Finite Group Databasebeta

← C2×#21455039 #30546352

Subgroups — C2×#21455039 #30546352

Order 15616.

5130 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D61C211yesmaximal, characteristic, complemented
2C22×#14519799C211yesmaximal, characteristic, complemented
3C22×#14519797C211yesmaximal, characteristic, complemented
4C2×#16840274C211yesmaximal, characteristic, complemented
5#21455039C2116yesmaximal, direct product factor
6C2×#16839927C211yesmaximal, characteristic, complemented
7C2×#16839925C211yesmaximal, characteristic, complemented
8C2×#16839910C211yesmaximal, characteristic, complemented
9C2×#16839908C211yesmaximal, characteristic, complemented
10C2×#16839919C211yesmaximal, characteristic, complemented
11C2×#16839902C211yesmaximal, characteristic, complemented
12C2×#16839914C211yesmaximal, characteristic, complemented
13C2×#16839897C211yesmaximal, characteristic, complemented
14C2×#16839756C211yesmaximal, characteristic, complemented
15C22×#14519689C211yesmaximal, characteristic, complemented
16C2×C61×#416C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222—21no—
19C22×#11758222C2211yescharacteristic
20C22×#11758222C2211yescharacteristic, complemented
21C22×#11758224—21no—
22C22×#11758224C2211yescharacteristic
23C2×#41×D61—28no—
24C2×#41×D61—28no—
25C2×#41×D61—24no—
26C2×#41×D61C2218yescomplemented
27C22×Q8×D61C2211yescharacteristic
28C22×D4×D61—21no—
29C22×D4×D61C2211yescharacteristic
30C23×C4×D61—21no—
31C23×C4×D61C2211yescharacteristic
32C2×#14519799—28no—
33C2×#14519799C2218yescomplemented
34C2×#14519797—28no—
35C2×#14519797C2218yescomplemented
36C22×Dic244C2211yescharacteristic, complemented
37C22×#11758202C2211yescharacteristic, complemented
38C22×#11758190C2211yescharacteristic, complemented
39C22×#11758190C2211yescharacteristic, complemented
40C22×#11758200C2211yescharacteristic, complemented
41C22×#11758201C2211yescharacteristic, complemented
42C22×D488C2211yescharacteristic, complemented
43C22×#11758199C2211yescharacteristic, complemented
44C23×#92418C2211yescharacteristic, complemented
45#16840274—24no—
46#16840274C2218yescomplemented
47C2×#14519761—21no—
48C2×#14519757C2211yescharacteristic
49C2×#14519757C2211yescharacteristic, complemented
50C2×#14519752C2211yescharacteristic
51C2×#14519752C2211yescharacteristic, complemented
52C2×#14519747—21no—
53C2×C4×D244—21no—
54C2×C4×D244—21no—
55#16839927C2218yescomplemented
56#16839925C2218yescomplemented
57#16839919C2218yescomplemented
58#16839914C2218yescomplemented
59#16839910C2218yescomplemented
60#16839908C2218yescomplemented
61#16839902C2218yescomplemented
62#16839897C2218yescomplemented
63#16839756C2218yescomplemented
64C2×#14519700C2211yescharacteristic, complemented
65C2×#14519700C2211yescharacteristic, complemented
66C2×#14519697C2211yescharacteristic, complemented
67C2×#14519697C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×#14519689C2211yescharacteristic, complemented
71C2×#14519689C2211yescharacteristic, complemented
72C2×#14519689C2218yescomplemented
73C22×#41×C61C2211yescharacteristic
74C23×C8×C61C2211yescharacteristic, complemented
75C2×#117×C61C2211yescharacteristic, complemented
