Finite Group Databasebeta

← #29696142

Subgroups — #29696142

Order 15616.

1696 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840402C211yesmaximal, characteristic
2C22⋊C4×C22⋊D61C212yesmaximal, complemented
3#21446802C212yesmaximal, complemented
4#21446272C212yesmaximal, complemented
5#21446271C212yesmaximal, complemented
6#21445893C211yesmaximal, characteristic, complemented
7#21445892C211yesmaximal, characteristic, complemented
8#21445806C211yesmaximal, characteristic, complemented
9#21445606C211yesmaximal, characteristic, complemented
10#342×D61C211yesmaximal, characteristic, complemented
11C2×C61×#342C211yesmaximal, characteristic, complemented
12C22×#11758222C411yescharacteristic, complemented
13C23×C22⋊D61C2211yescharacteristic
14#16840402—22no—
15#16840402—22no—
16#16840402—22no—
17#16840402—22no—
18C2×#14519763C411yescharacteristic, complemented
19C2×#14519760C411yescharacteristic, complemented
20C2×#14519759C411yescharacteristic, complemented
21C2×#14519754C2211yescharacteristic
22C2×#14519751C411yescharacteristic, complemented
23C2×#14519750C411yescharacteristic, complemented
24C2×#14519750C411yescharacteristic, complemented
25C2×#14519747C2211yescharacteristic
26C2×#14519746C2211yescharacteristic
27C2×C4×C22⋊D61—22no—
28C2×C4×C22⋊D61C411yescharacteristic, complemented
29C2×#14519737C2211yescharacteristic
30C2×C22⋊C4×D61C2212yes—
31C2×C22⋊C4×D61C2211yescharacteristic
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839662—22no—
35#16839641—22no—
36#16839638—22no—
37#16839620C2212yes—
38#16839618C2212yes—
39#16839617C2212yes—
40C22⋊C4×Dic61C2212yes—
41#16839529C2211yescharacteristic
42#16839529C2212yes—
43#16839529C2211yescharacteristic
44#16839528C2212yes—
45#16839528C2212yes—
46C22×C22⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2212yes—
48C61×#342C2211yescharacteristic
49C61×#342C2212yes—
50C61×#342C2211yescharacteristic
51C24×D61C2311yescharacteristic
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—44no—
57C22×Dic122C2×C411yescharacteristic, complemented
58C22×D244C2×C411yescharacteristic, complemented
59C22×D244C2×C411yescharacteristic, complemented
60C22×C22⋊D61—44no—
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic, complemented
66C22×C22⋊D61C2×C411yescharacteristic, complemented
67C22×C22⋊D61D412yes—
68C22×C22⋊D61D412yes—
69C22×C22⋊D61D412yes—
70C22×C22⋊D61D412yes—
71C22×C22⋊D61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61C2×C411yescharacteristic, complemented
75C22×C4×D61C2×C411yescharacteristic, complemented
76C22×C4×D61C2×C411yescharacteristic, complemented
77#14519763—22no—
78#14519763—22no—
79#14519760—22no—
80#14519760—22no—
81#14519759—22no—
82#14519759—22no—
83#14519754—22no—
84#14519754—22no—
85#14519751—22no—
86#14519751—22no—
87#14519750—22no—
88#14519750—22no—
89#14519750—22no—
90#14519750—22no—
91#14519747—22no—
92#14519747—22no—
93#14519746—22no—
94#14519746—22no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98C4×C22⋊D61—21no—
99C4×C22⋊D61—48no—
100#14519737—22no—
101#14519737—22no—
102C2×C4⋊Dic61C2×C411yescharacteristic, complemented
103C2×#11758196—22no—
104C2×#11758196C2×C411yescharacteristic, complemented
105C2×#11758196C2×C411yescharacteristic, complemented
106C2×#11758196C2×C411yescharacteristic, complemented
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—22no—
109C2×C22⋊Dic61C2×C411yescharacteristic, complemented
110C2×C22⋊Dic61C2×C411yescharacteristic, complemented
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2311yescharacteristic
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198C2×C411yescharacteristic, complemented
118C2×#11758198C2×C411yescharacteristic, complemented
119C2×#11758198C2×C411yescharacteristic, complemented
120C2×#11758198C2×C411yescharacteristic, complemented
121C2×#11758198C2×C411yescharacteristic, complemented
122C22⋊C4×D61—22no—
123C22⋊C4×D61—22no—
