Finite Group Databasebeta

← C2×#21455100 #30546432

Subgroups — C2×#21455100 #30546432

Order 15616.

4910 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic, complemented
2C22×#14519804C211yesmaximal, characteristic, complemented
3C22×SD16×D61C211yesmaximal, characteristic, complemented
4C2×#16840328C211yesmaximal, characteristic, complemented
5#21455100C2116yesmaximal, direct product factor
6C2×#16839910C211yesmaximal, characteristic, complemented
7C2×#16839909C211yesmaximal, characteristic, complemented
8C2×#16839906C211yesmaximal, characteristic, complemented
9C2×#16839905C211yesmaximal, characteristic, complemented
10C2×#16839902C211yesmaximal, characteristic, complemented
11C2×#16839901C211yesmaximal, characteristic, complemented
12C2×#16839899C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#16839757C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#448C211yesmaximal, characteristic, complemented
17C2×#14519825—28no—
18C2×#14519825—24no—
19C2×#14519825—28no—
20C2×#14519825C2218yescomplemented
21C22×#11758226—21no—
22C22×#11758226C2211yescharacteristic
23C22×#11758226C2211yescharacteristic, complemented
24C22×#11758222—21no—
25C22×#11758222—21no—
26C22×#11758222C2211yescharacteristic
27C22×#11758222C2211yescharacteristic, complemented
28C22×Q8×D61—21no—
29C22×Q8×D61C2211yescharacteristic
30C22×Q8×D61C2211yescharacteristic, complemented
31C22×D4×D61C2211yescharacteristic
32C2×#14519804—28no—
33C2×#14519804C2218yescomplemented
34C22×#11758190C2211yescharacteristic
35C22×#11758200C2211yescharacteristic
36C22×#11758201C2211yescharacteristic
37C22×#11758201C2211yescharacteristic
38C2×SD16×D61—28no—
39C2×SD16×D61C2218yescomplemented
40C22×D488C2211yescharacteristic
41C22×#11758199C2211yescharacteristic
42C22×#11758189C2211yescharacteristic
43C22×C8×D61C2211yescharacteristic
44#16840328—24no—
45#16840328C2218yescomplemented
46C2×#14519773—21no—
47C2×#14519763—21no—
48C2×#14519752C2211yescharacteristic
49C2×#14519751C2211yescharacteristic
50C2×#14519748C2211yescharacteristic
51C2×#14519747—21no—
52C2×#14519745—21no—
53C2×#14519735C2211yescharacteristic
54#16839910C2218yescomplemented
55#16839909C2218yescomplemented
56#16839906C2218yescomplemented
57#16839905C2218yescomplemented
58#16839902C2218yescomplemented
59#16839901C2218yescomplemented
60#16839899C2218yescomplemented
61#16839769C2218yescomplemented
62#16839757C2218yescomplemented
63C2×#14519702C2211yescharacteristic, complemented
64C2×#14519701C2211yescharacteristic, complemented
65C2×#14519701C2211yescharacteristic, complemented
66C2×#14519700C2211yescharacteristic, complemented
67C2×#14519699C2211yescharacteristic, complemented
68C2×#14519697C2211yescharacteristic, complemented
69#16839727C2218yescomplemented
70C2×C22⋊#92418C2211yescharacteristic, complemented
71C2×#14519689C2211yescharacteristic, complemented
72C2×#14519689C2211yescharacteristic, complemented
73C23×Q8×C61C2211yescharacteristic, complemented
74C22×SD16×C61C2211yescharacteristic
75C22×SD16×C61C2211yescharacteristic
76C2×#121×C61C2211yescharacteristic
