Finite Group Databasebeta

← C2×#21455897 #30548094

Subgroups — C2×#21455897 #30548094

Order 15616.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
3#21455897C2116yesmaximal, direct product factor
4C2×#16840094C211yesmaximal, characteristic, complemented
5C2×#16840074C211yesmaximal, characteristic
6C2×#16840072C211yesmaximal, characteristic, complemented
7C2×#16840071C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839982C211yesmaximal, characteristic, complemented
10C2×#16839919C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic
12C2×C4×Dic244C211yesmaximal, characteristic, complemented
13C2×C4×#11758202C211yesmaximal, characteristic, complemented
14C2×C4×#11758200C211yesmaximal, characteristic, complemented
15C2×#16839813C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21#16840294—24no—
22#16840294C2218yes—
23C2×#14519770—21no—
24C2×#14519768C2211yescharacteristic
25C2×#14519764C2211yescharacteristic
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×Dic122—21no—
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519742—21no—
34C2×#14519742C2211yescharacteristic
35C4×Q8×D61—24no—
36C4×Q8×D61C2218yescomplemented
37C2×C4×C22⋊D61—21no—
38C2×#14519736—21no—
39C2×C4⋊C4×D61—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840094C2218yescomplemented
44#16840074C2218yes—
45#16840072C2218yescomplemented
46#16840071C2218yescomplemented
47#16839983C2218yescomplemented
48#16839982C2218yescomplemented
49#16839919C2218yescomplemented
50#16839899C2218yes—
51C4×Dic244C2218yescomplemented
52C4×#11758202C2218yescomplemented
53C4×#11758200C2218yescomplemented
54#16839813C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C4×SD16×C61C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—24no—
81C2×Q8×D61—22no—
82C2×Q8×D61—24no—
83C2×Q8×D61C2314yes—
84C22×C22⋊D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×Dic244—24no—
91C2×Dic244C2314yes—
92C2×#11758202—24no—
93C2×#11758202C2314yes—
94C2×#11758200—24no—
95C2×#11758200C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519770—28no—
99#14519768—22no—
100#14519768C2314yes—
101#14519764—22no—
102#14519764C2314yes—
103#14519759—28no—
104#14519757—22no—
105#14519757C2314yes—
106#14519748—22no—
107#14519748C2314yes—
108Q8×Dic61—22no—
109Q8×Dic61C2314yes—
110C4×Dic122—22no—
111C4×Dic122—22no—
112C4×Dic122—28no—
113C4×Dic122C2314yes—
114C4×Dic122C2314yes—
115#14519742—22no—
116#14519742—28no—
117#14519742C2314yes—
118C4×C22⋊D61—28no—
119#14519736—28no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—28no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C42×D61—28no—
145C42×D61D414yes—
146C42×D61C2314yes—
147#14519711C2314yes—
148#14519710C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519698C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160C4×#92418C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yes—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61—21no—
183C23×D61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—22no—
186C2×Q8×C61#4114yes—
187C2×Q8×C61C2412yes—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—44no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—44no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209Q8×D61—216no—
210Q8×D61—28no—
211Q8×D61—28no—
212C2×C4×D61—28no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—24no—
219C2×C4×D61—44no—
220C2×C4×D61C2×D414yes—
221C2×C4×D61C2×D414yes—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—28no—
225C2×Dic122—21no—
226C2×Dic122—22no—
227C2×Dic122—24no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122#4114yes—
232C2×Dic122C2412yes—
233C2×Dic122C2412yes—
234SD16×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251#11758202—28no—
252#11758200—28no—
253#11758198—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D414yes—
272C4×Dic61C2×D414yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278Dic244—28no—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—22no—
286C22×D61#13514yes—
287C22×D61C22×D412yes—
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61C2×#4114yes—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—42no—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—48no—
