Finite Group Databasebeta

← C2×#21457331 #30554996

Subgroups — C2×#21457331 #30554996

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic, complemented
2C22×SD16×D61C211yesmaximal, characteristic, complemented
3C2×Q8×D244C211yesmaximal, characteristic, complemented
4C2×#16840407C211yesmaximal, characteristic
5#21457331C2116yesmaximal, direct product factor
6C2×#16840156C211yesmaximal, characteristic, complemented
7C2×#16840009C211yesmaximal, characteristic, complemented
8C2×#16840004C211yesmaximal, characteristic, complemented
9C2×#16839984C211yesmaximal, characteristic, complemented
10C2×#16839967C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839902C211yesmaximal, characteristic, complemented
14C2×#16839914C211yesmaximal, characteristic, complemented
15C2×#16839835C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic, complemented
20C22×D4×D61C2211yescharacteristic
21C2×#14519806—28no—
22C2×#14519806C2218yescomplemented
23C22×Dic244C2211yescharacteristic, complemented
24C22×Dic244C2211yescharacteristic, complemented
25C22×#11758202C2211yescharacteristic, complemented
26C22×#11758190C2211yescharacteristic
27C22×#11758190C2211yescharacteristic
28C22×#11758200C2211yescharacteristic
29C22×#11758200C2211yescharacteristic
30C22×#11758201C2211yescharacteristic
31C2×SD16×D61—28no—
32C2×SD16×D61C2218yescomplemented
33C22×#11758189C2211yescharacteristic, complemented
34C22×C8×D61C2211yescharacteristic
35Q8×D244—24no—
36Q8×D244C2218yescomplemented
37#16840407—24no—
38#16840407C2218yes—
39C2×#14519777—21no—
40C2×#14519777C2211yescharacteristic, complemented
41C2×#14519765C2211yescharacteristic
42C2×#14519761—21no—
43C2×#14519757—21no—
44C2×#14519757—21no—
45C2×#14519757C2211yescharacteristic
46C2×#14519757C2211yescharacteristic
47C2×#14519757C2211yescharacteristic, complemented
48C2×#14519752C2211yescharacteristic
49C2×#14519751—21no—
50C2×#14519747—21no—
51C2×C4×D244—21no—
52C2×C4×D244C2211yescharacteristic
53C22×#11758198—21no—
54#16840156C2218yescomplemented
55#16840009C2218yescomplemented
56#16840004C2218yescomplemented
57#16839984C2218yescomplemented
58#16839967C2218yescomplemented
59#16839925C2218yescomplemented
60#16839919C2218yescomplemented
61#16839914C2218yescomplemented
62#16839902C2218yescomplemented
63#16839835C2218yescomplemented
64C2×C4⋊#92418C2211yescharacteristic, complemented
65C2×#14519700C2211yescharacteristic, complemented
66C2×#14519700C2211yescharacteristic, complemented
67C2×#14519700C2211yescharacteristic, complemented
68C2×#14519697C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic, complemented
73C2×C4×D4×C61C2211yescharacteristic
74C61×#440C2218yescomplemented
75C2×#107×C61C2211yescharacteristic, complemented
76C2×#103×C61C2211yescharacteristic, complemented
77C2×#102×C61C2211yescharacteristic
78C2×#97×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C2×#11758224—24no—
81C2×#11758224—22no—
82C2×#11758224—42no—
83C2×#11758224C2314yes—
84C22×Dic122—21no—
85C22×Dic122—21no—
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—22no—
90C2×Q8×D61—22no—
91C2×Q8×D61—24no—
92C2×Q8×D61—24no—
93C2×Q8×D61—42no—
94C2×Q8×D61—42no—
95C2×Q8×D61C2314yes—
96C2×Q8×D61C2314yescomplemented
97C22×D244—21no—
98C22×D244D411yescharacteristic
99C22×D244C2311yescharacteristic
100C22×C22⋊D61—21no—
