Finite Group Databasebeta

← C2×#21451735 #29846421

Subgroups — C2×#21451735 #29846421

Order 15616.

2958 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic, complemented
2C22×D4×Dic61C211yesmaximal, characteristic
3#21451735C2116yesmaximal, direct product factor
4C2×#16839695C211yesmaximal, characteristic, complemented
5C2×#16839690C211yesmaximal, characteristic, complemented
6C2×#16839690C211yesmaximal, characteristic, complemented
7C2×#16839687C211yesmaximal, characteristic, complemented
8C2×#16839683C211yesmaximal, characteristic, complemented
9C2×#16839676C211yesmaximal, characteristic
10C2×#16839674C211yesmaximal, characteristic, complemented
11C2×#16839648C211yesmaximal, characteristic, complemented
12C2×#16839644C211yesmaximal, characteristic, complemented
13C2×#16839637C211yesmaximal, characteristic, complemented
14C2×#16839634C211yesmaximal, characteristic, complemented
15C2×#16839623C211yesmaximal, characteristic, complemented
16C2×C61×#394C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754—28no—
21C2×#14519754C2218yescomplemented
22C2×D4×Dic61—28no—
23C2×D4×Dic61C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×C22⋊Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839695C2218yescomplemented
39#16839690C2218yescomplemented
40#16839690C2218yescomplemented
41#16839687C2218yescomplemented
42#16839683C2218yescomplemented
43#16839676C2218yes—
44#16839674C2218yescomplemented
45#16839648C2218yescomplemented
46#16839644C2218yescomplemented
47#16839637C2218yescomplemented
48#16839634C2218yescomplemented
49#16839623C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C23×D4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C61×#394C2218yes—
68C2×#95×C61C2211yescharacteristic
69C22×Dic122—24no—
70C22×Dic122—42no—
71C22×Dic122—42no—
72C22×Dic122C2314yes—
73C23×Dic61—24no—
74C23×Dic61—42no—
75C23×Dic61—42no—
76C23×Dic61—42no—
77C23×Dic61—42no—
78C23×Dic61D418yes—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2314yes—
88C23×Dic61C2314yes—
89#14519754—232no—
90D4×Dic61—232no—
91C2×C4⋊Dic61—24no—
92C2×C4⋊Dic61—24no—
93C2×C4⋊Dic61—42no—
94C2×C4⋊Dic61C2314yes—
95C2×C4⋊Dic61C2314yes—
96C2×C4⋊Dic61C2314yes—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196—42no—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61—24no—
108C2×C22⋊Dic61—24no—
109C2×C22⋊Dic61—42no—
110C2×C22⋊Dic61—42no—
111C2×C22⋊Dic61C2314yes—
112C2×C22⋊Dic61C2314yes—
113C2×C22⋊Dic61C2314yes—
114C2×C22⋊Dic61C2314yes—
115C2×C22⋊Dic61C2314yes—
116C2×C22⋊Dic61C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130C25×C61C2311yescharacteristic
131C25×C61C2311yescharacteristic
132C22×D4×C61—24no—
133C22×D4×C61—24no—
134C22×D4×C61—24no—
135C22×D4×C61C2314yes—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—24no—
142C2×C4⋊C4×C61C2314yes—
143C2×C22⋊C4×C61—24no—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61—42no—
146C2×C22⋊C4×C61—42no—
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150C2×C22⋊C4×C61C2314yes—
151#95×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61C2×D414yes—
165C24×C61#4114yes—
166C24×C61C2412yes—
167C24×C61C2412yes—
168C24×C61C2411yescharacteristic
169C2×D4×C61—232no—
170C2×D4×C61—28no—
171C2×D4×C61—28no—
172C2×D4×C61—28no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
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#4114yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
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—28no—
216C22×Dic61—416no—
217C22×Dic61—44no—
218C22×Dic61—44no—
219C22×Dic61—44no—
220C22×Dic61—44no—
221C22×Dic61—416no—
222C22×Dic61C2×D414yes—
223C22×Dic61C2×D414yes—
224C22×Dic61C2×D4116yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C2×Dic122—28no—
234C2×Dic122—44no—
235C2×Dic122—44no—
236C2×Dic122—416no—
237C4⋊C4×C61—28no—
238C22⋊C4×C61—28no—
239C22⋊C4×C61—28no—
240C22⋊C4×C61—44no—
241C22⋊C4×C61—44no—
242C22⋊Dic61—28no—
243C22⋊Dic61—28no—
244C22⋊Dic61—28no—
245C22⋊Dic61—28no—
246C22⋊Dic61—44no—
247C22⋊Dic61—44no—
248C4⋊Dic61—28no—
249C4⋊Dic61—28no—
250C4⋊Dic61—44no—
251#11758196—28no—
