Finite Group Databasebeta

← C2×#21448489 #29838742

Subgroups — C2×#21448489 #29838742

Order 15616.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic
2C22×#14519737C211yesmaximal, characteristic
3C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21448489C2116yesmaximal, direct product factor
5C2×#16839660C211yesmaximal, characteristic, complemented
6C2×#16839657C211yesmaximal, characteristic, complemented
7C2×#16839656C211yesmaximal, characteristic, complemented
8C2×#16839649C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839636C211yesmaximal, characteristic, complemented
13C2×#16839634C211yesmaximal, characteristic, complemented
14C2×#16839624C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519759C4116yescomplemented
23C2×#14519759C2218yes—
24C2×#14519737—28no—
25C2×#14519737C2218yes—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C2×C4⋊C4×D61—28no—
35C2×C4⋊C4×D61C2218yescomplemented
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839660C2218yescomplemented
44#16839657C2218yescomplemented
45#16839656C2218yescomplemented
46#16839649C2218yescomplemented
47#16839645C2218yescomplemented
48#16839638C2218yes—
49#16839637C2218yescomplemented
50#16839636C2218yescomplemented
51#16839634C2218yescomplemented
52#16839624C2218yescomplemented
53C4×#11758198C2218yescomplemented
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
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
71C22×C22⋊D61—24no—
72C22×C22⋊D61—24no—
73C22×C22⋊D61C2×C418yes—
74C22×C22⋊D61C2314yes—
75C23×Dic61—24no—
76C23×Dic61—42no—
77C23×Dic61—42no—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2314yes—
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—42no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61—42no—
93C22×C4×D61C2×C418yescomplemented
94C22×C4×D61D418yes—
95C22×C4×D61C2314yes—
96C22×C4×D61C2314yes—
97C22×C4×D61C2314yes—
98#14519759C2×C4164yescomplemented
99#14519737—232no—
100C2×C4⋊Dic61—24no—
101C2×C4⋊Dic61—42no—
102C2×C4⋊Dic61C2×C418yescomplemented
103C2×C4⋊Dic61C2314yes—
104C2×C4⋊Dic61C2314yes—
105C2×C4⋊Dic61C2314yes—
106C2×#11758196—24no—
107C2×#11758196—24no—
108C2×#11758196—24no—
109C2×#11758196—42no—
110C2×#11758196C2×C418yescomplemented
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×#11758196C2314yes—
116C4⋊C4×D61—232no—
117C2×C22⋊Dic61—42no—
118C2×C22⋊Dic61C2×C418yescomplemented
119C2×C22⋊Dic61C2314yes—
120C2×C22⋊Dic61C2314yes—
121C2×#11758198—24no—
122C2×#11758198—24no—
123C2×#11758198C2×C418yescomplemented
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×C4×Dic61—24no—
128C2×C4×Dic61—42no—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139C25×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61—24no—
147C2×C4⋊C4×C61C2314yes—
148C2×C22⋊C4×C61—24no—
149C2×C22⋊C4×C61—42no—
150C2×C22⋊C4×C61C2×C418yescomplemented
151C2×C22⋊C4×C61C2314yes—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C2×C42×C61—42no—
155C2×C42×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61C22×C414yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61C22×C414yes—
172C23×D61C2×D414yes—
173C23×D61#4114yes—
174C23×D61C2412yes—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61C22×C414yes—
191C22×C4×C61C22×C414yes—
192C22×C4×C61C2×D414yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C2×C22⋊D61—232no—
200C2×C22⋊D61—28no—
201C2×C22⋊D61—28no—
202C2×C22⋊D61C22×C4116yes—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—28no—
221C22×Dic61—44no—
222C22×Dic61—44no—
223C22×Dic61—416no—
224C22×Dic61C22×C414yes—
225C22×Dic61C22×C414yes—
226C22×Dic61C22×C414yes—
227C22×Dic61C2×D414yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—232no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—416no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—416no—
245C2×C4×D61C22×C4116yescomplemented
246C2×C4×D61C2×D4116yes—
247C4⋊C4×C61—28no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—44no—
250C22⋊C4×C61C22×C4116yescomplemented
251C42×C61—44no—
252C22⋊Dic61—44no—
253C22⋊Dic61C22×C4116yescomplemented
254#11758198—28no—
255#11758198—28no—
256#11758198C22×C4116yescomplemented
257C4⋊Dic61—28no—
258C4⋊Dic61—44no—
259C4⋊Dic61C22×C4116yescomplemented
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—44no—
264#11758196C22×C4116yescomplemented
265C4×Dic61—28no—
266C4×Dic61—44no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61C23×C414yes—
281C23×C61C23×C412yes—
282C23×C61C22×D412yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C612−1+412yes—
287C23×C612−1+412yes—
288C23×C61C2511yescharacteristic
