Finite Group Databasebeta

← #29603152

Subgroups — #29603152

Order 15616.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519752C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic, complemented
3C2×#16839664C212yesmaximal, complemented
4C2×#16839663C211yesmaximal, characteristic, complemented
5C2×#16839661C211yesmaximal, characteristic, complemented
6C2×#16839619C211yesmaximal, characteristic, complemented
7C2×C4×#11758198C211yesmaximal, characteristic, complemented
8#21444065C212yesmaximal, complemented
9#21444059C212yesmaximal, complemented
10#21444057C212yesmaximal, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×D244C2212yes—
14C23×C4×D61C2211yescharacteristic
15C2×#14519752—24no—
16C2×#14519752—24no—
17C2×#14519752C418yescomplemented
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2212yes—
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2212yes—
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2212yes—
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2212yes—
28C22×C4×Dic61C2211yescharacteristic
29#16839664—28no—
30#16839664—24no—
31#16839663—24no—
32#16839661—24no—
33#16839619—24no—
34C4×#11758198—24no—
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2212yes—
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C4⋊C4×C61C2211yescharacteristic
41C22×C42×C61C2212yes—
42C22×C42×C61C2211yescharacteristic
43C4×C4⋊C4×C61—24no—
44C2×#95×C61C2212yes—
45C24×D61C2312yes—
46C24×D61C2311yescharacteristic
47C22×D244—24no—
48C22×D244—24no—
49C22×D244—24no—
50C22×D244—22no—
51C22×D244—24no—
52C22×D244—22no—
53C22×D244—22no—
54C22×D244—22no—
55C22×D244—22no—
56C22×D244—22no—
57C22×D244—42no—
58C22×D244—42no—
59C22×D244C2×C414yes—
60C22×D244C2×C418yes—
61C23×Dic61C2312yes—
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61C2×C414yes—
72#14519752—232no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—24no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—24no—
78C2×C4⋊Dic61—42no—
79C2×#11758198—22no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—24no—
87C2×#11758198—24no—
88C2×#11758198—24no—
89C2×#11758198—24no—
90C2×#11758198—24no—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198—24no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—42no—
97C2×#11758198—42no—
98C2×#11758198—42no—
99C2×#11758198—42no—
100C2×#11758198—42no—
101C2×#11758198C2×C418yes—
102C2×#11758198D414yescomplemented
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106#14519684—22no—
107#14519684—22no—
108#14519684—24no—
109#14519684—24no—
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2312yes—
112C23×C4×C61C2312yes—
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61C2×C414yes—
118C2×C4⋊C4×C61D414yes—
119C2×C4⋊C4×C61D414yes—
120C2×C4⋊C4×C61D414yescomplemented
121C2×C42×C61—22no—
122C2×C42×C61—22no—
123C2×C42×C61—24no—
124C2×C42×C61—24no—
125C2×C42×C61—42no—
126C2×C42×C61D414yescomplemented
127#95×C61—24no—
128C24×C61C2411yescharacteristic
129C23×D61—21no—
130C23×D61—21no—
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—21no—
134C23×D61—21no—
135C23×D61—21no—
136C23×D61—21no—
137C23×D61—21no—
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—22no—
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61C22×C414yes—
156C23×D61C22×C412yes—
157C23×D61C2×D412yes—
158C23×D61#4112yes—
159C22×C4×C61—22no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—22no—
179C22×C4×C61C22×C414yes—
180C22×C4×C61C22×C412yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D414yes—
