Finite Group Databasebeta

← C2×#21456637 #30550617

Subgroups — C2×#21456637 #30550617

Order 15616.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic, complemented
2C2×#121×D61C211yesmaximal, characteristic, complemented
3#21456637C2116yesmaximal, direct product factor
4C2×#16840086C211yesmaximal, characteristic, complemented
5C2×#16840094C211yesmaximal, characteristic, complemented
6C2×#16840077C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840014C211yesmaximal, characteristic, complemented
9C2×#16840009C211yesmaximal, characteristic, complemented
10C2×#16840007C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C2×#16839724C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic, complemented
18C22×D4×D61—21no—
19C22×D4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C22×#11758190C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic, complemented
23C22×D488C2211yescharacteristic, complemented
24C22×#11758199C2211yescharacteristic, complemented
25C22×#11758189C2211yescharacteristic, complemented
26C22×#11758189C2211yescharacteristic, complemented
27#16840274—24no—
28#16840274C2218yescomplemented
29C2×#14519761—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519757C2211yescharacteristic, complemented
32C2×#14519752C2211yescharacteristic
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic, complemented
35C2×#14519751C2211yescharacteristic
36C2×#14519750—21no—
37C2×#14519749—21no—
38C2×#14519748C2211yescharacteristic
39#121×D61—24no—
40#121×D61C2218yescomplemented
41C2×#14519747—21no—
42C2×C4×D244—21no—
43C2×C4×D244—21no—
44C2×C4⋊C4×D61C2211yescharacteristic
45C2×C22⋊C4×D61—21no—
46#16840094C2218yescomplemented
47#16840086C2218yescomplemented
48#16840077C2218yescomplemented
49#16840016C2218yescomplemented
50#16840014C2218yescomplemented
51#16840009C2218yescomplemented
52#16840007C2218yescomplemented
53#16839914C2218yescomplemented
54#16839909C2218yescomplemented
55#16839905C2218yescomplemented
56#16839897C2218yescomplemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519697C2211yescharacteristic, complemented
65#16839724C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic, complemented
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C24×D61D411yescharacteristic
79C2×#11758222—22no—
80C2×#11758222—42no—
81C2×#11758222—42no—
82C2×#11758222C2314yescomplemented
83C22×Dic122C2311yescharacteristic
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C2×D4×D61—28no—
94C2×D4×D61—22no—
95C2×D4×D61—42no—
96C2×D4×D61—42no—
97C2×D4×D61—48no—
98C2×D4×D61C2314yes—
99C23×Dic61D411yescharacteristic
100C22×C4×D61—21no—
101C22×C4×D61—21no—
102C22×C4×D61—42no—
103C22×C4×D61—42no—
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106C22×C4×D61D414yes—
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C2314yes—
110C2×#11758190—42no—
111C2×#11758190C2314yescomplemented
112C2×#11758200—42no—
113C2×#11758200C2314yescomplemented
114C2×D488—42no—
115C2×D488C2314yescomplemented
116C2×#11758199—42no—
117C2×#11758199C2314yescomplemented
118C2×#11758189—42no—
119C2×#11758189—42no—
120C2×#11758189C2314yescomplemented
121C2×#11758189C2314yescomplemented
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124#14519761—28no—
125#14519757—22no—
126#14519757—22no—
127#14519757C2314yes—
128#14519757C2314yescomplemented
129#14519752—22no—
130#14519752—22no—
131#14519752—22no—
132#14519752C2314yes—
133#14519752C2314yes—
134#14519752C2314yescomplemented
135#14519751—22no—
136#14519751C2314yes—
137#14519750—28no—
138#14519749—28no—
139#14519748—22no—
140#14519748C2314yes—
141#14519747—28no—
142C4×D244—28no—
143C4×D244—28no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61—21no—
146C2×C4⋊Dic61C2311yescharacteristic
147C2×#11758196—21no—
148C4⋊C4×D61—22no—
