Finite Group Databasebeta

← C2×#21457451 #30555144

Subgroups — C2×#21457451 #30555144

Order 15616.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519808C211yesmaximal, characteristic, complemented
2C22×#14519802C211yesmaximal, characteristic, complemented
3C2×#16840408C211yesmaximal, characteristic, complemented
4#21457451C2116yesmaximal, direct product factor
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840018C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839905C211yesmaximal, characteristic, complemented
12C2×#16839901C211yesmaximal, characteristic, complemented
13C2×#16839912C211yesmaximal, characteristic, complemented
14C2×C4×#11758201C211yesmaximal, characteristic, complemented
15C2×#16839840C211yesmaximal, characteristic, complemented
16C2×C61×#548C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C2×#14519808—28no—
20C2×#14519808C2218yescomplemented
21C2×#14519802—28no—
22C2×#14519802C2218yescomplemented
23C22×#11758202C2211yescharacteristic, complemented
24C22×#11758202C2211yescharacteristic, complemented
25C22×#11758200C2211yescharacteristic, complemented
26C22×#11758201C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C22×#11758194C2211yescharacteristic, complemented
34#16840408—24no—
35#16840408C2218yescomplemented
36C2×#14519765C2211yescharacteristic
37C2×#14519762—21no—
38C2×#14519756C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519745—21no—
42C2×C4×D244C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840144C2218yescomplemented
45#16840018C2218yescomplemented
46#16840013C2218yescomplemented
47#16839984C2218yescomplemented
48#16839974C2218yescomplemented
49#16839924C2218yescomplemented
50#16839912C2218yescomplemented
51#16839905C2218yescomplemented
52#16839901C2218yescomplemented
53C4×#11758201C2218yescomplemented
54#16839840C2218yescomplemented
55C2×#14519708C2211yescharacteristic, complemented
56C2×C4⋊#92418C2211yescharacteristic, complemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519701C2211yescharacteristic, complemented
59C2×#14519700C2211yescharacteristic, complemented
60C2×#14519698C2211yescharacteristic, complemented
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic, complemented
65C2×C4×#92418C2211yescharacteristic, complemented
66C22×#41×C61C2211yescharacteristic
67C23×Q8×C61C2211yescharacteristic, complemented
68C61×#548—24no—
69C61×#548C2218yescomplemented
70C2×#124×C61—21no—
71C2×#124×C61C2211yescharacteristic, complemented
72C2×C22⋊Q8×C61—21no—
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×#121×C61—21no—
75C2×#121×C61C2211yescharacteristic, complemented
76C2×C4×Q8×C61C2211yescharacteristic, complemented
77C2×C4×D4×C61—21no—
78C2×C4×D4×C61C2211yescharacteristic
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×D244C2314yes—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96#14519808—232no—
97#14519802—232no—
98C2×#11758202—24no—
99C2×#11758202—24no—
100C2×#11758202C2314yescomplemented
101C2×#11758202C2314yescomplemented
102C2×#11758200—42no—
103C2×#11758200C2314yescomplemented
104C2×#11758201—24no—
105C2×#11758201—24no—
106C2×#11758201—42no—
107C2×#11758201D418yescomplemented
108C2×#11758201C2314yes—
109C2×#11758201C2314yes—
110C2×#11758201C2314yes—
111C2×#11758201C2314yes—
112C2×#11758199—24no—
