Finite Group Databasebeta

← C2×#21456585 #30550548

Subgroups — C2×#21456585 #30550548

Order 15616.

2718 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic, complemented
2C2×#121×D61C211yesmaximal, characteristic, complemented
3#21456585C2116yesmaximal, direct product factor
4C2×#16840096C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840088C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16839998C211yesmaximal, characteristic, complemented
9C2×#16839996C211yesmaximal, characteristic, complemented
10C2×#16839993C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C22×#14519689C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic, complemented
18C22×D4×D61—21no—
19C22×D4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C22×#11758201C2211yescharacteristic, complemented
22C22×D488C2211yescharacteristic, complemented
23C22×#11758199C2211yescharacteristic, complemented
24C23×#92418C2211yescharacteristic, complemented
25#16840275—24no—
26#16840275C2218yescomplemented
27C2×#14519762—21no—
28C2×#14519753C2211yescharacteristic
29C2×#14519752C2211yescharacteristic
30C2×#14519752C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519751C2211yescharacteristic, complemented
33C2×#14519750—21no—
34C2×#14519749—21no—
35C2×#14519748C2211yescharacteristic
36#121×D61—24no—
37#121×D61C2218yescomplemented
38C2×#14519747—21no—
39C2×#14519739—21no—
40C2×#14519737—21no—
41C2×#14519735C2211yescharacteristic, complemented
42C2×C4⋊C4×D61C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840096C2218yescomplemented
45#16840088C2218yescomplemented
46#16840084C2218yescomplemented
47#16840082C2218yescomplemented
48#16839998C2218yescomplemented
49#16839996C2218yescomplemented
50#16839993C2218yescomplemented
51#16839911C2218yescomplemented
52#16839910C2218yescomplemented
53#16839906C2218yescomplemented
54#16839897C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519701C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic, complemented
61C2×#14519698C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519689C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2218yescomplemented
69C22×SD16×C61C2211yescharacteristic, complemented
70C23×C8×C61C2211yescharacteristic, complemented
71C2×C22⋊Q8×C61C2211yescharacteristic, complemented
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C24×D61D411yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—42no—
81C2×#11758226—42no—
82C2×#11758226C2314yescomplemented
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C2×D4×D61—28no—
93C2×D4×D61—22no—
94C2×D4×D61—42no—
95C2×D4×D61—42no—
96C2×D4×D61—48no—
97C2×D4×D61C2314yes—
98C23×Dic61D411yescharacteristic
99C22×C4×D61—21no—
100C22×C4×D61—21no—
101C22×C4×D61—42no—
102C22×C4×D61—42no—
103C22×C4×D61D411yescharacteristic
104C22×C4×D61D414yes—
105C22×C4×D61D411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2314yes—
109C2×#11758201—42no—
110C2×#11758201C2314yescomplemented
111C2×D488—42no—
112C2×D488C2314yescomplemented
113C2×#11758199—42no—
114C2×#11758199C2314yescomplemented
115C22×#92418—42no—
116C22×#92418C2311yescharacteristic
117C22×#92418C2311yescharacteristic
118C22×#92418C2314yescomplemented
119#14519762—28no—
120#14519753—22no—
121#14519753C2314yes—
122#14519752—22no—
123#14519752—22no—
124#14519752C2314yes—
125#14519752C2314yes—
126#14519751—22no—
127#14519751—22no—
128#14519751C2314yes—
129#14519751C2314yescomplemented
130#14519750—28no—
131#14519749—28no—
132#14519748—22no—
133#14519748C2314yes—
134#14519747—28no—
135#14519739—28no—
136#14519737—28no—
137#14519735—22no—
138#14519735C2314yescomplemented
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61C2314yes—
145C2×C22⋊Dic61—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C22⋊C4×D61—28no—
153C2×C4×Dic61—21no—
154#14519711C2314yescomplemented
155#14519710C2314yescomplemented
156#14519708C2314yescomplemented
157#14519701C2314yescomplemented