183C22×C4×C61C2×D414yes—
184C22×C4×C61C2×D414yes—
185C22×C4×C61C2×D412yes—
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2×D412yes—
191C22×C4×C61#4112yes—
192C22×C4×C61#4112yes—
193C22×C4×C61#4112yes—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61C22×C412yes—
220C22×Dic61C2×D412yes—
221C22×Dic61#4112yes—
222C2×D244—216no—
223C2×D244—216no—
224C2×D244—28no—
225C2×D244—28no—
226C2×D244—28no—
227C2×D244—48no—
228C2×D244—48no—
229C2×D244—48no—
230C2×D244—48no—
231C2×D244—48no—
232C2×D244—44no—
233C2×D244—44no—
234C2×D244—44no—
235C2×D244—44no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C4⋊C4×C61—28no—
244C4⋊C4×C61C22⋊C4116yescomplemented
245C42×C61—28no—
246C42×C61—48no—
247#11758198—28no—
248#11758198—216no—
249#11758198—28no—
250#11758198—48no—
251#11758198—48no—
252#11758198—48no—
253#11758198—48no—
254#11758198—48no—
255C4⋊Dic61—48no—
256C4⋊Dic61—44no—
257C4×Dic61—44no—
258C23×C61C23×C411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C2×#4111yescharacteristic
265C23×C61C2×#4111yescharacteristic
266C23×C61C2×#4111yescharacteristic
267C23×C61C2×#4111yescharacteristic
268C23×C61C2×#4111yescharacteristic
269C23×C61H(5,𝔽2)11yescharacteristic
270C23×C61H(5,𝔽2)11yescharacteristic
271C23×C61H(5,𝔽2)11yescharacteristic
272C23×C612−1+411yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—24no—
292C22×D61—24no—
293C22×D61—24no—
294C22×D61—24no—
295C22×D61—24no—
296C22×D61—24no—
297C22×D61—24no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319C22×D61—42no—
320C22×D61—42no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61C4×D414yes—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—24no—
350C2×C4×C61—24no—
351C2×C4×C61—24no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—24no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—24no—
360C2×C4×C61—24no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—42no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61C2×C22⋊C418yes—
370C2×C4×C61C2×C22⋊C414yes—
371C2×C4×C61C4×D414yes—
372C2×C4×C61C4×D414yes—
373C2×C4×C61#12114yes—
374C2×C4×C61#12114yes—
375C2×C4×C61#12114yescomplemented
376C2×C4×C61#12414yes—
377C2×C4×C61#12714yes—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61—42no—
406D244—432no—
407D244—416no—
408C4×D61—416no—
409#13998—611nomaximal, Sylow
410C22×C61C22×C22⋊C411yescharacteristic
411C22×C61C2×C4×D411yescharacteristic
412C22×C61C2×C4×D411yescharacteristic
413C22×C61C2×C4×D411yescharacteristic
414C22×C61C4×#4111yescharacteristic
415C22×C61#51811yescharacteristic
416C22×C61#52011yescharacteristic
417C22×C61C2×#12111yescharacteristic
418C22×C61C2×#12111yescharacteristic
419C22×C61C2×#12111yescharacteristic
420C22×C61#52511yescharacteristic
421C22×C61C2×#12411yescharacteristic
422C22×C61#52911yescharacteristic
423C22×C61C2×#12711yescharacteristic
424C22×C61#53211yescharacteristic
425C22×C61#53511yescharacteristic
426C22×C61#53711yescharacteristic
427C22×C61#54011yescharacteristic
428C22×C61#54211yescharacteristic
429C22×C61D4211yescharacteristic
430C22×C61D4211yescharacteristic
431C22×C61D4211yescharacteristic
432C22×C61#54611yescharacteristic
433C22×C61#54611yescharacteristic
434C22×C61#54611yescharacteristic
435C22×C61#54711yescharacteristic
436C22×C61#54811yescharacteristic
437C22×C61#54811yescharacteristic
438C22×C61#54811yescharacteristic
439C22×C61#55011yescharacteristic
440C22×C61#55011yescharacteristic
441C22×C61#55011yescharacteristic
