Finite Group Databasebeta

← C2×#21460216 #30587804

Subgroups — C2×#21460216 #30587804

Order 15616.

7810 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460216C2132yesmaximal, direct product factor
2C2×#16840509C214yesmaximal, complemented
3C2×#16840470C212yesmaximal, complemented
4C2×#16840467C212yesmaximal, complemented
5C2×#16840431C212yesmaximal, complemented
6C2×#16840430C212yesmaximal, complemented
7C2×#16840417C211yesmaximal, characteristic, complemented
8C2×#16840416C211yesmaximal, characteristic, complemented
9C2×#16840415C211yesmaximal, characteristic, complemented
10C2×#16840364C214yesmaximal, complemented
11C2×#16840343C212yesmaximal, complemented
12C2×#16840342C212yesmaximal, complemented
13C2×#16840341C212yesmaximal, complemented
14C2×#16840340C212yesmaximal, complemented
15C2×#16840317C211yesmaximal, characteristic, complemented
16C2×#16840309C211yesmaximal, characteristic, complemented
17C2×#16840309C211yesmaximal, characteristic, complemented
18C2×C61×#547C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×#11758222C2212yes—
21C22×#11758222C2212yes—
22C22×#11758222C2212yes—
23C22×#11758224C2212yes—
24#16840509C22164yescomplemented
25#16840470C22132yescomplemented
26#16840467C22132yescomplemented
27#16840431C22132yescomplemented
28#16840430C22132yescomplemented
29#16840417C22116yescomplemented
30#16840416C22116yescomplemented
31#16840415C22116yescomplemented
32#16840364C22164yescomplemented
33#16840343C22132yescomplemented
34#16840342C22132yescomplemented
35#16840341C22132yescomplemented
36#16840340C22132yescomplemented
37#16840317C22116yescomplemented
38#16840309C22116yescomplemented
39#16840309C22116yescomplemented
40C2×#14519777C2211yescharacteristic
41C2×#14519776C2211yescharacteristic
42C2×#14519776C2211yescharacteristic
43C2×#14519773C2211yescharacteristic
44C2×#14519773C2214yes—
45C2×#14519773C2211yescharacteristic
46C2×#14519768C2212yes—
47C2×#14519767C2214yes—
48C2×#14519763C2212yes—
49C2×#14519763C2212yes—
50C2×#14519762C2214yes—
51C2×#14519761C2214yes—
52C2×#14519759C2214yes—
53C2×#14519757C2212yes—
54C2×#14519757C2214yes—
55C2×#14519757C2212yes—
56C2×#14519756C2212yes—
57C2×#14519756C2214yes—
58C2×#14519755C2214yes—
59C2×#14519754C2214yes—
60C2×#14519753C2212yes—
61C2×#14519753C2212yes—
62C2×#14519752C2212yes—
63C2×#14519752C2211yescharacteristic
64C2×#14519752C2211yescharacteristic
65C2×#14519752C2214yes—
66C2×#14519751C2212yes—
67C2×#14519751C2214yes—
68C2×#14519751C2214yes—
69C2×#14519750C2214yes—
70C2×#14519750C2212yes—
71C2×#14519750C2212yes—
72C2×#14519750C2214yes—
73C2×#14519749C2214yes—
74C2×#14519749C2214yes—
75C2×#14519748C2212yes—
76C2×#14519748C2214yes—
77C2×#14519748C2211yescharacteristic
78C2×#14519748C2211yescharacteristic
