Finite Group Databasebeta

← C2×#21455448 #30547170

Subgroups — C2×#21455448 #30547170

Order 15616.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519809C211yesmaximal, characteristic, complemented
2C22×M16×D61C211yesmaximal, characteristic, complemented
3C2×#16840275C211yesmaximal, characteristic
4C2×C22⋊Q8×D61C211yesmaximal, characteristic, complemented
5#21455448C2116yesmaximal, direct product factor
6C2×#16840018C211yesmaximal, characteristic, complemented
7C2×#16840010C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16840002C211yesmaximal, characteristic, complemented
10C2×#16840000C211yesmaximal, characteristic, complemented
11C2×#16839994C211yesmaximal, characteristic, complemented
12C2×#16839992C211yesmaximal, characteristic, complemented
13C2×#16839801C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#16839769C211yesmaximal, characteristic, complemented
16C2×C61×#470C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519809—28no—
21C2×#14519809C2218yescomplemented
22C22×#11758202C2211yescharacteristic, complemented
23C22×#11758190C2211yescharacteristic, complemented
24C22×#11758201C2211yescharacteristic, complemented
25C22×#11758194C2211yescharacteristic
26C22×#11758189C2211yescharacteristic
27C22×#11758189C2211yescharacteristic
28C2×M16×D61—28no—
29C2×M16×D61C2218yescomplemented
30C22×C8×D61C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840275—24no—
33#16840275C2218yes—
34C2×#14519762—21no—
35C2×#14519757C2211yescharacteristic
36C2×#14519756C2211yescharacteristic
37C2×#14519755—21no—
38C2×#14519754—21no—
39C2×#14519753C2211yescharacteristic
40C2×#14519753C2211yescharacteristic
41C22⋊Q8×D61—24no—
42C22⋊Q8×D61C2218yescomplemented
43C2×#14519752C2211yescharacteristic
44C2×#14519751C2211yescharacteristic
45C2×#14519747—21no—
46C2×#14519739—21no—
47C2×#14519737—21no—
48C2×#14519735C2211yescharacteristic
49C2×C4⋊C4×D61—21no—
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C22⋊C4×D61—21no—
52#16840018C2218yescomplemented
53#16840010C2218yescomplemented
54#16840008C2218yescomplemented
55#16840002C2218yescomplemented
56#16840000C2218yescomplemented
57#16839994C2218yescomplemented
58#16839992C2218yescomplemented
59#16839801C2218yescomplemented
60C2×#14519711C2211yescharacteristic, complemented
61C2×#14519710C2211yescharacteristic, complemented
62C2×#14519708C2211yescharacteristic, complemented
63#16839769C2218yescomplemented
64#16839762C2218yescomplemented
65C2×#14519702C2211yescharacteristic, complemented
66C2×#14519701C2211yescharacteristic, complemented
67C2×#14519701C2211yescharacteristic, complemented
68C2×#14519700C2211yescharacteristic, complemented
69C2×#14519699C2211yescharacteristic, complemented
70C2×#14519697C2211yescharacteristic, complemented
71C22×Q16×C61C2211yescharacteristic, complemented
72C22×M16×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×C22⋊Q8×C61C2211yescharacteristic
75C61×#470C2218yescomplemented
76C2×#106×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#103×C61C2211yescharacteristic, complemented
79C24×D61D411yescharacteristic
80C2×#11758226—22no—
81C2×#11758226—24no—
82C2×#11758226—24no—
83C2×#11758226C2314yes—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C2×Q8×D61—22no—
87C2×Q8×D61—24no—
88C2×Q8×D61—24no—
89C2×Q8×D61C2314yes—
90C22×D244—21no—
91C22×D244—21no—
