Finite Group Databasebeta

← C2×#21455033 #30546346

Subgroups — C2×#21455033 #30546346

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×#14519797C211yesmaximal, characteristic, complemented
3C2×#16840269C211yesmaximal, characteristic, complemented
4#21455033C2116yesmaximal, direct product factor
5C2×#16839923C211yesmaximal, characteristic, complemented
6C2×#16839921C211yesmaximal, characteristic, complemented
7C2×#16839906C211yesmaximal, characteristic, complemented
8C2×#16839904C211yesmaximal, characteristic, complemented
9C2×#16839916C211yesmaximal, characteristic, complemented
10C2×#16839899C211yesmaximal, characteristic, complemented
11C2×#16839911C211yesmaximal, characteristic, complemented
12C2×#16839894C211yesmaximal, characteristic, complemented
13C2×#16839759C211yesmaximal, characteristic, complemented
14C2×#16839758C211yesmaximal, characteristic, complemented
15C22×#14519689C211yesmaximal, characteristic, complemented
16C22×#135×C61C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222—21no—
19C22×#11758222C2211yescharacteristic
20C22×#11758224—21no—
21C22×#11758224C2211yescharacteristic
22C2×#41×D61—28no—
23C2×#41×D61—28no—
24C2×#41×D61—24no—
25C2×#41×D61C2218yescomplemented
26C22×Q8×D61C2211yescharacteristic
27C22×D4×D61—21no—
28C22×D4×D61C2211yescharacteristic
29C23×C4×D61—21no—
30C23×C4×D61C2211yescharacteristic
31C2×#14519797—28no—
32C2×#14519797C2218yescomplemented
33C22×#11758202C2211yescharacteristic, complemented
34C22×#11758200C2211yescharacteristic, complemented
35C22×#11758201C2211yescharacteristic, complemented
36C22×#11758199C2211yescharacteristic, complemented
37C23×#92418C2211yescharacteristic, complemented
38#16840269—24no—
39#16840269C2218yescomplemented
40C2×#14519758—21no—
41C2×#14519753C2211yescharacteristic
42C2×#14519753C2211yescharacteristic, complemented
43C2×#14519748C2211yescharacteristic
44C2×#14519748C2211yescharacteristic, complemented
45C2×#14519745—21no—
46C2×C4×C22⋊D61—21no—
47C2×C4×C22⋊D61—21no—
48C2×#14519736C2211yescharacteristic, complemented
49#16839923C2218yescomplemented
50#16839921C2218yescomplemented
51#16839916C2218yescomplemented
52#16839911C2218yescomplemented
53#16839906C2218yescomplemented
54#16839904C2218yescomplemented
55#16839899C2218yescomplemented
56#16839894C2218yescomplemented
57#16839759C2218yescomplemented
58#16839758C2218yescomplemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic, complemented
64C2×#14519699C2211yescharacteristic, complemented
65C2×#14519698C2211yescharacteristic, complemented
66C2×#14519698C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#14519689C2211yescharacteristic, complemented
70C2×#14519689C2211yescharacteristic, complemented
71C2×#14519689C2218yescomplemented
72C22×#41×C61C2211yescharacteristic
73C22×#41×C61C2211yescharacteristic, complemented
74C2×#135×C61—28no—
75C2×#135×C61C2218yescomplemented
76C22×Q16×C61C2211yescharacteristic, complemented
