Finite Group Databasebeta

← C2×#21449481 #29847437

Subgroups — C2×#21449481 #29847437

Order 15616.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519757C211yesmaximal, characteristic, complemented
2C22×#14519755C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D61C211yesmaximal, characteristic
4C22×C22⋊C4×D61C211yesmaximal, characteristic
5#21449481C2116yesmaximal, direct product factor
6C2×#16839698C211yesmaximal, characteristic, complemented
7C2×#16839685C211yesmaximal, characteristic, complemented
8C2×#16839674C211yesmaximal, characteristic, complemented
9C2×#16839636C211yesmaximal, characteristic, complemented
10C2×#16839633C211yesmaximal, characteristic, complemented
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×#16839633C211yesmaximal, characteristic, complemented
13C2×#16839621C211yesmaximal, characteristic, complemented
14C2×#16839619C211yesmaximal, characteristic, complemented
15C2×#16839617C211yesmaximal, characteristic
16C2×C61×#396C211yesmaximal, characteristic, complemented
17C25×D61C2211yescharacteristic
18C23×Dic122C2211yescharacteristic, complemented
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C23×C4×D61C2211yescharacteristic
23C2×#14519757—28no—
24C2×#14519757C2218yescomplemented
25C2×#14519755—28no—
26C2×#14519755C2218yescomplemented
27C22×C4⋊Dic61C2211yescharacteristic, complemented
28C22×C4⋊Dic61C2211yescharacteristic, complemented
29C22×#11758196C2211yescharacteristic, complemented
30C22×#11758196C2211yescharacteristic, complemented
31C22×#11758196C2211yescharacteristic, complemented
32C22×#11758196C2211yescharacteristic, complemented
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C2×C22⋊C4×D61—28no—
45C2×C22⋊C4×D61—28no—
46C2×C22⋊C4×D61C2218yes—
47C2×C22⋊C4×D61C2218yes—
48#16839698C2218yescomplemented
49#16839685C2218yescomplemented
50#16839674C2218yescomplemented
51#16839636C2218yescomplemented
52#16839633C2218yescomplemented
53#16839633C2218yescomplemented
54#16839633C2218yescomplemented
55#16839621C2218yescomplemented
56#16839619C2218yescomplemented
57#16839617C2218yes—
58C2×#14519684C2211yescharacteristic, complemented
59C2×#14519684C2211yescharacteristic, complemented
60C2×#14519684C2211yescharacteristic, complemented
61C2×#14519684C2211yescharacteristic, complemented
62C2×#14519684C2211yescharacteristic, complemented
63C22×C4⋊C4×C61C2211yescharacteristic, complemented
64C22×C4⋊C4×C61C2211yescharacteristic, complemented
65C22×C4⋊C4×C61C2211yescharacteristic, complemented
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C61×#396C2218yescomplemented
70C2×#95×C61C2211yescharacteristic, complemented
71C24×D61—24no—
72C24×D61—24no—
73C24×D61—24no—
74C24×D61—24no—
75C24×D61—42no—
76C24×D61—42no—
77C24×D61Q818yescomplemented
78C24×D61C2314yes—
79C24×D61C2311yescharacteristic
80C24×D61C2311yescharacteristic
81C22×Dic122—24no—
82C22×Dic122—24no—
83C22×Dic122—42no—
84C22×Dic122C2314yescomplemented