92C22×D244C2311yescharacteristic
93C22×C22⋊D61—21no—
94C23×Dic61D411yescharacteristic
95C22×C4×D61—24no—
96C22×C4×D61—24no—
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99C22×C4×D61—21no—
100C22×C4×D61D411yescharacteristic
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D414yes—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2314yes—
105C22×C4×D61C2311yescharacteristic
106#14519809—232no—
107C2×#11758202—24no—
108C2×#11758202C2314yescomplemented
109C2×#11758190—24no—
110C2×#11758190C2314yescomplemented
111C2×#11758201—24no—
112C2×#11758201C2314yescomplemented
113C2×#11758194—24no—
114C2×#11758194C2314yes—
115C2×#11758189—24no—
116C2×#11758189D418yescomplemented
117C2×#11758189C2314yes—
118C2×#11758189C2314yes—
119M16×D61—232no—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—24no—
123C2×C8×D61—24no—
124C2×C8×D61C2314yes—
125C2×C8×D61C2314yes—
126#14519762—28no—
127#14519757—22no—
128#14519757C2314yes—
129#14519756—22no—
130#14519756C2314yes—
131#14519755—28no—
132#14519754—28no—
133#14519753—22no—
134#14519753—22no—
135#14519753C2314yes—
136#14519753C2314yes—
137#14519752—22no—
138#14519752C2314yes—
139#14519751—22no—
140#14519751C2314yes—
141#14519747—28no—
142#14519739—28no—
143#14519737—28no—
144#14519735—22no—
145#14519735C2314yes—
146C2×C4⋊Dic61—21no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×C4⋊Dic61C2311yescharacteristic
149C2×#11758196—21no—
150C2×#11758196—21no—
151C2×#11758196—21no—
152C2×#11758196—21no—
153C4⋊C4×D61—28no—
154C4⋊C4×D61—22no—
155C4⋊C4×D61C2314yes—
156C2×C22⋊Dic61—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C22⋊C4×D61—28no—
164C2×C4×Dic61—21no—
165#14519711C2314yescomplemented
166#14519710C2314yescomplemented
167#14519708C2314yescomplemented
168#14519702C2314yescomplemented
169#14519701C2314yescomplemented
170#14519701C2314yescomplemented
171#14519700C2314yescomplemented
172#14519699C2314yescomplemented
173#14519697C2314yescomplemented
174C22×Q8×C61C2311yescharacteristic
175C22×Q8×C61C2311yescharacteristic
176C23×C4×C61C2311yescharacteristic
177C2×Q16×C61—24no—
178C2×Q16×C61C2314yescomplemented
179C2×M16×C61—24no—
180C2×M16×C61C2314yes—
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183C22⋊Q8×C61—22no—
184C22⋊Q8×C61—22no—
185C22⋊Q8×C61C2314yes—
186C22⋊Q8×C61C2314yes—
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193#106×C61C2314yescomplemented
194#103×C61C2314yescomplemented
195#103×C61C2314yescomplemented
196C24×C61C2×D411yescharacteristic
197C23×D61—24no—
198C23×D61—24no—
199C23×D61—21no—
200C23×D61—42no—
201C23×D61C2×D414yes—
202C23×D61C2×D411yescharacteristic
203C23×D61C2×D411yescharacteristic
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—22no—
207C2×Q8×C61—22no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61C2412yes—
211C2×Q8×C61C2412yes—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2412yes—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—24no—
223C2×C22⋊D61—44no—
224C22×Dic61—24no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D414yes—
230C22×Dic61C2×D411yescharacteristic
231#11758226—28no—
232#11758226—28no—
233#11758226—48no—
234Q8×D61—28no—
235Q8×D61—28no—
236Q8×D61—48no—
237C2×D244—22no—
238C2×D244—22no—
239C2×D244—24no—
240C2×D244—24no—
241C2×D244—21no—
242C2×D244—44no—
243C2×D244—44no—
244C2×D244C2412yes—
