Finite Group Databasebeta

← C2×#21456785 #30551186

Subgroups — C2×#21456785 #30551186

Order 15616.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic, complemented
2C2×#124×D61C211yesmaximal, characteristic, complemented
3#21456785C2116yesmaximal, direct product factor
4C2×#16840146C211yesmaximal, characteristic, complemented
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840119C211yesmaximal, characteristic, complemented
7C2×#16839987C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839980C211yesmaximal, characteristic, complemented
10C2×#16839976C211yesmaximal, characteristic, complemented
11C2×#16839919C211yesmaximal, characteristic, complemented
12C2×#16839902C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic
15C2×#16839813C211yesmaximal, characteristic, complemented
16C2×C61×#488C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic, complemented
20C22×#11758202C2211yescharacteristic, complemented
21C22×#11758190C2211yescharacteristic
22C22×#11758190C2211yescharacteristic, complemented
23C22×#11758200C2211yescharacteristic
24C22×#11758201C2211yescharacteristic, complemented
25C22×D488C2211yescharacteristic
26C22×#11758199C2211yescharacteristic
27#16840297—24no—
28#16840297C2218yescomplemented
29C2×#14519772—21no—
30C2×#14519766C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519765C2211yescharacteristic, complemented
33C2×#14519764C2211yescharacteristic
34C2×#14519763—21no—
35C2×#14519763—21no—
36#124×D61—24no—
37#124×D61C2218yescomplemented
38C2×#14519762—21no—
39C2×#14519757C2211yescharacteristic
40C2×#14519752C2211yescharacteristic
41C2×#14519742C2211yescharacteristic, complemented
42C2×#14519739—21no—
43C2×#14519739C2211yescharacteristic, complemented
44C2×#14519735—21no—
45C2×C22⋊C4×D61—21no—
46C2×C22⋊C4×D61—21no—
47C2×C42×D61C2211yescharacteristic
48#16840146C2218yescomplemented
49#16840144C2218yescomplemented
50#16840119C2218yescomplemented
51#16839987C2218yescomplemented
52#16839983C2218yescomplemented
53#16839980C2218yescomplemented
54#16839976C2218yescomplemented
55#16839919C2218yescomplemented
56#16839914C2218yescomplemented
57#16839902C2218yescomplemented
58#16839897C2218yes—
59#16839813C2218yescomplemented
60C2×#14519706C2211yescharacteristic, complemented
61C2×#14519706C2211yescharacteristic, complemented
62C2×#14519700C2211yescharacteristic, complemented
63C2×#14519700C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic, complemented
69C2×#125×C61C2211yescharacteristic, complemented
70C2×#124×C61C2211yescharacteristic
71C61×#488C2218yescomplemented
72C2×#103×C61C2211yescharacteristic, complemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×Dic122C2311yescharacteristic
81C2×Q8×D61—22no—
82C2×Q8×D61—42no—
83C2×Q8×D61—42no—
84C2×Q8×D61C2314yes—
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C2×D4×D61—22no—
90C2×D4×D61—42no—
91C2×D4×D61—42no—
92C2×D4×D61C2314yes—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61D411yescharacteristic
96C22×C4×D61D411yescharacteristic
97C22×C4×D61C2311yescharacteristic
98C2×Dic244—42no—
99C2×Dic244C2314yescomplemented
100C2×#11758202—42no—
101C2×#11758202C2314yescomplemented
102C2×#11758190—42no—
103C2×#11758190—42no—
104C2×#11758190C2314yes—
105C2×#11758190C2314yescomplemented
106C2×#11758200—42no—
107C2×#11758200C2314yes—
108C2×#11758201—42no—
109C2×#11758201C2314yescomplemented
110C2×D488—42no—
111C2×D488C2314yes—
112C2×#11758199—42no—
113C2×#11758199C2314yes—
114C22×#92418C2311yescharacteristic
115C22×#92418C2311yescharacteristic
116#14519772—28no—
117#14519766—22no—
118#14519766C2314yes—
119#14519765—22no—
120#14519765—22no—
121#14519765C2314yes—
122#14519765C2314yescomplemented
123#14519764—22no—
124#14519764C2314yes—
125#14519763—28no—
126#14519763—28no—
127#14519762—28no—
128#14519757—22no—
129#14519757C2314yes—
130#14519752—22no—
131#14519752C2314yes—
132#14519742—22no—
133#14519742C2314yescomplemented
134#14519739—28no—
135#14519739—22no—
136#14519739C2314yescomplemented
137#14519735—28no—
138C2×C4⋊Dic61—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C22⋊C4×D61—28no—
152C22⋊C4×D61—28no—
153C2×C4×Dic61—21no—
154C2×C4×Dic61D411yescharacteristic
155C2×C4×Dic61D411yescharacteristic
156C2×C4×Dic61C2311yescharacteristic
157C42×D61D414yes—
158C42×D61C2314yes—
159#14519706C2314yescomplemented