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—28no—
292C22×D61—28no—
293C22×D61—28no—
294C22×D61—28no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61C4×D4116yes—
300C22×D61C23×C414yes—
301C22×D61C22×D414yes—
302C22×D61C2×#4114yes—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61—44no—
324C2×C4×C61C23×C414yes—
325C2×C4×C61C23×C414yes—
326C2×C4×C61C22×D414yes—
327C22⋊D61—232no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—28no—
331C2×Dic61—28no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—416no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61—44no—
353C2×Dic61C23×C414yes—
354C2×Dic61C23×C414yes—
355C2×Dic61C23×C414yes—
356C2×Dic61C22×D414yes—
357C4×D61—232no—
358C4×D61—416no—
359C4×D61—416no—
360C2×#2322—611nomaximal, Sylow
361C22×C61—24no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—416no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61C2×C4×D414yes—
370C22×C61#52014yes—
371C22×C61#52014yes—
372C22×C61#53414yes—
373C22×C61#53614yes—
374C22×C61#53914yes—
375C22×C61#53914yes—
376C22×C61C24×C411yescharacteristic
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C22×C61C2×2−1+411yescharacteristic
382C22×C61C2×2−1+411yescharacteristic
383C2×D61—232no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—24no—
390C2×D61C2×C4×D418yes—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397Dic61—24no—
398Dic61—24no—
399Dic61—24no—
400Dic61—24no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C22×#123—611no—
405C22×C4×D4—611no—
406C23×C4⋊C4—611no—
407#2322—6116no—
408C2×#389—611no—
409C2×#389—611no—
410C2×#388—611no—
411C2×#388D6111yescharacteristic, complemented
412C2×#387—611no—
413C2×#387—611no—
414C2×#386—611no—
415C2×#385—611no—
416C2×#385—611no—
417C2×#385—611no—
418C2×#381—611no—
419C2×C4×C22⋊C4—611no—
420C2×C61—44no—
421C2×C61#232218yescomplemented
422C2×C61C22×C4×D411yescharacteristic
423C2×C61C2×#52011yescharacteristic
424C2×C61C2×#52011yescharacteristic
425C2×C61C2×#53411yescharacteristic
426C2×C61C2×#53611yescharacteristic
427C2×C61C2×#53911yescharacteristic
428C2×C61C2×#53911yescharacteristic
429D61—28no—
430C23×D4—611no—
431C24×C4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C24×C4—611no—
435C2×#123—6116no—
436C2×#123—618no—
437C2×C4×D4—618no—
438C2×C4×D4—1228no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—611no—
447C22×C4⋊C4—618no—
448C22×C4⋊C4—1228no—
449C22×C4⋊C4C2×D6111yescharacteristic
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4C2×D6111yescharacteristic
456C22×C22⋊C4C2×D6111yescharacteristic
457C22×C22⋊C4C2×D6111yescharacteristic
458C22×C42—611no—
459C22×C42—611no—
460C22×C42C2×D6111yescharacteristic
461#389—618no—
462#389—618no—
463#388—618no—
464#388C2×D6118yescomplemented
465#387—618no—
466#387—618no—
467#386—618no—
468#385—618no—
469#385—618no—
470#385—618no—
471#381—618no—
472C4×C22⋊C4—618no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95—611no—
480C2×#95—611no—
481C2×#95C2×D6111yescharacteristic
482C2×#95C2×D6111yescharacteristic
483C61C2×#232211yescharacteristic, complemented, Sylow
484C25—611no—
485C25C22×D6111yescharacteristic
486C22×D4—618no—
487C22×D4—614no—
488C22×D4—1224no—
489C22×D4—1224no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—618no—
495C23×C4—614no—
496C23×C4—618no—
497C23×C4—614no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—614no—
502C23×C4—614no—
503C23×C4—1224no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—2442no—
508C23×C4—2442no—
509C23×C4—2442no—
510C23×C4—2442no—
511C23×C4—2442no—
512C23×C4—2442no—
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519#123—6164no—
520C4×D4—12232no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—618no—
523C2×C4⋊C4—618no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—12232no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4—1224no—
537C2×C4⋊C4—2442no—
538C2×C4⋊C4—2442no—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—618no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—618no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4C4×D6118yescomplemented
553C2×C22⋊C4C22×D6114yes—
554C2×C22⋊C4C22×D6114yes—
555C2×C22⋊C4C22×D6114yes—
556C2×C42—42no—
557C2×C42—614no—
558C2×C42—614no—
559C2×C42—1224no—
560C2×C42—2442no—
561C2×C42C22×D6114yes—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95C22×D6114yes—
571#95C22×D6114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—614no—
579C24—614no—
580C24—614no—
581C24—612no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24C2×C4×D6114yes—
587C24C23×D6112yes—
588C24C23×D6111yescharacteristic
589C2×D4—6116no—
