Finite Group Databasebeta

← C2×#21448261 #29838351

Subgroups — C2×#21448261 #29838351

Order 15616.

4134 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×C42×D61C211yesmaximal, characteristic, complemented
4#21448261C2116yesmaximal, direct product factor
5C2×#16839655C211yesmaximal, characteristic, complemented
6C2×#16839646C211yesmaximal, characteristic, complemented
7C2×#16839644C211yesmaximal, characteristic, complemented
8C2×#16839638C211yesmaximal, characteristic
9C2×#16839638C211yesmaximal, characteristic
10C2×#16839636C211yesmaximal, characteristic, complemented
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C2×#16839607C211yesmaximal, 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×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C2×C42×D61—28no—
42C2×C42×D61C2218yescomplemented
43#16839655C2218yescomplemented
44#16839646C2218yescomplemented
45#16839644C2218yescomplemented
46#16839638C2218yes—
47#16839638C2218yes—
48#16839636C2218yescomplemented
49#16839633C2218yescomplemented
50C4⋊C4×Dic61C2218yescomplemented
51C22⋊C4×Dic61C2218yescomplemented
52#16839609C2218yescomplemented
53#16839607C2218yescomplemented
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×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
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—24no—
93C22×C4×D61—24no—
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×#11758196C2×C418yescomplemented
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×C22⋊Dic61—24no—
109C2×C22⋊Dic61—24no—
110C2×C22⋊Dic61C2314yes—
111C2×C22⋊Dic61C2314yes—
112C2×#11758198—24no—
113C2×#11758198—24no—
114C2×#11758198C2×C418yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61C2×C418yescomplemented
123C2×C4×Dic61D418yescomplemented
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C42×D61—232no—
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—24no—
150C2×C22⋊C4×C61C2×C418yescomplemented
151C2×C22⋊C4×C61C2314yes—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C2×C42×C61—24no—
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×C61C22×C414yes—
190C22×C4×C61C22×C414yes—
191C22×C4×C61C2×D414yes—
192C22×C4×C61#4114yes—
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—232no—
212C22×Dic61—28no—
213C22×Dic61—28no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61C22×C414yes—
221C22×Dic61C22×C414yes—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C4116yescomplemented
224C22×Dic61C2×D414yes—
225C22×Dic61C2×D414yes—
226C22×Dic61#4114yes—
227C22×Dic61#4114yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×C4×D61—232no—
236C2×C4×D61—232no—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—28no—
240C2×C4×D61—28no—
241C2×C4×D61—232no—
242C2×C4×D61—28no—
243C2×C4×D61—28no—
244C2×C4×D61—28no—
245C2×C4×D61—28no—
246C2×C4×D61C22×C4116yes—
247C4⋊C4×C61—28no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61C22×C4116yescomplemented
251C42×C61—28no—
252C22⋊Dic61—28no—
253C22⋊Dic61—28no—
254#11758198—28no—
255#11758198—28no—
256#11758198C22×C4116yes—
257C4⋊Dic61—28no—
258#11758196—28no—
259#11758196—28no—
260#11758196C22×C4116yescomplemented
261C4×Dic61—28no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61—28no—
265C4×Dic61C22×C4116yescomplemented
266C4×Dic61C2×D4116yescomplemented
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×C61C2×#4112yes—
287C23×C61C2×#4112yes—
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—28no—
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×C61C23×C414yes—
324C2×C4×C61C23×C414yes—
325C2×C4×C61C22×D414yes—
326C2×C4×C61C2×#4114yes—
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—232no—
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×Dic61C4×D4116yes—
350C2×Dic61C23×C414yes—
351C2×Dic61C23×C414yes—
352C2×Dic61C23×C414yes—
353C2×Dic61C22×D414yes—
354C2×Dic61C22×D414yes—
355C2×Dic61C2×#4114yes—
