Finite Group Databasebeta

← C2×#21448747 #29839339

Subgroups — C2×#21448747 #29839339

Order 15616.

3894 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×#14519737C211yesmaximal, characteristic
2C22×#14519733C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21448747C2116yesmaximal, direct product factor
5C2×#16839655C211yesmaximal, characteristic, complemented
6C2×#16839649C211yesmaximal, characteristic, complemented
7C2×#16839643C211yesmaximal, characteristic, complemented
8C2×#16839638C211yesmaximal, characteristic
9C2×#16839638C211yesmaximal, characteristic
10C2×#16839626C211yesmaximal, characteristic, complemented
11C2×#16839621C211yesmaximal, characteristic, complemented
12C2×#16839620C211yesmaximal, characteristic, complemented
13C2×C4×#11758196C211yesmaximal, characteristic, complemented
14C2×C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519737C4116yescomplemented
23C2×#14519737C2218yes—
24C2×#14519733—28no—
25C2×#14519733C2218yescomplemented
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C2×C4⋊C4×D61—28no—
33C2×C4⋊C4×D61C2218yescomplemented
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839655C2218yescomplemented
44#16839649C2218yescomplemented
45#16839643C2218yescomplemented
46#16839638C2218yes—
47#16839638C2218yes—
48#16839626C2218yescomplemented
49#16839621C2218yescomplemented
50#16839620C2218yescomplemented
51C4×#11758196C2218yescomplemented
52C4×#11758198C2218yescomplemented
53#16839609C2218yescomplemented
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—24no—
77C23×Dic61C2×C418yescomplemented
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61C2×C418yes—
95C22×C4×D61C2314yes—
96C22×C4×D61C2314yes—
97C22×C4×D61C2314yes—
98#14519737C2×C4164yescomplemented
99#14519733—232no—
100C2×C4⋊Dic61—24no—
101C2×C4⋊Dic61C2314yes—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196—24no—
105C2×#11758196C2×C418yescomplemented
106C2×#11758196D418yescomplemented
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C4⋊C4×D61—232no—
113C2×C22⋊Dic61—24no—
114C2×C22⋊Dic61—42no—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×#11758198—24no—
118C2×#11758198—24no—
119C2×#11758198C2×C418yes—
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×C4×Dic61—24no—
124C2×C4×Dic61—24no—
125C2×C4×Dic61—42no—
126C2×C4×Dic61C2×C418yescomplemented
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
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×D61#4114yes—
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—232no—
210C22×Dic61—28no—
211C22×Dic61—28no—
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—22no—
221C22×Dic61C22×C414yes—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C414yes—
224C22×Dic61C22×C4116yescomplemented
225C22×Dic61C2×D414yes—
226C22×Dic61C2×D414yes—
227C22×Dic61#4114yes—
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—28no—
240C2×C4×D61—28no—
241C2×C4×D61—28no—
242C2×C4×D61—44no—
243C2×C4×D61—44no—
244C2×C4×D61—416no—
245C2×C4×D61—416no—
246C2×C4×D61C22×C4116yes—
247C4⋊C4×C61—28no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—44no—
250C22⋊C4×C61C22×C4116yescomplemented
251C42×C61—44no—
252C22⋊Dic61—28no—
253C22⋊Dic61—44no—
254#11758198—28no—
255#11758198—28no—
256#11758198C22×C4116yes—
257C4⋊Dic61—28no—
258#11758196—28no—
259#11758196—28no—
260#11758196—28no—
261#11758196C22×C4116yescomplemented
262#11758196C2×D4116yescomplemented
263C4×Dic61—28no—
264C4×Dic61—28no—
265C4×Dic61—44no—
266C4×Dic61C22×C4116yescomplemented
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×C61C2×#4112yes—
285C23×C61C2×#4112yes—
286C23×C61H(5,𝔽2)12yes—
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×D61#117116yescomplemented
300C22×D61C23×C414yes—
301C22×D61C2×#4114yes—
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—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—232no—
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—44no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61C4×D4116yes—
351C2×Dic61C23×C414yes—
352C2×Dic61C23×C414yes—
353C2×Dic61C23×C414yes—
354C2×Dic61C22×D414yes—
355C2×Dic61C22×D414yes—
356C2×Dic61C2×#4114yes—
357C4×D61—232no—
358C4×D61—416no—
359C4×D61—416no—
360C2×#2352—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×#11714yes—
370C22×C61C2×C4×D414yes—
371C22×C61#52014yes—
372C22×C61#54614yes—
373C22×C61#54814yes—
374C22×C61#55214yes—
375C22×C61#55314yes—
376C22×C61C24×C411yescharacteristic
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C22×C61C2×H(5,𝔽2)11yescharacteristic
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×#11718yescomplemented
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—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×C4×D418yes—
404C22×C4×D4—611no—
405C22×#117—611no—
406C23×C4⋊C4—611no—
407#2352—6116no—
408C2×#388—611no—
409C2×#388D6111yescharacteristic, complemented
410C2×#387—611no—
411C2×#387—611no—
412C2×#386—611no—
413C2×#386—611no—
414C2×#382—611no—
415C2×#380—611no—
416C2×#380—611no—
417C2×C4×C4⋊C4—611no—
418C2×C4×C22⋊C4—611no—
419C2×C4×C22⋊C4—611no—
420C2×C61—44no—
421C2×C61#235218yescomplemented
422C2×C61C22×#11711yescharacteristic
423C2×C61C22×C4×D411yescharacteristic
424C2×C61C2×#52011yescharacteristic
425C2×C61C2×#54611yescharacteristic
426C2×C61C2×#54811yescharacteristic
427C2×C61C2×#55211yescharacteristic
428C2×C61C2×#55311yescharacteristic
429D61—28no—
430C23×D4—611no—
431C24×C4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C24×C4—611no—
435C2×C4×D4—6116no—
436C2×C4×D4—618no—
437C2×#117—618no—
438C2×#117—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—618no—
446C22×C4⋊C4—1228no—
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4C2×D6111yescharacteristic
454C22×C22⋊C4C2×D6111yescharacteristic
