Finite Group Databasebeta

← C2×#21457656 #30556366

Subgroups — C2×#21457656 #30556366

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic, complemented
2C2×#16840408C211yesmaximal, characteristic
3#21457656C2116yesmaximal, direct product factor
4C2×#16840117C211yesmaximal, characteristic, complemented
5C2×#16840087C211yesmaximal, characteristic, complemented
6C2×#16840093C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16840003C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839985C211yesmaximal, characteristic, complemented
11C2×#16839926C211yesmaximal, characteristic, complemented
12C2×#16839915C211yesmaximal, characteristic, complemented
13C2×C4×#11758190C211yesmaximal, characteristic, complemented
14C2×#16839759C211yesmaximal, characteristic, complemented
15C22×#14519699C211yesmaximal, characteristic, complemented
16C2×C8×D4×C61C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic
22#16840452—24no—
23#16840452C2218yescomplemented
24#16840408—24no—
25#16840408C2218yes—
26C2×#14519770—21no—
27C2×#14519769C2211yescharacteristic, complemented
28C2×#14519767—21no—
29C2×#14519765C2211yescharacteristic
30C2×#14519762—21no—
31C2×#14519758—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519756C2211yescharacteristic, complemented
35C2×#14519751C2211yescharacteristic
36C2×#14519750—21no—
37C2×#14519745—21no—
38C2×C4×Dic122C2211yescharacteristic, complemented
39C2×C4×D244C2211yescharacteristic
40C2×#14519736C2211yescharacteristic, complemented
41C2×#14519733—21no—
42C22×C4⋊Dic61C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840117C2218yescomplemented
45#16840093C2218yescomplemented
46#16840087C2218yescomplemented
47#16840063C2218yescomplemented
48#16840003C2218yescomplemented
49#16839991C2218yescomplemented
50#16839985C2218yescomplemented
51#16839926C2218yescomplemented
52#16839915C2218yescomplemented
53C4×#11758190C2218yescomplemented
54C2×#14519711C2211yescharacteristic, complemented
55C2×#14519709C2211yescharacteristic, complemented
56C2×#14519709C2211yescharacteristic, complemented
57#16839759C2218yescomplemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2218yescomplemented
69C23×C8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic, complemented
71C2×C4×D4×C61C2211yescharacteristic
72C8×D4×C61C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic, complemented
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—42no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244—24no—
85C22×D244—21no—
86C22×D244—22no—
87C22×D244—42no—
88C22×D244C2311yescharacteristic
89C22×D244C2314yes—
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C2×Dic244—42no—
97C2×Dic244C2314yescomplemented
98C2×#11758190—24no—
99C2×#11758190—42no—
100C2×#11758190C2314yes—
101C2×#11758190C2314yes—
102#14519770—28no—
103#14519769—22no—
104#14519769C2314yescomplemented
105#14519767—28no—
106#14519765—22no—
107#14519765C2314yes—
108#14519762—28no—
109#14519758—28no—
110#14519756—22no—
111#14519756—22no—
112#14519756—22no—
113#14519756C2314yes—
114#14519756C2314yes—
115#14519756C2314yescomplemented
116#14519751—22no—
117#14519751C2314yes—
118#14519750—28no—
119#14519745—28no—
120C4×Dic122—22no—
121C4×Dic122C2314yescomplemented
122C4×D244—22no—
123C4×D244C2314yes—
124#14519736—22no—
125#14519736C2314yescomplemented
126#14519733—28no—
127C2×C4⋊Dic61—22no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2314yes—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C22⋊C4×D61—28no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519709C2314yescomplemented
153#14519709C2314yescomplemented
154#14519702C2314yescomplemented
155#14519702C2314yescomplemented
156#14519702C2314yescomplemented
157#14519702C2314yescomplemented
158#14519699C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163#14519699C2314yes—
164C22×D4×C61D411yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C22×C8×C61—42no—
168C22×C8×C61—42no—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2314yes—