76C61×#416C2218yescomplemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#103×C61C2211yescharacteristic, complemented
79C2×#102×C61C2211yescharacteristic, complemented
80C2×#102×C61C2211yescharacteristic, complemented
81C24×D61—21no—
82C24×D61D411yescharacteristic
83C2×#11758226—24no—
84C2×#11758226—24no—
85C2×#11758226—22no—
86C2×#11758226C2314yes—
87C2×#11758222—216no—
88C2×#11758222—24no—
89C2×#11758222—22no—
90C2×#11758222—22no—
91C2×#11758222—28no—
92C2×#11758222—24no—
93C2×#11758222—24no—
94C2×#11758222D418yescomplemented
95C2×#11758222C2314yes—
96C2×#11758222C2314yescomplemented
97C2×#11758224—216no—
98C2×#11758224—24no—
99C2×#11758224—28no—
100C2×#11758224—22no—
101C2×#11758224—24no—
102C2×#11758224C2314yes—
103#41×D61—264no—
104#41×D61—232no—
105#41×D61—232no—
106C22×Dic122—21no—
107C22×Dic122C2311yescharacteristic
108C22×Dic122C2311yescharacteristic
109C2×Q8×D61—24no—
110C2×Q8×D61—22no—
111C2×Q8×D61—24no—
112C2×Q8×D61C2314yes—
113C22×D244—21no—
114C22×D244—21no—
115C22×D244—21no—
116C22×D244C2311yescharacteristic
117C22×D244C2311yescharacteristic
118C22×C22⋊D61—21no—
119C22×C22⋊D61—21no—
120C22×C22⋊D61—21no—
121C22×C22⋊D61—21no—
122C2×D4×D61—216no—
123C2×D4×D61—28no—
124C2×D4×D61—24no—
125C2×D4×D61—24no—
126C2×D4×D61—22no—
127C2×D4×D61C2314yes—
128C23×Dic61—21no—
129C23×Dic61D411yescharacteristic
130C22×C4×D61—216no—
131C22×C4×D61—21no—
132C22×C4×D61—21no—
133C22×C4×D61—24no—
134C22×C4×D61—24no—
135C22×C4×D61—21no—
136C22×C4×D61—28no—
137C22×C4×D61—21no—
138C22×C4×D61D411yescharacteristic
139C22×C4×D61D411yescharacteristic
140C22×C4×D61D414yes—
141C22×C4×D61C2311yescharacteristic
142C22×C4×D61C2311yescharacteristic
143C22×C4×D61C2314yes—
144#14519799—232no—
145#14519797—232no—
146C2×Dic244—24no—
147C2×Dic244C2314yescomplemented
148C2×#11758202—24no—
149C2×#11758202C2314yescomplemented
150C2×#11758190—24no—
151C2×#11758190—24no—
152C2×#11758190C2314yescomplemented
153C2×#11758190C2314yescomplemented
154C2×#11758200—24no—
155C2×#11758200C2314yescomplemented
156C2×#11758201—24no—
157C2×#11758201C2314yescomplemented
158C2×D488—24no—
159C2×D488C2314yescomplemented
160C2×#11758199—24no—
161C2×#11758199C2314yescomplemented
162C22×#92418—24no—
163C22×#92418C2311yescharacteristic
164C22×#92418C2311yescharacteristic
165C22×#92418C2314yescomplemented
166#14519761—28no—
167#14519757—22no—
168#14519757—22no—
169#14519757C2314yes—
170#14519757C2314yescomplemented
171#14519752—22no—
172#14519752—22no—
173#14519752C2314yes—
174#14519752C2314yescomplemented
175#14519747—28no—
176C4×D244—28no—
177C4×D244—28no—
178C2×C4⋊Dic61—21no—
179C2×C4⋊Dic61—21no—
180C2×#11758198—21no—
181C2×#11758198—21no—
182C2×#11758198—21no—
183C2×#11758198—21no—
184#14519700C2314yescomplemented
185#14519700C2314yescomplemented
186#14519697C2314yescomplemented
187#14519697C2314yescomplemented
188#14519689C2314yes—
189#14519689C2314yes—
190#14519689C2314yescomplemented
191#14519689C2314yescomplemented
192C2×#41×C61—24no—
193C2×#41×C61—22no—
194C2×#41×C61D418yescomplemented
195C2×#41×C61C2314yes—
196C22×Q8×C61C2311yescharacteristic
197C22×D4×C61—21no—
198C22×D4×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61C2311yescharacteristic
201C22×C8×C61—24no—
202C22×C8×C61C2311yescharacteristic