77C61×#448C2218yescomplemented
78C2×#103×C61C2211yescharacteristic, complemented
79C2×#103×C61C2211yescharacteristic, complemented
80C2×C22⋊C8×C61C2211yescharacteristic, complemented
81C24×D61—21no—
82#14519825—264no—
83#14519825—232no—
84#14519825—232no—
85C2×#11758226—216no—
86C2×#11758226—24no—
87C2×#11758226—28no—
88C2×#11758226—24no—
89C2×#11758226—24no—
90C2×#11758226—22no—
91C2×#11758226—22no—
92C2×#11758226D418yescomplemented
93C2×#11758226C2314yes—
94C2×#11758226C2314yescomplemented
95C2×#11758222—216no—
96C2×#11758222—216no—
97C2×#11758222—22no—
98C2×#11758222—28no—
99C2×#11758222—28no—
100C2×#11758222—24no—
101C2×#11758222—24no—
102C2×#11758222—24no—
103C2×#11758222—24no—
104C2×#11758222D414yes—
105C2×#11758222C2314yes—
106C2×#11758222C2314yescomplemented
107C22×Dic122—21no—
108C22×Dic122—21no—
109C22×Dic122D411yescharacteristic
110C22×Dic122C2311yescharacteristic
111C2×Q8×D61—216no—
112C2×Q8×D61—24no—
113C2×Q8×D61—24no—
114C2×Q8×D61—22no—
115C2×Q8×D61—22no—
116C2×Q8×D61—28no—
117C2×Q8×D61—24no—
118C2×Q8×D61D418yescomplemented
119C2×Q8×D61C2314yes—
120C2×Q8×D61C2314yescomplemented
121C22×D244—21no—
122C22×D244—21no—
123C22×D244—21no—
124C22×D244D411yescharacteristic
125C22×D244C2311yescharacteristic
126C22×D244C2311yescharacteristic
127C22×C22⋊D61—21no—
128C22×C22⋊D61—21no—
129C22×C22⋊D61—21no—
130C22×C22⋊D61—21no—
131C22×C22⋊D61D411yescharacteristic
132C22×C22⋊D61D411yescharacteristic
133C2×D4×D61—24no—
134C2×D4×D61—24no—
135C2×D4×D61—22no—
136C2×D4×D61C2314yes—
137C22×C4×D61—21no—
138C22×C4×D61—21no—
139C22×C4×D61—21no—
140C22×C4×D61—21no—
141C22×C4×D61—21no—
142C22×C4×D61C2311yescharacteristic
143C22×C4×D61C2311yescharacteristic
144#14519804—232no—
145C2×#11758190—24no—
146C2×#11758190C2314yes—
147C2×#11758200—24no—
148C2×#11758200C2314yes—
149C2×#11758201—24no—
150C2×#11758201—24no—
151C2×#11758201C2314yes—
152C2×#11758201C2314yes—
153SD16×D61—232no—
154C2×D488—24no—
155C2×D488C2314yes—
156C2×#11758199—24no—
157C2×#11758199C2314yes—
158C2×#11758189—24no—
159C2×#11758189C2314yes—
160C22×#92418C2311yescharacteristic
161C22×#92418C2311yescharacteristic
162C2×C8×D61—24no—
163C2×C8×D61C2314yes—
164#14519773—28no—
165#14519763—28no—
166#14519752—22no—
167#14519752C2314yes—
168#14519751—22no—
169#14519751C2314yes—
170#14519748—22no—
171#14519748C2314yes—
172#14519747—28no—
173#14519745—28no—
174#14519735—22no—
175#14519735C2314yes—
176C2×C4⋊Dic61C2311yescharacteristic
177C2×C22⋊Dic61—21no—
178C2×#11758198—21no—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×C4×Dic61—21no—
182#14519702C2314yescomplemented
183#14519701C2314yescomplemented
184#14519701C2314yescomplemented
185#14519700C2314yescomplemented
186#14519699C2314yescomplemented
187#14519697C2314yescomplemented
188C22⋊#92418C2314yescomplemented
189#14519689C2314yescomplemented
190#14519689C2314yescomplemented
191C22×Q8×C61—24no—
192C22×Q8×C61—24no—
193C22×Q8×C61—21no—
194C22×Q8×C61—22no—
195C22×Q8×C61C2311yescharacteristic
196C22×Q8×C61C2311yescharacteristic
197C22×Q8×C61C2314yescomplemented
