Finite Group Databasebeta

← C2×#21448523 #29838792

Subgroups — C2×#21448523 #29838792

Order 15616.

4150 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
1C22×#14519750C211yesmaximal, characteristic
2C22×C4×D244C211yesmaximal, characteristic, complemented
3C22×#14519737C211yesmaximal, characteristic, complemented
4#21448523C2116yesmaximal, direct product factor
5C2×#16839652C211yesmaximal, characteristic, complemented
6C2×#16839649C211yesmaximal, characteristic, complemented
7C2×#16839646C211yesmaximal, characteristic, complemented
8C2×#16839640C211yesmaximal, characteristic, complemented
9C2×#16839639C211yesmaximal, characteristic, complemented
10C2×#16839638C211yesmaximal, characteristic, complemented
11C2×#16839638C211yesmaximal, characteristic, complemented
12C2×#16839637C211yesmaximal, characteristic, complemented
13C2×#16839636C211yesmaximal, characteristic, complemented
14C2×#16839619C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C22⋊D61C2211yescharacteristic
20C24×Dic61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C23×C4×D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25C2×#14519750C4116yescomplemented
26C2×#14519750C2218yes—
27C2×C4×D244—28no—
28C2×C4×D244C2218yescomplemented
29C2×#14519737—28no—
30C2×#14519737C2218yescomplemented
31C22×C4⋊Dic61C2211yescharacteristic
32C22×C4⋊Dic61C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839652C2218yescomplemented
44#16839649C2218yescomplemented
45#16839646C2218yescomplemented
46#16839640C2218yescomplemented
47#16839639C2218yescomplemented
48#16839638C2218yescomplemented
49#16839638C2218yescomplemented
50#16839637C2218yescomplemented
51#16839636C2218yescomplemented
52#16839619C2218yescomplemented
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61#95×D61C2218yescomplemented
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C61×#388C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C24×D61C2311yescharacteristic
72C22×D244—24no—
73C22×D244—24no—
74C22×D244C2×C418yescomplemented
75C22×D244C2314yes—
76C22×C22⋊D61—24no—
77C22×C22⋊D61—24no—
78C22×C22⋊D61—42no—
79C22×C22⋊D61—42no—
80C22×C22⋊D61C2×C418yescomplemented
81C22×C22⋊D61C2×C418yescomplemented
82C22×C22⋊D61C2314yes—
83C22×C22⋊D61C2314yes—
84C23×Dic61—24no—
85C23×Dic61—42no—
86C23×Dic61—42no—
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93C23×Dic61C2314yes—
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—42no—
97C22×C4×D61—42no—
98C22×C4×D61—42no—
99C22×C4×D61—42no—
100C22×C4×D61—42no—
101C22×C4×D61—42no—
102C22×C4×D61—42no—
103C22×C4×D61—42no—
104C22×C4×D61C2×C418yescomplemented
105C22×C4×D61D418yescomplemented
106C22×C4×D61C2314yes—
107C22×C4×D61C2314yes—
108C22×C4×D61C2314yes—
109C22×C4×D61C2314yes—
110#14519750C2×C4164yescomplemented
111C4×D244—232no—
112#14519737—232no—
113C2×C4⋊Dic61—24no—
114C2×C4⋊Dic61—42no—
115C2×C4⋊Dic61C2314yes—
116C2×C4⋊Dic61C2314yes—
117C2×#11758196—24no—
118C2×#11758196C2×C418yescomplemented
119C2×#11758196C2314yes—
120C2×#11758196C2314yes—
121C2×C22⋊Dic61—42no—
122C2×C22⋊Dic61C2314yes—
123C2×#11758198—24no—
124C2×#11758198—24no—
125C2×#11758198—24no—
126C2×#11758198—42no—
127C2×#11758198—42no—
128C2×#11758198C2×C418yescomplemented
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×C4×Dic61—24no—
136C2×C4×Dic61C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145C25×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61—42no—
153C2×C4⋊C4×C61C2314yes—
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61—42no—
156C2×C22⋊C4×C61C2×C418yescomplemented
