Finite Group Databasebeta

← #29700281

Subgroups — #29700281

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839901C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3C22×#14519701C211yesmaximal, characteristic, complemented
4#21448833C211yesmaximal, characteristic
5#21446703C211yesmaximal, characteristic, complemented
6#21446512C211yesmaximal, characteristic, complemented
7#21446457C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic
9#21446174C211yesmaximal, characteristic, complemented
10#21446156C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445649C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519737—21no—
22C22×C4⋊Dic61C2211yescharacteristic
23#16839901C418yescomplemented
24#16839860—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519701—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38C2×#14519688C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839654—21no—
42#16839639—21no—
43#16839636—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C23×Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#391—21no—
55C61×#391—21no—
56C61×#391C2211yescharacteristic
57C61×#391C2211yescharacteristic
58C61×#380—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C22×C4×D61—21no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758201—41no—
69C2×#11758201—41no—
70C2×#11758201C2×C414yescomplemented
71C2×#11758201C2×C414yescomplemented
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751C2×C414yes—
81C4×D244—22no—
82C4×D244—41no—
83#14519737—44no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96#14519710—22no—
97#14519710—41no—
98#14519701—22no—
99#14519701—22no—
100#14519701—22no—
101#14519701C2×C414yescomplemented
102#14519701C2×C414yescomplemented
103#14519701D414yescomplemented
104#14519697—22no—
105#14519697—41no—
106C22⋊#92418C2×C414yescomplemented
107#14519688—22no—
108#14519688—41no—
109#14519684—21no—
110#14519684—21no—
111C22×Q8×C61—21no—
112C22×Q8×C61—22no—
113C22×Q8×C61—22no—
114C22×Q8×C61—22no—
115C22×Q8×C61—41no—
116C22×Q8×C61—41no—
117C22×Q8×C61C2×C414yescomplemented
118C22×Q8×C61C2311yescharacteristic
119C22×Q8×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61C2311yescharacteristic
122C4×Q8×C61—22no—
123C4×Q8×C61—22no—
124C4×Q8×C61—41no—
125C4×Q8×C61—41no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61—21no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C2×Q8×C61—24no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—28no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×Q8×C61—42no—
158C2×Q8×C61—44no—
159C2×Q8×C61—44no—
160C2×Q8×C61—44no—
161C2×Q8×C61C22×C412yes—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C2×D412yes—
164C2×Q8×C61#4112yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61#4112yes—
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—24no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244C22×C412yes—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—81no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—42no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—42no—
216C42×C61—42no—
217#11758201—28no—
218#11758201—44no—
219#11758198—24no—
220#11758198—42no—
221#11758198—42no—
222#11758198—81no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61C2×D412yes—
230#11758196—42no—
231C4×Dic61—42no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—44no—
242C2×#92418C22×C412yes—
243C2×#92418C22×C412yes—
244C2×#92418C2×D412yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61C4×D412yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61#13712yes—
252C23×C61C22×D411yescharacteristic
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61—22no—
264Q8×C61—22no—
265Q8×C61—48no—
266Q8×C61—41no—
267Q8×C61—41no—
268Q8×C61C4×D414yescomplemented
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—48no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61C4×D412yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C22⋊D61—48no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
318D244—22no—
319D244—22no—
320D244—41no—
321D244—41no—
322C4×D61—84no—
323#92418—22no—
324#92418—22no—
325#92418—22no—
326#92418—41no—
327#22855—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61#44014yescomplemented
335C22×C61C2×C4×D411yescharacteristic
336C22×C61D4211yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×#13711yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57811yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—24no—
351C4×C61—42no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61C2×C4×D411yescharacteristic
359C4×C61#51811yescharacteristic
360C4×C61#54611yescharacteristic
361C4×C61#55111yescharacteristic
362Dic61—42no—
363Dic61—42no—
364Dic61—81no—
365C2×#448—611no—
366C2×#440—611no—
367C22×#103—611no—
368#2361—611no—
369Q8×C22⋊C4D6111yescharacteristic, complemented
370#1973—611no—
371#1935—611no—
372#1928—611no—
373#1893—611no—
374#1880—611no—
375#1877—611no—
376#1863—611no—
377#1852—611no—
378#1763—611no—
379#1752—611no—
380C2×C61—24no—
381C2×C61#235811yescharacteristic
382C2×C61C2×#44011yescharacteristic
383C2×C61#294711yescharacteristic
384C2×C61#326511yescharacteristic
385C2×C61#327011yescharacteristic
386C2×C61#330811yescharacteristic
387C2×C61#332011yescharacteristic
388D61—82no—
389C23×Q8C2×D6111yescharacteristic
390C22×SD16—611no—
391C22×SD16—611no—
392C23×C8—611no—
393C2×#121—611no—
394C2×C4×Q8C2×D6111yescharacteristic
395C2×C4×Q8C2×D6111yescharacteristic
396C2×C4×D4—611no—
397C2×C4×D4—1221no—
398C22×C4⋊C4—611no—
399#448—618no—
400#440—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—1224no—