160#14519706C2314yescomplemented
161#14519700C2314yescomplemented
162#14519700C2314yescomplemented
163#14519697C2314yes—
164#14519697C2314yes—
165#14519689C2314yes—
166#14519689C2314yes—
167C4×#92418C2314yescomplemented
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#125×C61—22no—
173#125×C61C2314yescomplemented
174#124×C61—22no—
175#124×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C42×C61C2311yescharacteristic
183#103×C61C2314yescomplemented
184#103×C61C2314yescomplemented
185#102×C61C2314yes—
186#102×C61C2314yes—
187C4×C8×C61C2314yescomplemented
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—44no—
194C23×D61—44no—
195C23×D61C2×D411yescharacteristic
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61C2412yes—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—22no—
203C2×D4×C61C2412yes—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217Q8×D61—44no—
218Q8×D61—44no—
219Q8×D61—48no—
220D4×D61—44no—
221D4×D61—44no—
222D4×D61—48no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—24no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—44no—
231C2×D244C2412yes—
232C2×D244C2412yes—
233C2×C4×D61—24no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—42no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61C2×D414yes—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D414yes—
244C2×C4×D61C2412yes—
245C2×Dic122—22no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—22no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—24no—
252C2×Dic122—44no—
253C2×Dic122C2412yes—
254C2×Dic122C2412yes—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61—24no—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C42×C61C2×D412yes—
268C42×C61C2412yes—
269C22⋊Dic61—24no—
270C22⋊Dic61—24no—
271#11758202—44no—
272#11758201—44no—
273#11758200—44no—
274#11758199—44no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284C4⋊Dic61—24no—
285#11758196—24no—
286C4×Dic61—24no—
287C4×Dic61C2×D412yes—
288C4×Dic61C2×D414yes—
289C4×Dic61C2×D414yes—
290C4×Dic61C2412yes—
291C2×#92418—22no—
292C2×#92418—22no—
293C2×#92418C2412yes—
294C2×#92418C2412yes—
295Dic244—44no—
296D488—44no—
297#11758190—44no—
298#11758190—44no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—48no—
309C22×D61—48no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—48no—
317C22×D61—816no—
318C22×D61#13514yes—
319C22×D61C22×D412yes—
320Q8×C61—22no—
321Q8×C61—22no—
322Q8×C61—42no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—42no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61—42no—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D412yes—
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61H(5,𝔽2)12yes—
338C2×C4×C61H(5,𝔽2)12yes—
339C2×C4×C61C2511yescharacteristic
340C22⋊D61—48no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351D244—22no—
352D244—22no—
353D244—22no—
354D244—22no—
355D244—48no—
356D244—42no—
357D244—42no—
358C4×D61—28no—
359C4×D61—24no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—44no—
363C4×D61—48no—
364C4×D61—48no—
365Dic122—22no—
366Dic122—22no—
367Dic122—22no—
368Dic122—22no—
369Dic122—48no—
370Dic122—42no—
371Dic122—42no—
372C8×C61—22no—
373C8×C61—22no—
374#92418—22no—
375#92418—22no—
376C2×#3211—611nomaximal, Sylow
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—84no—
381C22×C61#53512yes—
382C22×C61C2×#13512yes—
383C22×C61#57512yes—
384C22×C61C23×D411yescharacteristic
385C2×D61—22no—
386C2×D61—28no—
387C2×D61—22no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—816no—
395C2×D61—84no—
396C2×D61—84no—
397C2×D61C2×#13514yes—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#53512yes—
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405C4×C61C2×H(5,𝔽2)11yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—22no—
409Dic61—42no—
410Dic61—42no—
411C2×#529—611no—
412C22×#124—611no—
413#3211—6116no—
414C2×#495—611no—
415C2×#495—611no—
416C2×#488—611no—
417C2×#488D6111yescharacteristic, complemented
418C2×#464—611no—
419C2×#464—611no—
420C2×#463—611no—
421C2×#463—611no—
422C2×#451—611no—
423C2×#448—611no—
424C2×#450—611no—
425C2×#447—611no—
426C2×#431—611no—
427C2×C61—82no—
428C2×C61#321114yescomplemented
429C2×C61C2×#53511yescharacteristic
430C2×C61C22×#13511yescharacteristic
431C2×C61C2×#57511yescharacteristic
432D61—24no—
433D61—82no—
434D61—82no—