79C2×Q8×Dic61C2212yes—
80C2×#14519742C2212yes—
81C2×C4×D244C2211yescharacteristic
82C2×C4×D244C2211yescharacteristic
83C2×C4×C22⋊D61C2212yes—
84C2×C4×C22⋊D61C2214yes—
85C2×C4×C22⋊D61C2212yes—
86C2×#14519737C2214yes—
87C2×#14519735C2212yes—
88C22×C4⋊Dic61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C2212yes—
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×#11758226—48no—
102C2×#11758226C23116yes—
103C2×#11758222—48no—
104C2×#11758222—48no—
105C2×#11758222—48no—
106C2×#11758222C23116yes—
107C2×#11758222C23116yes—
108C2×#11758222C23116yes—
109C2×#11758224—48no—
110C2×#11758224C23116yes—
111C22×Dic122C2312yes—
112C22×Dic122C2312yes—
113C22×Dic122C2312yes—
114C22×D244C2311yescharacteristic
115C22×D244C2311yescharacteristic
116C22×D244C2312yes—
117C22×D244C2312yes—
118C22×D244C2314yes—
119C22×C22⋊D61C2312yes—
120C22×C22⋊D61C2312yes—
121C22×C22⋊D61C2312yes—
122C22×C22⋊D61C2312yes—
123C22×C22⋊D61C2312yes—
124C22×C22⋊D61C2314yes—
125C22×C22⋊D61C2314yes—
126C22×C22⋊D61C2312yes—
127C23×Dic61C2314yes—
128C22×C4×D61C2311yescharacteristic
129C22×C4×D61C2311yescharacteristic
130C22×C4×D61C2311yescharacteristic
131C22×C4×D61C2312yes—
132C22×C4×D61C2312yes—
133C22×C4×D61C2314yes—
134C22×C4×D61C2314yes—
135#14519777C2318yes—
136#14519776C2318yes—
137#14519776C2318yes—
138#14519773C2318yes—
139#14519773C2318yes—
140#14519773C23132yes—
141#14519768C23116yes—
142#14519767C23132yes—
143#14519763C23116yes—
144#14519763C23116yes—
145#14519762C23132yes—
146#14519761C23132yes—
147#14519759C23132yes—
148#14519757C23116yes—
149#14519757C23132yes—
150#14519757C23116yes—
151#14519756C23132yes—
152#14519756C23116yes—
153#14519755C23132yes—
154#14519754C23132yes—
155#14519753C23116yes—
156#14519753C23116yes—
157#14519752C2318yes—
158#14519752C2318yes—
159#14519752C23132yes—
160#14519752C23116yes—
161#14519751C23132yes—
162#14519751C23132yes—
163#14519751C23116yes—
164#14519750C23132yes—
165#14519750C23116yes—
166#14519750C23116yes—
167#14519750C23132yes—
168#14519749C23132yes—
169#14519749C23132yes—
170#14519748C23132yes—
171#14519748C2318yes—
172#14519748C2318yes—
173#14519748C23116yes—
174Q8×Dic61C23116yes—
175#14519742C23116yes—
176C4×D244C2318yes—
177C4×D244C2318yes—
178C4×C22⋊D61C23116yes—
179C4×C22⋊D61C23132yes—
180C4×C22⋊D61C23116yes—
181#14519737C23132yes—
182#14519735C23116yes—
183C2×C4⋊Dic61C2311yescharacteristic
184C2×C4⋊Dic61C2312yes—
185C2×C4⋊Dic61C2311yescharacteristic
186C2×C4⋊Dic61C23116yes—
187C2×C4⋊Dic61C2314yes—
188C2×C4⋊Dic61C2312yes—
189C2×C4⋊Dic61C2314yes—
190C2×#11758196C2314yes—
191C2×#11758196C2314yes—
192C2×#11758196C2312yes—
193C2×#11758196C2312yes—
194C2×#11758196C2314yes—
195C4⋊C4×D61C23116yes—
196C4⋊C4×D61C23116yes—
197C2×C22⋊Dic61C2312yes—
