Finite Group Databasebeta

← C2×#21455102 #30546434

Subgroups — C2×#21455102 #30546434

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×#14519824C211yesmaximal, characteristic, complemented
2C22×#14519801C211yesmaximal, characteristic, complemented
3C22×SD16×D61C211yesmaximal, characteristic, complemented
4C2×#16840328C211yesmaximal, characteristic, complemented
5#21455102C2116yesmaximal, direct product factor
6C2×#16839908C211yesmaximal, characteristic, complemented
7C2×#16839907C211yesmaximal, characteristic, complemented
8C2×#16839904C211yesmaximal, characteristic, complemented
9C2×#16839903C211yesmaximal, characteristic, complemented
10C2×#16839902C211yesmaximal, characteristic, complemented
11C2×#16839900C211yesmaximal, characteristic, complemented
12C2×#16839899C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#16839755C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C2×#14519824—24no—
18C2×#14519824—28no—
19C2×#14519824—28no—
20C2×#14519824C2218yescomplemented
21C22×#11758222—21no—
22C22×#11758222C2211yescharacteristic
23C22×#11758224—21no—
24C22×#11758224—21no—
25C22×#11758224C2211yescharacteristic
26C22×#11758224C2211yescharacteristic, complemented
27C23×Dic122—21no—
28C23×Dic122C2211yescharacteristic, complemented
29C22×Q8×D61C2211yescharacteristic
30C22×Q8×D61C2211yescharacteristic, complemented
31C22×D4×D61C2211yescharacteristic
32C2×#14519801—28no—
33C2×#14519801C2218yescomplemented
34C22×#11758190C2211yescharacteristic
35C22×#11758190C2211yescharacteristic
36C22×#11758200C2211yescharacteristic
37C22×#11758200C2211yescharacteristic
38C22×#11758201C2211yescharacteristic
39C2×SD16×D61—28no—
40C2×SD16×D61C2218yescomplemented
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#16839908C2218yescomplemented
55#16839907C2218yescomplemented
56#16839904C2218yescomplemented
57#16839903C2218yescomplemented
58#16839902C2218yescomplemented
59#16839900C2218yescomplemented
60#16839899C2218yescomplemented
61#16839769C2218yescomplemented
62#16839755C2218yescomplemented
63C2×#14519702C2211yescharacteristic, complemented
64C2×#14519702C2211yescharacteristic, complemented
65C2×#14519701C2211yescharacteristic, complemented
66C2×#14519700C2211yescharacteristic, complemented
67C2×#14519700C2211yescharacteristic, complemented
68C2×#14519698C2211yescharacteristic, complemented
69#16839727C2218yescomplemented
70C2×C22⋊#92418C2211yescharacteristic, complemented
71C2×#14519689C2211yescharacteristic, complemented
72C2×#14519689C2211yescharacteristic, complemented
73C22×#41×C61C2211yescharacteristic, complemented
74C22×SD16×C61C2211yescharacteristic
75C22×D8×C61C2211yescharacteristic
76C2×#121×C61C2211yescharacteristic
77C61×#449C2218yescomplemented
78C2×#103×C61C2211yescharacteristic, complemented
79C2×#102×C61C2211yescharacteristic, complemented
80C2×C22⋊C8×C61C2211yescharacteristic, complemented
81C24×D61—21no—