198C22×D4×C61—21no—
199C22×D4×C61C2311yescharacteristic
200C23×C4×C61—21no—
201C23×C4×C61C2311yescharacteristic
202C2×SD16×C61—24no—
203C2×SD16×C61—24no—
204C2×SD16×C61C2314yes—
205C2×SD16×C61C2314yes—
206C22×C8×C61C2311yescharacteristic
207C22×C8×C61C2311yescharacteristic
208#121×C61—22no—
209#121×C61C2314yes—
210C2×C4⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61—21no—
212#103×C61C2314yescomplemented
213#103×C61C2314yescomplemented
214C22⋊C8×C61C2314yescomplemented
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C23×D61—21no—
218C23×D61—21no—
219C23×D61—24no—
220C23×D61—44no—
221C23×D61—82no—
222C23×D61—82no—
223C23×D61C2×D411yescharacteristic
224C23×D61C2×D411yescharacteristic
225C2×Q8×C61—28no—
226C2×Q8×C61—216no—
227C2×Q8×C61—28no—
228C2×Q8×C61—28no—
229C2×Q8×C61—22no—
230C2×Q8×C61—22no—
231C2×Q8×C61—21no—
232C2×Q8×C61—21no—
233C2×Q8×C61—24no—
234C2×Q8×C61C2×D414yes—
235C2×Q8×C61C2×D414yes—
236C2×Q8×C61C2412yes—
237C2×Q8×C61C2412yes—
238C2×D4×C61—24no—
239C2×D4×C61—22no—
240C2×D4×C61—22no—
241C2×D4×C61—21no—
242C2×D4×C61—82no—
243C2×D4×C61C2412yes—
244C22×C4×C61—28no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—24no—
248C22×C4×C61—22no—
249C22×C4×C61—22no—
250C22×C4×C61—21no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D412yes—
253C22×C4×C61C2412yes—
254C22×C4×C61C2411yescharacteristic
255C2×C22⋊D61—28no—
256C2×C22⋊D61—24no—
257C2×C22⋊D61—24no—
258C2×C22⋊D61—24no—
259C2×C22⋊D61—24no—
260C2×C22⋊D61—24no—
261C2×C22⋊D61—24no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—82no—
264C2×C22⋊D61—82no—
265C2×C22⋊D61C2×D414yes—
266C2×C22⋊D61C2×D414yes—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61C2×D411yescharacteristic
270C22×Dic61C2×D411yescharacteristic
271#11758226—264no—
272#11758226—216no—
273#11758226—28no—
274#11758226—28no—
275#11758226—216no—
276#11758226—28no—
277#11758226C2×D4116yescomplemented
278Q8×D61—216no—
279Q8×D61—264no—
280Q8×D61—28no—
281Q8×D61—216no—
282Q8×D61—28no—
283Q8×D61—28no—
284Q8×D61C2×D4116yescomplemented
285D4×D61—28no—
286D4×D61—28no—
287D4×D61—48no—
288#11758222—264no—
289#11758222—216no—
290#11758222—264no—
291#11758222—28no—
292#11758222—216no—
293#11758222—28no—
294#11758222—28no—
295#11758222—28no—
296C2×D244—28no—
297C2×D244—28no—
298C2×D244—24no—
299C2×D244—24no—
300C2×D244—24no—
301C2×D244—21no—
302C2×D244—22no—
303C2×D244—22no—
304C2×D244—22no—
305C2×D244—21no—
306C2×D244—24no—
307C2×D244—82no—
308C2×D244C2×D414yes—
309C2×D244C2×D414yes—
310C2×D244C2412yes—
311C2×D244C2412yes—
312C2×C4×D61—28no—
313C2×C4×D61—28no—
314C2×C4×D61—28no—
315C2×C4×D61—28no—
316C2×C4×D61—24no—
317C2×C4×D61—24no—
318C2×C4×D61—24no—
319C2×C4×D61—22no—
320C2×C4×D61—22no—
321C2×C4×D61—28no—
322C2×C4×D61—24no—
323C2×C4×D61—24no—
324C2×C4×D61C2×D412yes—
325C2×C4×D61C2×D412yes—
326C2×C4×D61C2×D414yes—
327C2×C4×D61C2×D414yes—
328C2×C4×D61C2412yes—
329C2×C4×D61C2412yes—
330C2×Dic122—28no—
331C2×Dic122—21no—
332C2×Dic122—22no—
333C2×Dic122—24no—
334C2×Dic122—28no—
335C2×Dic122—24no—
336C2×Dic122—24no—
337C2×Dic122C2×D414yes—
