Finite Group Databasebeta

← C2×#21459729 #30588378

Subgroups — C2×#21459729 #30588378

Order 15616.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459729C2132yesmaximal, direct product factor
2C2×#16840486C211yesmaximal, characteristic, complemented
3C2×#16840482C211yesmaximal, characteristic, complemented
4C2×#16840476C212yesmaximal, complemented
5C2×#16840467C212yesmaximal, complemented
6C2×#16840457C214yesmaximal, complemented
7C2×#16840422C212yesmaximal, complemented
8C2×#16840419C212yesmaximal, complemented
9C2×#16840417C211yesmaximal, characteristic, complemented
10C2×#16840380C214yesmaximal, complemented
11C2×#16840341C212yesmaximal, complemented
12C2×#16840314C212yesmaximal, complemented
13C2×#16840309C211yesmaximal, characteristic, complemented
14C2×#16840308C212yesmaximal, complemented
15C2×C4⋊Q8×D61C211yesmaximal, characteristic, complemented
16C2×#16840243C212yesmaximal, complemented
17C2×C4×#11758224C211yesmaximal, characteristic, complemented
18C2×C61×#547C211yesmaximal, characteristic, complemented
19C22×#11758222C2212yes—
20C22×#11758222C2212yes—
21C22×#11758224C2211yescharacteristic
22C22×Q8×D61C2212yes—
23#16840486C22116yescomplemented
24#16840482C22116yescomplemented
25#16840476C22132yescomplemented
26#16840467C22132yescomplemented
27#16840457C22164yescomplemented
28#16840422C22132yescomplemented
29#16840419C22132yescomplemented
30#16840417C22116yescomplemented
31#16840380C22164yescomplemented
32#16840341C22132yescomplemented
33#16840314C22132yescomplemented
34#16840309C22116yescomplemented
35#16840308C22132yescomplemented
36C2×#14519777C2211yescharacteristic
37C2×#14519776C2212yes—
38C2×#14519776C2212yes—
39C2×#14519776C2211yescharacteristic
40C2×#14519775C2212yes—
41C4⋊Q8×D61C22116yescomplemented
42C2×#14519773C2211yescharacteristic
43C2×#14519772C2214yes—
44C2×#14519770C2214yes—
45C2×#14519767C2214yes—
46C2×#14519766C2212yes—
47C2×#14519764C2212yes—
48C2×#14519764C2214yes—
49C2×#14519763C2214yes—
50C2×#14519763C2212yes—
51C2×#14519759C2214yes—
52C2×#14519757C2212yes—
53C2×#14519756C2212yes—
54C2×#14519756C2214yes—
55C2×#14519756C2212yes—
56C2×#14519755C2214yes—
57C2×#14519754C2214yes—
58C2×#14519752C2211yescharacteristic
59C2×#14519750C2214yes—
60C2×#14519750C2212yes—
61C2×#14519749C2214yes—
62C2×#14519749C2214yes—
63C2×#14519748C2212yes—
64C2×#14519748C2211yescharacteristic
65C2×#14519748C2214yes—
66#16840243C22132yescomplemented
67C4×#11758224C22116yescomplemented
68C2×Q8×Dic61C2212yes—
69C2×C4×Dic122C2211yescharacteristic
70C2×#14519742C2211yescharacteristic
71C2×#14519742C2214yes—
72C2×#14519742C2212yes—
73C2×C4×D244C2211yescharacteristic
74C2×D4×Dic61C2211yescharacteristic