410C2×#102—611no—
411C2×#102—611no—
412C2×C22⋊C8—611no—
413C2×#97—611no—
414C2×#97—611no—
415#391—21no—
416#391—21no—
417#391C2×D6111yescharacteristic
418#391C2×D6111yescharacteristic
419#390—611no—
420#389—611no—
421#388—1221no—
422#386—1221no—
423#385—1221no—
424#380—21no—
425#380C2×D6111yescharacteristic
426C4×C4⋊C4—611no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2×D6111yescharacteristic
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#336—611no—
434#336—611no—
435C61#2285511yescharacteristic, complemented, Sylow
436C22×Q8—22no—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C4×D6114yescomplemented
443C22×Q8C22×D6111yescharacteristic
444C22×Q8C22×D6111yescharacteristic
445C22×D4—611no—
446C22×D4—1221no—
447C23×C4—21no—
448C23×C4—1221no—
449C23×C4—1221no—
450C23×C4C22×D6111yescharacteristic
451C2×SD16—614no—
452C2×SD16—614no—
453C2×SD16—1222no—
454C2×SD16—1222no—
455C2×SD16—2441no—
456C2×SD16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—2441no—
464#121—614no—
465#121—1222no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×D4—1222no—
471C4×D4—2441no—
472C4×D4—2444no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1222no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—2441no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4C22⋊D6111yescharacteristic
490C2×C22⋊C4C22⋊D6111yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—1221no—
494C2×C42C22×D6111yescharacteristic
495C2×C42C22×D6111yescharacteristic
496#107—1222no—
497#107—2441no—
498#103—614no—
499#103—614no—
500#103—614no—
501#103—1222no—
502#103—1222no—
503#103—1222no—
504#102—1222no—
505#102—2441no—
506C22⋊C8—614no—
507#97—1222no—
508#97—2441no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—1221no—
515#95—1221no—
516#95C22⋊D6111yescharacteristic
517#95C22⋊D6111yescharacteristic
518C24—1221no—
519C24C2×C22⋊D6111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—24no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D6112yes—
536C2×Q8C2×C4×D6112yes—
537C2×Q8D4×D6112yes—
538C2×Q8#1175822412yes—
539C2×D4—612no—
540C2×D4—1224no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—2442no—
547C2×D4—2442no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—4881no—
563C22×C4—4881no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4C2×C4×D6112yes—
569C22×C4#1175822212yes—
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C2×C22⋊D6111yescharacteristic
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C23×D6111yescharacteristic
576SD16—1228no—
577SD16—2444no—
578C2×C8—612no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—2444no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—2442no—
604C4⋊C4—2442no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—1224no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—2442no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—1222no—
624C23—2441no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23C4×C22⋊D6112yes—
631C23#1451980212yes—
632C23#1451980812yes—
633C23C22×C22⋊D6111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8#1451973714yescomplemented
643D4—1222no—
644D4—1222no—
645D4—2448no—
646D4—2441no—
647D4—2441no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—4884no—
682C2×C4—4884no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C4×C22⋊D6112yes—
691C2×C4C22×C4×D6111yescharacteristic
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982211yescharacteristic
697C8—1222no—
698C8—1222no—
699C8—1222no—
700C8—2441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22#1683986014yescomplemented
715C22C2×C4×C22⋊D6111yescharacteristic
716C22D4×C22⋊D6111yescharacteristic
717C22#1684040611yescharacteristic
718C22C2×#1451980211yescharacteristic
719C22C2×#1451980811yescharacteristic
720C22#1684057011yescharacteristic
721C22#1684057711yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—4881no—
732C4—2442no—
733C4—2442no—
734C4C2×#1451973711yescharacteristic
735C4#1684023511yescharacteristic
736C4#1684040211yescharacteristic
737C4#1684043811yescharacteristic
738C2—24no—
739C2—4882no—
740C2#2144879811yescharacteristic
741C2C2×#1683986011yescharacteristic
742C2#2145466211yescharacteristic
743C2#2145731511yescharacteristic
744C2#2145739011yescharacteristic
745C2#2145781011yescharacteristic
746C2#2145799011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingQ8×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterQ8×C22⋊C4D61
hypocenterC61#22855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839860C2semidirect
3. C22×#14519701C2semidirect
5. #21446703C2semidirect
6. #21446512C2semidirect
7. #21446457C2semidirect
9. #21446174C2semidirect
10. #21446156C2semidirect
11. #21446073C2semidirect
12. #21446006C2semidirect
13. #21445649C2semidirect
14. #21445597C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
23. #16839901C4semidirect
70. C2×#11758201C2×C4semidirect
71. C2×#11758201C2×C4semidirect
101. #14519701C2×C4semidirect
102. #14519701C2×C4semidirect
103. #14519701D4semidirect
106. C22⋊#92418C2×C4semidirect
117. C22×Q8×C61C2×C4semidirect
268. Q8×C61C4×D4semidirect
334. C22×C61#440semidirect
369. Q8×C22⋊C4D61semidirect
435. C61#22855semidirect
442. C22×Q8C4×D61semidirect
642. Q8#14519737semidirect
714. C22#16839860semidirect

Maximal subgroups

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

subgroupindex
C2×#168399012
C2×#168398602
C22×#145197012
#214488332
#214467032
#214465122
#214464572
#214462452
#214461742
#214461562
#214460732
#214460062
#214456492
#214455972
Q8×C22⋊C4×C612
#2285561