82#14519824—264no—
83#14519824—232no—
84#14519824—232no—
85C2×#11758222—216no—
86C2×#11758222—28no—
87C2×#11758222—24no—
88C2×#11758222—24no—
89C2×#11758222D414yes—
90C2×#11758222C2314yes—
91C2×#11758224—216no—
92C2×#11758224—216no—
93C2×#11758224—24no—
94C2×#11758224—28no—
95C2×#11758224—28no—
96C2×#11758224—22no—
97C2×#11758224—24no—
98C2×#11758224—22no—
99C2×#11758224—24no—
100C2×#11758224D418yescomplemented
101C2×#11758224C2314yes—
102C2×#11758224C2314yescomplemented
103C22×Dic122—216no—
104C22×Dic122—21no—
105C22×Dic122—22no—
106C22×Dic122—21no—
107C22×Dic122—21no—
108C22×Dic122—28no—
109C22×Dic122—24no—
110C22×Dic122—24no—
111C22×Dic122D411yescharacteristic
112C22×Dic122C2311yescharacteristic
113C22×Dic122C2311yescharacteristic
114C22×Dic122C2314yescomplemented
115C2×Q8×D61—24no—
116C2×Q8×D61—24no—
117C2×Q8×D61—22no—
118C2×Q8×D61—22no—
119C2×Q8×D61—24no—
120C2×Q8×D61D418yescomplemented
121C2×Q8×D61C2314yes—
122C2×Q8×D61C2314yescomplemented
123C22×D244—21no—
124C22×D244D411yescharacteristic
125C22×D244C2311yescharacteristic
126C22×C22⋊D61—21no—
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—
137C23×Dic61—21no—
138C23×Dic61—21no—
139C23×Dic61—21no—
140C22×C4×D61—21no—
141C22×C4×D61—21no—
142C22×C4×D61C2311yescharacteristic
143C22×C4×D61C2311yescharacteristic
144#14519801—232no—
145C2×#11758190—24no—
146C2×#11758190—24no—
147C2×#11758190C2314yes—
148C2×#11758190C2314yes—
149C2×#11758200—24no—
150C2×#11758200—24no—
151C2×#11758200C2314yes—
152C2×#11758200C2314yes—
153C2×#11758201—24no—
154C2×#11758201C2314yes—
155SD16×D61—232no—
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#14519702C2314yescomplemented
184#14519701C2314yescomplemented
185#14519700C2314yescomplemented
186#14519700C2314yescomplemented
187#14519698C2314yescomplemented
188C22⋊#92418C2314yescomplemented
189#14519689C2314yescomplemented
190#14519689C2314yescomplemented
191C2×#41×C61—24no—
192C2×#41×C61—24no—
193C2×#41×C61—22no—
194C2×#41×C61C2314yescomplemented
195C22×Q8×C61C2311yescharacteristic
196C22×D4×C61—21no—
197C22×D4×C61—21no—
198C22×D4×C61C2311yescharacteristic
199C22×D4×C61C2311yescharacteristic
200C23×C4×C61—21no—
201C23×C4×C61C2311yescharacteristic
202C2×SD16×C61—24no—
203C2×SD16×C61C2314yes—
204C2×D8×C61—24no—
205C2×D8×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#102×C61C2314yescomplemented
214C22⋊C8×C61C2314yescomplemented
215C24×C61—21no—
216C24×C61—21no—
217C24×C61C2×D411yescharacteristic
218C23×D61—21no—
219C23×D61—24no—
220C23×D61—44no—
221C23×D61—82no—
222C23×D61—82no—
223C23×D61C2×D411yescharacteristic
224C23×D61C2×D411yescharacteristic
225#41×C61—216no—
226#41×C61—28no—
227#41×C61—28no—
228C2×Q8×C61—22no—
229C2×Q8×C61—21no—
230C2×Q8×C61C2×D414yes—
231C2×Q8×C61C2412yes—
232C2×D4×C61—28no—
233C2×D4×C61—24no—
234C2×D4×C61—24no—
235C2×D4×C61—21no—
236C2×D4×C61—22no—
237C2×D4×C61—22no—
238C2×D4×C61—22no—
239C2×D4×C61—21no—