77C22×SD16×C61C2211yescharacteristic, complemented
78C22×SD16×C61C2211yescharacteristic, complemented
79C22×D8×C61C2211yescharacteristic, complemented
80C23×C8×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—28no—
91C2×#11758222D418yescomplemented
92C2×#11758222C2314yes—
93C2×#11758224—216no—
94C2×#11758224—24no—
95C2×#11758224—28no—
96C2×#11758224—22no—
97C2×#11758224—24no—
98C2×#11758224C2314yes—
99#41×D61—264no—
100#41×D61—232no—
101#41×D61—232no—
102C22×Dic122—21no—
103C22×Dic122C2311yescharacteristic
104C2×Q8×D61—24no—
105C2×Q8×D61—22no—
106C2×Q8×D61—24no—
107C2×Q8×D61C2314yes—
108C22×D244—21no—
109C22×D244C2311yescharacteristic
110C22×C22⋊D61—21no—
111C22×C22⋊D61—21no—
112C22×C22⋊D61—21no—
113C22×C22⋊D61—21no—
114C22×C22⋊D61—21no—
115C2×D4×D61—216no—
116C2×D4×D61—28no—
117C2×D4×D61—24no—
118C2×D4×D61—24no—
119C2×D4×D61—22no—
120C2×D4×D61C2314yes—
121C23×Dic61—21no—
122C23×Dic61D411yescharacteristic
123C22×C4×D61—216no—
124C22×C4×D61—21no—
125C22×C4×D61—21no—
126C22×C4×D61—24no—
127C22×C4×D61—24no—
128C22×C4×D61—21no—
129C22×C4×D61—28no—
130C22×C4×D61D411yescharacteristic
131C22×C4×D61D411yescharacteristic
132C22×C4×D61D414yes—
133C22×C4×D61C2311yescharacteristic
134C22×C4×D61C2311yescharacteristic
135C22×C4×D61C2314yes—
136#14519797—232no—
137C2×#11758202—24no—
138C2×#11758202C2314yescomplemented
139C2×#11758200—24no—
140C2×#11758200C2314yescomplemented
141C2×#11758201—24no—
142C2×#11758201C2314yescomplemented
143C2×#11758199—24no—
144C2×#11758199C2314yescomplemented
145C22×#92418—24no—
146C22×#92418C2311yescharacteristic
147C22×#92418C2311yescharacteristic
148C22×#92418C2314yescomplemented
149#14519758—28no—
150#14519753—22no—
151#14519753—22no—
152#14519753C2314yes—
153#14519753C2314yescomplemented
154#14519748—22no—
155#14519748—22no—
156#14519748C2314yes—
157#14519748C2314yescomplemented
158#14519745—28no—
159C4×C22⋊D61—28no—
160C4×C22⋊D61—28no—
161#14519736—22no—
162#14519736C2314yescomplemented
163C2×C4⋊Dic61C2311yescharacteristic
164C2×C4⋊Dic61C2311yescharacteristic
165C2×#11758196—21no—
166C2×#11758196—21no—
167C2×C22⋊Dic61—21no—
168C2×C22⋊Dic61—21no—
169C2×C22⋊Dic61—21no—
170C2×#11758198—21no—
171C2×#11758198—21no—
172C2×C4×Dic61—21no—
173#14519702C2314yescomplemented
174#14519702C2314yescomplemented
175#14519701C2314yescomplemented
176#14519701C2314yescomplemented
177#14519699C2314yescomplemented
178#14519699C2314yescomplemented
179#14519698C2314yescomplemented
180#14519698C2314yescomplemented
181#14519689C2314yes—
182#14519689C2314yes—
183#14519689C2314yescomplemented
184#14519689C2314yescomplemented
185C2×#41×C61—24no—
186C2×#41×C61—22no—
187C2×#41×C61—22no—
188C2×#41×C61—24no—
189C2×#41×C61—24no—
190C2×#41×C61D418yescomplemented
191C2×#41×C61C2314yes—
192C2×#41×C61C2314yescomplemented
193C22×Q8×C61C2311yescharacteristic
194C22×Q8×C61C2311yescharacteristic
195C22×D4×C61—21no—
196C22×D4×C61—21no—
197C22×D4×C61C2311yescharacteristic
198C22×D4×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61—21no—
