Finite Group Databasebeta

← C2×#21459398 #30587084

Subgroups — C2×#21459398 #30587084

Order 15616.

7522 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459398C2132yesmaximal, direct product factor
2C2×#16840492C211yesmaximal, characteristic, complemented
3C2×#16840490C211yesmaximal, characteristic, complemented
4C2×#16840489C212yesmaximal, complemented
5C2×#16840471C212yesmaximal, complemented
6C2×#16840467C212yesmaximal, complemented
7C2×#16840466C214yesmaximal, complemented
8C2×D4×Dic122C211yesmaximal, characteristic, complemented
9C2×#16840425C212yesmaximal, complemented
10C2×#16840318C212yesmaximal, complemented
11C2×#16840317C211yesmaximal, characteristic, complemented
12C2×#16840314C214yesmaximal, complemented
13C2×#16840314C212yesmaximal, complemented
14C2×C4×#11758224C211yesmaximal, characteristic
15C2×C4×#11758224C212yesmaximal
16C22×#14519742C212yesmaximal, complemented
17C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
18C2×C61×#554C211yesmaximal, characteristic, complemented
19C22×#11758224C2211yescharacteristic
20C23×Dic122C2212yes—
21C22×Q8×D61C2211yescharacteristic
22#16840492C22116yescomplemented
23#16840490C22116yescomplemented
24#16840489C22132yescomplemented
25#16840471C22132yescomplemented
26#16840467C22132yescomplemented
27#16840466C22164yescomplemented
28D4×Dic122C22116yescomplemented
29#16840425C22132yescomplemented
30#16840318C22132yescomplemented
31#16840317C22116yescomplemented
32#16840314C22164yescomplemented
33#16840314C22132yescomplemented
34C2×#14519777C2211yescharacteristic
35C2×#14519776C2214yes—
36C2×#14519776C2212yes—
37C2×#14519776C2212yes—
38C2×#14519776C2212yes—
39C2×#14519775C2212yes—
40C2×#14519775C2214yes—
41C2×#14519769C2212yes—
42C2×#14519768C2212yes—
43C2×#14519767C2214yes—
44C2×#14519767C2214yes—
45C2×#14519767C2214yes—
46C2×#14519757C2212yes—
47C2×#14519756C2212yes—
48C2×#14519756C2214yes—
49C2×#14519755C2214yes—
50C2×#14519755C2214yes—
51C2×#14519754C2214yes—
52C2×#14519754C2214yes—
53C2×#14519754C2214yes—
54C2×#14519753C2212yes—
55C4×#11758224C22132yes—
56C4×#11758224C22116yes—
57C2×Q8×Dic61C2211yescharacteristic
58C2×Q8×Dic61C2212yes—
59C2×C4×Dic122C2211yescharacteristic
60C2×C4×Dic122C2212yes—
61C2×C4×Dic122C2212yes—
62C2×C4×Dic122C2211yescharacteristic
63C2×#14519742C2211yescharacteristic
64C2×#14519742C2212yes—
65C2×#14519742C2212yes—
66C2×#14519742C2214yes—
67C2×#14519742C2212yes—
68C2×#14519742C2212yes—
69C2×#14519742C2214yes—
70C2×#14519742C2211yescharacteristic
71C2×#14519742C2212yes—
72C2×#14519742C2214yes—
73C2×#14519742C22132yescomplemented
74C4×Q8×D61C22116yescomplemented
75C2×D4×Dic61C2212yes—
76C2×D4×Dic61C2211yescharacteristic
