Finite Group Databasebeta

← C2×#21448528 #29838798

Subgroups — C2×#21448528 #29838798

Order 15616.

3566 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3C22×#14519737C211yesmaximal, characteristic
4#21448528C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839662C211yesmaximal, characteristic
7C2×#16839654C211yesmaximal, characteristic, complemented
8C2×#16839653C211yesmaximal, characteristic, complemented
9C2×#16839650C211yesmaximal, characteristic, complemented
10C2×#16839637C211yesmaximal, characteristic, complemented
11C2×#16839636C211yesmaximal, characteristic, complemented
12C2×#16839634C211yesmaximal, characteristic, complemented
13C2×#16839633C211yesmaximal, characteristic, complemented
14C2×#16839631C211yesmaximal, characteristic, complemented
15C2×#16839607C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519763C4116yescomplemented
22C2×#14519763C2218yes—
23C2×C4×Dic122—28no—
24C2×C4×Dic122C2218yescomplemented
25C2×#14519737—28no—
26C2×#14519737C2218yes—
27C22×C4⋊Dic61C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45#16839666C2218yescomplemented
46#16839662C2218yes—
47#16839654C2218yescomplemented
48#16839653C2218yescomplemented
49#16839650C2218yescomplemented
50#16839637C2218yescomplemented
51#16839636C2218yescomplemented
52#16839634C2218yescomplemented
53#16839633C2218yescomplemented
54#16839631C2218yescomplemented
55#16839607C2218yescomplemented
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×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2×C418yescomplemented
74C22×Dic122C2314yes—
75C22×C22⋊D61—24no—
76C22×C22⋊D61—24no—
77C22×C22⋊D61C2×C418yes—
78C22×C22⋊D61C2314yes—
79C23×Dic61—24no—
80C23×Dic61—42no—
81C23×Dic61—42no—
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2314yes—
89C23×Dic61C2311yescharacteristic
90C22×C4×D61—24no—
91C22×C4×D61—42no—
92C22×C4×D61—42no—
93C22×C4×D61C2314yes—
94#14519763C2×C4164yescomplemented
95C4×Dic122—232no—
96#14519737—232no—
97C2×C4⋊Dic61—24no—
98C2×C4⋊Dic61—42no—
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2314yes—
101C2×#11758196—24no—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196—42no—
105C2×#11758196—42no—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×C22⋊Dic61—42no—
112C2×C22⋊Dic61C2×C418yescomplemented
113C2×C22⋊Dic61C2314yes—
114C2×C22⋊Dic61C2314yes—
115C2×#11758198—24no—
116C2×#11758198—42no—
117C2×#11758198—42no—
118C2×#11758198C2×C418yescomplemented
119C2×#11758198C2×C418yescomplemented
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×C4×Dic61—24no—
126C2×C4×Dic61—24no—
127C2×C4×Dic61C2×C418yescomplemented
128C2×C4×Dic61D418yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
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—42no—
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—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×D61—22no—
172C23×D61—22no—
173C23×D61C22×C414yes—
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—28no—
219C22×Dic61—44no—
220C22×Dic61—44no—
221C22×Dic61—416no—
222C22×Dic61C22×C414yes—
223C22×Dic61C22×C414yes—
224C22×Dic61C22×C414yes—
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—28no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—416no—
239C2×Dic122—232no—
240C2×Dic122—28no—
241C2×Dic122—28no—
242C2×Dic122C22×C4116yescomplemented
243C4⋊C4×C61—44no—
244C22⋊C4×C61—28no—
245C22⋊C4×C61—44no—
246C22⋊C4×C61C22×C4116yescomplemented
247C42×C61—28no—
248C22⋊Dic61—44no—
249C22⋊Dic61C22×C4116yescomplemented
250#11758198—28no—
251#11758198—44no—
252#11758198—44no—
253#11758198C22×C4116yescomplemented
254#11758198C22×C4116yescomplemented
255C4⋊Dic61—28no—
256C4⋊Dic61—44no—
257#11758196—28no—
258#11758196—28no—
259#11758196—28no—
260#11758196—44no—
261#11758196—44no—
262C4×Dic61—28no—
263C4×Dic61—28no—
264C4×Dic61C22×C4116yescomplemented
265C4×Dic61C2×D4116yes—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—28no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61C23×C414yes—
280C23×C61C23×C412yes—
281C23×C61C22×D412yes—
282C23×C61C2×#4112yes—
283C23×C61H(5,𝔽2)12yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C612−1+412yes—
286C23×C612−1+412yes—
287C23×C61C2511yescharacteristic
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61C23×C414yes—
302C2×C4×C61—28no—
303C2×C4×C61—28no—
304C2×C4×C61—28no—
305C2×C4×C61—22no—
