Finite Group Databasebeta

← C2×#21450363 #29849476

Subgroups — C2×#21450363 #29849476

Order 15616.

1966 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450363C2116yesmaximal, direct product factor
2C2×#16839704C211yesmaximal, characteristic
3C2×#16839702C211yesmaximal, characteristic
4C2×#16839700C211yesmaximal, characteristic
5C2×#16839661C211yesmaximal, characteristic
6C2×#16839659C211yesmaximal, characteristic
7C2×#16839659C211yesmaximal, characteristic
8C2×#16839659C211yesmaximal, characteristic
9C2×#16839659C211yesmaximal, characteristic
10C2×#16839657C211yesmaximal, characteristic
11C2×#16839649C211yesmaximal, characteristic
12C2×#16839647C211yesmaximal, characteristic
13C2×#16839626C211yesmaximal, characteristic
14C2×C4⋊C4×Dic61C211yesmaximal, characteristic
15C2×#16839613C211yesmaximal, characteristic
16C2×C61×#400C211yesmaximal, characteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839704C2218yes—
35#16839702C2218yes—
36#16839700C2218yes—
37#16839661C2218yes—
38#16839659C2218yes—
39#16839659C2218yes—
40#16839659C2218yes—
41#16839659C2218yes—
42#16839657C2218yes—
43#16839649C2218yes—
44#16839647C2218yes—
45#16839626C2218yes—
46C4⋊C4×Dic61C2218yes—
47#16839613C2218yes—
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C61×#400C2218yes—
62C2×#95×C61C2211yescharacteristic
63C2×#95×C61C2211yescharacteristic
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C2×C4⋊Dic61—24no—
76C2×C4⋊Dic61—24no—
77C2×C4⋊Dic61—42no—
78C2×C4⋊Dic61—42no—
79C2×C4⋊Dic61C2314yes—
80C2×C4⋊Dic61C2314yes—
81C2×C4⋊Dic61C2314yes—
82C2×C4⋊Dic61C2314yes—
83C2×#11758196—24no—
84C2×#11758196—24no—
85C2×#11758196—24no—
86C2×#11758196—24no—
87C2×#11758196—24no—
88C2×#11758196—42no—
89C2×#11758196—42no—
90C2×#11758196Q818yes—
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×C4×Dic61—24no—
100C2×C4×Dic61—24no—
101C2×C4×Dic61—24no—
102C2×C4×Dic61—42no—
103C2×C4×Dic61—42no—
104C2×C4×Dic61C2314yes—
105C2×C4×Dic61C2314yes—
106C2×C4×Dic61C2314yes—
107C2×C4×Dic61C2314yes—
108C2×C4×Dic61C2314yes—
109#14519684C2314yes—
110#14519684C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120C23×C4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C23×C4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61—24no—
128C2×C4⋊C4×C61—24no—
129C2×C4⋊C4×C61C2314yes—
130C2×C4⋊C4×C61C2314yes—
131#95×C61C2314yes—
132#95×C61C2314yes—
133#95×C61C2314yes—
134#95×C61C2314yes—
135#95×C61C2314yes—
136C24×C61C2411yescharacteristic
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61C2×Q814yes—
157C22×C4×C61#4114yes—
158C22×C4×C61C2412yes—
159C22×C4×C61C2412yes—
160C22×C4×C61C2412yes—
161C22×C4×C61C2412yes—
162C22×C4×C61C2412yes—
163C22×C4×C61C2412yes—
164C22×C4×C61C2412yes—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61C2×Q814yes—
185C22×Dic61C2×Q814yes—
186C22×Dic61#4114yes—
187C22×Dic61#4114yes—
188C22×Dic61#4114yes—
189C22×Dic61C2412yes—
190C22×Dic61C2412yes—
191C22×Dic61C2412yes—
192C22×Dic61C2412yes—
193C22×Dic61C2412yes—
194C22×Dic61C2412yes—
195C22×Dic61C2412yes—
196C22×Dic61C2412yes—
197C4⋊C4×C61—28no—
198C4⋊C4×C61—28no—
199C4⋊Dic61—28no—
200C4⋊Dic61—28no—
201C4⋊Dic61—44no—
202C4⋊Dic61—44no—
203#11758196—28no—
204#11758196—28no—
205#11758196—28no—
206#11758196—28no—
207#11758196—28no—
208#11758196—44no—
209#11758196—44no—
210#11758196C2×Q8116yes—
211C4×Dic61—28no—
212C4×Dic61—28no—
213C4×Dic61—28no—
214C4×Dic61—44no—
215C4×Dic61—44no—
216C23×C61C22×Q812yes—
217C23×C61C2×#4112yes—
218C23×C61C2×#4112yes—
219C23×C61C2×#4112yes—
220C23×C61C2×#4112yes—
221C23×C61H(5,𝔽2)12yes—
