Finite Group Databasebeta

← C2×#21458894 #30561029

Subgroups — C2×#21458894 #30561029

Order 15616.

1938 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×#16840485C211yesmaximal, characteristic, complemented
2#21458894C2116yesmaximal, direct product factor
3C2×#16840157C211yesmaximal, characteristic, complemented
4C2×#16840154C211yesmaximal, characteristic, complemented
5C2×#16840144C211yesmaximal, characteristic
6C2×#16839984C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839972C211yesmaximal, characteristic, complemented
9C2×#16839969C211yesmaximal, characteristic, complemented
10C2×#16839977C211yesmaximal, characteristic
11C2×#16839974C211yesmaximal, characteristic
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×C4×#11758202C211yesmaximal, characteristic, complemented
16C2×C61×#556C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758201C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26#16840485—24no—
27#16840485C2218yescomplemented
28C2×#14519777C2211yescharacteristic
29C2×#14519772—21no—
30C2×#14519772—21no—
31C2×#14519765C2211yescharacteristic
32C2×#14519765C2211yescharacteristic
33C2×#14519753—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×#14519735—21no—
38#16840157C2218yescomplemented
39#16840154C2218yescomplemented
40#16840144C2218yes—
41#16839984C2218yescomplemented
42#16839981C2218yescomplemented
43#16839977C2218yes—
44#16839974C2218yes—
45#16839972C2218yescomplemented
46#16839969C2218yescomplemented
47#16839893C2218yescomplemented
48#16839862C2218yescomplemented
49#16839860C2218yescomplemented
50C4×#11758202C2218yescomplemented
51C2×#14519710C2211yescharacteristic
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#556—24no—
65C61×#556C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#126×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C2×C22⋊Q8×C61—21no—
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61—21no—
77C22×Dic122C2311yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C4×D61—21no—
81C2×#11758202—24no—
82C2×#11758202—42no—
83C2×#11758202—42no—
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758202C2314yes—
87C2×#11758202C2314yes—
88C2×#11758202C2314yes—
89C2×#11758200—24no—
90C2×#11758200—42no—
91C2×#11758200C2314yes—
92C2×#11758200C2314yes—
93C2×#11758201—24no—
94C2×#11758201—42no—
95C2×#11758201C2314yes—
96C2×#11758201C2314yes—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519777—22no—
104#14519777C2314yes—
105#14519772—28no—
106#14519772—28no—
107#14519765—22no—
108#14519765—22no—
109#14519765C2314yes—
110#14519765C2314yes—
111#14519753—28no—
112C4×Dic122—22no—
113C4×Dic122—22no—
114C4×Dic122C2314yes—
115C4×Dic122C2314yes—
116C4×D244—22no—
117C4×D244C2314yes—
118#14519735—28no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×C4×Dic61—21no—
130C2×C4×Dic61—21no—
131#14519710C2314yes—
132C4⋊#92418C2314yes—
133C4⋊#92418C2314yes—
134C4⋊#92418C2314yes—
135#14519701C2314yes—
136#14519701C2314yes—
137#14519700C2314yes—
138#14519700C2314yes—
139#14519698C2314yes—
140#14519697C2314yes—
141#14519688C2314yes—
142#14519688C2314yes—
143C4×#92418C2314yes—
144C22×Q8×C61D411yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C22×Q8×C61C2311yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C4⋊Q8×C61—22no—
150C4⋊Q8×C61C2314yes—
151#126×C61—28no—
152#126×C61—28no—
153#124×C61—22no—
154#124×C61—22no—
155#124×C61C2314yes—
156#124×C61C2314yes—
157C22⋊Q8×C61—28no—
158C4×Q8×C61—22no—
159C4×Q8×C61—22no—
160C4×Q8×C61D414yes—
161C4×Q8×C61C2314yes—
162C4×Q8×C61C2314yes—
163C4×Q8×C61C2314yes—
164C4×D4×C61—22no—
165C4×D4×C61C2314yes—
166#117×C61—28no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61—21no—
182C2×C42×C61C2311yescharacteristic
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C23×D61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—42no—
194C2×Q8×C61C2×D414yes—
195C2×Q8×C61C2412yes—
196C2×Q8×C61C2412yes—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—24no—
205C22×C4×C61—44no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244C2412yes—
220C2×C4×D61—24no—
221C2×C4×D61—44no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122C2412yes—
229C2×Dic122C2412yes—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2×D414yes—
236C4⋊C4×C61C2×D414yes—
237C4⋊C4×C61C2×D414yes—