442C22×C61#55311yescharacteristic
443C22×C61#55311yescharacteristic
444C22×C61#55511yescharacteristic
445C2×D61—24no—
446C2×D61—24no—
447C2×D61—24no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—42no—
458C2×D61—42no—
459C2×D61—42no—
460C2×D61—44no—
461C2×D61—44no—
462C2×D61—44no—
463C2×D61—44no—
464C2×D61—44no—
465C2×D61—44no—
466C2×D61—44no—
467C2×D61—82no—
468C2×D61—82no—
469C2×D61—82no—
470C2×D61—82no—
471C2×D61—82no—
472C2×D61—82no—
473C2×D61—82no—
474C2×D61—82no—
475C4×C61—28no—
476C4×C61—24no—
477C4×C61—42no—
478C4×C61—44no—
479C4×C61#39018yescomplemented
480Dic61—42no—
481Dic61—42no—
482Dic61—42no—
483Dic61—82no—
484C22×#121—611no—
485C2×#390—612no—
486C2×#390—611no—
487C2×#390—611no—
488C2×#389—611no—
489C2×#380—611no—
490C2×C4×C4⋊C4D6111yescharacteristic, complemented
491C2×C4×C22⋊C4—611no—
492#1439—612no—
493#1438—612no—
494#1437—612no—
495C2×C61C2×#39011yescharacteristic
496C2×C61C4×#12111yescharacteristic
497C2×C61#232411yescharacteristic
498C2×C61D4×C22⋊C411yescharacteristic
499C2×C61#234111yescharacteristic
500C2×C61#236111yescharacteristic
501C2×C61#236311yescharacteristic
502C2×C61#241411yescharacteristic
503C2×C61#241611yescharacteristic
504C2×C61#242611yescharacteristic
505C2×C61#242811yescharacteristic
506C2×C61#249011yescharacteristic
507C2×C61#249111yescharacteristic
508C2×C61#254011yescharacteristic
509C2×C61#254111yescharacteristic
510D61—44no—
511D61—84no—
512C23×D4—611no—
513C23×D4—612no—
514C24×C4—611no—
515C2×#121—618no—
516C2×#121—1224no—
517C2×#121—1224no—
518C22×C4⋊C4—611no—
519C22×C4⋊C4—612no—
520C22×C4⋊C4C2×D6111yescharacteristic
521C22×C4⋊C4C2×D6111yescharacteristic
522C22×C22⋊C4—612no—
523C22×C22⋊C4—611no—
524C22×C22⋊C4—612no—
525C22×C22⋊C4—611no—
526C22×C22⋊C4—612no—
527C22×C22⋊C4—612no—
528C22×C22⋊C4—612no—
529C22×C22⋊C4—612no—
530C22×C42—611no—
531C22×C42C2×D6112yes—
532C22×C42C2×D6111yescharacteristic
533#390—1228no—
534#390—1224no—
535#390—1224no—
536#389—1224no—
537#380—1224no—
538C4×C4⋊C4—24no—
539C4×C22⋊C4—1224no—
540C2×#95—611no—
541C2×#95—612no—
542C2×#95—612no—
543C2×#95—611no—
544C2×#95C2×D6112yes—
545C61#1399811yescharacteristic, complemented, Sylow
546C25—611no—
547C25—612no—
548C22×D4—614no—
549C22×D4—618no—
550C22×D4—1224no—
551C22×D4—1224no—
552C22×D4—1224no—
553C22×D4—1222no—
554C22×D4—1222no—
555C22×D4—1222no—
556C22×D4—1222no—
557C22×D4—1222no—
558C22×D4—1224no—
559C22×D4—1222no—
560C22×D4—2442no—
561C22×D4—2442no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—614no—
566C23×C4—612no—
567C23×C4—1222no—
568C23×C4—1222no—
569C23×C4—1222no—
570C23×C4—1222no—
571C23×C4—1222no—
572C23×C4—1222no—
573C23×C4C22×D6112yes—
574C23×C4C22×D6111yescharacteristic
575C23×C4C22×D6112yes—
576C23×C4C22×D6111yescharacteristic
577C23×C4C22×D6111yescharacteristic
578#121—12232no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—1224no—
582C2×C4⋊C4—1222no—
583C2×C4⋊C4—1224no—
584C2×C4⋊C4—1222no—
585C2×C4⋊C4—1222no—
586C2×C4⋊C4—2442no—
587C2×C4⋊C4C4×D6114yes—
588C2×C4⋊C4D24414yes—
589C2×C4⋊C4D24414yescomplemented
590C2×C4⋊C4C22⋊D6114yes—
591C2×C22⋊C4—618no—
592C2×C22⋊C4—614no—
593C2×C22⋊C4—1222no—
594C2×C22⋊C4—1222no—
595C2×C22⋊C4—1224no—
596C2×C22⋊C4—1222no—
597C2×C22⋊C4—1222no—
598C2×C22⋊C4—1222no—
599C2×C22⋊C4—1224no—
600C2×C22⋊C4—1224no—
601C2×C22⋊C4—1224no—
602C2×C22⋊C4—1224no—
603C2×C22⋊C4—1224no—
604C2×C22⋊C4—1224no—
605C2×C22⋊C4—1224no—
606C2×C22⋊C4—1224no—
607C2×C22⋊C4—1224no—
608C2×C22⋊C4—1224no—
609C2×C22⋊C4—1224no—