198C2×C22⋊Dic61C2314yes—
199C2×C22⋊Dic61C2312yes—
200C2×#11758198C2314yes—
201C2×#11758198C2314yes—
202C2×#11758198C2312yes—
203C2×#11758198C2314yes—
204C2×#11758198C2312yes—
205C2×#11758198C2312yes—
206C2×#11758198C2312yes—
207C2×C4×Dic61C2311yescharacteristic
208C2×C4×Dic61C2311yescharacteristic
209C2×C4×Dic61C2311yescharacteristic
210C2×C4×Dic61C2314yes—
211C42×D61C2318yes—
212C2×#41×C61—48no—
213C2×#41×C61C23116yes—
214C22×Q8×C61C2312yes—
215C22×D4×C61C2311yescharacteristic
216C22×D4×C61C2311yescharacteristic
217C22×D4×C61C2314yes—
218C23×C4×C61C2312yes—
219C23×C4×C61C2312yes—
220C23×C4×C61C2314yes—
221C4⋊Q8×C61C2318yes—
222#123×C61C23132yes—
223C22⋊Q8×C61C23116yes—
224#121×C61C23116yes—
225C4×D4×C61C2318yes—
226C4×D4×C61C2318yes—
227C2×C4⋊C4×C61C2312yes—
228C2×C4⋊C4×C61C2312yes—
229C2×C4⋊C4×C61C23116yes—
230C2×C4⋊C4×C61C2311yescharacteristic
231C2×C4⋊C4×C61C2314yes—
232C2×C4⋊C4×C61C2311yescharacteristic
233C2×C22⋊C4×C61C2314yes—
234C2×C22⋊C4×C61C2312yes—
235C2×C22⋊C4×C61C2312yes—
236C2×C42×C61C2311yescharacteristic
237C24×C61C2412yes—
238C24×C61C2412yes—
239C23×D61C2412yes—
240C23×D61C2411yescharacteristic
241C23×D61C2412yes—
242#41×C61—432no—
243C2×Q8×C61—28no—
244C2×Q8×C61C2418yes—
245C2×D4×C61—24no—
246C2×D4×C61—24no—
247C2×D4×C61—48no—
248C2×D4×C61C2414yes—
249C2×D4×C61C2414yes—
250C2×D4×C61C24116yes—
251C22×C4×C61—28no—
252C22×C4×C61—28no—
253C22×C4×C61—48no—
254C22×C4×C61C2412yes—
255C22×C4×C61C2414yes—
256C22×C4×C61C2411yescharacteristic
257C22×C4×C61C2412yes—
258C22×C4×C61C2418yes—
259C22×C4×C61C2418yes—
260C22×C4×C61C24116yes—
261C22×C4×C61C2411yescharacteristic
262C22×C4×C61C2411yescharacteristic
263C2×C22⋊D61—28no—
264C2×C22⋊D61—28no—
265C2×C22⋊D61—48no—
266C2×C22⋊D61—48no—
267C2×C22⋊D61—44no—
268C2×C22⋊D61—44no—
269C2×C22⋊D61—44no—
270C2×C22⋊D61—44no—
271C2×C22⋊D61C2418yes—
272C2×C22⋊D61C2418yes—
273C2×C22⋊D61C24116yes—
274C2×C22⋊D61C2418yes—
275C2×C22⋊D61C2418yes—
276C2×C22⋊D61C2418yes—
277C2×C22⋊D61C24116yes—
278C2×C22⋊D61C2418yes—
279C22×Dic61—48no—
280C22×Dic61C2412yes—
281C22×Dic61C2412yes—
282C22×Dic61C2414yes—
283C22×Dic61C2411yescharacteristic
284C22×Dic61C2411yescharacteristic
285C22×Dic61C24116yes—
286C22×Dic61C2411yescharacteristic
287#11758226—432no—
288#11758224—432no—
289#11758222—432no—
290#11758222—432no—
291#11758222—432no—
292C2×D244—24no—
293C2×D244—24no—
294C2×D244—44no—
295C2×D244—44no—
296C2×D244—48no—
297C2×D244C2414yes—
298C2×D244C2414yes—
299C2×D244C2418yes—
300C2×D244C2418yes—
301C2×D244C24116yes—
302C2×C4×D61—28no—
303C2×C4×D61—24no—
304C2×C4×D61—24no—
305C2×C4×D61—28no—
306C2×C4×D61—24no—
307C2×C4×D61—48no—
308C2×C4×D61—48no—
309C2×C4×D61C2418yes—
310C2×C4×D61C2414yes—
311C2×C4×D61C2414yes—
312C2×C4×D61C2418yes—