240C2×D4×C61—82no—
241C2×D4×C61C2×D414yes—
242C2×D4×C61C2412yes—
243C2×D4×C61C2412yes—
244C22×C4×C61—28no—
245C22×C4×C61—21no—
246C22×C4×C61—24no—
247C22×C4×C61—22no—
248C22×C4×C61—22no—
249C22×C4×C61—21no—
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D412yes—
252C22×C4×C61C2412yes—
253C22×C4×C61C2411yescharacteristic
254C2×C22⋊D61—28no—
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—24no—
263C2×C22⋊D61—44no—
264C2×C22⋊D61—82no—
265C2×C22⋊D61—82no—
266C2×C22⋊D61C2×D414yes—
267C2×C22⋊D61C2×D414yes—
268C22×Dic61—28no—
269C22×Dic61—28no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—24no—
273C22×Dic61—28no—
274C22×Dic61—24no—
275C22×Dic61—24no—
276C22×Dic61—21no—
277C22×Dic61C2×D411yescharacteristic
278C22×Dic61C2×D411yescharacteristic
279Q8×D61—216no—
280Q8×D61—28no—
281Q8×D61—216no—
282Q8×D61—28no—
283Q8×D61—28no—
284Q8×D61C2×D4116yescomplemented
285#11758224—264no—
286#11758224—216no—
287#11758224—264no—
288#11758224—28no—
289#11758224—216no—
290#11758224—28no—
291#11758224—28no—
292#11758224C2×D4116yescomplemented
293D4×D61—28no—
294D4×D61—28no—
295D4×D61—48no—
296#11758222—264no—
297#11758222—216no—
298#11758222—28no—
299#11758222—28no—
300C2×D244—24no—
301C2×D244—22no—
302C2×D244—22no—
303C2×D244—21no—
304C2×D244—24no—
305C2×D244—82no—
306C2×D244C2×D414yes—
307C2×D244C2412yes—
308C2×C4×D61—28no—
309C2×C4×D61—28no—
310C2×C4×D61—24no—
311C2×C4×D61—24no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61C2×D412yes—
315C2×C4×D61C2×D412yes—
316C2×C4×D61C2×D414yes—
317C2×C4×D61C2×D414yes—
318C2×C4×D61C2412yes—
319C2×C4×D61C2412yes—
320C2×Dic122—28no—
321C2×Dic122—28no—
322C2×Dic122—216no—
323C2×Dic122—264no—
324C2×Dic122—21no—
325C2×Dic122—21no—
326C2×Dic122—22no—
327C2×Dic122—22no—
328C2×Dic122—24no—
329C2×Dic122—28no—
330C2×Dic122—24no—
331C2×Dic122—24no—
332C2×Dic122—24no—
333C2×Dic122—28no—
334C2×Dic122—28no—
335C2×Dic122C2×D414yes—
336C2×Dic122C2×D414yes—
337C2×Dic122C2×D414yes—
338C2×Dic122C2412yes—
339C2×Dic122C2412yes—
340SD16×C61—28no—
341D8×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#11758200—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—
364#11758190—28no—
365#11758190—28no—
366#11758189—28no—
367C8×D61—28no—
368C23×C61—22no—
369C23×C61—24no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—42no—
375C23×C61—42no—
376C23×C61—42no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61C22×D412yes—
380C23×C61C22×D411yescharacteristic
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
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—24no—
398Q8×C61—22no—
399Q8×C61C22×D414yes—
400D4×C61—216no—
401D4×C61—24no—
402D4×C61—22no—
403D4×C61—22no—
404D4×C61—22no—
405D4×C61—42no—
406D4×C61—84no—
407D4×C61C22×D414yes—
408C2×C4×C61—216no—
409C2×C4×C61—22no—
410C2×C4×C61—24no—
411C2×C4×C61—22no—
412C2×C4×C61—24no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—42no—