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—24no—
92C22×C4×D61—24no—
93C22×C4×D61—24no—
94C22×C4×D61—24no—
95C22×C4×D61—24no—
96C22×C4×D61—24no—
97C22×C4×D61—24no—
98C22×C4×D61—24no—
99C22×C4×D61—42no—
100C22×C4×D61—42no—
101C22×C4×D61—42no—
102C22×C4×D61—42no—
103C22×C4×D61C2314yes—
104C22×C4×D61C2314yes—
105C22×C4×D61C2314yes—
106C22×C4×D61C2314yes—
107#14519757—232no—
108#14519755—232no—
109C2×C4⋊Dic61—24no—
110C2×C4⋊Dic61—24no—
111C2×C4⋊Dic61C2314yescomplemented
112C2×C4⋊Dic61C2314yescomplemented
113C2×#11758196—24no—
114C2×#11758196—24no—
115C2×#11758196—42no—
116C2×#11758196—42no—
117C2×#11758196C2314yescomplemented
118C2×#11758196C2314yescomplemented
119C2×#11758196C2314yescomplemented
120C2×#11758196C2314yescomplemented
121C2×C22⋊Dic61—24no—
122C2×C22⋊Dic61—24no—
123C2×C22⋊Dic61—42no—
124C2×C22⋊Dic61C2314yes—
125C2×C22⋊Dic61C2314yes—
126C2×C22⋊Dic61C2314yes—
127C2×#11758198—24no—
128C2×#11758198—24no—
129C2×#11758198—24no—
130C2×#11758198—24no—
131C2×#11758198—24no—
132C2×#11758198—24no—
133C2×#11758198D418yes—
134C2×#11758198D418yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137C2×#11758198C2314yes—
138C2×#11758198C2314yes—
139C2×#11758198C2314yes—
140C2×#11758198C2314yes—
141C2×#11758198C2314yes—
142C2×#11758198C2314yes—
143C22⋊C4×D61—232no—
144C22⋊C4×D61—232no—
145#14519684C2314yescomplemented
146#14519684C2314yescomplemented
147#14519684C2314yescomplemented
148#14519684C2314yescomplemented
149#14519684C2314yescomplemented
150C25×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C23×C4×C61C2311yescharacteristic
155C23×C4×C61C2311yescharacteristic
156C23×C4×C61C2311yescharacteristic
157C2×C4⋊C4×C61—24no—
158C2×C4⋊C4×C61—24no—
159C2×C4⋊C4×C61—42no—
160C2×C4⋊C4×C61C2314yescomplemented
161C2×C4⋊C4×C61C2314yescomplemented
162C2×C4⋊C4×C61C2314yescomplemented
163C2×C22⋊C4×C61—24no—
164C2×C22⋊C4×C61—24no—
165C2×C22⋊C4×C61—42no—
166C2×C22⋊C4×C61C2314yes—
167C2×C22⋊C4×C61C2314yes—
168C2×C22⋊C4×C61C2314yes—
169#95×C61C2314yescomplemented
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61—22no—
176C24×C61C2×Q814yes—
177C24×C61C2412yes—
178C24×C61C2411yescharacteristic
179C23×D61—22no—
180C23×D61—22no—
181C23×D61—22no—
182C23×D61—22no—
183C23×D61—22no—
184C23×D61—22no—
185C23×D61—22no—
186C23×D61—22no—
187C23×D61—232no—
188C23×D61—232no—
189C23×D61—28no—
190C23×D61—28no—
191C23×D61—28no—
192C23×D61—28no—
193C23×D61—416no—
194C23×D61—44no—
195C23×D61—44no—
196C23×D61—416no—
197C23×D61—416no—
198C23×D61—416no—
199C23×D61—416no—
200C23×D61C2×D414yes—
201C23×D61C2×D414yes—
202C23×D61C2×Q814yes—
203C23×D61C2×Q814yes—
204C23×D61C2×Q8116yescomplemented
205C23×D61#4114yes—
206C23×D61#4114yes—
207C23×D61C2412yes—
208C23×D61C2412yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61C2×D414yes—
226C22×C4×C61C2×D414yes—
227C22×C4×C61C2412yes—
228C22×C4×C61C2412yes—
229C22×C4×C61C2412yes—
230C22×C4×C61C2412yes—
231C22×C4×C61C2412yes—
232C22×C4×C61C2412yes—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—22no—