222C23×C612−1+412yes—
223C23×C61C2511yescharacteristic
224C2×C4×C61—28no—
225C2×C4×C61—28no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—44no—
246C2×C4×C61—44no—
247C2×C4×C61—44no—
248C2×C4×C61—44no—
249C2×C4×C61—44no—
250C2×C4×C61C22×Q814yes—
251C2×C4×C61C2×#4114yes—
252C2×Dic61—28no—
253C2×Dic61—28no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—44no—
274C2×Dic61—44no—
275C2×Dic61—44no—
276C2×Dic61—44no—
277C2×Dic61—44no—
278C2×Dic61#125116yes—
279C2×Dic61C22×Q814yes—
280C2×Dic61C22×Q814yes—
281C2×Dic61C2×#4114yes—
282C2×Dic61C2×#4114yes—
283C2×Dic61C2×#4114yes—
284C2×#2509—611nomaximal, Sylow
285C22×C61C2×#12514yes—
286C22×C61#52914yes—
287C22×C61#54214yes—
288C22×C61#55314yes—
289C22×C61#55414yes—
290C22×C61#55614yes—
291C22×C61#55714yes—
292C22×C61C23×Q811yescharacteristic
293C22×C61C22×#4111yescharacteristic
294C22×C61C22×#4111yescharacteristic
295C22×C61C22×#4111yescharacteristic
296C22×C61C22×#4111yescharacteristic
297C22×C61C2×H(5,𝔽2)11yescharacteristic
298C22×C61C2×2−1+411yescharacteristic
299C4×C61—24no—
300C4×C61—24no—
301C4×C61—42no—
302C4×C61—42no—
303C4×C61—42no—
304C4×C61—42no—
305C4×C61—42no—
306Dic61—24no—
307Dic61—24no—
308Dic61—42no—
309Dic61—42no—
310Dic61—42no—
311Dic61—42no—
312Dic61—42no—
313Dic61C2×#12518yes—
314#2509—6116no—
315C2×#400—611no—
316C2×#400—611no—
317C2×#400—611no—
318C2×#400D6111yescharacteristic
319C2×#389—611no—
320C2×#389—611no—
321C2×#389—611no—
322C2×#389—611no—
323C2×#389—611no—
324C2×#389—611no—
325C2×#387—611no—
326C2×#387—611no—
327C2×#382—611no—
328C2×C4×C4⋊C4—611no—
329C2×C4×C4⋊C4—611no—
330C2×C61#250918yescomplemented
331C2×C61C22×#12511yescharacteristic
332C2×C61C2×#52911yescharacteristic
333C2×C61C2×#54211yescharacteristic
334C2×C61C2×#55311yescharacteristic
335C2×C61C2×#55411yescharacteristic
336C2×C61C2×#55611yescharacteristic
337C2×C61C2×#55711yescharacteristic
338C22×C4⋊C4—611no—
339C22×C4⋊C4—611no—
340C22×C4⋊C4—611no—
341C22×C4⋊C4—611no—
342C22×C4⋊C4—611no—
343C22×C4⋊C4—611no—
344C22×C4⋊C4—611no—
345C22×C4⋊C4—611no—
346C22×C4⋊C4—611no—
347C22×C4⋊C4—611no—
348C22×C4⋊C4—611no—
349C22×C4⋊C4—611no—
350C22×C4⋊C4C2×D6111yescharacteristic
351C22×C4⋊C4C2×D6111yescharacteristic
352C22×C42—611no—
353C22×C42—611no—
354C22×C42—611no—
355C22×C42—611no—
356C22×C42—611no—
357#400—618no—
358#400—618no—
359#400—618no—
360#400C2×D6118yes—
361#389—618no—
362#389—618no—
363#389—618no—
364#389—618no—
365#389—618no—
366#389—618no—
367#387—618no—
368#387—618no—
369#382—618no—
370C4×C4⋊C4—618no—
371C4×C4⋊C4—618no—
372C2×#95—611no—
373C2×#95—611no—
374C2×#95—611no—
375C2×#95—611no—
376C2×#95—611no—
377C2×#95—611no—
378C2×#95—611no—
379C2×#95—611no—
380C2×#95—611no—
381C2×#95—611no—
382C2×#95—611no—
383C2×#95C2×D6111yescharacteristic
384C2×#95C2×D6111yescharacteristic
385C2×#95C2×D6111yescharacteristic
386C2×#95C2×D6111yescharacteristic
387C2×#95C2×D6111yescharacteristic
388C61C2×#250911yescharacteristic, complemented, Sylow
389C23×C4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4C22×D6111yescharacteristic
398C23×C4C22×D6111yescharacteristic
399C23×C4C22×D6111yescharacteristic
400C23×C4C22×D6111yescharacteristic
401C23×C4C22×D6111yescharacteristic
402C23×C4C22×D6111yescharacteristic
403C23×C4C22×D6111yescharacteristic
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—618no—
407C2×C4⋊C4—614no—
408C2×C4⋊C4—614no—
409C2×C4⋊C4—614no—
410C2×C4⋊C4—614no—
411C2×C4⋊C4—614no—
412C2×C4⋊C4—614no—
413C2×C4⋊C4—614no—
414C2×C4⋊C4—614no—
415C2×C4⋊C4—614no—
416C2×C4⋊C4—614no—
417C2×C4⋊C4—614no—