201C23×C4×C61C2311yescharacteristic
202#135×C61—232no—
203C2×Q16×C61—24no—
204C2×Q16×C61C2314yescomplemented
205C2×SD16×C61—24no—
206C2×SD16×C61—24no—
207C2×SD16×C61C2314yescomplemented
208C2×SD16×C61C2314yescomplemented
209C2×D8×C61—24no—
210C2×D8×C61C2314yescomplemented
211C22×C8×C61—24no—
212C22×C8×C61C2311yescharacteristic
213C22×C8×C61C2311yescharacteristic
214C22×C8×C61C2314yescomplemented
215C24×C61—21no—
216C24×C61—21no—
217C24×C61C2×D411yescharacteristic
218C23×D61—28no—
219C23×D61—24no—
220C23×D61—21no—
221C23×D61—24no—
222C23×D61—24no—
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×C61—28no—
232#41×C61—28no—
233#41×C61—48no—
234#41×C61C2×D4116yescomplemented
235C2×Q8×C61—22no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—22no—
239C2×Q8×C61—22no—
240C2×Q8×C61C2×D414yes—
241C2×Q8×C61C2412yes—
242C2×Q8×C61C2412yes—
243C2×D4×C61—28no—
244C2×D4×C61—24no—
245C2×D4×C61—24no—
246C2×D4×C61—21no—
247C2×D4×C61—22no—
248C2×D4×C61—22no—
249C2×D4×C61—22no—
250C2×D4×C61—21no—
251C2×D4×C61—44no—
252C2×D4×C61C2×D414yes—
253C2×D4×C61C2412yes—
254C2×D4×C61C2412yes—
255C22×C4×C61—21no—
256C22×C4×C61—28no—
257C22×C4×C61—24no—
258C22×C4×C61—21no—
259C22×C4×C61—24no—
260C22×C4×C61—44no—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D414yes—
264C22×C4×C61C2×D414yes—
265C22×C4×C61C2411yescharacteristic
266C22×C4×C61C2412yes—
267C2×C22⋊D61—28no—
268C2×C22⋊D61—28no—
269C2×C22⋊D61—28no—
270C2×C22⋊D61—24no—
271C2×C22⋊D61—24no—
272C2×C22⋊D61—24no—
273C2×C22⋊D61—24no—
274C2×C22⋊D61—24no—
275C2×C22⋊D61—44no—
276C2×C22⋊D61—44no—
277C22×Dic61—28no—
278C22×Dic61—24no—
279C22×Dic61—21no—
280C22×Dic61—24no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D414yes—
286#11758226—216no—
287#11758226—28no—
288#11758226—28no—
289Q8×D61—216no—
290Q8×D61—28no—
291Q8×D61—28no—
292#11758224—264no—
293#11758224—216no—
294#11758224—28no—
295#11758224—28no—
296D4×D61—264no—
297D4×D61—216no—
298D4×D61—28no—
299D4×D61—28no—
300#11758222—264no—
301#11758222—216no—
302#11758222—28no—
303#11758222C2×D4116yescomplemented
304C2×D244—28no—
305C2×D244—24no—
306C2×D244—21no—
307C2×D244—22no—
308C2×D244C2×D414yes—
309C2×D244C2412yes—
310C2×C4×D61—28no—
311C2×C4×D61—264no—
312C2×C4×D61—28no—
313C2×C4×D61—24no—
314C2×C4×D61—24no—
315C2×C4×D61—28no—
316C2×C4×D61—216no—
317C2×C4×D61—24no—
318C2×C4×D61—24no—
319C2×C4×D61—22no—
320C2×C4×D61—22no—
321C2×C4×D61—28no—
322C2×C4×D61—28no—
323C2×C4×D61—22no—
324C2×C4×D61—22no—
325C2×C4×D61—24no—
326C2×C4×D61C2×D414yes—
327C2×C4×D61C2×D412yes—
328C2×C4×D61C2×D412yes—
329C2×C4×D61C2×D414yes—
330C2×C4×D61C2412yes—
331C2×C4×D61C2412yes—
332C2×Dic122—28no—
333C2×Dic122—21no—
334C2×Dic122—22no—
335C2×Dic122—24no—
336C2×Dic122C2×D414yes—
337C2×Dic122C2412yes—
338Q16×C61—28no—
339SD16×C61—28no—
340SD16×C61—28no—
341D8×C61—28no—
342C2×C8×C61—22no—
343C2×C8×C61—22no—
344C2×C8×C61—28no—
345C2×C8×C61C2412yes—
346C2×C8×C61C2412yes—
347C22⋊Dic61—24no—
