Finite Group Databasebeta

← C2×#21457426 #30555117

Subgroups — C2×#21457426 #30555117

Order 15616.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519803C211yesmaximal, characteristic, complemented
2C22×#14519802C211yesmaximal, characteristic, complemented
3C2×#16840408C211yesmaximal, characteristic, complemented
4#21457426C2116yesmaximal, direct product factor
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840010C211yesmaximal, characteristic, complemented
7C2×#16840006C211yesmaximal, characteristic, complemented
8C2×#16839977C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839922C211yesmaximal, characteristic, complemented
12C2×#16839896C211yesmaximal, characteristic, complemented
13C2×#16839895C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×#16839840C211yesmaximal, characteristic, complemented
16C2×C61×#546C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic, complemented
19C2×#14519803—28no—
20C2×#14519803C2218yescomplemented
21C2×#14519802—28no—
22C2×#14519802C2218yescomplemented
23C22×#11758202C2211yescharacteristic, complemented
24C22×#11758200C2211yescharacteristic, complemented
25C22×#11758200C2211yescharacteristic, complemented
26C22×#11758201C2211yescharacteristic, complemented
27C22×#11758201C2211yescharacteristic, complemented
28C22×#11758199C2211yescharacteristic
29C22×#11758199C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic, complemented
33C22×#11758194C2211yescharacteristic, complemented
34#16840408—24no—
35#16840408C2218yescomplemented
36C2×#14519765C2211yescharacteristic, complemented
37C2×#14519762—21no—
38C2×#14519756C2211yescharacteristic, complemented
39C2×#14519751C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519745—21no—
42C2×C4×D244C2211yescharacteristic, complemented
43C2×C22⋊C4×D61—21no—
44#16840144C2218yescomplemented
45#16840010C2218yescomplemented
46#16840006C2218yescomplemented
47#16839977C2218yescomplemented
48#16839974C2218yescomplemented
49#16839924C2218yescomplemented
50#16839922C2218yescomplemented
51#16839896C2218yescomplemented
52#16839895C2218yescomplemented
53C4×#11758199C2218yescomplemented
54#16839840C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×C4⋊#92418C2211yescharacteristic, complemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519700C2211yescharacteristic, complemented
59C2×#14519698C2211yescharacteristic, complemented
60C2×#14519698C2211yescharacteristic, complemented
61C2×#14519697C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×C22⋊#92418C2211yescharacteristic, complemented
64C2×C22⋊#92418C2211yescharacteristic, complemented
65C2×C4×#92418C2211yescharacteristic, complemented
66C22×#41×C61C2211yescharacteristic
67C23×D4×C61C2211yescharacteristic, complemented
68C61×#546—24no—
69C61×#546C2218yescomplemented
70C2×#124×C61C2211yescharacteristic, complemented
71C2×#123×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic, complemented
73C2×#121×C61—21no—
74C2×#121×C61C2211yescharacteristic
75C2×#120×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C2×C4×D4×C61C2211yescharacteristic, complemented
78C22×C22⋊C4×C61—21no—
79C24×D61—21no—
80C2×#11758222—22no—
81C2×#11758222—24no—
82C2×#11758222—42no—
83C2×#11758222C2314yes—
84C22×Dic122C2311yescharacteristic
85C22×D244—24no—
86C22×D244—21no—
87C22×D244—22no—
88C22×D244—42no—
89C22×D244C2311yescharacteristic
90C22×D244C2311yescharacteristic
91C22×D244C2314yescomplemented
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96#14519803—232no—
97#14519802—232no—
98C2×#11758202—42no—
99C2×#11758202C2314yescomplemented
100C2×#11758200—24no—
101C2×#11758200—24no—
102C2×#11758200C2314yescomplemented