75C2×#14519739C2214yes—
76C2×C4×C22⋊D61C2212yes—
77C2×C4×C22⋊D61C2214yes—
78C2×C4×C22⋊D61C2214yes—
79C2×C4×C22⋊D61C2214yes—
80C2×C4×C22⋊D61C2212yes—
81C2×#14519737C2212yes—
82C2×#14519736C2212yes—
83C2×#14519735C2211yescharacteristic
84C2×#14519735C2212yes—
85C2×#14519733C2212yes—
86C2×#14519733C2214yes—
87C2×C4⋊C4×D61C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2212yes—
91C2×C42×D61C2211yescharacteristic
92C22×#41×C61C2212yes—
93C61×#547C22116yescomplemented
94C2×C4⋊Q8×C61C2211yescharacteristic
95C2×#123×C61C2214yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×#121×C61C2212yes—
98C2×C4×D4×C61C2211yescharacteristic
99C2×C4×D4×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2212yes—
101C2×#11758222—216no—
102C2×#11758222—48no—
103C2×#11758222C23116yes—
104C2×#11758222C23116yes—
105C2×#11758224—28no—
106C2×#11758224C2318yes—
107C22×Dic122C2312yes—
108C22×Dic122C2311yescharacteristic
109C22×Dic122C2312yes—
110C22×Dic122C2314yes—
111C2×Q8×D61—48no—
112C2×Q8×D61C23116yes—
113C22×D244C2312yes—
114C22×D244C2311yescharacteristic
115C22×C22⋊D61C2312yes—
116C22×C22⋊D61C2312yes—
117C22×C22⋊D61C2312yes—
118C22×C22⋊D61C2312yes—
119C22×C22⋊D61C2314yes—
120C23×Dic61C2312yes—
121C23×Dic61C2312yes—
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2312yes—
125C22×C4×D61C2314yes—
126C22×C4×D61C2314yes—
127C22×C4×D61C2311yescharacteristic
128#14519777C2318yes—
129#14519776C23116yes—
130#14519776C23116yes—
131#14519776C2318yes—
132#14519775C23116yes—
133#14519773C2318yes—
134#14519772C23132yes—
135#14519770C23132yes—
136#14519767C23132yes—
137#14519766C23116yes—
138#14519764C23132yes—
139#14519764C23116yes—
140#14519763C23132yes—
141#14519763C23116yes—
142#14519759C23132yes—
143#14519757C23116yes—
144#14519756C23116yes—
145#14519756C23132yes—
146#14519756C23116yes—
147#14519755C23132yes—
148#14519754C23132yes—
149#14519752C2318yes—
150#14519750C23116yes—
151#14519750C23132yes—
152#14519749C23132yes—
153#14519749C23132yes—
154#14519748C23132yes—
155#14519748C23116yes—
156#14519748C2318yes—
157Q8×Dic61C23116yes—
158C4×Dic122C2318yes—
159#14519742C2318yes—
160#14519742C23116yes—
161#14519742C23132yes—
162C4×D244C2318yes—
163D4×Dic61C2318yes—
164#14519739C23132yes—
165C4×C22⋊D61C23132yes—
166C4×C22⋊D61C23132yes—
167C4×C22⋊D61C23116yes—
168C4×C22⋊D61C23116yes—
169C4×C22⋊D61C23132yes—
170#14519737C23116yes—
171#14519736C23116yes—
172#14519735C23116yes—
173#14519735C2318yes—
174#14519733C23132yes—
175#14519733C23116yes—
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2312yes—
178C2×C4⋊Dic61C2311yescharacteristic
179C2×C4⋊Dic61C2311yescharacteristic
180C2×C4⋊Dic61C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2314yes—
