Finite Group Databasebeta

← C2×#21458532 #30559683

Subgroups — C2×#21458532 #30559683

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840481C211yesmaximal, characteristic, complemented
2C2×D4×Dic122C211yesmaximal, characteristic, complemented
3#21458532C2116yesmaximal, direct product factor
4C2×#16840121C211yesmaximal, characteristic, complemented
5C2×#16840120C211yesmaximal, characteristic, complemented
6C2×#16840111C211yesmaximal, characteristic, complemented
7C2×#16840058C211yesmaximal, characteristic, complemented
8C2×#16840055C211yesmaximal, characteristic, complemented
9C2×#16840040C211yesmaximal, characteristic, complemented
10C2×#16839975C211yesmaximal, characteristic
11C2×#16839965C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839863C211yesmaximal, characteristic, complemented
14C2×#16839862C211yesmaximal, characteristic, complemented
15C2×D8×Dic61C211yesmaximal, characteristic
16C2×C61×#463C211yesmaximal, characteristic
17C23×Dic122—21no—
18C22×#11758200C2211yescharacteristic
19#16840481—24no—
20#16840481C2218yescomplemented
21D4×Dic122—24no—
22D4×Dic122C2218yescomplemented
23C2×#14519777C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519776C2211yescharacteristic
26C2×#14519775C2211yescharacteristic
27C2×#14519770—21no—
28C2×#14519770—21no—
29C2×#14519764C2211yescharacteristic
30C2×#14519756—21no—
31C2×#14519754—21no—
32C2×#14519754—21no—
33C2×#14519754—21no—
34C2×Q8×Dic61C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×Dic122C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519733—21no—
41#16840121C2218yescomplemented
42#16840120C2218yescomplemented
43#16840111C2218yescomplemented
44#16840058C2218yescomplemented
45#16840055C2218yescomplemented
46#16840040C2218yescomplemented
47#16839975C2218yes—
48#16839965C2218yescomplemented
49#16839891C2218yescomplemented
50#16839863C2218yescomplemented
51#16839862C2218yescomplemented
52D8×Dic61C2218yes—
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519706C2211yescharacteristic
57C2×#14519706C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yes—
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122—21no—
80C22×Dic122—28no—
81C22×Dic122—48no—
82C22×Dic122D411yescharacteristic
83C22×Dic122C2311yescharacteristic
84C23×Dic61—21no—
85C23×Dic61—21no—
86C23×Dic61—21no—
87C2×#11758200—24no—
88C2×#11758200C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519777—22no—
92#14519777C2314yes—
93#14519776—22no—
94#14519776—22no—
95#14519776C2314yes—
96#14519776C2314yes—
97#14519775—22no—
98#14519775C2314yes—
99#14519770—28no—
100#14519770—28no—
101#14519764—22no—
102#14519764C2314yes—
103#14519756—28no—
104#14519754—28no—
105#14519754—28no—
106#14519754—28no—
107Q8×Dic61—22no—
108Q8×Dic61C2314yes—
109C4×Dic122—22no—
110C4×Dic122D414yes—
111C4×Dic122C2314yes—
112C4×Dic122C2314yes—
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61—22no—
116D4×Dic61C2314yes—
117D4×Dic61C2314yes—
118D4×Dic61C2314yes—
119#14519733—28no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61D411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142#14519711C2314yes—
143#14519711C2314yes—
144#14519710C2314yes—
145#14519706C2314yes—
146#14519706C2314yes—
147#14519702C2314yes—
148#14519702C2314yes—
149#14519701C2314yes—
150#14519701C2314yes—
151#14519700C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519688C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61C2311yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C2×SD16×C61—24no—
163C2×SD16×C61C2314yes—
164C2×D8×C61—24no—
165C2×D8×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#124×C61—22no—
169#124×C61C2314yes—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C4⋊C8×C61C2314yes—
178#103×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C24×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61#4114yes—
192C2×D4×C61C2412yes—
193C2×D4×C61C2412yes—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—44no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2411yescharacteristic
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—24no—
208C22×Dic61—44no—
209C22×Dic61—44no—
210C22×Dic61—44no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C2×Dic122—24no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—24no—
219C2×Dic122—21no—
220C2×Dic122—24no—
221C2×Dic122—24no—
222C2×Dic122—432no—
223C2×Dic122—44no—
224C2×Dic122—44no—
225C2×Dic122—44no—