157C2×C22⋊C4×C61C2314yes—
158C2×C22⋊C4×C61C2314yes—
159C2×C22⋊C4×C61C2314yes—
160C2×C42×C61—24no—
161C2×C42×C61C2314yes—
162#95×C61C2314yes—
163#95×C61C2314yes—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61C22×C414yes—
171C24×C61C2412yes—
172C24×C61C2411yescharacteristic
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C23×D61—22no—
180C23×D61—22no—
181C23×D61—22no—
182C23×D61—22no—
183C23×D61C22×C414yes—
184C23×D61C22×C414yes—
185C23×D61C2×D414yes—
186C23×D61#4114yes—
187C23×D61C2412yes—
188C23×D61C2412yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61C22×C414yes—
205C22×C4×C61C22×C414yes—
206C22×C4×C61C2×D414yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C2×C22⋊D61—232no—
214C2×C22⋊D61—28no—
215C2×C22⋊D61—28no—
216C2×C22⋊D61—416no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—44no—
219C2×C22⋊D61C22×C4116yescomplemented
220C2×C22⋊D61C22×C4116yescomplemented
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—28no—
237C22×Dic61—44no—
238C22×Dic61—44no—
239C22×Dic61—416no—
240C22×Dic61C22×C414yes—
241C22×Dic61C22×C414yes—
242C22×Dic61C2×D414yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C22×Dic61C2412yes—
248C22×Dic61C2412yes—
249C2×D244—232no—
250C2×D244—28no—
251C2×D244—28no—
252C2×D244C22×C4116yescomplemented
253C2×C4×D61—28no—
254C2×C4×D61—28no—
255C2×C4×D61—416no—
256C2×C4×D61—416no—
257C2×C4×D61—44no—
258C2×C4×D61—44no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61—44no—
263C2×C4×D61—44no—
264C2×C4×D61—44no—
265C2×C4×D61—416no—
266C2×C4×D61—416no—
267C2×C4×D61C22×C4116yescomplemented
268C2×C4×D61C2×D4116yescomplemented
269C4⋊C4×C61—44no—
270C22⋊C4×C61—28no—
271C22⋊C4×C61—44no—
272C22⋊C4×C61C22×C4116yescomplemented
273C42×C61—28no—
274C22⋊Dic61—44no—
275#11758198—28no—
276#11758198—28no—
277#11758198—28no—
278#11758198—44no—
279#11758198—44no—
280#11758198C22×C4116yescomplemented
281C4⋊Dic61—28no—
282C4⋊Dic61—44no—
283#11758196—28no—
284#11758196C22×C4116yescomplemented
285C4×Dic61—28no—
286C23×C61—28no—
287C23×C61—28no—
288C23×C61—28no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—44no—
296C23×C61—44no—
297C23×C61—44no—
298C23×C61—44no—
299C23×C61C23×C414yes—
300C23×C61C23×C412yes—
301C23×C61C22×D412yes—
302C23×C61C2×#4112yes—
303C23×C61H(5,𝔽2)12yes—
304C23×C61H(5,𝔽2)12yes—
305C23×C61H(5,𝔽2)12yes—
306C23×C612−1+412yes—
307C23×C61C2511yescharacteristic
308C22×D61—28no—
309C22×D61—28no—
310C22×D61—28no—
311C22×D61—28no—
312C22×D61—28no—
313C22×D61—28no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—28no—
319C22×D61—28no—
320C22×D61—28no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—44no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61—44no—
331C22×D61C4×D4116yes—
332C22×D61C23×C414yes—
333C22×D61C23×C414yes—
334C22×D61C22×D414yes—
335C22×D61C2×#4114yes—
336C2×C4×C61—28no—
337C2×C4×C61—28no—
338C2×C4×C61—28no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
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—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—44no—
355C2×C4×C61—44no—
356C2×C4×C61—44no—
357C2×C4×C61C23×C414yes—
358C2×C4×C61C23×C414yes—
359C2×C4×C61C22×D414yes—
360C22⋊D61—232no—
361C22⋊D61—416no—
362C2×Dic61—28no—
363C2×Dic61—28no—
364C2×Dic61—28no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—416no—
381C2×Dic61—44no—
382C2×Dic61—44no—
383C2×Dic61—44no—
384C2×Dic61C23×C414yes—
385C2×Dic61C23×C414yes—
386C2×Dic61C22×D414yes—
387D244—232no—
388C4×D61—416no—
389C4×D61—416no—
390C4×D61—416no—
391C4×D61—416no—
392C2×#2325—611nomaximal, Sylow
393C22×C61—24no—