302C2×C4×C61#13714yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×D412yes—
306C2×C4×C61C2×#4112yes—
307C2×C4×C61C2×#4112yes—
308C2×C4×C61C2511yescharacteristic
309C22⋊D61—48no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C4×D61—216no—
325C4×D61—28no—
326C4×D61—24no—
327C4×D61—28no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—48no—
331Dic122—216no—
332Dic122—24no—
333Dic122—22no—
334Dic122—22no—
335Dic122—22no—
336Dic122—42no—
337Dic122C2×#4114yes—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3108—611nomaximal, Sylow
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#52512yes—
348C22×C61C2×#13512yes—
349C22×C61C2×#13712yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—28no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61C2×#13514yes—
355C4×C61—24no—
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61#52512yes—
360C4×C61C2×#13714yes—
361C4×C61C22×#4111yescharacteristic
362C4×C61C22×#4111yescharacteristic
363Dic61—22no—
364Dic61—24no—
365Dic61—22no—
366Dic61—22no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370C2×#529—611no—
371C22×C4×Q8—611no—
372#3108—6116no—
373C2×#483—611no—
374C2×#480—611no—
375C2×#479—611no—
376C2×#479—611no—
377C2×#464—611no—
378C2×#464—611no—
379C2×#451—611no—
380C2×#448—611no—
381C2×C4×Q16—611no—
382C2×C4×Q16—611no—
383C2×C4×SD16—611no—
384C2×C4×SD16D6111yescharacteristic, complemented
385C2×#431—611no—
386C2×C61—82no—
387C2×C61#310814yescomplemented
388C2×C61C2×#52511yescharacteristic
389C2×C61C22×#13511yescharacteristic
390C2×C61C22×#13711yescharacteristic
391D61—24no—
392C23×Q8—611no—
393C22×Q16—611no—
394C22×Q16—611no—
395C22×SD16—611no—
396C22×SD16C2×D6111yescharacteristic
397#529—618no—
398#529—1224no—
399C2×#126—1221no—
400C2×#125—611no—
401C2×#124—611no—
402C2×#123—1221no—
403C2×C22⋊Q8—611no—
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—618no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—1221no—
411C2×C4×Q8—1221no—
412C2×C4×Q8—1224no—
413C2×C4×Q8C2×D6111yescharacteristic
414C2×C4×D4—1221no—
415C2×C4×D4C2×D6111yescharacteristic
416C2×#117—1221no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#483—618no—
422#480—618no—
423#479—618no—
424#479—618no—
425#464—618no—
426#464—618no—
427#451—618no—
428#448—618no—
429C4×Q16—618no—
430C4×Q16—618no—
431C4×SD16—618no—
432C4×SD16C2×D6118yescomplemented
433#431—618no—
434C2×#107—611no—
435C2×#107—611no—
436C2×#106—611no—
437C2×#106C2×D6111yescharacteristic
438C2×C4⋊C8—611no—
439C2×C4⋊C8—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103C2×D6111yescharacteristic
446C2×#102—611no—
447C2×#102C2×D6111yescharacteristic
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C4×C8—611no—
451C2×C4×C8C2×D6111yescharacteristic
452C61C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—614no—
454C22×Q8—611no—
455C22×Q8—611no—
456C22×Q8—1221no—
457C22×Q8—1222no—
458C22×Q8—1224no—
459C22×Q8—1224no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C2×Q16—614no—
470C2×Q16—614no—
471C2×Q16—1224no—
472C2×Q16—1224no—
473C2×SD16—24no—
474C2×SD16—614no—
475C2×SD16—1224no—
476C2×SD16C22×D6114yes—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8C22×D6111yescharacteristic
480C22×C8C22×D6111yescharacteristic
481#126—1228no—
482#125—614no—
483#125—1222no—
484#124—614no—
485#124—1222no—
486#123—1228no—
487C22⋊Q8—614no—
488C22⋊Q8—1222no—
489#121—614no—
490#121—1222no—
491C4×Q8—22no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—614no—
496C4×Q8—1228no—
497C4×Q8—1222no—
498C4×Q8—1228no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×Q8C22×D6114yes—
503C4×D4—22no—
504C4×D4—1228no—
505C4×D4C22×D6114yes—
506#117—1228no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1228no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—21no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—614no—
533C2×C42—614no—
534C2×C42—1228no—
535C2×C42—1221no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—614no—
541#107—614no—
542#106—614no—
543#106C22×D6114yes—
544C4⋊C8—614no—
545C4⋊C8—614no—
546#103—614no—
547#103—614no—