348C22⋊Dic61—24no—
349C22⋊Dic61—24no—
350#11758202—28no—
351#11758201—28no—
352#11758200—28no—
353#11758199—28no—
354#11758198—24no—
355#11758198—24no—
356C4⋊Dic61—21no—
357C4⋊Dic61—21no—
358C4⋊Dic61C2412yes—
359C4⋊Dic61C2412yes—
360#11758196—24no—
361#11758196—24no—
362C4×Dic61—24no—
363C2×#92418—22no—
364C2×#92418—22no—
365C2×#92418—28no—
366C2×#92418C2412yes—
367C2×#92418C2412yes—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—24no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—42no—
374C23×C61—42no—
375C23×C61—42no—
376C23×C61—42no—
377C23×C61—42no—
378C23×C61#12014yes—
379C23×C61C22×D412yes—
380C23×C61C22×D411yescharacteristic
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—216no—
384C22×D61—22no—
385C22×D61—24no—
386C22×D61—28no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—28no—
391C22×D61—44no—
392C22×D61—416no—
393C22×D61—432no—
394C22×D61—48no—
395C22×D61—42no—
396C22×D61—42no—
397C22×D61—48no—
398C22×D61#13514yescomplemented
399C22×D61C22×D412yes—
400C22×D61C22×D412yes—
401Q8×C61—24no—
402Q8×C61—22no—
403Q8×C61—22no—
404Q8×C61—22no—
405Q8×C61—42no—
406Q8×C61C22×D414yes—
407D4×C61—216no—
408D4×C61—24no—
409D4×C61—22no—
410D4×C61—22no—
411D4×C61—22no—
412D4×C61—48no—
413D4×C61—42no—
414D4×C61C22×D414yes—
415C2×C4×C61—24no—
416C2×C4×C61—22no—
417C2×C4×C61—216no—
418C2×C4×C61—22no—
419C2×C4×C61—42no—
420C2×C4×C61—48no—
421C2×C4×C61#12014yes—
422C2×C4×C61#12018yes—
423C2×C4×C61C22×D412yes—
424C2×C4×C61C22×D411yescharacteristic
425C2×C4×C61C22×D412yes—
426C2×C4×C61C22×D414yes—
427C2×C4×C61C22×D412yes—
428C2×C4×C61C22×D414yes—
429C2×C4×C61C2511yescharacteristic
430C22⋊D61—216no—
431C22⋊D61—216no—
432C22⋊D61—216no—
433C22⋊D61—48no—
434C22⋊D61—48no—
435C2×Dic61—216no—
436C2×Dic61—22no—
437C2×Dic61—24no—
438C2×Dic61—22no—
439C2×Dic61—28no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—42no—
444C2×Dic61—42no—
445C2×Dic61C22×D412yes—
446C2×Dic61C22×D412yes—
447D244—216no—
448D244—24no—
449D244—22no—
450D244C22×D414yes—
451C4×D61—216no—
452C4×D61—216no—
453C4×D61—28no—
454C4×D61—216no—
455C4×D61—28no—
456C4×D61—24no—
457C4×D61—24no—
458C4×D61—22no—
459C4×D61—22no—
460C4×D61—22no—
461C4×D61—22no—
462Dic122—216no—
463Dic122—24no—
464Dic122—22no—
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×C61—42no—
479C22×C61—42no—
480C22×C61—42no—
481C22×C61—84no—
482C22×C61C2×#12014yes—
483C22×C61C2×#12012yes—
484C22×C61C2×#13512yes—
485C22×C61#57512yes—
486C22×C61C23×D411yescharacteristic
487C2×D61—22no—
488C2×D61—28no—
489C2×D61—22no—
490C2×D61—22no—
491C2×D61—24no—
492C2×D61—22no—
493C2×D61—22no—
494C2×D61—416no—
495C2×D61—432no—
496C2×D61—44no—
497C2×D61—48no—
498C2×D61—42no—
499C2×D61—42no—
500C2×D61C2×#13514yescomplemented
501C4×C61—24no—
502C4×C61—42no—
503C4×C61C2×#12012yes—
504C4×C61C2×#12014yes—
505C4×C61C23×D411yescharacteristic
506C4×C61C23×D411yescharacteristic
507Dic61—22no—
508Dic61—24no—
509Dic61—22no—
510Dic61—42no—
511Dic61—42no—