590C2×D4—1228no—
591C2×D4—12232no—
592C2×D4—1228no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—614no—
609C22×C4—614no—
610C22×C4—614no—
611C22×C4—614no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—6116no—
617C22×C4—6116no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1228no—
622C22×C4—12232no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—1228no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—24416no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4—24416no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—24416no—
652C22×C4C2×C4×D6114yes—
653C22×C4C2×C4×D6114yes—
654C22×C4D4×D6114yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C4⋊C4—28no—
662C4⋊C4—6116no—
663C4⋊C4—6116no—
664C4⋊C4—1228no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—2444no—
669C4⋊C4—2444no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—6116no—
673C22⋊C4—6116no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—2444no—
677C22⋊C4C2×C4×D61116yescomplemented
678C42—44no—
679C42—1228no—
680C42—2444no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—6116no—
695C23—614no—
696C23—614no—
697C23—614no—
698C23—1228no—
699C23—1228no—
700C23—1228no—
701C23—1228no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1228no—
707C23—1228no—
708C23C22×C4×D6114yes—
709C23C22×C4×D6112yes—
710C23C2×D4×D6112yes—
711C23#41×D6112yes—
712C23#1451982212yes—
713C23#1451982312yes—
714C23#1451982412yes—
715C23#1451982412yes—
716C23C24×D6111yescharacteristic
717D4—12232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—12232no—
744C2×C4—1228no—
745C2×C4—1228no—
746C2×C4—1228no—
747C2×C4—1228no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—24416no—
766C2×C4—24416no—
767C2×C4—24416no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4C22×C4×D6114yes—
772C2×C4C22×C4×D6114yes—
773C2×C4C2×D4×D6114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—618no—
783C22—12232no—
784C22—1224no—
785C22—1224no—
786C22—1224no—
787C22—1224no—
788C22—1224no—
789C22—1224no—
790C22C4×D4×D6114yes—
791C22#1684024114yes—
792C22#1684024214yes—
793C22#1684032014yes—
794C22#1684033214yes—
795C22#1684035314yes—
796C22#1684035514yes—
797C22C23×C4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#1451982211yescharacteristic
801C22C2×#1451982311yescharacteristic
802C22C2×#1451982411yescharacteristic
803C22C2×#1451982411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—1224no—
811C4—1224no—
812C4—1224no—
813C4—1224no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—44no—
818C2—1228no—
819C2#2144848918yesdirect product factor
820C2C2×C4×D4×D6111yescharacteristic
821C2C2×#1684024111yescharacteristic
822C2C2×#1684024211yescharacteristic
823C2C2×#1684032011yescharacteristic
824C2C2×#1684033211yescharacteristic
825C2C2×#1684035311yescharacteristic
826C2C2×#1684035511yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2322
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D61C2semidirect
4. #21448489C2direct (N × H)
5. C2×#16839660C2semidirect
6. C2×#16839657C2semidirect
7. C2×#16839656C2semidirect
8. C2×#16839649C2semidirect
9. C2×#16839645C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839636C2semidirect
13. C2×#16839634C2semidirect
14. C2×#16839624C2semidirect
15. C2×C4×#11758198C2semidirect
16. C2×C61×#388C2semidirect
22. C2×#14519759C4semidirect
35. C2×C4⋊C4×D61C22semidirect
43. #16839660C22semidirect
44. #16839657C22semidirect
45. #16839656C22semidirect
46. #16839649C22semidirect
47. #16839645C22semidirect
49. #16839637C22semidirect
50. #16839636C22semidirect
51. #16839634C22semidirect
52. #16839624C22semidirect
53. C4×#11758198C22semidirect
67. C61×#388C22semidirect
93. C22×C4×D61C2×C4semidirect
98. #14519759C2×C4semidirect
102. C2×C4⋊Dic61C2×C4semidirect
110. C2×#11758196C2×C4semidirect
118. C2×C22⋊Dic61C2×C4semidirect
123. C2×#11758198C2×C4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
245. C2×C4×D61C22×C4semidirect
250. C22⋊C4×C61C22×C4semidirect
253. C22⋊Dic61C22×C4semidirect
256. #11758198C22×C4semidirect
259. C4⋊Dic61C22×C4semidirect
264. #11758196C22×C4semidirect
411. C2×#388D61semidirect
421. C2×C61#2322semidirect
464. #388C2×D61semidirect
483. C61C2×#2322semidirect
552. C2×C22⋊C4C4×D61semidirect
677. C22⋊C4C2×C4×D61semidirect
819. C2#21448489direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197592
C22×#145197372
C22×C4⋊C4×D612
#214484892
C2×#168396602
C2×#168396572
C2×#168396562
C2×#168396492
C2×#168396452
C2×#168396382
C2×#168396372
C2×#168396362
C2×#168396342
C2×#168396242
C2×C4×#117581982
C2×C61×#3882
C2×#232261