356C2×Dic61C2×#4114yes—
357C4×D61—232no—
358C4×D61—232no—
359C4×D61—232no—
360C2×#2290—611nomaximal, Sylow
361C22×C61—24no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—416no—
369C22×C61C2×#11714yes—
370C22×C61C2×C4×D414yes—
371C22×C61C4×#4114yes—
372C22×C61#52514yes—
373C22×C61#52514yes—
374C22×C61#52914yes—
375C22×C61#52914yes—
376C22×C61C24×C411yescharacteristic
377C22×C61C23×D411yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C22×#4111yescharacteristic
380C22×C61C22×#4111yescharacteristic
381C22×C61C22×#4111yescharacteristic
382C22×C61C22×#4111yescharacteristic
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—232no—
390C2×D61C2×#11718yescomplemented
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—24no—
395C4×C61—42no—
396C4×C61—42no—
397Dic61—24no—
398Dic61—24no—
399Dic61—24no—
400Dic61—24no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×C4×D418yes—
404C22×C4×D4—611no—
405C22×#117—611no—
406C23×C42—611no—
407#2290—6116no—
408C2×#388—611no—
409C2×#388D6111yescharacteristic, complemented
410C2×#387—611no—
411C2×#387—611no—
412C2×#386—611no—
413C2×#386—611no—
414C2×#385—611no—
415C2×#385—611no—
416C2×C4×C4⋊C4—611no—
417C2×C4×C22⋊C4—611no—
418C2×C4×C22⋊C4—611no—
419C2×#376—611no—
420C2×C61—44no—
421C2×C61#229018yescomplemented
422C2×C61C22×#11711yescharacteristic
423C2×C61C22×C4×D411yescharacteristic
424C2×C61C2×C4×#4111yescharacteristic
425C2×C61C2×#52511yescharacteristic
426C2×C61C2×#52511yescharacteristic
427C2×C61C2×#52911yescharacteristic
428C2×C61C2×#52911yescharacteristic
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⋊C4C2×D6111yescharacteristic
444C22×C22⋊C4—611no—
445C22×C22⋊C4—611no—
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4C2×D6111yescharacteristic
450C22×C22⋊C4C2×D6111yescharacteristic
451C22×C22⋊C4C2×D6111yescharacteristic
452C22×C42—611no—
453C22×C42—611no—
454C22×C42—611no—
455C22×C42—611no—
456C22×C42—611no—
457C22×C42—611no—
458C22×C42—618no—
459C22×C42—1228no—
460C22×C42C2×D6111yescharacteristic
461#388—618no—
462#388C2×D6118yescomplemented
463#387—618no—
464#387—618no—
465#386—618no—
466#386—618no—
467#385—618no—
468#385—618no—
469C4×C4⋊C4—618no—
470C4×C22⋊C4—618no—
471C4×C22⋊C4—618no—
472#376—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×#229011yescharacteristic, 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—611no—
497C23×C4—618no—
498C23×C4—614no—
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—1224no—
512C23×C4—1224no—
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—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—1224no—
528C2×C4⋊C4—1224no—
529C2×C4⋊C4—1224no—
530C2×C4⋊C4C22×D6114yes—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—618no—
534C2×C22⋊C4—614no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4—1224no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4C4×D6118yescomplemented
544C2×C22⋊C4C22×D6114yes—
545C2×C22⋊C4C22×D6114yes—
546C2×C22⋊C4C22×D6114yes—
547C2×C42—24no—
548C2×C42—618no—
549C2×C42—618no—
550C2×C42—614no—
551C2×C42—614no—
552C2×C42—614no—
553C2×C42—614no—
554C2×C42—614no—
555C2×C42—614no—
556C2×C42—12232no—
557C2×C42—1224no—
558C2×C42—1224no—
559C2×C42—1224no—
560C2×C42—1224no—
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—614no—
608C22×C4—614no—
609C22×C4—614no—
610C22×C4—612no—
611C22×C4—614no—
612C22×C4—614no—
613C22×C4—6116no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—6116no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—12232no—
626C22×C4—1228no—
627C22×C4—1228no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—12232no—
631C22×C4—12232no—
632C22×C4—1228no—
633C22×C4—12232no—
634C22×C4—1228no—
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—1228no—
644C22×C4—1228no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4C2×C4×D6114yes—
652C22×C4C2×C4×D6114yes—
653C22×C4D4×D6114yes—
654C22×C4#1175822414yes—
