Finite Group Databasebeta

← C2×#21455989 #30548160

Subgroups — C2×#21455989 #30548160

Order 15616.

2150 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×#16840291C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
3#21455989C2116yesmaximal, direct product factor
4C2×#16840096C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic
6C2×#16840070C211yesmaximal, characteristic, complemented
7C2×#16840069C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839916C211yesmaximal, characteristic, complemented
10C2×#16839899C211yesmaximal, characteristic
11C2×#16839869C211yesmaximal, characteristic, complemented
12C2×#16839866C211yesmaximal, characteristic, complemented
13C2×#16839863C211yesmaximal, characteristic, complemented
14C2×#16839859C211yesmaximal, characteristic, complemented
15C2×#16839818C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20#16840291—24no—
21#16840291C2218yes—
22C2×#14519770—21no—
23C2×#14519769C2211yescharacteristic
24C2×#14519759—21no—
25C2×#14519753C2211yescharacteristic
26C2×#14519748C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×Q8×Dic61C2211yescharacteristic
29C2×C4×Dic122—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519742—21no—
32C2×#14519742C2211yescharacteristic
33C4×Q8×D61—24no—
34C4×Q8×D61C2218yescomplemented
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519737—21no—
37C2×#14519733—21no—
38C2×C4⋊C4×D61—21no—
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42#16840096C2218yescomplemented
43#16840079C2218yes—
44#16840070C2218yescomplemented
45#16840069C2218yescomplemented
46#16839981C2218yescomplemented
47#16839916C2218yescomplemented
48#16839899C2218yes—
49#16839869C2218yescomplemented
50#16839866C2218yescomplemented
51#16839863C2218yescomplemented
52#16839859C2218yescomplemented
53#16839818C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C2×Q8×D61—24no—
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61C2314yes—
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758202—24no—
91C2×#11758202C2314yes—
92C2×#11758200—24no—
93C2×#11758200C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519770—28no—
97#14519769—22no—
98#14519769C2314yes—
99#14519759—28no—
100#14519753—22no—
101#14519753C2314yes—
102#14519748—22no—
103#14519748C2314yes—
104Q8×Dic61—22no—
105Q8×Dic61—22no—
106Q8×Dic61C2314yes—
107Q8×Dic61C2314yes—
108C4×Dic122—22no—
109C4×Dic122—28no—
110C4×Dic122C2314yes—
111#14519742—22no—
112#14519742—28no—
113#14519742C2314yes—
114D4×Dic61—22no—
115D4×Dic61C2314yes—
116#14519737—28no—
117#14519733—28no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—28no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61C2314yes—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61D411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61—28no—
143C42×D61D414yes—
144C42×D61C2314yes—
145#14519711C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149C4⋊#92418C2314yes—
150#14519702C2314yes—
151#14519702C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519701C2314yes—
155#14519698C2314yes—
156#14519689C2314yes—
157#14519689C2314yes—
158#14519687C2314yes—
159#14519687C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C2×Q16×C61—24no—
164C2×Q16×C61C2314yes—
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169#124×C61—22no—
170#124×C61C2314yes—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61#4114yes—
190C2×Q8×C61C2412yes—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—44no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213Q8×D61—216no—
214Q8×D61—28no—
215Q8×D61—28no—
216C2×C4×D61—28no—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—42no—
223C2×C4×D61—44no—
224C2×C4×D61C2×D414yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×D414yes—
227C2×C4×D61C2412yes—
228C2×Dic122—28no—
229C2×Dic122—21no—
230C2×Dic122—22no—
231C2×Dic122—24no—
232C2×Dic122#4114yes—
233C2×Dic122C2412yes—
234Q16×C61—28no—
235SD16×C61—28no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250#11758202—28no—
251#11758200—28no—
252#11758198—24no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61C2×D412yes—
272C4×Dic61C2×D414yes—
273C4×Dic61C2×D414yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—22no—
286C22×D61#13714yes—
287C22×D61C22×D412yes—
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293Q8×C61C2×#4114yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—42no—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2×#4112yes—
310C2×C4×C61C2511yescharacteristic
311C22⋊D61—48no—
312C2×Dic61—22no—
313C2×Dic61—24no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C4×D61—216no—
328C4×D61—28no—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—44no—
333C4×D61—48no—
334Dic122—216no—
335Dic122—24no—
336Dic122—22no—
337Dic122C2×#4114yes—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3117—611nomaximal, Sylow
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#52512yes—
348C22×C61C2×#13712yes—
349C22×C61#57512yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—28no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61C2×#13714yes—
355C4×C61—24no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61#52512yes—
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#3117—6116no—
373C2×#484—611no—
374C2×#481—611no—
375C2×#479—611no—
376C2×#479—611no—
377C2×#464—611no—
378C2×#464D6111yescharacteristic, complemented
379C2×#451—611no—
380C2×#448—611no—