512C23×#41—611no—
513C22×#135—611no—
514C22×#135D6111yescharacteristic, complemented
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×#416—611no—
527C22×C22⋊C8—611no—
528C2×C61—24no—
529C2×C61—44no—
530C2×C61—82no—
531C2×C61#300214yescomplemented
532C2×C61C22×#12011yescharacteristic
533C2×C61C22×#13511yescharacteristic
534C2×C61C2×#57511yescharacteristic
535D61—24no—
536D61—42no—
537D61—44no—
538C22×#41—618no—
539C22×#41—611no—
540C22×#41—611no—
541C22×#41—611no—
542C22×#41—1221no—
543C22×#41—1221no—
544C22×#41—1224no—
545C22×#41—1228no—
546C22×#41—1228no—
547C22×#41C2×D6111yescharacteristic
548C22×#41C2×D6111yescharacteristic, complemented
549C23×Q8—611no—
550C23×D4—611no—
551C23×D4—1221no—
552C24×C4—611no—
553C24×C4—1221no—
554C2×#135—28no—
555C2×#135—618no—
556C2×#135—1228no—
557C2×#135C2×D6118yescomplemented
558C22×Q16—611no—
559C22×Q16C2×D6111yescharacteristic, complemented
560C22×SD16—611no—
561C22×SD16—611no—
562C22×SD16C2×D6111yescharacteristic, complemented
563C22×SD16C2×D6111yescharacteristic, complemented
564C22×D8—611no—
565C22×D8C2×D6111yescharacteristic, complemented
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×#117—611no—
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#416—618no—
589C2×#103—611no—
590C2×#103—611no—
591C2×#103—611no—
592C2×#103—611no—
593C2×#102—611no—
594C2×#102—611no—
595C2×#102—611no—
596C2×#102—611no—
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—22no—
608C2×#41—24no—
609C2×#41—24no—
610C2×#41—614no—
611C2×#41—614no—
612C2×#41—618no—
613C2×#41—614no—
614C2×#41—1228no—
615C2×#41—12216no—
616C2×#41—1228no—
617C2×#41—1222no—
618C2×#41—1222no—
619C2×#41—1224no—
620C2×#41—12216no—
621C2×#41—1224no—
622C2×#41—12232no—
623C2×#41—12264no—
624C2×#41—12232no—
625C2×#41—1224no—
626C2×#41—1224no—
627C2×#41—1222no—
628C2×#41—1224no—
629C2×#41C22⋊D6118yescomplemented
630C2×#41C22×D6114yes—
631C2×#41C22×D6114yescomplemented
632C22×Q8—614no—
633C22×Q8—611no—
634C22×Q8—1221no—
635C22×Q8—1222no—
636C22×Q8—1224no—
637C22×Q8—1224no—
638C22×Q8C22×D6111yescharacteristic
639C22×Q8C22×D6111yescharacteristic
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—614no—
643C22×D4—611no—
644C22×D4—1221no—
645C22×D4—1222no—
646C22×D4—1221no—
647C22×D4—1224no—
648C22×D4—1228no—
649C22×D4—12216no—
650C22×D4—1221no—
651C22×D4—1221no—
652C22×D4—1224no—
653C22×D4—1221no—
654C22×D4—1221no—
655C22×D4C22×D6111yescharacteristic
656C22×D4C22×D6111yescharacteristic
657C23×C4—21no—
658C23×C4—21no—
659C23×C4—611no—
660C23×C4—614no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—614no—
666C23×C4—1221no—
667C23×C4—1228no—
668C23×C4—1221no—
669C23×C4—12216no—
670C23×C4—1221no—
671C23×C4—1224no—
672C23×C4—1221no—
673C23×C4—1224no—
674C23×C4C22×D6111yescharacteristic
675#135—232no—
676#135—12232no—
677C2×Q16—24no—
678C2×Q16—614no—
679C2×Q16—1224no—
680C2×Q16C22×D6114yescomplemented
681C2×SD16—24no—
682C2×SD16—24no—
683C2×SD16—614no—
684C2×SD16—614no—