149C4⋊C4×D61C2314yes—
150C2×C22⋊Dic61—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C22⋊C4×D61—28no—
158#14519710C2314yescomplemented
159#14519708C2314yescomplemented
160#14519702C2314yescomplemented
161#14519700C2314yescomplemented
162#14519699C2314yescomplemented
163#14519697C2314yescomplemented
164#14519697C2314yescomplemented
165#14519697C2314yescomplemented
166C22⋊#92418C2314yescomplemented
167#14519689C2314yes—
168#14519689C2314yes—
169C22×D4×C61—21no—
170C22×D4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#121×C61—22no—
175#121×C61C2314yes—
176#117×C61—22no—
177#117×C61C2314yescomplemented
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61—21no—
184#107×C61C2314yescomplemented
185#106×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187#102×C61C2314yescomplemented
188C22⋊C8×C61C2314yescomplemented
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—24no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—24no—
195C23×D61—42no—
196C23×D61—42no—
197C23×D61—44no—
198C23×D61—44no—
199C23×D61—44no—
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D411yescharacteristic
202C23×D61C2×D414yes—
203C2×D4×C61—24no—
204C2×D4×C61—21no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—44no—
208C2×D4×C61C2412yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—44no—
225C2×C22⋊D61—44no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—42no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D414yes—
232D4×D61—44no—
233D4×D61—44no—
234D4×D61—48no—
235D4×D61—432no—
236#11758222—44no—
237#11758222—44no—
238#11758222—48no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—24no—
244C2×D244—24no—
245C2×D244—24no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—44no—
249C2×D244—44no—
250C2×D244—44no—
251C2×D244C2412yes—
252C2×D244C2412yes—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—24no—
258C2×C4×D61—24no—
259C2×C4×D61—48no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61—44no—
265C2×C4×D61—44no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2×D414yes—
269C2×C4×D61C2×D414yes—
270C2×C4×D61C2412yes—
271C2×C4×D61C2412yes—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—21no—
275C2×Dic122C2412yes—
276C2×C8×C61—22no—
277C2×C8×C61—22no—
278C2×C8×C61C2412yes—
279C2×C8×C61C2412yes—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C2412yes—
284C4⋊C4×C61C2412yes—
285C4⋊C4×C61C2412yes—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C42×C61—24no—
289C22⋊Dic61—24no—
290#11758200—44no—
291#11758199—44no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295#11758198—24no—
296#11758198—24no—
297#11758198—24no—
298C4⋊Dic61—21no—
299C4⋊Dic61—24no—
300C4⋊Dic61—24no—
301C4⋊Dic61C2412yes—
302#11758196—24no—
303C2×#92418—22no—
304C2×#92418—22no—
305C2×#92418C2412yes—
306C2×#92418C2412yes—
307D488—44no—
308#11758190—44no—
309#11758189—44no—
310#11758189—44no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61C22×D412yes—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—28no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61—416no—
331C22×D61—48no—
332C22×D61—48no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—48no—
340C22×D61—816no—
341C22×D61AGL(1,ℤ/8)14yes—
342C22×D61C22×D412yes—
343C22×D61C22×D412yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—48no—
347D4×C61—42no—
348C2×C4×C61—22no—
349C2×C4×C61—24no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61H(5,𝔽2)12yes—
361C2×C4×C61H(5,𝔽2)12yes—
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—48no—
364C22⋊D61—48no—
365C22⋊D61—48no—
366C22⋊D61—48no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—44no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—22no—
377D244—22no—
378D244—22no—
379D244—22no—
380D244—48no—
381D244—48no—
382D244—48no—