238C4⋊C4×C61C2412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C42×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2×D412yes—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C42×C61C2412yes—
251C42×C61C2412yes—
252#11758202—28no—
253#11758202—44no—
254#11758202—44no—
255#11758202—44no—
256#11758201—28no—
257#11758201—44no—
258#11758200—28no—
259#11758200—44no—
260#11758199—44no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266C4⋊Dic61—24no—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418#4114yes—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282C23×C61—22no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—44no—
296Q8×C61—42no—
297Q8×C61—42no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—42no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—48no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C2×C4×C61H(5,𝔽2)12yes—
323C2×C4×C61C2511yescharacteristic
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330D244—22no—
331D244—22no—
332D244—42no—
333C4×D61—48no—
334Dic122—22no—
335Dic122—22no—
336Dic122—22no—
337Dic122—22no—
338Dic122—42no—
339Dic122—42no—
340#92418—22no—
341#92418—22no—
342#92418—22no—
343#92418C2×#4114yes—
344C2×#3402—611nomaximal, Sylow
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—84no—
349C22×C61#55012yes—
350C22×C61#57512yes—
351C22×C61#57812yes—
352C22×C61C23×D411yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—84no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61#55012yes—
367C4×C61C22×#4111yescharacteristic
368C4×C61C2×H(5,𝔽2)11yescharacteristic
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#556—611no—
373C2×#556D6111yescharacteristic, complemented
374#3402—6116no—
375C2×#497—611no—
376C2×#497—611no—
377C2×#495—611no—
378C2×#464—611no—
379C2×#464—611no—
380C2×#462—611no—
381C2×#462—611no—
382C2×#463—611no—
383C2×#463—611no—
384C2×#446—611no—
385C2×#440—611no—
386C2×#440—611no—
387C2×C4×Q16—611no—
388C2×C61—82no—
389C2×C61#340214yescomplemented
390C2×C61C2×#55011yescharacteristic
391C2×C61C2×#57511yescharacteristic
392C2×C61C2×#57811yescharacteristic
393D61—82no—
394C22×Q16—611no—
395C22×Q16—611no—
396C22×Q16—611no—
397C22×Q16—611no—
398C22×SD16—611no—
399C22×SD16—611no—
400C22×SD16—611no—
401C22×SD16—611no—
402C22×D8—611no—
403#556—24no—
404#556—618no—
405#556—1224no—
406#556C2×D6118yescomplemented
407C2×C4⋊Q8—611no—
408C2×C4⋊Q8C2×D6111yescharacteristic
409C2×#126—21no—
410C2×#126—21no—
411C2×#126—1221no—
412C2×#126—1221no—
413C2×#124—611no—
414C2×#124—611no—
415C2×#124C2×D6111yescharacteristic
416C2×#124C2×D6111yescharacteristic
417C2×C22⋊Q8—21no—
418C2×C22⋊Q8—1221no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×Q8C2×D6111yescharacteristic
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×Q8C2×D6111yescharacteristic
424C2×C4×D4—611no—
425C2×C4×D4C2×D6111yescharacteristic
426C2×#117—21no—
427C2×#117—1221no—
428#497—618no—
429#497—618no—
430#495—618no—
431#464—618no—
432#464—618no—
433#463—618no—
434#463—618no—
435#462—618no—
436#462—618no—
437#446—618no—
438#440—618no—
439#440—618no—
440C4×Q16—618no—
441C2×#107—611no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#97—611no—
452C2×#97—611no—
453C2×C4×C8—611no—
454C61C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×Q8—611no—
457C22×Q8C22⋊D6111yescharacteristic
458C22×Q8C22×D6111yescharacteristic
459C22×Q8C22×D6111yescharacteristic
460C22×D4—611no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C2×Q16—614no—
465C2×Q16—614no—
466C2×Q16—614no—
467C2×Q16—614no—
468C2×Q16—1224no—
469C2×Q16—2442no—
470C2×Q16—2442no—
471C2×Q16—2442no—
472C2×SD16—614no—
473C2×SD16—614no—
474C2×SD16—614no—
475C2×SD16—614no—
476C2×SD16—1224no—
477C2×SD16—1224no—
478C2×SD16—2442no—
479C2×SD16—2442no—
480C2×D8—614no—
481C2×D8—2442no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C4⋊Q8—22no—
487C4⋊Q8—614no—
488C4⋊Q8—1222no—
489C4⋊Q8C22×D6114yes—
490#126—28no—
491#126—28no—
492#126—1228no—
493#126—1228no—
494#124—22no—
495#124—22no—
496#124—614no—
497#124—614no—
498#124—1222no—
499#124—1222no—
500#124C22×D6114yes—
501#124C22×D6114yes—
502C22⋊Q8—28no—
503C22⋊Q8—1228no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—614no—
507C4×Q8—614no—
508C4×Q8—1222no—
509C4×Q8—1222no—
510C4×Q8C22⋊D6114yes—
511C4×Q8C22×D6114yes—
512C4×Q8C22×D6114yes—
513C4×Q8C22×D6114yes—