188C4⋊C4×D61C23116yes—
189C4⋊C4×D61C23116yes—
190C4⋊C4×D61C23116yes—
191C2×C22⋊Dic61C2312yes—
192C2×C22⋊Dic61C2314yes—
193C2×C22⋊Dic61C2314yes—
194C2×C22⋊Dic61C2314yes—
195C2×C22⋊Dic61C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×#11758198C2312yes—
200C2×#11758198C2312yes—
201C2×C4×Dic61C2311yescharacteristic
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2312yes—
205C2×C4×Dic61C2312yes—
206C2×C4×Dic61C2312yes—
207C2×C4×Dic61C23116yes—
208C2×C4×Dic61C2314yes—
209C2×C4×Dic61C2314yes—
210C42×D61C2318yes—
211C2×#41×C61—48no—
212C2×#41×C61C23116yes—
213C22×Q8×C61C2312yes—
214C22×D4×C61C2311yescharacteristic
215C22×D4×C61C2311yescharacteristic
216C22×D4×C61C2314yes—
217C23×C4×C61C2312yes—
218C23×C4×C61C2312yes—
219C23×C4×C61C2314yes—
220C4⋊Q8×C61C2318yes—
221#123×C61C23132yes—
222C22⋊Q8×C61C23116yes—
223#121×C61C23116yes—
224C4×D4×C61C2318yes—
225C4×D4×C61C2318yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C23116yes—
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C4⋊C4×C61C2314yes—
231C2×C4⋊C4×C61C2311yescharacteristic
232C2×C22⋊C4×C61C2312yes—
233C2×C22⋊C4×C61C2314yes—
234C2×C22⋊C4×C61C2312yes—
235C2×C42×C61C2311yescharacteristic
236C24×C61C2412yes—
237C24×C61C2412yes—
238C23×D61C2412yes—
239C23×D61C2411yescharacteristic
240#41×C61—432no—
241C2×Q8×C61—28no—
242C2×Q8×C61C2418yes—
243C2×D4×C61—24no—
244C2×D4×C61—24no—
245C2×D4×C61—48no—
246C2×D4×C61C2414yes—
247C2×D4×C61C2414yes—
248C2×D4×C61C24116yes—
249C22×C4×C61—28no—
250C22×C4×C61—28no—
251C22×C4×C61—48no—
252C22×C4×C61C2412yes—
253C22×C4×C61C2414yes—
254C22×C4×C61C2411yescharacteristic
255C22×C4×C61C2412yes—
256C22×C4×C61C2418yes—
257C22×C4×C61C2418yes—
258C22×C4×C61C24116yes—
259C22×C4×C61C2411yescharacteristic
260C22×C4×C61C2411yescharacteristic
261C2×C22⋊D61—28no—
262C2×C22⋊D61—28no—
263C2×C22⋊D61—28no—
264C2×C22⋊D61—28no—
265C2×C22⋊D61—48no—
266C2×C22⋊D61C2418yes—
267C2×C22⋊D61C2418yes—
268C2×C22⋊D61C2418yes—
269C2×C22⋊D61C2418yes—
270C2×C22⋊D61C24116yes—
271C22×Dic61—28no—
272C22×Dic61—28no—
273C22×Dic61C2414yes—
274C22×Dic61C2412yes—
275C22×Dic61C2411yescharacteristic
276C22×Dic61C2412yes—
277C22×Dic61C2418yes—
278C22×Dic61C2412yes—
279C22×Dic61C2418yes—
280C22×Dic61C2411yescharacteristic
281C22×Dic61C2411yescharacteristic
282Q8×D61—432no—
283#11758224—232no—
284#11758222—264no—
285#11758222—432no—
286C2×D244—28no—
287C2×D244—24no—
288C2×D244C2414yes—
289C2×D244C2418yes—
290C2×C4×D61—28no—
291C2×C4×D61—24no—
292C2×C4×D61—24no—
293C2×C4×D61—48no—
294C2×C4×D61—48no—
295C2×C4×D61#4118yescomplemented
296C2×C4×D61C2414yes—
297C2×C4×D61C2418yes—
298C2×C4×D61C2414yes—
299C2×C4×D61C24116yes—
300C2×C4×D61C24116yes—
301C2×C4×D61C2414yes—
302C2×Dic122—24no—