338C2×Dic122C2×D414yes—
339C2×Dic122C2412yes—
340SD16×C61—28no—
341SD16×C61—28no—
342C2×C8×C61—22no—
343C2×C8×C61—22no—
344C2×C8×C61C2412yes—
345C2×C8×C61C2412yes—
346C4⋊C4×C61—21no—
347C4⋊C4×C61C2412yes—
348C22⋊C4×C61—24no—
349C22⋊Dic61—24no—
350#11758201—28no—
351#11758201—28no—
352#11758200—28no—
353#11758199—28no—
354#11758198—24no—
355#11758198—24no—
356#11758198—24no—
357C4⋊Dic61—21no—
358C4⋊Dic61C2412yes—
359C4×Dic61—24no—
360C2×#92418—22no—
361C2×#92418—22no—
362C2×#92418C2412yes—
363C2×#92418C2412yes—
364D488—28no—
365#11758190—28no—
366#11758189—28no—
367C8×D61—28no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—42no—
373C23×C61—42no—
374C23×C61—42no—
375C23×C61C22×D412yes—
376C23×C61C22×D411yescharacteristic
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—24no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—42no—
386C22×D61—42no—
387C22×D61—42no—
388C22×D61—42no—
389C22×D61—42no—
390C22×D61—48no—
391C22×D61—84no—
392C22×D61—84no—
393C22×D61—816no—
394C22×D61#12014yes—
395C22×D61C22×D412yes—
396C22×D61C22×D412yes—
397Q8×C61—216no—
398Q8×C61—24no—
399Q8×C61—24no—
400Q8×C61—22no—
401Q8×C61—22no—
402Q8×C61C22×D414yes—
403Q8×C61C22×D414yes—
404D4×C61—22no—
405D4×C61—22no—
406D4×C61—42no—
407D4×C61—84no—
408C2×C4×C61—216no—
409C2×C4×C61—24no—
410C2×C4×C61—24no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—24no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—42no—
419C2×C4×C61C22×D412yes—
420C2×C4×C61C22×D411yescharacteristic
421C2×C4×C61C22×D412yes—
422C2×C4×C61C22×D412yes—
423C2×C4×C61C2511yescharacteristic
424C22⋊D61—216no—
425C22⋊D61—28no—
426C22⋊D61—28no—
427C22⋊D61—48no—
428C22⋊D61—84no—
429C22⋊D61—84no—
430C2×Dic61—22no—
431C2×Dic61—24no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—42no—
435C2×Dic61#12014yes—
436C2×Dic61C22×D412yes—
437C2×Dic61C22×D412yes—
438D244—216no—
439D244—216no—
440D244—28no—
441D244—24no—
442D244—22no—
443D244—22no—
444D244—22no—
445D244—42no—
446D244—84no—
447D244C22×D414yes—
448C4×D61—216no—
449C4×D61—216no—
450C4×D61—216no—
451C4×D61—216no—
452C4×D61—24no—
453C4×D61—22no—
454C4×D61—22no—
455C4×D61—216no—
456C4×D61#12018yes—
457C4×D61C22×D414yes—
458C4×D61C22×D414yes—
459Dic122—216no—
460Dic122—24no—
461Dic122—22no—
462Dic122—216no—
463Dic122—28no—
464Dic122C22×D414yes—
465C8×C61—22no—
466C8×C61—22no—
467#92418—22no—
468#92418—22no—
469C2×#3010—611nomaximal, Sylow
470C22×C61—22no—
471C22×C61—22no—
472C22×C61—22no—
473C22×C61—44no—
474C22×C61—42no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61—84no—
478C22×C61C2×#12012yes—
479C22×C61#57712yes—
480C22×C61#57712yes—
481C22×C61C23×D411yescharacteristic
482C2×D61—28no—
483C2×D61—22no—
484C2×D61—22no—
485C2×D61—22no—
486C2×D61—24no—
487C2×D61—22no—
488C2×D61—22no—
489C2×D61—44no—
490C2×D61—48no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—816no—
497C2×D61—84no—
498C2×D61C2×#12014yes—
499C4×C61—24no—
500C4×C61—24no—
501C4×C61—22no—
502C4×C61—42no—
503C4×C61C2×#12012yes—
504C4×C61C23×D411yescharacteristic
505C4×C61C23×D411yescharacteristic