383D244—42no—
384D244—42no—
385C4×D61—24no—
386C4×D61—24no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—22no—
391C4×D61—44no—
392C4×D61—44no—
393C4×D61—48no—
394C4×D61—48no—
395Dic122—22no—
396Dic122—22no—
397Dic122—42no—
398C8×C61—22no—
399C8×C61—22no—
400#92418—22no—
401#92418—22no—
402C2×#3194—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—44no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—84no—
411C22×C61#53412yes—
412C22×C61C2×AGL(1,ℤ/8)12yes—
413C22×C61#57512yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—22no—
416C2×D61—28no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—416no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—816no—
430C2×D61—84no—
431C2×D61—84no—
432C2×D61C2×AGL(1,ℤ/8)14yes—
433C4×C61—22no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61#53412yes—
438C4×C61C2×H(5,𝔽2)11yescharacteristic
439C4×C61C2×H(5,𝔽2)11yescharacteristic
440Dic61—22no—
441Dic61—22no—
442Dic61—42no—
443Dic61—42no—
444C2×#525—611no—
445C22×#121—611no—
446#3194—6116no—
447C2×#482—611no—
448C2×#482D6111yescharacteristic, complemented
449C2×#483—611no—
450C2×#480—611no—
451C2×#469—611no—
452C2×#469—611no—
453C2×#468—611no—
454C2×#468—611no—
455C2×#449—611no—
456C2×#449—611no—
457C2×#450—611no—
458C2×#447—611no—
459C2×#407—611no—
460C2×C61—42no—
461C2×C61—82no—
462C2×C61#319414yescomplemented
463C2×C61C2×#53411yescharacteristic
464C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
465C2×C61C2×#57511yescharacteristic
466D61—24no—
467D61—42no—
468D61—82no—
469D61—82no—
470C22×#41—611no—
471C23×D4—611no—
472C23×D4—1221no—
473C24×C4—611no—
474C22×SD16—611no—
475C22×SD16—611no—
476C22×D8—611no—
477C22×D8—611no—
478C22×M16—611no—
479C22×M16—611no—
480#525—618no—
481#525—1224no—
482C2×#123—1221no—
483C2×C22⋊Q8—611no—
484C2×C22⋊Q8—611no—
485C2×#121—611no—
486C2×#121—611no—
487C2×#121—618no—
488C2×#121—611no—
489C2×#121—611no—
490C2×#121—611no—
491C2×#121—1221no—
492C2×#121—1224no—
493C2×#121—1221no—
494C2×#121C2×D6111yescharacteristic
495C2×#120—1221no—
496C2×C4×D4—1221no—
497C2×C4×D4—1221no—
498C2×#117C2×D6111yescharacteristic, complemented
499C22×C4⋊C4—611no—
500C22×C22⋊C4—1221no—
501#483—618no—
502#482—618no—
503#482C2×D6118yescomplemented
504#480—618no—
505#469—618no—
506#469—618no—
507#468—618no—
508#468—618no—
509#450—618no—
510#449—618no—
511#449—618no—
512#447—618no—
513C2×#107—611no—
514C2×#107C2×D6111yescharacteristic, complemented
515C2×#106—611no—
516C2×#106C2×D6111yescharacteristic, complemented
517C2×#103—611no—
518C2×#103—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102C2×D6111yescharacteristic, complemented
524C2×#102C2×D6111yescharacteristic, complemented
525#407—618no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8C2×D6111yescharacteristic, complemented
530C61C2×#319411yescharacteristic, complemented, Sylow
531C25—611no—
532C25—1221no—
533C2×#41—614no—
534C2×#41—1222no—
535C2×#41—2442no—
536C2×#41—2442no—
537C22×Q8—611no—
538C22×D4—21no—
539C22×D4—614no—
540C22×D4—611no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1222no—
546C22×D4—1221no—
547C22×D4—1228no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4—1221no—
551C22×D4—2442no—
552C22×D4—2442no—
553C22×D4—2448no—
554C22×D4C22×D6111yescharacteristic
555C23×C4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—614no—
561C23×C4—614no—
562C23×C4—1221no—
563C23×C4—1221no—
564C23×C4—2442no—
565C23×C4—2442no—
566C23×C4C22×D6111yescharacteristic
567C2×SD16—614no—
568C2×SD16—614no—
569C2×SD16—2442no—
570C2×SD16—2442no—
571C2×D8—614no—
572C2×D8—614no—
573C2×D8—2442no—
574C2×D8—2442no—
575C2×M16—614no—
576C2×M16—614no—
577C2×M16—2442no—
578C2×M16—2442no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6111yescharacteristic
583#123—1228no—