610C2×C22⋊C4—2442no—
611C2×C22⋊C4—2442no—
612C2×C22⋊C4—2442no—
613C2×C22⋊C4—2442no—
614C2×C22⋊C4—2442no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—24no—
618C2×C42—24no—
619C2×C42—42no—
620C2×C42—1222no—
621C2×C42—1222no—
622C2×C42—1222no—
623C2×C42D24414yescomplemented
624#95—24no—
625#95—1222no—
626#95—1222no—
627#95—1224no—
628#95—1224no—
629C24—612no—
630C24—612no—
631C24—612no—
632C24—614no—
633C24—1221no—
634C24—1221no—
635C24—1221no—
636C24—1221no—
637C24—1221no—
638C24—1221no—
639C24—1221no—
640C24—1221no—
641C24—1221no—
642C24—1221no—
643C24—1221no—
644C24—1221no—
645C24—1222no—
646C24—1222no—
647C24—1222no—
648C24—1222no—
649C24—1222no—
650C24—1222no—
651C24—1222no—
652C24—1222no—
653C24—1222no—
654C24—1222no—
655C24—1222no—
656C24—1222no—
657C24—1222no—
658C24—1222no—
659C24C23×D6111yescharacteristic
660C2×D4—12216no—
661C2×D4—12216no—
662C2×D4—1228no—
663C2×D4—1228no—
664C2×D4—1228no—
665C2×D4—2448no—
666C2×D4—2448no—
667C2×D4—2448no—
668C2×D4—2448no—
669C2×D4—2448no—
670C2×D4—2444no—
671C2×D4—2444no—
672C2×D4—2444no—
673C2×D4—2444no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1228no—
716C22×C4—1228no—
717C22×C4—1228no—
718C22×C4—1222no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1222no—
725C22×C4—2444no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4—2444no—
729C22×C4C2×C4×D6114yes—
730C22×C4C2×C4×D6112yes—
731C22×C4C2×D24412yes—
732C22×C4C2×D24414yes—
733C22×C4C2×D24414yes—
734C22×C4C2×D24412yes—
735C22×C4C2×D24412yes—
736C22×C4C2×D24412yes—
737C22×C4C2×D24412yes—
738C22×C4#1175822212yes—
739C22×C4#1175822212yes—
740C22×C4D4×D6112yes—
741C22×C4#1175822612yes—
742C22×C4C2×C22⋊D6114yes—
743C22×C4C2×C22⋊D6112yes—
744C4⋊C4—28no—
745C4⋊C4—2448no—
746C4⋊C4—2444no—
747C4⋊C4#11758198116yescomplemented
748C22⋊C4—1228no—
749C22⋊C4—12216no—
750C22⋊C4—1228no—
751C22⋊C4—2448no—
752C22⋊C4—2448no—
753C22⋊C4—2448no—
754C22⋊C4—2448no—
755C22⋊C4—2448no—
756C42—28no—
757C42—48no—
758C42—2444no—
759C23—614no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—2442no—
786C23—2442no—
787C23—2442no—
788C23—2442no—
789C23—2442no—
790C23—2442no—
791C23—2442no—
792C23—2442no—
793C23—2442no—
794C23—2442no—
795C23—2442no—
796C23—2442no—
797C23—2442no—
798C23—2442no—
799C23—2442no—
800C23—2442no—
801C23—2442no—
802C23—2442no—
803C23—2442no—
804C23—2442no—
805C23—2442no—
806C23—2442no—
807C23—2442no—
808C23—2442no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2441no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23C22×C4×D6111yescharacteristic
830C23C2×D4×D6111yescharacteristic
831C23C22×C22⋊D6111yescharacteristic
832C23C22×D24411yescharacteristic
833C23C22×D24411yescharacteristic
834C23C22×D24411yescharacteristic
835C23#41×D6111yescharacteristic
836C23#41×D6111yescharacteristic
837C23C2×#1175822211yescharacteristic
838C23C2×#1175822211yescharacteristic
839C23C2×#1175822611yescharacteristic
840C23#1451982211yescharacteristic
841C23#1451982311yescharacteristic
842C23#1451982311yescharacteristic
843C23#1451982511yescharacteristic
844D4—24432no—
845D4—24416no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2442no—
885C2×C4—2442no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—24416no—
901C2×C4C2×#1175819818yes—
902C2×C4C2×#1175819814yes—
903C2×C4C4×D24414yes—
904C2×C4C4×D24414yes—
905C2×C4#1451975114yes—
906C2×C4#1451975114yes—
907C2×C4#1451975214yescomplemented
908C2×C4#1451976514yes—
909C2×C4#1451977414yes—
910C22—1224no—
911C22—1224no—