418C2×C4⋊C4—614no—
419C2×C4⋊C4—1224no—
420C2×C4⋊C4—1224no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—1224no—
423C2×C4⋊C4—1224no—
424C2×C4⋊C4—1224no—
425C2×C4⋊C4—1224no—
426C2×C4⋊C4—2442no—
427C2×C4⋊C4—2442no—
428C2×C4⋊C4—2442no—
429C2×C4⋊C4—2442no—
430C2×C4⋊C4C22×D6114yes—
431C2×C4⋊C4C22×D6114yes—
432C2×C42—614no—
433C2×C42—614no—
434C2×C42—614no—
435C2×C42—614no—
436C2×C42—614no—
437C2×C42—1224no—
438C2×C42—1224no—
439C2×C42—1224no—
440C2×C42—2442no—
441C2×C42—2442no—
442#95—614no—
443#95—614no—
444#95—614no—
445#95—614no—
446#95—614no—
447#95—614no—
448#95—614no—
449#95—614no—
450#95—614no—
451#95—614no—
452#95—614no—
453#95C22×D6114yes—
454#95C22×D6114yes—
455#95C22×D6114yes—
456#95C22×D6114yes—
457#95C22×D6114yes—
458C24C23×D6111yescharacteristic
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—614no—
479C22×C4—614no—
480C22×C4—614no—
481C22×C4—612no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—612no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4#1175822414yes—
511C22×C4Q8×D6114yes—
512C22×C4C23×D6112yes—
513C22×C4C23×D6112yes—
514C22×C4C23×D6112yes—
515C22×C4C23×D6112yes—
516C22×C4C23×D6112yes—
517C22×C4C23×D6112yes—
518C22×C4C23×D6112yes—
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—6116no—
522C4⋊C4—1228no—
523C4⋊C4—1228no—
524C4⋊C4—1228no—
525C4⋊C4—1228no—
526C4⋊C4—1228no—
527C4⋊C4—1228no—
528C4⋊C4—1228no—
529C4⋊C4—2444no—
530C4⋊C4—2444no—
531C4⋊C4—2444no—
532C4⋊C4—2444no—
533C42—1228no—
534C42—1228no—
535C42—1228no—
536C42—2444no—
537C42—2444no—
538C23C2×Q8×D6112yes—
539C23#41×D6112yes—
540C23#41×D6112yes—
541C23#41×D6112yes—
542C23C2×#1175822412yes—
543C23#1451982312yes—
544C23#1451982412yes—
545C23C24×D6111yescharacteristic
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—6116no—
573C2×C4—614no—
574C2×C4—614no—
575C2×C4—614no—
576C2×C4—614no—
577C2×C4—614no—
578C2×C4—1228no—
579C2×C4—1228no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—2444no—
600C2×C4—2444no—
601C2×C4—2444no—
602C2×C4—2444no—
603C2×C4—2444no—
604C2×C4C2×Q8×D6114yes—
605C2×C4C2×#1175822414yes—
606C22#125×D6114yes—
607C22#1684028914yes—
608C22#1684037814yes—
609C22#1684046314yes—
610C22#1684047014yes—
611C22#1684048114yes—
612C22#1684048914yes—
613C22C22×Q8×D6111yescharacteristic
614C22C2×#41×D6111yescharacteristic
615C22C2×#41×D6111yescharacteristic
616C22C2×#41×D6111yescharacteristic
617C22C22×#1175822411yescharacteristic
618C22C2×#1451982311yescharacteristic
619C22C2×#1451982411yescharacteristic
620C4—24no—
621C4—24no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—618no—
628C4—1224no—
629C4—1224no—
630C4—2442no—
631C4—2442no—
632C4—2442no—
633C4—2442no—
634C4—2442no—
635C2#2145036318yesdirect product factor
636C2C2×#125×D6111yescharacteristic
637C2C2×#1684028911yescharacteristic
638C2C2×#1684037811yescharacteristic
639C2C2×#1684046311yescharacteristic
640C2C2×#1684047011yescharacteristic
641C2C2×#1684048111yescharacteristic
642C2C2×#1684048911yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#400C2
socle, prime radicalC24×C61C24
hypercenterC2×#400D61
hypocenterC61C2×#2509
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21450363C2direct (N × H)
330. C2×C61#2509semidirect
388. C61C2×#2509semidirect
635. C2#21450363direct (N × H)

Maximal subgroups

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

subgroupindex
#214503632
C2×#168397042
C2×#168397022
C2×#168397002
C2×#168396612
C2×#168396592
C2×#168396572
C2×#168396492
C2×#168396472
C2×#168396262
C2×C4⋊C4×Dic612
C2×#168396132
C2×C61×#4002
C2×#250961