584C22⋊Q8—614no—
585C22⋊Q8—614no—
586C22⋊Q8—1222no—
587C22⋊Q8—1222no—
588#121—22no—
589#121—614no—
590#121—614no—
591#121—614no—
592#121—614no—
593#121—614no—
594#121—1228no—
595#121—1222no—
596#121—1222no—
597#121—1222no—
598#121—1222no—
599#121—1228no—
600#121—1222no—
601#121C22×D6114yes—
602#120—1228no—
603C4×D4—1228no—
604C4×D4—1228no—
605#117—22no—
606#117C22×D6114yescomplemented
607C2×C4⋊C4—611no—
608C2×C4⋊C4—614no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4C22×D6111yescharacteristic
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C4⋊C4C22×D6111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—1228no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C42—21no—
627#107—614no—
628#107C22×D6114yescomplemented
629#106—614no—
630#106C22×D6114yescomplemented
631#103—614no—
632#103—614no—
633#102—614no—
634#102—614no—
635#102—614no—
636#102—614no—
637#102C22×D6114yescomplemented
638#102C22×D6114yescomplemented
639C22⋊C8—614no—
640C22⋊C8—614no—
641C22⋊C8—614no—
642C22⋊C8C22×D6114yescomplemented
643C24—21no—
644C24—611no—
645C24—611no—
646C24—614no—
647C24—1224no—
648C24—1224no—
649C24—1221no—
650C24—1221no—
651C24—2442no—
652C24—2442no—
653C24—2444no—
654C24—2444no—
655C24—2444no—
656C24D4×D6111yescharacteristic
657#41—2444no—
658#41—2444no—
659#41—2448no—
660C2×Q8—612no—
661C2×Q8—1221no—
662C2×Q8—1222no—
663C2×Q8—1222no—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—612no—
670C2×D4—612no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4—2444no—
689C2×D4—2448no—
690C2×D4—2444no—
691C2×D4—24432no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4C23×D6112yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—614no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—614no—
709C22×C4—614no—
710C22×C4—1224no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1224no—
718C22×C4—2448no—
719C22×C4—2444no—
720C22×C4—2444no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4—2444no—
724C22×C4—2444no—
725C22×C4—2442no—
726C22×C4D4×D6112yes—
727C22×C4D4×D6111yescharacteristic
728C22×C4C23×D6112yes—
729C22×C4C23×D6111yescharacteristic
730SD16—2444no—
731SD16—2444no—
732D8—2444no—
733D8—2444no—
734M16—2444no—
735M16—2444no—
736C2×C8—22no—
737C2×C8—22no—
738C2×C8—612no—
739C2×C8—612no—
740C2×C8—1222no—
741C2×C8—1222no—
742C2×C8C23×D6112yes—
743C2×C8C23×D6112yes—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—612no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1221no—
752C4⋊C4C23×D6112yes—
753C4⋊C4C23×D6112yes—
754C4⋊C4C23×D6112yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C42—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—614no—
773C23—612no—
774C23—612no—
775C23—1228no—
776C23—1222no—
777C23—1222no—
778C23—1222no—
779C23—1222no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—48816no—
784C23—2444no—
785C23—2444no—
786C23—2448no—
787C23—2448no—
788C23—2448no—
789C23—24416no—
790C23—2442no—
791C23—2442no—
792C23—2442no—
793C23—2442no—
794C23—2442no—
795C23—2442no—
796C23C2×D4×D6112yes—
797C23C2×D4×D6111yescharacteristic
798Q8—1222no—
799Q8—1222no—
800Q8—2442no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—1222no—
806D4—1222no—
807D4—1222no—
808D4—1222no—
809D4—2448no—
810D4—2448no—
811D4—2448no—
812D4—2448no—
813D4—2448no—
814D4—2448no—
815D4—2448no—
816D4—2442no—
817D4—2442no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1224no—
833C2×C4—1224no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—2444no—
841C2×C4—2444no—
842C2×C4—2448no—
843C2×C4—2448no—
844C2×C4—2444no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4C2×D4×D6112yes—
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4#1451982312yes—
850C2×C4#1451982312yes—
851C2×C4C24×D6111yescharacteristic
852C8—22no—
853C8—22no—
854C8—1222no—