252#11758196—28no—
253#11758196—28no—
254#11758196—44no—
255C4×Dic61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—28no—
261C23×C61—28no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61—44no—
281C23×C61—44no—
282C23×C61C22×D414yes—
283C23×C61C22×D412yes—
284C23×C61C2×#4114yes—
285C23×C61C2×#4112yes—
286C23×C61C2×#4112yes—
287C23×C61H(5,𝔽2)12yes—
288C23×C61H(5,𝔽2)12yes—
289C23×C612−1+412yes—
290C23×C612−1+412yes—
291C23×C61C2511yescharacteristic
292D4×C61—232no—
293C2×C4×C61—28no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—44no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61C2×#4114yes—
313C2×Dic61—28no—
314C2×Dic61—28no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—416no—
338C2×Dic61—416no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61—44no—
345C2×Dic61C22×D414yes—
346C2×Dic61C22×D414yes—
347Dic122—416no—
348C2×#2638—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—24no—
353C22×C61—24no—
354C22×C61—24no—
355C22×C61—416no—
356C22×C61—416no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61#52514yes—
366C22×C61#53414yes—
367C22×C61#53614yes—
368C22×C61#53914yes—
369C22×C61#53914yes—
370C22×C61#54214yes—
371C22×C61#54214yes—
372C22×C61C23×D411yescharacteristic
373C22×C61C22×#4111yescharacteristic
374C22×C61C22×#4111yescharacteristic
375C22×C61C2×H(5,𝔽2)11yescharacteristic
376C22×C61C2×H(5,𝔽2)11yescharacteristic
377C22×C61C2×2−1+411yescharacteristic
378C22×C61C2×2−1+411yescharacteristic
379C4×C61—24no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384Dic61—24no—
385Dic61—24no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392C22×C22⋊Q8—611no—
393C22×C4×D4—611no—
394#2638—6116no—
395C2×#398—611no—
396C2×#397—611no—
397C2×#397—611no—
398C2×#397—611no—
399C2×#395—611no—
400C2×#394—611no—
401C2×#394D6111yescharacteristic
402C2×#393—611no—
403C2×#387—611no—
404C2×#387—611no—
405C2×#385—611no—
406C2×#385—611no—
407C2×#381—611no—
408C2×C61—44no—
409C2×C61—44no—
410C2×C61#263818yescomplemented
411C2×C61C2×#52511yescharacteristic
412C2×C61C2×#53411yescharacteristic
413C2×C61C2×#53611yescharacteristic
414C2×C61C2×#53911yescharacteristic
415C2×C61C2×#53911yescharacteristic
416C2×C61C2×#54211yescharacteristic
417C2×C61C2×#54211yescharacteristic
418C23×Q8—611no—
419C23×D4C2×D6111yescharacteristic
420C24×C4—611no—
421C24×C4—611no—
422C2×C22⋊Q8—618no—
423C2×C22⋊Q8—1228no—
424C2×C4×D4—618no—
425C2×C4×D4—1228no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—611no—
433C22×C4⋊C4C2×D6111yescharacteristic
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4C2×D6111yescharacteristic
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4C2×D6111yescharacteristic
444C22×C42—611no—
445#398—618no—
446#397—618no—
447#397—618no—
448#397—618no—
449#395—618no—
450#394—618no—
451#394C2×D6118yes—
452#393—618no—
453#387—618no—
454#387—618no—
455#385—618no—
456#385—618no—
457#381—618no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—611no—
467C2×#95—611no—
468C2×#95—611no—
469C2×#95C2×D6111yescharacteristic
470C61C2×#263811yescharacteristic, complemented, Sylow
471C25C22×D6111yescharacteristic
472C25C22×D6111yescharacteristic
473C22×Q8—614no—
474C22×Q8—1224no—
475C22×Q8—2442no—
476C22×Q8—2442no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4C22×D6114yes—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—618no—
484C23×C4—614no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—614no—
492C23×C4—1224no—
493C23×C4—2442no—
494C23×C4—2442no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502C22⋊Q8—12232no—
503C4×D4—12232no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—614no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—1224no—
515C2×C4⋊C4—1224no—
516C2×C4⋊C4—1224no—
517C2×C4⋊C4—2442no—
518C2×C4⋊C4—2442no—
519C2×C4⋊C4C22×D6114yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—614no—
525C2×C22⋊C4—614no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—614no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—614no—
530C2×C22⋊C4—1224no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—2442no—