417C2×C4×C61C22×D412yes—
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D412yes—
420C2×C4×C61C22×D412yes—
421C2×C4×C61C2511yescharacteristic
422C22⋊D61—216no—
423C22⋊D61—28no—
424C22⋊D61—216no—
425C22⋊D61—28no—
426C22⋊D61—48no—
427C22⋊D61—84no—
428C22⋊D61—84no—
429C2×Dic61—216no—
430C2×Dic61—216no—
431C2×Dic61—22no—
432C2×Dic61—24no—
433C2×Dic61—24no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—216no—
437C2×Dic61—22no—
438C2×Dic61—42no—
439C2×Dic61#12014yes—
440C2×Dic61C22×D412yes—
441C2×Dic61C22×D412yes—
442D244—28no—
443D244—22no—
444D244—22no—
445D244—42no—
446D244—84no—
447C4×D61—216no—
448C4×D61—216no—
449C4×D61—24no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61#12018yes—
453C4×D61C22×D414yes—
454C4×D61C22×D414yes—
455Dic122—216no—
456Dic122—216no—
457Dic122—24no—
458Dic122—24no—
459Dic122—22no—
460Dic122—22no—
461Dic122—28no—
462Dic122—216no—
463Dic122C22×D414yes—
464Dic122C22×D414yes—
465C8×C61—22no—
466C8×C61—22no—
467#92418—22no—
468#92418—22no—
469C2×#3010—611nomaximal, Sylow
470C22×C61—22no—
471C22×C61—24no—
472C22×C61—22no—
473C22×C61—22no—
474C22×C61—44no—
475C22×C61—48no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61—42no—
479C22×C61—42no—
480C22×C61—42no—
481C22×C61—84no—
482C22×C61C2×#12012yes—
483C22×C61#57712yes—
484C22×C61#57712yes—
485C22×C61C23×D411yescharacteristic
486C2×D61—28no—
487C2×D61—22no—
488C2×D61—22no—
489C2×D61—22no—
490C2×D61—22no—
491C2×D61—22no—
492C2×D61—44no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—816no—
497C2×D61—84no—
498C2×D61C2×#12014yes—
499C4×C61—22no—
500C4×C61—24no—
501C4×C61—42no—
502C4×C61C2×#12012yes—
503C4×C61C23×D411yescharacteristic
504C4×C61C23×D411yescharacteristic
505Dic61—22no—
506Dic61—24no—
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×#449D6111yescharacteristic, complemented
519C2×#448—611no—
520C2×#448—611no—
521C2×#448—611no—
522C2×#448—611no—
523C2×#419—611no—
524C2×#416—611no—
525C2×#408—611no—
526C2×C61—42no—
527C2×C61—44no—
528C2×C61—82no—
529C2×C61#301014yescomplemented
530C2×C61C22×#12011yescharacteristic
531C2×C61C2×#57711yescharacteristic
532C2×C61C2×#57711yescharacteristic
533D61—24no—
534D61—42no—
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—1221no—
544C22×#41—1221no—
545C22×#41—1221no—
546C22×#41C2×D6111yescharacteristic, complemented
547C23×Q8—611no—
548C23×Q8—611no—
549C23×Q8—611no—
550C23×Q8—1221no—
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—611no—
560C22×SD16—1228no—
561C22×SD16C2×D6111yescharacteristic
562C22×D8—611no—
563C22×D8C2×D6111yescharacteristic
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#449C2×D6118yescomplemented
581#448—618no—
582#448—618no—
583#448—618no—
584#448—618no—
585#419—618no—
586#416—618no—
587C2×#103—611no—
588C2×#103—611no—
589C2×#103—611no—
590C2×#103—611no—
591C2×#103—611no—
592C2×#103C2×D6111yescharacteristic, complemented
593C2×#102—611no—