685C2×SD16—1224no—
686C2×SD16—1224no—
687C2×SD16C22×D6114yescomplemented
688C2×SD16C22×D6114yescomplemented
689C2×D8—24no—
690C2×D8—614no—
691C2×D8—1224no—
692C2×D8C22×D6114yescomplemented
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—614no—
714#117—1222no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—611no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—1221no—
725#103—614no—
726#103—614no—
727#103—614no—
728#103—614no—
729#102—614no—
730#102—614no—
731#102—614no—
732#102—614no—
733C22⋊C8—614no—
734C22⋊C8—614no—
735C22⋊C8—614no—
736C22⋊C8—614no—
737C24—21no—
738C24—21no—
739C24—611no—
740C24—611no—
741C24—614no—
742C24—1224no—
743C24—1224no—
744C24—1228no—
745C24—1221no—
746C24—1224no—
747C24—2442no—
748C24—2444no—
749C24—2444no—
750C24D4×D6111yescharacteristic
751#41—28no—
752#41—216no—
753#41—28no—
754#41—28no—
755#41—48no—
756#41—6116no—
757#41—12264no—
758#41—1228no—
759#41—12264no—
760#41—12216no—
761#41—1228no—
762#41—12216no—
763#41—1228no—
764#41—1228no—
765#41—1228no—
766#41—12216no—
767#41C2×C22⋊D61116yescomplemented
768C2×Q8—22no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—614no—
774C2×Q8—612no—
775C2×Q8—1224no—
776C2×Q8—1228no—
777C2×Q8—1228no—
778C2×Q8—12216no—
779C2×Q8—1228no—
780C2×Q8—1221no—
781C2×Q8—1222no—
782C2×Q8C2×C22⋊D6114yes—
783C2×Q8C23×D6112yes—
784C2×Q8C23×D6112yes—
785C2×D4—24no—
786C2×D4—28no—
787C2×D4—24no—
788C2×D4—21no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—44no—
794C2×D4—614no—
795C2×D4—612no—
796C2×D4—1224no—
797C2×D4—1228no—
798C2×D4—1224no—
799C2×D4—1228no—
800C2×D4—12264no—
801C2×D4—12216no—
802C2×D4—1224no—
803C2×D4—1228no—
804C2×D4—1228no—
805C2×D4—1224no—
806C2×D4—1228no—
807C2×D4—1228no—
808C2×D4—1224no—
809C2×D4—1224no—
810C2×D4—1221no—
811C2×D4—1222no—
812C2×D4—2444no—
813C2×D4—2444no—
814C2×D4C2×C22⋊D6114yes—
815C2×D4C23×D6112yes—
816C2×D4C23×D6112yes—
817C22×C4—21no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—24no—
822C22×C4—44no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—614no—
826C22×C4—614no—
827C22×C4—614no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—1224no—
833C22×C4—1224no—
834C22×C4—1228no—
835C22×C4—1228no—
836C22×C4—12264no—
837C22×C4—1224no—
838C22×C4—1228no—
839C22×C4—1221no—
840C22×C4—1224no—
841C22×C4—1222no—
842C22×C4—1222no—
843C22×C4—1228no—
844C22×C4—1224no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1228no—
848C22×C4—1224no—
849C22×C4—1224no—
850C22×C4—12216no—
851C22×C4—1228no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4D4×D6114yes—
855C22×C4D4×D6112yes—
856C22×C4D4×D6111yescharacteristic
857C22×C4C2×C22⋊D6114yes—
858C22×C4C23×D6111yescharacteristic
859C22×C4C23×D6112yes—
860Q16—28no—
861Q16—1228no—
862SD16—28no—
863SD16—28no—
864SD16—1228no—
865SD16—1228no—
866D8—28no—
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—612no—
879C4⋊C4—612no—
880C4⋊C4—1224no—
881C4⋊C4—1224no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C22⋊C4—1224no—