226C2×Dic122C2×D414yes—
227C2×Dic122C2412yes—
228SD16×C61—28no—
229D8×C61—28no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C42×C61C2×D412yes—
240C42×C61C2412yes—
241C22⋊Dic61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246#11758200—28no—
247C4⋊Dic61—24no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61C2×D414yes—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262#11758196C2×D414yes—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61C2×D412yes—
266C4×Dic61C2×D412yes—
267C4×Dic61C2412yes—
268C4×Dic61C2412yes—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273C23×C61—24no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C22×D411yescharacteristic
282Q8×C61—22no—
283Q8×C61—22no—
284Q8×C61—42no—
285D4×C61—24no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—42no—
290D4×C61C2×#4114yes—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—48no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4112yes—
302C2×C4×C612−1+412yes—
303C2×C4×C61C2511yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—48no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—48no—
317C2×Dic61—48no—
318C2×Dic61AGL(1,ℤ/8)14yes—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323Dic122—28no—
324Dic122—22no—
325Dic122—22no—
326Dic122—48no—
327Dic122—48no—
328Dic122—42no—
329Dic122—48no—
330C8×C61—22no—
331C8×C61—22no—
332#92418—22no—
333#92418—22no—
334C2×#3367—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—48no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—84no—
343C22×C61#54812yes—
344C22×C61C2×AGL(1,ℤ/8)12yes—
345C22×C61#57812yes—
346C22×C61C23×D411yescharacteristic
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#54812yes—
352C4×C61C22×#4111yescharacteristic
353C4×C61C2×2−1+411yescharacteristic
354Dic61—22no—
355Dic61—22no—
356Dic61—22no—
357Dic61—42no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361Dic61C2×AGL(1,ℤ/8)14yes—
362C2×#556—611no—
363C2×D4×Q8—611no—
364#3367—6116no—
365C2×#489—611no—
366C2×#489—611no—
367C2×#487—611no—
368C2×#477—611no—
369C2×#477—611no—
370C2×#474—611no—
371C2×#463—611no—
372C2×#463D6111yescharacteristic
373C2×#461—611no—
374C2×#446—611no—
375C2×#440—611no—
376C2×#440—611no—
377C2×C4×D8—611no—
378C2×C61—44no—
379C2×C61—82no—
380C2×C61#336714yescomplemented
381C2×C61C2×#54811yescharacteristic
382C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C61C2×#57811yescharacteristic
384C23×Q8—1221no—
385C22×SD16—611no—
386C22×SD16C2×D6111yescharacteristic
387C22×D8C2×D6111yescharacteristic
388#556—618no—
389#556—1224no—
390D4×Q8—618no—
391D4×Q8—1224no—
392C2×C4⋊Q8—611no—
393C2×C4⋊Q8—611no—
394C2×C4⋊Q8—611no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#126—1221no—
398C2×#124—611no—
399C2×#124C2×D6111yescharacteristic
400C2×C22⋊Q8—1221no—
401C2×C22⋊Q8—1221no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×C4×Q8—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4C2×D6111yescharacteristic
411C2×#117—1221no—
412#489—618no—
413#489—618no—
414#487—618no—
415#477—618no—
416#477—618no—
417#474—618no—
418#463—618no—
419#463C2×D6118yes—
420#461—618no—
421#446—618no—
422#440—618no—
423#440—618no—
424C4×D8—618no—
425C2×#107—611no—
426C2×#107—611no—
427C2×#107—611no—
428C2×C4⋊C8—611no—
429C2×C4⋊C8—611no—
430C2×C4⋊C8C2×D6111yescharacteristic
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103C2×D6111yescharacteristic
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102C2×D6111yescharacteristic
441C2×#97—611no—
442C2×#97—611no—
443C2×C4×C8—611no—
444C61C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—611no—
446C22×Q8—611no—
447C22×Q8—1221no—
448C22×Q8—1221no—
449C22×Q8—1228no—
450C22×Q8—1221no—
451C22×Q8—2448no—
452C22×Q8C22×D6111yescharacteristic
453C22×D4C22×D6111yescharacteristic
454C22×D4C22×D6111yescharacteristic
455C23×C4—21no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C2×SD16—24no—
460C2×SD16—614no—
461C2×SD16—1224no—
462C2×SD16C22×D6114yes—
463C2×D8—24no—
464C2×D8C22×D6114yes—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4⋊Q8—614no—
470C4⋊Q8—614no—
471C4⋊Q8—614no—
472C4⋊Q8—614no—
473C4⋊Q8—1222no—
474C4⋊Q8—1222no—
475C4⋊Q8—1222no—
476C4⋊Q8—1222no—
477#126—1228no—
478#126—1228no—
479#124—22no—
480#124—614no—
481#124—1222no—
482#124C22×D6114yes—
483C22⋊Q8—1228no—
484C22⋊Q8—1228no—
485C22⋊Q8—1228no—
486C22⋊Q8—1228no—
487C4×Q8—614no—
488C4×Q8—614no—
489C4×Q8—614no—