101C22×C22⋊D61—21no—
102C2×D4×D61—24no—
103C2×D4×D61—22no—
104C2×D4×D61—42no—
105C2×D4×D61C2314yes—
106C23×Dic61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111#14519806—232no—
112C2×Dic244—24no—
113C2×Dic244—42no—
114C2×Dic244C2314yescomplemented
115C2×Dic244C2314yescomplemented
116C2×#11758202—24no—
117C2×#11758202C2314yescomplemented
118C2×#11758190—24no—
119C2×#11758190—42no—
120C2×#11758190C2314yes—
121C2×#11758190C2314yes—
122C2×#11758200—24no—
123C2×#11758200—24no—
124C2×#11758200C2314yes—
125C2×#11758200C2314yes—
126C2×#11758201—24no—
127C2×#11758201C2314yes—
128SD16×D61—232no—
129C2×#11758189—24no—
130C2×#11758189C2314yescomplemented
131C22×#92418C2311yescharacteristic
132C22×#92418C2311yescharacteristic
133C2×C8×D61—24no—
134C2×C8×D61C2314yes—
135#14519777—22no—
136#14519777—28no—
137#14519777C2314yescomplemented
138#14519765—22no—
139#14519765C2314yes—
140#14519761—28no—
141#14519757—22no—
142#14519757—22no—
143#14519757—22no—
144#14519757—28no—
145#14519757—28no—
146#14519757C2314yes—
147#14519757C2314yes—
148#14519757C2314yescomplemented
149#14519752—22no—
150#14519752C2314yes—
151#14519751—28no—
152#14519747—28no—
153C4×D244—28no—
154C4×D244D414yes—
155C4×D244C2314yes—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61—21no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61D411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—28no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C4⋊#92418C2314yescomplemented
172#14519700C2314yescomplemented
173#14519700C2314yescomplemented
174#14519700C2314yescomplemented
175#14519697C2314yes—
176#14519689C2314yes—
177#14519689C2314yescomplemented
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61C2311yescharacteristic
180C23×C4×C61—21no—
181C2×SD16×C61D418yescomplemented
182C2×SD16×C61C2314yes—
183C22×C8×C61C2311yescharacteristic
184C22×C8×C61C2311yescharacteristic
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yescomplemented
187C4×D4×C61—22no—
188C4×D4×C61C2314yes—
189C2×C4⋊C4×C61—21no—
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61—21no—
193C2×C42×C61—21no—
194C2×C42×C61C2311yescharacteristic
195#107×C61C2314yescomplemented
196#103×C61C2314yescomplemented
197#102×C61C2314yes—
198#97×C61C2314yescomplemented
199C24×C61—21no—
200C23×D61—21no—
201C23×D61—24no—
202C23×D61—44no—
203C23×D61—44no—
204C23×D61—82no—
205C23×D61C2×D411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C2×Q8×C61—21no—
208C2×Q8×C61—22no—
209C2×Q8×C61C2×D414yes—
210C2×Q8×C61C2412yes—
211C2×D4×C61—21no—
212C2×D4×C61—22no—
213C2×D4×C61C2×D414yes—
214C2×D4×C61C2412yes—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—82no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—24no—
231C22×Dic61—44no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234Q8×D61—28no—
235Q8×D61—28no—
236Q8×D61—44no—
237Q8×D61—44no—
238Q8×D61—48no—
239Q8×D61—48no—
240#11758224—28no—
241#11758224—44no—
242#11758224—48no—
243D4×D61—28no—
244D4×D61—44no—
245D4×D61—48no—
246C2×D244—24no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—21no—
250C2×D244—24no—
251C2×D244—82no—
252C2×D244C2×D414yes—
253C2×D244C2412yes—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—24no—
259C2×C4×D61—24no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—22no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—24no—