394C22×C61—24no—
395C22×C61—24no—
396C22×C61—416no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61C2×C4×D414yes—
402C22×C61#51814yes—
403C22×C61#52014yes—
404C22×C61#53414yes—
405C22×C61#53714yes—
406C22×C61#53814yes—
407C22×C61#53914yes—
408C22×C61C24×C411yescharacteristic
409C22×C61C23×D411yescharacteristic
410C22×C61C22×#4111yescharacteristic
411C22×C61C2×H(5,𝔽2)11yescharacteristic
412C22×C61C2×H(5,𝔽2)11yescharacteristic
413C22×C61C2×H(5,𝔽2)11yescharacteristic
414C22×C61C2×2−1+411yescharacteristic
415C2×D61—232no—
416C2×D61—24no—
417C2×D61—24no—
418C2×D61—24no—
419C2×D61—24no—
420C2×D61—24no—
421C2×D61—24no—
422C2×D61—24no—
423C2×D61—24no—
424C2×D61—24no—
425C2×D61—416no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61C2×C4×D418yes—
431C4×C61—24no—
432C4×C61—24no—
433C4×C61—24no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61—42no—
437Dic61—24no—
438Dic61—24no—
439Dic61—24no—
440Dic61—42no—
441Dic61—42no—
442Dic61—42no—
443C22×#121—611no—
444C22×C4×D4—611no—
445C22×C4×D4—611no—
446#2325—6116no—
447C2×#388—611no—
448C2×#388D6111yescharacteristic, complemented
449C2×#387—611no—
450C2×#387—611no—
451C2×#386—611no—
452C2×#386—611no—
453C2×#386—611no—
454C2×#386—611no—
455C2×#385—611no—
456C2×#385—611no—
457C2×#380—611no—
458C22×#95—611no—
459C2×C61—44no—
460C2×C61#232518yescomplemented
461C2×C61C22×C4×D411yescharacteristic
462C2×C61C2×#51811yescharacteristic
463C2×C61C2×#52011yescharacteristic
464C2×C61C2×#53411yescharacteristic
465C2×C61C2×#53711yescharacteristic
466C2×C61C2×#53811yescharacteristic
467C2×C61C2×#53911yescharacteristic
468D61—28no—
469D61—44no—
470C23×D4—611no—
471C23×D4—611no—
472C23×D4—611no—
473C24×C4—611no—
474C24×C4—611no—
475C24×C4—611no—
476C24×C4—611no—
477C24×C4—611no—
478C2×#121—6116no—
479C2×#121—618no—
480C2×C4×D4—618no—
481C2×C4×D4—618no—
482C2×C4×D4—1228no—
483C2×C4×D4—1228no—
484C22×C4⋊C4—611no—
485C22×C4⋊C4—611no—
486C22×C4⋊C4—611no—
487C22×C4⋊C4—611no—
488C22×C4⋊C4C2×D6111yescharacteristic
489C22×C22⋊C4—611no—
490C22×C22⋊C4—611no—
491C22×C22⋊C4—611no—
492C22×C22⋊C4—611no—
493C22×C22⋊C4—611no—
494C22×C22⋊C4—611no—
495C22×C22⋊C4—611no—
496C22×C22⋊C4C2×D6111yescharacteristic
497C22×C22⋊C4C2×D6111yescharacteristic
498C22×C22⋊C4C2×D6111yescharacteristic
499C22×C42—611no—
500C22×C42C2×D6111yescharacteristic
501#388—618no—
502#388C2×D6118yescomplemented
503#387—618no—
504#387—618no—
505#386—618no—
506#386—618no—
507#386—618no—
508#386—618no—
509#385—618no—
510#385—618no—
511#380—618no—
512C2×#95—611no—
513C2×#95—611no—
514C2×#95—611no—
515C2×#95—611no—
516C2×#95—611no—
517C2×#95—611no—
518C2×#95—611no—
519C2×#95—611no—
520C2×#95—618no—
521C2×#95C2×D6111yescharacteristic
522C2×#95C2×D6111yescharacteristic
523C61C2×#232511yescharacteristic, complemented, Sylow
524C25—611no—
525C25—611no—
526C25C22×D6111yescharacteristic
527C22×D4—618no—
528C22×D4—614no—
529C22×D4—618no—
530C22×D4—614no—
531C22×D4—618no—
532C22×D4—614no—
533C22×D4—1224no—
534C22×D4—1224no—
535C22×D4—1224no—
536C22×D4—1224no—
537C22×D4—2442no—
538C22×D4—2442no—
539C23×C4—611no—
540C23×C4—611no—
541C23×C4—611no—
542C23×C4—618no—
543C23×C4—618no—
544C23×C4—614no—
545C23×C4—614no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—614no—
550C23×C4—614no—
551C23×C4—614no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1224no—
555C23×C4—2442no—
556C23×C4—2442no—
557C23×C4—2442no—
558C23×C4—2442no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4—2442no—
562C23×C4—2442no—
563C23×C4—2442no—
564C23×C4—2442no—
565C23×C4C22×D6111yescharacteristic
