Finite Group Databasebeta

← C2×#21457217 #30552898

Subgroups — C2×#21457217 #30552898

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic, complemented
2C2×#16840291C211yesmaximal, characteristic, complemented
3#21457217C2116yesmaximal, direct product factor
4C2×#16840070C211yesmaximal, characteristic, complemented
5C2×#16840067C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16840060C211yesmaximal, characteristic, complemented
8C2×#16840019C211yesmaximal, characteristic, complemented
9C2×#16840012C211yesmaximal, characteristic
10C2×#16840007C211yesmaximal, characteristic, complemented
11C2×#16840005C211yesmaximal, characteristic, complemented
12C2×#16839982C211yesmaximal, characteristic, complemented
13C2×#16839981C211yesmaximal, characteristic, complemented
14C2×#16839975C211yesmaximal, characteristic, complemented
15C2×#16839784C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21#16840294—24no—
22#16840294C2218yescomplemented
23#16840291—24no—
24#16840291C2218yescomplemented
25C2×#14519770—21no—
26C2×#14519770—21no—
27C2×#14519769C2211yescharacteristic
28C2×#14519768C2211yescharacteristic
29C2×#14519764C2211yescharacteristic
30C2×#14519759—21no—
31C2×#14519759—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519753C2211yescharacteristic
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×Q8×Dic61C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×#14519737—21no—
41C2×#14519736—21no—
42C2×#14519733—21no—
43C2×C42×D61C2211yescharacteristic
44#16840070C2218yescomplemented
45#16840067C2218yescomplemented
46#16840062C2218yescomplemented
47#16840060C2218yescomplemented
48#16840019C2218yescomplemented
49#16840012C2218yes—
50#16840007C2218yescomplemented
51#16840005C2218yescomplemented
52#16839982C2218yescomplemented
53#16839981C2218yescomplemented
54#16839975C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59#16839784C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519698C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C22×C4×D61D411yescharacteristic
82C22×C4×D61D411yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758200—42no—
87C2×#11758200C2314yes—
88C2×#11758189—42no—
89C2×#11758189—42no—
90C2×#11758189C2314yes—
91C2×#11758189C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519770—28no—
95#14519770—28no—
96#14519769—22no—
97#14519769C2314yes—
98#14519768—22no—
99#14519768C2314yes—
100#14519764—22no—
101#14519764C2314yes—
102#14519759—28no—
103#14519759—28no—
104#14519757—22no—
105#14519757C2314yes—
106#14519753—22no—
107#14519753C2314yes—
108#14519748—22no—
109#14519748—22no—
110#14519748C2314yes—
111#14519748C2314yes—
112Q8×Dic61—22no—
113Q8×Dic61C2314yes—
114C4×Dic122—22no—
115C4×Dic122C2314yes—
116D4×Dic61—22no—
117D4×Dic61C2314yes—
118C4×C22⋊D61—28no—
119#14519737—28no—
120#14519736—28no—
121#14519733—28no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C42×D61D414yes—
146C42×D61C2314yes—
147#14519711C2314yes—
148#14519710C2314yes—
149#14519709C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—42no—
165C2×SD16×C61C2314yes—
166C2×D8×C61—42no—
167C2×D8×C61C2314yes—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170#124×C61—22no—
171#124×C61C2314yes—
172C4×D4×C61—22no—
173C4×D4×C61C2314yes—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C2×D4×C61C2412yes—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—44no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—44no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2×D414yes—
223C2×C4×D61C2×D414yes—
224C2×C4×D61C2412yes—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—21no—
228C2×Dic122C2412yes—
229SD16×C61—44no—
230D8×C61—44no—
231C2×C8×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61C2412yes—
234C2×C8×C61C2412yes—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C42×C61C2×D412yes—
241C42×C61C2412yes—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247#11758202—44no—
248#11758200—44no—
249#11758198—24no—
250#11758198—24no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61C2×D412yes—