594C2×#102C2×D6111yescharacteristic, complemented
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—24no—
606C2×#41—24no—
607C2×#41—22no—
608C2×#41—614no—
609C2×#41—614no—
610C2×#41—618no—
611C2×#41—614no—
612C2×#41—614no—
613C2×#41—1224no—
614C2×#41—1224no—
615C2×#41—1228no—
616C2×#41—12216no—
617C2×#41—1222no—
618C2×#41—1224no—
619C2×#41—1222no—
620C2×#41—1228no—
621C2×#41—1228no—
622C2×#41—1224no—
623C2×#41—12216no—
624C2×#41—12216no—
625C2×#41—1224no—
626C2×#41C22×D6114yescomplemented
627C22×Q8—611no—
628C22×Q8—618no—
629C22×Q8—614no—
630C22×Q8—614no—
631C22×Q8—611no—
632C22×Q8—611no—
633C22×Q8—614no—
634C22×Q8—1221no—
635C22×Q8—1221no—
636C22×Q8—1224no—
637C22×Q8—1224no—
638C22×Q8—1228no—
639C22×Q8—12216no—
640C22×Q8—1222no—
641C22×Q8—1224no—
642C22×Q8—1222no—
643C22×Q8—1224no—
644C22×Q8—1224no—
645C22×Q8—1221no—
646C22×Q8—1222no—
647C22×Q8C22×D6111yescharacteristic
648C22×D4—21no—
649C22×D4—21no—
650C22×D4—611no—
651C22×D4—611no—
652C22×D4—614no—
653C22×D4—611no—
654C22×D4—611no—
655C22×D4—1221no—
656C22×D4—1224no—
657C22×D4—1224no—
658C22×D4—1222no—
659C22×D4—1221no—
660C22×D4—1221no—
661C22×D4—1221no—
662C22×D4—1221no—
663C22×D4—1221no—
664C22×D4C22×D6111yescharacteristic
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—614no—
678C2×SD16—614no—
679C2×SD16—614no—
680C2×SD16—614no—
681C2×SD16—614no—
682C2×SD16—1224no—
683C2×SD16—1224no—
684C2×SD16—12232no—
685C2×SD16—1224no—
686C2×SD16—1224no—
687C2×SD16—1224no—
688C2×SD16C22×D6114yes—
689C2×D8—24no—
690C2×D8—614no—
691C2×D8—1224no—
692C2×D8C22×D6114yes—
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#103—614no—
728#103C22×D6114yescomplemented
729#102—614no—
730#102C22×D6114yescomplemented
731C22⋊C8—614no—
732C22⋊C8—614no—
733C22⋊C8—614no—
734C22⋊C8C22×D6114yescomplemented
735C24—21no—
736C24—21no—
737C24—611no—
738C24—611no—
739C24—1224no—
740C24—1221no—
741C24—4882no—
742C24—4882no—
743C24—2444no—
744C24D4×D6111yescharacteristic
745#41—216no—
746#41—28no—
747#41—28no—
748#41—6116no—
749#41—12216no—
750#41—1228no—
751#41—1228no—
752#41—12264no—
753#41—12216no—
754#41—1228no—
755#41—1228no—
756#41—12264no—
757#41—12264no—
758#41—12216no—
759#41—1228no—
760C2×Q8—22no—
761C2×Q8—21no—
762C2×Q8—614no—
763C2×Q8—6116no—
764C2×Q8—614no—
765C2×Q8—614no—
766C2×Q8—612no—
767C2×Q8—612no—
768C2×Q8—1224no—
769C2×Q8—1228no—
770C2×Q8—1224no—
771C2×Q8—1224no—
772C2×Q8—1228no—
773C2×Q8—1228no—
774C2×Q8—1228no—
775C2×Q8—1228no—
776C2×Q8—12264no—
777C2×Q8—12216no—
778C2×Q8—12216no—
779C2×Q8—1228no—
780C2×Q8—1228no—
781C2×Q8—12216no—
782C2×Q8—1228no—
783C2×Q8—1222no—
784C2×Q8—1222no—
785C2×Q8—1224no—
786C2×Q8—1221no—
787C2×Q8—1221no—
788C2×Q8D4×D6114yes—
789C2×Q8C23×D6112yes—
790C2×D4—28no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—82no—
799C2×D4—614no—
800C2×D4—614no—
801C2×D4—614no—
802C2×D4—612no—
803C2×D4—1224no—
804C2×D4—1224no—
805C2×D4—1228no—
806C2×D4—1228no—
