Finite Group Databasebeta

← C2×#21458171 #30558431

Subgroups — C2×#21458171 #30558431

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840412C211yesmaximal, characteristic
3#21458171C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840078C211yesmaximal, characteristic, complemented
7C2×#16840091C211yesmaximal, characteristic, complemented
8C2×#16840090C211yesmaximal, characteristic, complemented
9C2×#16840045C211yesmaximal, characteristic, complemented
10C2×#16840050C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×SD16×Dic61C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
14C22×#14519709C211yesmaximal, characteristic, complemented
15C2×#106×D61C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×C8×D61C2211yescharacteristic
19#16840470—24no—
20#16840470C2218yescomplemented
21#16840412—24no—
22#16840412C2218yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519759—21no—
27C2×#14519758—21no—
28C2×#14519757—21no—
29C2×#14519754—21no—
30C2×#14519754—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519748C2211yescharacteristic
33C2×Q8×Dic61C2211yescharacteristic
34C2×D4×Dic61C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×#14519737—21no—
37C22×C4⋊Dic61C2211yescharacteristic
38C22×C4⋊Dic61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16840159C2218yescomplemented
42#16840091C2218yescomplemented
43#16840090C2218yescomplemented
44#16840079C2218yescomplemented
45#16840078C2218yescomplemented
46#16840050C2218yescomplemented
47#16840045C2218yescomplemented
48#16839988C2218yescomplemented
49SD16×Dic61C2218yescomplemented
50C8×C22⋊D61C2218yescomplemented
51C2×#14519709C2211yescharacteristic
52C2×#14519709C2211yescharacteristic
53C2×#14519709C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519709C2218yescomplemented
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60#106×D61C2218yescomplemented
61C2×#14519706C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61D411yescharacteristic
83C23×Dic61—21no—
84C23×Dic61—21no—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—24no—
92C2×C8×D61C2314yes—
93#14519776—22no—
94#14519776—22no—
95#14519776C2314yes—
96#14519776C2314yes—
97#14519767—28no—
98#14519759—28no—
99#14519758—28no—
100#14519757—28no—
101#14519754—28no—
102#14519754—28no—
103#14519753—22no—
104#14519753C2314yes—
105#14519748—22no—
106#14519748C2314yes—
107Q8×Dic61—22no—
108Q8×Dic61C2314yes—
109D4×Dic61—22no—
110D4×Dic61C2314yes—
111C4×C22⋊D61D414yes—
112C4×C22⋊D61C2314yes—
113#14519737—28no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2314yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2314yes—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2314yes—
134C4⋊C4×D61C2314yes—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198D411yescharacteristic
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519709C2314yes—
143#14519709C2314yes—
144#14519709C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61—21no—
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C2×SD16×C61—24no—
163C2×SD16×C61C2314yes—
164C22×C8×C61—24no—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61C2314yes—
170#121×C61—22no—
171#121×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177#106×C61C2314yes—
178#103×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C24×C61C2×D411yescharacteristic
182C23×D61C2×D411yescharacteristic
183C2×Q8×C61—21no—
184C2×Q8×C61—22no—
185C2×Q8×C61—22no—
186C2×Q8×C61C2412yes—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—44no—
192C2×D4×C61C2412yes—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61SD1618yescomplemented
205C2×C22⋊D61C2×D414yes—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—24no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61—44no—
215C22×Dic61—82no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758224—432no—
220C2×C4×D61—22no—
221C2×C4×D61—22no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—44no—
225C2×C4×D61—82no—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2412yes—
228C2×Dic122—24no—
229C2×Dic122—24no—
230C2×Dic122—44no—
231C2×Dic122—82no—
232SD16×C61—28no—
233C2×C8×C61—22no—
234C2×C8×C61—28no—
235C2×C8×C61#4114yescomplemented
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2412yes—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61C2×D414yes—
248#11758198—24no—
249#11758198C2×D414yes—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196C2×D414yes—
267C4×Dic61—24no—
268C4×Dic61C2×D412yes—