912C22—1224no—
913C22—4882no—
914C22—4882no—
915C22—4882no—
916C22—4882no—
917C22—4882no—
918C22—4882no—
919C22—4882no—
920C22—4882no—
921C22—2444no—
922C22—2444no—
923C22—2444no—
924C22—2444no—
925C22—2444no—
926C22—2444no—
927C22—2444no—
928C22—2442no—
929C22—2442no—
930C22—2442no—
931C22—2442no—
932C22—2442no—
933C22—2442no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22—2442no—
938C22—2442no—
939C22—2442no—
940C22C22×#1175819811yescharacteristic
941C22C4×D4×D6111yescharacteristic
942C22C2×C4×D24411yescharacteristic
943C22C2×C4×D24411yescharacteristic
944C22C4×#1175822611yescharacteristic
945C22#1684023411yescharacteristic
946C22#1684024411yescharacteristic
947C22C2×#1451975111yescharacteristic
948C22C2×#1451975111yescharacteristic
949C22C2×#1451975211yescharacteristic
950C22#1684027411yescharacteristic
951C22C2×#1451976511yescharacteristic
952C22#1684029911yescharacteristic
953C22C2×#1451977411yescharacteristic
954C22#1684030911yescharacteristic
955C22#1684033111yescharacteristic
956C22#1684034311yescharacteristic
957C22#1684036311yescharacteristic
958C22#1684038411yescharacteristic
959C22D4×C22⋊D6111yescharacteristic
960C22D4×D24411yescharacteristic
961C22D4×D24411yescharacteristic
962C22#1684040011yescharacteristic
963C22#1684040711yescharacteristic
964C22#1684040711yescharacteristic
965C22#1684041311yescharacteristic
966C22#1684042311yescharacteristic
967C22#1684042411yescharacteristic
968C22#1684042411yescharacteristic
969C22#1684043111yescharacteristic
970C22#1684043411yescharacteristic
971C22#1684043411yescharacteristic
972C22#1684045611yescharacteristic
973C22#1684046011yescharacteristic
974C22#1684047511yescharacteristic
975C4—24no—
976C4—28no—
977C4—42no—
978C4—44no—
979C4—4882no—
980C4—2442no—
981C4—2442no—
982C4—2442no—
983C4#1683966418yescomplemented
984C2—4884no—
985C2—2444no—
986C2C2×#1683966411yescharacteristic
987C2C4×#1451975211yescharacteristic
988C2#2144851311yescharacteristic
989C2D4×#1175819811yescharacteristic
990C2#2144865711yescharacteristic
991C2#2144883711yescharacteristic
992C2#2144885911yescharacteristic
993C2#2144923111yescharacteristic
994C2#2144925311yescharacteristic
995C2#2144937911yescharacteristic
996C2#2144940111yescharacteristic
997C2#2145016511yescharacteristic
998C2#2145017611yescharacteristic
999C2#2145075311yescharacteristic
1000C2#2145076111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC22×#14519752C2
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#13998
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839664C2semidirect
3. C2×#16839664C2semidirect
4. C2×#16839663C2semidirect
5. C2×#16839661C2semidirect
6. C2×#16839619C2semidirect
7. C2×C4×#11758198C2semidirect
8. #21444065C2semidirect
9. #21444059C2semidirect
10. #21444057C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
17. C2×#14519752C4semidirect
102. C2×#11758198D4semidirect
120. C2×C4⋊C4×C61D4semidirect
126. C2×C42×C61D4semidirect
244. C4⋊C4×C61C22⋊C4semidirect
375. C2×C4×C61#121semidirect
479. C4×C61#390semidirect
490. C2×C4×C4⋊C4D61semidirect
545. C61#13998semidirect
589. C2×C4⋊C4D244semidirect
623. C2×C42D244semidirect
747. C4⋊C4#11758198semidirect
907. C2×C4#14519752semidirect
983. C4#16839664semidirect

Maximal subgroups

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

subgroupindex
C22×#145197522
C2×#168396642
C2×#168396632
C2×#168396612
C2×#168396192
C2×C4×#117581982
#214440652
#214440592
#214440572
C2×C4×C4⋊C4×C612
#1399861