435C23×Q8—611no—
436C23×D4—611no—
437C22×Q16—611no—
438C22×Q16—611no—
439C22×SD16—611no—
440C22×SD16—611no—
441C22×SD16—611no—
442C22×SD16—611no—
443C22×D8—611no—
444C22×D8—611no—
445#529—618no—
446#529—1224no—
447C2×#126—1221no—
448C2×#125C2×D6111yescharacteristic, complemented
449C2×#124—611no—
450C2×#124—611no—
451C2×#124—618no—
452C2×#124—611no—
453C2×#124—611no—
454C2×#124—1221no—
455C2×#124—1221no—
456C2×#124—1224no—
457C2×#124C2×D6111yescharacteristic
458C2×#123—1221no—
459C2×C22⋊Q8—611no—
460C2×#121—611no—
461C2×C4×Q8—611no—
462C2×C4×D4—611no—
463C2×C4×D4—1221no—
464C2×#117—1221no—
465C22×C22⋊C4—1221no—
466C22×C22⋊C4—1221no—
467C22×C42—611no—
468#495—618no—
469#495—618no—
470#488—618no—
471#488C2×D6118yescomplemented
472#464—618no—
473#464—618no—
474#463—618no—
475#463—618no—
476#451—618no—
477#450—618no—
478#448—618no—
479#447—618no—
480#431—618no—
481C2×C4⋊C8—611no—
482C2×C4⋊C8—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103C2×D6111yescharacteristic, complemented
486C2×#103C2×D6111yescharacteristic, complemented
487C2×#102—611no—
488C2×#102—611no—
489C2×#102C2×D6111yescharacteristic
490C2×#102C2×D6111yescharacteristic
491C2×C22⋊C8—611no—
492C2×C22⋊C8—611no—
493C2×C4×C8—611no—
494C2×C4×C8C2×D6111yescharacteristic, complemented
495C61C2×#321111yescharacteristic, complemented, Sylow
496C25—1221no—
497C22×Q8—614no—
498C22×Q8—611no—
499C22×Q8—611no—
500C22×Q8—1221no—
501C22×Q8—1222no—
502C22×Q8—2442no—
503C22×Q8—2442no—
504C22×Q8C22×D6111yescharacteristic
505C22×D4—614no—
506C22×D4—611no—
507C22×D4—611no—
508C22×D4—1221no—
509C22×D4—1222no—
510C22×D4—1221no—
511C22×D4—2442no—
512C22×D4—2442no—
513C22×D4C22×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×Q16—614no—
520C2×Q16—614no—
521C2×Q16—2442no—
522C2×Q16—2442no—
523C2×SD16—614no—
524C2×SD16—614no—
525C2×SD16—614no—
526C2×SD16—614no—
527C2×SD16—2442no—
528C2×SD16—2442no—
529C2×SD16—2442no—
530C2×SD16—2442no—
531C2×D8—614no—
532C2×D8—614no—
533C2×D8—2442no—
534C2×D8—2442no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539#126—1228no—
540#125—22no—
541#125C22×D6114yescomplemented
542#124—22no—
543#124—614no—
544#124—614no—
545#124—614no—
546#124—614no—
547#124—1228no—
548#124—1228no—
549#124—1222no—
550#124—1222no—
551#124—1222no—
552#124—1222no—
553#124C22×D6114yes—
554#123—1228no—
555C22⋊Q8—614no—
556C22⋊Q8—1222no—
557#121—614no—
558#121—1222no—
559C4×Q8—614no—
560C4×Q8—1222no—
561C4×D4—614no—
562C4×D4—1222no—
563C4×D4—1228no—
564#117—1228no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1228no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—614no—
590C2×C42—614no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—614no—
594C4⋊C8—614no—
595#103—614no—
596#103—614no—
597#103C22×D6114yescomplemented
598#103C22×D6114yescomplemented
599#102—614no—
600#102—614no—
601#102C22×D6114yes—
602#102C22×D6114yes—
603C22⋊C8—614no—
604C22⋊C8—614no—
605C4×C8—614no—
606C4×C8C22×D6114yescomplemented
607C24—21no—
608C24—611no—
609C24—1224no—
610C24—1221no—
611C24—1221no—
612C24—2444no—
613C24—2444no—
614C24—2444no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—612no—
619C2×Q8—612no—
620C2×Q8—1224no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1222no—
624C2×Q8—1222no—
625C2×Q8—1222no—
626C2×Q8—1222no—
627C2×Q8—2444no—
628C2×Q8—2444no—
629C2×Q8—2444no—
630C2×Q8—2448no—
631C2×Q8C23×D6112yes—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1222no—
642C2×D4—1222no—
643C2×D4—1222no—
644C2×D4—1222no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4—2448no—
649C2×D4—2444no—
650C2×D4C23×D6112yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—614no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—614no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1224no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—2442no—
669C22×C4—2444no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—2444no—
675Q16—2444no—
676SD16—2444no—
677SD16—2444no—
678SD16—2444no—
679SD16—2444no—
680D8—2444no—
681D8—2444no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—612no—
685C2×C8—612no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8C23×D6112yes—
689C2×C8C23×D6112yes—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4C23×D6112yes—
697C4⋊C4C23×D6112yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C42—614no—
712C42—612no—