268C4×Dic61C2×D414yes—
269C4×Dic61C2×D414yes—
270C4×Dic61C2412yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275#11758189—44no—
276#11758189—44no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61C22×D411yescharacteristic
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61C22×D412yes—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—42no—
298D4×C61—42no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—48no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61C22×D412yes—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61H(5,𝔽2)12yes—
310C2×C4×C612−1+412yes—
311C2×C4×C61C2511yescharacteristic
312C22⋊D61—48no—
313C22⋊D61—48no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—48no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—44no—
333C4×D61—44no—
334Dic122—22no—
335Dic122—22no—
336Dic122—42no—
337C8×C61—22no—
338C8×C61—22no—
339#92418—22no—
340#92418—22no—
341C2×#3256—611nomaximal, Sylow
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—84no—
349C22×C61—84no—
350C22×C61#53712yes—
351C22×C61#57512yes—
352C22×C61#57512yes—
353C22×C61C23×D411yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—44no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#53712yes—
363C4×C61C2×H(5,𝔽2)11yescharacteristic
364C4×C61C2×2−1+411yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—22no—
368Dic61—42no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#529—611no—
373C2×#529—611no—
374#3256—6116no—
375C2×#479—611no—
376C2×#479—611no—
377C2×#478—611no—
378C2×#478—611no—
379C2×#470—611no—
380C2×#469—611no—
381C2×#468—611no—
382C2×#468—611no—
383C2×#464—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#463D6111yescharacteristic, complemented
387C2×#423—611no—
388C2×C61—82no—
389C2×C61—82no—
390C2×C61#325614yescomplemented
391C2×C61C2×#53711yescharacteristic
392C2×C61C2×#57511yescharacteristic
393C2×C61C2×#57511yescharacteristic
394D61—42no—
395C22×Q16—611no—
396C22×SD16—611no—
397C22×SD16C2×D6111yescharacteristic
398C22×D8C2×D6111yescharacteristic
399C22×M16—611no—
400C22×M16—611no—
401#529—618no—
402#529—618no—
403#529—1224no—
404#529—1224no—
405C2×#126—1221no—
406C2×#126—1221no—
407C2×#125—611no—
408C2×#125—611no—
409C2×#124—611no—
410C2×#124C2×D6111yescharacteristic
411C2×#123—1221no—
412C2×#123—1221no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×#121—611no—
416C2×#121—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×D4—611no—
420C2×C4×D4—1221no—
421C2×C4×D4—1221no—
422C2×C4×D4C2×D6111yescharacteristic
423C2×#117—1221no—
424C2×#117—1221no—
425C22×C42—611no—
426#479—618no—
427#479—618no—
428#478—618no—
429#478—618no—
430#470—618no—
431#469—618no—
432#468—618no—
433#468—618no—
434#464—618no—
435#464—618no—
436#463—618no—
437#463C2×D6118yescomplemented
438C2×#107—611no—
439C2×#107—611no—
440C2×#106—611no—
441C2×#106—611no—
442#423—618no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8C2×D6111yescharacteristic
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103C2×D6111yescharacteristic
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102C2×D6111yescharacteristic
455C61C2×#325611yescharacteristic, complemented, Sylow
456C22×Q8—611no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4C22×D6111yescharacteristic
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C2×Q16—614no—
468C2×Q16—2442no—
469C2×SD16—42no—
470C2×SD16—614no—
471C2×SD16—2442no—
472C2×SD16C22×D6114yes—
473C2×D8—42no—
474C2×D8C22×D6114yes—
475C2×M16—614no—
476C2×M16—614no—
477C2×M16—2442no—
478C2×M16—2442no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483#126—1228no—
484#126—1228no—
485#125—614no—
486#125—614no—
487#125—1222no—
488#125—1222no—
489#124—22no—
490#124—614no—
491#124—1222no—
492#124C22×D6114yes—
493#123—1228no—
494#123—1228no—
495C22⋊Q8—614no—
496C22⋊Q8—614no—
497C22⋊Q8—1222no—
498C22⋊Q8—1222no—
499#121—614no—
500#121—614no—
501#121—1222no—
502#121—1222no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×D4—22no—
508C4×D4—614no—