158#14519699C2314yescomplemented
159#14519699C2314yescomplemented
160#14519698C2314yescomplemented
161#14519697C2314yescomplemented
162#14519697C2314yescomplemented
163#14519689C2314yes—
164#14519689C2314yes—
165#14519689C2314yescomplemented
166#14519689C2314yescomplemented
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yescomplemented
173C22×C8×C61—42no—
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2314yescomplemented
177C22⋊Q8×C61—22no—
178C22⋊Q8×C61C2314yescomplemented
179#121×C61—22no—
180#121×C61C2314yes—
181C2×C4⋊C4×C61—21no—
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186#106×C61C2314yescomplemented
187#103×C61C2314yescomplemented
188#102×C61C2314yescomplemented
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—24no—
192C23×D61—24no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—24no—
196C23×D61—42no—
197C23×D61—44no—
198C23×D61—44no—
199C23×D61—44no—
200C23×D61C2×D411yescharacteristic
201C23×D61C2×D414yes—
202C23×D61C2×D411yescharacteristic
203C2×Q8×C61—21no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61C2412yes—
207C2×D4×C61—24no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—44no—
212C2×D4×C61C2412yes—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
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—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—42no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D414yes—
236#11758226—44no—
237#11758226—44no—
238#11758226—48no—
239D4×D61—44no—
240D4×D61—44no—
241D4×D61—48no—
242D4×D61—432no—
243C2×D244—22no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—22no—
247C2×D244—24no—
248C2×D244—24no—
249C2×D244—24no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—44no—
253C2×D244—44no—
254C2×D244—44no—
255C2×D244C2412yes—
256C2×D244C2412yes—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—24no—
262C2×C4×D61—24no—
263C2×C4×D61—48no—
264C2×C4×D61—44no—
265C2×C4×D61—44no—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—44no—
269C2×C4×D61—44no—
270C2×C4×D61C2×D412yes—
271C2×C4×D61C2×D412yes—
272C2×C4×D61C2×D414yes—
273C2×C4×D61C2×D414yes—
274C2×C4×D61C2412yes—
275C2×C4×D61C2412yes—
276SD16×C61—44no—
277C2×C8×C61—22no—
278C2×C8×C61—22no—
279C2×C8×C61—44no—
280C2×C8×C61C2412yes—
281C2×C8×C61C2412yes—
282C4⋊C4×C61—24no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C2412yes—
286C4⋊C4×C61C2412yes—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—24no—
289C22⋊Dic61—24no—
290#11758201—44no—
291#11758199—44no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295#11758198—24no—
296#11758198—24no—
297#11758198—24no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61C2412yes—
301C4⋊Dic61C2412yes—
302#11758196—24no—
303#11758196—24no—
304C4×Dic61—24no—
305C2×#92418—22no—
306C2×#92418—22no—
307C2×#92418—44no—
308C2×#92418C2412yes—
309C2×#92418C2412yes—
310D488—44no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61AGL(1,ℤ/8)14yes—
318C23×C61C22×D412yes—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—28no—
326C22×D61—28no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—44no—
330C22×D61—416no—
331C22×D61—48no—
332C22×D61—48no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—48no—
340C22×D61—816no—
341C22×D61#13514yes—
342C22×D61C22×D412yes—
343C22×D61C22×D412yes—
344Q8×C61—22no—
345Q8×C61—22no—
346Q8×C61—42no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—48no—
350D4×C61—42no—
351C2×C4×C61—22no—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61H(5,𝔽2)12yes—
364C2×C4×C61H(5,𝔽2)12yes—
365C2×C4×C61C2511yescharacteristic
366C22⋊D61—48no—
367C22⋊D61—48no—
368C22⋊D61—48no—
369C22⋊D61—48no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—44no—
375C2×Dic61—42no—
376C2×Dic61—42no—
377C2×Dic61C22×D412yes—
378C2×Dic61C22×D412yes—
379D244—22no—
380D244—22no—
381D244—22no—
382D244—22no—
383D244—48no—
384D244—48no—
385D244—48no—
386D244—42no—
387D244—42no—
388C4×D61—24no—
