Finite Group Databasebeta

← C2×#21448518 #29838787

Subgroups — C2×#21448518 #29838787

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×#14519752C211yesmaximal, characteristic
2C22×C4×D244C211yesmaximal, characteristic, complemented
3C22×#14519739C211yesmaximal, characteristic, complemented
4#21448518C2116yesmaximal, direct product factor
5C2×#16839653C211yesmaximal, characteristic, complemented
6C2×#16839651C211yesmaximal, characteristic, complemented
7C2×#16839648C211yesmaximal, characteristic, complemented
8C2×#16839640C211yesmaximal, characteristic, complemented
9C2×#16839640C211yesmaximal, characteristic, complemented
10C2×#16839640C211yesmaximal, characteristic, complemented
11C2×#16839640C211yesmaximal, characteristic, complemented
12C2×#16839636C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×D244C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C23×C4×D61C2211yescharacteristic
24C23×C4×D61C2211yescharacteristic
25C2×#14519752C4116yescomplemented
26C2×#14519752C2218yes—
27C2×C4×D244—28no—
28C2×C4×D244C2218yescomplemented
29C2×#14519739—28no—
30C2×#14519739C2218yescomplemented
31C22×C4⋊Dic61C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839653C2218yescomplemented
46#16839651C2218yescomplemented
47#16839648C2218yescomplemented
48#16839640C2218yescomplemented
49#16839640C2218yescomplemented
50#16839640C2218yescomplemented
51#16839640C2218yescomplemented
52#16839636C2218yescomplemented
53#16839633C2218yescomplemented
54#16839621C2218yescomplemented
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61#95×D61C2218yescomplemented
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C61×#387C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C24×D61C2311yescharacteristic
71C24×D61C2311yescharacteristic
72C24×D61C2311yescharacteristic
73C22×D244—24no—
74C22×D244—24no—
75C22×D244—24no—
76C22×D244—24no—
77C22×D244—42no—
78C22×D244—42no—
79C22×D244C2×C418yescomplemented
80C22×D244C2×C418yescomplemented
81C22×D244C2×C418yescomplemented
82C22×D244C2314yes—
83C22×D244C2314yes—
84C22×D244C2314yes—
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—42no—
94C22×C4×D61—42no—
95C22×C4×D61—42no—
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×D61C2×C418yescomplemented
104C22×C4×D61D418yescomplemented
105C22×C4×D61C2314yes—
106C22×C4×D61C2314yes—
107C22×C4×D61C2314yes—
108C22×C4×D61C2314yes—
109C22×C4×D61C2314yes—
110#14519752C2×C4164yescomplemented
111C4×D244—232no—
112#14519739—232no—
113C2×C4⋊Dic61—24no—
114C2×C4⋊Dic61C2314yes—
115C2×#11758196—42no—
116C2×#11758196—42no—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×#11758198—24no—
120C2×#11758198—24no—
121C2×#11758198—24no—
122C2×#11758198—24no—
123C2×#11758198—42no—
124C2×#11758198—42no—
125C2×#11758198—42no—
126C2×#11758198—42no—
127C2×#11758198C2×C418yescomplemented
128C2×#11758198C2×C418yescomplemented
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137C2×#11758198C2314yes—
138C2×#11758198C2314yes—
139C2×C4×Dic61—24no—
140C2×C4×Dic61C2314yes—
141#14519684C2314yes—
142#14519684C2314yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61—24no—
155C2×C4⋊C4×C61C2×C418yescomplemented
156C2×C4⋊C4×C61C2314yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C42×C61—24no—
159C2×C42×C61C2314yes—
160#95×C61C2314yes—
161#95×C61C2314yes—
162#95×C61C2314yes—
163#95×C61C2314yes—
164C24×C61C2411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
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×D61C22×C414yes—
182C23×D61C22×C414yes—
183C23×D61C22×C414yes—
184C23×D61C2×D414yes—
185C23×D61#4114yes—
186C23×D61C2412yes—
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×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61C22×C414yes—
207C22×C4×C61C22×C414yes—
208C22×C4×C61C22×C414yes—