455C22×C22⋊C4C2×D6111yescharacteristic
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—611no—
459C22×C42—611no—
460C22×C42C2×D6111yescharacteristic
461#388—618no—
462#388C2×D6118yescomplemented
463#387—618no—
464#387—618no—
465#386—618no—
466#386—618no—
467#382—618no—
468#380—618no—
469#380—618no—
470C4×C4⋊C4—618no—
471C4×C22⋊C4—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×#235211yescharacteristic, complemented, Sylow
484C25—611no—
485C25C22×D6111yescharacteristic
486C22×D4—618no—
487C22×D4—614no—
488C22×D4—1224no—
489C22×D4—1224no—
490C23×C4—611no—
491C23×C4—618no—
492C23×C4—614no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
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—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—1224no—
511C23×C4—2442no—
512C23×C4—2442no—
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C23×C4C22×D6111yescharacteristic
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519C4×D4—6164no—
520#117—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—12232no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4C22×D6114yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—618no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—614no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—1224no—
545C2×C22⋊C4—1224no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—2442no—
548C2×C22⋊C4C4×D6118yescomplemented
549C2×C22⋊C4C22×D6114yes—
550C2×C22⋊C4C22×D6114yes—
551C2×C22⋊C4C22×D6114yes—
552C2×C42—42no—
553C2×C42—618no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—614no—
557C2×C42—614no—
558C2×C42—1224no—
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—12232no—
591C2×D4—1228no—
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—612no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—6116no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—6116no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1228no—
624C22×C4—12232no—
625C22×C4—1228no—
626C22×C4—1228no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—12232no—
631C22×C4—1228no—
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—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1228no—
648C22×C4—2444no—
649C22×C4—2444no—
650C22×C4—24416no—
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—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—6116no—
671C22⋊C4—1228no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—2444no—
675C22⋊C4C2×C4×D61116yescomplemented
676C42—44no—
677C42—6116no—
678C42—1228no—
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#41×D6112yes—
713C23#41×D6112yes—
714C23#1451982212yes—
715C23#1451982412yes—
716C23C24×D6111yescharacteristic
717D4—12232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
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—6116no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—614no—
745C2×C4—614no—
746C2×C4—12232no—
747C2×C4—12232no—
748C2×C4—1228no—
749C2×C4—1228no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1228no—
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—1222no—
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—1224no—
784C22—12232no—
785C22—1224no—
786C22—1224no—
787C22—1224no—
788C22—1224no—
789C22—1224no—
790C22#117×D6114yes—
791C22C4×D4×D6114yes—
792C22#1684024114yes—
793C22#1684040114yes—
794C22#1684042014yes—
795C22#1684044814yes—
796C22#1684045714yes—
797C22C23×C4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#41×D6111yescharacteristic
801C22C2×#41×D6111yescharacteristic
802C22C2×#1451982211yescharacteristic
803C22C2×#1451982411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—618no—
811C4—1224no—
812C4—1224no—
813C4—1224no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—44no—
818C2—1228no—
819C2#2144874718yesdirect product factor
820C2C2×#117×D6111yescharacteristic
821C2C2×C4×D4×D6111yescharacteristic
822C2C2×#1684024111yescharacteristic
823C2C2×#1684040111yescharacteristic
824C2C2×#1684042011yescharacteristic
825C2C2×#1684044811yescharacteristic
826C2C2×#1684045711yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2352
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519733C2semidirect
3. C22×C4⋊C4×D61C2semidirect
4. #21448747C2direct (N × H)
5. C2×#16839655C2semidirect
6. C2×#16839649C2semidirect
7. C2×#16839643C2semidirect
10. C2×#16839626C2semidirect
11. C2×#16839621C2semidirect
12. C2×#16839620C2semidirect
13. C2×C4×#11758196C2semidirect
14. C2×C4×#11758198C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#388C2semidirect
22. C2×#14519737C4semidirect
25. C2×#14519733C22semidirect
33. C2×C4⋊C4×D61C22semidirect
43. #16839655C22semidirect
44. #16839649C22semidirect
45. #16839643C22semidirect
48. #16839626C22semidirect
49. #16839621C22semidirect
50. #16839620C22semidirect
51. C4×#11758196C22semidirect
52. C4×#11758198C22semidirect
53. #16839609C22semidirect
67. C61×#388C22semidirect
77. C23×Dic61C2×C4semidirect
98. #14519737C2×C4semidirect
105. C2×#11758196C2×C4semidirect
106. C2×#11758196D4semidirect
126. C2×C4×Dic61C2×C4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
224. C22×Dic61C22×C4semidirect
250. C22⋊C4×C61C22×C4semidirect
261. #11758196C22×C4semidirect
262. #11758196C2×D4semidirect
266. C4×Dic61C22×C4semidirect
299. C22×D61#117semidirect
390. C2×D61C2×#117semidirect
409. C2×#388D61semidirect
421. C2×C61#2352semidirect
462. #388C2×D61semidirect
483. C61C2×#2352semidirect
548. C2×C22⋊C4C4×D61semidirect
675. C22⋊C4C2×C4×D61semidirect
819. C2#21448747direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×#145197332
C22×C4⋊C4×D612
#214487472
C2×#168396552
C2×#168396492
C2×#168396432
C2×#168396382
C2×#168396262
C2×#168396212
C2×#168396202
C2×C4×#117581962
C2×C4×#117581982
C2×#168396092
C2×C61×#3882
C2×#235261