713C42—614no—
714C42—612no—
715C42—1224no—
716C42D4×D6112yes—
717C42C23×D6112yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—614no—
723C23—612no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—48816no—
729C23—2448no—
730C23—2448no—
731C23—2448no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23—2442no—
738C23C2×D4×D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—1222no—
743Q8—1222no—
744Q8—1222no—
745Q8—1222no—
746Q8—2448no—
747Q8—2442no—
748Q8—2442no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—1222no—
753D4—1222no—
754D4—1222no—
755D4—1222no—
756D4—2448no—
757D4—2448no—
758D4—2442no—
759D4—2442no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—612no—
771C2×C4—1228no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1224no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—2444no—
781C2×C4—2448no—
782C2×C4—2448no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4C2×D4×D6112yes—
786C2×C4C2×D4×D6112yes—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4#1451982312yes—
789C2×C4#1451982312yes—
790C2×C4C24×D6111yescharacteristic
791C8—22no—
792C8—22no—
793C8—1222no—
794C8—1222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—614no—
800C22—1222no—
801C22—1228no—
802C22—1222no—
803C22—48816no—
804C22—4884no—
805C22—4884no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22#1684033012yes—
813C22#135×D6112yes—
814C22#1684055912yes—
815C22C22×D4×D6111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4#1684033012yes—
827C4C2×#1451982311yescharacteristic
828C4C2×#1451982311yescharacteristic
829C2—82no—
830C2—1224no—
831C2—4882no—
832C2—4882no—
833C2#2145678514yesdirect product factor
834C2C2×#1684033011yescharacteristic
835C2C2×#135×D6111yescharacteristic
836C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#488C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
hypercenterC2×#488D61
hypocenterC61C2×#3211
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16840297C2semidirect
2. C2×#124×D61C2semidirect
3. #21456785C2direct (N × H)
4. C2×#16840146C2semidirect
5. C2×#16840144C2semidirect
6. C2×#16840119C2semidirect
7. C2×#16839987C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839976C2semidirect
11. C2×#16839919C2semidirect
12. C2×#16839902C2semidirect
13. C2×#16839914C2semidirect
15. C2×#16839813C2semidirect
16. C2×C61×#488C2semidirect
19. C22×Dic244C22semidirect
20. C22×#11758202C22semidirect
22. C22×#11758190C22semidirect
24. C22×#11758201C22semidirect
28. #16840297C22semidirect
32. C2×#14519765C22semidirect
37. #124×D61C22semidirect
41. C2×#14519742C22semidirect
43. C2×#14519739C22semidirect
48. #16840146C22semidirect
49. #16840144C22semidirect
50. #16840119C22semidirect
51. #16839987C22semidirect
52. #16839983C22semidirect
53. #16839980C22semidirect
54. #16839976C22semidirect
55. #16839919C22semidirect
56. #16839914C22semidirect
57. #16839902C22semidirect
59. #16839813C22semidirect
60. C2×#14519706C22semidirect
61. C2×#14519706C22semidirect
62. C2×#14519700C22semidirect
63. C2×#14519700C22semidirect
68. C2×C4×#92418C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#488C22semidirect
72. C2×#103×C61C22semidirect
73. C2×#103×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
99. C2×Dic244C23semidirect
101. C2×#11758202C23semidirect
105. C2×#11758190C23semidirect
109. C2×#11758201C23semidirect
122. #14519765C23semidirect
133. #14519742C23semidirect
136. #14519739C23semidirect
159. #14519706C23semidirect
160. #14519706C23semidirect
161. #14519700C23semidirect
162. #14519700C23semidirect
167. C4×#92418C23semidirect
173. #125×C61C23semidirect
183. #103×C61C23semidirect
184. #103×C61C23semidirect
187. C4×C8×C61C23semidirect
417. C2×#488D61semidirect
428. C2×C61#3211semidirect
448. C2×#125C2×D61semidirect
471. #488C2×D61semidirect
485. C2×#103C2×D61semidirect
486. C2×#103C2×D61semidirect
494. C2×C4×C8C2×D61semidirect
495. C61C2×#3211semidirect
541. #125C22×D61semidirect
597. #103C22×D61semidirect
598. #103C22×D61semidirect
606. C4×C8C22×D61semidirect
833. C2#21456785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402972
C2×#124×D612
#214567852
C2×#168401462
C2×#168401442
C2×#168401192
C2×#168399872
C2×#168399832
C2×#168399802
C2×#168399762
C2×#168399192
C2×#168399022
C2×#168399142
C2×#168398972
C2×#168398132
C2×C61×#4882
C2×#321161