245C2×C4×D61—24no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—24no—
249C2×C4×D61—216no—
250C2×C4×D61—28no—
251C2×C4×D61—28no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—24no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61—44no—
258C2×C4×D61C2×D414yes—
259C2×C4×D61C2×D414yes—
260C2×C4×D61C2×D412yes—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2×D414yes—
263C2×C4×D61#4114yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122—24no—
270C2×Dic122—44no—
271C2×Dic122C2412yes—
272Q16×C61—28no—
273M16×C61—28no—
274C2×C8×C61—22no—
275C2×C8×C61C2×D414yes—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—24no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C2412yes—
283C4⋊C4×C61C2412yes—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊Dic61—24no—
287#11758202—28no—
288#11758201—28no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—24no—
298C4⋊Dic61C2412yes—
299C4⋊Dic61C2412yes—
300#11758196—24no—
301#11758196—24no—
302#11758196—24no—
303#11758196—24no—
304C4×Dic61—24no—
305#11758194—28no—
306C2×#92418—22no—
307C2×#92418C2×D414yes—
308C2×#92418C2412yes—
309C2×#92418C2412yes—
310#11758190—28no—
311#11758189—28no—
312#11758189C2×D4116yescomplemented
313C8×D61—28no—
314C8×D61—28no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61C22×D412yes—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—28no—
325C22×D61—28no—
326C22×D61—22no—
327C22×D61—44no—
328C22×D61—416no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61#12114yes—
333C22×D61#13714yescomplemented
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—22no—
339Q8×C61—22no—
340Q8×C61—42no—
341Q8×C61—42no—
342C2×C4×C61—22no—
343C2×C4×C61—24no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D412yes—
357C2×C4×C61C2×#4112yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—48no—
360C2×Dic61—22no—
361C2×Dic61—28no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—42no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61#12114yes—
369C2×Dic61C22×D412yes—
370C2×Dic61C22×D412yes—
371D244—22no—
372D244—22no—
373D244—48no—
374D244—48no—
375D244—42no—
376C4×D61—28no—
377C4×D61—24no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—28no—
381C4×D61—48no—
382C4×D61—48no—
383C4×D61—48no—
384C4×D61#12118yes—
385C4×D61C22×D414yes—
386C4×D61C2×#4114yes—
387Dic122—22no—
388Dic122—22no—
389Dic122—42no—
390Dic122—48no—
391C8×C61—22no—
392C8×C61C22×D414yes—
393#92418—22no—
394#92418C22×D414yes—
395C2×#3056—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—44no—
400C22×C61C2×#12112yes—
401C22×C61C2×#13712yes—
402C22×C61#57512yes—
403C22×C61C23×D411yescharacteristic
404C2×D61—22no—
405C2×D61—28no—
406C2×D61—28no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—416no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—84no—
415C2×D61C2×#12114yes—
416C2×D61C2×#13714yescomplemented
417C4×C61—22no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61C2×#12112yes—
423C4×C61C23×D411yescharacteristic
424C4×C61C22×#4111yescharacteristic
425Dic61—22no—
426Dic61—42no—
427Dic61—42no—
428Dic61—42no—
429Dic61C2×#12114yes—
430C22×#137—611no—
431C23×M16—611no—
432C2×#525—611no—
433C22×C22⋊Q8—611no—
434#3056—6116no—
435C2×#470—611no—
436C2×#470D6111yescharacteristic, complemented
437C2×#468—611no—
438C2×#468—611no—
439C2×#467—611no—
440C2×#467—611no—
441C2×#465—611no—
442C2×#465—611no—