113C2×#11758199—24no—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C2×#11758194—24no—
117C2×#11758194—24no—
118C2×#11758194C2314yes—
119C2×#11758194C2314yescomplemented
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124#14519765—22no—
125#14519765C2314yes—
126#14519762—28no—
127#14519756—22no—
128#14519756C2314yes—
129#14519751—22no—
130#14519751C2314yes—
131#14519750—28no—
132#14519745—28no—
133C4×D244—22no—
134C4×D244C2314yes—
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#14519708C2314yescomplemented
144C4⋊#92418C2314yescomplemented
145#14519701C2314yescomplemented
146#14519701C2314yescomplemented
147#14519700C2314yescomplemented
148#14519698C2314yescomplemented
149#14519697C2314yes—
150#14519697C2314yes—
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yescomplemented
153C4×#92418C2314yescomplemented
154C2×#41×C61—22no—
155C2×#41×C61—24no—
156C2×#41×C61—42no—
157C2×#41×C61C2314yes—
158C22×Q8×C61—22no—
159C22×Q8×C61—21no—
160C22×Q8×C61—24no—
161C22×Q8×C61—42no—
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2314yescomplemented
165C22×D4×C61—21no—
166C22×D4×C61—21no—
167C22×D4×C61D411yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C23×C4×C61C2311yescharacteristic
173#124×C61—28no—
174#124×C61—22no—
175#124×C61C2314yescomplemented
176C22⋊Q8×C61—22no—
177C22⋊Q8×C61—28no—
178C22⋊Q8×C61C2314yes—
179#121×C61—28no—
180#121×C61—22no—
181#121×C61C2314yescomplemented
182C4×Q8×C61—22no—
183C4×Q8×C61C2314yescomplemented
184C4×D4×C61—28no—
185C4×D4×C61D414yes—
186C4×D4×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61D411yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61D411yescharacteristic
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61C2×D411yescharacteristic
201C24×C61C2×D411yescharacteristic
202C23×D61—21no—
203C23×D61—21no—
204C23×D61—24no—
205C23×D61—44no—
206C23×D61—44no—
207C23×D61—82no—
208#41×C61—28no—
209#41×C61—44no—
210#41×C61—48no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—24no—
214C2×Q8×C61—22no—
215C2×Q8×C61—28no—
216C2×Q8×C61—22no—
217C2×Q8×C61—22no—
218C2×Q8×C61—44no—
219C2×Q8×C61—44no—
220C2×Q8×C61—48no—
221C2×Q8×C61C2×D414yes—
222C2×Q8×C61C2412yes—
223C2×Q8×C61C2412yes—
224C2×D4×C61—24no—
225C2×D4×C61—24no—
226C2×D4×C61—22no—
227C2×D4×C61—21no—
228C2×D4×C61—22no—
229C2×D4×C61—42no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61C2×D414yes—
233C2×D4×C61C2412yes—
234C22×C4×C61—21no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—24no—
243C22×C4×C61—44no—
244C22×C4×C61—44no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D412yes—
249C22×C4×C61C2×D412yes—
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2412yes—
252C22×C4×C61C2412yes—
253C22×C4×C61C2411yescharacteristic
254C2×C22⋊D61—24no—
255C2×C22⋊D61—24no—
256C2×C22⋊D61—44no—
257C2×C22⋊D61—82no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260#11758222—28no—
261#11758222—44no—
262#11758222—48no—
263C2×D244—21no—
264C2×D244—22no—
265C2×D244—22no—
266C2×D244—22no—
267C2×D244—28no—
268C2×D244—24no—
269C2×D244—21no—
270C2×D244—44no—
271C2×D244—48no—
272C2×D244—44no—
273C2×D244C2×D414yes—
274C2×D244C2412yes—
275C2×D244C2412yes—
276C2×C4×D61—24no—
277C2×C4×D61—24no—
278C2×C4×D61—44no—
279C2×C4×D61—82no—
280C2×Dic122—22no—
281C2×Dic122—22no—
282C2×Dic122—21no—
283C2×Dic122C2412yes—
284C4⋊C4×C61—24no—
