Finite Group Databasebeta

← C2×#21459522 #30587949

Subgroups — C2×#21459522 #30587949

Order 15616.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459522C2132yesmaximal, direct product factor
2C2×#16840472C212yesmaximal, complemented
3C2×#16840467C212yesmaximal, complemented
4C2×#16840462C212yesmaximal, complemented
5C2×#16840456C212yesmaximal, complemented
6C2×#16840453C212yesmaximal, complemented
7C2×#16840451C212yesmaximal, complemented
8C2×#16840417C212yesmaximal, complemented
9C2×#16840413C212yesmaximal, complemented
10C2×#16840390C211yesmaximal, characteristic, complemented
11C2×#16840354C214yesmaximal, complemented
12C2×#16840340C211yesmaximal, characteristic, complemented
13C2×#16840274C211yesmaximal, characteristic, complemented
14C2×#16840271C214yesmaximal, complemented
15C2×#16840269C211yesmaximal, characteristic, complemented
16C2×#16840243C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
18C2×C61×#520C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20C22×#11758222C2214yes—
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2212yes—
23#16840472C22132yescomplemented
24#16840467C22132yescomplemented
25#16840462C22132yescomplemented
26#16840456C22132yescomplemented
27#16840453C22132yescomplemented
28#16840451C22132yescomplemented
29#16840417C22132yescomplemented
30#16840413C22132yescomplemented
31#16840390C22116yescomplemented
32#16840354C22164yescomplemented
33#16840340C22116yescomplemented
34C2×#14519777C2212yescomplemented
35C2×#14519776C2212yescomplemented
36C2×#14519771C2214yescomplemented
37C2×#14519770C2214yescomplemented
38C2×#14519769C2212yescomplemented
39C2×#14519769C2214yescomplemented
40C2×#14519768C2212yescomplemented
41C2×#14519767C2214yescomplemented
42#16840274C22116yescomplemented
43#16840271C22164yescomplemented
44#16840269C22116yescomplemented
45C2×#14519762C2214yes—
46C2×#14519761C2212yes—
47C2×#14519760C2214yescomplemented
48C2×#14519759C2214yes—
49C2×#14519759C2214yescomplemented
50C2×#14519758C2212yes—
51C2×#14519757C2211yescharacteristic
52C2×#14519757C2211yescharacteristic
53C2×#14519756C2214yescomplemented
54C2×#14519756C2212yescomplemented
55C2×#14519755C2214yes—
56C2×#14519755C2214yescomplemented
57C2×#14519754C2214yes—
58C2×#14519753C2211yescharacteristic
59C2×#14519753C2211yescharacteristic
60C2×#14519753C2212yescomplemented
61C2×#14519752C2211yescharacteristic
62C2×#14519752C2211yescharacteristic
63C2×#14519751C2212yescomplemented
64C2×#14519750C2214yes—
65C2×#14519749C2214yes—
66C2×#14519748C2211yescharacteristic
67C2×#14519748C2211yescharacteristic
68C2×#14519748C2212yescomplemented
69C2×#14519747C2212yes—
70C2×#14519745C2212yes—
71#16840243C22116yescomplemented
72C2×#14519742C2212yescomplemented
73C2×C4×D244C2212yes—
74C2×C4×D244C2214yes—
75C2×C4×D244C2212yes—
76C2×#14519739C2212yescomplemented
77C2×C4×C22⋊D61C2214yes—
78C2×C4×C22⋊D61C2212yes—
79C2×C4×C22⋊D61C2212yes—
80C2×C4×C22⋊D61C2214yes—
81C2×#14519736C2211yescharacteristic
82C2×#14519735C2212yescomplemented
83C2×#14519734C2214yes—