77C2×C4×C22⋊D61C2212yes—
78C2×C4×C22⋊D61C2214yes—
79C2×#14519737C2214yes—
80C2×#14519737C2212yes—
81C2×#14519735C2212yes—
82C2×#14519735C2211yescharacteristic
83C2×#14519733C2214yes—
84C2×#14519733C2212yes—
85C22×#11758196C2214yes—
86C2×C4⋊C4×D61C2212yes—
87C2×C4⋊C4×D61C2211yescharacteristic
88C22×C4×Dic61C2214yes—
89C22×C4×Dic61C2212yes—
90C2×C42×D61C2211yescharacteristic
91C2×C42×D61C2212yes—
92C61×#554C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#125×C61C2212yes—
95C2×C22⋊Q8×C61C2212yes—
96C2×C22⋊Q8×C61C2214yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×D4×C61C2211yescharacteristic
99C2×C4×D4×C61C2212yes—
100C22×C4⋊C4×C61C2212yes—
101C2×#11758224Q8116yescomplemented
102C2×#11758224C2318yes—
103C22×Dic122—216no—
104C22×Dic122C2314yes—
105C22×Dic122C2312yes—
106C22×Dic122C2312yes—
107C22×Dic122C23116yes—
108C22×Dic122C2314yes—
109C22×Dic122C2311yescharacteristic
110C22×Dic122C2311yescharacteristic
111C2×Q8×D61—28no—
112C2×Q8×D61C2318yes—
113C22×C22⋊D61C2312yes—
114C23×Dic61C2314yes—
115C23×Dic61C2312yes—
116C23×Dic61C2312yes—
117C22×C4×D61C2312yes—
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2312yes—
121C22×C4×D61C2311yescharacteristic
122#14519777C2318yes—
123#14519776C23116yes—
124#14519776C23116yes—
125#14519776C23132yes—
126#14519776C23116yes—
127#14519775C23132yes—
128#14519775C23116yes—
129#14519769C23116yes—
130#14519768C23116yes—
131#14519767C23132yes—
132#14519767C23132yes—
133#14519767C23132yes—
134#14519757C23116yes—
135#14519756C23132yes—
136#14519756C23116yes—
137#14519755C23132yes—
138#14519755C23132yes—
139#14519754C23132yes—
140#14519754C23132yes—
141#14519754C23132yes—
142#14519753C23116yes—
143Q8×Dic61C2318yes—
144Q8×Dic61C23116yes—
145C4×Dic122C23116yes—
146C4×Dic122C2318yes—
147C4×Dic122C23116yes—
148C4×Dic122C2318yes—
149#14519742C23132yes—
150#14519742C23116yes—
151#14519742C2318yes—
152#14519742C23116yes—
153#14519742C23116yes—
154#14519742C23116yes—
155#14519742C23132yes—
156#14519742C2318yes—
157#14519742C23116yes—
158#14519742C23132yes—
159D4×Dic61C2318yes—
160D4×Dic61C23116yes—
161C4×C22⋊D61C23132yes—
162C4×C22⋊D61C23116yes—
163#14519737C23116yes—
164#14519737C23132yes—
165#14519735C23116yes—
166#14519735C2318yes—
167#14519733C23132yes—
168#14519733C23116yes—
169C2×C4⋊Dic61C2312yes—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2312yes—
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2312yes—
174C2×C4⋊Dic61C2314yes—
175C2×#11758196C23132yes—
176C2×#11758196C2312yes—
177C2×#11758196C2312yes—
178C2×#11758196C2312yes—
179C2×#11758196C2314yes—
180C2×#11758196C2314yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