203C22×C8×C61C2311yescharacteristic
204C22×C8×C61C2314yescomplemented
205#117×C61—22no—
206#117×C61C2314yescomplemented
207C2×C4⋊C4×C61C2311yescharacteristic
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C22⋊C4×C61—21no—
210C2×C42×C61—21no—
211#103×C61C2314yescomplemented
212#103×C61C2314yescomplemented
213#102×C61C2314yescomplemented
214#102×C61C2314yescomplemented
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C23×D61—28no—
218C23×D61—24no—
219C23×D61—21no—
220C23×D61—24no—
221C23×D61—24no—
222C23×D61—21no—
223C23×D61—42no—
224C23×D61—44no—
225C23×D61—44no—
226C23×D61C2×D411yescharacteristic
227C23×D61C2×D414yes—
228C23×D61C2×D411yescharacteristic
229#41×C61—216no—
230#41×C61—28no—
231#41×C61C2×D4116yescomplemented
232C2×Q8×C61—22no—
233C2×Q8×C61—21no—
234C2×Q8×C61C2×D414yes—
235C2×Q8×C61C2412yes—
236C2×D4×C61—28no—
237C2×D4×C61—24no—
238C2×D4×C61—21no—
239C2×D4×C61—22no—
240C2×D4×C61C2×D414yes—
241C2×D4×C61C2412yes—
242C22×C4×C61—21no—
243C22×C4×C61—28no—
244C22×C4×C61—24no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D414yes—
250C22×C4×C61C2×D414yes—
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2412yes—
253C2×C22⋊D61—28no—
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—44no—
261C22×Dic61—28no—
262C22×Dic61—24no—
263C22×Dic61—21no—
264C22×Dic61—24no—
265C22×Dic61—21no—
266C22×Dic61C2×D411yescharacteristic
267C22×Dic61C2×D411yescharacteristic
268C22×Dic61C2×D414yes—
269#11758226—216no—
270#11758226—28no—
271#11758226—28no—
272Q8×D61—216no—
273Q8×D61—28no—
274Q8×D61—28no—
275#11758224—264no—
276#11758224—216no—
277#11758224—28no—
278#11758224—28no—
279D4×D61—264no—
280D4×D61—216no—
281D4×D61—28no—
282D4×D61—28no—
283#11758222—264no—
284#11758222—216no—
285#11758222—28no—
286#11758222—28no—
287#11758222—28no—
288#11758222—48no—
289#11758222C2×D4116yescomplemented
290C2×D244—28no—
291C2×D244—24no—
292C2×D244—21no—
293C2×D244—22no—
294C2×D244—22no—
295C2×D244—22no—
296C2×D244—24no—
297C2×D244—24no—
298C2×D244—21no—
299C2×D244—44no—
300C2×D244—44no—
301C2×D244C2×D414yes—
302C2×D244C2412yes—
303C2×D244C2412yes—
304C2×C4×D61—28no—
305C2×C4×D61—264no—
306C2×C4×D61—28no—
307C2×C4×D61—24no—
308C2×C4×D61—24no—
309C2×C4×D61—28no—
310C2×C4×D61—216no—
311C2×C4×D61—24no—
312C2×C4×D61—24no—
313C2×C4×D61—22no—
314C2×C4×D61—22no—
315C2×C4×D61—28no—
316C2×C4×D61—28no—
317C2×C4×D61—22no—
318C2×C4×D61—22no—
319C2×C4×D61—24no—
320C2×C4×D61—24no—
321C2×C4×D61—44no—
322C2×C4×D61C2×D414yes—
323C2×C4×D61C2×D412yes—
324C2×C4×D61C2×D412yes—
325C2×C4×D61C2×D414yes—
326C2×C4×D61C2412yes—
327C2×C4×D61C2412yes—
328C2×Dic122—28no—
329C2×Dic122—21no—
330C2×Dic122—22no—
331C2×Dic122—24no—
332C2×Dic122—22no—
333C2×Dic122—22no—
334C2×Dic122—21no—
335C2×Dic122C2×D414yes—
336C2×Dic122C2412yes—
337C2×Dic122C2412yes—
338C2×C8×C61—22no—
339C2×C8×C61—22no—
340C2×C8×C61—28no—
341C2×C8×C61C2412yes—
342C2×C8×C61C2412yes—
343C4⋊C4×C61—21no—
344C4⋊C4×C61—21no—
345C4⋊C4×C61C2412yes—
346C4⋊C4×C61C2412yes—
347C22⋊C4×C61—24no—
348C42×C61—24no—
349#11758202—28no—
350#11758201—28no—
351#11758200—28no—
352#11758199—28no—
353#11758198—24no—
354#11758198—24no—
355#11758198—24no—
356#11758198—24no—
357C4⋊Dic61—24no—
358C4⋊Dic61—24no—
359C2×#92418—22no—