506Dic61—22no—
507Dic61—24no—
508Dic61—42no—
509Dic61C2×#12014yes—
510C22×2−1+4—611no—
511C22×AGL(1,ℤ/8)—611no—
512C23×SD16—611no—
513C2×#535—611no—
514#3010—6116no—
515C2×#449—611no—
516C2×#449—611no—
517C2×#449—611no—
518C2×#449—611no—
519C2×#448—611no—
520C2×#448—611no—
521C2×#448—611no—
522C2×#448D6111yescharacteristic, complemented
523C2×#419—611no—
524C2×#416—611no—
525C2×#408—611no—
526C2×C61—42no—
527C2×C61—82no—
528C2×C61#301014yescomplemented
529C2×C61C22×#12011yescharacteristic
530C2×C61C2×#57711yescharacteristic
531C2×C61C2×#57711yescharacteristic
532D61—24no—
533D61—42no—
534D61—44no—
535D61—82no—
536C2×2−1+4—618no—
537C2×2−1+4—1228no—
538C2×2−1+4—1228no—
539C2×2−1+4—1224no—
540C22×#41—611no—
541C22×#41—611no—
542C22×#41—611no—
543C22×#41—611no—
544C22×#41—1221no—
545C22×#41—1221no—
546C22×#41—1221no—
547C23×Q8—611no—
548C23×Q8—611no—
549C23×Q8—1221no—
550C23×Q8C2×D6111yescharacteristic, complemented
551C23×D4—611no—
552C2×AGL(1,ℤ/8)—618no—
553C2×AGL(1,ℤ/8)—1228no—
554C22×SD16—611no—
555C22×SD16—611no—
556C22×SD16—611no—
557C22×SD16—618no—
558C22×SD16—611no—
559C22×SD16—1228no—
560C22×SD16C2×D6111yescharacteristic
561C22×SD16C2×D6111yescharacteristic
562C22×D8—611no—
563C22×D8—611no—
564C22×M16—611no—
565C23×C8—611no—
566#535—618no—
567#535—1224no—
568C2×#127—1221no—
569C2×#124—1221no—
570C2×#121—611no—
571C2×#121—611no—
572C2×#121—611no—
573C2×#121C2×D6111yescharacteristic
574C2×#120—1221no—
575C2×#120—1221no—
576C2×#117—611no—
577#449—618no—
578#449—618no—
579#449—618no—
580#449—618no—
581#448—618no—
582#448—618no—
583#448—618no—
584#448C2×D6118yescomplemented
585#419—618no—
586#416—618no—
587C2×#103—611no—
588C2×#103—611no—
589C2×#103—611no—
590C2×#103—611no—
591C2×#103C2×D6111yescharacteristic, complemented
592C2×#103C2×D6111yescharacteristic, complemented
593C2×#102—611no—
594C2×#102—611no—
595#408—618no—
596C2×C22⋊C8—611no—
597C2×C22⋊C8—611no—
598C2×C22⋊C8—611no—
599C2×C22⋊C8C2×D6111yescharacteristic, complemented
600C61C2×#301011yescharacteristic, complemented, Sylow
601C25—1221no—
6022−1+4—12232no—
6032−1+4—12232no—
6042−1+4—12264no—
605C2×#41—614no—
606C2×#41—614no—
607C2×#41—618no—
608C2×#41—614no—
609C2×#41—614no—
610C2×#41—614no—
611C2×#41—1224no—
612C2×#41—1224no—
613C2×#41—1224no—
614C2×#41—1228no—
615C2×#41—1228no—
616C2×#41—1224no—
617C2×#41—12216no—
618C2×#41—12216no—
619C2×#41—1222no—
620C2×#41—1224no—
621C2×#41—1222no—
622C2×#41—1224no—
623C2×#41—1228no—
624C2×#41—12216no—
625C2×#41—1224no—
626C2×#41—1222no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—21no—
630C22×Q8—22no—
631C22×Q8—611no—
632C22×Q8—618no—
633C22×Q8—614no—
634C22×Q8—614no—
635C22×Q8—611no—
636C22×Q8—1221no—
637C22×Q8—1221no—
638C22×Q8—1222no—
639C22×Q8—1224no—
640C22×Q8—1222no—
641C22×Q8—1224no—
642C22×Q8—1228no—
643C22×Q8—12216no—
644C22×Q8—1224no—
645C22×Q8C22×D6111yescharacteristic
646C22×Q8C22×D6111yescharacteristic
647C22×Q8C22×D6114yescomplemented
648C22×D4—21no—
649C22×D4—611no—
650C22×D4—611no—
651C22×D4—614no—
652C22×D4—611no—
653C22×D4—611no—
654C22×D4—611no—
