Finite Group Databasebeta

← C2×#21458612 #30559701

Subgroups — C2×#21458612 #30559701

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840495C211yesmaximal, characteristic, complemented
2C2×D4×Dic122C211yesmaximal, characteristic, complemented
3#21458612C2116yesmaximal, direct product factor
4C2×#16840122C211yesmaximal, characteristic, complemented
5C2×#16840120C211yesmaximal, characteristic, complemented
6C2×#16840107C211yesmaximal, characteristic, complemented
7C2×#16840046C211yesmaximal, characteristic, complemented
8C2×#16840052C211yesmaximal, characteristic, complemented
9C2×#16840051C211yesmaximal, characteristic, complemented
10C2×#16839977C211yesmaximal, characteristic, complemented
11C2×#16839975C211yesmaximal, characteristic, complemented
12C2×#16839955C211yesmaximal, characteristic
13C2×#16839890C211yesmaximal, characteristic, complemented
14C2×#16839871C211yesmaximal, characteristic, complemented
15C2×#16839853C211yesmaximal, characteristic, complemented
16C2×C61×#442C211yesmaximal, characteristic, complemented
17C23×Dic122—21no—
18C22×#11758200C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20#16840495—24no—
21#16840495C2218yescomplemented
22D4×Dic122—24no—
23D4×Dic122C2218yescomplemented
24C2×#14519777C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519776C2211yescharacteristic
27C2×#14519773C2211yescharacteristic
28C2×#14519765C2211yescharacteristic
29C2×#14519764C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519760—21no—
32C2×#14519759—21no—
33C2×#14519756—21no—
34C2×#14519754—21no—
35C2×#14519754—21no—
36C2×C4×Dic122C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×C4×C22⋊D61—21no—
42#16840122C2218yescomplemented
43#16840120C2218yescomplemented
44#16840107C2218yescomplemented
45#16840052C2218yescomplemented
46#16840051C2218yescomplemented
47#16840046C2218yescomplemented
48#16839977C2218yescomplemented
49#16839975C2218yescomplemented
50#16839955C2218yes—
51#16839890C2218yescomplemented
52#16839871C2218yescomplemented
53#16839853C2218yescomplemented
54C2×#14519708C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#442C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122—21no—
80C22×Dic122—28no—
81C22×Dic122—48no—
82C22×Dic122D411yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C23×Dic61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C2×#11758200—24no—
91C2×#11758200C2314yes—
92C2×#11758199—24no—
93C2×#11758199C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519777—22no—
97#14519777C2314yes—
98#14519776—22no—
99#14519776—22no—
100#14519776C2314yes—
101#14519776C2314yes—
102#14519773—22no—
103#14519773C2314yes—
104#14519765—22no—
105#14519765C2314yes—
106#14519764—22no—
107#14519764C2314yes—
108#14519763—28no—
109#14519760—28no—
110#14519759—28no—
111#14519756—28no—
112#14519754—28no—
113#14519754—28no—
114C4×Dic122D414yes—
115C4×Dic122C2314yes—
116#14519742—22no—
117#14519742C2314yes—
118D4×Dic61—22no—
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121D4×Dic61C2314yes—
122#14519739—22no—
123#14519739C2314yes—
124C4×C22⋊D61—28no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61D411yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×#11758196D411yescharacteristic
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144#14519708C2314yes—
145#14519708C2314yes—
146C4⋊#92418C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519702C2314yes—
151#14519700C2314yes—
152#14519699C2314yes—
153#14519699C2314yes—
154#14519698C2314yes—
155#14519698C2314yes—
156#14519697C2314yes—
157#14519687C2314yes—
158C8×Dic61C2314yes—
159C22×D4×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C23×C4×C61—21no—
163C2×D8×C61—24no—
164C2×D8×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4×D4×C61—22no—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176#106×C61C2314yes—
177#102×C61C2314yes—
178#102×C61C2314yes—
179#97×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C23×D61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—22no—
188C2×D4×C61#4114yes—
189C2×D4×C61C2412yes—
190C2×D4×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—24no—
194C22×C4×C61—24no—
195C22×C4×C61—44no—
196C22×C4×C61—82no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—82no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—24no—
209C22×Dic61—44no—
210C22×Dic61—44no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—21no—
218C2×D244C2412yes—
219C2×C4×D61—24no—
220C2×C4×D61—82no—