103C2×#11758200C2314yescomplemented
104C2×#11758201—24no—
105C2×#11758201—24no—
106C2×#11758201C2314yescomplemented
107C2×#11758201C2314yescomplemented
108C2×#11758199—24no—
109C2×#11758199—24no—
110C2×#11758199—42no—
111C2×#11758199D418yescomplemented
112C2×#11758199C2314yes—
113C2×#11758199C2314yes—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C2×#11758194—24no—
117C2×#11758194—24no—
118C2×#11758194C2314yescomplemented
119C2×#11758194C2314yescomplemented
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124#14519765—22no—
125#14519765C2314yescomplemented
126#14519762—28no—
127#14519756—22no—
128#14519756C2314yescomplemented
129#14519751—22no—
130#14519751C2314yes—
131#14519750—28no—
132#14519745—28no—
133C4×D244—22no—
134C4×D244C2314yescomplemented
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C22⋊C4×D61—28no—
143#14519710C2314yescomplemented
144C4⋊#92418C2314yescomplemented
145#14519701C2314yescomplemented
146#14519700C2314yescomplemented
147#14519698C2314yescomplemented
148#14519698C2314yescomplemented
149#14519697C2314yescomplemented
150#14519697C2314yescomplemented
151C22⋊#92418C2314yescomplemented
152C22⋊#92418C2314yescomplemented
153C4×#92418C2314yescomplemented
154C25×C61—21no—
155C2×#41×C61—22no—
156C2×#41×C61—24no—
157C2×#41×C61—42no—
158C2×#41×C61C2314yes—
159C22×Q8×C61C2311yescharacteristic
160C22×D4×C61—24no—
161C22×D4×C61—21no—
162C22×D4×C61—21no—
163C22×D4×C61—22no—
164C22×D4×C61—21no—
165C22×D4×C61—42no—
166C22×D4×C61D411yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2314yescomplemented
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C23×C4×C61C2311yescharacteristic
174#124×C61—22no—
175#124×C61C2314yescomplemented
176#123×C61—28no—
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yescomplemented
179#121×C61—22no—
180#121×C61—28no—
181#121×C61C2314yes—
182#120×C61—28no—
183C4×D4×C61—22no—
184C4×D4×C61D414yes—
185C4×D4×C61C2314yes—
186C4×D4×C61C2314yescomplemented
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61D411yescharacteristic
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61—28no—
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C22⋊C4×C61D411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61—21no—
201C24×C61—24no—
202C24×C61—44no—
203C24×C61—44no—
204C24×C61—82no—
205C24×C61C2×D411yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—24no—
210C23×D61—44no—
211C23×D61—44no—
212C23×D61—82no—
213#41×C61—28no—
214#41×C61—44no—
215#41×C61—48no—
216C2×Q8×C61—21no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61C2412yes—
220C2×D4×C61—28no—
221C2×D4×C61—24no—
222C2×D4×C61—24no—
223C2×D4×C61—21no—
224C2×D4×C61—22no—
225C2×D4×C61—24no—
226C2×D4×C61—21no—
227C2×D4×C61—22no—
228C2×D4×C61—22no—
229C2×D4×C61—44no—
230C2×D4×C61—48no—
231C2×D4×C61—42no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—82no—
235C2×D4×C61C2×D414yes—
236C2×D4×C61C2×D414yes—
237C2×D4×C61C2412yes—
238C2×D4×C61C2412yes—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—24no—
246C22×C4×C61—24no—
247C22×C4×C61—44no—
248C22×C4×C61—82no—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2412yes—
256C22×C4×C61C2412yes—
257C22×C4×C61C2411yescharacteristic
258C2×C22⋊D61—24no—
259C2×C22⋊D61—24no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61—82no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264#11758222—28no—
265#11758222—44no—
266#11758222—48no—
267C2×D244—21no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—22no—
271C2×D244—28no—
272C2×D244—21no—
273C2×D244—24no—
274C2×D244—44no—
275C2×D244—48no—
276C2×D244—44no—
277C2×D244C2×D414yes—
278C2×D244C2412yes—
279C2×D244C2412yes—