313C2×C4×D61C2414yes—
314C2×C4×D61C24116yes—
315C2×C4×D61C24116yes—
316C2×Dic122—28no—
317C2×Dic122—44no—
318C2×Dic122—44no—
319C2×Dic122C2418yes—
320C2×Dic122C2418yes—
321C2×Dic122C2418yes—
322C4⋊C4×C61C2414yes—
323C4⋊C4×C61C2418yes—
324C4⋊C4×C61C24116yes—
325C4⋊C4×C61C2414yes—
326C4⋊C4×C61C2418yes—
327C22⋊C4×C61C2418yes—
328C22⋊C4×C61C2418yes—
329C22⋊C4×C61C24116yes—
330C42×C61C2414yes—
331C22⋊Dic61C2418yes—
332C22⋊Dic61C24116yes—
333C22⋊Dic61C2418yes—
334#11758198C24116yes—
335#11758198C24116yes—
336#11758198C2418yes—
337#11758198C24116yes—
338#11758198C2418yes—
339#11758198C2418yes—
340#11758198C2418yes—
341C4⋊Dic61C2414yes—
342C4⋊Dic61C2418yes—
343C4⋊Dic61C2414yes—
344C4⋊Dic61C24116yes—
345C4⋊Dic61C2418yes—
346C4⋊Dic61C24116yes—
347#11758196C24116yes—
348#11758196C24116yes—
349#11758196C2418yes—
350#11758196C2418yes—
351#11758196C24116yes—
352C4×Dic61C2414yes—
353C4×Dic61C2414yes—
354C4×Dic61C2414yes—
355C4×Dic61C24116yes—
356C23×C61—24no—
357C23×C61—24no—
358C23×C61—24no—
359C23×C61—24no—
360C23×C61—24no—
361C23×C61—24no—
362C23×C61C2514yes—
363C23×C61C2514yes—
364C23×C61C2511yescharacteristic
365C22×D61—24no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—24no—
369C22×D61—24no—
370C22×D61—24no—
371C22×D61—22no—
372C22×D61—24no—
373C22×D61—24no—
374C22×D61C2514yes—
375C22×D61C2512yes—
376C22×D61C2514yes—
377Q8×C61—216no—
378D4×C61—28no—
379D4×C61—28no—
380D4×C61—416no—
381C2×C4×C61—24no—
382C2×C4×C61—24no—
383C2×C4×C61—28no—
384C2×C4×C61—22no—
385C2×C4×C61—216no—
386C2×C4×C61—216no—
387C2×C4×C61—416no—
388C2×C4×C61H(5,𝔽2)14yes—
389C2×C4×C61H(5,𝔽2)14yes—
390C2×C4×C61C2518yes—
391C2×C4×C61C2512yes—
392C2×C4×C61C2514yes—
393C2×C4×C61C2514yes—
394C2×C4×C61C2512yes—
395C2×C4×C61C2512yes—
396C22⋊D61—216no—
397C22⋊D61—216no—
398C22⋊D61—416no—
399C22⋊D61—48no—
400C22⋊D61—48no—
401C22⋊D61—48no—
402C22⋊D61—48no—
403C22⋊D61—416no—
404C2×Dic61—28no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—24no—
408C2×Dic61—24no—
409C2×Dic61—416no—
410C2×Dic612−1+414yes—
411C2×Dic61C2512yes—
412C2×Dic61C2512yes—
413C2×Dic61C2518yes—
414C2×Dic61C2514yes—
415C2×Dic61C2514yes—
416C2×Dic61C2512yes—
417D244—28no—
418D244—28no—
419D244—48no—
420D244—48no—
421D244—416no—
422C4×D61—28no—
423C4×D61—28no—
424C4×D61—216no—
425C4×D61—216no—
426C4×D61—28no—
427C4×D61—416no—
428C4×D61—416no—
429Dic122—216no—
430Dic122—48no—
431Dic122—48no—
432C2×#3548—611nomaximal, Sylow
433C22×C61—24no—
434C22×C61—24no—
435C22×C61—24no—
436C22×C61—24no—
437C22×C61—24no—
438C22×C61—24no—
439C22×C61—48no—
440C22×C61—48no—
441C22×C61C2×H(5,𝔽2)12yes—
442C22×C61C2×H(5,𝔽2)12yes—
443C22×C61C2×2−1+412yes—
444C22×C61C2611yescharacteristic
445C2×D61—24no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—24no—