885C22⋊C4—1224no—
886C22⋊C4—1224no—
887C22⋊C4—1224no—
888C22⋊C4—1224no—
889C42—1224no—
890C23—22no—
891C23—22no—
892C23—24no—
893C23—22no—
894C23—22no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—614no—
901C23—612no—
902C23—612no—
903C23—1228no—
904C23—12216no—
905C23—1222no—
906C23—1222no—
907C23—1224no—
908C23—1228no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—2444no—
914C23—24416no—
915C23—2448no—
916C23—2448no—
917C23—24432no—
918C23—2442no—
919C23—2442no—
920C23#1451974514yes—
921C23C2×D4×D6112yes—
922C23C2×D4×D6111yescharacteristic
923Q8—24no—
924Q8—22no—
925Q8—22no—
926Q8—22no—
927Q8—42no—
928Q8—614no—
929Q8—12216no—
930Q8—1224no—
931Q8—1222no—
932Q8C22×C22⋊D6114yes—
933D4—216no—
934D4—24no—
935D4—22no—
936D4—22no—
937D4—22no—
938D4—48no—
939D4—42no—
940D4—614no—
941D4—12216no—
942D4—12216no—
943D4—12216no—
944D4—12216no—
945D4—1224no—
946D4—1222no—
947D4—2448no—
948D4—2448no—
949D4C22×C22⋊D6114yes—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—216no—
953C2×C4—22no—
954C2×C4—42no—
955C2×C4—48no—
956C2×C4—612no—
957C2×C4—612no—
958C2×C4—12216no—
959C2×C4—12216no—
960C2×C4—12216no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1228no—
964C2×C4—1224no—
965C2×C4—1222no—
966C2×C4—1228no—
967C2×C4—1224no—
968C2×C4—1224no—
969C2×C4—1228no—
970C2×C4—12216no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4#1451974514yes—
980C2×C4#1451974518yes—
981C2×C4C2×D4×D6112yes—
982C2×C4C2×D4×D6111yescharacteristic
983C2×C4C2×D4×D6112yes—
984C2×C4C2×D4×D6114yes—
985C2×C4C22×C22⋊D6112yes—
986C2×C4C22×C22⋊D6114yes—
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—42no—
1000C22—42no—
1001C22—42no—
1002C22—84no—
1003C22—614no—
1004C22—1222no—
1005C22—1222no—
1006C22—1228no—
1007C22—1222no—
1008C22—1222no—
1009C22—1224no—
1010C22—1222no—
1011C22—24416no—
1012C22—24432no—
1013C22—2442no—
1014C22—2442no—
1015C22—2444no—
1016C22—2448no—
1017C22C2×#1451974514yes—
1018C22C2×#1451974512yes—
1019C22#135×D6112yes—
1020C22#1684055912yes—
1021C22C22×D4×D6111yescharacteristic
1022C4—24no—
1023C4—42no—
1024C4—1222no—
1025C4—1222no—
1026C4—1224no—
1027C4—2442no—
1028C4—2442no—
1029C4C2×#1451974514yes—
1030C4C2×#1451974512yes—
1031C4C22×D4×D6111yescharacteristic
1032C4C23×C22⋊D6111yescharacteristic
1033C2—24no—
1034C2—44no—
1035C2—82no—
1036C2—1224no—
1037C2—2442no—
1038C2—2444no—
1039C2#2145503314yesdirect product factor
1040C2C22×#1451974511yescharacteristic
1041C2C2×#135×D6111yescharacteristic
1042C2C2×#1684055911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#135×C61C2
socleC23×C61C22×D4
hypercenterC22×#135D61
hypocenterC61C2×#3002
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#41×D61C2semidirect
2. C22×#14519797C2semidirect
3. C2×#16840269C2semidirect
4. #21455033C2direct (N × H)
5. C2×#16839923C2semidirect
6. C2×#16839921C2semidirect
7. C2×#16839906C2semidirect
8. C2×#16839904C2semidirect
9. C2×#16839916C2semidirect
10. C2×#16839899C2semidirect