174C22×C8×C61C2314yescomplemented
175C4×D4×C61D414yes—
176C4×D4×C61C2314yes—
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61C2314yescomplemented
182C22⋊C8×C61C2314yes—
183C22⋊C8×C61C2314yescomplemented
184C4×C8×C61C2314yescomplemented
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—82no—
193C2×D4×C61—24no—
194C2×D4×C61C2×D414yes—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—82no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—44no—
220#11758222—28no—
221#11758222—44no—
222#11758222—48no—
223C2×D244—21no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—28no—
228C2×D244—24no—
229C2×D244—21no—
230C2×D244—44no—
231C2×D244—48no—
232C2×D244—44no—
233C2×D244#4114yes—
234C2×D244C2412yes—
235C2×D244C2412yes—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—44no—
239C2×C4×D61—82no—
240C2×Dic122—22no—
241C2×Dic122—22no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122C2412yes—
247C2×Dic122C2412yes—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61—22no—
252C2×C8×C61—44no—
253C2×C8×C61—44no—
254C2×C8×C61C2412yes—
255C2×C8×C61C2412yes—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C4⋊C4×C61C2×D414yes—
259C22⋊C4×C61C2×D414yes—
260C22⋊C4×C61C2×D414yes—
261C42×C61C2×D412yes—
262C42×C61C2412yes—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61C2412yes—
277C4⋊Dic61C2412yes—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286C4×Dic61—24no—
287C4×Dic61—24no—
288Dic244—44no—
289#11758190—28no—
290#11758190—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61#13514yes—
297C23×C61C22×D412yes—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—24no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—48no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—48no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—84no—
311C22×D61—816no—
312D4×C61—28no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—24no—
318C2×C4×C61—24no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4112yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—48no—
332C22⋊D61—84no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—48no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346D244—24no—
347D244—22no—
348D244—22no—
349D244—22no—
350D244—48no—
351D244—42no—
352D244C2×#4114yes—
353C4×D61—48no—
354C4×D61—84no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—42no—
360Dic122—42no—
361C8×C61—22no—
362C8×C61—22no—
363C8×C61—22no—
364C8×C61—22no—
365C2×#3296—611nomaximal, Sylow
366C22×C61—22no—
367C22×C61—28no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—44no—
373C22×C61#54612yes—
374C22×C61C2×#13514yes—
375C22×C61C2×#13512yes—
376C22×C61#57712yes—
377C22×C61C23×D411yescharacteristic
378C2×D61—24no—
379C2×D61—48no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—816no—
386C2×D61—84no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61#54612yes—
392C4×C61C22×#4111yescharacteristic
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400C2×#552—611no—
401C2×#546—611no—
402#3296—6116no—
403C2×#488—611no—
404C2×#482—611no—
405C2×#483—611no—
406C2×#478—611no—
407C2×#467—611no—
408C2×#465—611no—
409C2×#464—611no—
410C2×#452—611no—
411C2×#450—611no—
412C2×C4×SD16—611no—
413C2×C8×D4D6111yescharacteristic, complemented
414C2×#416—611no—
415C22×#102—611no—
416C2×C61—24no—
417C2×C61—42no—
418C2×C61#329614yescomplemented
419C2×C61C2×#54611yescharacteristic
420C2×C61C22×#13511yescharacteristic
421C2×C61C2×#57711yescharacteristic
422D61—44no—
423D61—82no—
424C22×#41—611no—
425C23×D4—611no—
426C22×Q16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C23×C8C2×D6111yescharacteristic
430C23×C8C2×D6111yescharacteristic, complemented
431#552—618no—
432#552—1224no—
433#546—618no—
434#546—1224no—
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#124—611no—
439C2×#123—1221no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—611no—
444C2×#121—611no—
445C2×#121—1221no—
