Finite Group Databasebeta

← #29695487

Subgroups — #29695487

Order 15616.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C22×#14519697C211yesmaximal, characteristic, complemented
5#21446751C211yesmaximal, characteristic, complemented
6#21446633C211yesmaximal, characteristic, complemented
7#21446255C211yesmaximal, characteristic, complemented
8#21446240C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21445816C211yesmaximal, characteristic, complemented
12#21445757C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C23×#92418C2211yescharacteristic
20#16840408—24no—
21#16840408C418yescomplemented
22C2×#14519765C2211yescharacteristic
23C2×#14519762—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519750—21no—
27C2×#14519745—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30#16839834—24no—
31C2×C4⋊#92418C2211yescharacteristic, complemented
32#16839761—24no—
33C2×#14519700C2211yescharacteristic, complemented
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519700C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519697—24no—
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×C22⋊#92418C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic, complemented
48C2×#14519688C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C2×C4×D4×C61—21no—
54C2×C4×D4×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic, complemented
57C61×#389—21no—
58C61×#385—21no—
59C61×#385—21no—
60C61×#384C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic, complemented
63C4×C4⋊C4×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244—22no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—41no—
77C22×D244—41no—
78C22×D244C2×C414yescomplemented
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C2×#11758194—22no—
86C2×#11758194—22no—
87C2×#11758194—41no—
88C22×#92418—22no—
89C22×#92418—22no—
90C22×#92418—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519765—22no—
96#14519765C2×C414yescomplemented
97#14519762—28no—
98#14519756—22no—
99#14519756C2×C414yescomplemented
100#14519751—22no—
101#14519751C2×C414yescomplemented
102#14519750—28no—
103#14519745—28no—
104C4×D244—22no—
105C4×D244C2×C414yescomplemented
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×C22⋊Dic61—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C22⋊C4×D61—28no—
114C4⋊#92418—22no—
115#14519700—22no—
116#14519700—22no—
117#14519700—41no—
118#14519700—41no—
119#14519697—22no—
120#14519697—22no—
121#14519697—22no—
122#14519697—22no—
123#14519697—22no—
124#14519697—41no—
125#14519697—41no—
126#14519697D414yescomplemented
127C22⋊#92418—22no—
128C22⋊#92418—22no—
129#14519688—22no—
130C22×D4×C61D411yescharacteristic
131C23×C4×C61—21no—
132C23×C4×C61—21no—
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C4×D4×C61—44no—
136C4×D4×C61C2×C414yes—
137C4×D4×C61D414yes—
138C2×C4⋊C4×C61—22no—
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—41no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61D411yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61D411yescharacteristic
154C2×C22⋊C4×C61D411yescharacteristic
155C2×C42×C61—21no—
156C2×C42×C61C2311yescharacteristic
157#95×C61—21no—
158#95×C61—21no—
159#95×C61—21no—
160C24×C61C2×D411yescharacteristic
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—24no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—81no—
170C23×D61—81no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61C22⋊C414yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61—42no—
189C22×C4×C61—42no—
190C22×C4×C61—81no—
191C22×C4×C61—81no—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209#11758222—28no—
210#11758222—44no—
211#11758222—44no—
212#11758222—44no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—28no—
221C2×D244—24no—
222C2×D244—21no—
223C2×D244—44no—
224C2×D244—44no—
225C2×D244—44no—
226C2×D244—42no—
227C2×D244—42no—
228C2×D244C22×C412yes—
229C2×D244C22×C412yes—
230C2×D244C2×D412yes—
231C2×D244#4112yes—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22×C412yes—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—42no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—81no—
255C4⋊C4×C61C22⋊C414yes—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61C22⋊C414yes—
260C22⋊C4×C61C22⋊C414yes—
261C42×C61—42no—
262C42×C61C22×C412yes—
263C42×C61C2×D412yes—
264C22⋊Dic61—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C412yes—
271#11758196—24no—
272#11758194—44no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—44no—
285C2×#92418C2×D412yes—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61C2×C22⋊C412yes—
297C23×C61C2×C22⋊C412yes—