221C2×Dic122—24no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—24no—
225C2×Dic122—21no—
226C2×Dic122—24no—
227C2×Dic122—24no—
228C2×Dic122—432no—
229C2×Dic122—44no—
230C2×Dic122—44no—
231C2×Dic122—44no—
232C2×Dic122C2×D414yes—
233C2×Dic122C2412yes—
234D8×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61C2×D412yes—
246C42×C61C2412yes—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251#11758200—28no—
252#11758199—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61C2×D414yes—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196C2×D414yes—
266#11758196C2×D414yes—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2×D412yes—
270C4×Dic61C2412yes—
271C4×Dic61C2412yes—
272C2×#92418—22no—
273C2×#92418—22no—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C23×C61—24no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61—42no—
289D4×C61—24no—
290D4×C61—22no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—42no—
294D4×C61C2×#4114yes—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—48no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—84no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4112yes—
307C2×C4×C612−1+412yes—
308C2×C4×C61C2511yescharacteristic
309C22⋊D61—48no—
310C22⋊D61—84no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—48no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61—48no—
322C2×Dic61AGL(1,ℤ/8)14yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327D244—22no—
328D244—22no—
329D244—42no—
330C4×D61—84no—
331Dic122—28no—
332Dic122—22no—
333Dic122—22no—
334Dic122—48no—
335Dic122—48no—
336Dic122—42no—
337Dic122—48no—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3373—611nomaximal, Sylow
343C22×C61—24no—
344C22×C61—48no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—84no—
351C22×C61#54812yes—
352C22×C61C2×AGL(1,ℤ/8)12yes—
353C22×C61#57712yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—84no—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61#54812yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C2×2−1+411yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372Dic61C2×AGL(1,ℤ/8)14yes—
373C2×#559—611no—
374C2×D4×Q8—611no—
375#3373—6116no—
376C2×#489—611no—
377C2×#489—611no—
378C2×#486—611no—
379C2×#475—611no—
380C2×#476—611no—
381C2×#476—611no—
382C2×#463—611no—
383C2×#463—611no—
384C2×#459—611no—
385C2×#446—611no—
386C2×#442—611no—
387C2×#442D6111yescharacteristic, complemented
388C2×C4×SD16—611no—
389C2×C61—44no—
390C2×C61—82no—
391C2×C61#337314yescomplemented
392C2×C61C2×#54811yescharacteristic
393C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C61C2×#57711yescharacteristic
395D61—82no—
396C23×Q8—1221no—
397C22×SD16—611no—
398C22×D8—611no—
399C22×D8C2×D6111yescharacteristic
400#559—618no—
401#559—1224no—
402D4×Q8—618no—
403D4×Q8—1224no—
404C2×C4⋊Q8—611no—
405C2×C4⋊Q8—611no—
406C2×C4⋊Q8—611no—
407C2×#127—611no—
408C2×#124—611no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×#123—1221no—
413C2×C22⋊Q8—1221no—
414C2×C22⋊Q8—1221no—
415C2×C22⋊Q8—1221no—
416C2×C4×Q8—611no—
417C2×C4×Q8—611no—
418C2×C4×D4—611no—
419C2×C4×D4—611no—
420C2×C4×D4—611no—
421C2×C4×D4—1221no—
422C2×C4×D4C2×D6111yescharacteristic
423C2×C4×D4C2×D6111yescharacteristic
424#489—618no—
425#489—618no—
426#486—618no—
427#476—618no—
428#476—618no—
429#475—618no—
430#463—618no—
431#463—618no—
432#459—618no—
433#446—618no—
434#442—618no—
435#442C2×D6118yescomplemented
436C4×SD16—618no—
437C2×#106—611no—
438C2×#106—611no—
439C2×#106C2×D6111yescharacteristic
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C4⋊C8—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102C2×D6111yescharacteristic
452C2×#102C2×D6111yescharacteristic
453C2×#97—611no—
454C2×#97C2×D6111yescharacteristic
455C2×C4×C8—611no—
456C61C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×Q8—611no—
459C22×Q8—1221no—
460C22×Q8—1221no—
461C22×Q8—1228no—
462C22×Q8—1221no—
463C22×Q8—2448no—
464C22×D4—611no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4C22×D6111yescharacteristic
468C22×D4C22×D6111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4—1221no—
474C2×SD16—614no—
475C2×SD16—1224no—
476C2×D8—24no—
477C2×D8—614no—
478C2×D8—1224no—
479C2×D8C22×D6114yes—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C4⋊Q8—614no—
485C4⋊Q8—614no—
486C4⋊Q8—614no—
487C4⋊Q8—1222no—
488C4⋊Q8—1222no—
489C4⋊Q8—1222no—
490#127—614no—
491#127—1222no—
492#124—614no—
493#124—614no—
494#124—1222no—
495#124—1228no—
496#124—1222no—
497#123—1228no—
498#123—1228no—