446C2×#120—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—611no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117—611no—
451C2×#117—1221no—
452C22×C4⋊C4—611no—
453C22×C22⋊C4—1221no—
454#488—618no—
455#483—618no—
456#482—618no—
457#478—618no—
458#467—618no—
459#465—618no—
460#464—618no—
461#452—618no—
462#450—618no—
463C4×SD16—618no—
464C8×D4C2×D6118yescomplemented
465C2×#107—611no—
466C2×#106—611no—
467C2×#106—611no—
468C2×C4⋊C8C2×D6111yescharacteristic, complemented
469#416—618no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—618no—
481C2×C22⋊C8C2×D6111yescharacteristic
482C2×C22⋊C8C2×D6111yescharacteristic, complemented
483C2×C4×C8C2×D6111yescharacteristic, complemented
484C61C2×#329611yescharacteristic, complemented, Sylow
485C25—1221no—
486C2×#41—614no—
487C2×#41—1224no—
488C2×#41—1222no—
489C2×#41—2442no—
490C22×Q8—611no—
491C22×Q8—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—614no—
495C22×D4—1224no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1222no—
500C22×D4—2442no—
501C22×D4D24411yescharacteristic
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×Q16—614no—
508C2×Q16—2442no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1224no—
512C2×SD16—2442no—
513C22×C8—42no—
514C22×C8—42no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6114yes—
520C22×C8C22×D6114yescomplemented
521#126—1228no—
522#125—614no—
523#125—1228no—
524#125—1222no—
525#124—614no—
526#124—1222no—
527#123—1228no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535#121—614no—
536#121—1222no—
537#121—1228no—
538#120—1228no—
539C4×Q8—614no—
540C4×Q8—1222no—
541C4×D4—614no—
542C4×D4—1222no—
543C4×D4D24414yes—
544C4×D4C22×D6114yes—
545#117—614no—
546#117—1222no—
547#117—1228no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1222no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4D24411yescharacteristic
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1228no—
571C2×C22⋊C4D24411yescharacteristic
572C2×C22⋊C4D24411yescharacteristic
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42C22×D6111yescharacteristic
576#107—614no—
577#106—614no—
578#106—614no—
579C4⋊C8C22×D6114yescomplemented
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588#102—614no—
589#102—614no—
590C22⋊C8C22×D6114yes—
591C22⋊C8C22×D6114yescomplemented
592C4×C8C22×D6114yescomplemented
593C24—1221no—
594C24—1224no—
595C24—1221no—
596C24—4882no—
597C24—2444no—
598C24—2444no—
599C24C2×D24411yescharacteristic
600C24C2×D24411yescharacteristic
601#41—1228no—
602#41—2444no—
603#41—2448no—
604C2×Q8—612no—
605C2×Q8—612no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1222no—
609C2×Q8—1222no—
610C2×Q8—1222no—
611C2×Q8—1222no—
612C2×D4—24no—
613C2×D4—614no—
614C2×D4—612no—
615C2×D4—612no—
616C2×D4—1228no—
617C2×D4—1224no—
618C2×D4—1224no—
619C2×D4—1221no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—1222no—
625C2×D4—4882no—
626C2×D4—2444no—
627C2×D4—2448no—
628C2×D4—2444no—
629C2×D4—2444no—
630C2×D4C2×D24414yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—1224no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1224no—
643C22×C4—1224no—
644C22×C4—4882no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4C2×D24412yes—
648C22×C4C2×D24412yes—
649C22×C4C2×D24411yescharacteristic
650C22×C4C2×D24411yescharacteristic
651C22×C4C2×D24411yescharacteristic
652C22×C4C2×D24411yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657SD16—1228no—
658SD16—2444no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—44no—
665C2×C8C23×D6112yes—
666C2×C8C23×D6112yes—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1224no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1224no—
684C4⋊C4C2×D24414yes—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4C2×D24414yes—
694C22⋊C4C2×D24414yes—
695C42—1224no—
696C42—1224no—
697C42C2×D24412yes—
698C42C23×D6112yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—1222no—
705C23—1224no—
706C23—1222no—
707C23—48816no—
708C23—4884no—
709C23—2448no—
710C23—2448no—