298C23×C61AGL(1,ℤ/8)12yes—
299C23×C61#13712yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—48no—
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—41no—
315C22×D61—41no—
316C22×D61—48no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61—84no—
322D4×C61—28no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—84no—
352C2×C4×C61—84no—
353C2×C4×C61C2×C22⋊C412yes—
354C2×C4×C61C2×C22⋊C412yes—
355C2×C4×C61C2×C22⋊C412yes—
356C2×C4×C61C2×C22⋊C412yes—
357C2×C4×C61C23×C411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C22⋊D61—48no—
364C22⋊D61—84no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—48no—
377D244—41no—
378D244—41no—
379D244C4×D414yescomplemented
380C4×D61—48no—
381C4×D61—84no—
382Dic122—22no—
383Dic122—22no—
384Dic122—41no—
385Dic122—41no—
386#92418—22no—
387#92418—41no—
388#92418—41no—
389#92418—41no—
390#22419—611nomaximal, Sylow
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61#41714yescomplemented
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C61C2×#13711yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C2×D61—24no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—22no—
430C4×C61—22no—
431C4×C61—42no—
432C4×C61—81no—
433C4×C61—81no—
434C4×C61—81no—
435C4×C61C2×C4×D411yescharacteristic
436C4×C61#51811yescharacteristic
437C4×C61D4211yescharacteristic
438C4×C61#54611yescharacteristic
439Dic61—42no—
440Dic61—42no—
441C2×#546—611no—
442C2×#435—611no—
443C2×#417—611no—
444C22×#102—611no—
445D4×C4⋊C4D6111yescharacteristic, complemented
446#1983—611no—
447#1959—611no—
448#1895—611no—
449#1892—611no—
450#1874—611no—
451#1872—611no—
452#1802—611no—
453#1788—611no—
454#1786—611no—
455#1762—611no—
456C2×C61—24no—
457C2×C61—42no—
458C2×C61D4×C22⋊C411yescharacteristic
459C2×C61C2×#41711yescharacteristic
460C2×C61#289711yescharacteristic
461C2×C61#326411yescharacteristic
462C2×C61#326611yescharacteristic
463C2×C61#330611yescharacteristic
464C2×C61#331411yescharacteristic
465D61—44no—
466D61—82no—
467C22×#41—611no—
468C23×D4—611no—
469C22×M16—611no—
470C23×C8—611no—
471#546—618no—
472#546—1224no—
473C2×#124—611no—
474C2×#123—1221no—
475C2×C22⋊Q8—611no—
476C2×#121—611no—
477C2×#121—1221no—
478C2×#120—1221no—
479C2×C4×D4—21no—
480C2×C4×D4—611no—
481C2×C4×D4C2×D6111yescharacteristic
482C22×C4⋊C4C2×D6111yescharacteristic
483C22×C4⋊C4C2×D6111yescharacteristic, complemented
484C22×C22⋊C4—1221no—
485#435—1224no—
486C2×C4⋊C8—611no—
487#417—1224no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102—611no—
500C2×#102—1224no—
501C2×C22⋊C8—611no—
502C2×C22⋊C8—611no—
503C2×#97—611no—
504#389—21no—
505#385—21no—
506#385—21no—
507#384C2×D6111yescharacteristic, complemented
508#380C2×D6111yescharacteristic
509#380C2×D6111yescharacteristic, complemented
510C4×C4⋊C4C2×D6111yescharacteristic, complemented
511#340—611no—
512#340—611no—
513#340—611no—
514#340—611no—
515C61#2241911yescharacteristic, complemented, Sylow
516C25—1221no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C22×Q8—611no—
524C22×D4—614no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—1222no—
528C22×D4—1222no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—2441no—
534C22×D4—2441no—
535C22×D4C22⋊D6111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—1221no—
539C23×C4—1221no—
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—611no—
549C22×C8—1222no—
550C22×C8—1222no—
551C22×C8—2441no—
552#124—614no—
553#124—1222no—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1222no—
559#121—1228no—
560#120—1228no—
561C4×D4—44no—
562C4×D4—614no—
563C4×D4—1222no—
564C4×D4C4×D6114yes—
565C4×D4D24414yes—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4C22⋊D6111yescharacteristic
577C2×C4⋊C4C22×D6111yescharacteristic
578C2×C4⋊C4C22×D6111yescharacteristic
579C2×C4⋊C4C22×D6111yescharacteristic
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1228no—
589C2×C22⋊C4C22⋊D6111yescharacteristic
590C2×C22⋊C4C22⋊D6111yescharacteristic
591C2×C42—21no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—1222no—
594#103—1222no—
595#103—1222no—
596#103—2441no—
597#103—2441no—
598#102—614no—
599#102—1222no—
600#102—1222no—
601#102—1222no—
602#102—1222no—
603#102—1222no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608#97—1222no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—1221no—
613C24—1224no—
614C24—1221no—
615C24—4881no—
616C24—4881no—
617C24—2442no—
618C24—2442no—
619C24—2442no—
620C24—2442no—
621C24C2×C22⋊D6111yescharacteristic
622C24C2×C22⋊D6111yescharacteristic
623#41—1228no—
624#41—2444no—
625#41—2444no—
626#41—2444no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—612no—