276C2×Dic122—24no—
277C2×Dic122—44no—
278C2×Dic122—44no—
279C2×Dic122C2412yes—
280C2×Dic122C2412yes—
281C2×Dic122C2412yes—
282SD16×C61C2×D4116yescomplemented
283C2×C8×C61—22no—
284C2×C8×C61C2×D414yes—
285C2×C8×C61C2412yes—
286C2×C8×C61C2412yes—
287C4⋊C4×C61—24no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C2412yes—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—24no—
293C42×C61—24no—
294C42×C61C2×D412yes—
295C42×C61C2412yes—
296#11758202—28no—
297#11758201—28no—
298#11758200—28no—
299#11758200—28no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306#11758198C2×D414yes—
307#11758198C2×D414yes—
308C4⋊Dic61—24no—
309C4⋊Dic61—24no—
310C4⋊Dic61—24no—
311C4⋊Dic61—24no—
312C4⋊Dic61—24no—
313C4⋊Dic61C2×D414yes—
314C2×#92418—22no—
315C2×#92418—22no—
316C2×#92418C2412yes—
317C2×#92418C2412yes—
318Dic244—28no—
319Dic244—44no—
320#11758190—28no—
321#11758190—44no—
322#11758189—28no—
323C8×D61—28no—
324C23×C61—24no—
325C23×C61—22no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—48no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—48no—
340C22×D61—84no—
341C22×D61—816no—
342C22×D61#13714yescomplemented
343C22×D61C22×D412yes—
344C22×D61C22×D412yes—
345Q8×C61—24no—
346Q8×C61—22no—
347Q8×C61C22×D414yes—
348D4×C61—24no—
349D4×C61—22no—
350D4×C61C22×D414yes—
351C2×C4×C61—24no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—84no—
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D412yes—
364C2×C4×C61H(5,𝔽2)12yes—
365C2×C4×C61C2511yescharacteristic
366C22⋊D61—48no—
367C22⋊D61—48no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—48no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61C22×D412yes—
378C2×Dic61C22×D412yes—
379D244—28no—
380D244—22no—
381D244—22no—
382D244—42no—
383D244—84no—
384C4×D61—24no—
385C4×D61—24no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—48no—
391C4×D61—48no—
392Dic122—22no—
393Dic122—22no—
394Dic122—22no—
395Dic122—22no—
396Dic122—22no—
397Dic122—22no—
398Dic122—48no—
399Dic122—48no—
400Dic122—42no—
401Dic122—42no—
402Dic122—42no—
403C8×C61—22no—
404C8×C61C22×D414yes—
405#92418—22no—
406#92418—22no—
407C2×#3266—611nomaximal, Sylow
408C22×C61—24no—
409C22×C61—48no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61D4212yes—
413C22×C61C2×#13712yes—
414C22×C61#57712yes—
415C22×C61C23×D411yescharacteristic
416C2×D61—22no—
417C2×D61—28no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—816no—
427C2×D61—84no—
428C2×D61C2×#13714yescomplemented
429C4×C61—24no—
430C4×C61—22no—
431C4×C61—22no—
432C4×C61—42no—
433C4×C61—42no—
434C4×C61D4212yes—
435C4×C61C23×D411yescharacteristic
436C4×C61C2×H(5,𝔽2)11yescharacteristic
437Dic61—22no—
438Dic61—22no—
439Dic61—42no—
440Dic61—42no—
441Dic61—42no—
442C22×#137—611no—
443C23×SD16—611no—
444C2×D4×Q8—611no—
445C2×#546—611no—
446#3266—6116no—
447C2×#497—611no—
448C2×#468—611no—
449C2×#467—611no—
450C2×#464—611no—
451C2×#461—611no—
452C2×#452—611no—
453C2×#451—611no—
454C2×#448—611no—
455C2×#450—611no—
456C2×#440D6111yescharacteristic, complemented
457C2×#435—611no—
458C2×C61—44no—
459C2×C61#326614yescomplemented
460C2×C61C2×D4211yescharacteristic
461C2×C61C22×#13711yescharacteristic
462C2×C61C2×#57711yescharacteristic
463D61—24no—
464D61—42no—
465D61—82no—
466C22×#41—611no—
467C23×Q8—611no—
468C23×Q8—611no—
