Finite Group Databasebeta

← C2×#21456041 #30548285

Subgroups — C2×#21456041 #30548285

Order 15616.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840379C211yesmaximal, characteristic
2C2×#16840240C211yesmaximal, characteristic, complemented
3#21456041C2116yesmaximal, direct product factor
4C2×#16840104C211yesmaximal, characteristic, complemented
5C2×#16840083C211yesmaximal, characteristic
6C2×#16840055C211yesmaximal, characteristic, complemented
7C2×#16840045C211yesmaximal, characteristic, complemented
8C2×#16839982C211yesmaximal, characteristic, complemented
9C2×#16839982C211yesmaximal, characteristic, complemented
10C2×#16839918C211yesmaximal, characteristic, complemented
11C2×#16839866C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×SD16×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#448C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19#16840379—24no—
20#16840379C2218yes—
21C2×#14519776C2211yescharacteristic
22C2×#14519770—21no—
23C2×#14519764—21no—
24C2×#14519764C2211yescharacteristic
25C2×#14519758—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519754—21no—
28#16840240—24no—
29#16840240C2218yescomplemented
30C2×Q8×Dic61—21no—
31C2×Q8×Dic61—21no—
32C2×Q8×Dic61C2211yescharacteristic
33C2×Q8×Dic61C2211yescharacteristic
34C2×Q8×Dic61C2211yescharacteristic
35C2×Q8×Dic61C2211yescharacteristic
36C2×#14519742C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519736—21no—
39C2×#14519736—21no—
40C2×#14519736C2211yescharacteristic
41C2×#14519736C2211yescharacteristic
42#16840104C2218yescomplemented
43#16840083C2218yes—
44#16840055C2218yescomplemented
45#16840045C2218yescomplemented
46#16839982C2218yescomplemented
47#16839982C2218yescomplemented
48#16839918C2218yescomplemented
49#16839866C2218yescomplemented
50#16839863C2218yescomplemented
51#16839854C2218yescomplemented
52SD16×Dic61C2218yescomplemented
53#16839820C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C23×Q8×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#448C2218yes—
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C23×Dic61—21no—
80C2×#11758202—24no—
81C2×#11758202—24no—
82C2×#11758202C2314yes—
83C2×#11758202C2314yes—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519776—22no—
87#14519776C2314yes—
88#14519770—28no—
89#14519764—28no—
90#14519764—22no—
91#14519764C2314yes—
92#14519758—28no—
93#14519756—22no—
94#14519756C2314yes—
95#14519754—28no—
96Q8×Dic61—28no—
97Q8×Dic61—28no—
98Q8×Dic61—22no—
99Q8×Dic61—22no—
100Q8×Dic61—22no—
101Q8×Dic61—22no—
102Q8×Dic61C2314yes—
103Q8×Dic61C2314yes—
104Q8×Dic61C2314yes—
105Q8×Dic61C2314yes—
106#14519742—22no—
107#14519742C2314yes—
108D4×Dic61—22no—
109D4×Dic61C2314yes—
110#14519736—22no—
111#14519736—28no—
112#14519736—28no—
113#14519736D414yes—
114#14519736C2314yes—
115#14519736C2314yes—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61D411yescharacteristic
121C2×C4⋊Dic61D411yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61D411yescharacteristic
134C2×C22⋊Dic61D411yescharacteristic
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519702C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61—24no—
159C22×Q8×C61—24no—
160C22×Q8×C61—21no—
161C22×Q8×C61—22no—
162C22×Q8×C61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C2×SD16×C61—24no—
170C2×SD16×C61—24no—
171C2×SD16×C61C2314yes—
172C2×SD16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#121×C61—22no—
176#121×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#103×C61C2314yes—
180#103×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C2×Q8×C61—216no—
185C2×Q8×C61—28no—
186C2×Q8×C61—28no—
187C2×Q8×C61—28no—
188C2×Q8×C61—24no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61#4114yes—
194C2×Q8×C61#4114yes—
195C2×Q8×C61C2412yes—
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—82no—
202C2×D4×C61C2412yes—
203C22×C4×C61—28no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—82no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—24no—
228C2×Dic122—82no—
229C2×Dic122C2412yes—
230SD16×C61—28no—
231SD16×C61—28no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61C2412yes—
235C2×C8×C61C2412yes—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61C2×D414yes—
245C22⋊Dic61C2×D414yes—
246#11758202—28no—
247#11758202—28no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61C2×D414yes—
256C4⋊Dic61C2×D414yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D412yes—
271C4×Dic61C2412yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D412yes—
285C23×C61C22×D411yescharacteristic
286Q8×C61—216no—
287Q8×C61—24no—
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61C2×#4114yes—
292Q8×C61C2×#4114yes—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—42no—
296D4×C61—84no—
297C2×C4×C61—216no—
298C2×C4×C61—24no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—42no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4112yes—
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2511yescharacteristic
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—84no—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329C2×Dic61C22×D412yes—
330Dic122—22no—
331Dic122—22no—
332Dic122—42no—
333Dic122—84no—
334C8×C61—22no—
335C8×C61—22no—
336#92418—22no—
337#92418—22no—
338C2×#3121—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—84no—
347C22×C61#52512yes—
348C22×C61#57712yes—
349C22×C61#57812yes—
350C22×C61C23×D411yescharacteristic
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61#52512yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C22×#4111yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—22no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366C2×#542—611no—
367C2×#519—611no—
368#3121—6116no—
369C2×#485—611no—