185C2×#11758196C2312yes—
186C2×#11758196C2314yes—
187C2×#11758196C2314yes—
188C4⋊C4×D61C23116yes—
189C4⋊C4×D61C2318yes—
190C2×C22⋊Dic61C2314yes—
191C2×C22⋊Dic61C2312yes—
192C2×#11758198C2314yes—
193C2×#11758198C2312yes—
194C2×C4×Dic61C2312yes—
195C2×C4×Dic61C2311yescharacteristic
196C2×C4×Dic61C2312yes—
197C2×C4×Dic61C2311yescharacteristic
198C2×C4×Dic61C2311yescharacteristic
199C2×C4×Dic61C2312yes—
200C2×C4×Dic61C2312yes—
201C2×C4×Dic61C2314yes—
202C2×C4×Dic61C2312yes—
203C2×C4×Dic61C2314yes—
204C2×C4×Dic61C2314yes—
205C2×C4×Dic61C2312yes—
206C2×C4×Dic61C23132yes—
207C2×C4×Dic61C23116yes—
208C42×D61C2318yes—
209C42×D61C23116yes—
210C22×Q8×C61C2311yescharacteristic
211C22×Q8×C61C2312yes—
212C22×D4×C61C2311yescharacteristic
213C23×C4×C61C2312yes—
214C23×C4×C61C2314yes—
215C4⋊Q8×C61C2318yes—
216#125×C61C23116yes—
217C22⋊Q8×C61C23132yes—
218C22⋊Q8×C61C23116yes—
219C4×Q8×C61C2318yes—
220C4×D4×C61C23116yes—
221C4×D4×C61C2318yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C23116yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C4⋊C4×C61C2314yes—
229C2×C4⋊C4×C61C2314yes—
230C2×C22⋊C4×C61C2314yes—
231C2×C22⋊C4×C61C2312yes—
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2312yes—
234C24×C61C2412yes—
235C23×D61C2411yescharacteristic
236C2×Q8×C61—24no—
237C2×Q8×C61—44no—
238C2×Q8×C61C2414yes—
239C2×Q8×C61C2418yes—
240C2×D4×C61C2×Q818yescomplemented
241C2×D4×C61C2414yes—
242C22×C4×C61—28no—
243C22×C4×C61—48no—
244C22×C4×C61C2412yes—
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2412yes—
247C22×C4×C61C2412yes—
248C22×C4×C61C2418yes—
249C22×C4×C61C2414yes—
250C22×C4×C61C24116yes—
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61C2×Q8116yescomplemented
254C2×C22⋊D61C2418yes—
255C22×Dic61—216no—
256C22×Dic61—44no—
257C22×Dic61C2×Q8116yescomplemented
258C22×Dic61C2411yescharacteristic
259C22×Dic61C2412yes—
260C22×Dic61C2411yescharacteristic
261C22×Dic61C2412yes—
262C22×Dic61C2414yes—
263C22×Dic61C24116yes—
264C22×Dic61C2418yes—
265C22×Dic61C2411yescharacteristic
266C22×Dic61C2412yes—
267C22×Dic61C2418yes—
268C22×Dic61C2412yes—
269Q8×D61—232no—
270#11758224C2×Q8164yescomplemented
271C2×C4×D61—24no—
272C2×C4×D61—28no—
273C2×C4×D61—44no—
274C2×C4×D61—42no—
275C2×C4×D61C2×Q818yescomplemented
276C2×C4×D61C2418yes—
277C2×C4×D61C2414yes—
278C2×C4×D61C2414yes—
279C2×C4×D61C2418yes—
280C2×C4×D61C2414yes—
281C2×Dic122—28no—
282C2×Dic122—28no—
283C2×Dic122—216no—
284C2×Dic122—264no—
285C2×Dic122—48no—
286C2×Dic122C2×Q818yescomplemented
287C2×Dic122#4118yescomplemented
288C2×Dic122C2418yes—
289C2×Dic122C24116yes—
290C2×Dic122C2418yes—
291C2×Dic122C24116yes—
292C2×Dic122C2414yes—