469C23×D4—611no—
470C2×#137—618no—
471C2×#137—1228no—
472C22×Q16—611no—
473C22×Q16—611no—
474C22×Q16—611no—
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—618no—
479C22×SD16—611no—
480C22×SD16—611no—
481C22×SD16—1228no—
482C22×SD16C2×D6111yescharacteristic
483C22×M16—611no—
484C23×C8—611no—
485D4×Q8—618no—
486D4×Q8—1224no—
487#546—618no—
488#546—1224no—
489C2×C4⋊Q8—611no—
490C2×C4⋊Q8—1221no—
491C2×#124—611no—
492C2×#123—1221no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—611no—
496C2×C22⋊Q8—1221no—
497C2×C22⋊Q8—1221no—
498C2×#121—611no—
499C2×#121—1221no—
500C2×#120—1221no—
501C2×C4×Q8C2×D6111yescharacteristic, complemented
502C2×C4×D4—611no—
503C2×C4×D4—1221no—
504C2×C4×D4C2×D6111yescharacteristic
505C22×C22⋊C4—1221no—
506#497—618no—
507#468—618no—
508#467—618no—
509#464—618no—
510#461—618no—
511#452—618no—
512#451—618no—
513#450—618no—
514#448—618no—
515#440C2×D6118yescomplemented
516#435—618no—
517C2×#107C2×D6111yescharacteristic, complemented
518C2×C4⋊C8—611no—
519C2×#103—611no—
520C2×#103—611no—
521C2×#103—611no—
522C2×#103C2×D6111yescharacteristic, complemented
523C2×#102—611no—
524C2×#102C2×D6111yescharacteristic
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×#97C2×D6111yescharacteristic, complemented
528C61C2×#326611yescharacteristic, complemented, Sylow
529C25—1221no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—2442no—
534C22×Q8—614no—
535C22×Q8—614no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—611no—
539C22×Q8—1221no—
540C22×Q8—1221no—
541C22×Q8—1222no—
542C22×Q8—1222no—
543C22×Q8—1224no—
544C22×Q8—1224no—
545C22×Q8—2442no—
546C22×Q8—2442no—
547C22×Q8C22×D6111yescharacteristic
548C22×D4—614no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—1221no—
552C22×D4—1222no—
553C22×D4—1221no—
554C22×D4—1224no—
555C22×D4—1221no—
556C22×D4—2442no—
557C22×D4C22×D6111yescharacteristic
558C23×C4—21no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—1221no—
562C23×C4—1221no—
563C23×C4—1221no—
564#137—12232no—
565C2×Q16—614no—
566C2×Q16—614no—
567C2×Q16—614no—
568C2×Q16—1224no—
569C2×Q16—1224no—
570C2×Q16—2442no—
571C2×SD16—614no—
572C2×SD16—614no—
573C2×SD16—614no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—1224no—
577C2×SD16—1224no—
578C2×SD16—1224no—
579C2×SD16—12232no—
580C2×SD16—1224no—
581C2×SD16—2442no—
582C2×SD16D24418yescomplemented
583C2×SD16C22×D6114yes—
584C2×M16—614no—
585C2×M16—1224no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—614no—
589C22×C8—1224no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—614no—
593C4⋊Q8—1228no—
594C4⋊Q8—1222no—
595#124—614no—
596#124—1222no—
597#123—1228no—
598C22⋊Q8—614no—
599C22⋊Q8—614no—
600C22⋊Q8—614no—
601C22⋊Q8—1228no—
602C22⋊Q8—1228no—
603C22⋊Q8—1222no—
604C22⋊Q8—1222no—
605C22⋊Q8—1222no—
606#121—614no—
607#121—1228no—
608#121—1222no—
609#120—1228no—
610C4×Q8—22no—
611C4×Q8C22×D6114yescomplemented
612C4×D4—22no—
613C4×D4—614no—
614C4×D4—614no—
615C4×D4—1228no—
616C4×D4C22×D6114yes—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4C22×D6111yescharacteristic
625C2×C4⋊C4C22×D6111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—1228no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—21no—
637C2×C42C22×D6111yescharacteristic
638#107C22×D6114yescomplemented
639C4⋊C8—614no—
640#103—614no—
641#103—614no—