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6111yescharacteristic
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571#121—6164no—
572C4×D4—12232no—
573C4×D4—12232no—
574C2×C4⋊C4—42no—
575C2×C4⋊C4—618no—
576C2×C4⋊C4—614no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—614no—
579C2×C4⋊C4—614no—
580C2×C4⋊C4—1224no—
581C2×C4⋊C4—1224no—
582C2×C4⋊C4—2442no—
583C2×C4⋊C4C22×D6114yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—618no—
587C2×C22⋊C4—614no—
588C2×C22⋊C4—614no—
589C2×C22⋊C4—614no—
590C2×C22⋊C4—614no—
591C2×C22⋊C4—614no—
592C2×C22⋊C4—614no—
593C2×C22⋊C4—614no—
594C2×C22⋊C4—1224no—
595C2×C22⋊C4—1224no—
596C2×C22⋊C4—1224no—
597C2×C22⋊C4—2442no—
598C2×C22⋊C4—2442no—
599C2×C22⋊C4—2442no—
600C2×C22⋊C4C4×D6118yescomplemented
601C2×C22⋊C4C22×D6114yes—
602C2×C22⋊C4C22×D6114yes—
603C2×C22⋊C4C22×D6114yes—
604C2×C42—24no—
605C2×C42—614no—
606C2×C42—1224no—
607C2×C42C22×D6114yes—
608#95—614no—
609#95—614no—
610#95—614no—
611#95—614no—
612#95—614no—
613#95—614no—
614#95—614no—
615#95—614no—
616#95C22×D6114yes—
617#95C22×D6114yes—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—614no—
625C24—614no—
626C24—614no—
627C24—612no—
628C24—614no—
629C24—612no—
630C24—1222no—
631C24—1222no—
632C24—1222no—
633C24—1222no—
634C24—1222no—
635C24—1222no—
636C24—1222no—
637C24—1222no—
638C24—1222no—
639C24—1222no—
640C24C2×C4×D6114yes—
641C24C23×D6112yes—
642C24C23×D6111yescharacteristic
643C2×D4—6116no—
644C2×D4—6116no—
645C2×D4—6116no—
646C2×D4—1228no—
647C2×D4—12232no—
648C2×D4—1228no—
649C2×D4—1228no—
650C2×D4—12232no—
651C2×D4—1228no—
652C2×D4—24416no—
653C2×D4—2444no—
654C2×D4—2444no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—614no—
671C22×C4—614no—
672C22×C4—614no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—6116no—
677C22×C4—6116no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—1228no—
682C22×C4—1228no—
683C22×C4—1222no—
684C22×C4—1222no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1222no—
693C22×C4—1222no—
694C22×C4—1222no—
695C22×C4—1222no—
696C22×C4—1222no—
697C22×C4—1222no—
698C22×C4—1228no—
699C22×C4—24416no—
700C22×C4—24416no—
701C22×C4—2444no—
702C22×C4—2444no—
703C22×C4—2444no—
704C22×C4—2444no—
705C22×C4—2444no—
706C22×C4—2444no—
707C22×C4—2444no—
708C22×C4—2444no—
709C22×C4—24416no—
710C22×C4—24416no—
711C22×C4—2444no—
712C22×C4—2444no—
713C22×C4—24416no—
714C22×C4C2×C4×D6114yes—
715C22×C4C2×C4×D6114yes—
716C22×C4D4×D6114yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6112yes—
719C22×C4C23×D6112yes—
720C22×C4C23×D6112yes—
721C22×C4C23×D6112yes—
722C22×C4C23×D6112yes—
723C4⋊C4—44no—
724C4⋊C4—6116no—
725C4⋊C4—1228no—
726C4⋊C4—1228no—
727C4⋊C4—2444no—
728C22⋊C4—28no—
729C22⋊C4—44no—
730C22⋊C4—6116no—
731C22⋊C4—1228no—
732C22⋊C4—1228no—
733C22⋊C4—1228no—
734C22⋊C4—2444no—
735C22⋊C4—2444no—
736C22⋊C4—2444no—
737C22⋊C4C2×C4×D61116yescomplemented
738C42—28no—
739C42—1228no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—6116no—
754C23—614no—
755C23—614no—
756C23—614no—
757C23—614no—
758C23—1228no—
759C23—1228no—
760C23—1228no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1228no—
766C23—1228no—
767C23—1228no—
768C23—1228no—
769C23—1228no—
770C23—1228no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—2444no—
778C23—2444no—
779C23—2444no—
780C23—2444no—
781C23C22×C4×D6114yes—
782C23C22×C4×D6112yes—
783C23C2×D4×D6112yes—
784C23#41×D6112yes—
785C23#1451982212yes—
786C23#1451982312yes—
787C23#1451982312yes—
788C23#1451982412yes—
789C23C24×D6111yescharacteristic
790D4—12232no—
791D4—12232no—