84C22×C4⋊Dic61C2211yescharacteristic
85C22×#11758196C2212yes—
86C2×C4⋊C4×D61C2212yes—
87C2×C4⋊C4×D61C2212yes—
88C2×C4⋊C4×D61C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C2×C4⋊C4×D61C22116yescomplemented
91C2×C4⋊C4×D61C2212yescomplemented
92C22×#41×C61C2211yescharacteristic
93C61×#520C22116yescomplemented
94C2×C4×Q8×C61C2212yescomplemented
95C2×C4×D4×C61C2214yes—
96C2×C4×D4×C61C2212yescomplemented
97C2×#117×C61C2211yescharacteristic
98C2×#117×C61C2212yescomplemented
99C22×C4⋊C4×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2212yescomplemented
101C24×D61C2311yescharacteristic
102C2×#11758222—28no—
103C2×#11758222—416no—
104C2×#11758222C2318yes—
105C2×#11758222C23132yes—
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2314yes—
108C22×D244C2311yescharacteristic
109C22×D244C2312yes—
110C22×D244C2312yes—
111C22×C22⋊D61C2312yes—
112C22×C22⋊D61C2312yes—
113C22×C22⋊D61C2312yes—
114C22×C22⋊D61C2314yes—
115C23×Dic61C2311yescharacteristic
116C23×Dic61C2312yes—
117C22×C4×D61—28no—
118C22×C4×D61—48no—
119C22×C4×D61C2314yes—
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2318yes—
125C22×C4×D61C2312yes—
126C22×C4×D61C2314yes—
127C22×C4×D61C23116yes—
128C22×C4×D61C2314yes—
129#14519777C23116yescomplemented
130#14519776C23116yescomplemented
131#14519771C23132yescomplemented
132#14519770C23132yescomplemented
133#14519769C23132yescomplemented
134#14519769C23116yescomplemented
135#14519768C23116yescomplemented
136#14519767C23132yescomplemented
137#14519762C23132yes—
138#14519761C23116yes—
139#14519760C23132yescomplemented
140#14519759C23132yes—
141#14519759C23132yescomplemented
142#14519758C23116yes—
143#14519757C2318yes—
144#14519757C2318yes—
145#14519756C23116yescomplemented
146#14519756C23132yescomplemented
147#14519755C23132yes—
148#14519755C23132yescomplemented
149#14519754C23132yes—
150#14519753C2318yes—
151#14519753C2318yes—
152#14519753C23116yescomplemented
153#14519752C2318yes—
154#14519752C2318yes—
155#14519751C23116yescomplemented
156#14519750C23132yes—
157#14519749C23132yes—
158#14519748C2318yes—
159#14519748C2318yes—
160#14519748C23116yescomplemented
161#14519747C23116yes—
162#14519745C23116yes—
163#14519742C23116yescomplemented
164C4×D244C23116yes—
165C4×D244C23132yes—
166C4×D244C23116yes—
167#14519739C23116yescomplemented
168C4×C22⋊D61C23116yes—
169C4×C22⋊D61C23116yes—
170C4×C22⋊D61C23132yes—
171C4×C22⋊D61C23132yes—
172#14519736C2318yes—
173#14519735C23116yescomplemented
174#14519734C23132yes—
175C2×C4⋊Dic61C2312yes—
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2318yes—
178C2×C4⋊Dic61C2311yescharacteristic
179C2×C4⋊Dic61C2311yescharacteristic
180C2×C4⋊Dic61C2314yes—
181C2×C4⋊Dic61C2312yes—
182C2×C4⋊Dic61C2312yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
185C2×#11758196C23116yes—
186C2×#11758196C2314yes—
187C2×#11758196C2314yes—
188C2×#11758196C2314yes—
189C2×#11758196C2312yes—
190C2×#11758196C2312yes—
191C2×#11758196C2314yes—
192C4⋊C4×D61C23116yes—
193C4⋊C4×D61C23116yes—
194C4⋊C4×D61C23116yes—
195C4⋊C4×D61C23116yes—