514C4×D4—22no—
515C4×D4—614no—
516C4×D4—1222no—
517C4×D4C22×D6114yes—
518#117—28no—
519#117—1228no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4C22⋊D6111yescharacteristic
530C2×C4⋊C4C22⋊D6111yescharacteristic
531C2×C4⋊C4C22⋊D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548C2×C42C22×D6111yescharacteristic
549C2×C42C22×D6111yescharacteristic
550#107—614no—
551C4⋊C8—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103—614no—
558#102—614no—
559#102—614no—
560#97—614no—
561#97—614no—
562C4×C8—614no—
563C24—21no—
564C24—1221no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—612no—
573C2×Q8—612no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×Q8—1222no—
577C2×Q8—1222no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8C2×C22⋊D6114yes—
581C2×Q8C23×D6112yes—
582C2×Q8C23×D6112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—612no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4C23×D6112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1224no—
600C22×C4—2444no—
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—1228no—
609Q16—2444no—
610Q16—2444no—
611Q16—2444no—
612SD16—1228no—
613SD16—1228no—
614SD16—2444no—
615SD16—2444no—
616D8—2444no—
617C2×C8—614no—
618C2×C8—612no—
619C2×C8—612no—
620C2×C8—612no—
621C2×C8—612no—
622C2×C8—1222no—
623C2×C8—1222no—
624C2×C8—1222no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—612no—
631C4⋊C4—1221no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4C2×C22⋊D6114yes—
637C4⋊C4C2×C22⋊D6114yes—
638C4⋊C4C2×C22⋊D6114yes—
639C4⋊C4C23×D6112yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—24no—
651C42—24no—
652C42—1224no—
653C42—1224no—
654C42C2×C22⋊D6112yes—
655C42C2×C22⋊D6112yes—
656C42C2×C22⋊D6112yes—
657C42C23×D6112yes—
658C42C23×D6112yes—
659C42C23×D6112yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C22×C22⋊D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—1222no—
677Q8—1222no—
678Q8—1222no—
679Q8—1222no—
680Q8—2442no—
681Q8—2442no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1222no—
686D4—1222no—
687D4—2442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—2448no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4C22×C22⋊D6112yes—
709C2×C4C22×C22⋊D6112yes—
710C2×C4C22×C22⋊D6112yes—
711C2×C4C22×C22⋊D6112yes—
712C2×C4C22×C22⋊D6112yes—
713C2×C4C22×C22⋊D6112yes—
714C2×C4C22×C22⋊D6111yescharacteristic
715C2×C4#41×D6112yes—
716C2×C4#1451982312yes—
717C2×C4C24×D6111yescharacteristic
718C8—614no—
719C8—1222no—
720C8—1222no—
721C8—1222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4884no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22#1684043112yes—
731C22#1684056012yes—
732C22#1684057712yes—
733C22C23×C22⋊D6111yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2442no—
744C4—2442no—
745C4—2442no—
746C4#1684043112yes—
747C4C2×#41×D6111yescharacteristic
748C4C2×#1451982311yescharacteristic
749C2—82no—
750C2—4882no—
751C2#2145889414yesdirect product factor
752C2C2×#1684043111yescharacteristic
753C2C2×#1684056011yescharacteristic
754C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#556C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#556D61
hypocenterC61C2×#3402
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
2. #21458894C2direct (N × H)
3. C2×#16840157C2semidirect
4. C2×#16840154C2semidirect
6. C2×#16839984C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839972C2semidirect
9. C2×#16839969C2semidirect
12. C2×#16839893C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839860C2semidirect
15. C2×C4×#11758202C2semidirect
16. C2×C61×#556C2semidirect
27. #16840485C22semidirect
38. #16840157C22semidirect
39. #16840154C22semidirect
41. #16839984C22semidirect
42. #16839981C22semidirect
45. #16839972C22semidirect
46. #16839969C22semidirect
47. #16839893C22semidirect
48. #16839862C22semidirect
49. #16839860C22semidirect
50. C4×#11758202C22semidirect
65. C61×#556C22semidirect
373. C2×#556D61semidirect
389. C2×C61#3402semidirect
406. #556C2×D61semidirect
454. C61C2×#3402semidirect
751. C2#21458894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
#214588942
C2×#168401572
C2×#168401542
C2×#168401442
C2×#168399842
C2×#168399812
C2×#168399722
C2×#168399692
C2×#168399772
C2×#168399742
C2×#168398932
C2×#168398622
C2×#168398602
C2×C4×#117582022
C2×C61×#5562
C2×#340261