285C4⋊C4×C61—24no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61C2×D414yes—
288C4⋊C4×C61C2412yes—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61C2×D414yes—
294C22⋊C4×C61C2×D414yes—
295C42×C61—24no—
296C42×C61C2×D412yes—
297C42×C61C2412yes—
298C22⋊Dic61—24no—
299#11758202—28no—
300#11758202—28no—
301#11758201—28no—
302#11758201—28no—
303#11758201—44no—
304#11758201C2×D4116yescomplemented
305#11758200—44no—
306#11758199—28no—
307#11758199—28no—
308#11758198—24no—
309#11758198—24no—
310#11758198—24no—
311#11758198—24no—
312C4⋊Dic61—21no—
313C4⋊Dic61C2412yes—
314#11758196—24no—
315#11758194—28no—
316#11758194—28no—
317C2×#92418—22no—
318C2×#92418—22no—
319C2×#92418—22no—
320C2×#92418C2×D414yes—
321C2×#92418C2412yes—
322C2×#92418C2412yes—
323C2×#92418C2412yes—
324C2×#92418C2412yes—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61C22×D412yes—
336C23×C61C22×D412yes—
337C23×C61C22×D411yescharacteristic
338C22×D61—24no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—48no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—48no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—42no—
348C22×D61—84no—
349C22×D61—816no—
350Q8×C61—24no—
351Q8×C61—22no—
352Q8×C61—22no—
353Q8×C61—22no—
354Q8×C61—48no—
355Q8×C61—42no—
356Q8×C61C22×D414yes—
357D4×C61—22no—
358D4×C61—22no—
359D4×C61—44no—
360D4×C61—48no—
361D4×C61—48no—
362D4×C61—42no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—24no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—24no—
370C2×C4×C61—24no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—48no—
378C2×C4×C61—48no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61C22×D412yes—
382C2×C4×C61C22×D412yes—
383C2×C4×C61C22×D412yes—
384C2×C4×C61C22×D412yes—
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C22×D412yes—
387C2×C4×C61H(5,𝔽2)12yes—
388C2×C4×C61C2511yescharacteristic
389C22⋊D61—48no—
390C22⋊D61—84no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—42no—
394C2×Dic61—42no—
395D244—24no—
396D244—22no—
397D244—22no—
398D244—22no—
399D244—48no—
400D244—42no—
401D244C22×D414yes—
402C4×D61—48no—
403C4×D61—84no—
404Dic122—22no—
405Dic122—22no—
406Dic122—42no—
407#92418—22no—
408#92418—22no—
409#92418—22no—
410#92418C22×D414yes—
411C2×#3275—611nomaximal, Sylow
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—44no—
419C22×C61—44no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—84no—
424C22×C61D4212yes—
425C22×C61#57512yes—
426C22×C61#57712yes—
427C22×C61C23×D411yescharacteristic
428C2×D61—24no—
429C2×D61—48no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—42no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—816no—
436C2×D61—84no—
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—24no—
440C4×C61—22no—
441C4×C61—22no—
442C4×C61—42no—
443C4×C61—42no—
444C4×C61D4212yes—
445C4×C61C23×D411yescharacteristic
446C4×C61C2×H(5,𝔽2)11yescharacteristic
447Dic61—42no—
448Dic61—42no—
449C22×#137—611no—
450C22×AGL(1,ℤ/8)—611no—
451C2×#548D6111yescharacteristic, complemented
452C2×#546—611no—
453#3275—6116no—
454C2×#495—611no—
455C2×#470—611no—
456C2×#469—611no—
457C2×#464—611no—
458C2×#463—611no—
459C2×#452—611no—
460C2×#449—611no—
461C2×#448—611no—
462C2×#450—611no—
463C2×C4×SD16—611no—
464C2×#436—611no—
465C2×C61—42no—
466C2×C61—42no—
467C2×C61—82no—
468C2×C61#327514yescomplemented