360C2×#92418—22no—
361C2×#92418—28no—
362C2×#92418C2412yes—
363C2×#92418C2412yes—
364Dic244—28no—
365D488—28no—
366#11758190—28no—
367#11758190—28no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—24no—
371C23×C61—22no—
372C23×C61—42no—
373C23×C61—42no—
374C23×C61#12014yes—
375C23×C61C22×D412yes—
376C23×C61C22×D411yescharacteristic
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—216no—
380C22×D61—22no—
381C22×D61—24no—
382C22×D61—28no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—28no—
387C22×D61—22no—
388C22×D61—44no—
389C22×D61—416no—
390C22×D61—432no—
391C22×D61—48no—
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—48no—
395C22×D61—42no—
396C22×D61—42no—
397C22×D61—42no—
398C22×D61#13514yescomplemented
399C22×D61C22×D412yes—
400C22×D61C22×D412yes—
401Q8×C61—24no—
402Q8×C61—22no—
403Q8×C61C22×D414yes—
404D4×C61—216no—
405D4×C61—24no—
406D4×C61—22no—
407D4×C61C22×D414yes—
408C2×C4×C61—24no—
409C2×C4×C61—22no—
410C2×C4×C61—216no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61#12014yes—
416C2×C4×C61#12018yes—
417C2×C4×C61C22×D412yes—
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D412yes—
420C2×C4×C61C22×D414yes—
421C2×C4×C61C22×D412yes—
422C2×C4×C61C22×D414yes—
423C2×C4×C61C2511yescharacteristic
424C22⋊D61—216no—
425C22⋊D61—216no—
426C22⋊D61—216no—
427C22⋊D61—48no—
428C2×Dic61—216no—
429C2×Dic61—22no—
430C2×Dic61—24no—
431C2×Dic61—22no—
432C2×Dic61—28no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—42no—
436C2×Dic61C22×D412yes—
437C2×Dic61C22×D412yes—
438D244—216no—
439D244—24no—
440D244—22no—
441D244—22no—
442D244—22no—
443D244—48no—
444D244—48no—
445D244—42no—
446D244C22×D414yes—
447C4×D61—216no—
448C4×D61—216no—
449C4×D61—28no—
450C4×D61—216no—
451C4×D61—28no—
452C4×D61—24no—
453C4×D61—24no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—48no—
459Dic122—216no—
460Dic122—24no—
461Dic122—22no—
462Dic122—22no—
463Dic122—22no—
464Dic122—42no—
465Dic122C22×D414yes—
466C8×C61—22no—
467C8×C61—22no—
468#92418—22no—
469#92418—22no—
470C2×#3002—611nomaximal, Sylow
471C22×C61—28no—
472C22×C61—22no—
473C22×C61—22no—
474C22×C61—24no—
475C22×C61—48no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61C2×#12014yes—
479C22×C61C2×#12012yes—
480C22×C61C2×#13512yes—
481C22×C61#57512yes—
482C22×C61C23×D411yescharacteristic
483C2×D61—22no—
484C2×D61—28no—
485C2×D61—22no—
486C2×D61—22no—
487C2×D61—24no—
488C2×D61—22no—
489C2×D61—22no—
490C2×D61—416no—
491C2×D61—432no—
492C2×D61—44no—
493C2×D61—48no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—42no—
497C2×D61—42no—
498C2×D61—42no—
499C2×D61—84no—
500C2×D61C2×#13514yescomplemented
501C4×C61—24no—
502C4×C61—42no—
503C4×C61—42no—
504C4×C61C2×#12012yes—
505C4×C61C2×#12014yes—
506C4×C61C23×D411yescharacteristic
507C4×C61C23×D411yescharacteristic
508Dic61—22no—
509Dic61—24no—
510Dic61—22no—
511Dic61—42no—
512C23×#41—611no—
513C22×#135—611no—
514C22×#135—611no—
515C2×#525—611no—
516#3002—6116no—
517C2×#452—611no—
518C2×#452—611no—
519C2×#449—611no—
520C2×#449—611no—
521C2×#451—611no—
522C2×#448—611no—
523C2×#450—611no—
524C2×#447—611no—
525C2×#416—611no—
526C2×#416D6111yescharacteristic, complemented
527C22×C22⋊C8—611no—
528C2×C61—24no—