389C4×D61—24no—
390C4×D61—22no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—44no—
395C4×D61—44no—
396C4×D61—48no—
397C4×D61—48no—
398C8×C61—22no—
399C8×C61—22no—
400#92418—22no—
401#92418—22no—
402C2×#3188—611nomaximal, Sylow
403C22×C61—28no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—84no—
410C22×C61#53412yes—
411C22×C61C2×#13512yes—
412C22×C61C2×AGL(1,ℤ/8)14yes—
413C22×C61C2×AGL(1,ℤ/8)12yes—
414C22×C61C23×D411yescharacteristic
415C2×D61—28no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—416no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—816no—
430C2×D61—84no—
431C2×D61—84no—
432C2×D61C2×#13514yes—
433C4×C61—22no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61#53412yes—
438C4×C61C2×H(5,𝔽2)11yescharacteristic
439C4×C61C2×H(5,𝔽2)11yescharacteristic
440Dic61—22no—
441Dic61—22no—
442Dic61—42no—
443Dic61—42no—
444C2×#525—611no—
445C22×#121—611no—
446#3188—6116no—
447C2×#484—611no—
448C2×#481—611no—
449C2×#482—611no—
450C2×#482—611no—
451C2×#466—611no—
452C2×#466—611no—
453C2×#465—611no—
454C2×#465D6111yescharacteristic, complemented
455C2×#449—611no—
456C2×#449—611no—
457C2×#450—611no—
458C2×#447—611no—
459C22×C22⋊C8—611no—
460C2×C61—24no—
461C2×C61—82no—
462C2×C61#318814yescomplemented
463C2×C61C2×#53411yescharacteristic
464C2×C61C22×#13511yescharacteristic
465C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
466D61—24no—
467D61—42no—
468D61—82no—
469D61—82no—
470C22×#41—611no—
471C23×D4—611no—
472C23×D4—1221no—
473C24×C4—611no—
474C22×SD16—611no—
475C22×SD16C2×D6111yescharacteristic, complemented
476C22×D8—611no—
477C22×D8—611no—
478C23×C8—611no—
479C23×C8C2×D6111yescharacteristic, complemented
480#525—618no—
481#525—1224no—
482C2×#123—1221no—
483C2×C22⋊Q8—611no—
484C2×C22⋊Q8C2×D6111yescharacteristic, complemented
485C2×#121—611no—
486C2×#121—611no—
487C2×#121—611no—
488C2×#121—618no—
489C2×#121—611no—
490C2×#121—611no—
491C2×#121—1221no—
492C2×#121—1224no—
493C2×#121—1221no—
494C2×#121C2×D6111yescharacteristic
495C2×#120—1221no—
496C2×C4×D4—1221no—
497C2×C4×D4—1221no—
498C2×#117—611no—
499C22×C4⋊C4—611no—
500C22×C22⋊C4—1221no—
501#484—618no—
502#482—618no—
503#482—618no—
504#481—618no—
505#466—618no—
506#466—618no—
507#465—618no—
508#465C2×D6118yescomplemented
509#450—618no—
510#449—618no—
511#449—618no—
512#447—618no—
513C2×#107—611no—
514C2×#107—611no—
515C2×#106—611no—
516C2×#106C2×D6111yescharacteristic, complemented
517C2×#103—611no—
518C2×#103C2×D6111yescharacteristic, complemented
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102C2×D6111yescharacteristic, complemented
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—618no—
530C61C2×#318811yescharacteristic, complemented, Sylow
531C25—611no—
532C25—1221no—
533C2×#41—614no—
534C2×#41—1222no—
535C2×#41—2442no—
536C2×#41—2442no—
537C22×Q8C22×D6111yescharacteristic
538C22×D4—21no—
539C22×D4—614no—
540C22×D4—611no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1222no—
546C22×D4—1221no—
547C22×D4—1228no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4—1221no—
551C22×D4—2442no—
552C22×D4—2442no—
553C22×D4—2448no—
554C22×D4C22×D6111yescharacteristic
555C23×C4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—614no—
561C23×C4—614no—
562C23×C4—1221no—
563C23×C4—1221no—
564C23×C4—2442no—
565C23×C4—2442no—
566C23×C4C22×D6111yescharacteristic
567C2×SD16—42no—
568C2×SD16—614no—
569C2×SD16—2442no—
570C2×SD16C22×D6114yescomplemented
571C2×D8—614no—
572C2×D8—614no—
573C2×D8—2442no—
574C2×D8—2442no—
575C22×C8—42no—
576C22×C8—611no—
577C22×C8—611no—
578C22×C8—614no—
579C22×C8—2442no—
580C22×C8C22×D6111yescharacteristic
581C22×C8C22×D6111yescharacteristic
582C22×C8C22×D6114yescomplemented
583#123—1228no—
584C22⋊Q8—22no—
585C22⋊Q8—614no—
586C22⋊Q8—1222no—
587C22⋊Q8C22×D6114yescomplemented
588#121—22no—
589#121—614no—
590#121—614no—
591#121—614no—
592#121—614no—
593#121—614no—
594#121—1228no—
595#121—1222no—
596#121—1222no—
