
526C2×C4⋊C8—611no—
527C2×#103—611no—
528C2×#103—611no—
529C2×#103—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C4×C8—611no—
536C61C2×#328211yescharacteristic, complemented, Sylow
537C25—1221no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—24no—
541C2×#41—24no—
542C2×#41—42no—
543C2×#41—42no—
544C2×#41C22×D6114yes—
545C2×#41C22×D6114yescomplemented
546C22×Q8—614no—
547C22×Q8—611no—
548C22×Q8—1221no—
549C22×Q8—1222no—
550C22×Q8—1224no—
551C22×Q8—2442no—
552C22×Q8C22×D6111yescharacteristic
553C22×Q8C22×D6111yescharacteristic
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—611no—
557C22×D4—614no—
558C22×D4—611no—
559C22×D4—1222no—
560C22×D4—1221no—
561C22×D4—1224no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—2442no—
565C22×D4C22×D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—611no—
570C23×C4—1221no—
571C23×C4—1221no—
572C23×C4C22×D6111yescharacteristic
573#135—232no—
574C2×Q16—24no—
575C2×Q16—614no—
576C2×Q16—2442no—
577C2×Q16C22×D6114yescomplemented
578C2×SD16—24no—
579C2×SD16—614no—
580C2×SD16—614no—
581C2×SD16—614no—
582C2×SD16—1224no—
583C2×SD16—1224no—
584C2×SD16—12232no—
585C2×SD16—1224no—
586C2×SD16C22⋊D6118yescomplemented
587C2×SD16C22×D6114yes—
588C2×SD16C22×D6114yescomplemented
589C2×D8—24no—
590C2×D8—614no—
591C2×D8—2442no—
592C2×D8C22×D6114yes—
593C22×C8—24no—
594C22×C8—611no—
595C22×C8—611no—
596C22×C8—614no—
597C22×C8—1224no—
598C22×C8C22×D6111yescharacteristic
599C22×C8C22×D6111yescharacteristic
600C22×C8C22×D6114yescomplemented
601#124—614no—
602#124—614no—
603#124—1222no—
604#124—1222no—
605#124—1228no—
606#123—1228no—
607C22⋊Q8—614no—
608C22⋊Q8—614no—
609C22⋊Q8—1228no—
610C22⋊Q8—1222no—
611C22⋊Q8—1222no—
612#121—614no—
613#121—614no—
614#121—1228no—
615#121—1222no—
616#121—1228no—
617#121—1222no—
618#120—1228no—
619C4×Q8—614no—
620C4×Q8—1222no—
621C4×D4—614no—
622C4×D4—614no—
623C4×D4—614no—
624C4×D4—1222no—
625C4×D4—1228no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—1228no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C42—611no—
645C2×C42—1221no—
646#106—614no—
647C4⋊C8—614no—
648#103—614no—
649#103—614no—
650#103—614no—
651#102—614no—
652#102—614no—
653#102—614no—
654C22⋊C8—614no—
655C22⋊C8—614no—
656C4×C8—614no—
657C24—21no—
658C24—21no—
659C24—611no—
660C24—1224no—
661C24—1221no—
662C24—4882no—
663C24—2444no—
664C24—2444no—
665C24D4×D6111yescharacteristic
666#41—28no—
667#41—28no—
668#41—44no—
669#41—44no—
670#41—48no—
671#41—48no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—612no—
678C2×Q8—1224no—
679C2×Q8—1221no—
680C2×Q8—1228no—
681C2×Q8—1222no—
682C2×Q8—1222no—
683C2×Q8—2444no—
684C2×Q8—2444no—
685C2×Q8—2448no—
686C2×Q8C2×C22⋊D6114yes—
687C2×Q8C23×D6112yes—
688C2×Q8C23×D6112yes—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—614no—
699C2×D4—612no—
700C2×D4—1224no—
701C2×D4—1224no—
702C2×D4—1228no—
703C2×D4—1224no—
704C2×D4—1224no—
705C2×D4—1221no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—4882no—
709C2×D4—2444no—
710C2×D4—2448no—
711C2×D4—2444no—
712C2×D4—2444no—
713C2×D4C2×C22⋊D6114yes—
714C2×D4C23×D6112yes—
715C2×D4C23×D6112yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—1222no—
732C22×C4—1222no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—4882no—
737C22×C4—2444no—
738C22×C4D4×D6112yes—
739C22×C4D4×D6111yescharacteristic
740C22×C4C23×D6112yes—
741C22×C4C23×D6111yescharacteristic
742Q16—28no—
743Q16—2444no—
744SD16—28no—
745SD16—1228no—
746SD16—1228no—
747SD16—1228no—
748SD16C2×C22⋊D61116yescomplemented
749D8—28no—
750D8—2444no—
751C2×C8—22no—
752C2×C8—28no—
753C2×C8—612no—
754C2×C8—612no—
755C2×C8—1222no—
756C2×C8—1222no—
757C2×C8—1228no—
758C2×C8C2×C22⋊D6114yes—
759C2×C8C23×D6112yes—
760C2×C8C23×D6112yes—
761C4⋊C4—614no—
762C4⋊C4—612no—
763C4⋊C4—612no—
764C4⋊C4—1224no—
765C4⋊C4—1224no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1224no—
769C22⋊C4—614no—
770C22⋊C4—614no—
771C22⋊C4—1224no—
772C22⋊C4—1224no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C22⋊C4—1224no—
778C22⋊C4—1224no—
779C22⋊C4—1224no—
780C42—612no—
781C42—612no—
782C42—1224no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—24no—
788C23—22no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—614no—
795C23—612no—
796C23—1222no—
797C23—1222no—
798C23—1222no—
799C23—48816no—
800C23—4884no—
801C23—2448no—
802C23—2448no—
803C23—2442no—
804C23—2442no—
805C23—2442no—
806C23C2×D4×D6112yes—
807C23C2×D4×D6111yescharacteristic
808Q8—22no—