237C22×Dic61—22no—
238C22×Dic61—22no—
239C22×Dic61—22no—
240C22×Dic61—22no—
241C22×Dic61—22no—
242C22×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61—22no—
245C22×Dic61—22no—
246C22×Dic61—22no—
247C22×Dic61—22no—
248C22×Dic61—22no—
249C22×Dic61C2×D414yes—
250C22×Dic61C2×D414yes—
251C22×Dic61C2412yes—
252C22×Dic61C2412yes—
253C22×Dic61C2412yes—
254C22×Dic61C2412yes—
255C22×Dic61C2412yes—
256C22×Dic61C2412yes—
257C2×C4×D61—28no—
258C2×C4×D61—28no—
259C2×C4×D61—28no—
260C2×C4×D61—28no—
261C2×C4×D61—28no—
262C2×C4×D61—28no—
263C2×C4×D61—28no—
264C2×C4×D61—28no—
265C2×C4×D61—44no—
266C2×C4×D61—44no—
267C2×C4×D61—44no—
268C2×C4×D61—44no—
269C2×C4×D61—416no—
270C2×C4×D61—416no—
271C2×C4×D61—416no—
272C2×C4×D61—416no—
273C2×Dic122—28no—
274C2×Dic122—28no—
275C2×Dic122—44no—
276C2×Dic122—416no—
277C4⋊C4×C61—28no—
278C4⋊C4×C61—28no—
279C4⋊C4×C61—44no—
280C22⋊C4×C61—28no—
281C22⋊C4×C61—28no—
282C22⋊C4×C61—44no—
283C22⋊Dic61—28no—
284C22⋊Dic61—28no—
285C22⋊Dic61—44no—
286#11758198—28no—
287#11758198—28no—
288#11758198—28no—
289#11758198—28no—
290#11758198—28no—
291#11758198—28no—
292#11758198C2×D4116yes—
293#11758198C2×D4116yes—
294C4⋊Dic61—28no—
295C4⋊Dic61—28no—
296#11758196—28no—
297#11758196—28no—
298#11758196—44no—
299#11758196—44no—
300C23×C61—28no—
301C23×C61—28no—
302C23×C61—28no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—44no—
310C23×C61—44no—
311C23×C61—44no—
312C23×C61—44no—
313C23×C61C22×D412yes—
314C23×C61C22×D412yes—
315C23×C61C22×Q814yes—
316C23×C61C22×Q812yes—
317C23×C61C2×#4112yes—
318C23×C61C2×#4112yes—
319C23×C61H(5,𝔽2)12yes—
320C23×C61H(5,𝔽2)12yes—
321C23×C61C2511yescharacteristic
322C22×D61—28no—
323C22×D61—28no—
324C22×D61—28no—
325C22×D61—28no—
326C22×D61—28no—
327C22×D61—28no—
328C22×D61—28no—
329C22×D61—28no—
330C22×D61—28no—
331C22×D61—28no—
332C22×D61—28no—
333C22×D61—28no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—232no—
343C22×D61—232no—
344C22×D61—416no—
345C22×D61—4128no—
346C22×D61—416no—
347C22×D61—416no—
348C22×D61—416no—
349C22×D61—416no—
350C22×D61C22⋊Q8116yescomplemented
351C22×D61C22⋊Q8116yescomplemented
352C22×D61C22×D414yes—
353C22×D61C22×D414yes—
354C22×D61C22×Q814yes—
355C22×D61C22×Q814yes—
356C22×D61C2×#4114yes—
357C22×D61C2×#4114yes—
358C2×C4×C61—28no—
359C2×C4×C61—28no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—44no—
377C2×C4×C61—44no—
378C2×C4×C61—44no—
379C2×C4×C61—44no—
380C2×C4×C61C22×D414yes—
381C2×C4×C61C22×D414yes—
382C2×Dic61—28no—
383C2×Dic61—28no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—44no—
401C2×Dic61—44no—
402C2×Dic61—44no—
403C2×Dic61—44no—
404C2×Dic61C22×D414yes—
405C2×Dic61C22×D414yes—
406C4×D61—416no—
407C4×D61—416no—
408C4×D61—416no—
409C4×D61—416no—
410Dic122—416no—
411C2×#2437—611nomaximal, Sylow
412C22×C61—24no—
413C22×C61—24no—
414C22×C61—24no—
415C22×C61—416no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61C2×C22⋊Q814yes—
421C22×C61C2×C22⋊Q814yes—