807C2×D4—1224no—
808C2×D4—1224no—
809C2×D4—1224no—
810C2×D4—1228no—
811C2×D4—1224no—
812C2×D4—1224no—
813C2×D4—1228no—
814C2×D4—1224no—
815C2×D4—1224no—
816C2×D4—1222no—
817C2×D4—1222no—
818C2×D4—1221no—
819C2×D4—4882no—
820C2×D4—4882no—
821C2×D4—4882no—
822C2×D4—2448no—
823C2×D4—2444no—
824C2×D4D4×D6114yes—
825C2×D4C23×D6112yes—
826C2×D4C23×D6112yes—
827C22×C4—28no—
828C22×C4—21no—
829C22×C4—24no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—611no—
834C22×C4—612no—
835C22×C4—614no—
836C22×C4—614no—
837C22×C4—612no—
838C22×C4—611no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—1228no—
842C22×C4—1224no—
843C22×C4—1224no—
844C22×C4—1228no—
845C22×C4—1228no—
846C22×C4—1224no—
847C22×C4—1224no—
848C22×C4—1228no—
849C22×C4—1228no—
850C22×C4—1224no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1222no—
854C22×C4—1222no—
855C22×C4—1221no—
856C22×C4D4×D6112yes—
857C22×C4D4×D6111yescharacteristic
858C22×C4C23×D6112yes—
859C22×C4C23×D6111yescharacteristic
860SD16—28no—
861SD16—1228no—
862SD16—1228no—
863SD16—1228no—
864SD16—1228no—
865SD16—1228no—
866D8—28no—
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—24no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—614no—
900C23—612no—
901C23—612no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—4884no—
909C23—4884no—
910C23—48816no—
911C23—2448no—
912C23—2442no—
913C23—2442no—
914C23—2442no—
915C23C2×D4×D6112yes—
916C23C2×D4×D6111yescharacteristic
917Q8—24no—
918Q8—22no—
919Q8—614no—
920Q8—614no—
921Q8—1228no—
922Q8—12216no—
923Q8—12216no—
924Q8—12216no—
925Q8—1224no—
926Q8—1224no—
927Q8—1222no—
928Q8—1222no—
929Q8C2×D4×D6114yes—
930D4—216no—
931D4—24no—
932D4—22no—
933D4—22no—
934D4—22no—
935D4—42no—
936D4—84no—
937D4—1228no—
938D4—1228no—
939D4—1228no—
940D4—12216no—
941D4—12216no—
942D4—1222no—
943D4—1222no—
944D4—4884no—
945D4—4884no—
946D4—4884no—
947D4—2448no—
948D4—2442no—
949D4C2×D4×D6114yes—
950C2×C4—216no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—42no—
959C2×C4—614no—
960C2×C4—612no—
961C2×C4—618no—
962C2×C4—614no—
963C2×C4—614no—
964C2×C4—612no—
965C2×C4—12216no—
966C2×C4—12216no—
967C2×C4—12216no—
968C2×C4—12216no—
969C2×C4—12216no—
970C2×C4—1222no—
971C2×C4—1224no—
972C2×C4—1224no—
973C2×C4—1222no—
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—24no—
991C22—22no—
992C22—22no—
993C22—42no—
994C22—42no—
995C22—44no—
996C22—48no—
997C22—42no—
998C22—42no—
999C22—42no—
1000C22—84no—
1001C22—614no—
1002C22—1222no—
1003C22—1222no—
1004C22—1228no—
1005C22—1222no—
1006C22—1222no—
1007C22—1222no—
1008C22—48816no—
1009C22—4884no—
1010C22—2442no—
1011C22—2442no—
1012C22—2442no—
1013C22—2444no—
1014C22#120×D6112yes—
1015C22#1684056912yes—
1016C22#1684057212yes—
1017C22C22×D4×D6111yescharacteristic
1018C4—22no—
1019C4—24no—
1020C4—42no—
1021C4—614no—
1022C4—1222no—
1023C4—1224no—
1024C4—1224no—
1025C4—2442no—
1026C4#120×D6112yes—