443C2×#428—611no—
444C2×#417—611no—
445C2×#419—611no—
446C2×C61—42no—
447C2×C61#305614yescomplemented
448C2×C61C22×#12111yescharacteristic
449C2×C61C22×#13711yescharacteristic
450C2×C61C2×#57511yescharacteristic
451D61—24no—
452D61—24no—
453D61—82no—
454C22×#41—611no—
455C23×Q8—611no—
456C24×C4—611no—
457C2×#137—618no—
458C2×#137—1228no—
459C22×Q16—611no—
460C22×Q16C2×D6111yescharacteristic, complemented
461C22×SD16—611no—
462C22×SD16—611no—
463C22×M16—611no—
464C22×M16—618no—
465C22×M16—611no—
466C22×M16—611no—
467C22×M16—1228no—
468C22×M16C2×D6111yescharacteristic
469C23×C8—611no—
470C23×C8—611no—
471#525—618no—
472#525—1224no—
473C2×#123—1221no—
474C2×C22⋊Q8—611no—
475C2×C22⋊Q8—611no—
476C2×C22⋊Q8—611no—
477C2×C22⋊Q8—618no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—1221no—
480C2×C22⋊Q8—1221no—
481C2×C22⋊Q8—1224no—
482C2×C22⋊Q8C2×D6111yescharacteristic
483C2×C22⋊Q8C2×D6111yescharacteristic
484C2×#121—611no—
485C2×#121—611no—
486C2×#120—1221no—
487C2×C4×D4—1221no—
488C2×C4×D4—1221no—
489C2×#117—611no—
490C22×C4⋊C4—611no—
491C22×C4⋊C4—1221no—
492C22×C22⋊C4—1221no—
493#470—618no—
494#470C2×D6118yescomplemented
495#468—618no—
496#468—618no—
497#467—618no—
498#467—618no—
499#465—618no—
500#465—618no—
501#428—618no—
502C2×#107—611no—
503C2×#107—611no—
504C2×#106—611no—
505C2×#106C2×D6111yescharacteristic, complemented
506#419—618no—
507#417—618no—
508C2×#103—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#103—611no—
512C2×#103C2×D6111yescharacteristic, complemented
513C2×#103C2×D6111yescharacteristic, complemented
514C2×#102—611no—
515C2×#102—611no—
516C61C2×#305611yescharacteristic, complemented, Sylow
517C25—611no—
518C2×#41—614no—
519C2×#41—1222no—
520C2×#41—1224no—
521C2×#41—1224no—
522C22×Q8—614no—
523C22×Q8—611no—
524C22×Q8—1221no—
525C22×Q8—1222no—
526C22×Q8—1224no—
527C22×Q8—1224no—
528C22×Q8C22×D6111yescharacteristic
529C22×Q8C22×D6111yescharacteristic
530C22×D4—611no—
531C22×D4—1221no—
532C22×D4—1221no—
533C22×D4—1221no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—611no—
537C23×C4—611no—
538C23×C4—614no—
539C23×C4—611no—
540C23×C4—614no—
541C23×C4—1224no—
542C23×C4—1224no—
543C23×C4—1221no—
544C23×C4—1221no—
545C23×C4—1221no—
546C23×C4C22×D6111yescharacteristic
547#137—12232no—
548C2×Q16—24no—
549C2×Q16—614no—
550C2×Q16—1224no—
551C2×Q16C22×D6114yescomplemented
552C2×SD16—614no—
553C2×SD16—614no—
554C2×SD16—1224no—
555C2×SD16—1224no—
556C2×M16—24no—
557C2×M16—614no—
558C2×M16—618no—
559C2×M16—614no—
560C2×M16—614no—
561C2×M16—1224no—
562C2×M16—1224no—
563C2×M16—12232no—
564C2×M16C22×D6114yes—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—614no—
568C22×C8—614no—
569C22×C8—1224no—
570C22×C8—1224no—
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6111yescharacteristic
573#123—1228no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—614no—
577C22⋊Q8—614no—
578C22⋊Q8—614no—
579C22⋊Q8—614no—
580C22⋊Q8—1228no—
581C22⋊Q8—1228no—
582C22⋊Q8—1222no—
583C22⋊Q8—1222no—
584C22⋊Q8—1222no—
585C22⋊Q8—1222no—
586C22⋊Q8C22×D6114yes—
587C22⋊Q8C22×D6114yes—
588#121—614no—
589#121—614no—
590#121—1222no—
591#121—1222no—
592#120—1228no—
593C4×D4—1228no—
594C4×D4—1228no—
595#117—614no—
596#117—1222no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1228no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4C22×D6111yescharacteristic