422C22×C61#54314yes—
423C22×C61D4214yes—
424C22×C61#54614yes—
425C22×C61#54614yes—
426C22×C61#55114yes—
427C22×C61C23×D411yescharacteristic
428C22×C61C23×D411yescharacteristic
429C22×C61C23×Q811yescharacteristic
430C22×C61C22×#4111yescharacteristic
431C22×C61C22×#4111yescharacteristic
432C22×C61C2×H(5,𝔽2)11yescharacteristic
433C22×C61C2×H(5,𝔽2)11yescharacteristic
434C2×D61—24no—
435C2×D61—24no—
436C2×D61—24no—
437C2×D61—24no—
438C2×D61—232no—
439C2×D61—232no—
440C2×D61—24no—
441C2×D61—24no—
442C2×D61—24no—
443C2×D61—24no—
444C2×D61—24no—
445C2×D61—24no—
446C2×D61—24no—
447C2×D61—24no—
448C2×D61—464no—
449C2×D61C2×C22⋊Q818yescomplemented
450C2×D61C2×C22⋊Q818yescomplemented
451C4×C61—24no—
452C4×C61—24no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61—42no—
456C4×C61—42no—
457Dic61—24no—
458Dic61—24no—
459Dic61—42no—
460Dic61—42no—
461Dic61—42no—
462Dic61—42no—
463C22×C22⋊Q8—611no—
464C22×C22⋊Q8—611no—
465C23×C22⋊C4—611no—
466C23×C22⋊C4—611no—
467#2437—6116no—
468C2×#399—611no—
469C2×#396—611no—
470C2×#396D6111yescharacteristic, complemented
471C2×#393—611no—
472C2×#385—611no—
473C2×#385—611no—
474C2×#385—611no—
475C2×#385—611no—
476C2×#380—611no—
477C2×#380—611no—
478C2×#379—611no—
479C2×C61—44no—
480C2×C61#243718yescomplemented
481C2×C61C22×C22⋊Q811yescharacteristic
482C2×C61C22×C22⋊Q811yescharacteristic
483C2×C61C2×#54311yescharacteristic
484C2×C61C2×D4211yescharacteristic
485C2×C61C2×#54611yescharacteristic
486C2×C61C2×#54611yescharacteristic
487C2×C61C2×#55111yescharacteristic
488D61—28no—
489D61—28no—
490C26—611no—
491C23×Q8—611no—
492C24×C4—611no—
493C24×C4—611no—
494C24×C4—611no—
495C24×C4—611no—
496C2×C22⋊Q8—618no—
497C2×C22⋊Q8—618no—
498C2×C22⋊Q8—1228no—
499C2×C22⋊Q8—1228no—
500C22×C4⋊C4—611no—
501C22×C4⋊C4—611no—
502C22×C4⋊C4—611no—
503C22×C4⋊C4—611no—
504C22×C4⋊C4—611no—
505C22×C4⋊C4—611no—
506C22×C4⋊C4C2×D6111yescharacteristic, complemented
507C22×C4⋊C4C2×D6111yescharacteristic, complemented
508C22×C4⋊C4C2×D6111yescharacteristic, complemented
509C22×C22⋊C4—611no—
510C22×C22⋊C4—611no—
511C22×C22⋊C4—611no—
512C22×C22⋊C4—611no—
513C22×C22⋊C4—611no—
514C22×C22⋊C4—611no—
515C22×C22⋊C4—611no—
516C22×C22⋊C4—611no—
517C22×C22⋊C4—611no—
518C22×C22⋊C4—611no—
519C22×C22⋊C4—611no—
520C22×C22⋊C4—618no—
521C22×C22⋊C4—618no—
522C22×C22⋊C4—1228no—
523C22×C22⋊C4—1228no—
524C22×C22⋊C4C2×D6111yescharacteristic
525C22×C22⋊C4C2×D6111yescharacteristic
526C22×C22⋊C4C2×D6111yescharacteristic
527#399—618no—
528#396—618no—
529#396C2×D6118yescomplemented
530#393—618no—
531#385—618no—
532#385—618no—
533#385—618no—
534#385—618no—
535#380—618no—
536#380—618no—
537#379—618no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95C2×D6111yescharacteristic, complemented
544C61C2×#243711yescharacteristic, complemented, Sylow
545C25—611no—
546C25—611no—
547C25—618no—
548C25—614no—
549C25—1224no—
550C25—1224no—
551C25—1224no—
552C25—1224no—
553C25—2442no—
554C25—2442no—
555C25C22×D6111yescharacteristic