370C2×#482—611no—
371C2×#477—611no—
372C2×#475—611no—
373C2×#464—611no—
374C2×#464—611no—
375C2×#451—611no—
376C2×#448D6111yescharacteristic
377C2×#441—611no—
378C2×#440—611no—
379C2×C4×Q16—611no—
380C2×C4×SD16—611no—
381C2×#433—611no—
382C2×C61—42no—
383C2×C61—82no—
384C2×C61#312114yescomplemented
385C2×C61C2×#52511yescharacteristic
386C2×C61C2×#57711yescharacteristic
387C2×C61C2×#57811yescharacteristic
388C23×Q8C2×D6111yescharacteristic
389C22×Q16—611no—
390C22×Q16—611no—
391C22×SD16C2×D6111yescharacteristic
392C22×SD16C2×D6111yescharacteristic
393#542—618no—
394#542—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#124—611no—
398C2×#124—1221no—
399C2×#123—1221no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—1221no—
402C2×#121C2×D6111yescharacteristic
403#519—618no—
404#519—1224no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—1221no—
411C2×C4×Q8—1221no—
412C2×C4×D4—611no—
413C2×#117—611no—
414C2×#117—611no—
415C2×#117—1221no—
416C2×#117—1221no—
417#485—618no—
418#482—618no—
419#477—618no—
420#475—618no—
421#464—618no—
422#464—618no—
423#451—618no—
424#448C2×D6118yes—
425#441—618no—
426#440—618no—
427C4×Q16—618no—
428C4×SD16—618no—
429#433—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103C2×D6111yescharacteristic
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8C2×D6111yescharacteristic
446C2×#97—611no—
447C2×C4×C8—611no—
448C61C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—611no—
454C22×Q8—1221no—
455C22×Q8C22×D6114yes—
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—614no—
464C2×Q16—614no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×SD16—24no—
468C2×SD16—24no—
469C2×SD16C22×D6114yes—
470C2×SD16C22×D6114yes—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—1228no—
478#124—614no—
479#124—1222no—
480#124—1228no—
481#123—1228no—
482C22⋊Q8—614no—
483C22⋊Q8—1228no—
484C22⋊Q8—1222no—
485#121—22no—
486#121C22×D6114yes—
487C4×Q8—614no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×Q8—614no—
491C4×Q8—614no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1228no—
498C4×Q8—1228no—
499C4×D4—614no—
500C4×D4—1222no—
501#117—614no—
502#117—614no—
503#117—614no—
504#117—1228no—
505#117—1228no—
506#117—1222no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540C4⋊C8—614no—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103C22×D6114yes—
547#103C22×D6114yes—
548#102—614no—
549#102—614no—
550C22⋊C8—614no—
551C22⋊C8C22×D6114yes—
552#97—614no—
553C4×C8—614no—
554C24—21no—
555C24D4×D6111yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1221no—
568C2×Q8—1222no—
569C2×Q8—1222no—
570C2×Q8—4882no—
571C2×Q8#1175822414yes—
572C2×Q8#1175822414yes—
573C2×Q8C23×D6112yes—
574C2×Q8C23×D6112yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D6112yes—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1224no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—4882no—
598C22×C4D4×D6112yes—
599C22×C4D4×D6111yescharacteristic
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602Q16—1228no—
603Q16—1228no—
604SD16—28no—
605SD16—28no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8C23×D6112yes—
613C2×C8C23×D6112yes—
614C4⋊C4—21no—
615C4⋊C4—614no—
616C4⋊C4—614no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1224no—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—614no—
633C22⋊C4—614no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—612no—
640C42—612no—
641C42—612no—
642C42—612no—
643C42—1224no—
644C42—1224no—
645C42—1224no—
646C42—1224no—
647C42—1224no—
648C42—1224no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×D4×D6112yes—
657C23C2×D4×D6111yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—1222no—
664Q8—1222no—
665Q8—4884no—
666Q8—2442no—
667Q8C2×#1175822414yes—
668Q8C2×#1175822414yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—4884no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4C2×D4×D6112yes—
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C2×#1175822412yes—
704C2×C4C2×#1175822412yes—
705C2×C4C24×D6111yescharacteristic
706C8—22no—
707C8—22no—
708C8—1222no—
709C8—1222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1684026812yes—
719C22#1684056812yes—
720C22#1684057812yes—
721C22C22×D4×D6111yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—1222no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4#1684026812yes—
735C4C22×#1175822411yescharacteristic
736C4C22×#1175822411yescharacteristic
737C2—42no—
738C2—82no—
739C2#2145604114yesdirect product factor
740C2C2×#1684026811yescharacteristic
741C2C2×#1684056811yescharacteristic
742C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#448D61
hypocenterC61C2×#3121
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C2×#16840240C2semidirect
3. #21456041C2direct (N × H)
4. C2×#16840104C2semidirect
6. C2×#16840055C2semidirect
7. C2×#16840045C2semidirect
8. C2×#16839982C2semidirect
9. C2×#16839982C2semidirect
10. C2×#16839918C2semidirect
11. C2×#16839866C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839854C2semidirect
14. C2×SD16×Dic61C2semidirect
15. C2×#16839820C2semidirect
29. #16840240C22semidirect
42. #16840104C22semidirect
44. #16840055C22semidirect
45. #16840045C22semidirect
46. #16839982C22semidirect
47. #16839982C22semidirect
48. #16839918C22semidirect
49. #16839866C22semidirect
50. #16839863C22semidirect
51. #16839854C22semidirect
52. SD16×Dic61C22semidirect
53. #16839820C22semidirect
384. C2×C61#3121semidirect
448. C61C2×#3121semidirect
739. C2#21456041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168402402
#214560412
C2×#168401042
C2×#168400832
C2×#168400552
C2×#168400452
C2×#168399822
C2×#168399182
C2×#168398662
C2×#168398632
C2×#168398542
C2×SD16×Dic612
C2×#168398202
C2×C61×#4482
C2×#312161