469C2×C61C2×D4211yescharacteristic
470C2×C61C2×#57511yescharacteristic
471C2×C61C2×#57711yescharacteristic
472D61—44no—
473D61—82no—
474C22×#41—611no—
475C22×#41C2×D6111yescharacteristic
476C23×Q8C2×D6111yescharacteristic, complemented
477C23×D4—611no—
478C2×#137—618no—
479C2×#137—1228no—
480C2×AGL(1,ℤ/8)—618no—
481C2×AGL(1,ℤ/8)—1228no—
482C22×Q16—611no—
483C22×Q16—611no—
484C22×SD16—611no—
485C22×SD16—611no—
486C22×SD16—611no—
487C22×SD16—611no—
488C22×SD16—611no—
489C22×D8—611no—
490C22×D8—611no—
491C22×M16—611no—
492C22×M16—611no—
493#548—24no—
494#548C2×D6118yescomplemented
495#546—618no—
496#546—1224no—
497C2×#124—21no—
498C2×#124—611no—
499C2×#124C2×D6111yescharacteristic, complemented
500C2×#123—1221no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8—611no—
503C2×C22⋊Q8C2×D6111yescharacteristic
504C2×#121—21no—
505C2×#121—611no—
506C2×#121—1221no—
507C2×#121C2×D6111yescharacteristic, complemented
508C2×#120—1221no—
509C2×C4×Q8C2×D6111yescharacteristic, complemented
510C2×C4×D4—21no—
511C2×C4×D4—611no—
512C2×C4×D4C2×D6111yescharacteristic
513C22×C22⋊C4—1221no—
514#495—618no—
515#470—618no—
516#469—618no—
517#464—618no—
518#463—618no—
519#452—618no—
520#450—618no—
521#449—618no—
522#448—618no—
523C4×SD16—618no—
524#436—618no—
525C2×#106—611no—
526C2×C4⋊C8—611no—
527C2×#103—611no—
528C2×#103—611no—
529C2×#103—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C4×C8—611no—
536C61C2×#327511yescharacteristic, complemented, Sylow
537C25—1221no—
538C2×#41—22no—
539C2×#41—24no—
540C2×#41—42no—
541C2×#41—614no—
542C2×#41—1224no—
543C2×#41—1222no—
544C2×#41—2442no—
545C2×#41C22×D6114yes—
546C22×Q8—21no—
547C22×Q8—22no—
548C22×Q8—24no—
549C22×Q8—42no—
550C22×Q8—611no—
551C22×Q8C22×D6111yescharacteristic
552C22×Q8C22×D6111yescharacteristic
553C22×Q8C22×D6114yescomplemented
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—614no—
559C22×D4—1224no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—1222no—
564C22×D4—2442no—
565C22×D4C22⋊D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—1221no—
570C23×C4—1221no—
571C23×C4C22×D6111yescharacteristic
572C23×C4C22×D6111yescharacteristic
573#137—12232no—
574AGL(1,ℤ/8)—12232no—
575C2×Q16—614no—
576C2×Q16—614no—
577C2×Q16—1224no—
578C2×Q16—1224no—
579C2×SD16—618no—
580C2×SD16—614no—
581C2×SD16—614no—
582C2×SD16—614no—
583C2×SD16—614no—
584C2×SD16—614no—
585C2×SD16—1224no—
586C2×SD16—1224no—
587C2×SD16—2442no—
588C2×SD16—2442no—
589C2×D8—614no—
590C2×D8—614no—
591C2×D8—1224no—
592C2×D8—1224no—
593C2×M16—614no—
594C2×M16—614no—
595C2×M16—1224no—
596C2×M16—1224no—
597C22×C8—611no—
598C22×C8—611no—
599C22×C8—611no—
600C22×C8—611no—
601#124—28no—
602#124—22no—
603#124—614no—
604#124—1222no—
605#124C22×D6114yescomplemented
606#123—1228no—
607C22⋊Q8—22no—
608C22⋊Q8—28no—
609C22⋊Q8—614no—
610C22⋊Q8—1222no—
611C22⋊Q8C22×D6114yes—
612#121—28no—
613#121—22no—
614#121—614no—
615#121—1222no—
616#121—1228no—
617#121C22×D6114yescomplemented
618#120—1228no—
619C4×Q8—22no—
620C4×Q8C22×D6114yescomplemented
621C4×D4—28no—
622C4×D4—614no—
623C4×D4—1222no—
624C4×D4C22⋊D6114yes—
625C4×D4C22×D6114yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4C22⋊D6111yescharacteristic
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1228no—
642C2×C22⋊C4C22⋊D6111yescharacteristic