655C22×D4—1221no—
656C22×D4—1221no—
657C22×D4—1221no—
658C22×D4—1224no—
659C22×D4—1224no—
660C22×D4—1222no—
661C22×D4—1221no—
662C22×D4—1221no—
663C22×D4—1221no—
664C22×D4—1221no—
665C22×D4C22×D6111yescharacteristic
666C23×C4—21no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—1221no—
670C23×C4—1221no—
671C23×C4—1221no—
672C23×C4—1221no—
673C23×C4—1221no—
674C23×C4C22×D6111yescharacteristic
675AGL(1,ℤ/8)—12232no—
676C2×SD16—24no—
677C2×SD16—24no—
678C2×SD16—614no—
679C2×SD16—614no—
680C2×SD16—614no—
681C2×SD16—614no—
682C2×SD16—1224no—
683C2×SD16—12232no—
684C2×SD16—1224no—
685C2×SD16—1224no—
686C2×SD16—1224no—
687C2×SD16C22×D6114yes—
688C2×SD16C22×D6114yes—
689C2×D8—614no—
690C2×D8—614no—
691C2×D8—1224no—
692C2×D8—1224no—
693C2×M16—614no—
694C2×M16—1224no—
695C22×C8—611no—
696C22×C8—611no—
697C22×C8—614no—
698C22×C8—1224no—
699C22×C8C22×D6111yescharacteristic
700C22×C8C22×D6111yescharacteristic
701#127—1228no—
702#124—1228no—
703#121—22no—
704#121—614no—
705#121—614no—
706#121—614no—
707#121—1222no—
708#121—1222no—
709#121—1222no—
710#121C22×D6114yes—
711#120—1228no—
712#120—1228no—
713#117—614no—
714#117—1222no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4C22×D6111yescharacteristic
717C2×C22⋊C4—21no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C42—1221no—
723#103—614no—
724#103—614no—
725#103—614no—
726#103—614no—
727#103C22×D6114yescomplemented
728#103C22×D6114yescomplemented
729#102—614no—
730#102—614no—
731C22⋊C8—614no—
732C22⋊C8—614no—
733C22⋊C8—614no—
734C22⋊C8C22×D6114yescomplemented
735C24—21no—
736C24—611no—
737C24—611no—
738C24—1224no—
739C24—1221no—
740C24—1221no—
741C24—4882no—
742C24—4882no—
743C24—2444no—
744C24D4×D6111yescharacteristic
745#41—6116no—
746#41—12216no—
747#41—1228no—
748#41—1228no—
749#41—1228no—
750#41—1228no—
751#41—12264no—
752#41—12264no—
753#41—12216no—
754#41—12216no—
755#41—1228no—
756#41—1228no—
757#41—12264no—
758#41—12216no—
759#41—1228no—
760C2×Q8—28no—
761C2×Q8—216no—
762C2×Q8—28no—
763C2×Q8—28no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—24no—
769C2×Q8—614no—
770C2×Q8—6116no—
771C2×Q8—614no—
772C2×Q8—612no—
773C2×Q8—1228no—
774C2×Q8—1224no—
775C2×Q8—1224no—
776C2×Q8—1224no—
777C2×Q8—1228no—
778C2×Q8—12216no—
779C2×Q8—1228no—
780C2×Q8—1228no—
781C2×Q8—12264no—
782C2×Q8—12216no—
783C2×Q8—1228no—
784C2×Q8—1222no—
785C2×Q8—1221no—
786C2×Q8D4×D6114yes—
787C2×Q8D4×D6114yes—
788C2×Q8C23×D6112yes—
789C2×Q8C23×D6112yes—
790C2×D4—24no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—82no—
795C2×D4—614no—
796C2×D4—614no—
797C2×D4—614no—
798C2×D4—614no—
799C2×D4—612no—
800C2×D4—612no—
801C2×D4—1224no—
802C2×D4—1228no—
803C2×D4—1224no—
804C2×D4—1224no—
805C2×D4—1228no—
806C2×D4—1224no—
807C2×D4—1228no—
808C2×D4—1228no—
809C2×D4—1224no—
810C2×D4—1224no—
811C2×D4—1224no—
812C2×D4—1228no—
813C2×D4—1224no—
814C2×D4—1224no—
815C2×D4—1224no—
816C2×D4—1221no—
817C2×D4—1222no—
818C2×D4—1222no—
819C2×D4—1222no—
820C2×D4—1221no—
821C2×D4—4882no—
822C2×D4—4882no—
823C2×D4—4882no—
824C2×D4—2448no—
825C2×D4—2444no—