209C22×C4×C61C2×D414yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2412yes—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
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×Dic61C22×C414yes—
231C22×Dic61C2×D414yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C2×D244—232no—
238C2×D244—232no—
239C2×D244—28no—
240C2×D244—28no—
241C2×D244—28no—
242C2×D244—28no—
243C2×D244—416no—
244C2×D244—44no—
245C2×D244—44no—
246C2×D244C22×C4116yescomplemented
247C2×D244C22×C4116yescomplemented
248C2×D244C22×C4116yescomplemented
249C2×C4×D61—28no—
250C2×C4×D61—28no—
251C2×C4×D61—28no—
252C2×C4×D61—416no—
253C2×C4×D61—416no—
254C2×C4×D61—44no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
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—416no—
265C2×C4×D61—416no—
266C2×C4×D61—416no—
267C2×C4×D61C22×C4116yescomplemented
268C2×C4×D61C2×D4116yescomplemented
269C4⋊C4×C61—28no—
270C4⋊C4×C61C22×C4116yescomplemented
271C42×C61—28no—
272#11758198—28no—
273#11758198—28no—
274#11758198—28no—
275#11758198—28no—
276#11758198—44no—
277#11758198—44no—
278#11758198—44no—
279#11758198—44no—
280#11758198C22×C4116yescomplemented
281#11758198C22×C4116yescomplemented
282C4⋊Dic61—28no—
283#11758196—44no—
284#11758196—44no—
285C4×Dic61—28no—
286C23×C61C23×C412yes—
287C23×C61C22×D412yes—
288C23×C61C2×#4112yes—
289C23×C61H(5,𝔽2)12yes—
290C23×C61H(5,𝔽2)12yes—
291C23×C61H(5,𝔽2)12yes—
292C23×C612−1+412yes—
293C23×C61C2511yescharacteristic
294C22×D61—28no—
295C22×D61—28no—
296C22×D61—28no—
297C22×D61—28no—
298C22×D61—28no—
299C22×D61—28no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—28no—
305C22×D61—28no—
306C22×D61—28no—
307C22×D61—28no—
308C22×D61—28no—
309C22×D61—28no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—44no—
323C22×D61—44no—
324C22×D61—44no—
325C22×D61—44no—
326C22×D61—44no—
327C22×D61—44no—
328C22×D61—44no—
329C22×D61—44no—
330C22×D61C4×D4116yes—
331C22×D61C23×C414yes—
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—28no—
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—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—44no—
358C2×C4×C61—44no—
359C2×C4×C61—44no—
360C2×C4×C61C23×C414yes—
361C2×C4×C61C23×C414yes—
362C2×C4×C61C23×C414yes—
363C2×C4×C61C22×D414yes—
364C2×Dic61—28no—
365C2×Dic61—28no—
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—44no—
380C2×Dic61—44no—
381C2×Dic61—44no—
382C2×Dic61C23×C414yes—
383C2×Dic61C22×D414yes—
384D244—232no—
385D244—232no—
386D244—416no—
387C4×D61—416no—
388C4×D61—416no—
389C4×D61—416no—
390C4×D61—416no—
391C4×D61—416no—
392C2×#2325—611nomaximal, Sylow
393C22×C61C2×C4×D414yes—
394C22×C61#51814yes—
395C22×C61#52014yes—
396C22×C61#53414yes—
397C22×C61#53714yes—
398C22×C61#53814yes—
399C22×C61#53914yes—
400C22×C61C24×C411yescharacteristic
401C22×C61C23×D411yescharacteristic
402C22×C61C22×#4111yescharacteristic
403C22×C61C2×H(5,𝔽2)11yescharacteristic
404C22×C61C2×H(5,𝔽2)11yescharacteristic
405C22×C61C2×H(5,𝔽2)11yescharacteristic
406C22×C61C2×2−1+411yescharacteristic
407C2×D61—232no—
408C2×D61—24no—
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—24no—
413C2×D61—24no—
414C2×D61—24no—
415C2×D61—24no—
416C2×D61—24no—
417C2×D61—24no—
418C2×D61—24no—
419C2×D61—24no—
420C2×D61—416no—
421C2×D61—416no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
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—24no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61—42no—
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×#388—611no—
449C2×#387—611no—
450C2×#387D6111yescharacteristic, complemented
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#232518yescomplemented
460C2×C61C22×C4×D411yescharacteristic
461C2×C61C2×#51811yescharacteristic
462C2×C61C2×#52011yescharacteristic
463C2×C61C2×#53411yescharacteristic
464C2×C61C2×#53711yescharacteristic