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—44no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61C23×C414yes—
324C2×C4×C61C23×C414yes—
325C2×C4×C61C22×D414yes—
326C22⋊D61—232no—
327C2×Dic61—28no—
328C2×Dic61—28no—
329C2×Dic61—28no—
330C2×Dic61—22no—
331C2×Dic61—22no—
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—416no—
346C2×Dic61—44no—
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—
356C4×D61—416no—
357Dic122—232no—
358C2×#2326—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—416no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61C2×C4×D414yes—
368C22×C61#52014yes—
369C22×C61#52014yes—
370C22×C61#53514yes—
371C22×C61#53614yes—
372C22×C61#54214yes—
373C22×C61#54214yes—
374C22×C61C24×C411yescharacteristic
375C22×C61C23×D411yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C2×H(5,𝔽2)11yescharacteristic
378C22×C61C2×H(5,𝔽2)11yescharacteristic
379C22×C61C2×2−1+411yescharacteristic
380C22×C61C2×2−1+411yescharacteristic
381C2×D61—24no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—416no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—24no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61C2×C4×D418yes—
402C22×#124—611no—
403C22×C4×Q8—611no—
404C22×C4×D4—611no—
405#2326—6116no—
406C2×#391—611no—
407C2×#390—611no—
408C2×#388—611no—
409C2×#388—611no—
410C2×#388—611no—
411C2×#388D6111yescharacteristic, complemented
412C2×#385—611no—
413C2×#385—611no—
414C2×#385—611no—
415C2×#385—611no—
416C2×#384—611no—
417C2×#376—611no—
418C2×C61—44no—
419C2×C61#232618yescomplemented
420C2×C61C22×C4×D411yescharacteristic
421C2×C61C2×#52011yescharacteristic
422C2×C61C2×#52011yescharacteristic
423C2×C61C2×#53511yescharacteristic
424C2×C61C2×#53611yescharacteristic
425C2×C61C2×#54211yescharacteristic
426C2×C61C2×#54211yescharacteristic
427D61—44no—
428C23×Q8—611no—
429C23×D4—611no—
430C24×C4—611no—
431C24×C4—611no—
432C2×#124—6116no—
433C2×#124—618no—
434C2×C4×Q8—618no—
435C2×C4×Q8—1228no—
436C2×C4×D4—618no—
437C2×C4×D4—1228no—
438C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
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#391—618no—
462#390—618no—
463#388—618no—
464#388—618no—
465#388—618no—
466#388C2×D6118yescomplemented
467#385—618no—
468#385—618no—
469#385—618no—
470#385—618no—
471#384—618no—
472#376—618no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95C2×D6111yescharacteristic
480C2×#95C2×D6111yescharacteristic
481C61C2×#232611yescharacteristic, complemented, Sylow
482C25—611no—
483C25C22×D6111yescharacteristic
484C22×Q8—618no—
485C22×Q8—614no—
486C22×Q8—1224no—
487C22×Q8—1224no—
488C22×D4—618no—
489C22×D4—614no—
490C22×D4—1224no—
491C22×D4—1224no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—614no—
500C23×C4—614no—
501C23×C4—1224no—
502C23×C4—1224no—
503C23×C4—2442no—
504C23×C4—2442no—
505C23×C4—2442no—
506C23×C4—2442no—
507C23×C4C22×D6111yescharacteristic
508C23×C4C22×D6111yescharacteristic
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#124—6164no—
514C4×Q8—12232no—
515C4×D4—12232no—
516C2×C4⋊C4—42no—
517C2×C4⋊C4—614no—
518C2×C4⋊C4—614no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—1224no—
525C2×C4⋊C4—1224no—
526C2×C4⋊C4—1224no—
527C2×C4⋊C4—1224no—
528C2×C4⋊C4—2442no—
529C2×C4⋊C4—2442no—
530C2×C4⋊C4—2442no—
531C2×C4⋊C4C22×D6114yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—618no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—618no—
537C2×C22⋊C4—618no—
538C2×C22⋊C4—614no—
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—2442no—
546C2×C22⋊C4—2442no—
547C2×C22⋊C4—2442no—
548C2×C22⋊C4C4×D6118yescomplemented
549C2×C22⋊C4C22×D6114yes—
550C2×C22⋊C4C22×D6114yes—
551C2×C22⋊C4C22×D6114yes—
552C2×C42—24no—
553C2×C42—618no—
554C2×C42—618no—
555C2×C42—614no—
556C2×C42—614no—
557C2×C42—614no—
558C2×C42—614no—
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#95C22×D6114yes—
569#95C22×D6114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24C2×C4×D6114yes—
585C24C23×D6112yes—
586C24C23×D6111yescharacteristic
587C2×Q8—6116no—
588C2×Q8—1228no—
589C2×Q8—12232no—
590C2×Q8—1228no—
591C2×D4—6116no—
592C2×D4—1228no—
593C2×D4—12232no—
594C2×D4—1228no—
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—22no—
609C22×C4—22no—
610C22×C4—614no—
611C22×C4—614no—
612C22×C4—614no—
613C22×C4—612no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—614no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1228no—
624C22×C4—1228no—