303C2×Dic122—28no—
304C2×Dic122—28no—
305C2×Dic122—48no—
306C2×Dic122C2418yes—
307C2×Dic122C2414yes—
308C2×Dic122C2418yes—
309C2×Dic122C24116yes—
310C4⋊C4×C61C2414yes—
311C4⋊C4×C61C2418yes—
312C4⋊C4×C61C24116yes—
313C4⋊C4×C61C2414yes—
314C4⋊C4×C61C2418yes—
315C22⋊C4×C61C2418yes—
316C22⋊C4×C61C2418yes—
317C22⋊C4×C61C24116yes—
318C42×C61C2414yes—
319C22⋊Dic61C2418yes—
320C22⋊Dic61C24116yes—
321C22⋊Dic61C24116yes—
322C22⋊Dic61C24116yes—
323C22⋊Dic61C2418yes—
324#11758198C2418yes—
325#11758198C24116yes—
326#11758198C24116yes—
327#11758198C2418yes—
328#11758198C2418yes—
329C4⋊Dic61C2418yes—
330C4⋊Dic61C2418yes—
331C4⋊Dic61C2414yes—
332C4⋊Dic61C2414yes—
333C4⋊Dic61C24116yes—
334#11758196C24116yes—
335#11758196C24116yes—
336#11758196C24116yes—
337#11758196C2418yes—
338#11758196C2418yes—
339#11758196C2418yes—
340#11758196C24116yes—
341C4×Dic61C2414yes—
342C4×Dic61C2414yes—
343C4×Dic61C2414yes—
344C4×Dic61C2418yes—
345C4×Dic61C2418yes—
346C4×Dic61C2418yes—
347C4×Dic61C24116yes—
348C4×Dic61C24116yes—
349C23×C61—24no—
350C23×C61—24no—
351C23×C61—24no—
352C23×C61—24no—
353C23×C61—24no—
354C23×C61—24no—
355C23×C61C2514yes—
356C23×C61C2514yes—
357C23×C61C2511yescharacteristic
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—24no—
361C22×D61—24no—
362C22×D61—24no—
363C22×D61C2×#4114yes—
364C22×D61C2514yes—
365C22×D61C2512yes—
366Q8×C61—216no—
367D4×C61—28no—
368D4×C61—28no—
369D4×C61—416no—
370C2×C4×C61—24no—
371C2×C4×C61—28no—
372C2×C4×C61—24no—
373C2×C4×C61—22no—
374C2×C4×C61—216no—
375C2×C4×C61—216no—
376C2×C4×C61—416no—
377C2×C4×C61C2×#4114yes—
378C2×C4×C61H(5,𝔽2)14yes—
379C2×C4×C61C2514yes—
380C2×C4×C61C2514yes—
381C2×C4×C61C2512yes—
382C2×C4×C61C2518yes—
383C2×C4×C61C2512yes—
384C2×C4×C61C2512yes—
385C22⋊D61—216no—
386C22⋊D61—216no—
387C22⋊D61—216no—
388C22⋊D61—216no—
389C22⋊D61—416no—
390C2×Dic61—24no—
391C2×Dic61—24no—
392C2×Dic61—28no—
393C2×Dic61—22no—
394C2×Dic61—24no—
395C2×Dic61—216no—
396C2×Dic61—216no—
397C2×Dic61C2×#4114yes—
398C2×Dic612−1+414yes—
399C2×Dic61C2514yes—
400C2×Dic61C2514yes—
401C2×Dic61C2514yes—
402C2×Dic61C2512yes—
403C2×Dic61C2518yes—
404C2×Dic61C2512yes—
405C2×Dic61C2512yes—
406D244—216no—
407D244—28no—
408C4×D61—216no—
409C4×D61—28no—
410C4×D61—28no—
411C4×D61—416no—
412C4×D61—416no—
413C4×D61C2×#41116yescomplemented
414Dic122—28no—
415Dic122—216no—
416Dic122—216no—
417Dic122—416no—
418C2×#3511—611nomaximal, Sylow
419C22×C61—24no—
420C22×C61—24no—
421C22×C61—24no—
422C22×C61—24no—
423C22×C61—24no—
424C22×C61—24no—
425C22×C61—48no—
426C22×C61—48no—
427C22×C61C22×#4112yes—
428C22×C61C2×H(5,𝔽2)12yes—
429C22×C61C2×2−1+412yes—
430C22×C61C2611yescharacteristic
431C2×D61—22no—
432C2×D61—22no—