196C4⋊C4×D61C23116yescomplemented
197C2×C22⋊Dic61C2312yes—
198C2×C22⋊Dic61C2312yes—
199C2×C22⋊Dic61C2312yes—
200C2×C22⋊Dic61C2314yes—
201C2×#11758198C2312yes—
202C2×#11758198C2312yes—
203C2×#11758198C2314yes—
204C2×#11758198C2312yes—
205C2×#11758198C2312yes—
206C2×#11758198C2314yes—
207C2×#11758198C2312yes—
208C2×#11758198C2312yes—
209C2×C4×Dic61C2314yes—
210C2×C4×Dic61C2312yes—
211C2×#41×C61—28no—
212C2×#41×C61C2318yes—
213C22×Q8×C61C2311yescharacteristic
214C22×D4×C61C2312yes—
215C22×D4×C61C2311yescharacteristic
216C23×C4×C61C2312yes—
217C23×C4×C61C2312yes—
218C23×C4×C61C2314yes—
219C23×C4×C61C2311yescharacteristic
220C4×Q8×C61C23116yescomplemented
221C4×D4×C61C23132yes—
222C4×D4×C61C23116yescomplemented
223#117×C61C2318yes—
224#117×C61C23116yescomplemented
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C4⋊C4×C61C2318yes—
228C2×C4⋊C4×C61C2311yescharacteristic
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C4⋊C4×C61C2314yes—
231C2×C4⋊C4×C61C23116yescomplemented
232C2×C22⋊C4×C61C2312yes—
233C2×C22⋊C4×C61C2314yes—
234C2×C42×C61C2314yes—
235C2×C42×C61C2312yes—
236C24×C61C2412yes—
237C24×C61C2411yescharacteristic
238C23×D61—24no—
239C23×D61—24no—
240C23×D61—24no—
241C23×D61C2414yes—
242C23×D61C2412yes—
243C23×D61C2411yescharacteristic
244C23×D61C2411yescharacteristic
245#41×C61—232no—
246C2×Q8×C61—24no—
247C2×Q8×C61C2414yes—
248C2×D4×C61—28no—
249C2×D4×C61—24no—
250C2×D4×C61C2418yes—
251C2×D4×C61C2414yes—
252C22×C4×C61—28no—
253C22×C4×C61—44no—
254C22×C4×C61—48no—
255C22×C4×C61#4118yescomplemented
256C22×C4×C61C2414yes—
257C22×C4×C61C2412yes—
258C22×C4×C61C2412yes—
259C22×C4×C61C2412yes—
260C22×C4×C61C2418yes—
261C22×C4×C61C2418yes—
262C22×C4×C61C24116yes—
263C22×C4×C61C2411yescharacteristic
264C22×C4×C61C2411yescharacteristic
265C22×C4×C61C2414yes—
266C2×C22⋊D61—28no—
267C2×C22⋊D61—28no—
268C2×C22⋊D61—28no—
269C2×C22⋊D61—48no—
270C2×C22⋊D61C2418yes—
271C2×C22⋊D61C2418yes—
272C2×C22⋊D61C2418yes—
273C2×C22⋊D61C24116yes—
274C22×Dic61—24no—
275C22×Dic61—44no—
276C22×Dic61C2414yes—
277C22×Dic61C2411yescharacteristic
278C22×Dic61C2411yescharacteristic
279C22×Dic61C2414yes—
280C22×Dic61C2412yes—
281C22×Dic61C2412yes—
282C22×Dic61C2412yes—
283C22×Dic61C2418yes—
284#11758222—232no—
285#11758222—464no—
286C2×D244—28no—
287C2×D244—28no—
288C2×D244—24no—
289C2×D244C2418yes—
290C2×D244C2414yes—
291C2×D244C2418yes—
292C2×C4×D61—216no—
293C2×C4×D61—24no—
294C2×C4×D61—24no—
295C2×C4×D61—24no—
296C2×C4×D61—24no—
297C2×C4×D61—28no—
298C2×C4×D61—232no—
299C2×C4×D61—432no—
300C2×C4×D61—48no—
301C2×C4×D61—48no—
302C2×C4×D61C24116yes—
303C2×C4×D61C2414yes—
304C2×C4×D61C2414yes—
305C2×C4×D61C2414yes—
306C2×C4×D61C2414yes—
307C2×C4×D61C2418yes—
308C2×C4×D61C24116yes—
309C2×C4×D61C24116yes—
310C2×Dic122—24no—
311C2×Dic122—48no—
312C2×Dic122C2414yes—
313C2×Dic122C24116yes—
314C4⋊C4×C61C2418yes—
315C4⋊C4×C61C2418yes—
316C4⋊C4×C61C2414yes—
317C4⋊C4×C61C24116yes—
318C4⋊C4×C61C2414yes—
319C22⋊C4×C61C2418yes—
320C22⋊C4×C61C24116yes—
321C42×C61C2418yes—
322C42×C61C24116yes—
323C22⋊Dic61C2418yes—
