Finite Group Databasebeta

← C2×#23769425 #34454949

Subgroups — C2×#23769425 #34454949

Order 20224.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23769425C2116yesmaximal, direct product factor
2C2×#19098504C211yesmaximal, characteristic, complemented
3C2×#19098501C211yesmaximal, characteristic, complemented
4C2×#19098492C211yesmaximal, characteristic
5C2×#19098492C211yesmaximal, characteristic
6C2×#19098487C211yesmaximal, characteristic
7C2×#19098483C211yesmaximal, characteristic, complemented
8C2×#19098476C211yesmaximal, characteristic
9C2×#19098467C211yesmaximal, characteristic, complemented
10C2×#19098455C211yesmaximal, characteristic
11C2×#19098453C211yesmaximal, characteristic
12C2×#19098453C211yesmaximal, characteristic
13C2×#19098450C211yesmaximal, characteristic, complemented
14C2×#19098448C211yesmaximal, characteristic, complemented
15C2×#19098414C211yesmaximal, characteristic, complemented
16C2×#400×C79C211yesmaximal, characteristic, complemented
17C23×Dic158C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×Dic79⋊C4C2211yescharacteristic
20C22×Dic79⋊C4C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×Dic79⋊C4C2211yescharacteristic
24C22×(C2×D79)⋊C4C2211yescharacteristic
25C22×(C2×D79)⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32C22×C4×Dic79C2211yescharacteristic
33C22×C4×Dic79C2211yescharacteristic
34#19098504C2218yescomplemented
35#19098501C2218yescomplemented
36#19098492C2218yes—
37#19098492C2218yes—
38#19098487C2218yes—
39#19098483C2218yescomplemented
40#19098476C2218yes—
41#19098467C2218yescomplemented
42#19098455C2218yes—
43#19098453C2218yes—
44#19098453C2218yes—
45#19098450C2218yescomplemented
46#19098448C2218yescomplemented
47#19098414C2218yescomplemented
48C2×C79⋊#95C2211yescharacteristic
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C22×C4⋊C4×C79C2211yescharacteristic
60C22×C4⋊C4×C79C2211yescharacteristic
61#400×C79C2218yescomplemented
62C2×#95×C79C2211yescharacteristic
63C2×#95×C79C2211yescharacteristic
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C22×Dic158—24no—
69C22×Dic158—42no—
70C22×Dic158—42no—
71C22×Dic158C2314yes—
72C23×Dic79C2311yescharacteristic
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C2×C4⋊Dic79—24no—
80C2×C4⋊Dic79C2314yes—
81C2×Dic79⋊C4—24no—
82C2×Dic79⋊C4—24no—
83C2×Dic79⋊C4—24no—
84C2×Dic79⋊C4—42no—
85C2×Dic79⋊C4—42no—
86C2×Dic79⋊C4C2314yes—
87C2×Dic79⋊C4C2314yes—
88C2×Dic79⋊C4C2314yes—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×(C2×D79)⋊C4—24no—
92C2×(C2×D79)⋊C4—24no—
93C2×(C2×D79)⋊C4—24no—
94C2×(C2×D79)⋊C4—42no—
95C2×(C2×D79)⋊C4—42no—
96C2×(C2×D79)⋊C4—42no—
97C2×(C2×D79)⋊C4—42no—
98C2×(C2×D79)⋊C4C2314yes—
99C2×(C2×D79)⋊C4C2314yes—
100C2×(C2×D79)⋊C4C2314yes—
101C2×(C2×D79)⋊C4C2314yes—
102C2×(C2×D79)⋊C4C2314yes—