433C2×D61—28no—
434C2×D61—24no—
435C2×D61—24no—
436C2×D61—24no—
437C2×D61—48no—
438C2×D61C22×#4114yes—
439C4×C61—24no—
440C4×C61—28no—
441C4×C61—24no—
442C4×C61—22no—
443C4×C61C22×#4114yes—
444C4×C61C2×H(5,𝔽2)14yes—
445Dic61—24no—
446Dic61—24no—
447Dic61—28no—
448Dic61—22no—
449Dic61—24no—
450Dic61C22×#4114yes—
451Dic61C2×2−1+414yes—
452#3511—6132no—
453C2×#556—611no—
454C2×#556—611no—
455C2×#555—612no—
456C2×#554—612no—
457C2×#553—614no—
458C2×#548—612no—
459C2×#548—612no—
460C2×#547—611no—
461C2×#547D6111yescharacteristic, complemented
462C2×#542—614no—
463C2×#537—612no—
464C2×#533—612no—
465C2×#532—612no—
466C2×#532—611no—
467C22×C4⋊Q8—611no—
468C2×#520—612no—
469C2×C4×#41—611no—
470C2×C61—44no—
471C2×C61—44no—
472C2×C61#351114yescomplemented
473C2×C61C23×#4111yescharacteristic
474C2×C61C22×H(5,𝔽2)11yescharacteristic
475C2×C61C22×2−1+411yescharacteristic
476D61—24no—
477D61—44no—
478C22×#41—611no—
479C22×#41—612no—
480C22×#41—612no—
481C22×#41C2×D6112yes—
482C23×Q8—612no—
483#556—6116no—
484#556—6116no—
485#555—6132no—
486#554—6132no—
487#553—6164no—
488#548—6132no—
489#548—6132no—
490#547—6116no—
491#547C2×D61116yescomplemented
492#542—6164no—
493#537—6132no—
494#533—6132no—
495#532—6132no—
496#532—6116no—
497C2×C4⋊Q8—612no—
498C2×C4⋊Q8—6116no—
499C2×C4⋊Q8—612no—
500C2×C4⋊Q8—612no—
501C2×C4⋊Q8—611no—
502C2×C4⋊Q8—611no—
503C2×C4⋊Q8C2×D6111yescharacteristic
504C2×#127—611no—
505C2×#126—614no—
506C2×#126—614no—
507C2×#125—614no—
508C2×#124—612no—
509C2×#124—612no—
510C2×#124—614no—
511C2×#124—612no—
512C2×#124—614no—
513C2×#123—614no—
514C2×#123C2×D6114yes—
515C2×C22⋊Q8—612no—
516C2×C22⋊Q8—612no—
517C2×C22⋊Q8—614no—
518C2×C22⋊Q8—614no—
519C2×C22⋊Q8—612no—
520C2×C22⋊Q8—614no—
521C2×C22⋊Q8C2×D6112yes—
522C2×#121—611no—
523C2×#121—612no—
524C2×#121—614no—
525C2×#121—614no—
526C2×#121—614no—
527C2×#121—611no—
528C2×#121—612no—
529C2×#121—614no—
530C2×#121C2×D6112yes—
531#520—6132no—
532C4×#41—6116no—
533C2×C4×Q8—612no—
534C2×C4×Q8—611no—
535C2×C4×Q8—614no—
536C2×C4×Q8—612no—
537C2×C4×Q8—611no—
538C2×C4×D4—611no—
539C2×C4×D4—612no—
540C2×C4×D4—614no—
541C2×C4×D4—614no—
542C2×C4×D4—614no—
543C2×C4×D4—612no—
544C2×C4×D4—614no—
545C2×C4×D4—612no—
546C2×C4×D4—611no—
547C2×C4×D4C2×D6111yescharacteristic
548C2×C4×D4C2×D6111yescharacteristic
549C2×#117—612no—
550C2×#117—611no—
551C2×#117—612no—
552C2×#117—612no—
553C2×#117—614no—
554C22×C4⋊C4—612no—
555C22×C4⋊C4—612no—
556C22×C4⋊C4—612no—
557C22×C4⋊C4C2×D6112yes—
558C22×C42—612no—
559C22×C42—611no—
560C61C2×#351111yescharacteristic, complemented, Sylow
561C2×#41—48no—
562C2×#41—618no—
563C2×#41—6116no—
564C2×#41—6116no—
565C2×#41—12216no—
566C2×#41—1228no—
567C2×#41—2448no—