529C2×C61—44no—
530C2×C61#300214yescomplemented
531C2×C61C22×#12011yescharacteristic
532C2×C61C22×#13511yescharacteristic
533C2×C61C2×#57511yescharacteristic
534D61—24no—
535D61—42no—
536D61—44no—
537D61—82no—
538C22×#41—618no—
539C22×#41—611no—
540C22×#41—611no—
541C22×#41—611no—
542C22×#41—611no—
543C22×#41—1221no—
544C22×#41—1221no—
545C22×#41—1224no—
546C22×#41—1228no—
547C22×#41—1228no—
548C22×#41C2×D6111yescharacteristic
549C23×Q8—611no—
550C23×D4—611no—
551C23×D4—1221no—
552C24×C4—611no—
553C24×C4—1221no—
554C2×#135—618no—
555C2×#135—618no—
556C2×#135—1228no—
557C2×#135—1228no—
558C22×Q16—611no—
559C22×Q16—611no—
560C22×SD16—611no—
561C22×SD16—611no—
562C22×SD16—611no—
563C22×SD16—611no—
564C22×D8—611no—
565C22×D8—611no—
566C23×C8—611no—
567C23×C8C2×D6111yescharacteristic, complemented
568#525—618no—
569#525—1224no—
570C2×#123—1221no—
571C2×C22⋊Q8—611no—
572C2×C22⋊Q8—611no—
573C2×#121—611no—
574C2×#121—611no—
575C2×#120—1221no—
576C2×C4×D4—1221no—
577C2×C4×D4—1221no—
578C2×#117C2×D6111yescharacteristic, complemented
579#452—618no—
580#452—618no—
581#451—618no—
582#450—618no—
583#449—618no—
584#449—618no—
585#448—618no—
586#447—618no—
587#416—618no—
588#416C2×D6118yescomplemented
589C2×#103—611no—
590C2×#103—611no—
591C2×#103C2×D6111yescharacteristic, complemented
592C2×#103C2×D6111yescharacteristic, complemented
593C2×#102—611no—
594C2×#102—611no—
595C2×#102C2×D6111yescharacteristic, complemented
596C2×#102C2×D6111yescharacteristic, complemented
597C2×C22⋊C8—611no—
598C2×C22⋊C8—611no—
599C2×C22⋊C8—611no—
600C2×C22⋊C8—611no—
601C2×C22⋊C8—618no—
602C61C2×#300211yescharacteristic, complemented, Sylow
603C25—611no—
604C25—1221no—
605C2×#41—22no—
606C2×#41—24no—
607C2×#41—614no—
608C2×#41—614no—
609C2×#41—618no—
610C2×#41—614no—
611C2×#41—614no—
612C2×#41—1228no—
613C2×#41—12216no—
614C2×#41—1228no—
615C2×#41—1222no—
616C2×#41—1222no—
617C2×#41—1224no—
618C2×#41—12216no—
619C2×#41—1224no—
620C2×#41—12232no—
621C2×#41—12264no—
622C2×#41—12232no—
623C2×#41—1224no—
624C2×#41—1224no—
625C2×#41—1224no—
626C2×#41—1222no—
627C2×#41—1222no—
628C2×#41—1224no—
629C2×#41—1224no—
630C2×#41D24418yescomplemented
631C2×#41C22×D6114yes—
632C22×Q8—614no—
633C22×Q8—611no—
634C22×Q8—611no—
635C22×Q8—1221no—
636C22×Q8—1222no—
637C22×Q8—1224no—
638C22×Q8—1224no—
639C22×Q8C22×D6111yescharacteristic
640C22×D4—21no—
641C22×D4—614no—
642C22×D4—611no—
643C22×D4—611no—
644C22×D4—1221no—
645C22×D4—1221no—
646C22×D4—1221no—
647C22×D4—1222no—
648C22×D4—1221no—
649C22×D4—1224no—
650C22×D4—1228no—
651C22×D4—12216no—
652C22×D4—1221no—
653C22×D4—1221no—
654C22×D4—1224no—
655C22×D4—1221no—
656C22×D4C22×D6111yescharacteristic
657C23×C4—21no—
658C23×C4—611no—
659C23×C4—614no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—614no—
665C23×C4—1221no—
666C23×C4—1228no—
667C23×C4—1221no—
668C23×C4—12216no—
669C23×C4—1221no—
670C23×C4—1224no—
671C23×C4—1224no—
672C23×C4—1221no—
673C23×C4—1221no—
674C23×C4C22×D6111yescharacteristic
675#135—12232no—
676#135—12232no—
677C2×Q16—614no—
678C2×Q16—614no—
679C2×Q16—1224no—
680C2×Q16—1224no—
681C2×SD16—614no—
682C2×SD16—614no—
683C2×SD16—614no—
684C2×SD16—614no—
685C2×SD16—1224no—
686C2×SD16—1224no—
687C2×SD16—1224no—