280C2×C4×D61—24no—
281C2×C4×D61—24no—
282C2×C4×D61—44no—
283C2×C4×D61—82no—
284C2×Dic122—22no—
285C2×Dic122—22no—
286C2×Dic122—21no—
287C2×Dic122C2412yes—
288C4⋊C4×C61—24no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61C2×D414yes—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—24no—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—24no—
297C22⋊C4×C61C2×D414yes—
298C22⋊C4×C61C2×D414yes—
299C42×C61C2×D412yes—
300C42×C61C2412yes—
301C22⋊Dic61—24no—
302#11758202—44no—
303#11758201—28no—
304#11758201—28no—
305#11758200—28no—
306#11758200—28no—
307#11758199—28no—
308#11758199—28no—
309#11758199—44no—
310#11758199C2×D4116yescomplemented
311#11758198—24no—
312#11758198—24no—
313#11758198—24no—
314#11758198—24no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317#11758196—24no—
318#11758194—28no—
319#11758194—28no—
320C2×#92418—22no—
321C2×#92418—22no—
322C2×#92418—22no—
323C2×#92418C2×D414yes—
324C2×#92418C2412yes—
325C2×#92418C2412yes—
326C2×#92418C2412yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—24no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—22no—
337C23×C61—48no—
338C23×C61—48no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—42no—
344C23×C61—84no—
345C23×C61—816no—
346C23×C61C22×D412yes—
347C23×C61C22×D412yes—
348C23×C61C22×D411yescharacteristic
349C22×D61—24no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—48no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—48no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—84no—
360C22×D61—816no—
361Q8×C61—22no—
362Q8×C61—22no—
363Q8×C61—42no—
364D4×C61—24no—
365D4×C61—22no—
366D4×C61—22no—
367D4×C61—22no—
368D4×C61—44no—
369D4×C61—48no—
370D4×C61—48no—
371D4×C61—42no—
372D4×C61—84no—
373D4×C61C22×D414yes—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—24no—
379C2×C4×C61—24no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—48no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—84no—
390C2×C4×C61C22×D412yes—
391C2×C4×C61C22×D412yes—
392C2×C4×C61C22×D412yes—
393C2×C4×C61C22×D412yes—
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D412yes—
396C2×C4×C61H(5,𝔽2)12yes—
397C2×C4×C61C2511yescharacteristic
398C22⋊D61—48no—
399C22⋊D61—84no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404D244—24no—
405D244—22no—
406D244—22no—
407D244—22no—
408D244—48no—
409D244—42no—
410D244C22×D414yes—
411C4×D61—48no—
412C4×D61—84no—
413Dic122—22no—
414Dic122—22no—
415Dic122—42no—
416#92418—22no—
417#92418—22no—
418#92418—22no—
419#92418C22×D414yes—
420C2×#3273—611nomaximal, Sylow
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—24no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—22no—
428C22×C61—44no—
429C22×C61—44no—
430C22×C61—48no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—816no—
437C22×C61—84no—
438C22×C61D4212yes—
439C22×C61#57512yes—
440C22×C61#57612yes—
441C22×C61C23×D411yescharacteristic
442C2×D61—24no—
443C2×D61—48no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—816no—
450C2×D61—84no—
451C4×C61—22no—
452C4×C61—22no—
453C4×C61—22no—
454C4×C61—22no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61D4212yes—
458C4×C61C23×D411yescharacteristic
459C4×C61C2×H(5,𝔽2)11yescharacteristic
460Dic61—42no—
461Dic61—42no—
462C22×AGL(1,ℤ/8)—611no—
463C22×AGL(1,ℤ/8)—611no—
464C2×#546—611no—
465C2×#546D6111yescharacteristic, complemented
466#3273—6116no—
467C2×#495—611no—
468C2×#468—611no—
469C2×#468—611no—
470C2×#463—611no—
471C2×#463—611no—
472C2×#452—611no—
473C2×#452—611no—
474C2×#447—611no—
475C2×#447—611no—
476C2×C4×D8—611no—
477C2×#436—611no—
478C2×C61—42no—
479C2×C61—42no—
480C2×C61—44no—
481C2×C61—82no—
482C2×C61#327314yescomplemented