625C22×C4—1222no—
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—2444no—
641C22×C4—2444no—
642C22×C4—24416no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—24416no—
646C22×C4C2×C4×D6114yes—
647C22×C4C2×C4×D6114yes—
648C22×C4D4×D6114yes—
649C22×C4C23×D6112yes—
650C22×C4C23×D6112yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C4⋊C4—44no—
656C4⋊C4—1228no—
657C4⋊C4—1228no—
658C4⋊C4—1228no—
659C4⋊C4—1228no—
660C4⋊C4—2444no—
661C4⋊C4—2444no—
662C4⋊C4—2444no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—6116no—
666C22⋊C4—6116no—
667C22⋊C4—6116no—
668C22⋊C4—1228no—
669C22⋊C4—2444no—
670C22⋊C4—2444no—
671C22⋊C4—2444no—
672C22⋊C4C2×C4×D61116yescomplemented
673C42—28no—
674C42—6116no—
675C42—6116no—
676C42—1228no—
677C42—1228no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—614no—
692C23—1228no—
693C23—1228no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—2444no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23C22×C4×D6114yes—
706C23C22×C4×D6112yes—
707C23C2×D4×D6112yes—
708C23#41×D6112yes—
709C23#1451982212yes—
710C23#1451982312yes—
711C23#1451982412yes—
712C23#1451982412yes—
713C23C24×D6111yescharacteristic
714Q8—12232no—
715D4—12232no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
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—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—6116no—
738C2×C4—614no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—1228no—
745C2×C4—1228no—
746C2×C4—1222no—
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—24416no—
763C2×C4—24416no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4C22×C4×D6114yes—
768C2×C4C22×C4×D6114yes—
769C2×C4C2×D4×D6114yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—416no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—24416no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22C4×D4×D6114yes—
787C22#1684024114yes—
788C22#1684024214yes—
789C22#1684032814yes—
790C22#1684033414yes—
791C22#1684037614yes—
792C22#1684037814yes—
793C22C23×C4×D6111yescharacteristic
794C22C22×D4×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C2×#1451982211yescharacteristic
797C22C2×#1451982311yescharacteristic
798C22C2×#1451982411yescharacteristic
799C22C2×#1451982411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—618no—
807C4—1224no—
808C4—1224no—
809C4—1224no—
810C4—2442no—
811C4—2442no—
812C4—2442no—
813C2—44no—
814C2—2444no—
815C2#2144852818yesdirect product factor
816C2C2×C4×D4×D6111yescharacteristic
817C2C2×#1684024111yescharacteristic
818C2C2×#1684024211yescharacteristic
819C2C2×#1684032811yescharacteristic
820C2C2×#1684033411yescharacteristic
821C2C2×#1684037611yescharacteristic
822C2C2×#1684037811yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2326
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
4. #21448528C2direct (N × H)
5. C2×#16839666C2semidirect
7. C2×#16839654C2semidirect
8. C2×#16839653C2semidirect
9. C2×#16839650C2semidirect
10. C2×#16839637C2semidirect
11. C2×#16839636C2semidirect
12. C2×#16839634C2semidirect
13. C2×#16839633C2semidirect
14. C2×#16839631C2semidirect
15. C2×#16839607C2semidirect
16. C2×C61×#388C2semidirect
21. C2×#14519763C4semidirect
24. C2×C4×Dic122C22semidirect
45. #16839666C22semidirect
47. #16839654C22semidirect
48. #16839653C22semidirect
49. #16839650C22semidirect
50. #16839637C22semidirect
51. #16839636C22semidirect
52. #16839634C22semidirect
53. #16839633C22semidirect
54. #16839631C22semidirect
55. #16839607C22semidirect
67. C61×#388C22semidirect
73. C22×Dic122C2×C4semidirect
94. #14519763C2×C4semidirect
112. C2×C22⋊Dic61C2×C4semidirect
118. C2×#11758198C2×C4semidirect
119. C2×#11758198C2×C4semidirect
127. C2×C4×Dic61C2×C4semidirect
150. C2×C22⋊C4×C61C2×C4semidirect
242. C2×Dic122C22×C4semidirect
246. C22⋊C4×C61C22×C4semidirect
249. C22⋊Dic61C22×C4semidirect
253. #11758198C22×C4semidirect
254. #11758198C22×C4semidirect
264. C4×Dic61C22×C4semidirect
411. C2×#388D61semidirect
419. C2×C61#2326semidirect
466. #388C2×D61semidirect
481. C61C2×#2326semidirect
548. C2×C22⋊C4C4×D61semidirect
672. C22⋊C4C2×C4×D61semidirect
815. C2#21448528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×C4×Dic1222
C22×#145197372
#214485282
C2×#168396662
C2×#168396622
C2×#168396542
C2×#168396532
C2×#168396502
C2×#168396372
C2×#168396362
C2×#168396342
C2×#168396332
C2×#168396312
C2×#168396072
C2×C61×#3882
C2×#232661