381C2×#441—611no—
382C2×#441—611no—
383C2×#440—611no—
384C2×#440—611no—
385C2×#432—611no—
386C2×C61—82no—
387C2×C61#311714yescomplemented
388C2×C61C2×#52511yescharacteristic
389C2×C61C22×#13711yescharacteristic
390C2×C61C2×#57511yescharacteristic
391D61—24no—
392C23×Q8—611no—
393C22×Q16—611no—
394C22×Q16C2×D6111yescharacteristic
395C22×SD16—611no—
396C22×SD16C2×D6111yescharacteristic
397#529—618no—
398#529—1224no—
399C2×#126—1221no—
400C2×#125—611no—
401C2×#124C2×D6111yescharacteristic
402C2×#123—1221no—
403C2×C22⋊Q8—611no—
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—618no—
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—611no—
415C2×C4×D4—1221no—
416C2×#117—1221no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#484—618no—
422#481—618no—
423#479—618no—
424#479—618no—
425#464—618no—
426#464C2×D6118yescomplemented
427#451—618no—
428#448—618no—
429#441—618no—
430#441—618no—
431#440—618no—
432#440—618no—
433#432—618no—
434C2×#107—611no—
435C2×#107—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×C4⋊C8—611no—
439C2×C4⋊C8C2×D6111yescharacteristic
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×#97—611no—
451C2×#97—611no—
452C61C2×#311711yescharacteristic, complemented, Sylow
453C22×Q8—614no—
454C22×Q8—611no—
455C22×Q8—1221no—
456C22×Q8—1222no—
457C22×Q8—1224no—
458C22×Q8—1224no—
459C22×Q8C22×D6111yescharacteristic
460C22×Q8C22×D6111yescharacteristic
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C2×Q16—24no—
470C2×Q16—614no—
471C2×Q16—1224no—
472C2×Q16C22×D6114yes—
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—22no—
485#124C22×D6114yes—
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—614no—
504C4×D4—1222no—
505C4×D4—1228no—
506#117—1228no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1228no—
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⋊C4—1221no—
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
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#106—614no—
544C4⋊C8—614no—
545C4⋊C8C22×D6114yes—
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—
556#97—614no—
557#97—614no—
558C24—21no—
559C24—611no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—614no—
566C2×Q8—612no—
567C2×Q8—1224no—
568C2×Q8—1228no—
569C2×Q8—1228no—
570C2×Q8—12216no—
571C2×Q8—1228no—
572C2×Q8—1221no—
573C2×Q8—1222no—
574C2×Q8#1175822414yes—
575C2×Q8C23×D6112yes—
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—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—614no—
590C22×C4—612no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—1224no—
594C22×C4—1224no—
595C22×C4—1228no—
596C22×C4—1224no—
597C22×C4—1224no—
598C22×C4—1221no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—2442no—
605C22×C4—2444no—
606C22×C4—2444no—
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610Q16—28no—
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—612no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1224no—
638C4⋊C4C23×D6112yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
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—22no—
667Q8—22no—
668Q8—42no—
669Q8—614no—
670Q8—12216no—
671Q8—1224no—
672Q8—1222no—
673Q8C2×#1175822414yes—
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—22no—
684C2×C4—42no—
685C2×C4—42no—
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—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—2444no—
703C2×C4—2448no—
704C2×C4—2448no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4C2×D4×D6112yes—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4#41×D6112yes—
712C2×C4C2×#1175822412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—1222no—
717C8—1222no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—614no—
723C22—1222no—
724C22—1222no—
725C22—1228no—
726C22#1684027212yes—
727C22#137×D6112yes—
728C22#1684055912yes—
729C22C22×D4×D6111yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—1224no—
739C4—2442no—
740C4—2442no—
741C4—2442no—
742C4#1684027212yes—
743C4C2×#41×D6111yescharacteristic
744C4C22×#1175822411yescharacteristic
745C2—82no—
746C2—1224no—
747C2#2145598914yesdirect product factor
748C2C2×#1684027211yescharacteristic
749C2C2×#137×D6111yescharacteristic
750C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×#464D61
hypocenterC61C2×#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D61C2semidirect
3. #21455989C2direct (N × H)
4. C2×#16840096C2semidirect
6. C2×#16840070C2semidirect
7. C2×#16840069C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839916C2semidirect
11. C2×#16839869C2semidirect
12. C2×#16839866C2semidirect
13. C2×#16839863C2semidirect
14. C2×#16839859C2semidirect
15. C2×#16839818C2semidirect
16. C2×C61×#464C2semidirect
34. C4×Q8×D61C22semidirect
42. #16840096C22semidirect
44. #16840070C22semidirect
45. #16840069C22semidirect
46. #16839981C22semidirect
47. #16839916C22semidirect
49. #16839869C22semidirect
50. #16839866C22semidirect
51. #16839863C22semidirect
52. #16839859C22semidirect
53. #16839818C22semidirect
73. C61×#464C22semidirect
378. C2×#464D61semidirect
387. C2×C61#3117semidirect
426. #464C2×D61semidirect
452. C61C2×#3117semidirect
747. C2#21455989direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402912
C2×C4×Q8×D612
#214559892
C2×#168400962
C2×#168400792
C2×#168400702
C2×#168400692
C2×#168399812
C2×#168399162
C2×#168398992
C2×#168398692
C2×#168398662
C2×#168398632
C2×#168398592
C2×#168398182
C2×C61×#4642
C2×#311761