483C2×C61C2×D4211yescharacteristic
484C2×C61C2×#57511yescharacteristic
485C2×C61C2×#57611yescharacteristic
486D61—44no—
487D61—82no—
488C22×#41—611no—
489C22×#41C2×D6111yescharacteristic
490C23×D4—611no—
491C23×D4C2×D6111yescharacteristic, complemented
492C2×AGL(1,ℤ/8)—618no—
493C2×AGL(1,ℤ/8)—618no—
494C2×AGL(1,ℤ/8)—1228no—
495C2×AGL(1,ℤ/8)—1228no—
496C22×Q16—611no—
497C22×SD16—611no—
498C22×SD16—611no—
499C22×SD16—611no—
500C22×SD16—611no—
501C22×D8—611no—
502C22×D8—611no—
503C22×D8—611no—
504C22×D8—611no—
505C22×M16—611no—
506C22×M16—611no—
507#546—24no—
508#546—618no—
509#546—1224no—
510#546C2×D6118yescomplemented
511C2×#124—611no—
512C2×#124C2×D6111yescharacteristic, complemented
513C2×#123—21no—
514C2×#123—1221no—
515C2×C22⋊Q8—611no—
516C2×C22⋊Q8C2×D6111yescharacteristic, complemented
517C2×#121—21no—
518C2×#121—611no—
519C2×#121—1221no—
520C2×#121C2×D6111yescharacteristic
521C2×#120—21no—
522C2×#120—1221no—
523C2×C4×D4—611no—
524C2×C4×D4C2×D6111yescharacteristic
525C2×C4×D4C2×D6111yescharacteristic, complemented
526C22×C22⋊C4—21no—
527C22×C22⋊C4—1221no—
528#495—618no—
529#468—618no—
530#468—618no—
531#463—618no—
532#463—618no—
533#452—618no—
534#452—618no—
535#447—618no—
536#447—618no—
537C4×D8—618no—
538#436—618no—
539C2×#107—611no—
540C2×C4⋊C8—611no—
541C2×#103—611no—
542C2×#103—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×#102—611no—
546C2×#102—611no—
547C2×C22⋊C8—611no—
548C2×C22⋊C8—611no—
549C2×C4×C8—611no—
550C61C2×#327311yescharacteristic, complemented, Sylow
551C25—21no—
552C25—1221no—
553C2×#41—22no—
554C2×#41—24no—
555C2×#41—42no—
556C2×#41—614no—
557C2×#41—1224no—
558C2×#41—1222no—
559C2×#41—2442no—
560C2×#41C22×D6114yes—
561C22×Q8—611no—
562C22×Q8C22×D6111yescharacteristic
563C22×D4—24no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—22no—
568C22×D4—42no—
569C22×D4—611no—
570C22×D4—611no—
571C22×D4—614no—
572C22×D4—1224no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1222no—
577C22×D4—2442no—
578C22×D4C22⋊D6111yescharacteristic
579C22×D4C22×D6111yescharacteristic
580C22×D4C22×D6111yescharacteristic
581C22×D4C22×D6114yescomplemented
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588AGL(1,ℤ/8)—12232no—
589AGL(1,ℤ/8)—12232no—
590C2×Q16—614no—
591C2×Q16—2442no—
592C2×SD16—614no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×SD16—614no—
596C2×SD16—1224no—
597C2×SD16—1224no—
598C2×SD16—1224no—
599C2×SD16—1224no—
600C2×D8—618no—
601C2×D8—614no—
602C2×D8—614no—
603C2×D8—614no—
604C2×D8—614no—
605C2×D8—1224no—
606C2×D8—1224no—
607C2×D8—2442no—
608C2×M16—614no—
609C2×M16—614no—
610C2×M16—1224no—
611C2×M16—1224no—
612C22×C8—611no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—611no—
616#124—22no—
617#124—614no—
618#124—1222no—
619#124C22×D6114yescomplemented
620#123—28no—
621#123—1228no—
622C22⋊Q8—22no—
623C22⋊Q8—614no—
624C22⋊Q8—1222no—
625C22⋊Q8C22×D6114yescomplemented
626#121—22no—
627#121—28no—
628#121—614no—
629#121—1222no—
630#121—1228no—
631#121C22×D6114yes—
632#120—28no—
633#120—1228no—
634C4×D4—22no—
635C4×D4—614no—
636C4×D4—1222no—
637C4×D4C22⋊D6114yes—
638C4×D4C22×D6114yes—
639C4×D4C22×D6114yescomplemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4C22⋊D6111yescharacteristic
644C2×C4⋊C4C22×D6111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—28no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1228no—
657C2×C22⋊C4C22⋊D6111yescharacteristic
658C2×C22⋊C4C22⋊D6111yescharacteristic
659C2×C42C22×D6111yescharacteristic
660#107—614no—
661C4⋊C8—614no—
662#103—614no—
663#103—614no—
664#102—614no—
665#102—614no—
666#102—614no—
667#102—614no—
668C22⋊C8—614no—
669C22⋊C8—614no—