465C2×C61C2×#53811yescharacteristic
466C2×C61C2×#53911yescharacteristic
467D61—28no—
468D61—44no—
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⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
497C22×C22⋊C4—611no—
498C22×C22⋊C4—611no—
499C22×C42—611no—
500C22×C42C2×D6111yescharacteristic
501#388—618no—
502#388—618no—
503#387—618no—
504#387C2×D6118yescomplemented
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—618no—
519C2×#95C2×D6111yescharacteristic
520C2×#95C2×D6111yescharacteristic
521C2×#95C2×D6111yescharacteristic
522C2×#95C2×D6111yescharacteristic
523C61C2×#232511yescharacteristic, complemented, Sylow
524C25—611no—
525C25—611no—
526C25—611no—
527C22×D4—618no—
528C22×D4—618no—
529C22×D4—618no—
530C22×D4—614no—
531C22×D4—614no—
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—618no—
542C23×C4—618no—
543C23×C4—614no—
544C23×C4—614no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—614no—
549C23×C4—614no—
550C23×C4—614no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—2442no—
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×C4C22×D6111yescharacteristic
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—24no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—614no—
577C2×C4⋊C4—614no—
578C2×C4⋊C4—1224no—
579C2×C4⋊C4—2442no—
580C2×C4⋊C4—2442no—
581C2×C4⋊C4C4×D6118yescomplemented
582C2×C4⋊C4C22×D6114yes—
583C2×C4⋊C4C22×D6114yes—
584C2×C22⋊C4—618no—
585C2×C22⋊C4—618no—
586C2×C22⋊C4—614no—
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—614no—
595C2×C22⋊C4—614no—
596C2×C22⋊C4—1224no—
597C2×C22⋊C4—1224no—
598C2×C22⋊C4—1224no—
599C2×C22⋊C4—1224no—
600C2×C22⋊C4—2442no—
601C2×C22⋊C4—2442no—
602C2×C22⋊C4—2442no—
603C2×C22⋊C4—2442no—
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#95C22×D6114yes—
615#95C22×D6114yes—
616#95C22×D6114yes—
617#95C22×D6114yes—
618C24—614no—
619C24—614no—
620C24—614no—
621C24—612no—
622C24—614no—
623C24—614no—
624C24—612no—
625C24—612no—
626C24—1222no—
627C24—1222no—
628C24—1222no—
629C24—1222no—
630C24—1222no—
631C24—1222no—
632C24—1222no—
633C24—1222no—
634C24—1222no—
635C24—1222no—
636C24—1222no—
637C24—1222no—
638C24—1222no—
639C24—1222no—
640C24—1222no—
641C24—1222no—
642C24C23×D6111yescharacteristic
643C2×D4—6116no—
644C2×D4—6116no—
645C2×D4—6116no—
646C2×D4—1228no—
647C2×D4—1228no—
648C2×D4—12232no—
649C2×D4—12232no—
650C2×D4—1228no—
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—22no—
671C22×C4—22no—
672C22×C4—614no—
673C22×C4—614no—
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—1228no—
697C22×C4—24416no—
698C22×C4—24416no—
699C22×C4—2444no—
700C22×C4—2444no—
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—24416no—
712C22×C4C2×C4×D6114yes—
713C22×C4C2×C4×D6114yes—
714C22×C4C2×C4×D6114yes—
715C22×C4D4×D6114yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6112yes—
718C22×C4C23×D6112yes—
719C22×C4C23×D6112yes—
720C22×C4C23×D6112yes—
721C22×C4C23×D6112yes—
722C22×C4C23×D6112yes—
723C4⋊C4—28no—
724C4⋊C4—1228no—
725C4⋊C4—2444no—
726C4⋊C4—2444no—
727C4⋊C4C2×C4×D61116yescomplemented
728C22⋊C4—6116no—
729C22⋊C4—6116no—
730C22⋊C4—1228no—
731C22⋊C4—1228no—
732C22⋊C4—1228no—
733C22⋊C4—1228no—
734C22⋊C4—2444no—
735C22⋊C4—2444no—
736C22⋊C4—2444no—
737C22⋊C4—2444no—
738C42—28no—
739C42—1228no—
740C23—6116no—
741C23—614no—
742C23—614no—
743C23—614no—
744C23—614no—
745C23—614no—
746C23—1228no—
747C23—1228no—
748C23—1228no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1228no—
754C23—1228no—
755C23—1228no—
756C23—1228no—
757C23—1228no—
758C23—1228no—
759C23—1228no—
760C23—1228no—
761C23—1228no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1222no—
774C23—2444no—
775C23—2444no—
776C23—2444no—
777C23—2444no—
778C23—2444no—
779C23—2444no—
780C23—2444no—
781C23—2444no—
782C23C22×C4×D6112yes—
783C23C2×D4×D6112yes—