597#121—1222no—
598#121—1228no—
599#121—1222no—
600#121—1222no—
601#121C22×D6114yes—
602#120—1228no—
603C4×D4—1228no—
604C4×D4—1228no—
605#117—614no—
606#117—1222no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—614no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C4⋊C4C22×D6111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—1228no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C42—1221no—
627#107—614no—
628#107—614no—
629#106—614no—
630#106C22×D6114yescomplemented
631#103—614no—
632#103C22×D6114yescomplemented
633#102—614no—
634#102—614no—
635#102—614no—
636#102—614no—
637#102—614no—
638#102C22×D6114yescomplemented
639C22⋊C8—614no—
640C22⋊C8—614no—
641C22⋊C8—614no—
642C22⋊C8—614no—
643C24—21no—
644C24—611no—
645C24—611no—
646C24—614no—
647C24—1224no—
648C24—1224no—
649C24—1224no—
650C24—1221no—
651C24—1221no—
652C24—2442no—
653C24—2444no—
654C24—2444no—
655C24—2444no—
656C24D4×D6111yescharacteristic
657#41—2444no—
658#41—2444no—
659#41—2448no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8C23×D6112yes—
664C2×D4—24no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—612no—
670C2×D4—612no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1224no—
677C2×D4—1224no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1222no—
683C2×D4—1222no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4—2444no—
689C2×D4—2448no—
690C2×D4—2444no—
691C2×D4—24432no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4C23×D6112yes—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—614no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—614no—
709C22×C4—614no—
710C22×C4—1224no—
711C22×C4—1224no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1222no—
715C22×C4—1222no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—2448no—
719C22×C4—2444no—
720C22×C4—2444no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4—2444no—
724C22×C4—2444no—
725C22×C4—2442no—
726C22×C4D4×D6112yes—
727C22×C4D4×D6111yescharacteristic
728C22×C4C23×D6112yes—
729C22×C4C23×D6111yescharacteristic
730SD16—44no—
731SD16—2444no—
732D8—2444no—
733D8—2444no—
734C2×C8—22no—
735C2×C8—22no—
736C2×C8—44no—
737C2×C8—612no—
738C2×C8—612no—
739C2×C8—1222no—
740C2×C8—1222no—
741C2×C8—2444no—
742C2×C8C23×D6112yes—
743C2×C8C23×D6112yes—
744C4⋊C4—24no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—612no—
748C4⋊C4—612no—
749C4⋊C4—1224no—
750C4⋊C4—1224no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4C23×D6112yes—
754C4⋊C4C23×D6112yes—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C22⋊C4—1224no—
761C22⋊C4—1224no—
762C22⋊C4—1224no—
763C22⋊C4—1224no—
764C42—1224no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—614no—
772C23—612no—
773C23—612no—
774C23—1228no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1228no—
779C23—1222no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—48816no—
784C23—2444no—
785C23—24416no—
786C23—2448no—
787C23—2448no—
788C23—2448no—
789C23—2442no—
790C23—2442no—
791C23—2442no—
792C23—2442no—
793C23—2442no—
794C23—2442no—
795C23#1451980414yes—
796C23C2×D4×D6112yes—
797C23C2×D4×D6111yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—42no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—1222no—
806D4—1222no—
807D4—1222no—
808D4—1222no—
809D4—2448no—
810D4—2448no—
811D4—2448no—
812D4—2448no—
813D4—2448no—
814D4—2448no—
815D4—2448no—
816D4—2442no—
817D4—2442no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1224no—
833C2×C4—1224no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—2444no—
841C2×C4—2444no—
842C2×C4—2448no—
843C2×C4—2448no—
844C2×C4—2444no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4C2×D4×D6112yes—
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4#1451982212yes—
850C2×C4#1451982312yes—
851C2×C4C24×D6111yescharacteristic
852C8—22no—
853C8—22no—
854C8—1222no—
855C8—1222no—
856C22—22no—
857C22—22no—
858C22—28no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—84no—