451C2×D61—22no—
452C2×D61—24no—
453C2×D61—24no—
454C2×D61—48no—
455C2×D61—44no—
456C2×D61—48no—
457C4×C61—24no—
458C4×C61—24no—
459C4×C61—28no—
460C4×C61—22no—
461C4×C61C2×H(5,𝔽2)14yes—
462C4×C61C2×H(5,𝔽2)14yes—
463Dic61—28no—
464Dic61—22no—
465Dic61—22no—
466Dic61—24no—
467Dic61—24no—
468Dic61C2×2−1+414yes—
469#3548—6132no—
470C2×#562—614no—
471C2×#554—612no—
472C2×#554—612no—
473C2×#550—612no—
474C2×#550—612no—
475C2×#547—611no—
476C2×#547—611no—
477C2×#547—611no—
478C2×#547D6111yescharacteristic, complemented
479C2×#540—614no—
480C2×#537—612no—
481C2×#537—612no—
482C2×#537—612no—
483C2×#537—612no—
484C2×#533—611no—
485C2×#532—611no—
486C2×#532—611no—
487C2×C61—44no—
488C2×C61—44no—
489C2×C61#354814yescomplemented
490C2×C61C22×H(5,𝔽2)11yescharacteristic
491C2×C61C22×H(5,𝔽2)11yescharacteristic
492C2×C61C22×2−1+411yescharacteristic
493D61—44no—
494D61—42no—
495D61—44no—
496C22×#41—612no—
497C22×#41—612no—
498C22×#41—612no—
499C22×#41—612no—
500C22×#41—612no—
501C22×#41C2×D6112yes—
502#562—6164no—
503#554—6132no—
504#554—6132no—
505#550—6132no—
506#550—6132no—
507#547—6116no—
508#547—6116no—
509#547—6116no—
510#547C2×D61116yescomplemented
511#540—6164no—
512#537—6132no—
513#537—6132no—
514#537—6132no—
515#537—6132no—
516#533—6116no—
517#532—6116no—
518#532—6116no—
519C2×C4⋊Q8—611no—
520C2×C4⋊Q8—611no—
521C2×C4⋊Q8—611no—
522C2×C4⋊Q8C2×D6111yescharacteristic
523C2×#127—611no—
524C2×#127—611no—
525C2×#127—614no—
526C2×#125—614no—
527C2×#125—612no—
528C2×#124—612no—
529C2×#124—612no—
530C2×#123—614no—
531C2×#123—614no—
532C2×#123—614no—
533C2×#123C2×D6114yes—
534C2×C22⋊Q8—612no—
535C2×C22⋊Q8—612no—
536C2×C22⋊Q8—612no—
537C2×C22⋊Q8—614no—
538C2×C22⋊Q8—614no—
539C2×C22⋊Q8—612no—
540C2×C22⋊Q8—612no—
541C2×C22⋊Q8—614no—
542C2×C22⋊Q8—614no—
543C2×C22⋊Q8C2×D6112yes—
544C2×#121—611no—
545C2×#121—611no—
546C2×#121—612no—
547C2×#121—614no—
548C2×#121—614no—
549C2×#121—614no—
550C2×#121—614no—
551C2×#121—612no—
552C2×#121—614no—
553C2×#121—611no—
554C2×#121—611no—
555C2×#121—614no—
556C2×#121—612no—
557C2×#121—612no—
558C2×#121—612no—
559C2×#121—614no—
560C2×#121—614no—
561C2×#121C2×D6112yes—
562C2×C4×Q8—612no—
563C2×C4×Q8—612no—
564C2×C4×D4—612no—
565C2×C4×D4—612no—
566C2×C4×D4—614no—
567C2×C4×D4—614no—
568C2×C4×D4—611no—
569C2×C4×D4—611no—
570C2×C4×D4C2×D6111yescharacteristic
571C2×C4×D4C2×D6111yescharacteristic
572C2×#117—612no—
573C22×C4⋊C4—612no—
574C22×C4⋊C4—612no—
575C22×C4⋊C4—612no—
576C22×C4⋊C4C2×D6112yes—
577C22×C42—611no—
578C61C2×#354811yescharacteristic, complemented, Sylow
579C2×#41—48no—
580C2×#41—6116no—
581C2×#41—6116no—
582C2×#41—6116no—
583C2×#41—6116no—
584C2×#41—6116no—
585C2×#41—2448no—
586C2×#41—2448no—
587C2×#41—2448no—
588C2×#41—2448no—