556C22×Q8—614no—
557C22×Q8—1224no—
558C22×Q8—1224no—
559C22×Q8—2442no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—614no—
567C23×C4—614no—
568C23×C4—614no—
569C23×C4—614no—
570C23×C4—1224no—
571C23×C4—1224no—
572C23×C4—1224no—
573C23×C4—1224no—
574C23×C4—1224no—
575C23×C4—1224no—
576C23×C4—1224no—
577C23×C4—1224no—
578C23×C4—2442no—
579C23×C4—2442no—
580C23×C4—2442no—
581C23×C4—2442no—
582C23×C4C22×D6111yescharacteristic
583C23×C4C22×D6111yescharacteristic
584C23×C4C22×D6111yescharacteristic
585C23×C4C22×D6111yescharacteristic
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588C22⋊Q8—12232no—
589C22⋊Q8—12232no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—42no—
593C2×C4⋊C4—614no—
594C2×C4⋊C4—614no—
595C2×C4⋊C4—614no—
596C2×C4⋊C4—614no—
597C2×C4⋊C4—614no—
598C2×C4⋊C4—614no—
599C2×C4⋊C4—1224no—
600C2×C4⋊C4—1224no—
601C2×C4⋊C4—1224no—
602C2×C4⋊C4—1224no—
603C2×C4⋊C4—2442no—
604C2×C4⋊C4—2442no—
605C2×C4⋊C4C22×D6114yescomplemented
606C2×C4⋊C4C22×D6114yescomplemented
607C2×C4⋊C4C22×D6114yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—618no—
612C2×C22⋊C4—618no—
613C2×C22⋊C4—614no—
614C2×C22⋊C4—614no—
615C2×C22⋊C4—614no—
616C2×C22⋊C4—614no—
617C2×C22⋊C4—614no—
618C2×C22⋊C4—614no—
619C2×C22⋊C4—614no—
620C2×C22⋊C4—614no—
621C2×C22⋊C4—614no—
622C2×C22⋊C4—614no—
623C2×C22⋊C4—614no—
624C2×C22⋊C4—12232no—
625C2×C22⋊C4—12232no—
626C2×C22⋊C4—1224no—
627C2×C22⋊C4—1224no—
628C2×C22⋊C4—1224no—
629C2×C22⋊C4—1224no—
630C2×C22⋊C4—1224no—
631C2×C22⋊C4—1224no—
632C2×C22⋊C4—1224no—
633C2×C22⋊C4—1224no—
634C2×C22⋊C4—2442no—
635C2×C22⋊C4C22×D6114yes—
636C2×C22⋊C4C22×D6114yes—
637C2×C22⋊C4C22×D6114yes—
638#95—614no—
639#95—614no—
640#95—614no—
641#95—614no—
642#95—614no—
643#95C22×D6114yescomplemented
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—614no—
651C24—614no—
652C24—614no—
653C24—614no—
654C24—614no—
655C24—614no—
656C24—612no—
657C24—612no—
658C24—6116no—
659C24—1228no—
660C24—1228no—
661C24—12232no—
662C24—12232no—
663C24—1228no—
664C24—1228no—
665C24—1222no—
666C24—1222no—
667C24—1222no—
668C24—1222no—
669C24—1222no—
670C24—1222no—
671C24—1222no—
672C24—1222no—
673C24—2444no—
674C24—2444no—
675C24—24416no—
676C24—24416no—
677C24—24416no—
678C24—24416no—
679C24—24416no—
680C24Q8×D6114yes—
681C24C23×D6112yes—
682C24C23×D6111yescharacteristic
683C2×Q8—1228no—
684C2×Q8—1228no—
685C2×Q8—2444no—
686C2×Q8—24416no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—614no—
704C22×C4—614no—
705C22×C4—612no—
706C22×C4—612no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—612no—
710C22×C4—612no—
711C22×C4—1228no—
712C22×C4—1228no—
713C22×C4—1228no—
714C22×C4—1228no—
715C22×C4—1228no—
716C22×C4—1228no—
717C22×C4—1222no—
718C22×C4—1222no—
719C22×C4—1222no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1222no—
725C22×C4—1222no—
726C22×C4—1222no—
727C22×C4—1222no—
728C22×C4—1222no—
729C22×C4—1222no—
730C22×C4—1222no—
731C22×C4—1222no—
732C22×C4—1222no—
733C22×C4—1228no—