568C2×#41C22×D61116yes—
569C22×Q8—6116no—
570C22×Q8—611no—
571C22×Q8—612no—
572C22×Q8—612no—
573C22×Q8—614no—
574C22×Q8—2448no—
575C22×Q8C22×D6112yes—
576C22×D4—612no—
577C22×D4—612no—
578C22×D4—612no—
579C22×D4—612no—
580C22×D4—614no—
581C22×D4—612no—
582C22×D4—611no—
583C22×D4C22×D6111yescharacteristic
584C22×D4C22×D6111yescharacteristic
585C22×D4C22×D6114yes—
586C23×C4—611no—
587C23×C4—612no—
588C23×C4—612no—
589C23×C4—611no—
590C23×C4—612no—
591C23×C4—611no—
592C23×C4—614no—
593C23×C4—614no—
594C23×C4C22×D6112yes—
595C23×C4C22×D6112yes—
596C23×C4C22×D6114yes—
597C4⋊Q8—6116no—
598C4⋊Q8—6116no—
599C4⋊Q8—6116no—
600C4⋊Q8—618no—
601C4⋊Q8—618no—
602C4⋊Q8C22×D6118yes—
603#127—618no—
604#126—6132no—
605#126—6132no—
606#125—6132no—
607#124—6116no—
608#124—6116no—
609#124—6132no—
610#124—6116no—
611#124—6132no—
612#123—6132no—
613#123C22×D61132yes—
614C22⋊Q8—6116no—
615C22⋊Q8—6116no—
616C22⋊Q8—6132no—
617C22⋊Q8—6116no—
618C22⋊Q8—6132no—
619C22⋊Q8—6132no—
620C22⋊Q8C22×D61116yes—
621#121—6132no—
622#121—618no—
623#121—6132no—
624#121—6116no—
625#121—6132no—
626#121—618no—
627#121—6116no—
628#121—6132no—
629#121C22×D61116yes—
630C4×Q8—6116no—
631C4×Q8—618no—
632C4×Q8—6132no—
633C4×Q8—6116no—
634C4×Q8—618no—
635C4×D4—618no—
636C4×D4—6116no—
637C4×D4—6132no—
638C4×D4—6132no—
639C4×D4—6132no—
640C4×D4—6116no—
641C4×D4—6132no—
642C4×D4—6116no—
643C4×D4—618no—
644C4×D4C22×D6118yes—
645C4×D4C22×D6118yes—
646#117—6116no—
647#117—618no—
648#117—6116no—
649#117—6116no—
650#117—6132no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—614no—
653C2×C4⋊C4—614no—
654C2×C4⋊C4—614no—
655C2×C4⋊C4—612no—
656C2×C4⋊C4—611no—
657C2×C4⋊C4—612no—
658C2×C4⋊C4—612no—
659C2×C4⋊C4—612no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—614no—
662C2×C4⋊C4—614no—
663C2×C4⋊C4—6116no—
664C2×C4⋊C4—6116no—
665C2×C4⋊C4—6116no—
666C2×C4⋊C4C22×D6111yescharacteristic
667C2×C4⋊C4C22×D6112yes—
668C2×C4⋊C4C22×D6112yes—
669C2×C4⋊C4C22×D6114yes—
670C2×C4⋊C4C22×D61116yes—
671C2×C4⋊C4C22×D6111yescharacteristic
672C2×C22⋊C4—614no—
673C2×C22⋊C4—612no—
674C2×C22⋊C4—614no—
675C2×C22⋊C4—614no—
676C2×C22⋊C4—612no—
677C2×C22⋊C4—612no—
678C2×C22⋊C4—614no—
679C2×C22⋊C4—614no—
680C2×C22⋊C4—612no—
681C2×C22⋊C4—612no—
682C2×C22⋊C4C22×D6112yes—
683C2×C22⋊C4C22×D6114yes—
684C2×C22⋊C4C22×D6112yes—
685C2×C42—612no—
686C2×C42—614no—
687C2×C42—614no—
688C2×C42—611no—
689C2×C42—612no—
690C2×C42—611no—
691C2×C42—612no—
692C2×C42—6116no—
693C2×C42—611no—
694C2×C42—618no—
695C2×C42C22×D6111yescharacteristic
696C24—611no—
697C24—612no—
698C24C23×D6112yes—
699C24C23×D6112yes—
700#41—432no—
701#41—12264no—
702#41—12232no—
703#41—24432no—
704C2×Q8—28no—
705C2×Q8—614no—
706C2×Q8—618no—