610C2×C4⋊C4C22×D6111yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1228no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C42—1221no—
622#107—614no—
623#107—614no—
624#106—614no—
625#106C22×D6114yescomplemented
626#103—614no—
627#103—614no—
628#103—614no—
629#103—614no—
630#103C22×D6114yescomplemented
631#103C22×D6114yescomplemented
632#102—614no—
633#102—614no—
634C24—611no—
635C24—611no—
636C24—614no—
637C24—1224no—
638C24—1224no—
639C24—1221no—
640C24—2442no—
641C24D4×D6111yescharacteristic
642#41—1228no—
643#41—1228no—
644#41—2448no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—612no—
652C2×Q8—1224no—
653C2×Q8—1228no—
654C2×Q8—1228no—
655C2×Q8—1221no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8—2444no—
659C2×Q8—2448no—
660C2×Q8C23×D6112yes—
661C2×Q8C23×D6112yes—
662C2×D4—612no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1222no—
667C2×D4—1221no—
668C2×D4—1222no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2444no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—611no—
679C22×C4—612no—
680C22×C4—614no—
681C22×C4—614no—
682C22×C4—612no—
683C22×C4—614no—
684C22×C4—611no—
685C22×C4—614no—
686C22×C4—614no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—1228no—
690C22×C4—1224no—
691C22×C4—12216no—
692C22×C4—1228no—
693C22×C4—1224no—
694C22×C4—1224no—
695C22×C4—1224no—
696C22×C4—1224no—
697C22×C4—1224no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—2444no—
704C22×C4—2444no—
705C22×C4—2444no—
706C22×C4D4×D6112yes—
707C22×C4D4×D6111yescharacteristic
708C22×C4C23×D6112yes—
709C22×C4C23×D6111yescharacteristic
710Q16—28no—
711Q16—1228no—
712SD16—1228no—
713SD16—1228no—
714M16—28no—
715M16—6116no—
716M16—1228no—
717M16—1228no—
718C2×C8—22no—
719C2×C8—614no—
720C2×C8—612no—
721C2×C8—612no—
722C2×C8—1228no—
723C2×C8—1222no—
724C2×C8—1228no—
725C2×C8D4×D6114yes—
726C2×C8C23×D6112yes—
727C2×C8C23×D6112yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—1224no—
735C4⋊C4—1224no—
736C4⋊C4—1224no—
737C4⋊C4—1224no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1224no—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1224no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—1224no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—614no—
757C23—614no—
758C23—612no—
759C23—612no—
760C23—1228no—
761C23—1228no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—2444no—
768C23—24416no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23C2×D4×D6112yes—
773C23C2×D4×D6111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—42no—
780Q8—1222no—
781Q8—1222no—
782Q8—2448no—
783Q8—2442no—
784D4—1222no—
785D4—1222no—
786D4—2448no—
787D4—2448no—
788D4—2448no—
789D4—2442no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—614no—
803C2×C4—612no—
804C2×C4—618no—
805C2×C4—614no—
806C2×C4—614no—
807C2×C4—612no—
808C2×C4—1228no—
809C2×C4—1228no—
810C2×C4—1228no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—2448no—
819C2×C4—2448no—
820C2×C4—2448no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4C2×D4×D6112yes—
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6112yes—
827C2×C4#41×D6112yes—
828C2×C4C24×D6111yescharacteristic
829C8—22no—
830C8—614no—
831C8—1222no—
832C8C2×D4×D6114yes—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—614no—