734C22×C4—1228no—
735C22×C4—2444no—
736C22×C4—2444no—
737C22×C4—2444no—
738C22×C4—2444no—
739C22×C4—24416no—
740C22×C4—24416no—
741C22×C4—24416no—
742C22×C4—24416no—
743C22×C4D4×D6114yes—
744C22×C4D4×D6114yes—
745C22×C4C23×D6112yes—
746C22×C4C23×D6112yes—
747C22×C4C23×D6112yes—
748C22×C4C23×D6112yes—
749C22×C4C23×D6112yes—
750C22×C4C23×D6112yes—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—1228no—
755C4⋊C4—1228no—
756C4⋊C4—1228no—
757C4⋊C4—1228no—
758C4⋊C4—2444no—
759C4⋊C4—2444no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—44no—
763C22⋊C4—6116no—
764C22⋊C4—6116no—
765C22⋊C4—1228no—
766C22⋊C4—1228no—
767C22⋊C4—1228no—
768C22⋊C4—1228no—
769C22⋊C4—1228no—
770C22⋊C4—1228no—
771C22⋊C4—1228no—
772C22⋊C4—1228no—
773C22⋊C4—2444no—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—28no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—6116no—
788C23—6116no—
789C23—614no—
790C23—614no—
791C23—614no—
792C23—614no—
793C23—614no—
794C23—614no—
795C23—12232no—
796C23—12232no—
797C23—1228no—
798C23—1228no—
799C23—1222no—
800C23—1222no—
801C23—1222no—
802C23—1222no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1228no—
808C23—1228no—
809C23—1228no—
810C23—1228no—
811C23—1228no—
812C23—1228no—
813C23—1228no—
814C23—1228no—
815C23—1228no—
816C23—1228no—
817C23—24416no—
818C23—244128no—
819C23—24416no—
820C23—24416no—
821C23—24416no—
822C23—24416no—
823C23C2×D4×D6112yes—
824C23C2×D4×D6112yes—
825C23C2×Q8×D6114yes—
826C23C2×Q8×D6112yes—
827C23#41×D6112yes—
828C23#41×D6112yes—
829C23#1451982212yes—
830C23#1451982312yes—
831C23C24×D6111yescharacteristic
832Q8—24416no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—614no—
856C2×C4—614no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1228no—
862C2×C4—1228no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—24416no—
876C2×C4—24416no—
877C2×C4—24416no—
878C2×C4—24416no—
879C2×C4—2444no—
880C2×C4—2444no—
881C2×C4—2444no—
882C2×C4—2444no—
883C2×C4C2×D4×D6114yes—
884C2×C4C2×D4×D6114yes—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—416no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—618no—
894C22—618no—
895C22—12232no—
896C22—12232no—
897C22—1224no—
898C22—1224no—
899C22—1224no—
900C22—1224no—
901C22—1224no—
902C22—1224no—
903C22—1224no—
904C22—1224no—
905C22—1224no—
906C22—1224no—
907C22—1224no—
908C22—1224no—
909C22—24464no—
910C22C22⋊Q8×D6114yes—
911C22C22⋊Q8×D6114yes—
912C22#1684038714yes—
913C22#1684039614yes—
914C22#1684040114yes—
915C22#1684040914yes—
916C22#1684043714yes—
917C22C22×D4×D6111yescharacteristic
918C22C22×D4×D6111yescharacteristic
919C22C22×Q8×D6111yescharacteristic
920C22C2×#41×D6111yescharacteristic
921C22C2×#41×D6111yescharacteristic
922C22C2×#1451982211yescharacteristic
923C22C2×#1451982311yescharacteristic
924C4—24no—
925C4—24no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—1224no—
931C4—1224no—
932C4—2442no—
933C4—2442no—
934C4—2442no—
935C4—2442no—
936C2—44no—