688C2×SD16—1224no—
689C2×D8—614no—
690C2×D8—614no—
691C2×D8—1224no—
692C2×D8—1224no—
693C22×C8—24no—
694C22×C8—611no—
695C22×C8—611no—
696C22×C8—614no—
697C22×C8—1224no—
698C22×C8C22×D6111yescharacteristic
699C22×C8C22×D6111yescharacteristic
700C22×C8C22×D6114yescomplemented
701#123—1228no—
702C22⋊Q8—614no—
703C22⋊Q8—614no—
704C22⋊Q8—1222no—
705C22⋊Q8—1222no—
706#121—614no—
707#121—614no—
708#121—1222no—
709#121—1222no—
710#120—1228no—
711C4×D4—1228no—
712C4×D4—1228no—
713#117—22no—
714#117C22×D6114yescomplemented
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4C22×D6111yescharacteristic
718C2×C4⋊C4C22×D6111yescharacteristic
719C2×C22⋊C4—21no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—21no—
725#103—614no—
726#103—614no—
727#103C22×D6114yescomplemented
728#103C22×D6114yescomplemented
729#102—614no—
730#102—614no—
731#102C22×D6114yescomplemented
732#102C22×D6114yescomplemented
733C22⋊C8—614no—
734C22⋊C8—614no—
735C22⋊C8—614no—
736C22⋊C8—614no—
737C24—21no—
738C24—611no—
739C24—611no—
740C24—614no—
741C24—1224no—
742C24—1224no—
743C24—1228no—
744C24—1221no—
745C24—1224no—
746C24—1221no—
747C24—2442no—
748C24—2444no—
749C24—2444no—
750C24D4×D6111yescharacteristic
751#41—28no—
752#41—216no—
753#41—6116no—
754#41—12264no—
755#41—1228no—
756#41—12264no—
757#41—12216no—
758#41—1228no—
759#41—12216no—
760#41—1228no—
761#41—1228no—
762#41—1228no—
763#41—12216no—
764#41—1228no—
765#41—1228no—
766#41—2448no—
767#41C2×D244116yescomplemented
768C2×Q8—22no—
769C2×Q8—21no—
770C2×Q8—614no—
771C2×Q8—612no—
772C2×Q8—612no—
773C2×Q8—1224no—
774C2×Q8—1228no—
775C2×Q8—1228no—
776C2×Q8—12216no—
777C2×Q8—1228no—
778C2×Q8—1221no—
779C2×Q8—1221no—
780C2×Q8—1222no—
781C2×Q8—1222no—
782C2×Q8—1222no—
783C2×Q8C2×D24414yes—
784C2×Q8C23×D6112yes—
785C2×D4—24no—
786C2×D4—28no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—614no—
790C2×D4—612no—
791C2×D4—612no—
792C2×D4—1224no—
793C2×D4—1228no—
794C2×D4—1224no—
795C2×D4—1224no—
796C2×D4—1224no—
797C2×D4—1228no—
798C2×D4—12264no—
799C2×D4—12216no—
800C2×D4—1224no—
801C2×D4—1228no—
802C2×D4—1228no—
803C2×D4—1224no—
804C2×D4—1228no—
805C2×D4—1228no—
806C2×D4—1224no—
807C2×D4—1221no—
808C2×D4—1222no—
809C2×D4—1221no—
810C2×D4—1222no—
811C2×D4—1222no—
812C2×D4—2444no—
813C2×D4—2444no—
814C2×D4—2444no—
815C2×D4C2×D24414yes—
816C2×D4C23×D6112yes—
817C22×C4—21no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—614no—
825C22×C4—614no—
826C22×C4—614no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—1224no—
832C22×C4—1224no—
833C22×C4—1228no—
834C22×C4—1228no—
835C22×C4—12264no—
836C22×C4—1224no—
837C22×C4—1228no—
838C22×C4—1221no—
839C22×C4—1224no—
840C22×C4—1222no—
841C22×C4—1222no—
842C22×C4—1228no—
843C22×C4—1224no—
844C22×C4—1222no—
845C22×C4—1222no—
846C22×C4—1228no—
847C22×C4—1224no—
848C22×C4—1224no—
849C22×C4—12216no—
850C22×C4—1228no—
851C22×C4—1221no—
852C22×C4—1224no—
853C22×C4—2444no—
854C22×C4C2×D24414yes—
855C22×C4D4×D6114yes—
856C22×C4D4×D6112yes—
857C22×C4D4×D6111yescharacteristic
858C22×C4C23×D6111yescharacteristic
859C22×C4C23×D6112yes—
860Q16—1228no—
861Q16—1228no—
862SD16—1228no—
863SD16—1228no—
864SD16—1228no—
865SD16—1228no—
866D8—1228no—
867D8—1228no—
868C2×C8—22no—