838C22—614no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1228no—
843C22—1228no—
844C22—1222no—
845C22—4884no—
846C22—24416no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22#121×D6112yes—
851C22#137×D6112yes—
852C22#1684056112yes—
853C22C22×D4×D6111yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—614no—
860C4—1222no—
861C4—2442no—
862C4—2442no—
863C4—2442no—
864C4#121×D6112yes—
865C4C22×D4×D6111yescharacteristic
866C4C2×#41×D6111yescharacteristic
867C2—42no—
868C2—1224no—
869C2—1224no—
870C2—4882no—
871C2#2145544814yesdirect product factor
872C2C2×#121×D6111yescharacteristic
873C2C2×#137×D6111yescharacteristic
874C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#470C2
socleC23×C61C22×D4
prime radicalC2×#16840275C2
hypercenterC2×#470D61
hypocenterC61C2×#3056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#14519809C2semidirect
2. C22×M16×D61C2semidirect
4. C2×C22⋊Q8×D61C2semidirect
5. #21455448C2direct (N × H)
6. C2×#16840018C2semidirect
7. C2×#16840010C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16840002C2semidirect
10. C2×#16840000C2semidirect
11. C2×#16839994C2semidirect
12. C2×#16839992C2semidirect
13. C2×#16839801C2semidirect
14. C2×#16839762C2semidirect
15. C2×#16839769C2semidirect
16. C2×C61×#470C2semidirect
21. C2×#14519809C22semidirect
22. C22×#11758202C22semidirect
23. C22×#11758190C22semidirect
24. C22×#11758201C22semidirect
29. C2×M16×D61C22semidirect
42. C22⋊Q8×D61C22semidirect
52. #16840018C22semidirect
53. #16840010C22semidirect
54. #16840008C22semidirect
55. #16840002C22semidirect
56. #16840000C22semidirect
57. #16839994C22semidirect
58. #16839992C22semidirect
59. #16839801C22semidirect
60. C2×#14519711C22semidirect
61. C2×#14519710C22semidirect
62. C2×#14519708C22semidirect
63. #16839769C22semidirect
64. #16839762C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519701C22semidirect
67. C2×#14519701C22semidirect
68. C2×#14519700C22semidirect
69. C2×#14519699C22semidirect
70. C2×#14519697C22semidirect
71. C22×Q16×C61C22semidirect
75. C61×#470C22semidirect
76. C2×#106×C61C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#103×C61C22semidirect
108. C2×#11758202C23semidirect
110. C2×#11758190C23semidirect
112. C2×#11758201C23semidirect
116. C2×#11758189D4semidirect
165. #14519711C23semidirect
166. #14519710C23semidirect
167. #14519708C23semidirect
168. #14519702C23semidirect
169. #14519701C23semidirect
170. #14519701C23semidirect
171. #14519700C23semidirect
172. #14519699C23semidirect
173. #14519697C23semidirect
178. C2×Q16×C61C23semidirect
193. #106×C61C23semidirect
194. #103×C61C23semidirect
195. #103×C61C23semidirect
312. #11758189C2×D4semidirect
333. C22×D61#137semidirect
416. C2×D61C2×#137semidirect
436. C2×#470D61semidirect
447. C2×C61#3056semidirect
460. C22×Q16C2×D61semidirect
494. #470C2×D61semidirect
505. C2×#106C2×D61semidirect
512. C2×#103C2×D61semidirect
513. C2×#103C2×D61semidirect
516. C61C2×#3056semidirect
551. C2×Q16C22×D61semidirect
625. #106C22×D61semidirect
630. #103C22×D61semidirect
631. #103C22×D61semidirect
871. C2#21455448direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198092
C22×M16×D612
C2×#168402752
C2×C22⋊Q8×D612
#214554482
C2×#168400182
C2×#168400102
C2×#168400082
C2×#168400022
C2×#168400002
C2×#168399942
C2×#168399922
C2×#168398012
C2×#168397622
C2×#168397692
C2×C61×#4702
C2×#305661