509C4×D4—1222no—
510C4×D4—1228no—
511C4×D4—1228no—
512C4×D4C22×D6114yes—
513#117—1228no—
514#117—1228no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
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—611no—
540C2×C42—614no—
541C2×C42—614no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#107—614no—
546#107—614no—
547#106—614no—
548#106—614no—
549C4⋊C8—614no—
550C4⋊C8—614no—
551C4⋊C8—614no—
552C4⋊C8C22×D6114yes—
553#103—614no—
554#103—614no—
555#103—614no—
556#103C22×D6114yes—
557#102—614no—
558#102—614no—
559#102—614no—
560#102C22×D6114yes—
561C24—21no—
562C24—21no—
563C24—611no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—612no—
568C2×Q8—1221no—
569C2×Q8—1222no—
570C2×Q8—1222no—
571C2×Q8C23×D6112yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—1224no—
579C2×D4—1224no—
580C2×D4—2444no—
581C2×D4—2444no—
582C2×D4C23×D6112yes—
583C2×D4C23×D6112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—612no—
592C22×C4—612no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—1224no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4—2444no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—2444no—
609SD16—44no—
610SD16—2444no—
611D8—44no—
612M16—2444no—
613M16—2444no—
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—21no—
623C4⋊C4—612no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C42—614no—
649C42—612no—
650C42—614no—
651C42—612no—
652C42—1224no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—612no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1222no—
673Q8—1222no—
674Q8—2442no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—42no—
681D4—2448no—
682D4—2448no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1224no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—2444no—
704C2×C4—2444no—
705C2×C4—2448no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4C2×D4×D6112yes—
711C2×C4C2×D4×D6112yes—
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#1451982212yes—
714C2×C4#1451982412yes—
715C2×C4C24×D6111yescharacteristic
716C8—22no—
717C8—22no—
718C8—1222no—
719C8—1222no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—2444no—
732C22#1684034112yes—
733C22#1684055812yes—
734C22#1684055912yes—
735C22C22×D4×D6111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—1222no—
741C4—1222no—
742C4—1222no—
743C4—2442no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4#1684034112yes—
748C4C2×#1451982211yescharacteristic
749C4C2×#1451982411yescharacteristic
750C2—82no—
751C2—82no—
752C2—2442no—
753C2#2145721714yesdirect product factor
754C2C2×#1684034111yescharacteristic
755C2C2×#1684055811yescharacteristic
756C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC2×#16840012C2
hypercenterC2×#463D61
hypocenterC61C2×#3256
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840294C2semidirect
2. C2×#16840291C2semidirect
3. #21457217C2direct (N × H)
4. C2×#16840070C2semidirect
5. C2×#16840067C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16840060C2semidirect
8. C2×#16840019C2semidirect
10. C2×#16840007C2semidirect
11. C2×#16840005C2semidirect
12. C2×#16839982C2semidirect
13. C2×#16839981C2semidirect
14. C2×#16839975C2semidirect
15. C2×#16839784C2semidirect
16. C2×C61×#463C2semidirect
22. #16840294C22semidirect
24. #16840291C22semidirect
44. #16840070C22semidirect
45. #16840067C22semidirect
46. #16840062C22semidirect
47. #16840060C22semidirect
48. #16840019C22semidirect
50. #16840007C22semidirect
51. #16840005C22semidirect
52. #16839982C22semidirect
53. #16839981C22semidirect
54. #16839975C22semidirect
59. #16839784C22semidirect
73. C61×#463C22semidirect
386. C2×#463D61semidirect
390. C2×C61#3256semidirect
437. #463C2×D61semidirect
455. C61C2×#3256semidirect
753. C2#21457217direct (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×#168402912
#214572172
C2×#168400702
C2×#168400672
C2×#168400622
C2×#168400602
C2×#168400192
C2×#168400122
C2×#168400072
C2×#168400052
C2×#168399822
C2×#168399812
C2×#168399752
C2×#168397842
C2×C61×#4632
C2×#325661