324C22⋊Dic61C2418yes—
325C22⋊Dic61C2418yes—
326C22⋊Dic61C24116yes—
327#11758198C2418yes—
328#11758198C2418yes—
329#11758198C24116yes—
330#11758198C2418yes—
331#11758198C2418yes—
332#11758198C24116yes—
333#11758198C2418yes—
334#11758198C2418yes—
335C4⋊Dic61C2418yes—
336C4⋊Dic61C2418yes—
337C4⋊Dic61C2414yes—
338C4⋊Dic61C2414yes—
339C4⋊Dic61C24116yes—
340C4⋊Dic61C2418yes—
341C4⋊Dic61C2418yes—
342#11758196C24116yes—
343#11758196C24116yes—
344#11758196C24116yes—
345#11758196C24116yes—
346#11758196C24116yes—
347#11758196C2418yes—
348#11758196C2418yes—
349#11758196C24116yes—
350C4×Dic61C24116yes—
351C4×Dic61C2418yes—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—24no—
355C23×C61—24no—
356C23×C61—24no—
357C23×C61C2×#4114yes—
358C23×C61C2514yes—
359C23×C61C2512yes—
360C23×C61C2511yescharacteristic
361C22×D61—232no—
362C22×D61—28no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—28no—
368C22×D61—28no—
369C22×D61—24no—
370C22×D61—24no—
371C22×D61—24no—
372C22×D61H(5,𝔽2)14yes—
373C22×D612−1+414yes—
374C22×D61C2514yes—
375C22×D61C2512yes—
376C22×D61C2512yes—
377Q8×C61—28no—
378D4×C61—216no—
379D4×C61—28no—
380C2×C4×C61—24no—
381C2×C4×C61—24no—
382C2×C4×C61—28no—
383C2×C4×C61—24no—
384C2×C4×C61—216no—
385C2×C4×C61—48no—
386C2×C4×C61—416no—
387C2×C4×C61C2×#4114yes—
388C2×C4×C61C2×#4114yes—
389C2×C4×C61C2×#41116yescomplemented
390C2×C4×C61C2518yes—
391C2×C4×C61C2514yes—
392C2×C4×C61C2514yes—
393C2×C4×C61C2514yes—
394C2×C4×C61C2512yes—
395C2×C4×C61C2512yes—
396C22⋊D61—216no—
397C22⋊D61—216no—
398C22⋊D61—216no—
399C22⋊D61—416no—
400C2×Dic61—24no—
401C2×Dic61—28no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—24no—
405C2×Dic61—28no—
406C2×Dic61—24no—
407C2×Dic61—48no—
408C2×Dic61C2514yes—
409C2×Dic61C2514yes—
410C2×Dic61C2514yes—
411C2×Dic61C2512yes—
412C2×Dic61C2512yes—
413C2×Dic61C2518yes—
414D244—216no—
415D244—216no—
416D244—28no—
417C4×D61—232no—
418C4×D61—28no—
419C4×D61—28no—
420C4×D61—28no—
421C4×D61—28no—
422C4×D61—216no—
423C4×D61—416no—
424C4×D61—416no—
425Dic122—28no—
426Dic122—416no—
427C2×#3492—611nomaximal, Sylow
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—28no—
431C22×C61—24no—
432C22×C61—24no—
433C22×C61—24no—
434C22×C61—48no—
435C22×C61C22×#4114yes—
436C22×C61C22×#4112yes—
437C22×C61C2×H(5,𝔽2)12yes—
438C22×C61C2×2−1+412yes—
439C22×C61C2611yescharacteristic
440C2×D61—232no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—28no—
446C2×D61—28no—
447C2×D61—24no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—48no—
451C2×D61C2×H(5,𝔽2)14yes—
452C2×D61C2×2−1+414yes—
453C4×C61—24no—
454C4×C61—24no—
455C4×C61—28no—
456C4×C61—24no—
457C4×C61C22×#4114yes—
458C4×C61C22×#4114yes—
459Dic61—24no—
460Dic61—22no—
461Dic61—22no—
462Dic61—24no—
463Dic61—28no—
464Dic61—24no—
465#3492—6132no—
466C2×#554—612no—
467C2×#554—612no—
468C2×#553—612no—
469C2×#553—612no—
470C2×#552—612no—
471C2×#552—612no—
472C2×#547—612no—
473C2×#547—612no—
474C2×#544—611no—
475C2×#539—614no—
476C2×#537—611no—
477C2×#525—611no—
478C2×#525—614no—
479C2×#525—611no—