535C2×C22⋊C4—2442no—
536C2×C22⋊C4C22×D6114yes—
537C2×C22⋊C4C22×D6114yes—
538C2×C22⋊C4C22×D6114yes—
539C2×C22⋊C4C22×D6114yes—
540C2×C42—614no—
541C2×C42—1224no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95—614no—
551#95—614no—
552#95—614no—
553#95C22×D6114yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24D4×D6114yes—
567C24#1175822414yes—
568C24C23×D6112yes—
569C24C23×D6112yes—
570C24C23×D6111yescharacteristic
571C2×Q8—1228no—
572C2×Q8—2444no—
573C2×Q8—2444no—
574C2×Q8—24416no—
575C2×D4—232no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—6116no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—1228no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—24416no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2444no—
631C22×C4—2444no—
632C22×C4—24416no—
633C22×C4#1175822414yes—
634C22×C4C23×D6112yes—
635C22×C4C23×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6112yes—
638C22×C4C23×D6112yes—
639C4⋊C4—28no—
640C4⋊C4—1228no—
641C4⋊C4—1228no—
642C4⋊C4—1228no—
643C4⋊C4—1228no—
644C4⋊C4—1228no—
645C4⋊C4—2444no—
646C4⋊C4—2444no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—1228no—
652C22⋊C4—1228no—
653C22⋊C4—1228no—
654C22⋊C4—1228no—
655C22⋊C4—2444no—
656C22⋊C4—2444no—
657C42—1228no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C2×D4×D6114yes—
685C23C2×D4×D6112yes—
686C23C2×#1175822414yes—
687C23C2×#1175822412yes—
688C23C2×#1175822412yes—
689C23#1451982212yes—
690C23#1451982312yes—
691C23#1451982412yes—
692C23#1451982412yes—
693C23C24×D6111yescharacteristic
694Q8—24416no—
695D4—232no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—614no—
716C2×C4—614no—
717C2×C4—1228no—
718C2×C4—1228no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—24416no—
742C2×C4—24416no—
743C2×C4—2444no—
744C2×C4—2444no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4C2×#1175822414yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—416no—
759C22—416no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22#1684026814yes—
767C22#1684032014yes—
768C22#1684033414yes—
769C22#1684035614yes—
770C22#1684035714yes—
771C22#1684037914yes—
772C22#1684038114yes—
773C22C22×D4×D6111yescharacteristic
774C22C22×#1175822411yescharacteristic
775C22C22×#1175822411yescharacteristic
776C22C2×#1451982211yescharacteristic
777C22C2×#1451982311yescharacteristic
778C22C2×#1451982411yescharacteristic
779C22C2×#1451982411yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—1224no—
786C4—1224no—
787C4—2442no—
788C4—2442no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C2—44no—
794C2—44no—
795C2#2145173518yesdirect product factor
796C2C2×#1684026811yescharacteristic
797C2C2×#1684032011yescharacteristic
798C2C2×#1684033411yescharacteristic
799C2C2×#1684035611yescharacteristic
800C2C2×#1684035711yescharacteristic
801C2C2×#1684037911yescharacteristic
802C2C2×#1684038111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#394C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#394D61
hypocenterC61C2×#2638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#14519754C2semidirect
3. #21451735C2direct (N × H)
4. C2×#16839695C2semidirect
5. C2×#16839690C2semidirect
6. C2×#16839690C2semidirect
7. C2×#16839687C2semidirect
8. C2×#16839683C2semidirect
10. C2×#16839674C2semidirect
11. C2×#16839648C2semidirect
12. C2×#16839644C2semidirect
13. C2×#16839637C2semidirect
14. C2×#16839634C2semidirect
15. C2×#16839623C2semidirect
21. C2×#14519754C22semidirect
38. #16839695C22semidirect
39. #16839690C22semidirect
40. #16839690C22semidirect
41. #16839687C22semidirect
42. #16839683C22semidirect
44. #16839674C22semidirect
45. #16839648C22semidirect
46. #16839644C22semidirect
47. #16839637C22semidirect
48. #16839634C22semidirect
49. #16839623C22semidirect
410. C2×C61#2638semidirect
470. C61C2×#2638semidirect
795. C2#21451735direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×D4×Dic612
#214517352
C2×#168396952
C2×#168396902
C2×#168396872
C2×#168396832
C2×#168396762
C2×#168396742
C2×#168396482
C2×#168396442
C2×#168396372
C2×#168396342
C2×#168396232
C2×C61×#3942
C2×#263861