670C4×C8—614no—
671C24—21no—
672C24—21no—
673C24—24no—
674C24—44no—
675C24—44no—
676C24—82no—
677C24—1221no—
678C24—1224no—
679C24—1221no—
680C24—4882no—
681C24—2444no—
682C24—2444no—
683C24C2×C22⋊D6111yescharacteristic
684C24C2×C22⋊D6111yescharacteristic
685#41—28no—
686#41—44no—
687#41—48no—
688#41—1228no—
689#41—2444no—
690#41—2448no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—612no—
695C2×Q8—1221no—
696C2×Q8—1222no—
697C2×Q8—1222no—
698C2×Q8C23×D6112yes—
699C2×D4—28no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—21no—
704C2×D4—24no—
705C2×D4—21no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—614no—
715C2×D4—612no—
716C2×D4—612no—
717C2×D4—1228no—
718C2×D4—1224no—
719C2×D4—1224no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1224no—
723C2×D4—1221no—
724C2×D4—1222no—
725C2×D4—1222no—
726C2×D4—4882no—
727C2×D4—2444no—
728C2×D4—2448no—
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4D4×D6114yes—
732C2×D4C2×C22⋊D6114yes—
733C2×D4C23×D6112yes—
734C2×D4C23×D6112yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—44no—
744C22×C4—82no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—4882no—
750C22×C4—2444no—
751C22×C4C2×C22⋊D6112yes—
752C22×C4C2×C22⋊D6112yes—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6111yescharacteristic
756C22×C4C2×C22⋊D6111yescharacteristic
757C22×C4C23×D6112yes—
758C22×C4C23×D6112yes—
759C22×C4C23×D6111yescharacteristic
760Q16—2444no—
761SD16—1228no—
762SD16—1228no—
763SD16—1228no—
764SD16—1228no—
765D8—6116no—
766D8—1228no—
767D8—1228no—
768D8—2444no—
769M16—1228no—
770M16—1228no—
771C2×C8—614no—
772C2×C8—612no—
773C2×C8—612no—
774C2×C8—612no—
775C2×C8—612no—
776C2×C8—1222no—
777C2×C8—1222no—
778C2×C8—1222no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—612no—
782C4⋊C4—1221no—
783C4⋊C4—1224no—
784C4⋊C4C2×C22⋊D6114yes—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4—1224no—
794C22⋊C4—1224no—
795C22⋊C4—1224no—
796C22⋊C4C2×C22⋊D6114yes—
797C22⋊C4C2×C22⋊D6114yes—
798C42C2×C22⋊D6112yes—
799C42C23×D6112yes—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—48no—
810C23—48no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—84no—
817C23—816no—
818C23—1222no—
819C23—1224no—
820C23—1222no—
821C23—4884no—
822C23—48816no—
823C23—2448no—
824C23—2448no—
825C23—2442no—
826C23—2442no—
827C23—2442no—
828C23—2442no—
829C23—2442no—
830C23C22×C22⋊D6112yes—
831C23C22×C22⋊D6112yes—
832C23C22×C22⋊D6111yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—42no—
836Q8—1222no—
837Q8—1222no—
838Q8—2442no—
839D4—22no—
840D4—22no—
841D4—22no—
842D4—24no—
843D4—44no—
844D4—48no—
845D4—48no—
846D4—42no—
847D4—84no—
848D4—614no—
849D4—1222no—
850D4—1222no—
851D4—1222no—
852D4—1224no—
853D4—4884no—
854D4—2448no—
855D4—2448no—
856D4—2442no—
857D4C2×D4×D6114yes—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—48no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—84no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—4884no—
877C2×C4—2448no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4C2×D4×D6112yes—
881C2×C4C22×C22⋊D6112yes—
882C2×C4C22×C22⋊D6112yes—
883C2×C4C22×C22⋊D6112yes—
884C2×C4C22×C22⋊D6112yes—
885C2×C4C22×C22⋊D6111yescharacteristic
886C2×C4#1451982212yes—
887C2×C4C24×D6111yescharacteristic
888C8—614no—
889C8—1222no—
890C8—1222no—
891C8—1222no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—44no—
900C22—44no—
901C22—48no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—84no—
909C22—1224no—
910C22—48816no—
911C22—4884no—
912C22—2442no—
913C22—2442no—
914C22—2442no—
915C22—2448no—
916C22—2442no—
917C22—2442no—
918C22D4×C22⋊D6112yes—
919C22#1684056012yes—
920C22#1684056512yes—