499C22⋊Q8—1228no—
500C22⋊Q8—1228no—
501C22⋊Q8—1228no—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515C4×D4C22×D6114yes—
516C4×D4C22×D6114yes—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1221no—
540C2×C42C22×D6111yescharacteristic
541#106—614no—
542#106—614no—
543#106C22×D6114yes—
544C4⋊C8—614no—
545C4⋊C8—614no—
546C4⋊C8—614no—
547#103—614no—
548#103—614no—
549#103—614no—
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#102C22×D6114yes—
556#102C22×D6114yes—
557#97—614no—
558#97C22×D6114yes—
559C4×C8—614no—
560C24—21no—
561C24—21no—
562C24—1221no—
563C2×Q8—614no—
564C2×Q8—612no—
565C2×Q8—1224no—
566C2×Q8—1224no—
567C2×Q8—1224no—
568C2×Q8—1221no—
569C2×Q8—1224no—
570C2×Q8—1222no—
571C2×Q8—1222no—
572C2×Q8—2444no—
573C2×Q8—2444no—
574C2×Q8—2444no—
575C2×Q8—24432no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—612no—
582C2×D4—1224no—
583C2×D4—1224no—
584C2×D4—1221no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—4882no—
588C2×D4—2444no—
589C2×D4#1175822214yes—
590C2×D4C23×D6112yes—
591C2×D4C23×D6112yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—4882no—
609C22×C4—2444no—
610C22×C4—2444no—
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4C23×D6111yescharacteristic
614SD16—1228no—
615D8—28no—
616D8—1228no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—1222no—
622C2×C8—1222no—
623C2×C8C23×D6112yes—
624C2×C8C23×D6112yes—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—614no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—612no—
631C4⋊C4—612no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1224no—
638C4⋊C4C23×D6112yes—
639C4⋊C4C23×D6112yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C42—612no—
650C42—612no—
651C42—612no—
652C42—612no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—1228no—
670Q8—1222no—
671Q8—1222no—
672Q8—2448no—
673Q8—2448no—
674Q8—2448no—
675Q8—2442no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—24no—
680D4—42no—
681D4—1222no—
682D4—1222no—
683D4—4884no—
684D4—2448no—
685D4—2442no—
686D4C2×#1175822214yes—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4—614no—
696C2×C4—612no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4884no—
707C2×C4—2448no—
708C2×C4—2448no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822212yes—
716C2×C4#1451982412yes—
717C2×C4C24×D6111yescharacteristic
718C8—22no—
719C8—22no—
720C8—1222no—
721C8—1222no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—48no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—4884no—
731C22—2442no—
732C22—2442no—
733C22—2442no—
734C22#1684042112yes—
735C22AGL(1,ℤ/8)×D6112yes—
736C22#1684057212yes—
737C22C22×D4×D6111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—614no—
743C4—1222no—
744C4—1222no—
745C4—1222no—
746C4—2442no—
747C4—2442no—
748C4—2442no—
749C4#1684042112yes—
750C4C22×#1175822211yescharacteristic
751C4C2×#1451982411yescharacteristic
752C2—44no—
753C2—82no—
754C2—4882no—
755C2#2145861214yesdirect product factor
756C2C2×#1684042111yescharacteristic
757C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
758C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#442C2
socleC23×C61C22×D4
prime radicalC2×#16839955C2
hypercenterC2×#442D61
hypocenterC61C2×#3373
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16840495C2semidirect
2. C2×D4×Dic122C2semidirect
3. #21458612C2direct (N × H)
4. C2×#16840122C2semidirect
5. C2×#16840120C2semidirect
6. C2×#16840107C2semidirect
7. C2×#16840046C2semidirect
8. C2×#16840052C2semidirect
9. C2×#16840051C2semidirect
10. C2×#16839977C2semidirect
11. C2×#16839975C2semidirect
13. C2×#16839890C2semidirect
14. C2×#16839871C2semidirect
15. C2×#16839853C2semidirect
16. C2×C61×#442C2semidirect
21. #16840495C22semidirect
23. D4×Dic122C22semidirect
42. #16840122C22semidirect
43. #16840120C22semidirect
44. #16840107C22semidirect
45. #16840052C22semidirect
46. #16840051C22semidirect
47. #16840046C22semidirect
48. #16839977C22semidirect
49. #16839975C22semidirect
51. #16839890C22semidirect
52. #16839871C22semidirect
53. #16839853C22semidirect
72. C61×#442C22semidirect
387. C2×#442D61semidirect
391. C2×C61#3373semidirect
435. #442C2×D61semidirect
456. C61C2×#3373semidirect
755. C2#21458612direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×D4×Dic1222
#214586122
C2×#168401222
C2×#168401202
C2×#168401072
C2×#168400462
C2×#168400522
C2×#168400512
C2×#168399772
C2×#168399752
C2×#168399552
C2×#168398902
C2×#168398712
C2×#168398532
C2×C61×#4422
C2×#337361