639C2×D4—1228no—
640C2×D4—1224no—
641C2×D4—1224no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1224no—
651C2×D4—4881no—
652C2×D4—4881no—
653C2×D4—2444no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4#1175819814yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1224no—
682C22×C4—1224no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C2×C4×D6112yes—
688C22×C4C2×C4×D6112yes—
689C22×C4C2×D24412yes—
690C22×C4C2×D24412yes—
691C22×C4C2×C22⋊D6111yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C2×C22⋊D6111yescharacteristic
695C22×C4C23×D6111yescharacteristic
696M16—2444no—
697C2×C8—612no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—2444no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—81no—
721C4⋊C4—612no—
722C4⋊C4—1221no—
723C4⋊C4—1224no—
724C4⋊C4#1175819814yes—
725C4⋊C4D4×D6112yes—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4#1175819814yes—
734C22⋊C4#1175819814yes—
735C42—42no—
736C42C2×C4×D6112yes—
737C42C2×D24412yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—4884no—
757C23—2448no—
758C23—2448no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23C2×#1175819812yes—
770C23C2×#1175819812yes—
771C23#1451980312yes—
772C23#1451980812yes—
773C23C22×C22⋊D6111yescharacteristic
774Q8—1222no—
775Q8—1222no—
776Q8—2441no—
777Q8—2441no—
778D4—28no—
779D4—614no—
780D4—1222no—
781D4—1222no—
782D4—1222no—
783D4—1222no—
784D4—1222no—
785D4—4884no—
786D4—2448no—
787D4—2448no—
788D4—2441no—
789D4—2441no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—4884no—
823C2×C4—2448no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4C2×#1175819812yes—
829C2×C4C2×#1175819812yes—
830C2×C4C2×#1175819812yes—
831C2×C4C2×#1175819812yes—
832C2×C4C22×C4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×D24411yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#1451982211yescharacteristic
837C2×C4#1451982311yescharacteristic
838C8—1222no—
839C8—2441no—
840C8—2441no—
841C8—2441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—1224no—
856C22—48816no—
857C22—4881no—
858C22—4881no—
859C22—4881no—
860C22—4881no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22#1683976114yescomplemented
871C22C22×#1175819811yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22#1684040011yescharacteristic
874C22C2×#1451980311yescharacteristic
875C22C2×#1451980811yescharacteristic
876C22#1684056511yescharacteristic
877C22#1684057011yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—2442no—
887C4—2442no—
888C4C4×D4×D6111yescharacteristic
889C4#1684023411yescharacteristic
890C4D4×D24411yescharacteristic
891C4#1684040711yescharacteristic
892C2—24no—
893C2—42no—
894C2—4882no—
895C2—2444no—
896C2D4×#1175819811yescharacteristic
897C2C2×#1683976111yescharacteristic
898C2#2145434211yescharacteristic
899C2#2145729511yescharacteristic
900C2#2145733011yescharacteristic
901C2#2145777411yescharacteristic
902C2#2145789411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C4⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenterD4×C4⋊C4D61
hypocenterC61#22419
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839834C2semidirect
3. C2×#16839761C2semidirect
4. C22×#14519697C2semidirect
5. #21446751C2semidirect
6. #21446633C2semidirect
7. #21446255C2semidirect
8. #21446240C2semidirect
9. #21446136C2semidirect
10. #21446126C2semidirect
11. #21445816C2semidirect
12. #21445757C2semidirect
13. #21445749C2semidirect
14. #21445647C2semidirect
15. D4×C4⋊C4×C61C2semidirect
18. C22×#11758194C22semidirect
21. #16840408C4semidirect
31. C2×C4⋊#92418C22semidirect
33. C2×#14519700C22semidirect
34. C2×#14519700C22semidirect
35. C2×#14519700C22semidirect
36. C2×#14519700C22semidirect
47. C2×C22⋊#92418C22semidirect
48. C2×#14519688C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
56. C22×C4⋊C4×C61C22semidirect
60. C61×#384C22semidirect
62. C61×#380C22semidirect
63. C4×C4⋊C4×C61C22semidirect
70. C2×#11758222C2×C4semidirect
78. C22×D244C2×C4semidirect
96. #14519765C2×C4semidirect
99. #14519756C2×C4semidirect
101. #14519751C2×C4semidirect
105. C4×D244C2×C4semidirect
126. #14519697D4semidirect
379. D244C4×D4semidirect
404. C22×C61#417semidirect
445. D4×C4⋊C4D61semidirect
483. C22×C4⋊C4C2×D61semidirect
507. #384C2×D61semidirect
509. #380C2×D61semidirect
510. C4×C4⋊C4C2×D61semidirect
515. C61#22419semidirect
870. C22#16839761semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168398342
C2×#168397612
C22×#145196972
#214467512
#214466332
#214462552
#214462402
#214461362
#214461262
#214458162
#214457572
#214457492
#214456472
D4×C4⋊C4×C612
#2241961