863C22—614no—
864C22—1222no—
865C22—1222no—
866C22—1228no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—48816no—
871C22—4884no—
872C22—4884no—
873C22—24416no—
874C22—2442no—
875C22—2442no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22—2442no—
880C22—2444no—
881C22#1684032012yes—
882C22#135×D6112yes—
883C22C2×#1451980414yes—
884C22C2×#1451980412yes—
885C22C22×D4×D6111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—1222no—
891C4—1222no—
892C4—2442no—
893C4—2442no—
894C4#1684032012yes—
895C4C2×#1451982211yescharacteristic
896C4C2×#1451982311yescharacteristic
897C2—24no—
898C2—82no—
899C2—1224no—
900C2—4882no—
901C2—4882no—
902C2—2442no—
903C2#2145658514yesdirect product factor
904C2C2×#1684032011yescharacteristic
905C2C2×#135×D6111yescharacteristic
906C2C22×#1451980411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
hypercenterC2×#465D61
hypocenterC61C2×#3188
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840275C2semidirect
2. C2×#121×D61C2semidirect
3. #21456585C2direct (N × H)
4. C2×#16840096C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840088C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16839998C2semidirect
9. C2×#16839996C2semidirect
10. C2×#16839993C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839906C2semidirect
13. C2×#16839911C2semidirect
14. C2×#16839897C2semidirect
15. C22×#14519689C2semidirect
16. C2×C61×#465C2semidirect
17. C22×#11758226C22semidirect
21. C22×#11758201C22semidirect
22. C22×D488C22semidirect
23. C22×#11758199C22semidirect
24. C23×#92418C22semidirect
26. #16840275C22semidirect
32. C2×#14519751C22semidirect
37. #121×D61C22semidirect
41. C2×#14519735C22semidirect
44. #16840096C22semidirect
45. #16840088C22semidirect
46. #16840084C22semidirect
47. #16840082C22semidirect
48. #16839998C22semidirect
49. #16839996C22semidirect
50. #16839993C22semidirect
51. #16839911C22semidirect
52. #16839910C22semidirect
53. #16839906C22semidirect
54. #16839897C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519701C22semidirect
59. C2×#14519699C22semidirect
60. C2×#14519699C22semidirect
61. C2×#14519698C22semidirect
62. C2×#14519697C22semidirect
63. C2×#14519697C22semidirect
66. C2×#14519689C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
69. C22×SD16×C61C22semidirect
70. C23×C8×C61C22semidirect
71. C2×C22⋊Q8×C61C22semidirect
73. C61×#465C22semidirect
74. C2×#106×C61C22semidirect
75. C2×#103×C61C22semidirect
76. C2×#102×C61C22semidirect
82. C2×#11758226C23semidirect
110. C2×#11758201C23semidirect
112. C2×D488C23semidirect
114. C2×#11758199C23semidirect
118. C22×#92418C23semidirect
129. #14519751C23semidirect
138. #14519735C23semidirect
154. #14519711C23semidirect
155. #14519710C23semidirect
156. #14519708C23semidirect
157. #14519701C23semidirect
158. #14519699C23semidirect
159. #14519699C23semidirect
160. #14519698C23semidirect
161. #14519697C23semidirect
162. #14519697C23semidirect
165. #14519689C23semidirect
166. #14519689C23semidirect
172. C2×SD16×C61C23semidirect
176. C22×C8×C61C23semidirect
178. C22⋊Q8×C61C23semidirect
186. #106×C61C23semidirect
187. #103×C61C23semidirect
188. #102×C61C23semidirect
454. C2×#465D61semidirect
462. C2×C61#3188semidirect
475. C22×SD16C2×D61semidirect
479. C23×C8C2×D61semidirect
484. C2×C22⋊Q8C2×D61semidirect
508. #465C2×D61semidirect
516. C2×#106C2×D61semidirect
518. C2×#103C2×D61semidirect
524. C2×#102C2×D61semidirect
530. C61C2×#3188semidirect
570. C2×SD16C22×D61semidirect
582. C22×C8C22×D61semidirect
587. C22⋊Q8C22×D61semidirect
630. #106C22×D61semidirect
632. #103C22×D61semidirect
638. #102C22×D61semidirect
903. C2#21456585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×#121×D612
#214565852
C2×#168400962
C2×#168400822
C2×#168400882
C2×#168400842
C2×#168399982
C2×#168399962
C2×#168399932
C2×#168399102
C2×#168399062
C2×#168399112
C2×#168398972
C22×#145196892
C2×C61×#4652
C2×#318861