124C22⋊C4×D61—24no—
125C22⋊C4×D61—42no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61C2×C411yescharacteristic, complemented
128#14519691—24no—
129#14519691—42no—
130#14519684—22no—
131#14519684—22no—
132C25×C61C2311yescharacteristic
133C23×C4×C61—22no—
134C23×C4×C61C2×C411yescharacteristic, complemented
135C23×C4×C61C2×C411yescharacteristic, complemented
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—24no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—42no—
141C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
142C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
143C2×C22⋊C4×C61C2312yes—
144C2×C22⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61C2312yes—
147C24×C61—22no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C24×C61C2×D412yes—
155C24×C61C2×D412yes—
156C24×C61C2411yescharacteristic
157C23×D61—22no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—42no—
161C23×D61—81no—
162C23×D61C22×C411yescharacteristic
163C23×D61C22×C411yescharacteristic
164C23×D61C22×C411yescharacteristic
165C23×D61C2×D412yes—
166C23×D61C2×D412yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—22no—
173C22×C4×C61—44no—
174C22×C4×C61—42no—
175C22×C4×C61—44no—
176C22×C4×C61—82no—
177C22×C4×C61—81no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C2×C22⋊D61—24no—
183C2×C22⋊D61—28no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—44no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—44no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—81no—
199C2×C22⋊D61C22⋊C411yescharacteristic
200C2×C22⋊D61C22⋊C411yescharacteristic
201C2×C22⋊D61C22⋊C411yescharacteristic
202C2×C22⋊D61C22⋊C412yes—
203C2×C22⋊D61C22⋊C412yes—
204C2×C22⋊D61C22⋊C412yes—
205C2×C22⋊D61C22⋊C412yes—
206C2×C22⋊D61C22⋊C412yes—
207C2×C22⋊D61C22⋊C412yes—
208C2×C22⋊D61C22⋊C411yescharacteristic
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—42no—
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C2×D412yes—
218C22×Dic61C2×D412yes—
219#11758222—44no—
220#11758222—44no—
221#11758222—44no—
222#11758222—44no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—22no—
226C2×D244—42no—
227C2×D244—81no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—82no—
239C2×C4×D61—81no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—42no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—44no—
251C22⋊C4×C61#4114yescomplemented
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61—22no—
257C22⋊Dic61—22no—
258C22⋊Dic61—22no—
259C22⋊Dic61—22no—
260C22⋊Dic61—44no—
261C22⋊Dic61—82no—
262#11758198—22no—
263#11758198—22no—
264#11758198—21no—
265#11758198—21no—
266#11758198—22no—
267#11758198—22no—
268#11758198—44no—
269#11758198—44no—
270#11758198—82no—
271C4⋊Dic61—22no—
272#11758196—22no—
273#11758196—21no—
274#11758196—21no—
275#11758196—22no—
276#11758196—44no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—44no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—24no—
285C23×C61—22no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—42no—
293C23×C61—41no—
294C23×C61—42no—
295C23×C61—41no—
296C23×C61—42no—
297C23×C61—41no—
298C23×C61—84no—
299C23×C61—82no—
300C23×C61—82no—
301C23×C61C2×C22⋊C412yes—
302C23×C61C2×C22⋊C411yescharacteristic
303C23×C61C2×C22⋊C411yescharacteristic
304C23×C61C23×C411yescharacteristic
305C23×C61C22×D412yes—
306C23×C61C2×#4112yes—
307C23×C61H(5,𝔽2)11yescharacteristic
308C23×C612−1+411yescharacteristic
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—24no—
318C22×D61—22no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—41no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—42no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—82no—
331C22×D61—84no—
332C22×D61—82no—
333C22×D61C2×C22⋊C412yes—
334C22×D61C2×C22⋊C411yescharacteristic
335C22×D61C2×C22⋊C411yescharacteristic
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—24no—