642#103—614no—
643#103C22×D6114yescomplemented
644#102—614no—
645#102C22×D6114yes—
646C22⋊C8—614no—
647C22⋊C8—614no—
648#97C22×D6114yescomplemented
649C24—21no—
650C24—611no—
651C24—611no—
652C24—1224no—
653C24—1221no—
654C24—4882no—
655C24—2444no—
656C24—2444no—
657#41—1228no—
658#41—2444no—
659#41—2448no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—612no—
663C2×Q8—612no—
664C2×Q8—612no—
665C2×Q8—1224no—
666C2×Q8—1224no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1228no—
671C2×Q8—1228no—
672C2×Q8—1222no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—2444no—
679C2×Q8—2444no—
680C2×Q8—2444no—
681C2×Q8—2444no—
682C2×Q8—2448no—
683C2×Q8—2448no—
684C2×Q8C2×D24414yes—
685C2×Q8C23×D6112yes—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—614no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1228no—
694C2×D4—1224no—
695C2×D4—1221no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—4882no—
699C2×D4—2444no—
700C2×D4—2448no—
701C2×D4—2444no—
702C2×D4—2444no—
703C2×D4C2×D24414yes—
704C2×D4C23×D6112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—24no—
709C22×C4—82no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—1224no—
717C22×C4—1224no—
718C22×C4—1224no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4—2444no—
729C22×C4D4×D6111yescharacteristic
730C22×C4D4×D6111yescharacteristic
731C22×C4C23×D6111yescharacteristic
732Q16—1228no—
733Q16—1228no—
734Q16—2444no—
735SD16—1228no—
736SD16—1228no—
737SD16—1228no—
738SD16—1228no—
739SD16—2444no—
740SD16C2×D244116yescomplemented
741M16—1228no—
742C2×C8—22no—
743C2×C8—612no—
744C2×C8—612no—
745C2×C8—1222no—
746C2×C8—1222no—
747C2×C8—1228no—
748C2×C8C2×D24414yes—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—614no—
755C4⋊C4—1224no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1224no—
760C4⋊C4C23×D6112yes—
761C4⋊C4C23×D6112yes—
762C22⋊C4—24no—
763C22⋊C4—614no—
764C22⋊C4—614no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—1224no—
769C22⋊C4—1224no—
770C22⋊C4—1224no—
771C42—24no—
772C42D4×D6112yes—
773C42C23×D6112yes—
774C23—22no—
775C23—24no—
776C23—42no—
777C23—42no—
778C23—614no—
779C23—612no—
780C23—612no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—48816no—
788C23—4884no—
789C23—2448no—
790C23—2448no—
791C23—2442no—
792C23—2442no—
793C23—2442no—
794C23C2×D4×D6111yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—1222no—
798Q8—1222no—
799Q8—1222no—
800Q8—1222no—
801Q8—1222no—
802Q8—1222no—
803Q8—2448no—
804Q8—2448no—
805Q8—2442no—
806Q8—2442no—
807Q8—2442no—
808Q8C22×D24414yes—
809D4—22no—
810D4—24no—
811D4—1228no—
812D4—1222no—
813D4—1222no—
814D4—4884no—
815D4—2448no—
816D4—2448no—
817D4—2442no—
818D4C22×D24414yes—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1224no—
837C2×C4—1224no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—2448no—
842C2×C4—2448no—
843C2×C4—2448no—
844C2×C4—2442no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4C2×D4×D6112yes—
848C2×C4C2×D4×D6112yes—
849C2×C4C2×D4×D6111yescharacteristic
850C2×C4C22×D24412yes—
851C2×C4#1451982312yes—
852C2×C4C24×D6111yescharacteristic
853C8—22no—
854C8—1222no—
855C8—1222no—
856C8C22×D24414yes—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—48no—
861C22—614no—
862C22—1222no—
863C22—1222no—
864C22—1228no—
865C22—1222no—