784C23#41×D6112yes—
785C23#1451982312yes—
786C23#1451982312yes—
787C23#1451982312yes—
788C23#1451982512yes—
789C23C24×D6111yescharacteristic
790D4—12232no—
791D4—12232no—
792D4—24416no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
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—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—614no—
818C2×C4—614no—
819C2×C4—1228no—
820C2×C4—1228no—
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—24416no—
835C2×C4—24416no—
836C2×C4—24416no—
837C2×C4—24416no—
838C2×C4—24416no—
839C2×C4—2444no—
840C2×C4—2444no—
841C2×C4—2444no—
842C2×C4C22×C4×D6114yes—
843C2×C4C22×C4×D6114yes—
844C2×C4C22×C4×D6114yes—
845C2×C4C2×D4×D6114yes—
846C22—618no—
847C22—1224no—
848C22—12232no—
849C22—1224no—
850C22—1224no—
851C22—1224no—
852C22—1224no—
853C22—1224no—
854C22—1224no—
855C22—1224no—
856C22—1224no—
857C22—1224no—
858C22—1224no—
859C22—1224no—
860C22—24416no—
861C22—24416no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22C4×D4×D6114yes—
871C22#1684023614yes—
872C22#1684024414yes—
873C22#1684032314yes—
874C22#1684034214yes—
875C22#1684035114yes—
876C22#1684036014yes—
877C22C23×C4×D6111yescharacteristic
878C22C22×D4×D6111yescharacteristic
879C22C2×#41×D6111yescharacteristic
880C22C2×#1451982311yescharacteristic
881C22C2×#1451982311yescharacteristic
882C22C2×#1451982311yescharacteristic
883C22C2×#1451982511yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—1224no—
892C4—1224no—
893C4—2442no—
894C4—2442no—
895C4—2442no—
896C2—1228no—
897C2—2444no—
898C2—2444no—
899C2#2144851818yesdirect product factor
900C2C2×C4×D4×D6111yescharacteristic
901C2C2×#1684023611yescharacteristic
902C2C2×#1684024411yescharacteristic
903C2C2×#1684032311yescharacteristic
904C2C2×#1684034211yescharacteristic
905C2C2×#1684035111yescharacteristic
906C2C2×#1684036011yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC22×#14519752C2
cosocleC23×C61C25
hypercenterC2×#387D61
hypocenterC61C2×#2325
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×D244C2semidirect
3. C22×#14519739C2semidirect
4. #21448518C2direct (N × H)
5. C2×#16839653C2semidirect
6. C2×#16839651C2semidirect
7. C2×#16839648C2semidirect
8. C2×#16839640C2semidirect
9. C2×#16839640C2semidirect
10. C2×#16839640C2semidirect
11. C2×#16839640C2semidirect
12. C2×#16839636C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839621C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#387C2semidirect
25. C2×#14519752C4semidirect
28. C2×C4×D244C22semidirect
30. C2×#14519739C22semidirect
45. #16839653C22semidirect
46. #16839651C22semidirect
47. #16839648C22semidirect
48. #16839640C22semidirect
49. #16839640C22semidirect
50. #16839640C22semidirect
51. #16839640C22semidirect
52. #16839636C22semidirect
53. #16839633C22semidirect
54. #16839621C22semidirect
61. #95×D61C22semidirect
65. C61×#387C22semidirect
79. C22×D244C2×C4semidirect
80. C22×D244C2×C4semidirect
81. C22×D244C2×C4semidirect
103. C22×C4×D61C2×C4semidirect
104. C22×C4×D61D4semidirect
110. #14519752C2×C4semidirect
127. C2×#11758198C2×C4semidirect
128. C2×#11758198C2×C4semidirect
155. C2×C4⋊C4×C61C2×C4semidirect
246. C2×D244C22×C4semidirect
247. C2×D244C22×C4semidirect
248. C2×D244C22×C4semidirect
267. C2×C4×D61C22×C4semidirect
268. C2×C4×D61C2×D4semidirect
270. C4⋊C4×C61C22×C4semidirect
280. #11758198C22×C4semidirect
281. #11758198C22×C4semidirect
450. C2×#387D61semidirect
459. C2×C61#2325semidirect
504. #387C2×D61semidirect
523. C61C2×#2325semidirect
581. C2×C4⋊C4C4×D61semidirect
727. C4⋊C4C2×C4×D61semidirect
899. C2#21448518direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197522
C22×C4×D2442
C22×#145197392
#214485182
C2×#168396532
C2×#168396512
C2×#168396482
C2×#168396402
C2×#168396362
C2×#168396332
C2×#168396212
C2×#95×D612
C2×C61×#3872
C2×#232561