341C2×C4×C61—42no—
342C2×C4×C61—42no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—81no—
353C2×C4×C61—81no—
354C2×C4×C61—88no—
355C22⋊D61—22no—
356C22⋊D61—24no—
357C22⋊D61—22no—
358C22⋊D61—24no—
359C22⋊D61—22no—
360C22⋊D61—24no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—42no—
364C22⋊D61—42no—
365C22⋊D61—42no—
366C22⋊D61—42no—
367C22⋊D61—42no—
368C22⋊D61—82no—
369C22⋊D61#9914yescomplemented
370C2×Dic61—24no—
371C2×Dic61—22no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—41no—
378C2×Dic61—42no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—42no—
384C2×Dic61—42no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C412yes—
389C2×Dic61C2×C22⋊C411yescharacteristic
390D244—42no—
391D244—42no—
392D244—82no—
393C4×D61—42no—
394C4×D61—42no—
395C4×D61—42no—
396C4×D61—42no—
397C4×D61—81no—
398C4×D61—81no—
399C4×D61—88no—
400Dic122—42no—
401Dic122—42no—
402#22476—611nomaximal, Sylow
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—21no—
406C22×C61—22no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—22no—
411C22×C61—21no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—21no—
415C22×C61—42no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—44no—
419C22×C61—44no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—82no—
423C22×C61—82no—
424C22×C61—81no—
425C22×C61—81no—
426C22×C61C2×#9912yes—
427C22×C61C22×C22⋊C411yescharacteristic
428C22×C61C4×#4111yescharacteristic
429C22×C61#52011yescharacteristic
430C22×C61#54612yes—
431C22×C61#54712yes—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—22no—
436C2×D61—21no—
437C2×D61—22no—
438C2×D61—21no—
439C2×D61—22no—
440C2×D61—44no—
441C2×D61—44no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—82no—
448C2×D61—82no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61C2×#9912yes—
454C4×C61—44no—
455C4×C61—41no—
456C4×C61—41no—
457C4×C61—41no—
458C4×C61—41no—
459C4×C61—82no—
460Dic61—21no—
461Dic61—22no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61—82no—
466Dic61—82no—
467Dic61C2×#9912yes—
468C2×#546—611no—
469D4×C22⋊C4—612no—
470#1996—612no—
471#1898—612no—
472#1898—612no—
473#1819—611no—
474#1819—611no—
475#1799—611no—
476C4×#99—611no—
477C2×#342—611no—
478C2×#342D6111yescharacteristic, complemented
479C2×C61—22no—
480C2×C61—22no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—22no—
484C2×C61—41no—
485C2×C61—42no—
486C2×C61#233911yescharacteristic
487C2×C61C22×#9911yescharacteristic
488C2×C61#288311yescharacteristic
489D61—22no—
490D61—41no—
491D61—42no—
492D61—81no—
493C22×#41—611no—
494C23×D4—611no—
495#546—1222no—
496#546—1222no—
497#546—1222no—
498#546—1222no—
499C2×#124—611no—
500C2×#123—611no—
501C2×#123—611no—
502C2×C22⋊Q8—611no—
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—611no—
506C2×#120—611no—
507C2×#120—611no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×C4×D4—1222no—
511C22×C22⋊C4—611no—
512C22×C22⋊C4—612no—
513C22×C22⋊C4C2×D6111yescharacteristic
514C22×C22⋊C4C2×D6112yes—
515C2×#99—612no—
516C2×#99—612no—
517#390—1222no—
518#386—1222no—
519#386—1222no—
520#380—612no—
521#379—612no—
522#379—612no—
523C4×C22⋊C4—612no—
524#342—611no—
525#342—611no—
526#342—612no—
527#342—612no—
528#342—612no—
529#342C2×D6111yescharacteristic
530#342C2×D6112yes—
531#342C2×D6111yescharacteristic
532C61#2247611yescharacteristic, complemented, Sylow
533C25—611no—
534C25C22×D6111yescharacteristic
535C2×#41—1221no—
536C2×#41—1221no—
537C2×#41—1221no—
538C2×#41—1221no—
539C2×#41—2444no—
540C22×Q8—611no—
541C22×D4—611no—
542C22×D4—612no—
543C22×D4—611no—
544C22×D4—611no—
545C22×D4—611no—
546C22×D4—612no—
547C22×D4—612no—
548C22×D4—612no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—611no—
553C22×D4—611no—
554C22×D4—2444no—
555C23×C4—22no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—1222no—
561C23×C4C4×D6111yescharacteristic, complemented