269C4×Dic61C2412yes—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418C2412yes—
273C2×#92418C2412yes—
274C8×D61—28no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C2×SD1614yes—
282C23×C61C22×D412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—22no—
286C22×D61C2×SD1614yes—
287C22×D61C22×D412yes—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—42no—
291D4×C61—22no—
292D4×C61—22no—
293D4×C61—48no—
294D4×C61—42no—
295C2×C4×C61—22no—
296C2×C4×C61—24no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C612−1+412yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—48no—
311C22⋊D61C2×SD16116yescomplemented
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—48no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—48no—
324C2×Dic61—84no—
325C2×Dic61C2×SD1614yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328C2×Dic61C22×D412yes—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—48no—
333C4×D61—84no—
334Dic122—48no—
335Dic122—84no—
336C8×C61—22no—
337C8×C61C2×#4114yescomplemented
338#92418—22no—
339#92418—22no—
340C2×#3335—611nomaximal, Sylow
341C22×C61—28no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—84no—
348C22×C61#54712yes—
349C22×C61C22×SD1614yes—
350C22×C61C22×SD1612yes—
351C22×C61#57712yes—
352C22×C61C23×D411yescharacteristic
353C2×D61—28no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61C22×SD1614yes—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61#54712yes—
362C4×C61C22×#4111yescharacteristic
363C4×C61C2×2−1+411yescharacteristic
364Dic61—22no—
365Dic61—22no—
366Dic61—42no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370Dic61C22×SD1614yes—
371C2×#554—611no—
372C2×#547—611no—
373#3335—6116no—
374C2×#498—611no—
375C2×#481—611no—
376C2×#481—611no—
377C2×#483—611no—
378C2×#483—611no—
379C2×#475—611no—
380C2×#476—611no—
381C2×#465—611no—
382C2×#465D6111yescharacteristic, complemented
383C2×C4×SD16—611no—
384C2×C8×D4—611no—
385C22×#106—611no—
386C22×#106—611no—
387C2×C61—24no—
388C2×C61—82no—
389C2×C61#333514yescomplemented
390C2×C61C2×#54711yescharacteristic
391C2×C61C23×SD1611yescharacteristic
392C2×C61C2×#57711yescharacteristic
393D61—24no—
394C22×#41—1221no—
395C22×SD16C2×D6111yescharacteristic
396C23×C8—611no—
397C23×C8C2×D6111yescharacteristic
398#554—618no—
399#554—1224no—
400#547—618no—
401#547—1224no—
402C2×C4⋊Q8—611no—
403C2×C4⋊Q8—611no—
404C2×#125—1221no—
405C2×#123—1221no—
406C2×#123—1221no—
407C2×C22⋊Q8—611no—
408C2×C22⋊Q8—1221no—
409C2×C22⋊Q8—1221no—
410C2×C22⋊Q8—1221no—
411C2×C22⋊Q8C2×D6111yescharacteristic
412C2×#121—611no—
413C2×#121C2×D6111yescharacteristic
414C2×C4×Q8—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—1221no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422#498—618no—
423#483—618no—
424#483—618no—
425#481—618no—
426#481—618no—
427#476—618no—
428#475—618no—
429#465—618no—
430#465C2×D6118yescomplemented
431C4×SD16—618no—
432C8×D4—618no—
433C2×#106—611no—
434C2×#106—618no—
435C2×#106—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×#106—611no—
439C2×#106—611no—
440C2×#106—611no—
441C2×#106—611no—
442C2×#106—618no—
443C2×#106C2×D6111yescharacteristic
444C2×C4⋊C8—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103C2×D6111yescharacteristic
448C2×#102—611no—
449C2×#102—611no—
450C2×#102C2×D6111yescharacteristic
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×C4×C8—611no—
454C61C2×#333511yescharacteristic, complemented, Sylow
455C2×#41—1228no—
456C2×#41—2448no—
457C22×Q8—1221no—
458C22×Q8—1221no—
459C22×Q8C22×D6111yescharacteristic
460C22×D4—21no—
461C22×D4—611no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—24no—
472C2×SD16C22×D6114yes—
473C22×C8—24no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—614no—
477C22×C8—1224no—
478C22×C8C22×D6111yescharacteristic
479C22×C8C22×D6114yes—
480C22×C8C22×D6111yescharacteristic
481C4⋊Q8—614no—
482C4⋊Q8—614no—
483C4⋊Q8—1222no—
484C4⋊Q8—1222no—
485#125—1228no—
486#123—1228no—
487#123—1228no—
488C22⋊Q8—22no—
489C22⋊Q8—614no—
490C22⋊Q8—1228no—
491C22⋊Q8—1228no—
492C22⋊Q8—1228no—
493C22⋊Q8—1222no—
494C22⋊Q8C22×D6114yes—
495#121—22no—
496#121—614no—
497#121—1222no—
498#121C22×D6114yes—
499C4×Q8—614no—
500C4×Q8—1222no—
501C4×D4—614no—
502C4×D4—614no—
503C4×D4—614no—
504C4×D4—1222no—
505C4×D4—1228no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
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⋊C4—1222no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—611no—
538C2×C42—1221no—
539#106—614no—
540#106—614no—
541#106—614no—
542#106—614no—