826C2×D4C23×D6112yes—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—611no—
835C22×C4—612no—
836C22×C4—614no—
837C22×C4—614no—
838C22×C4—612no—
839C22×C4—611no—
840C22×C4—612no—
841C22×C4—612no—
842C22×C4—1228no—
843C22×C4—1224no—
844C22×C4—1224no—
845C22×C4—1228no—
846C22×C4—1224no—
847C22×C4—1224no—
848C22×C4—1228no—
849C22×C4—1228no—
850C22×C4—1228no—
851C22×C4—1221no—
852C22×C4—1222no—
853C22×C4—1222no—
854C22×C4—1224no—
855C22×C4—1221no—
856C22×C4D4×D6112yes—
857C22×C4D4×D6111yescharacteristic
858C22×C4C23×D6112yes—
859C22×C4C23×D6111yescharacteristic
860SD16—28no—
861SD16—28no—
862SD16—1228no—
863SD16—1228no—
864SD16—1228no—
865SD16—1228no—
866D8—1228no—
867D8—1228no—
868M16—1228no—
869C2×C8—22no—
870C2×C8—22no—
871C2×C8—612no—
872C2×C8—612no—
873C2×C8—1228no—
874C2×C8—1222no—
875C2×C8—1222no—
876C2×C8C23×D6112yes—
877C2×C8C23×D6112yes—
878C4⋊C4—21no—
879C4⋊C4—612no—
880C4⋊C4—1221no—
881C4⋊C4C23×D6112yes—
882C22⋊C4—24no—
883C22⋊C4—1224no—
884C22⋊C4—1224no—
885C22⋊C4—1224no—
886C22⋊C4—1224no—
887C42—1224no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—614no—
896C23—612no—
897C23—612no—
898C23—1222no—
899C23—1222no—
900C23—1224no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—4884no—
907C23—4884no—
908C23—48816no—
909C23—2448no—
910C23—2442no—
911C23—2442no—
912C23—2442no—
913C23—2442no—
914C23—2442no—
915C23C2×D4×D6112yes—
916C23C2×D4×D6111yescharacteristic
917Q8—216no—
918Q8—24no—
919Q8—24no—
920Q8—22no—
921Q8—22no—
922Q8—614no—
923Q8—12216no—
924Q8—1228no—
925Q8—12216no—
926Q8—1224no—
927Q8—1222no—
928Q8C2×D4×D6114yes—
929Q8C2×D4×D6114yes—
930D4—22no—
931D4—22no—
932D4—42no—
933D4—84no—
934D4—614no—
935D4—1228no—
936D4—12216no—
937D4—12216no—
938D4—1228no—
939D4—1228no—
940D4—12216no—
941D4—1224no—
942D4—1222no—
943D4—1222no—
944D4—1222no—
945D4—4884no—
946D4—4884no—
947D4—4884no—
948D4—2448no—
949D4—2442no—
950C2×C4—216no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—42no—
961C2×C4—614no—
962C2×C4—612no—
963C2×C4—618no—
964C2×C4—614no—
965C2×C4—614no—
966C2×C4—612no—
967C2×C4—12216no—
968C2×C4—12216no—
969C2×C4—12216no—
970C2×C4—12216no—
971C2×C4—12216no—
972C2×C4—1222no—
973C2×C4—1224no—
974C2×C4—1222no—
975C2×C4—1224no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—2442no—
980C2×C4C2×D4×D6112yes—
981C2×C4C2×D4×D6111yescharacteristic
982C2×C4C2×D4×D6112yes—
983C2×C4C2×D4×D6112yes—
984C2×C4C24×D6111yescharacteristic
985C8—22no—
986C8—22no—
987C8—1222no—
988C8—1222no—
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—42no—
994C22—42no—
995C22—42no—
996C22—84no—
997C22—614no—
998C22—1222no—
999C22—1222no—
1000C22—1228no—
1001C22—1224no—
1002C22—1222no—
1003C22—1222no—
1004C22—1222no—
1005C22—48816no—
1006C22—4884no—
1007C22—2442no—
1008C22—2442no—
1009C22—2442no—
1010C22—2442no—
1011C22—2442no—
1012C22—2444no—
1013C22—2448no—
1014C22#120×D6112yes—
1015C22#1684056812yes—
1016C22#1684057112yes—
1017C22C22×D4×D6111yescharacteristic
1018C4—24no—
1019C4—24no—
1020C4—22no—
1021C4—42no—
1022C4—614no—
1023C4—1222no—
1024C4—1224no—