562C23×C4C4×D6111yescharacteristic, complemented
563#124—1222no—
564#124—1222no—
565#123—1222no—
566#123—1222no—
567#123—1222no—
568#123—1222no—
569C22⋊Q8—1222no—
570C22⋊Q8—1222no—
571#121—1222no—
572#121—1222no—
573#121—1222no—
574#121—1222no—
575#121—1222no—
576#121—1222no—
577#120—1222no—
578#120—1222no—
579#120—1222no—
580#120—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—2448no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—611no—
602C2×C22⋊C4—611no—
603C2×C22⋊C4—611no—
604C2×C22⋊C4—611no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—612no—
607C2×C22⋊C4—612no—
608C2×C22⋊C4—1222no—
609C2×C22⋊C4—1222no—
610C2×C22⋊C4—1224no—
611C2×C22⋊C4—1222no—
612C2×C22⋊C4—1222no—
613C2×C22⋊C4—1222no—
614C2×C22⋊C4—1222no—
615C2×C22⋊C4—1222no—
616C2×C22⋊C4—2442no—
617C2×C22⋊C4C4×D6111yescharacteristic, complemented
618C2×C22⋊C4C4×D6111yescharacteristic, complemented
619C2×C22⋊C4C22×D6112yes—
620C2×C22⋊C4C22×D6111yescharacteristic
621C2×C22⋊C4C22×D6111yescharacteristic
622C2×C22⋊C4C22×D6112yes—
623C2×C42—611no—
624C2×C42—1222no—
625#99—1224no—
626#99—2442no—
627#95—1222no—
628#95—1222no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—42no—
633C24—81no—
634C24—611no—
635C24—612no—
636C24—611no—
637C24—612no—
638C24—611no—
639C24—1222no—
640C24—1221no—
641C24—1221no—
642C24—4881no—
643C24—2442no—
644C24C2×C4×D6111yescharacteristic
645C24C2×C4×D6111yescharacteristic
646C24D4×D6112yes—
647C24D4×D6112yes—
648C24C23×D6111yescharacteristic
649#41—2444no—
650#41—2444no—
651#41—2444no—
652#41—2444no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—2442no—
656C2×D4—611no—
657C2×D4—611no—
658C2×D4—611no—
659C2×D4—611no—
660C2×D4—612no—
661C2×D4—612no—
662C2×D4—612no—
663C2×D4—612no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—1222no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1228no—
670C2×D4—1224no—
671C2×D4—1222no—
672C2×D4—1222no—
673C2×D4—1222no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—4881no—
679C2×D4—4881no—
680C2×D4—2442no—
681C2×D4—2444no—
682C2×D4—2442no—
683C2×D4—2442no—
684C2×D4—2444no—
685C2×D4—2442no—
686C2×D4—2444no—
687C2×D4—2442no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—44no—
697C22×C4—82no—
698C22×C4—81no—
699C22×C4—611no—
700C22×C4—612no—
701C22×C4—611no—
702C22×C4—612no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—4882no—
715C22×C4—4881no—
716C22×C4—2444no—
717C22×C4—2442no—
718C22×C4—2444no—
719C22×C4—2442no—
720C22×C4—2442no—
721C22×C4C2×C4×D6111yescharacteristic
722C22×C4C2×C4×D6111yescharacteristic
723C22×C4C2×C4×D6111yescharacteristic
724C22×C4C2×C4×D6111yescharacteristic
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1222no—
728C4⋊C4—1222no—
729C4⋊C4—1222no—
730C4⋊C4—2444no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—44no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1222no—
745C22⋊C4—1222no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1222no—
753C22⋊C4—4882no—
754C22⋊C4—4882no—
755C22⋊C4—2444no—
756C22⋊C4—2444no—
757C22⋊C4—2444no—
758C22⋊C4#1175822214yescomplemented
759C42—1221no—
760C42—1221no—
761C42—2444no—
762C23—21no—
763C23—24no—
764C23—22no—
765C23—21no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—41no—
773C23—42no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—41no—
778C23—41no—
779C23—42no—
780C23—84no—
781C23—82no—
782C23—82no—
783C23—611no—
784C23—612no—
785C23—611no—
786C23—1224no—
787C23—1222no—
788C23—1221no—
789C23—1221no—
790C23—1222no—
791C23—1222no—
792C23—1221no—
793C23—1221no—
794C23—1222no—
795C23—1222no—
796C23—1221no—
797C23—1221no—
798C23—1221no—
799C23—4884no—
800C23—4882no—
801C23—4882no—
802C23—2442no—
803C23—2441no—
804C23—2442no—
805C23—2441no—
806C23—2442no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23C22⋊C4×D6112yes—
811C23C22⋊C4×D6111yescharacteristic
812C23C22⋊C4×D6111yescharacteristic
813C23C22×C4×D6111yescharacteristic