11. C2×#16839911C2semidirect
12. C2×#16839894C2semidirect
13. C2×#16839759C2semidirect
14. C2×#16839758C2semidirect
15. C22×#14519689C2semidirect
16. C22×#135×C61C2semidirect
25. C2×#41×D61C22semidirect
32. C2×#14519797C22semidirect
33. C22×#11758202C22semidirect
34. C22×#11758200C22semidirect
35. C22×#11758201C22semidirect
36. C22×#11758199C22semidirect
37. C23×#92418C22semidirect
39. #16840269C22semidirect
42. C2×#14519753C22semidirect
44. C2×#14519748C22semidirect
48. C2×#14519736C22semidirect
49. #16839923C22semidirect
50. #16839921C22semidirect
51. #16839916C22semidirect
52. #16839911C22semidirect
53. #16839906C22semidirect
54. #16839904C22semidirect
55. #16839899C22semidirect
56. #16839894C22semidirect
57. #16839759C22semidirect
58. #16839758C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519701C22semidirect
63. C2×#14519699C22semidirect
64. C2×#14519699C22semidirect
65. C2×#14519698C22semidirect
66. C2×#14519698C22semidirect
69. C2×#14519689C22semidirect
70. C2×#14519689C22semidirect
71. C2×#14519689C22semidirect
73. C22×#41×C61C22semidirect
75. C2×#135×C61C22semidirect
76. C22×Q16×C61C22semidirect
77. C22×SD16×C61C22semidirect
78. C22×SD16×C61C22semidirect
79. C22×D8×C61C22semidirect
80. C23×C8×C61C22semidirect
91. C2×#11758222D4semidirect
138. C2×#11758202C23semidirect
140. C2×#11758200C23semidirect
142. C2×#11758201C23semidirect
144. C2×#11758199C23semidirect
148. C22×#92418C23semidirect
153. #14519753C23semidirect
157. #14519748C23semidirect
162. #14519736C23semidirect
173. #14519702C23semidirect
174. #14519702C23semidirect
175. #14519701C23semidirect
176. #14519701C23semidirect
177. #14519699C23semidirect
178. #14519699C23semidirect
179. #14519698C23semidirect
180. #14519698C23semidirect
183. #14519689C23semidirect
184. #14519689C23semidirect
190. C2×#41×C61D4semidirect
192. C2×#41×C61C23semidirect
204. C2×Q16×C61C23semidirect
207. C2×SD16×C61C23semidirect
208. C2×SD16×C61C23semidirect
210. C2×D8×C61C23semidirect
214. C22×C8×C61C23semidirect
234. #41×C61C2×D4semidirect
303. #11758222C2×D4semidirect
398. C22×D61#135semidirect
500. C2×D61C2×#135semidirect
514. C22×#135D61semidirect
531. C2×C61#3002semidirect
548. C22×#41C2×D61semidirect
557. C2×#135C2×D61semidirect
559. C22×Q16C2×D61semidirect
562. C22×SD16C2×D61semidirect
563. C22×SD16C2×D61semidirect
565. C22×D8C2×D61semidirect
567. C23×C8C2×D61semidirect
602. C61C2×#3002semidirect
629. C2×#41C22⋊D61semidirect
631. C2×#41C22×D61semidirect
680. C2×Q16C22×D61semidirect
687. C2×SD16C22×D61semidirect
688. C2×SD16C22×D61semidirect
692. C2×D8C22×D61semidirect
700. C22×C8C22×D61semidirect
767. #41C2×C22⋊D61semidirect
1039. C2#21455033direct (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×#145197972
C2×#168402692
#214550332
C2×#168399232
C2×#168399212
C2×#168399062
C2×#168399042
C2×#168399162
C2×#168398992
C2×#168399112
C2×#168398942
C2×#168397592
C2×#168397582
C22×#145196892
C22×#135×C612
C2×#300261