543#106—614no—
544#106—614no—
545#106—614no—
546#106—614no—
547#106C22×D6114yes—
548C4⋊C8—614no—
549#103—614no—
550#103—614no—
551#103C22×D6114yes—
552#102—614no—
553#102—614no—
554#102C22×D6114yes—
555C22⋊C8—614no—
556C22⋊C8—614no—
557C4×C8—614no—
558C24—21no—
559C24—611no—
560C24D4×D6111yescharacteristic
561#41—24432no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—1224no—
566C2×Q8—1224no—
567C2×Q8—4882no—
568C2×Q8—2444no—
569C2×Q8C23×D6112yes—
570C2×D4—24no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—614no—
576C2×D4—618no—
577C2×D4—1224no—
578C2×D4—2444no—
579C2×D4C23×D6112yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—1224no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—4882no—
602C22×C4—4882no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4—2444no—
606C22×C4D4×D6112yes—
607C22×C4D4×D6111yescharacteristic
608C22×C4C23×D6112yes—
609C22×C4C23×D6111yescharacteristic
610SD16—28no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—612no—
614C2×C8—612no—
615C2×C8—1222no—
616C2×C8—1222no—
617C2×C8—1228no—
618C2×C8#1175822414yescomplemented
619C2×C8C23×D6112yes—
620C2×C8C23×D6112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—614no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1221no—
641C4⋊C4C23×D6112yes—
642C4⋊C4C23×D6112yes—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—614no—
646C22⋊C4—614no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—612no—
651C42—612no—
652C42—1224no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—614no—
660C23—612no—
661C23—1222no—
662C23—1222no—
663C23SD16×D6114yes—
664C23C2×D4×D6112yes—
665C23C2×D4×D6111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—4884no—
670Q8—2448no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—6116no—
676D4—2448no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—614no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—612no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1224no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—4884no—
701C2×C4—4884no—
702C2×C4—2448no—
703C2×C4—2448no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2448no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4C2×#1175822412yes—
712C2×C4#1451982412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—1222no—
716C8—1222no—
717C8C2×#1175822414yescomplemented
718C22—22no—
719C22—22no—
720C22—28no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—614no—
726C22—1222no—
727C22—1222no—
728C22—1228no—
729C22#1684041212yes—
730C22C2×SD16×D6114yes—
731C22C2×SD16×D6112yes—
732C22#1684056912yes—
733C22C22×D4×D6111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—614no—
739C4—1222no—
740C4—1222no—
741C4—2442no—
742C4—2442no—
743C4—2442no—
744C4—2442no—
745C4#1684041212yes—
746C4C22×#1175822411yescharacteristic
747C4C2×#1451982411yescharacteristic
748C2—24no—
749C2—82no—
750C2—1224no—
751C2#2145817114yesdirect product factor
752C2C2×#1684041211yescharacteristic
753C2C22×SD16×D6111yescharacteristic
754C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840412C2
hypercenterC2×#465D61
hypocenterC61C2×#3335
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
3. #21458171C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840078C2semidirect
7. C2×#16840091C2semidirect
8. C2×#16840090C2semidirect
9. C2×#16840045C2semidirect
10. C2×#16840050C2semidirect
11. C2×#16839988C2semidirect
12. C2×SD16×Dic61C2semidirect
13. C2×C8×C22⋊D61C2semidirect
14. C22×#14519709C2semidirect
15. C2×#106×D61C2semidirect
16. C2×C61×#465C2semidirect
20. #16840470C22semidirect
41. #16840159C22semidirect
42. #16840091C22semidirect
43. #16840090C22semidirect
44. #16840079C22semidirect
45. #16840078C22semidirect
46. #16840050C22semidirect
47. #16840045C22semidirect
48. #16839988C22semidirect
49. SD16×Dic61C22semidirect
50. C8×C22⋊D61C22semidirect
55. C2×#14519709C22semidirect
60. #106×D61C22semidirect
73. C61×#465C22semidirect
204. C2×C22⋊D61SD16semidirect
235. C2×C8×C61#41semidirect
311. C22⋊D61C2×SD16semidirect
337. C8×C61C2×#41semidirect
382. C2×#465D61semidirect
389. C2×C61#3335semidirect
430. #465C2×D61semidirect
454. C61C2×#3335semidirect
618. C2×C8#11758224semidirect
717. C8C2×#11758224semidirect
751. C2#21458171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168404122
#214581712
C2×#168401592
C2×#168400792
C2×#168400782
C2×#168400912
C2×#168400902
C2×#168400452
C2×#168400502
C2×#168399882
C2×SD16×Dic612
C2×C8×C22⋊D612
C22×#145197092
C2×#106×D612
C2×C61×#4652
C2×#333561