643C2×C22⋊C4C22⋊D6111yescharacteristic
644C2×C42—21no—
645C2×C42C22×D6111yescharacteristic
646#106—614no—
647C4⋊C8—614no—
648#103—614no—
649#103—614no—
650#103—614no—
651#102—614no—
652#102—614no—
653#102—614no—
654C22⋊C8—614no—
655C22⋊C8—614no—
656C4×C8—614no—
657C24—21no—
658C24—1221no—
659C24—1224no—
660C24—1221no—
661C24—4882no—
662C24—2444no—
663C24—2444no—
664C24C2×C22⋊D6111yescharacteristic
665C24C2×C22⋊D6111yescharacteristic
666#41—28no—
667#41—44no—
668#41—48no—
669#41—1228no—
670#41—2444no—
671#41—2448no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—22no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—48no—
682C2×Q8—612no—
683C2×Q8—1221no—
684C2×Q8—1222no—
685C2×Q8—1222no—
686C2×Q8D4×D6114yes—
687C2×Q8C23×D6112yes—
688C2×Q8C23×D6112yes—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—22no—
692C2×D4—21no—
693C2×D4—22no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—614no—
698C2×D4—612no—
699C2×D4—612no—
700C2×D4—1228no—
701C2×D4—1224no—
702C2×D4—1224no—
703C2×D4—1222no—
704C2×D4—1221no—
705C2×D4—1224no—
706C2×D4—1221no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—4882no—
710C2×D4—2444no—
711C2×D4—2448no—
712C2×D4—2444no—
713C2×D4—2444no—
714C2×D4C2×C22⋊D6114yes—
715C2×D4C23×D6112yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—4882no—
732C22×C4—2444no—
733C22×C4C2×C22⋊D6112yes—
734C22×C4C2×C22⋊D6112yes—
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C2×C22⋊D6111yescharacteristic
738C22×C4C2×C22⋊D6111yescharacteristic
739C22×C4C23×D6112yes—
740C22×C4C23×D6112yes—
741C22×C4C23×D6111yescharacteristic
742Q16—1228no—
743Q16—1228no—
744SD16—6116no—
745SD16—1228no—
746SD16—1228no—
747SD16—2444no—
748SD16—2444no—
749D8—1228no—
750D8—1228no—
751M16—1228no—
752M16—1228no—
753C2×C8—614no—
754C2×C8—612no—
755C2×C8—612no—
756C2×C8—612no—
757C2×C8—612no—
758C2×C8—1222no—
759C2×C8—1222no—
760C2×C8—1222no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—21no—
764C4⋊C4—612no—
765C4⋊C4—1221no—
766C4⋊C4—1224no—
767C4⋊C4C2×C22⋊D6114yes—
768C4⋊C4C23×D6112yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—1224no—
774C22⋊C4—1224no—
775C22⋊C4—1224no—
776C22⋊C4—1224no—
777C22⋊C4—1224no—
778C22⋊C4C2×C22⋊D6114yes—
779C22⋊C4C2×C22⋊D6114yes—
780C42—24no—
781C42C2×C22⋊D6112yes—
782C42C23×D6112yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—1222no—
794C23—1224no—
795C23—1222no—
796C23—4884no—
797C23—48816no—
798C23—2448no—
799C23—2448no—
800C23—2442no—
801C23—2442no—
802C23—2442no—
803C23—2442no—
804C23—2442no—
805C23C22×C22⋊D6112yes—
806C23C22×C22⋊D6112yes—
807C23C22×C22⋊D6111yescharacteristic
808Q8—22no—
809Q8—24no—
810Q8—22no—
811Q8—22no—
812Q8—48no—
813Q8—42no—
814Q8—1222no—
815Q8—1222no—
816Q8—2442no—
817Q8C2×D4×D6114yes—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—48no—
822D4—48no—
823D4—42no—
824D4—614no—
825D4—1222no—
826D4—1222no—
827D4—1222no—
828D4—1224no—
829D4—4884no—
830D4—2448no—
831D4—2448no—
832D4—2442no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—48no—
848C2×C4—48no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—4884no—
854C2×C4—2448no—
855C2×C4—2442no—
856C2×C4—2442no—
857C2×C4C2×D4×D6112yes—
858C2×C4C22×C22⋊D6112yes—
859C2×C4C22×C22⋊D6112yes—
860C2×C4C22×C22⋊D6112yes—
861C2×C4C22×C22⋊D6112yes—
862C2×C4C22×C22⋊D6111yescharacteristic
863C2×C4#1451982212yes—