855C8—1222no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—614no—
865C22—1222no—
866C22—1222no—
867C22—1228no—
868C22—1222no—
869C22—1222no—
870C22—1222no—
871C22—48816no—
872C22—4884no—
873C22—4884no—
874C22—24416no—
875C22—2442no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22—2444no—
882C22#1684032312yes—
883C22AGL(1,ℤ/8)×D6112yes—
884C22#1684055912yes—
885C22C22×D4×D6111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—1222no—
891C4—1222no—
892C4—2442no—
893C4—2442no—
894C4#1684032312yes—
895C4C2×#1451982311yescharacteristic
896C4C2×#1451982311yescharacteristic
897C2—42no—
898C2—82no—
899C2—1224no—
900C2—4882no—
901C2—4882no—
902C2—2442no—
903C2#2145663714yesdirect product factor
904C2C2×#1684032311yescharacteristic
905C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
906C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840274C2semidirect
2. C2×#121×D61C2semidirect
3. #21456637C2direct (N × H)
4. C2×#16840086C2semidirect
5. C2×#16840094C2semidirect
6. C2×#16840077C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840014C2semidirect
9. C2×#16840009C2semidirect
10. C2×#16840007C2semidirect
11. C2×#16839909C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839897C2semidirect
15. C2×#16839724C2semidirect
16. C2×C61×#482C2semidirect
17. C22×#11758222C22semidirect
21. C22×#11758190C22semidirect
22. C22×#11758200C22semidirect
23. C22×D488C22semidirect
24. C22×#11758199C22semidirect
25. C22×#11758189C22semidirect
26. C22×#11758189C22semidirect
28. #16840274C22semidirect
31. C2×#14519757C22semidirect
34. C2×#14519752C22semidirect
40. #121×D61C22semidirect
46. #16840094C22semidirect
47. #16840086C22semidirect
48. #16840077C22semidirect
49. #16840016C22semidirect
50. #16840014C22semidirect
51. #16840009C22semidirect
52. #16840007C22semidirect
53. #16839914C22semidirect
54. #16839909C22semidirect
55. #16839905C22semidirect
56. #16839897C22semidirect
57. C2×#14519710C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
61. C2×#14519699C22semidirect
62. C2×#14519697C22semidirect
63. C2×#14519697C22semidirect
64. C2×#14519697C22semidirect
65. #16839724C22semidirect
66. C2×C22⋊#92418C22semidirect
70. C2×#117×C61C22semidirect
71. C61×#482C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#102×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
82. C2×#11758222C23semidirect
111. C2×#11758190C23semidirect
113. C2×#11758200C23semidirect
115. C2×D488C23semidirect
117. C2×#11758199C23semidirect
120. C2×#11758189C23semidirect
121. C2×#11758189C23semidirect
128. #14519757C23semidirect
134. #14519752C23semidirect
158. #14519710C23semidirect
159. #14519708C23semidirect
160. #14519702C23semidirect
161. #14519700C23semidirect
162. #14519699C23semidirect
163. #14519697C23semidirect
164. #14519697C23semidirect
165. #14519697C23semidirect
166. C22⋊#92418C23semidirect
177. #117×C61C23semidirect
184. #107×C61C23semidirect
185. #106×C61C23semidirect
186. #102×C61C23semidirect
187. #102×C61C23semidirect
188. C22⋊C8×C61C23semidirect
448. C2×#482D61semidirect
462. C2×C61#3194semidirect
498. C2×#117C2×D61semidirect
503. #482C2×D61semidirect
514. C2×#107C2×D61semidirect
516. C2×#106C2×D61semidirect
523. C2×#102C2×D61semidirect
524. C2×#102C2×D61semidirect
529. C2×C22⋊C8C2×D61semidirect
530. C61C2×#3194semidirect
606. #117C22×D61semidirect
628. #107C22×D61semidirect
630. #106C22×D61semidirect
637. #102C22×D61semidirect
638. #102C22×D61semidirect
642. C22⋊C8C22×D61semidirect
903. C2#21456637direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402742
C2×#121×D612
#214566372
C2×#168400862
C2×#168400942
C2×#168400772
C2×#168400162
C2×#168400142
C2×#168400092
C2×#168400072
C2×#168399092
C2×#168399052
C2×#168399142
C2×#168398972
C2×#168397242
C2×C61×#4822
C2×#319461