1027C4C22×D4×D6111yescharacteristic
1028C4C22×D4×D6111yescharacteristic
1029C2—42no—
1030C2—44no—
1031C2—82no—
1032C2—1224no—
1033C2—4882no—
1034C2—2442no—
1035C2#2145510214yesdirect product factor
1036C2C2×#120×D6111yescharacteristic
1037C2C2×#1684056911yescharacteristic
1038C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C22×#14519824C2semidirect
2. C22×#14519801C2semidirect
3. C22×SD16×D61C2semidirect
4. C2×#16840328C2semidirect
5. #21455102C2direct (N × H)
6. C2×#16839908C2semidirect
7. C2×#16839907C2semidirect
8. C2×#16839904C2semidirect
9. C2×#16839903C2semidirect
10. C2×#16839902C2semidirect
11. C2×#16839900C2semidirect
12. C2×#16839899C2semidirect
13. C2×#16839769C2semidirect
14. C2×#16839755C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#449C2semidirect
20. C2×#14519824C22semidirect
26. C22×#11758224C22semidirect
28. C23×Dic122C22semidirect
30. C22×Q8×D61C22semidirect
33. C2×#14519801C22semidirect
40. C2×SD16×D61C22semidirect
45. #16840328C22semidirect
54. #16839908C22semidirect
55. #16839907C22semidirect
56. #16839904C22semidirect
57. #16839903C22semidirect
58. #16839902C22semidirect
59. #16839900C22semidirect
60. #16839899C22semidirect
61. #16839769C22semidirect
62. #16839755C22semidirect
63. C2×#14519702C22semidirect
64. C2×#14519702C22semidirect
65. C2×#14519701C22semidirect
66. C2×#14519700C22semidirect
67. C2×#14519700C22semidirect
68. C2×#14519698C22semidirect
69. #16839727C22semidirect
70. C2×C22⋊#92418C22semidirect
71. C2×#14519689C22semidirect
72. C2×#14519689C22semidirect
73. C22×#41×C61C22semidirect
77. C61×#449C22semidirect
78. C2×#103×C61C22semidirect
79. C2×#102×C61C22semidirect
80. C2×C22⋊C8×C61C22semidirect
100. C2×#11758224D4semidirect
102. C2×#11758224C23semidirect
114. C22×Dic122C23semidirect
120. C2×Q8×D61D4semidirect
122. C2×Q8×D61C23semidirect
182. #14519702C23semidirect
183. #14519702C23semidirect
184. #14519701C23semidirect
185. #14519700C23semidirect
186. #14519700C23semidirect
187. #14519698C23semidirect
188. C22⋊#92418C23semidirect
189. #14519689C23semidirect
190. #14519689C23semidirect
194. C2×#41×C61C23semidirect
212. #103×C61C23semidirect
213. #102×C61C23semidirect
214. C22⋊C8×C61C23semidirect
284. Q8×D61C2×D4semidirect
292. #11758224C2×D4semidirect
518. C2×#449D61semidirect
529. C2×C61#3010semidirect
546. C22×#41C2×D61semidirect
580. #449C2×D61semidirect
592. C2×#103C2×D61semidirect
594. C2×#102C2×D61semidirect
599. C2×C22⋊C8C2×D61semidirect
600. C61C2×#3010semidirect
626. C2×#41C22×D61semidirect
728. #103C22×D61semidirect
730. #102C22×D61semidirect
734. C22⋊C8C22×D61semidirect
1035. C2#21455102direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198242
C22×#145198012
C22×SD16×D612
C2×#168403282
#214551022
C2×#168399082
C2×#168399072
C2×#168399042
C2×#168399032
C2×#168399022
C2×#168399002
C2×#168398992
C2×#168397692
C2×#168397552
C2×#168397272
C2×C61×#4492
C2×#301061