548#103—614no—
549#103—614no—
550#103—614no—
551#103C22×D6114yes—
552#102—614no—
553#102C22×D6114yes—
554C22⋊C8—614no—
555C22⋊C8—614no—
556C4×C8—614no—
557C4×C8C22×D6114yes—
558C24—21no—
559C24—611no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—614no—
563C2×Q8—612no—
564C2×Q8—612no—
565C2×Q8—1224no—
566C2×Q8—1228no—
567C2×Q8—1228no—
568C2×Q8—12216no—
569C2×Q8—1228no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8—1222no—
575C2×Q8#1175822214yes—
576C2×Q8C23×D6112yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—1224no—
581C2×D4—2444no—
582C2×D4C23×D6112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—614no—
592C22×C4—614no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1228no—
598C22×C4—1224no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1224no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—2444no—
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610Q16—1228no—
611Q16—1228no—
612SD16—28no—
613SD16—1228no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8C23×D6112yes—
621C2×C8C23×D6112yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4C23×D6112yes—
638C4⋊C4C23×D6112yes—
639C22⋊C4—24no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C42—24no—
645C42—614no—
646C42—612no—
647C42—614no—
648C42—612no—
649C42—1224no—
650C42—1224no—
651C42—1224no—
652C42—1224no—
653C42D4×D6112yes—
654C42C23×D6112yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—614no—
660C23—612no—
661C23—1222no—
662C23—1222no—
663C23C2×D4×D6111yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—614no—
667Q8—12216no—
668Q8—1224no—
669Q8—1222no—
670Q8—1222no—
671Q8—1222no—
672Q8—2442no—
673Q8C2×#1175822214yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—2448no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—1228no—
690C2×C4—12216no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1224no—
697C2×C4—1228no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—2448no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4#1451980614yes—
708C2×C4C2×D4×D6112yes—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4C2×D4×D6112yes—
711C2×C4#41×D6112yes—
712C2×C4C2×#1175822212yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—1222no—
717C8—1222no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—614no—
723C22—1228no—
724C22—1222no—
725C22—1222no—
726C22#1684027112yes—
727C22#135×D6112yes—
728C22C2×#1451980612yes—
729C22C22×D4×D6111yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—1222no—
735C4—1222no—
736C4—1222no—
737C4—1224no—
738C4—2442no—
739C4—2442no—
740C4—2442no—
741C4#1684027112yes—
742C4C2×#1451980614yes—
743C4C2×#41×D6111yescharacteristic
744C4C22×#1175822211yescharacteristic
745C2—82no—
746C2—1224no—
747C2#2145589714yesdirect product factor
748C2C2×#1684027111yescharacteristic
749C2C2×#135×D6111yescharacteristic
750C2C22×#1451980611yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×C4×SD16D61
hypocenterC61C2×#3108
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D61C2semidirect
3. #21455897C2direct (N × H)
4. C2×#16840094C2semidirect
6. C2×#16840072C2semidirect
7. C2×#16840071C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839982C2semidirect
10. C2×#16839919C2semidirect
12. C2×C4×Dic244C2semidirect
13. C2×C4×#11758202C2semidirect
14. C2×C4×#11758200C2semidirect
15. C2×#16839813C2semidirect
16. C2×C4×SD16×C61C2semidirect
36. C4×Q8×D61C22semidirect
43. #16840094C22semidirect
45. #16840072C22semidirect
46. #16840071C22semidirect
47. #16839983C22semidirect
48. #16839982C22semidirect
49. #16839919C22semidirect
51. C4×Dic244C22semidirect
52. C4×#11758202C22semidirect
53. C4×#11758200C22semidirect
54. #16839813C22semidirect
72. C4×SD16×C61C22semidirect
384. C2×C4×SD16D61semidirect
387. C2×C61#3108semidirect
432. C4×SD16C2×D61semidirect
452. C61C2×#3108semidirect
747. C2#21455897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402942
C2×C4×Q8×D612
#214558972
C2×#168400942
C2×#168400742
C2×#168400722
C2×#168400712
C2×#168399832
C2×#168399822
C2×#168399192
C2×#168398992
C2×C4×Dic2442
C2×C4×#117582022
C2×C4×#117582002
C2×#168398132
C2×C4×SD16×C612
C2×#310861