589C2×#41—2448no—
590C2×#41C22×D61116yes—
591C22×Q8—612no—
592C22×Q8—612no—
593C22×Q8—612no—
594C22×Q8C22×D6112yes—
595C22×D4—612no—
596C22×D4—612no—
597C22×D4—612no—
598C22×D4—612no—
599C22×D4—614no—
600C22×D4—614no—
601C22×D4—612no—
602C22×D4—612no—
603C22×D4—611no—
604C22×D4—611no—
605C22×D4—612no—
606C22×D4—612no—
607C22×D4—614no—
608C22×D4C22×D6111yescharacteristic
609C22×D4C22×D6111yescharacteristic
610C22×D4C22×D6114yes—
611C23×C4—614no—
612C23×C4—612no—
613C23×C4—612no—
614C23×C4—611no—
615C23×C4—611no—
616C23×C4—611no—
617C23×C4—614no—
618C23×C4—614no—
619C23×C4C22×D6112yes—
620C23×C4C22×D6112yes—
621C23×C4C22×D6114yes—
622C4⋊Q8—618no—
623C4⋊Q8—618no—
624C4⋊Q8—618no—
625C4⋊Q8C22×D6118yes—
626#127—618no—
627#127—618no—
628#127—6132no—
629#125—6116no—
630#125—6132no—
631#124—6116no—
632#124—6116no—
633#123—6132no—
634#123—6132no—
635#123—6132no—
636#123C22×D61132yes—
637C22⋊Q8—6116no—
638C22⋊Q8—6116no—
639C22⋊Q8—6116no—
640C22⋊Q8—6132no—
641C22⋊Q8—6116no—
642C22⋊Q8—6116no—
643C22⋊Q8—6132no—
644C22⋊Q8—6132no—
645C22⋊Q8—6132no—
646C22⋊Q8C22×D61116yes—
647#121—618no—
648#121—618no—
649#121—6132no—
650#121—6116no—
651#121—6132no—
652#121—6132no—
653#121—6132no—
654#121—6116no—
655#121—6132no—
656#121—618no—
657#121—618no—
658#121—6132no—
659#121—6116no—
660#121—6116no—
661#121—6116no—
662#121—6132no—
663#121—6132no—
664#121C22×D61116yes—
665C4×Q8—6116no—
666C4×Q8—6116no—
667C4×D4—6116no—
668C4×D4—6116no—
669C4×D4—6132no—
670C4×D4—6132no—
671C4×D4—618no—
672C4×D4—618no—
673C4×D4C22×D6118yes—
674C4×D4C22×D6118yes—
675#117—6116no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4—611no—
678C2×C4⋊C4—612no—
679C2×C4⋊C4—614no—
680C2×C4⋊C4—614no—
681C2×C4⋊C4—614no—
682C2×C4⋊C4—6116no—
683C2×C4⋊C4—612no—
684C2×C4⋊C4—612no—
685C2×C4⋊C4—612no—
686C2×C4⋊C4—614no—
687C2×C4⋊C4—614no—
688C2×C4⋊C4—6116no—
689C2×C4⋊C4—6116no—
690C2×C4⋊C4C22×D6111yescharacteristic
691C2×C4⋊C4C22×D6112yes—
692C2×C4⋊C4C22×D6111yescharacteristic
693C2×C4⋊C4C22×D6114yes—
694C2×C4⋊C4C22×D61116yes—
695C2×C4⋊C4C22×D6112yes—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—612no—
698C2×C22⋊C4—612no—
699C2×C22⋊C4—614no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—612no—
703C2×C22⋊C4—612no—
704C2×C22⋊C4—612no—
705C2×C22⋊C4—612no—
706C2×C22⋊C4C22×D6114yes—
707C2×C22⋊C4C22×D6112yes—
708C2×C22⋊C4C22×D6112yes—
709C2×C42—614no—
710C2×C42—611no—
711C2×C42—611no—
712C2×C42—611no—
713C2×C42—618no—
714C2×C42C22×D6111yescharacteristic
715C24—611no—
716C24—612no—
717C24—612no—
718C24C23×D6112yes—
719C24C23×D6112yes—
720#41—432no—
721#41—24432no—
722#41—24432no—
723#41—24432no—
724#41—24432no—
725#41—24432no—
726C2×Q8—28no—
727C2×Q8—618no—
728C2×Q8—618no—
729C2×Q8—618no—
730C2×Q8—1228no—
731C2×Q8—2444no—