937C2—1228no—
938C2—1228no—
939C2#2144948118yesdirect product factor
940C2C2×C22⋊Q8×D6111yescharacteristic
941C2C2×C22⋊Q8×D6111yescharacteristic
942C2C2×#1684038711yescharacteristic
943C2C2×#1684039611yescharacteristic
944C2C2×#1684040111yescharacteristic
945C2C2×#1684040911yescharacteristic
946C2C2×#1684043711yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#396C2
socleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×#396D61
hypocenterC61C2×#2437
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14519757C2semidirect
2. C22×#14519755C2semidirect
5. #21449481C2direct (N × H)
6. C2×#16839698C2semidirect
7. C2×#16839685C2semidirect
8. C2×#16839674C2semidirect
9. C2×#16839636C2semidirect
10. C2×#16839633C2semidirect
11. C2×#16839633C2semidirect
12. C2×#16839633C2semidirect
13. C2×#16839621C2semidirect
14. C2×#16839619C2semidirect
16. C2×C61×#396C2semidirect
18. C23×Dic122C22semidirect
24. C2×#14519757C22semidirect
26. C2×#14519755C22semidirect
27. C22×C4⋊Dic61C22semidirect
28. C22×C4⋊Dic61C22semidirect
29. C22×#11758196C22semidirect
30. C22×#11758196C22semidirect
31. C22×#11758196C22semidirect
32. C22×#11758196C22semidirect
48. #16839698C22semidirect
49. #16839685C22semidirect
50. #16839674C22semidirect
51. #16839636C22semidirect
52. #16839633C22semidirect
53. #16839633C22semidirect
54. #16839633C22semidirect
55. #16839621C22semidirect
56. #16839619C22semidirect
58. C2×#14519684C22semidirect
59. C2×#14519684C22semidirect
60. C2×#14519684C22semidirect
61. C2×#14519684C22semidirect
62. C2×#14519684C22semidirect
63. C22×C4⋊C4×C61C22semidirect
64. C22×C4⋊C4×C61C22semidirect
65. C22×C4⋊C4×C61C22semidirect
69. C61×#396C22semidirect
70. C2×#95×C61C22semidirect
77. C24×D61Q8semidirect
84. C22×Dic122C23semidirect
111. C2×C4⋊Dic61C23semidirect
112. C2×C4⋊Dic61C23semidirect
117. C2×#11758196C23semidirect
118. C2×#11758196C23semidirect
119. C2×#11758196C23semidirect
120. C2×#11758196C23semidirect
145. #14519684C23semidirect
146. #14519684C23semidirect
147. #14519684C23semidirect
148. #14519684C23semidirect
149. #14519684C23semidirect
160. C2×C4⋊C4×C61C23semidirect
161. C2×C4⋊C4×C61C23semidirect
162. C2×C4⋊C4×C61C23semidirect
169. #95×C61C23semidirect
204. C23×D61C2×Q8semidirect
350. C22×D61C22⋊Q8semidirect
351. C22×D61C22⋊Q8semidirect
449. C2×D61C2×C22⋊Q8semidirect
450. C2×D61C2×C22⋊Q8semidirect
470. C2×#396D61semidirect
480. C2×C61#2437semidirect
506. C22×C4⋊C4C2×D61semidirect
507. C22×C4⋊C4C2×D61semidirect
508. C22×C4⋊C4C2×D61semidirect
529. #396C2×D61semidirect
543. C2×#95C2×D61semidirect
544. C61C2×#2437semidirect
605. C2×C4⋊C4C22×D61semidirect
606. C2×C4⋊C4C22×D61semidirect
607. C2×C4⋊C4C22×D61semidirect
643. #95C22×D61semidirect
939. C2#21449481direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197572
C22×#145197552
C22×C22⋊C4×D612
#214494812
C2×#168396982
C2×#168396852
C2×#168396742
C2×#168396362
C2×#168396332
C2×#168396212
C2×#168396192
C2×#168396172
C2×C61×#3962
C2×#243761