864C2×C4C24×D6111yescharacteristic
865C8—614no—
866C8—1222no—
867C8—1222no—
868C8—1222no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—1224no—
882C22—48816no—
883C22—4884no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2448no—
888C22—2442no—
889C22—2442no—
890C22D4×C22⋊D6112yes—
891C22#1684056012yes—
892C22#1684057012yes—
893C22C23×C22⋊D6111yescharacteristic
894C4—22no—
895C4—22no—
896C4—24no—
897C4—22no—
898C4—22no—
899C4—42no—
900C4—42no—
901C4—2442no—
902C4—2442no—
903C4D4×C22⋊D6112yes—
904C4C22×D4×D6111yescharacteristic
905C4C2×#1451982211yescharacteristic
906C2—42no—
907C2—42no—
908C2—82no—
909C2—4882no—
910C2—2444no—
911C2#2145745114yesdirect product factor
912C2C2×D4×C22⋊D6111yescharacteristic
913C2C2×#1684056011yescharacteristic
914C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61C2×#3275
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519808C2semidirect
2. C22×#14519802C2semidirect
3. C2×#16840408C2semidirect
4. #21457451C2direct (N × H)
5. C2×#16840144C2semidirect
6. C2×#16840018C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839905C2semidirect
12. C2×#16839901C2semidirect
13. C2×#16839912C2semidirect
14. C2×C4×#11758201C2semidirect
15. C2×#16839840C2semidirect
16. C2×C61×#548C2semidirect
20. C2×#14519808C22semidirect
22. C2×#14519802C22semidirect
23. C22×#11758202C22semidirect
24. C22×#11758202C22semidirect
25. C22×#11758200C22semidirect
33. C22×#11758194C22semidirect
35. #16840408C22semidirect
44. #16840144C22semidirect
45. #16840018C22semidirect
46. #16840013C22semidirect
47. #16839984C22semidirect
48. #16839974C22semidirect
49. #16839924C22semidirect
50. #16839912C22semidirect
51. #16839905C22semidirect
52. #16839901C22semidirect
53. C4×#11758201C22semidirect
54. #16839840C22semidirect
55. C2×#14519708C22semidirect
56. C2×C4⋊#92418C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519701C22semidirect
59. C2×#14519700C22semidirect
60. C2×#14519698C22semidirect
64. C2×C22⋊#92418C22semidirect
65. C2×C4×#92418C22semidirect
67. C23×Q8×C61C22semidirect
69. C61×#548C22semidirect
71. C2×#124×C61C22semidirect
75. C2×#121×C61C22semidirect
76. C2×C4×Q8×C61C22semidirect
100. C2×#11758202C23semidirect
101. C2×#11758202C23semidirect
103. C2×#11758200C23semidirect
107. C2×#11758201D4semidirect
119. C2×#11758194C23semidirect
143. #14519708C23semidirect
144. C4⋊#92418C23semidirect
145. #14519701C23semidirect
146. #14519701C23semidirect
147. #14519700C23semidirect
148. #14519698C23semidirect
152. C22⋊#92418C23semidirect
153. C4×#92418C23semidirect
164. C22×Q8×C61C23semidirect
175. #124×C61C23semidirect
181. #121×C61C23semidirect
183. C4×Q8×C61C23semidirect
304. #11758201C2×D4semidirect
451. C2×#548D61semidirect
468. C2×C61#3275semidirect
476. C23×Q8C2×D61semidirect
494. #548C2×D61semidirect
499. C2×#124C2×D61semidirect
507. C2×#121C2×D61semidirect
509. C2×C4×Q8C2×D61semidirect
536. C61C2×#3275semidirect
553. C22×Q8C22×D61semidirect
605. #124C22×D61semidirect
617. #121C22×D61semidirect
620. C4×Q8C22×D61semidirect
911. C2#21457451direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C22×#145198022
C2×#168404082
#214574512
C2×#168401442
C2×#168400182
C2×#168400132
C2×#168399842
C2×#168399742
C2×#168399242
C2×#168399052
C2×#168399012
C2×#168399122
C2×C4×#117582012
C2×#168398402
C2×C61×#5482
C2×#327561