809Q8—24no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—1222no—
814Q8—1222no—
815Q8—2448no—
816Q8—2442no—
817Q8C22×C22⋊D6114yes—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—24no—
822D4—48no—
823D4—48no—
824D4—42no—
825D4—1228no—
826D4—1222no—
827D4—1222no—
828D4—4884no—
829D4—2448no—
830D4—2448no—
831D4—2442no—
832D4C22×C22⋊D6114yes—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—48no—
841C2×C4—48no—
842C2×C4—42no—
843C2×C4—612no—
844C2×C4—612no—
845C2×C4—612no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1224no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—4884no—
856C2×C4—2448no—
857C2×C4—2442no—
858C2×C4—2442no—
859C2×C4—2442no—
860C2×C4C2×D4×D6112yes—
861C2×C4C2×D4×D6111yescharacteristic
862C2×C4C22×C22⋊D6112yes—
863C2×C4#1451982212yes—
864C2×C4C24×D6111yescharacteristic
865C8—22no—
866C8—1222no—
867C8—1222no—
868C8C22×C22⋊D6114yes—
869C22—22no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—42no—
874C22—42no—
875C22—44no—
876C22—48no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—614no—
882C22—1222no—
883C22—1222no—
884C22—1228no—
885C22—48816no—
886C22—4884no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22D4×C22⋊D6112yes—
891C22#135×D6112yes—
892C22#1684056912yes—
893C22C22×D4×D6111yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—1222no—
898C4—1222no—
899C4—1222no—
900C4—2442no—
901C4—2442no—
902C4—2442no—
903C4D4×C22⋊D6112yes—
904C4C23×C22⋊D6111yescharacteristic
905C4C2×#1451982211yescharacteristic
906C2—42no—
907C2—44no—
908C2—82no—
909C2—1224no—
910C2—4882no—
911C2#2145752014yesdirect product factor
912C2C2×D4×C22⋊D6111yescharacteristic
913C2C2×#135×D6111yescharacteristic
914C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#135×C61C2
socleC23×C61C22×D4
hypercenterC22×#135D61
hypocenterC61C2×#3282
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×SD16×D61C2semidirect
2. C2×#16840419C2semidirect
3. C2×#16840400C2semidirect
4. #21457520C2direct (N × H)
5. C2×#16840143C2semidirect
6. C2×#16839991C2semidirect
7. C2×#16839988C2semidirect
8. C2×#16839986C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839916C2semidirect
13. C2×#16839894C2semidirect
14. C2×SD16×Dic61C2semidirect
15. C2×C8×C22⋊D61C2semidirect
16. C22×#135×C61C2semidirect
19. C22×#11758202C22semidirect
24. C2×SD16×D61C22semidirect
28. #16840419C22semidirect
30. #16840400C22semidirect
33. C2×#14519764C22semidirect
36. C2×#14519756C22semidirect
43. C2×Q8×Dic61C22semidirect
48. #16840143C22semidirect
49. #16839991C22semidirect
50. #16839988C22semidirect
51. #16839986C22semidirect
52. #16839975C22semidirect
53. #16839924C22semidirect
54. #16839916C22semidirect
55. #16839907C22semidirect
56. #16839894C22semidirect
57. SD16×Dic61C22semidirect
58. C8×C22⋊D61C22semidirect
59. C2×#14519709C22semidirect
60. C2×#14519706C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519701C22semidirect
63. C2×#14519701C22semidirect
66. C2×#14519698C22semidirect
67. C2×C22⋊#92418C22semidirect
69. C2×C8×Dic61C22semidirect
71. C22×#41×C61C22semidirect
73. C2×#135×C61C22semidirect
74. C22×Q16×C61C22semidirect
76. C22×SD16×C61C22semidirect
78. C23×C8×C61C22semidirect
99. C2×#11758202C23semidirect
117. #14519764C23semidirect
121. #14519756C23semidirect
132. Q8×Dic61C23semidirect
158. #14519709C23semidirect
159. #14519706C23semidirect
160. #14519702C23semidirect
161. #14519701C23semidirect
162. #14519701C23semidirect
165. #14519698C23semidirect
166. C22⋊#92418C23semidirect
168. C8×Dic61C23semidirect
176. C2×#41×C61C23semidirect
188. C2×Q16×C61C23semidirect
190. C2×SD16×C61D4semidirect
192. C2×SD16×C61C23semidirect
198. C22×C8×C61C23semidirect
286. SD16×C61C2×D4semidirect
348. C22×D61#135semidirect
436. C2×D61C2×#135semidirect
449. C22×#135D61semidirect
468. C2×C61#3282semidirect
475. C22×#41C2×D61semidirect
479. C2×#135C2×D61semidirect
481. C22×Q16C2×D61semidirect
488. C22×SD16C2×D61semidirect
492. C23×C8C2×D61semidirect
536. C61C2×#3282semidirect
545. C2×#41C22×D61semidirect
577. C2×Q16C22×D61semidirect
586. C2×SD16C22⋊D61semidirect
588. C2×SD16C22×D61semidirect
600. C22×C8C22×D61semidirect
748. SD16C2×C22⋊D61semidirect
911. C2#21457520direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×#168404192
C2×#168404002
#214575202
C2×#168401432
C2×#168399912
C2×#168399882
C2×#168399862
C2×#168399752
C2×#168399242
C2×#168399072
C2×#168399162
C2×#168398942
C2×SD16×Dic612
C2×C8×C22⋊D612
C22×#135×C612
C2×#328261