792D4—24416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—614no—
815C2×C4—614no—
816C2×C4—614no—
817C2×C4—1228no—
818C2×C4—1228no—
819C2×C4—1228no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—24416no—
836C2×C4—24416no—
837C2×C4—24416no—
838C2×C4—24416no—
839C2×C4—24416no—
840C2×C4—2444no—
841C2×C4—2444no—
842C2×C4—2444no—
843C2×C4C22×C4×D6114yes—
844C2×C4C22×C4×D6114yes—
845C2×C4C2×D4×D6114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—618no—
855C22—1224no—
856C22—1224no—
857C22—12232no—
858C22—1224no—
859C22—1224no—
860C22—1224no—
861C22—1224no—
862C22—1224no—
863C22—1224no—
864C22—1224no—
865C22—24416no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22C4×D4×D6114yes—
871C22#1684023414yes—
872C22#1684024214yes—
873C22#1684032314yes—
874C22#1684034114yes—
875C22#1684034614yes—
876C22#1684035314yes—
877C22C23×C4×D6111yescharacteristic
878C22C22×D4×D6111yescharacteristic
879C22C2×#41×D6111yescharacteristic
880C22C2×#1451982211yescharacteristic
881C22C2×#1451982311yescharacteristic
882C22C2×#1451982311yescharacteristic
883C22C2×#1451982411yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—1224no—
891C4—1224no—
892C4—1224no—
893C4—2442no—
894C4—2442no—
895C4—2442no—
896C2—44no—
897C2—1228no—
898C2—2444no—
899C2#2144852318yesdirect product factor
900C2C2×C4×D4×D6111yescharacteristic
901C2C2×#1684023411yescharacteristic
902C2C2×#1684024211yescharacteristic
903C2C2×#1684032311yescharacteristic
904C2C2×#1684034111yescharacteristic
905C2C2×#1684034611yescharacteristic
906C2C2×#1684035311yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC22×#14519750C2
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2325
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×D244C2semidirect
3. C22×#14519737C2semidirect
4. #21448523C2direct (N × H)
5. C2×#16839652C2semidirect
6. C2×#16839649C2semidirect
7. C2×#16839646C2semidirect
8. C2×#16839640C2semidirect
9. C2×#16839639C2semidirect
10. C2×#16839638C2semidirect
11. C2×#16839638C2semidirect
12. C2×#16839637C2semidirect
13. C2×#16839636C2semidirect
14. C2×#16839619C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#388C2semidirect
25. C2×#14519750C4semidirect
28. C2×C4×D244C22semidirect
30. C2×#14519737C22semidirect
43. #16839652C22semidirect
44. #16839649C22semidirect
45. #16839646C22semidirect
46. #16839640C22semidirect
47. #16839639C22semidirect
48. #16839638C22semidirect
49. #16839638C22semidirect
50. #16839637C22semidirect
51. #16839636C22semidirect
52. #16839619C22semidirect
61. #95×D61C22semidirect
67. C61×#388C22semidirect
74. C22×D244C2×C4semidirect
80. C22×C22⋊D61C2×C4semidirect
81. C22×C22⋊D61C2×C4semidirect
104. C22×C4×D61C2×C4semidirect
105. C22×C4×D61D4semidirect
110. #14519750C2×C4semidirect
118. C2×#11758196C2×C4semidirect
128. C2×#11758198C2×C4semidirect
156. C2×C22⋊C4×C61C2×C4semidirect
219. C2×C22⋊D61C22×C4semidirect
220. C2×C22⋊D61C22×C4semidirect
252. C2×D244C22×C4semidirect
267. C2×C4×D61C22×C4semidirect
268. C2×C4×D61C2×D4semidirect
272. C22⋊C4×C61C22×C4semidirect
280. #11758198C22×C4semidirect
284. #11758196C22×C4semidirect
448. C2×#388D61semidirect
460. C2×C61#2325semidirect
502. #388C2×D61semidirect
523. C61C2×#2325semidirect
600. C2×C22⋊C4C4×D61semidirect
737. C22⋊C4C2×C4×D61semidirect
899. C2#21448523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197502
C22×C4×D2442
C22×#145197372
#214485232
C2×#168396522
C2×#168396492
C2×#168396462
C2×#168396402
C2×#168396392
C2×#168396382
C2×#168396372
C2×#168396362
C2×#168396192
C2×#95×D612
C2×C61×#3882
C2×#232561