711C23—2442no—
712C23—2442no—
713C23—2442no—
714C23—2442no—
715C23—2442no—
716C23#1451979914yes—
717C23C22×D24412yes—
718C23C22×D24412yes—
719C23C22×D24411yescharacteristic
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—1222no—
724Q8—2442no—
725Q8—2442no—
726D4—28no—
727D4—614no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1224no—
732D4—4884no—
733D4—2448no—
734D4—2448no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—4884no—
753C2×C4—2448no—
754C2×C4—2448no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C22×D24412yes—
762C2×C4C22×D24412yes—
763C2×C4C22×D24412yes—
764C2×C4C22×D24412yes—
765C2×C4C22×D24411yescharacteristic
766C2×C4#41×D6112yes—
767C2×C4#1451982212yes—
768C2×C4C24×D6111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—22no—
774C22—22no—
775C22—28no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—1224no—
781C22—48816no—
782C22—4884no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2448no—
789C22#1684040712yes—
790C22C2×#1451979914yes—
791C22C2×#1451979912yes—
792C22#1684057412yes—
793C22C23×D24411yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—2442no—
799C4—2442no—
800C4—2442no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4#1684040712yes—
805C4C2×#41×D6111yescharacteristic
806C4C2×#1451982211yescharacteristic
807C2—24no—
808C2—42no—
809C2—4882no—
810C2—2444no—
811C2#2145765614yesdirect product factor
812C2C2×#1684040711yescharacteristic
813C2C22×#1451979911yescharacteristic
814C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenterC2×C8×D4D61
hypocenterC61C2×#3296
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840452C2semidirect
3. #21457656C2direct (N × H)
4. C2×#16840117C2semidirect
5. C2×#16840087C2semidirect
6. C2×#16840093C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16840003C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839985C2semidirect
11. C2×#16839926C2semidirect
12. C2×#16839915C2semidirect
13. C2×C4×#11758190C2semidirect
14. C2×#16839759C2semidirect
15. C22×#14519699C2semidirect
16. C2×C8×D4×C61C2semidirect
19. C22×Dic244C22semidirect
23. #16840452C22semidirect
27. C2×#14519769C22semidirect
34. C2×#14519756C22semidirect
38. C2×C4×Dic122C22semidirect
40. C2×#14519736C22semidirect
44. #16840117C22semidirect
45. #16840093C22semidirect
46. #16840087C22semidirect
47. #16840063C22semidirect
48. #16840003C22semidirect
49. #16839991C22semidirect
50. #16839985C22semidirect
51. #16839926C22semidirect
52. #16839915C22semidirect
53. C4×#11758190C22semidirect
54. C2×#14519711C22semidirect
55. C2×#14519709C22semidirect
56. C2×#14519709C22semidirect
57. #16839759C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519702C22semidirect
68. C2×#14519699C22semidirect
70. C23×C8×C61C22semidirect
72. C8×D4×C61C22semidirect
73. C2×C4⋊C8×C61C22semidirect
75. C2×C22⋊C8×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
97. C2×Dic244C23semidirect
104. #14519769C23semidirect
115. #14519756C23semidirect
121. C4×Dic122C23semidirect
125. #14519736C23semidirect
151. #14519711C23semidirect
152. #14519709C23semidirect
153. #14519709C23semidirect
154. #14519702C23semidirect
155. #14519702C23semidirect
156. #14519702C23semidirect
157. #14519702C23semidirect
174. C22×C8×C61C23semidirect
181. C4⋊C8×C61C23semidirect
183. C22⋊C8×C61C23semidirect
184. C4×C8×C61C23semidirect
413. C2×C8×D4D61semidirect
418. C2×C61#3296semidirect
430. C23×C8C2×D61semidirect
464. C8×D4C2×D61semidirect
468. C2×C4⋊C8C2×D61semidirect
482. C2×C22⋊C8C2×D61semidirect
483. C2×C4×C8C2×D61semidirect
484. C61C2×#3296semidirect
520. C22×C8C22×D61semidirect
579. C4⋊C8C22×D61semidirect
591. C22⋊C8C22×D61semidirect
592. C4×C8C22×D61semidirect
811. C2#21457656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168404082
#214576562
C2×#168401172
C2×#168400872
C2×#168400932
C2×#168400632
C2×#168400032
C2×#168399912
C2×#168399852
C2×#168399262
C2×#168399152
C2×C4×#117581902
C2×#168397592
C22×#145196992
C2×C8×D4×C612
C2×#329661