103C2×(C2×D79)⋊C4C2314yes—
104C2×(C2×D79)⋊C4C2314yes—
105C2×C4×Dic79—24no—
106C2×C4×Dic79—42no—
107C2×C4×Dic79—42no—
108C2×C4×Dic79C2314yes—
109C2×C4×Dic79C2314yes—
110C2×C4×Dic79C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C23×C4×C79C2311yescharacteristic
123C23×C4×C79C2311yescharacteristic
124C23×C4×C79C2311yescharacteristic
125C23×C4×C79C2311yescharacteristic
126C23×C4×C79C2311yescharacteristic
127C23×C4×C79C2311yescharacteristic
128C23×C4×C79C2311yescharacteristic
129C2×C4⋊C4×C79—42no—
130C2×C4⋊C4×C79—42no—
131C2×C4⋊C4×C79C2314yes—
132C2×C4⋊C4×C79C2314yes—
133#95×C79C2314yes—
134#95×C79C2314yes—
135#95×C79C2314yes—
136#95×C79C2314yes—
137#95×C79C2314yes—
138C23×D79—22no—
139C23×D79—22no—
140C23×D79—22no—
141C23×D79—22no—
142C23×D79—22no—
143C23×D79—22no—
144C23×D79—22no—
145C23×D79C2412yes—
146C2×Dic158—28no—
147C2×Dic158—44no—
148C2×Dic158—44no—
149C2×Dic158—416no—
150C22×Dic79—22no—
151C22×Dic79—22no—
152C22×Dic79—22no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—22no—
156C22×Dic79—22no—
157C22×Dic79—22no—
158C22×Dic79—22no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—22no—
168C22×Dic79#4114yes—
169C22×Dic79#4114yes—
170C22×Dic79#4114yes—
171C22×Dic79C2412yes—
172C22×Dic79C2412yes—
173C22×Dic79C2412yes—
174C22×Dic79C2412yes—
175C22×Dic79C2412yes—
176C22×Dic79C2412yes—
177C22×Dic79C2412yes—
178C4⋊Dic79—28no—
179Dic79⋊C4—28no—
180Dic79⋊C4—28no—
181Dic79⋊C4—28no—
182Dic79⋊C4—44no—
183Dic79⋊C4—44no—
184(C2×D79)⋊C4—28no—
185(C2×D79)⋊C4—28no—
186(C2×D79)⋊C4—28no—
187(C2×D79)⋊C4—44no—
188(C2×D79)⋊C4—44no—
189(C2×D79)⋊C4—44no—
190(C2×D79)⋊C4—44no—
191C4×Dic79—28no—
192C4×Dic79—44no—
193C4×Dic79—44no—
194C24×C79C2411yescharacteristic
195C22×C4×C79—22no—
196C22×C4×C79—22no—
197C22×C4×C79—22no—
198C22×C4×C79—22no—
199C22×C4×C79—22no—
200C22×C4×C79—22no—
201C22×C4×C79—22no—
202C22×C4×C79—22no—
203C22×C4×C79—22no—
204C22×C4×C79—22no—
205C22×C4×C79—22no—
206C22×C4×C79—22no—
207C22×C4×C79—22no—
208C22×C4×C79—22no—
209C22×C4×C79—22no—
210C22×C4×C79—22no—
211C22×C4×C79—22no—
212C22×C4×C79—22no—
213C22×C4×C79—22no—
214C22×C4×C79—22no—
215C22×C4×C79—22no—
216C22×C4×C79C2412yes—
217C22×C4×C79C2412yes—
218C22×C4×C79C2412yes—
219C22×C4×C79C2412yes—
220C22×C4×C79C2412yes—
221C22×C4×C79C2412yes—
222C22×C4×C79C2412yes—
223C4⋊C4×C79—44no—
224C4⋊C4×C79—44no—
225C23×C79C2×#4112yes—
226C23×C79C2×#4112yes—
227C23×C79C2×#4112yes—
228C23×C79H(5,𝔽2)12yes—
229C23×C79H(5,𝔽2)12yes—
230C23×C792−1+412yes—
231C23×C792−1+412yes—
232C23×C79C2511yescharacteristic
233C22×D79—22no—
234C22×D79—22no—
235C22×D79—22no—
236C22×D79—22no—
237C22×D79—22no—
238C22×D79—22no—
239C22×D79—22no—
240C22×D79—44no—
241C22×D79—44no—
242C22×D79—44no—
243C22×D79—44no—
244C22×D79—44no—
245C22×D79—44no—
246C22×D79—44no—
247C2×C4×C79—22no—
248C2×C4×C79—22no—