480C2×#520—611no—
481C2×#520D6111yescharacteristic, complemented
482C23×C4⋊C4—611no—
483C2×C61—24no—
484C2×C61—44no—
485C2×C61#349214yescomplemented
486C2×C61C23×#4111yescharacteristic
487C2×C61C22×H(5,𝔽2)11yescharacteristic
488C2×C61C22×2−1+411yescharacteristic
489D61—24no—
490D61—24no—
491D61—44no—
492C22×#41—611no—
493C22×#41—614no—
494C22×#41C2×D6111yescharacteristic
495C24×C4—611no—
496C24×C4—612no—
497#554—6132no—
498#554—6132no—
499#553—6132no—
500#553—6132no—
501#552—6132no—
502#552—6132no—
503#547—6132no—
504#547—6132no—
505#544—6116no—
506#539—6164no—
507#537—6116no—
508C2×C4⋊Q8—612no—
509C2×C4⋊Q8—612no—
510C2×#126—614no—
511C2×#126—614no—
512C2×#125—614no—
513C2×#125—612no—
514C2×#125—614no—
515C2×#125—612no—
516#525—6116no—
517#525—6164no—
518#525—6116no—
519C2×#123—612no—
520C2×#123—614no—
521C2×#123—614no—
522C2×#123—614no—
523C2×#123—614no—
524C2×#123—612no—
525C2×C22⋊Q8—611no—
526C2×C22⋊Q8—611no—
527C2×C22⋊Q8—612no—
528C2×C22⋊Q8—612no—
529C2×C22⋊Q8—614no—
530C2×C22⋊Q8—614no—
531C2×C22⋊Q8—614no—
532C2×C22⋊Q8—611no—
533C2×C22⋊Q8—611no—
534C2×C22⋊Q8—614no—
535C2×#121—611no—
536C2×#121—611no—
537C2×#121—612no—
538C2×#121—614no—
539C2×#121—612no—
540C2×#121—611no—
541C2×#121—611no—
542C2×#121—614no—
543C2×#120—612no—
544C2×#120—612no—
545#520—6116no—
546#520C2×D61116yescomplemented
547C2×C4×Q8—612no—
548C2×C4×Q8C2×D6112yescomplemented
549C2×C4×D4—614no—
550C2×C4×D4—612no—
551C2×C4×D4—614no—
552C2×C4×D4—612no—
553C2×C4×D4—612no—
554C2×C4×D4—612no—
555C2×C4×D4—614no—
556C2×C4×D4—612no—
557C2×C4×D4C2×D6114yes—
558C2×C4×D4C2×D6112yescomplemented
559C2×#117—611no—
560C2×#117—612no—
561C2×#117—614no—
562C2×#117C2×D6111yescharacteristic
563C2×#117C2×D6112yescomplemented
564C22×C4⋊C4—612no—
565C22×C4⋊C4—611no—
566C22×C4⋊C4—612no—
567C22×C4⋊C4—612no—
568C22×C4⋊C4—612no—
569C22×C4⋊C4—612no—
570C22×C4⋊C4—6116no—
571C22×C4⋊C4—612no—
572C22×C4⋊C4C2×D6111yescharacteristic
573C22×C4⋊C4C2×D6112yescomplemented
574C61C2×#349211yescharacteristic, complemented, Sylow
575C25—611no—
576C2×#41—28no—
577C2×#41—618no—
578C2×#41—6132no—
579C2×#41—1228no—
580C2×#41—24416no—
581C2×#41C22×D6118yes—
582C22×Q8—611no—
583C22×Q8—614no—
584C22×Q8C22×D6111yescharacteristic
585C22×D4—612no—
586C22×D4—612no—
587C22×D4—612no—
588C22×D4—614no—
589C22×D4—612no—
590C22×D4—611no—
591C22×D4—612no—
592C22×D4C22×D6112yes—
593C22×D4C22×D6111yescharacteristic
594C23×C4—611no—
595C23×C4—612no—
596C23×C4—614no—
597C23×C4—611no—
598C23×C4—611no—
599C23×C4—611no—
600C23×C4—611no—
601C23×C4—618no—
602C23×C4—612no—
603C23×C4—614no—
604C23×C4—6116no—
605C23×C4—614no—
606C23×C4—1228no—
607C23×C4—2448no—
608C23×C4C22×D6112yes—
609C23×C4C22×D6112yes—
610C23×C4C22×D6114yes—
611C23×C4C22×D6111yescharacteristic
612C4⋊Q8—6116no—
613C4⋊Q8—6116no—
614#126—6132no—
615#126—6132no—
616#125—6132no—
617#125—6116no—
618#125—6132no—
619#125—6116no—
620#123—6116no—
621#123—6132no—
622#123—6132no—
623#123—6116no—
624#123—6132no—
625#123—6132no—
626C22⋊Q8—618no—
627C22⋊Q8—618no—
628C22⋊Q8—6116no—
629C22⋊Q8—6116no—