732C2×Q8—2444no—
733C2×Q8C23×D6118yes—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—48no—
737C2×D4—618no—
738C2×D4—618no—
739C2×D4—618no—
740C2×D4—618no—
741C2×D4—6116no—
742C2×D4—6116no—
743C2×D4—618no—
744C2×D4—618no—
745C2×D4—614no—
746C2×D4—614no—
747C2×D4—618no—
748C2×D4—618no—
749C2×D4—6116no—
750C2×D4—1228no—
751C2×D4—1228no—
752C2×D4—1224no—
753C2×D4—1224no—
754C2×D4—2444no—
755C2×D4—2448no—
756C2×D4—2444no—
757C2×D4—2444no—
758C2×D4—2444no—
759C2×D4—2444no—
760C2×D4—2444no—
761C2×D4—2448no—
762C2×D4—2448no—
763C2×D4C23×D6114yes—
764C2×D4C23×D6114yes—
765C2×D4C23×D61116yes—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—48no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—614no—
773C22×C4—612no—
774C22×C4—612no—
775C22×C4—6116no—
776C22×C4—614no—
777C22×C4—614no—
778C22×C4—614no—
779C22×C4—618no—
780C22×C4—618no—
781C22×C4—6116no—
782C22×C4—6116no—
783C22×C4—1224no—
784C22×C4—1228no—
785C22×C4—1224no—
786C22×C4—1228no—
787C22×C4—1224no—
788C22×C4—2448no—
789C22×C4—2448no—
790C22×C4—2448no—
791C22×C4C23×D6118yes—
792C22×C4C23×D6118yes—
793C22×C4C23×D6111yescharacteristic
794C22×C4C23×D6114yes—
795C22×C4C23×D6112yes—
796C22×C4C23×D6112yes—
797C22×C4C23×D61116yes—
798C22×C4C23×D6111yescharacteristic
799C22×C4C23×D6111yescharacteristic
800C4⋊C4—614no—
801C4⋊C4—614no—
802C4⋊C4—618no—
803C4⋊C4—6116no—
804C4⋊C4—6116no—
805C4⋊C4—6116no—
806C4⋊C4—618no—
807C4⋊C4—618no—
808C4⋊C4—6116no—
809C4⋊C4—618no—
810C4⋊C4—6116no—
811C4⋊C4C23×D6114yes—
812C4⋊C4C23×D6118yes—
813C4⋊C4C23×D6114yes—
814C4⋊C4C23×D61116yes—
815C4⋊C4C23×D6118yes—
816C22⋊C4—6116no—
817C22⋊C4—618no—
818C22⋊C4—618no—
819C22⋊C4—6116no—
820C22⋊C4—6116no—
821C22⋊C4—6116no—
822C22⋊C4—618no—
823C22⋊C4—618no—
824C22⋊C4—618no—
825C22⋊C4—618no—
826C22⋊C4C23×D61116yes—
827C22⋊C4C23×D6118yes—
828C22⋊C4C23×D6118yes—
829C42—614no—
830C42—614no—
831C42—614no—
832C42—6116no—
833C42C23×D6114yes—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—612no—
841C23—614no—
842C23—614no—
843C23—1224no—
844C23—1222no—
845C23—1224no—
846C23—1222no—
847C23—1224no—
848C23—1224no—
849C23—1222no—
850C23—1224no—
851C23—1224no—
852C23C24×D6114yes—
853C23C24×D6114yes—
854C23C24×D6111yescharacteristic
855Q8—216no—
856Q8—12216no—
857Q8—2448no—
858Q8—2448no—
859D4—28no—
860D4—28no—
861D4—416no—
862D4—12216no—
863D4—12216no—
864D4—1228no—
865D4—1228no—
866D4—2448no—
867D4—24416no—
868D4—2448no—
869D4—2448no—
870D4—2448no—
871D4—2448no—
872D4—2448no—
873D4—24416no—
874D4—24416no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—216no—
880C2×C4—216no—
881C2×C4—416no—
882C2×C4—614no—
883C2×C4—612no—
884C2×C4—612no—
885C2×C4—612no—
886C2×C4—618no—
887C2×C4—614no—
888C2×C4—614no—
889C2×C4—1228no—
890C2×C4—1224no—