921C22C23×C22⋊D6111yescharacteristic
922C4—22no—
923C4—22no—
924C4—22no—
925C4—22no—
926C4—42no—
927C4—42no—
928C4—2442no—
929C4—2442no—
930C4D4×C22⋊D6112yes—
931C4C22×D4×D6111yescharacteristic
932C4C2×#1451982211yescharacteristic
933C2—42no—
934C2—42no—
935C2—44no—
936C2—82no—
937C2—4882no—
938C2—2444no—
939C2#2145742614yesdirect product factor
940C2C2×D4×C22⋊D6111yescharacteristic
941C2C2×#1684056011yescharacteristic
942C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61C2×#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#14519803C2semidirect
2. C22×#14519802C2semidirect
3. C2×#16840408C2semidirect
4. #21457426C2direct (N × H)
5. C2×#16840144C2semidirect
6. C2×#16840010C2semidirect
7. C2×#16840006C2semidirect
8. C2×#16839977C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839922C2semidirect
12. C2×#16839896C2semidirect
13. C2×#16839895C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×#16839840C2semidirect
16. C2×C61×#546C2semidirect
18. C23×D244C22semidirect
20. C2×#14519803C22semidirect
22. C2×#14519802C22semidirect
23. C22×#11758202C22semidirect
24. C22×#11758200C22semidirect
25. C22×#11758200C22semidirect
26. C22×#11758201C22semidirect
27. C22×#11758201C22semidirect
32. C22×#11758194C22semidirect
33. C22×#11758194C22semidirect
35. #16840408C22semidirect
36. C2×#14519765C22semidirect
38. C2×#14519756C22semidirect
42. C2×C4×D244C22semidirect
44. #16840144C22semidirect
45. #16840010C22semidirect
46. #16840006C22semidirect
47. #16839977C22semidirect
48. #16839974C22semidirect
49. #16839924C22semidirect
50. #16839922C22semidirect
51. #16839896C22semidirect
52. #16839895C22semidirect
53. C4×#11758199C22semidirect
54. #16839840C22semidirect
55. C2×#14519710C22semidirect
56. C2×C4⋊#92418C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519700C22semidirect
59. C2×#14519698C22semidirect
60. C2×#14519698C22semidirect
61. C2×#14519697C22semidirect
62. C2×#14519697C22semidirect
63. C2×C22⋊#92418C22semidirect
64. C2×C22⋊#92418C22semidirect
65. C2×C4×#92418C22semidirect
67. C23×D4×C61C22semidirect
69. C61×#546C22semidirect
70. C2×#124×C61C22semidirect
72. C2×C22⋊Q8×C61C22semidirect
77. C2×C4×D4×C61C22semidirect
91. C22×D244C23semidirect
99. C2×#11758202C23semidirect
102. C2×#11758200C23semidirect
103. C2×#11758200C23semidirect
106. C2×#11758201C23semidirect
107. C2×#11758201C23semidirect
111. C2×#11758199D4semidirect
118. C2×#11758194C23semidirect
119. C2×#11758194C23semidirect
125. #14519765C23semidirect
128. #14519756C23semidirect
134. C4×D244C23semidirect
143. #14519710C23semidirect
144. C4⋊#92418C23semidirect
145. #14519701C23semidirect
146. #14519700C23semidirect
147. #14519698C23semidirect
148. #14519698C23semidirect
149. #14519697C23semidirect
150. #14519697C23semidirect
151. C22⋊#92418C23semidirect
152. C22⋊#92418C23semidirect
153. C4×#92418C23semidirect
169. C22×D4×C61C23semidirect
175. #124×C61C23semidirect
178. C22⋊Q8×C61C23semidirect
186. C4×D4×C61C23semidirect
310. #11758199C2×D4semidirect
465. C2×#546D61semidirect
482. C2×C61#3273semidirect
491. C23×D4C2×D61semidirect
510. #546C2×D61semidirect
512. C2×#124C2×D61semidirect
516. C2×C22⋊Q8C2×D61semidirect
525. C2×C4×D4C2×D61semidirect
550. C61C2×#3273semidirect
581. C22×D4C22×D61semidirect
619. #124C22×D61semidirect
625. C22⋊Q8C22×D61semidirect
639. C4×D4C22×D61semidirect
939. C2#21457426direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198032
C22×#145198022
C2×#168404082
#214574262
C2×#168401442
C2×#168400102
C2×#168400062
C2×#168399772
C2×#168399742
C2×#168399242
C2×#168399222
C2×#168398962
C2×#168398952
C2×C4×#117581992
C2×#168398402
C2×C61×#5462
C2×#327361