630C22⋊Q8—6132no—
631C22⋊Q8—618no—
632C22⋊Q8—6132no—
633C22⋊Q8—618no—
634C22⋊Q8—6132no—
635C22⋊Q8—6132no—
636#121—6132no—
637#121—618no—
638#121—618no—
639#121—6116no—
640#121—6116no—
641#121—618no—
642#121—618no—
643#121—6132no—
644#120—6116no—
645#120—6116no—
646C4×Q8—6116no—
647C4×Q8C22×D61116yescomplemented
648C4×D4—6132no—
649C4×D4—6116no—
650C4×D4—6132no—
651C4×D4—6116no—
652C4×D4—6116no—
653C4×D4—6116no—
654C4×D4—6132no—
655C4×D4—6116no—
656C4×D4C22×D61132yes—
657C4×D4C22×D61116yescomplemented
658#117—618no—
659#117—6116no—
660#117—6132no—
661#117C22×D6118yes—
662#117C22×D61116yescomplemented
663C2×C4⋊C4—612no—
664C2×C4⋊C4—612no—
665C2×C4⋊C4—614no—
666C2×C4⋊C4—614no—
667C2×C4⋊C4—618no—
668C2×C4⋊C4—6116no—
669C2×C4⋊C4—611no—
670C2×C4⋊C4—614no—
671C2×C4⋊C4—611no—
672C2×C4⋊C4—614no—
673C2×C4⋊C4—614no—
674C2×C4⋊C4—612no—
675C2×C4⋊C4—612no—
676C2×C4⋊C4—614no—
677C2×C4⋊C4—614no—
678C2×C4⋊C4—612no—
679C2×C4⋊C4—612no—
680C2×C4⋊C4—6116no—
681C2×C4⋊C4—6116no—
682C2×C4⋊C4—6116no—
683C2×C4⋊C4—6116no—
684C2×C4⋊C4—6116no—
685C2×C4⋊C4C22×D6112yes—
686C2×C4⋊C4C22×D6112yes—
687C2×C4⋊C4C22×D6118yes—
688C2×C4⋊C4C22×D6111yescharacteristic
689C2×C4⋊C4C22×D6114yes—
690C2×C4⋊C4C22×D6111yescharacteristic
691C2×C4⋊C4C22×D61116yescomplemented
692C2×C22⋊C4—612no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—612no—
695C2×C22⋊C4—612no—
696C2×C22⋊C4—612no—
697C2×C22⋊C4—612no—
698C2×C22⋊C4—614no—
699C2×C22⋊C4—612no—
700C2×C22⋊C4—612no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—612no—
703C2×C22⋊C4—612no—
704C2×C22⋊C4C22×D6112yes—
705C2×C22⋊C4C22×D6114yes—
706C2×C42—614no—
707C2×C42—612no—
708C2×C42C22×D6114yes—
709C2×C42C22×D6112yes—
710C24—611no—
711C24—611no—
712C24—614no—
713C24—612no—
714C24—1224no—
715C24—1224no—
716C24—1224no—
717C24C23×D6112yes—
718C24C23×D6111yescharacteristic
719#41—232no—
720#41—12232no—
721#41—24464no—
722C2×Q8—24no—
723C2×Q8—614no—
724C2×Q8—6116no—
725C2×Q8—1224no—
726C2×Q8—2448no—
727C2×Q8C23×D6114yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—618no—
731C2×D4—618no—
732C2×D4—618no—
733C2×D4—6116no—
734C2×D4—618no—
735C2×D4—614no—
736C2×D4—618no—
737C2×D4—1228no—
738C2×D4—1228no—
739C2×D4—1228no—
740C2×D4—1228no—
741C2×D4—1228no—
742C2×D4—1224no—
743C2×D4—2448no—
744C2×D4C23×D6118yes—
745C2×D4C23×D6114yes—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—614no—
750C22×C4—612no—
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—614no—
756C22×C4—618no—
757C22×C4—6116no—
758C22×C4—614no—
759C22×C4—614no—
760C22×C4—614no—
761C22×C4—614no—
762C22×C4—618no—
763C22×C4—6116no—
764C22×C4—6116no—
765C22×C4—12216no—
766C22×C4—1224no—
767C22×C4—1224no—
768C22×C4—1224no—
769C22×C4—1224no—
770C22×C4—1224no—
771C22×C4—1228no—
772C22×C4—12232no—
773C22×C4—2448no—
774C22×C4—2448no—
775C22×C4—24432no—
776C22×C4—2444no—
777C22×C4#1175822218yescomplemented
778C22×C4C23×D6118yes—
779C22×C4C23×D6114yes—
780C22×C4C23×D6112yes—
781C22×C4C23×D6112yes—
782C22×C4C23×D6112yes—
783C22×C4C23×D6118yes—
784C22×C4C23×D61116yes—
785C22×C4C23×D6111yescharacteristic