293C2×Dic122C2414yes—
294C4⋊C4×C61C2414yes—
295C4⋊C4×C61C24116yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C24116yes—
301C22⋊C4×C61C24116yes—
302C22⋊C4×C61C2418yes—
303C42×C61C2418yes—
304C42×C61C2414yes—
305C22⋊Dic61C2418yes—
306C22⋊Dic61C24116yes—
307#11758198C24116yes—
308#11758198C2418yes—
309C4⋊Dic61C2418yes—
310C4⋊Dic61C2414yes—
311C4⋊Dic61C2418yes—
312C4⋊Dic61C2414yes—
313C4⋊Dic61C2418yes—
314C4⋊Dic61C24116yes—
315#11758196C2418yes—
316#11758196C2418yes—
317#11758196C2418yes—
318#11758196C24116yes—
319#11758196C24116yes—
320#11758196C24116yes—
321#11758196C2418yes—
322#11758196C24116yes—
323#11758196C24116yes—
324#11758196C2418yes—
325#11758196C24116yes—
326#11758196C24116yes—
327C4×Dic61C2418yes—
328C4×Dic61C2414yes—
329C4×Dic61C2418yes—
330C4×Dic61C2414yes—
331C4×Dic61C2414yes—
332C4×Dic61C2418yes—
333C4×Dic61C2418yes—
334C4×Dic61C24116yes—
335C4×Dic61C2418yes—
336C4×Dic61C24116yes—
337C4×Dic61C24116yes—
338C4×Dic61C2418yes—
339C23×C61—24no—
340C23×C61—24no—
341C23×C61C22×Q818yes—
342C23×C61C2514yes—
343C23×C61C2511yescharacteristic
344C22×D61—22no—
345C22×D61—22no—
346C22×D61C22×Q814yes—
347C22×D61C2512yes—
348Q8×C61—28no—
349Q8×C61—48no—
350D4×C61C22×Q8116yescomplemented
351C2×C4×C61—24no—
352C2×C4×C61—24no—
353C2×C4×C61—28no—
354C2×C4×C61—24no—
355C2×C4×C61—22no—
356C2×C4×C61—216no—
357C2×C4×C61—416no—
358C2×C4×C61C22×Q814yes—
359C2×C4×C61C2×#4114yes—
360C2×C4×C61C2514yes—
361C2×C4×C61C2518yes—
362C2×C4×C61C2514yes—
363C2×C4×C61C2512yes—
364C2×C4×C61C2514yes—
365C2×C4×C61C2512yes—
366C2×C4×C61C2512yes—
367C22⋊D61C22×Q8132yescomplemented
368C2×Dic61—22no—
369C2×Dic61—28no—
370C2×Dic61—24no—
371C2×Dic61—24no—
372C2×Dic61—22no—
373C2×Dic61—232no—
374C2×Dic61—48no—
375C2×Dic61C22×Q818yes—
376C2×Dic61C22×Q814yes—
377C2×Dic61C22×Q8132yescomplemented
378C2×Dic61C2×#4118yes—
379C2×Dic61C2512yes—
380C2×Dic61C2514yes—
381C2×Dic61C2514yes—
382C2×Dic61C2518yes—
383C2×Dic61C2512yes—
384C2×Dic61C2512yes—
385C2×Dic61C2514yes—
386C2×Dic61C2514yes—
387C4×D61—28no—
388C4×D61—216no—
389C4×D61—48no—
390C4×D61—44no—
391C4×D61C22×Q8116yescomplemented
392Dic122—216no—
393Dic122—232no—
394Dic122—216no—
395Dic122—416no—
396Dic122C22×Q8116yescomplemented
397Dic122C2×#41116yescomplemented
398C2×Q8×#41—611nomaximal, Sylow
399C22×C61—24no—
400C22×C61—24no—
401C22×C61—216no—
402C22×C61C23×Q818yes—
403C22×C61C23×Q812yes—
404C22×C61C22×#4112yes—
405C22×C61#58512yes—
406C22×C61C2611yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—28no—
410C2×D61C23×Q814yes—
411C4×C61—24no—
412C4×C61—24no—
413C4×C61—28no—
414C4×C61—24no—
415C4×C61—22no—
416C4×C61C23×Q814yes—
417C4×C61C22×#4114yes—
418Dic61—22no—