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—1228no—
664C4⋊C4—1228no—
665C4⋊C4—1228no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—6116no—
669C22⋊C4—1228no—
670C22⋊C4—1228no—
671C22⋊C4—1228no—
672C22⋊C4—1228no—
673C22⋊C4C2×C4×D61116yescomplemented
674C42—28no—
675C42—6116no—
676C42—6116no—
677C42—1228no—
678C42—1228no—
679C42—1228no—
680C42—1228no—
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—1228no—
703C23—1228no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23C22×C4×D6114yes—
709C23C22×C4×D6112yes—
710C23C2×D4×D6112yes—
711C23#41×D6112yes—
712C23#41×D6112yes—
713C23#41×D6112yes—
714C23#41×D6112yes—
715C23C2×#1175822412yes—
716C23C24×D6111yescharacteristic
717D4—12232no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
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—6116no—
739C2×C4—614no—
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—12232no—
749C2×C4—12232no—
750C2×C4—1228no—
751C2×C4—1228no—
752C2×C4—1228no—
753C2×C4—1228no—
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—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4C22×C4×D6114yes—
771C2×C4C22×C4×D6114yes—
772C2×C4C2×D4×D6114yes—
773C2×C4C2×#1175822414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—618no—
783C22—1224no—
784C22—1224no—
785C22—12232no—
786C22—1224no—
787C22—1224no—
788C22—1224no—
789C22—1224no—
790C22#117×D6114yes—
791C22C4×D4×D6114yes—
792C22C4×#1175822414yes—
793C22#1684027014yes—
794C22#1684027214yes—
795C22#1684029114yes—
796C22#1684029514yes—
797C22C23×C4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#41×D6111yescharacteristic
801C22C2×#41×D6111yescharacteristic
802C22C2×#41×D6111yescharacteristic
803C22C22×#1175822411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—618no—
811C4—1224no—
812C4—1224no—
813C4—1224no—
814C4—1224no—
815C4—2442no—
816C4—2442no—
817C2—44no—
818C2—1228no—
819C2#2144826118yesdirect product factor
820C2C2×#117×D6111yescharacteristic
821C2C2×C4×D4×D6111yescharacteristic
822C2C2×C4×#1175822411yescharacteristic
823C2C2×#1684027011yescharacteristic
824C2C2×#1684027211yescharacteristic
825C2C2×#1684029111yescharacteristic
826C2C2×#1684029511yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2290
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×C42×D61C2semidirect
4. #21448261C2direct (N × H)
5. C2×#16839655C2semidirect
6. C2×#16839646C2semidirect
7. C2×#16839644C2semidirect
10. C2×#16839636C2semidirect
11. C2×#16839633C2semidirect
12. C2×C4⋊C4×Dic61C2semidirect
13. C2×C22⋊C4×Dic61C2semidirect
14. C2×#16839609C2semidirect
15. C2×#16839607C2semidirect
16. C2×C61×#388C2semidirect
22. C2×#14519737C4semidirect
25. C2×#14519733C22semidirect
42. C2×C42×D61C22semidirect
43. #16839655C22semidirect
44. #16839646C22semidirect
45. #16839644C22semidirect
48. #16839636C22semidirect
49. #16839633C22semidirect
50. C4⋊C4×Dic61C22semidirect
51. C22⋊C4×Dic61C22semidirect
52. #16839609C22semidirect
53. #16839607C22semidirect
67. C61×#388C22semidirect
77. C23×Dic61C2×C4semidirect
98. #14519737C2×C4semidirect
104. C2×#11758196C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
123. C2×C4×Dic61D4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
223. C22×Dic61C22×C4semidirect
250. C22⋊C4×C61C22×C4semidirect
260. #11758196C22×C4semidirect
265. C4×Dic61C22×C4semidirect
266. C4×Dic61C2×D4semidirect
299. C22×D61#117semidirect
390. C2×D61C2×#117semidirect
409. C2×#388D61semidirect
421. C2×C61#2290semidirect
462. #388C2×D61semidirect
483. C61C2×#2290semidirect
543. C2×C22⋊C4C4×D61semidirect
673. C22⋊C4C2×C4×D61semidirect
819. C2#21448261direct (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×C42×D612
#214482612
C2×#168396552
C2×#168396462
C2×#168396442
C2×#168396382
C2×#168396362
C2×#168396332
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×#168396092
C2×#168396072
C2×C61×#3882
C2×#229061