786C22×C4C23×D6111yescharacteristic
787C22×C4C23×D6114yes—
788C4⋊C4—6116no—
789C4⋊C4—6116no—
790C4⋊C4—618no—
791C4⋊C4—618no—
792C4⋊C4—614no—
793C4⋊C4—6116no—
794C4⋊C4—6116no—
795C4⋊C4—6116no—
796C4⋊C4—618no—
797C4⋊C4—6116no—
798C4⋊C4—618no—
799C4⋊C4—614no—
800C4⋊C4—618no—
801C4⋊C4—6116no—
802C4⋊C4—618no—
803C4⋊C4C23×D6118yes—
804C4⋊C4C23×D6118yes—
805C4⋊C4C23×D6114yes—
806C4⋊C4C23×D61116yes—
807C4⋊C4C23×D6114yes—
808C22⋊C4—618no—
809C22⋊C4—6116no—
810C22⋊C4—618no—
811C22⋊C4—618no—
812C22⋊C4—618no—
813C22⋊C4—618no—
814C22⋊C4—6116no—
815C22⋊C4—618no—
816C22⋊C4—618no—
817C22⋊C4—6116no—
818C22⋊C4—618no—
819C22⋊C4—618no—
820C22⋊C4C23×D6118yes—
821C22⋊C4C23×D61116yes—
822C42—6116no—
823C42—618no—
824C42C23×D61116yes—
825C42C23×D6118yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—614no—
832C23—614no—
833C23—612no—
834C23—612no—
835C23—614no—
836C23—1228no—
837C23—1228no—
838C23—12232no—
839C23—1228no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—1224no—
845C23—1224no—
846C23—1224no—
847C23C2×#1175822214yes—
848C23C24×D6114yes—
849C23C24×D6112yes—
850C23C24×D6111yescharacteristic
851Q8—28no—
852Q8—1228no—
853Q8—24416no—
854D4—216no—
855D4—28no—
856D4—12216no—
857D4—12216no—
858D4—12216no—
859D4—12216no—
860D4—12216no—
861D4—1228no—
862D4—24416no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—614no—
871C2×C4—614no—
872C2×C4—614no—
873C2×C4—612no—
874C2×C4—612no—
875C2×C4—618no—
876C2×C4—12232no—
877C2×C4—1228no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1224no—
881C2×C4—1228no—
882C2×C4—1224no—
883C2×C4—1224no—
884C2×C4—1228no—
885C2×C4—1228no—
886C2×C4—1228no—
887C2×C4—1228no—
888C2×C4—12216no—
889C2×C4—24416no—
890C2×C4—24416no—
891C2×C4—2448no—
892C2×C4C2×#1175822214yes—
893C2×C4C2×#1175822214yes—
894C2×C4C2×#11758222116yescomplemented
895C2×C4C24×D6118yes—
896C2×C4C24×D6114yes—
897C2×C4C24×D6114yes—
898C2×C4C24×D6114yes—
899C2×C4C24×D6112yes—
900C2×C4C24×D6112yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—614no—
909C22—614no—
910C22—12232no—
911C22—1228no—
912C22—1228no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1224no—
918C22—1224no—
919C22—1224no—
920C22—2448no—
921C22C22×#1175822214yes—
922C22C22×#1175822212yes—
923C22H(5,𝔽2)×D6112yes—
924C222−1+4×D6112yes—
925C22C25×D6111yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—1222no—
931C4—1222no—
932C4—1224no—
933C4—1228no—
934C4—1224no—
935C4—1224no—
936C4C22×#1175822214yes—
937C4C22×#1175822214yes—
938C2—24no—
939C2—44no—
940C2—1224no—
941C2—1224no—
942C2—2444no—
943C2#2145952214yesdirect product factor
944C2C23×#1175822211yescharacteristic
945C2C2×H(5,𝔽2)×D6111yescharacteristic
946C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#520C2
socleC23×C61C25
hypercenterC2×#520D61
hypocenterC61C2×#3492
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21459522C2direct (N × H)
2. C2×#16840472C2semidirect
3. C2×#16840467C2semidirect
4. C2×#16840462C2semidirect
5. C2×#16840456C2semidirect
6. C2×#16840453C2semidirect
7. C2×#16840451C2semidirect