419Dic61—28no—
420Dic61—24no—
421Dic61—24no—
422Dic61—22no—
423Dic61C23×Q818yes—
424Dic61C23×Q814yes—
425Dic61C22×#4118yes—
426Q8×#41—6132no—
427C2×Q82—611no—
428C2×#557—612no—
429C2×#557—611no—
430C2×#554—614no—
431C2×#554—612no—
432C2×#554—612no—
433C2×#554D6111yescharacteristic, complemented
434C2×D4×Q8—612no—
435C2×D4×Q8—611no—
436C2×#533—611no—
437C2×#533—612no—
438C2×#533—612no—
439C2×#533—614no—
440C2×C4×#41—612no—
441C2×C4×#41—611no—
442C22×C4×Q8—611no—
443C22×C4×Q8—612no—
444C2×C61—28no—
445C2×C61Q8×#4114yescomplemented
446C2×C61C24×Q811yescharacteristic
447C2×C61C23×#4111yescharacteristic
448C2×C61C2×#58511yescharacteristic
449D61—24no—
450C22×#41—611no—
451C23×Q8—611no—
452C23×Q8—612no—
453Q82—6116no—
454#557—6132no—
455#557—6116no—
456#554—6164no—
457#554—6132no—
458#554—6132no—
459#554C2×D61116yescomplemented
460D4×Q8—6132no—
461D4×Q8—6116no—
462#533—6116no—
463#533—6132no—
464#533—6132no—
465#533—6164no—
466C2×C4⋊Q8—612no—
467C2×C4⋊Q8—614no—
468C2×C4⋊Q8—614no—
469C2×C4⋊Q8—612no—
470C2×C4⋊Q8—612no—
471C2×C4⋊Q8—612no—
472C2×C4⋊Q8—611no—
473C2×C4⋊Q8C2×D6111yescharacteristic
474C2×#125—614no—
475C2×#125—614no—
476C2×#125—614no—
477C2×#125—612no—
478C2×#125—612no—
479C2×#125C2×D6112yes—
480C2×C22⋊Q8—612no—
481C2×C22⋊Q8—612no—
482C2×C22⋊Q8—614no—
483C2×C22⋊Q8—614no—
484C2×C22⋊Q8—614no—
485C2×C22⋊Q8—612no—
486C2×C22⋊Q8—614no—
487C2×C22⋊Q8—614no—
488C2×C22⋊Q8—614no—
489C2×C22⋊Q8C2×D6112yes—
490C2×C22⋊Q8C2×D6114yes—
491C4×#41—6132no—
492C4×#41—6116no—
493C2×C4×Q8—611no—
494C2×C4×Q8—612no—
495C2×C4×Q8—6116no—
496C2×C4×Q8—611no—
497C2×C4×Q8—612no—
498C2×C4×Q8—612no—
499C2×C4×Q8—614no—
500C2×C4×Q8—612no—
501C2×C4×Q8—614no—
502C2×C4×Q8—612no—
503C2×C4×Q8—611no—
504C2×C4×Q8—612no—
505C2×C4×Q8—614no—
506C2×C4×Q8—6132no—
507C2×C4×Q8—611no—
508C2×C4×Q8—612no—
509C2×C4×Q8—612no—
510C2×C4×Q8—611no—
511C2×C4×Q8C2×D6111yescharacteristic
512C2×C4×D4—612no—
513C2×C4×D4—611no—
514C2×C4×D4—612no—
515C2×C4×D4—614no—
516C2×C4×D4—614no—
517C2×C4×D4—612no—
518C2×C4×D4C2×D6111yescharacteristic
519C2×C4×D4C2×D6112yes—
520C2×#117—612no—
521C2×#117—611no—
522C2×#117—614no—
523C2×#117—612no—
524C22×C4⋊C4—614no—
525C22×C4⋊C4—612no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4C2×D6112yes—
528C22×C42—614no—
529C22×C42—612no—
530C22×C42—611no—
531C22×C42—612no—
532C61C2×Q8×#4111yescharacteristic, complemented, Sylow
533C2×#41—6116no—
534C2×#41—618no—
535C22×Q8—618no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—614no—
539C22×Q8—612no—
540C22×Q8—612no—
541C22×Q8—6116no—
542C22×Q8—614no—
543C22×Q8—12216no—
544C22×Q8—1228no—
545C22×Q8C22×D6111yescharacteristic
546C22×Q8C22×D6112yes—
547C22×D4—612no—