869C2×C8—22no—
870C2×C8—28no—
871C2×C8—612no—
872C2×C8—612no—
873C2×C8—1222no—
874C2×C8—1222no—
875C2×C8—1228no—
876C2×C8C23×D6112yes—
877C2×C8C23×D6112yes—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—1224no—
881C4⋊C4—1224no—
882C4⋊C4C23×D6112yes—
883C4⋊C4C23×D6112yes—
884C22⋊C4—24no—
885C22⋊C4—1224no—
886C22⋊C4—1224no—
887C22⋊C4—1224no—
888C22⋊C4—1224no—
889C42—24no—
890C23—22no—
891C23—22no—
892C23—24no—
893C23—22no—
894C23—42no—
895C23—42no—
896C23—614no—
897C23—612no—
898C23—612no—
899C23—1228no—
900C23—12216no—
901C23—1222no—
902C23—1222no—
903C23—1224no—
904C23—1228no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—2444no—
911C23—24416no—
912C23—2448no—
913C23—2448no—
914C23—24432no—
915C23—2442no—
916C23—2442no—
917C23—2442no—
918C23—2442no—
919C23—2442no—
920C23#1451974714yes—
921C23C2×D4×D6112yes—
922C23C2×D4×D6111yescharacteristic
923Q8—24no—
924Q8—22no—
925Q8—614no—
926Q8—12216no—
927Q8—1224no—
928Q8—1222no—
929Q8—1222no—
930Q8—1222no—
931Q8—2442no—
932Q8C22×D24414yes—
933D4—216no—
934D4—24no—
935D4—22no—
936D4—614no—
937D4—12216no—
938D4—12216no—
939D4—12216no—
940D4—12216no—
941D4—1224no—
942D4—1222no—
943D4—1222no—
944D4—1222no—
945D4—2448no—
946D4—2448no—
947D4—2448no—
948D4—2442no—
949D4C22×D24414yes—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—216no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—612no—
958C2×C4—612no—
959C2×C4—12216no—
960C2×C4—12216no—
961C2×C4—12216no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1228no—
965C2×C4—1224no—
966C2×C4—1222no—
967C2×C4—1228no—
968C2×C4—1224no—
969C2×C4—1224no—
970C2×C4—1228no—
971C2×C4—12216no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—2442no—
978C2×C4—2448no—
979C2×C4#1451974714yes—
980C2×C4#1451974718yes—
981C2×C4C2×D4×D6112yes—
982C2×C4C2×D4×D6111yescharacteristic
983C2×C4C2×D4×D6112yes—
984C2×C4C2×D4×D6114yes—
985C2×C4C22×D24412yes—
986C2×C4C22×D24414yes—
987C2×C4C24×D6111yescharacteristic
988C8—22no—
989C8—22no—
990C8—1222no—
991C8—1222no—
992C22—22no—
993C22—22no—
994C22—28no—
995C22—24no—
996C22—42no—
997C22—42no—
998C22—48no—
999C22—614no—
1000C22—1222no—
1001C22—1222no—
1002C22—1228no—
1003C22—1222no—
1004C22—1222no—
1005C22—1224no—
1006C22—1222no—
1007C22—4884no—
1008C22—24416no—
1009C22—24432no—
1010C22—2442no—
1011C22—2442no—
1012C22—2442no—
1013C22—2442no—
1014C22—2442no—
1015C22—2444no—
1016C22—2448no—
1017C22C2×#1451974714yes—
1018C22C2×#1451974712yes—
1019C22#135×D6112yes—
1020C22#1684055912yes—
1021C22C22×D4×D6111yescharacteristic
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—1222no—
1026C4—1222no—
1027C4—1224no—
1028C4—2442no—
1029C4C2×#1451974714yes—
1030C4C2×#1451974712yes—
1031C4C22×D4×D6111yescharacteristic
1032C4C23×D24411yescharacteristic
1033C2—24no—
1034C2—44no—
1035C2—1224no—
1036C2—4882no—
1037C2—2442no—
1038C2—2444no—
1039C2#2145503914yesdirect product factor
1040C2C22×#1451974711yescharacteristic
1041C2C2×#135×D6111yescharacteristic
1042C2C2×#1684055911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#416C2
socleC23×C61C22×D4
hypercenterC2×#416D61
hypocenterC61C2×#3002
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C22×#41×D61C2semidirect
2. C22×#14519799C2semidirect