866C22—1222no—
867C22—1222no—
868C22—48816no—
869C22—4884no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22—2444no—
874C22D4×D24412yes—
875C22#137×D6112yes—
876C22#1684057212yes—
877C22C22×D4×D6111yescharacteristic
878C4—24no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—1222no—
884C4—1222no—
885C4—2442no—
886C4—2442no—
887C4—2442no—
888C4D4×D24412yes—
889C4C23×D24411yescharacteristic
890C4C2×#1451982311yescharacteristic
891C2—44no—
892C2—1224no—
893C2—4882no—
894C2—2442no—
895C2#2145733114yesdirect product factor
896C2C2×D4×D24411yescharacteristic
897C2C2×#137×D6111yescharacteristic
898C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#16840407C2
hypercenterC2×#440D61
hypocenterC61C2×#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#14519806C2semidirect
2. C22×SD16×D61C2semidirect
3. C2×Q8×D244C2semidirect
5. #21457331C2direct (N × H)
6. C2×#16840156C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16840004C2semidirect
9. C2×#16839984C2semidirect
10. C2×#16839967C2semidirect
11. C2×#16839925C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839902C2semidirect
14. C2×#16839914C2semidirect
15. C2×#16839835C2semidirect
16. C2×C61×#440C2semidirect
19. C22×Q8×D61C22semidirect
22. C2×#14519806C22semidirect
23. C22×Dic244C22semidirect
24. C22×Dic244C22semidirect
25. C22×#11758202C22semidirect
32. C2×SD16×D61C22semidirect
33. C22×#11758189C22semidirect
36. Q8×D244C22semidirect
40. C2×#14519777C22semidirect
47. C2×#14519757C22semidirect
54. #16840156C22semidirect
55. #16840009C22semidirect
56. #16840004C22semidirect
57. #16839984C22semidirect
58. #16839967C22semidirect
59. #16839925C22semidirect
60. #16839919C22semidirect
61. #16839914C22semidirect
62. #16839902C22semidirect
63. #16839835C22semidirect
64. C2×C4⋊#92418C22semidirect
65. C2×#14519700C22semidirect
66. C2×#14519700C22semidirect
67. C2×#14519700C22semidirect
70. C2×#14519689C22semidirect
72. C2×C4×Q8×C61C22semidirect
74. C61×#440C22semidirect
75. C2×#107×C61C22semidirect
76. C2×#103×C61C22semidirect
78. C2×#97×C61C22semidirect
96. C2×Q8×D61C23semidirect
114. C2×Dic244C23semidirect
115. C2×Dic244C23semidirect
117. C2×#11758202C23semidirect
130. C2×#11758189C23semidirect
137. #14519777C23semidirect
148. #14519757C23semidirect
171. C4⋊#92418C23semidirect
172. #14519700C23semidirect
173. #14519700C23semidirect
174. #14519700C23semidirect
177. #14519689C23semidirect
181. C2×SD16×C61D4semidirect
186. C4×Q8×C61C23semidirect
195. #107×C61C23semidirect
196. #103×C61C23semidirect
198. #97×C61C23semidirect
282. SD16×C61C2×D4semidirect
342. C22×D61#137semidirect
428. C2×D61C2×#137semidirect
456. C2×#440D61semidirect
459. C2×C61#3266semidirect
501. C2×C4×Q8C2×D61semidirect
515. #440C2×D61semidirect
517. C2×#107C2×D61semidirect
522. C2×#103C2×D61semidirect
527. C2×#97C2×D61semidirect
528. C61C2×#3266semidirect
582. C2×SD16D244semidirect
611. C4×Q8C22×D61semidirect
638. #107C22×D61semidirect
643. #103C22×D61semidirect
648. #97C22×D61semidirect
740. SD16C2×D244semidirect
895. C2#21457331direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198062
C22×SD16×D612
C2×Q8×D2442
C2×#168404072
#214573312
C2×#168401562
C2×#168400092
C2×#168400042
C2×#168399842
C2×#168399672
C2×#168399252
C2×#168399192
C2×#168399022
C2×#168399142
C2×#168398352
C2×C61×#4402
C2×#326661