548C22×D4C22×D6111yescharacteristic
549C23×C4—612no—
550C23×C4—611no—
551C23×C4—614no—
552C23×C4—612no—
553C23×C4—612no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—612no—
557C23×C4C22×D6112yes—
558C23×C4C22×D6114yes—
559C4⋊Q8—6116no—
560C4⋊Q8—6132no—
561C4⋊Q8—6132no—
562C4⋊Q8—6116no—
563C4⋊Q8—6116no—
564C4⋊Q8—6116no—
565C4⋊Q8—618no—
566C4⋊Q8C22×D6118yes—
567#125—6132no—
568#125—6132no—
569#125—6132no—
570#125—6116no—
571#125—6116no—
572#125C22×D61116yes—
573C22⋊Q8—6116no—
574C22⋊Q8—6116no—
575C22⋊Q8—6132no—
576C22⋊Q8—6132no—
577C22⋊Q8—6116no—
578C22⋊Q8—6132no—
579C22⋊Q8—6132no—
580C22⋊Q8—6132no—
581C22⋊Q8—6132no—
582C22⋊Q8C22×D61116yes—
583C22⋊Q8C22×D61132yes—
584C4×Q8—618no—
585C4×Q8—6116no—
586C4×Q8—618no—
587C4×Q8—6116no—
588C4×Q8—6116no—
589C4×Q8—6132no—
590C4×Q8—6116no—
591C4×Q8—6132no—
592C4×Q8—6116no—
593C4×Q8—618no—
594C4×Q8—6116no—
595C4×Q8—6132no—
596C4×Q8—618no—
597C4×Q8—6116no—
598C4×Q8—6116no—
599C4×Q8—618no—
600C4×Q8C22×D6118yes—
601C4×D4—6116no—
602C4×D4—618no—
603C4×D4—6116no—
604C4×D4—6132no—
605C4×D4—6132no—
606C4×D4—6116no—
607C4×D4C22×D6118yes—
608C4×D4C22×D61116yes—
609#117—6116no—
610#117—618no—
611#117—6132no—
612#117—6116no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—614no—
616C2×C4⋊C4—612no—
617C2×C4⋊C4—612no—
618C2×C4⋊C4—614no—
619C2×C4⋊C4—612no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—6132no—
622C2×C4⋊C4—614no—
623C2×C4⋊C4—612no—
624C2×C4⋊C4—612no—
625C2×C4⋊C4—614no—
626C2×C4⋊C4—612no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—614no—
629C2×C4⋊C4—614no—
630C2×C4⋊C4—614no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—6116no—
633C2×C4⋊C4—618no—
634C2×C4⋊C4C22×D6111yescharacteristic
635C2×C4⋊C4C22×D6112yes—
636C2×C4⋊C4C22×D6114yes—
637C2×C4⋊C4C22×D6112yes—
638C2×C4⋊C4C22×D61116yes—
639C2×C4⋊C4C22×D6112yes—
640C2×C4⋊C4C22×D6111yescharacteristic
641C2×C4⋊C4C22×D6114yes—
642C2×C22⋊C4—614no—
643C2×C22⋊C4—612no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—612no—
646C2×C22⋊C4C22×D6114yes—
647C2×C22⋊C4C22×D6112yes—
648C2×C42—614no—
649C2×C42—612no—
650C2×C42—611no—
651C2×C42—612no—
652C2×C42—612no—
653C2×C42—614no—
654C2×C42—611no—
655C2×C42—614no—
656C2×C42—612no—
657C2×C42—612no—
658C2×C42—612no—
659C2×C42—611no—
660C2×C42—6132no—
661C2×C42—6116no—
662C2×C42—618no—
663C2×C42—6116no—
664C2×C42C22×D6112yes—
665C2×C42C22×D6111yescharacteristic
666C24—611no—
667C24C23×D6112yes—
668#41—6164no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—618no—
672C2×Q8—618no—
673C2×Q8—614no—
674C2×Q8—614no—
675C2×Q8—6116no—
676C2×Q8—618no—
677C2×Q8—618no—
678C2×Q8—6116no—
679C2×Q8—12216no—
680C2×Q8—1228no—
681C2×Q8—12264no—