891C2×C4—1222no—
892C2×C4—1224no—
893C2×C4—1222no—
894C2×C4—1228no—
895C2×C4—12216no—
896C2×C4—1228no—
897C2×C4—12216no—
898C2×C4—1228no—
899C2×C4—24416no—
900C2×C4—24416no—
901C2×C4—24416no—
902C2×C4#1451982214yes—
903C2×C4#1451982314yes—
904C2×C4C24×D6112yes—
905C2×C4C24×D6118yes—
906C2×C4C24×D6114yes—
907C2×C4C24×D6114yes—
908C2×C4C24×D6112yes—
909C2×C4C24×D6112yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—48no—
917C22—48no—
918C22—1224no—
919C22—1222no—
920C22—1224no—
921C22—1222no—
922C22—1224no—
923C22—1224no—
924C22—1222no—
925C22—1224no—
926C22—1224no—
927C22—2444no—
928C22—2448no—
929C22—2448no—
930C22C2×#1451982212yes—
931C22C2×#1451982312yes—
932C222−1+4×D6112yes—
933C22C25×D6111yescharacteristic
934C4—24no—
935C4—28no—
936C4—24no—
937C4—22no—
938C4—614no—
939C4—1224no—
940C4—1222no—
941C4—1224no—
942C4—1222no—
943C4—1228no—
944C4C2×#1451982214yes—
945C4C2×#1451982314yes—
946C2—44no—
947C2—44no—
948C2—2442no—
949C2—2444no—
950C2—2444no—
951C2#2146021614yesdirect product factor
952C2C22×#1451982211yescharacteristic
953C2C22×#1451982311yescharacteristic
954C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#547C2
socleC23×C61C25
hypercenterC2×#547D61
hypocenterC61C2×#3548
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #21460216C2direct (N × H)
2. C2×#16840509C2semidirect
3. C2×#16840470C2semidirect
4. C2×#16840467C2semidirect
5. C2×#16840431C2semidirect
6. C2×#16840430C2semidirect
7. C2×#16840417C2semidirect
8. C2×#16840416C2semidirect
9. C2×#16840415C2semidirect
10. C2×#16840364C2semidirect
11. C2×#16840343C2semidirect
12. C2×#16840342C2semidirect
13. C2×#16840341C2semidirect
14. C2×#16840340C2semidirect
15. C2×#16840317C2semidirect
16. C2×#16840309C2semidirect
17. C2×#16840309C2semidirect
18. C2×C61×#547C2semidirect
24. #16840509C22semidirect
25. #16840470C22semidirect
26. #16840467C22semidirect
27. #16840431C22semidirect
28. #16840430C22semidirect
29. #16840417C22semidirect
30. #16840416C22semidirect
31. #16840415C22semidirect
32. #16840364C22semidirect
33. #16840343C22semidirect
34. #16840342C22semidirect
35. #16840341C22semidirect
36. #16840340C22semidirect
37. #16840317C22semidirect
38. #16840309C22semidirect
39. #16840309C22semidirect
93. C61×#547C22semidirect
478. C2×#547D61semidirect
489. C2×C61#3548semidirect
510. #547C2×D61semidirect
578. C61C2×#3548semidirect
951. C2#21460216direct (N × H)

Maximal subgroups

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

subgroupindex
#214602162
C2×#168405092
C2×#168404702
C2×#168404672
C2×#168404312
C2×#168404302
C2×#168404172
C2×#168404162
C2×#168404152
C2×#168403642
C2×#168403432
C2×#168403422
C2×#168403412
C2×#168403402
C2×#168403172
C2×#168403092
C2×C61×#5472
C2×#354861