490C4×Q8—614no—
491C4×Q8—1222no—
492C4×Q8—1222no—
493C4×D4—22no—
494C4×D4—614no—
495C4×D4—614no—
496C4×D4—614no—
497C4×D4—1222no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4C22×D6114yes—
501#117—1228no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4C22×D6111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42C22×D6111yescharacteristic
529#107—614no—
530#107—614no—
531#107—614no—
532C4⋊C8—614no—
533C4⋊C8—614no—
534C4⋊C8C22×D6114yes—
535#103—614no—
536#103—614no—
537#103—614no—
538#103—614no—
539#103—614no—
540#103C22×D6114yes—
541#102—614no—
542#102—614no—
543#102—614no—
544#102C22×D6114yes—
545#97—614no—
546#97—614no—
547C4×C8—614no—
548C24—21no—
549C24—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—614no—
554C2×Q8—612no—
555C2×Q8—1224no—
556C2×Q8—1224no—
557C2×Q8—1224no—
558C2×Q8—1221no—
559C2×Q8—1224no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—2444no—
563C2×Q8—2444no—
564C2×Q8—2444no—
565C2×Q8—24432no—
566C2×Q8C23×D6112yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4#1175822414yes—
573C2×D4C23×D6112yes—
574C2×D4C23×D6112yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4D4×D6111yescharacteristic
594C22×C4D4×D6111yescharacteristic
595C22×C4C23×D6111yescharacteristic
596SD16—28no—
597SD16—1228no—
598D8—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1222no—
604C2×C8—1222no—
605C2×C8C23×D6112yes—
606C2×C8C23×D6112yes—
607C4⋊C4—21no—
608C4⋊C4—614no—
609C4⋊C4—614no—
610C4⋊C4—614no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—612no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4C23×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—1224no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C42—612no—
634C42—612no—
635C42—612no—
636C42—612no—
637C42—1224no—
638C42—1224no—
639C42D4×D6112yes—
640C42C23×D6112yes—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23C2×D4×D6111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1228no—
654Q8—1222no—
655Q8—1222no—
656Q8—2448no—
657Q8—2448no—
658Q8—2448no—
659Q8—2442no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—24no—
664D4—42no—
665D4C2×#1175822414yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—48no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—614no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—2448no—
686C2×C4—2448no—
687C2×C4—2448no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4C2×D4×D6112yes—
693C2×C4C2×D4×D6112yes—
694C2×C4C2×D4×D6111yescharacteristic
695C2×C4C2×#1175822412yes—
696C2×C4#1451982412yes—
697C2×C4C24×D6111yescharacteristic
698C8—22no—
699C8—22no—
700C8—1222no—
701C8—1222no—
702C22—24no—
703C22—42no—
704C22—48no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1684041812yes—
711C22AGL(1,ℤ/8)×D6112yes—
712C22#1684057612yes—
713C22C22×D4×D6111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—614no—
719C4—1222no—
720C4—1222no—
721C4—1222no—
722C4—2442no—
723C4—2442no—
724C4—2442no—
725C4—2442no—
726C4#1684041812yes—
727C4C22×#1175822411yescharacteristic
728C4C2×#1451982411yescharacteristic
729C2—44no—
730C2—82no—
731C2#2145853214yesdirect product factor
732C2C2×#1684041811yescharacteristic
733C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
734C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
hypercenterC2×#463D61
hypocenterC61C2×#3367
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×#16840481C2semidirect
2. C2×D4×Dic122C2semidirect
3. #21458532C2direct (N × H)
4. C2×#16840121C2semidirect
5. C2×#16840120C2semidirect
6. C2×#16840111C2semidirect
7. C2×#16840058C2semidirect
8. C2×#16840055C2semidirect
9. C2×#16840040C2semidirect
11. C2×#16839965C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839863C2semidirect
14. C2×#16839862C2semidirect
20. #16840481C22semidirect
22. D4×Dic122C22semidirect
41. #16840121C22semidirect
42. #16840120C22semidirect
43. #16840111C22semidirect
44. #16840058C22semidirect
45. #16840055C22semidirect
46. #16840040C22semidirect
48. #16839965C22semidirect
49. #16839891C22semidirect
50. #16839863C22semidirect
51. #16839862C22semidirect
380. C2×C61#3367semidirect
444. C61C2×#3367semidirect
731. C2#21458532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404812
C2×D4×Dic1222
#214585322
C2×#168401212
C2×#168401202
C2×#168401112
C2×#168400582
C2×#168400552
C2×#168400402
C2×#168399752
C2×#168399652
C2×#168398912
C2×#168398632
C2×#168398622
C2×D8×Dic612
C2×C61×#4632
C2×#336761