682C2×Q8—12232no—
683C2×Q8—1228no—
684C2×Q8—2448no—
685C2×Q8C23×D6114yes—
686C2×Q8C23×D6118yes—
687C2×D4—6116no—
688C2×D4—618no—
689C2×D4Q8×D6118yescomplemented
690C2×D4C23×D6114yes—
691C22×C4—28no—
692C22×C4—48no—
693C22×C4—6116no—
694C22×C4—618no—
695C22×C4—611no—
696C22×C4—612no—
697C22×C4—612no—
698C22×C4—618no—
699C22×C4—614no—
700C22×C4—6116no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—614no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—618no—
707C22×C4—618no—
708C22×C4—614no—
709C22×C4—614no—
710C22×C4—618no—
711C22×C4—1228no—
712C22×C4—12216no—
713C22×C4—1224no—
714C22×C4—2444no—
715C22×C4—2442no—
716C22×C4—2444no—
717C22×C4C23×D6118yes—
718C22×C4C23×D6112yes—
719C22×C4C23×D6114yes—
720C22×C4C23×D6112yes—
721C22×C4C23×D6111yescharacteristic
722C22×C4C23×D6112yes—
723C22×C4C23×D61116yes—
724C22×C4C23×D6111yescharacteristic
725C22×C4C23×D6111yescharacteristic
726C4⋊C4—618no—
727C4⋊C4—6116no—
728C4⋊C4—6116no—
729C4⋊C4—618no—
730C4⋊C4—6116no—
731C4⋊C4—618no—
732C4⋊C4—618no—
733C4⋊C4—614no—
734C4⋊C4—6116no—
735C4⋊C4—618no—
736C4⋊C4—618no—
737C4⋊C4—6116no—
738C4⋊C4—6116no—
739C4⋊C4—6116no—
740C4⋊C4—618no—
741C4⋊C4—614no—
742C4⋊C4—6116no—
743C4⋊C4—618no—
744C4⋊C4C23×D6114yes—
745C4⋊C4C23×D6118yes—
746C4⋊C4C23×D61116yes—
747C4⋊C4C23×D6118yes—
748C4⋊C4C23×D6118yes—
749C4⋊C4C23×D6114yes—
750C4⋊C4C23×D61116yes—
751C22⋊C4—6116no—
752C22⋊C4—618no—
753C22⋊C4—6116no—
754C22⋊C4—618no—
755C22⋊C4C23×D61116yes—
756C22⋊C4C23×D6118yes—
757C42—618no—
758C42—614no—
759C42—6116no—
760C42—618no—
761C42—614no—
762C42—618no—
763C42—618no—
764C42—6116no—
765C42—614no—
766C42—6116no—
767C42—618no—
768C42—618no—
769C42C23×D6118yes—
770C42C23×D6114yes—
771C23—24no—
772C23—24no—
773C23—614no—
774C23—612no—
775C23—1222no—
776C23—1222no—
777C23C2×Q8×D6118yes—
778C23C24×D6114yes—
779C23C24×D6111yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—6116no—
783Q8—6116no—
784Q8—12232no—
785Q8—12216no—
786Q8—12216no—
787Q8—24416no—
788D4—6132no—
789D4C2×Q8×D61116yescomplemented
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—216no—
796C2×C4—416no—
797C2×C4—614no—
798C2×C4—618no—
799C2×C4—6132no—
800C2×C4—618no—
801C2×C4—612no—
802C2×C4—614no—
803C2×C4—614no—
804C2×C4—6116no—
805C2×C4—612no—
806C2×C4—618no—
807C2×C4—612no—
808C2×C4—614no—
809C2×C4—614no—
810C2×C4—12216no—
811C2×C4—12232no—
812C2×C4—1222no—
813C2×C4—1228no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1224no—
817C2×C4—1228no—
818C2×C4—2448no—
819C2×C4—2444no—
820C2×C4—2448no—
821C2×C4C2×Q8×D6114yes—
822C2×C4#41×D6114yes—
823C2×C4C24×D6114yes—
824C2×C4C24×D6118yes—
825C2×C4C24×D6114yes—
826C2×C4C24×D6112yes—
827C2×C4C24×D6114yes—