8. C2×#16840417C2semidirect
9. C2×#16840413C2semidirect
10. C2×#16840390C2semidirect
11. C2×#16840354C2semidirect
12. C2×#16840340C2semidirect
13. C2×#16840274C2semidirect
14. C2×#16840271C2semidirect
15. C2×#16840269C2semidirect
16. C2×#16840243C2semidirect
17. C22×C4⋊C4×D61C2semidirect
18. C2×C61×#520C2semidirect
23. #16840472C22semidirect
24. #16840467C22semidirect
25. #16840462C22semidirect
26. #16840456C22semidirect
27. #16840453C22semidirect
28. #16840451C22semidirect
29. #16840417C22semidirect
30. #16840413C22semidirect
31. #16840390C22semidirect
32. #16840354C22semidirect
33. #16840340C22semidirect
34. C2×#14519777C22semidirect
35. C2×#14519776C22semidirect
36. C2×#14519771C22semidirect
37. C2×#14519770C22semidirect
38. C2×#14519769C22semidirect
39. C2×#14519769C22semidirect
40. C2×#14519768C22semidirect
41. C2×#14519767C22semidirect
42. #16840274C22semidirect
43. #16840271C22semidirect
44. #16840269C22semidirect
47. C2×#14519760C22semidirect
49. C2×#14519759C22semidirect
53. C2×#14519756C22semidirect
54. C2×#14519756C22semidirect
56. C2×#14519755C22semidirect
60. C2×#14519753C22semidirect
63. C2×#14519751C22semidirect
68. C2×#14519748C22semidirect
71. #16840243C22semidirect
72. C2×#14519742C22semidirect
76. C2×#14519739C22semidirect
82. C2×#14519735C22semidirect
90. C2×C4⋊C4×D61C22semidirect
91. C2×C4⋊C4×D61C22semidirect
93. C61×#520C22semidirect
94. C2×C4×Q8×C61C22semidirect
96. C2×C4×D4×C61C22semidirect
98. C2×#117×C61C22semidirect
100. C22×C4⋊C4×C61C22semidirect
129. #14519777C23semidirect
130. #14519776C23semidirect
131. #14519771C23semidirect
132. #14519770C23semidirect
133. #14519769C23semidirect
134. #14519769C23semidirect
135. #14519768C23semidirect
136. #14519767C23semidirect
139. #14519760C23semidirect
141. #14519759C23semidirect
145. #14519756C23semidirect
146. #14519756C23semidirect
148. #14519755C23semidirect
152. #14519753C23semidirect
155. #14519751C23semidirect
160. #14519748C23semidirect
163. #14519742C23semidirect
167. #14519739C23semidirect
173. #14519735C23semidirect
196. C4⋊C4×D61C23semidirect
220. C4×Q8×C61C23semidirect
222. C4×D4×C61C23semidirect
224. #117×C61C23semidirect
231. C2×C4⋊C4×C61C23semidirect
255. C22×C4×C61#41semidirect
389. C2×C4×C61C2×#41semidirect
481. C2×#520D61semidirect
485. C2×C61#3492semidirect
546. #520C2×D61semidirect
548. C2×C4×Q8C2×D61semidirect
558. C2×C4×D4C2×D61semidirect
563. C2×#117C2×D61semidirect
573. C22×C4⋊C4C2×D61semidirect
574. C61C2×#3492semidirect
647. C4×Q8C22×D61semidirect
657. C4×D4C22×D61semidirect
662. #117C22×D61semidirect
691. C2×C4⋊C4C22×D61semidirect
777. C22×C4#11758222semidirect
894. C2×C4C2×#11758222semidirect
943. C2#21459522direct (N × H)

Maximal subgroups

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

subgroupindex
#214595222
C2×#168404722
C2×#168404672
C2×#168404622
C2×#168404562
C2×#168404532
C2×#168404512
C2×#168404172
C2×#168404132
C2×#168403902
C2×#168403542
C2×#168403402
C2×#168402742
C2×#168402712
C2×#168402692
C2×#168402432
C22×C4⋊C4×D612
C2×C61×#5202
C2×#349261