707C2×Q8—618no—
708C2×Q8—6116no—
709C2×Q8—1228no—
710C2×Q8—1224no—
711C2×Q8—1228no—
712C2×Q8—2448no—
713C2×Q8—24432no—
714C2×Q8C23×D6118yes—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—48no—
718C2×D4—618no—
719C2×D4—618no—
720C2×D4—618no—
721C2×D4—618no—
722C2×D4—6116no—
723C2×D4—618no—
724C2×D4—614no—
725C2×D4—1228no—
726C2×D4—1228no—
727C2×D4—1228no—
728C2×D4—1228no—
729C2×D4—1228no—
730C2×D4—1224no—
731C2×D4—2448no—
732C2×D4C23×D6114yes—
733C2×D4C23×D6114yes—
734C2×D4C23×D61116yes—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—48no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—618no—
741C22×C4—614no—
742C22×C4—618no—
743C22×C4—618no—
744C22×C4—612no—
745C22×C4—611no—
746C22×C4—612no—
747C22×C4—612no—
748C22×C4—614no—
749C22×C4—614no—
750C22×C4—614no—
751C22×C4—618no—
752C22×C4—6116no—
753C22×C4—6116no—
754C22×C4—1224no—
755C22×C4—1228no—
756C22×C4—1228no—
757C22×C4—1228no—
758C22×C4—1224no—
759C22×C4—2448no—
760C22×C4—2448no—
761C22×C4C23×D6118yes—
762C22×C4C23×D6118yes—
763C22×C4C23×D6112yes—
764C22×C4C23×D6112yes—
765C22×C4C23×D6111yescharacteristic
766C22×C4C23×D6114yes—
767C22×C4C23×D61116yes—
768C22×C4C23×D6111yescharacteristic
769C22×C4C23×D6111yescharacteristic
770C4⋊C4—618no—
771C4⋊C4—6116no—
772C4⋊C4—6116no—
773C4⋊C4—6116no—
774C4⋊C4—618no—
775C4⋊C4—618no—
776C4⋊C4—618no—
777C4⋊C4—618no—
778C4⋊C4—6116no—
779C4⋊C4—614no—
780C4⋊C4—614no—
781C4⋊C4—6116no—
782C4⋊C4C23×D6114yes—
783C4⋊C4C23×D6118yes—
784C4⋊C4C23×D6118yes—
785C4⋊C4C23×D61116yes—
786C4⋊C4C23×D6114yes—
787C22⋊C4—6116no—
788C22⋊C4—618no—
789C22⋊C4—6116no—
790C22⋊C4—6116no—
791C22⋊C4—618no—
792C22⋊C4—618no—
793C22⋊C4—6116no—
794C22⋊C4—6116no—
795C22⋊C4—618no—
796C22⋊C4—618no—
797C22⋊C4C23×D6118yes—
798C22⋊C4C23×D61116yes—
799C22⋊C4C23×D6118yes—
800C42—614no—
801C42—618no—
802C42—614no—
803C42—618no—
804C42—614no—
805C42—618no—
806C42—6116no—
807C42—6116no—
808C42C23×D6114yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—614no—
816C23—612no—
817C23—614no—
818C23—1222no—
819C23—1222no—
820C23—1224no—
821C23—1224no—
822C23—1224no—
823C23C24×D6114yes—
824C23C24×D6114yes—
825C23C24×D6111yescharacteristic
826Q8—216no—
827Q8—12216no—
828Q8—1228no—
829Q8—12216no—
830Q8—24416no—
831D4—28no—
832D4—28no—
833D4—416no—
834D4—12216no—
835D4—12216no—
836D4—12216no—
837D4—12216no—
838D4—12216no—
839D4—1228no—
840D4—24416no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—22no—
845C2×C4—216no—
846C2×C4—216no—
847C2×C4—416no—
848C2×C4—614no—
849C2×C4—614no—
850C2×C4—612no—
851C2×C4—612no—
852C2×C4—6116no—
853C2×C4—614no—
854C2×C4—612no—
855C2×C4—614no—
856C2×C4—614no—
857C2×C4—618no—
858C2×C4—1228no—
859C2×C4—12216no—
860C2×C4—12216no—