3. C22×#14519797C2semidirect
4. C2×#16840274C2semidirect
5. #21455039C2direct (N × H)
6. C2×#16839927C2semidirect
7. C2×#16839925C2semidirect
8. C2×#16839910C2semidirect
9. C2×#16839908C2semidirect
10. C2×#16839919C2semidirect
11. C2×#16839902C2semidirect
12. C2×#16839914C2semidirect
13. C2×#16839897C2semidirect
14. C2×#16839756C2semidirect
15. C22×#14519689C2semidirect
16. C2×C61×#416C2semidirect
20. C22×#11758222C22semidirect
26. C2×#41×D61C22semidirect
33. C2×#14519799C22semidirect
35. C2×#14519797C22semidirect
36. C22×Dic244C22semidirect
37. C22×#11758202C22semidirect
38. C22×#11758190C22semidirect
39. C22×#11758190C22semidirect
40. C22×#11758200C22semidirect
41. C22×#11758201C22semidirect
42. C22×D488C22semidirect
43. C22×#11758199C22semidirect
44. C23×#92418C22semidirect
46. #16840274C22semidirect
49. C2×#14519757C22semidirect
51. C2×#14519752C22semidirect
55. #16839927C22semidirect
56. #16839925C22semidirect
57. #16839919C22semidirect
58. #16839914C22semidirect
59. #16839910C22semidirect
60. #16839908C22semidirect
61. #16839902C22semidirect
62. #16839897C22semidirect
63. #16839756C22semidirect
64. C2×#14519700C22semidirect
65. C2×#14519700C22semidirect
66. C2×#14519697C22semidirect
67. C2×#14519697C22semidirect
70. C2×#14519689C22semidirect
71. C2×#14519689C22semidirect
72. C2×#14519689C22semidirect
74. C23×C8×C61C22semidirect
75. C2×#117×C61C22semidirect
76. C61×#416C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#103×C61C22semidirect
79. C2×#102×C61C22semidirect
80. C2×#102×C61C22semidirect
94. C2×#11758222D4semidirect
96. C2×#11758222C23semidirect
147. C2×Dic244C23semidirect
149. C2×#11758202C23semidirect
152. C2×#11758190C23semidirect
153. C2×#11758190C23semidirect
155. C2×#11758200C23semidirect
157. C2×#11758201C23semidirect
159. C2×D488C23semidirect
161. C2×#11758199C23semidirect
165. C22×#92418C23semidirect
170. #14519757C23semidirect
174. #14519752C23semidirect
184. #14519700C23semidirect
185. #14519700C23semidirect
186. #14519697C23semidirect
187. #14519697C23semidirect
190. #14519689C23semidirect
191. #14519689C23semidirect
194. C2×#41×C61D4semidirect
204. C22×C8×C61C23semidirect
206. #117×C61C23semidirect
211. #103×C61C23semidirect
212. #103×C61C23semidirect
213. #102×C61C23semidirect
214. #102×C61C23semidirect
231. #41×C61C2×D4semidirect
289. #11758222C2×D4semidirect
398. C22×D61#135semidirect
500. C2×D61C2×#135semidirect
526. C2×#416D61semidirect
530. C2×C61#3002semidirect
567. C23×C8C2×D61semidirect
578. C2×#117C2×D61semidirect
588. #416C2×D61semidirect
591. C2×#103C2×D61semidirect
592. C2×#103C2×D61semidirect
595. C2×#102C2×D61semidirect
596. C2×#102C2×D61semidirect
602. C61C2×#3002semidirect
630. C2×#41D244semidirect
700. C22×C8C22×D61semidirect
714. #117C22×D61semidirect
727. #103C22×D61semidirect
728. #103C22×D61semidirect
731. #102C22×D61semidirect
732. #102C22×D61semidirect
767. #41C2×D244semidirect
1039. C2#21455039direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D612
C22×#145197992
C22×#145197972
C2×#168402742
#214550392
C2×#168399272
C2×#168399252
C2×#168399102
C2×#168399082
C2×#168399192
C2×#168399022
C2×#168399142
C2×#168398972
C2×#168397562
C22×#145196892
C2×C61×#4162
C2×#300261