814C23C2×D4×D6112yes—
815C23C2×#1175822212yes—
816C23#1451982211yescharacteristic
817C23#1451982511yescharacteristic
818Q8—2442no—
819Q8—2442no—
820D4—614no—
821D4—1224no—
822D4—1222no—
823D4—1224no—
824D4—1222no—
825D4—1224no—
826D4—1222no—
827D4—4882no—
828D4—4882no—
829D4—2442no—
830D4—2442no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4—2442no—
836D4—2442no—
837D4—2442no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—88no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—612no—
860C2×C4—1224no—
861C2×C4—1222no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—4888no—
868C2×C4—4881no—
869C2×C4—4881no—
870C2×C4—2442no—
871C2×C4—2442no—
872C2×C4—2442no—
873C2×C4—2442no—
874C2×C4—2442no—
875C2×C4—2441no—
876C2×C4—2442no—
877C2×C4—2442no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2441no—
883C2×C4—2441no—
884C22—22no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—21no—
893C22—22no—
894C22—21no—
895C22—22no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—82no—
904C22—82no—
905C22—81no—
906C22—81no—
907C22—612no—
908C22—1221no—
909C22—1221no—
910C22—1221no—
911C22—1222no—
912C22—1221no—
913C22—1222no—
914C22—1222no—
915C22—1221no—
916C22—4881no—
917C22—4881no—
918C22—4882no—
919C22—4882no—
920C22—4881no—
921C22—4881no—
922C22—2444no—
923C22—2444no—
924C22—2442no—
925C22—2442no—
926C22—2441no—
927C22—2441no—
928C22—2441no—
929C22#99×D6112yes—
930C22C2×C22⋊C4×D6111yescharacteristic
931C22C4×#1175822211yescharacteristic
932C22#1684024311yescharacteristic
933C22#1684040212yes—
934C22#1684041312yes—
935C4—44no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—82no—
941C4—612no—
942C4—1221no—
943C4—1222no—
944C4—4882no—
945C4—4882no—
946C4—2441no—
947C4—2441no—
948C4—2441no—
949C2—22no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—21no—
954C2—41no—
955C2—42no—
956C2—1222no—
957C2—4881no—
958C2—2441no—
959C2—2442no—
960C2#2144864611yescharacteristic
961C2C2×#99×D6111yescharacteristic
962C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840402C2
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61#22476
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C22⋊D61C2semidirect
3. #21446802C2semidirect
4. #21446272C2semidirect
5. #21446271C2semidirect
6. #21445893C2semidirect
7. #21445892C2semidirect
8. #21445806C2semidirect
9. #21445606C2semidirect
10. #342×D61C2semidirect
11. C2×C61×#342C2semidirect
12. C22×#11758222C4semidirect
18. C2×#14519763C4semidirect
19. C2×#14519760C4semidirect
20. C2×#14519759C4semidirect
22. C2×#14519751C4semidirect
23. C2×#14519750C4semidirect
24. C2×#14519750C4semidirect
28. C2×C4×C22⋊D61C4semidirect
57. C22×Dic122C2×C4semidirect
58. C22×D244C2×C4semidirect
59. C22×D244C2×C4semidirect
65. C22×C22⋊D61C2×C4semidirect
66. C22×C22⋊D61C2×C4semidirect
74. C22×C4×D61C2×C4semidirect
75. C22×C4×D61C2×C4semidirect
76. C22×C4×D61C2×C4semidirect
102. C2×C4⋊Dic61C2×C4semidirect
104. C2×#11758196C2×C4semidirect
105. C2×#11758196C2×C4semidirect
106. C2×#11758196C2×C4semidirect
109. C2×C22⋊Dic61C2×C4semidirect
110. C2×C22⋊Dic61C2×C4semidirect
117. C2×#11758198C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
120. C2×#11758198C2×C4semidirect
121. C2×#11758198C2×C4semidirect
127. C2×C4×Dic61C2×C4semidirect
134. C23×C4×C61C2×C4semidirect
135. C23×C4×C61C2×C4semidirect
141. C2×C22⋊C4×C61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
251. C22⋊C4×C61#41semidirect
369. C22⋊D61#99semidirect
478. C2×#342D61semidirect
532. C61#22476semidirect
561. C23×C4C4×D61semidirect
562. C23×C4C4×D61semidirect
617. C2×C22⋊C4C4×D61semidirect
618. C2×C22⋊C4C4×D61semidirect
758. C22⋊C4#11758222semidirect

Maximal subgroups

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

subgroupindex
C2×#168404022
C22⋊C4×C22⋊D612
#214468022
#214462722
#214462712
#214458932
#214458922
#214458062
#214456062
#342×D612
C2×C61×#3422
#2247661