1025C4—2442no—
1026C4#120×D6112yes—
1027C4C22×D4×D6111yescharacteristic
1028C4C22×D4×D6111yescharacteristic
1029C2—42no—
1030C2—82no—
1031C2—1224no—
1032C2—4882no—
1033C2—2442no—
1034C2—2444no—
1035C2#2145510014yesdirect product factor
1036C2C2×#120×D6111yescharacteristic
1037C2C2×#1684056811yescharacteristic
1038C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#448C2
socleC23×C61C22×D4
hypercenterC2×#448D61
hypocenterC61C2×#3010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×#14519825C2semidirect
2. C22×#14519804C2semidirect
3. C22×SD16×D61C2semidirect
4. C2×#16840328C2semidirect
5. #21455100C2direct (N × H)
6. C2×#16839910C2semidirect
7. C2×#16839909C2semidirect
8. C2×#16839906C2semidirect
9. C2×#16839905C2semidirect
10. C2×#16839902C2semidirect
11. C2×#16839901C2semidirect
12. C2×#16839899C2semidirect
13. C2×#16839769C2semidirect
14. C2×#16839757C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#448C2semidirect
20. C2×#14519825C22semidirect
23. C22×#11758226C22semidirect
27. C22×#11758222C22semidirect
30. C22×Q8×D61C22semidirect
33. C2×#14519804C22semidirect
39. C2×SD16×D61C22semidirect
45. #16840328C22semidirect
54. #16839910C22semidirect
55. #16839909C22semidirect
56. #16839906C22semidirect
57. #16839905C22semidirect
58. #16839902C22semidirect
59. #16839901C22semidirect
60. #16839899C22semidirect
61. #16839769C22semidirect
62. #16839757C22semidirect
63. C2×#14519702C22semidirect
64. C2×#14519701C22semidirect
65. C2×#14519701C22semidirect
66. C2×#14519700C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519697C22semidirect
69. #16839727C22semidirect
70. C2×C22⋊#92418C22semidirect
71. C2×#14519689C22semidirect
72. C2×#14519689C22semidirect
73. C23×Q8×C61C22semidirect
77. C61×#448C22semidirect
78. C2×#103×C61C22semidirect
79. C2×#103×C61C22semidirect
80. C2×C22⋊C8×C61C22semidirect
92. C2×#11758226D4semidirect
94. C2×#11758226C23semidirect
106. C2×#11758222C23semidirect
118. C2×Q8×D61D4semidirect
120. C2×Q8×D61C23semidirect
182. #14519702C23semidirect
183. #14519701C23semidirect
184. #14519701C23semidirect
185. #14519700C23semidirect
186. #14519699C23semidirect
187. #14519697C23semidirect
188. C22⋊#92418C23semidirect
189. #14519689C23semidirect
190. #14519689C23semidirect
197. C22×Q8×C61C23semidirect
212. #103×C61C23semidirect
213. #103×C61C23semidirect
214. C22⋊C8×C61C23semidirect
277. #11758226C2×D4semidirect
284. Q8×D61C2×D4semidirect
522. C2×#448D61semidirect
528. C2×C61#3010semidirect
550. C23×Q8C2×D61semidirect
584. #448C2×D61semidirect
591. C2×#103C2×D61semidirect
592. C2×#103C2×D61semidirect
599. C2×C22⋊C8C2×D61semidirect
600. C61C2×#3010semidirect
647. C22×Q8C22×D61semidirect
727. #103C22×D61semidirect
728. #103C22×D61semidirect
734. C22⋊C8C22×D61semidirect
1035. C2#21455100direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198252
C22×#145198042
C22×SD16×D612
C2×#168403282
#214551002
C2×#168399102
C2×#168399092
C2×#168399062
C2×#168399052
C2×#168399022
C2×#168399012
C2×#168398992
C2×#168397692
C2×#168397572
C2×#168397272
C2×C61×#4482
C2×#301061