861C2×C4—1224no—
862C2×C4—1224no—
863C2×C4—1222no—
864C2×C4—1228no—
865C2×C4—1224no—
866C2×C4—12216no—
867C2×C4—1228no—
868C2×C4—24416no—
869C2×C4—24416no—
870C2×C4#41×D6114yes—
871C2×C4#1451982214yes—
872C2×C4C24×D6114yes—
873C2×C4C24×D6114yes—
874C2×C4C24×D6112yes—
875C2×C4C24×D6118yes—
876C2×C4C24×D6112yes—
877C2×C4C24×D6112yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—48no—
885C22—48no—
886C22—614no—
887C22—1228no—
888C22—1222no—
889C22—1222no—
890C22—1224no—
891C22—1224no—
892C22—1224no—
893C22—2448no—
894C22C2×#41×D6112yes—
895C22C2×#1451982212yes—
896C222−1+4×D6112yes—
897C22C25×D6111yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—22no—
902C4—614no—
903C4—614no—
904C4—1224no—
905C4—1224no—
906C4—1222no—
907C4—1228no—
908C4—1224no—
909C4C2×#41×D6114yes—
910C4C2×#1451982214yes—
911C2—44no—
912C2—44no—
913C2—1224no—
914C2—2444no—
915C2#2145972914yesdirect product factor
916C2C22×#41×D6111yescharacteristic
917C2C22×#1451982211yescharacteristic
918C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#547C2
socleC23×C61C25
hypercenterC2×#547D61
hypocenterC61C2×#3511
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #21459729C2direct (N × H)
2. C2×#16840486C2semidirect
3. C2×#16840482C2semidirect
4. C2×#16840476C2semidirect
5. C2×#16840467C2semidirect
6. C2×#16840457C2semidirect
7. C2×#16840422C2semidirect
8. C2×#16840419C2semidirect
9. C2×#16840417C2semidirect
10. C2×#16840380C2semidirect
11. C2×#16840341C2semidirect
12. C2×#16840314C2semidirect
13. C2×#16840309C2semidirect
14. C2×#16840308C2semidirect
15. C2×C4⋊Q8×D61C2semidirect
16. C2×#16840243C2semidirect
17. C2×C4×#11758224C2semidirect
18. C2×C61×#547C2semidirect
23. #16840486C22semidirect
24. #16840482C22semidirect
25. #16840476C22semidirect
26. #16840467C22semidirect
27. #16840457C22semidirect
28. #16840422C22semidirect
29. #16840419C22semidirect
30. #16840417C22semidirect
31. #16840380C22semidirect
32. #16840341C22semidirect
33. #16840314C22semidirect
34. #16840309C22semidirect
35. #16840308C22semidirect
41. C4⋊Q8×D61C22semidirect
66. #16840243C22semidirect
67. C4×#11758224C22semidirect
93. C61×#547C22semidirect
295. C2×C4×D61#41semidirect
413. C4×D61C2×#41semidirect
461. C2×#547D61semidirect
472. C2×C61#3511semidirect
491. #547C2×D61semidirect
560. C61C2×#3511semidirect
915. C2#21459729direct (N × H)

Maximal subgroups

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

subgroupindex
#214597292
C2×#168404862
C2×#168404822
C2×#168404762
C2×#168404672
C2×#168404572
C2×#168404222
C2×#168404192
C2×#168404172
C2×#168403802
C2×#168403412
C2×#168403142
C2×#168403092
C2×#168403082
C2×C4⋊Q8×D612
C2×#168402432
C2×C4×#117582242
C2×C61×#5472
C2×#351161