828C2×C4C24×D6112yes—
829C2×C4C24×D6112yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—614no—
834C22—1222no—
835C22—1222no—
836C22—1228no—
837C22C22×Q8×D6118yes—
838C22C22×Q8×D6112yes—
839C22C2×#41×D6112yes—
840C22#1684059712yes—
841C22C25×D6111yescharacteristic
842C4—24no—
843C4—24no—
844C4—24no—
845C4—28no—
846C4—22no—
847C4—614no—
848C4—618no—
849C4—618no—
850C4—1222no—
851C4—1228no—
852C4—1222no—
853C4—1224no—
854C4—1224no—
855C4C22×Q8×D6114yes—
856C4C2×#41×D6114yes—
857C2—28no—
858C2—1224no—
859C2#2145939814yesdirect product factor
860C2C23×Q8×D6111yescharacteristic
861C2C22×#41×D6111yescharacteristic
862C2C2×#1684059711yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#554C2
socleC23×C61C25
prime radicalC22×#11758224C22
hypercenterC2×#554D61
hypocenterC61C2×Q8×#41
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21459398C2direct (N × H)
2. C2×#16840492C2semidirect
3. C2×#16840490C2semidirect
4. C2×#16840489C2semidirect
5. C2×#16840471C2semidirect
6. C2×#16840467C2semidirect
7. C2×#16840466C2semidirect
8. C2×D4×Dic122C2semidirect
9. C2×#16840425C2semidirect
10. C2×#16840318C2semidirect
11. C2×#16840317C2semidirect
12. C2×#16840314C2semidirect
13. C2×#16840314C2semidirect
16. C22×#14519742C2semidirect
17. C2×C4×Q8×D61C2semidirect
18. C2×C61×#554C2semidirect
22. #16840492C22semidirect
23. #16840490C22semidirect
24. #16840489C22semidirect
25. #16840471C22semidirect
26. #16840467C22semidirect
27. #16840466C22semidirect
28. D4×Dic122C22semidirect
29. #16840425C22semidirect
30. #16840318C22semidirect
31. #16840317C22semidirect
32. #16840314C22semidirect
33. #16840314C22semidirect
73. C2×#14519742C22semidirect
74. C4×Q8×D61C22semidirect
92. C61×#554C22semidirect
101. C2×#11758224Q8semidirect
240. C2×D4×C61C2×Q8semidirect
253. C2×C22⋊D61C2×Q8semidirect
257. C22×Dic61C2×Q8semidirect
270. #11758224C2×Q8semidirect
275. C2×C4×D61C2×Q8semidirect
286. C2×Dic122C2×Q8semidirect
287. C2×Dic122#41semidirect
350. D4×C61C22×Q8semidirect
367. C22⋊D61C22×Q8semidirect
377. C2×Dic61C22×Q8semidirect
391. C4×D61C22×Q8semidirect
396. Dic122C22×Q8semidirect
397. Dic122C2×#41semidirect
433. C2×#554D61semidirect
445. C2×C61Q8×#41semidirect
459. #554C2×D61semidirect
532. C61C2×Q8×#41semidirect
689. C2×D4Q8×D61semidirect
789. D4C2×Q8×D61semidirect
859. C2#21459398direct (N × H)

Maximal subgroups

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

subgroupindex
#214593982
C2×#168404922
C2×#168404902
C2×#168404892
C2×#168404712
C2×#168404672
C2×#168404662
C2×D4×Dic1222
C2×#168404252
C2×#168403182
C2×#168403172
C2×#168403142
C2×C4×#117582242
C22×#145197422
C2×C4×Q8×D612
C2×C61×#5542
C2×Q8×#4161