249C2×C4×C79—22no—
250C2×C4×C79—22no—
251C2×C4×C79—22no—
252C2×C4×C79—22no—
253C2×C4×C79—22no—
254C2×C4×C79—22no—
255C2×C4×C79—22no—
256C2×C4×C79—22no—
257C2×C4×C79—22no—
258C2×C4×C79—22no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—22no—
262C2×C4×C79—22no—
263C2×C4×C79—22no—
264C2×C4×C79—22no—
265C2×C4×C79—22no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—44no—
269C2×C4×C79—44no—
270C2×C4×C79—44no—
271C2×C4×C79—44no—
272C2×C4×C79—44no—
273C2×C4×C79—44no—
274C2×C4×C79—44no—
275C2×Dic79—28no—
276C2×Dic79—28no—
277C2×Dic79—28no—
278C2×Dic79—22no—
279C2×Dic79—22no—
280C2×Dic79—22no—
281C2×Dic79—22no—
282C2×Dic79—22no—
283C2×Dic79—22no—
284C2×Dic79—22no—
285C2×Dic79—22no—
286C2×Dic79—22no—
287C2×Dic79—22no—
288C2×Dic79—22no—
289C2×Dic79—22no—
290C2×Dic79—22no—
291C2×Dic79—22no—
292C2×Dic79—22no—
293C2×Dic79—22no—
294C2×Dic79—22no—
295C2×Dic79—22no—
296C2×Dic79—44no—
297C2×Dic79—44no—
298C2×Dic79—44no—
299C2×Dic79—44no—
300C2×Dic79C2×#4114yes—
301C2×Dic79C2×#4114yes—
302C2×Dic79C2×#4114yes—
303Dic158—416no—
304C22×C79#52914yes—
305C22×C79#53814yes—
306C22×C79#53914yes—
307C22×C79#54114yes—
308C22×C79#54214yes—
309C22×C79#54214yes—
310C22×C79#54214yes—
311C22×C79C22×#4111yescharacteristic
312C22×C79C22×#4111yescharacteristic
313C22×C79C22×#4111yescharacteristic
314C22×C79C2×H(5,𝔽2)11yescharacteristic
315C22×C79C2×H(5,𝔽2)11yescharacteristic
316C22×C79C2×2−1+411yescharacteristic
317C22×C79C2×2−1+411yescharacteristic
318C2×D79—42no—
319C2×D79—42no—
320C2×D79—42no—
321C2×D79—42no—
322C2×D79—42no—
323C2×D79—42no—
324C2×D79—42no—
325C2×D79—88no—
326C4×C79—42no—
327C4×C79—42no—
328C4×C79—42no—
329C4×C79—42no—
330C4×C79—42no—
331C4×C79—42no—
332C4×C79—42no—
333Dic79—24no—
334Dic79—24no—
335Dic79—24no—
336Dic79—42no—
337Dic79—42no—
338Dic79—42no—
339Dic79—42no—
340C2×#2650—791nomaximal, Sylow
341C2×C79#265018yescomplemented
342C2×C79C2×#52911yescharacteristic
343C2×C79C2×#53811yescharacteristic
344C2×C79C2×#53911yescharacteristic
345C2×C79C2×#54111yescharacteristic
346C2×C79C2×#54211yescharacteristic
347C2×C79C2×#54211yescharacteristic
348C2×C79C2×#54211yescharacteristic
349D79—82no—
350#2650—7916no—
351C2×#400—791no—
352C2×#400—791no—
353C2×#400D7911yescharacteristic, complemented
354C2×#397—791no—
355C2×#397—791no—
356C2×#396—791no—
357C2×#395—791no—
358C2×#393—791no—
359C2×#391—791no—
360C2×#388—791no—
361C2×#388—791no—
362C2×#388—791no—
363C2×#387—791no—
364C2×#387—791no—
365C2×C4×C4⋊C4—791no—
366C79C2×#265011yescharacteristic, complemented, Sylow
367C23×Q8—791no—
368C22×C4⋊C4—791no—
369C22×C4⋊C4—791no—
370C22×C4⋊C4—791no—
371C22×C4⋊C4—791no—
372C22×C4⋊C4—791no—
373C22×C4⋊C4—791no—
374C22×C4⋊C4C2×D7911yescharacteristic
375C22×C4⋊C4C2×D7911yescharacteristic
376C22×C22⋊C4—791no—
377C22×C22⋊C4—791no—
378C22×C22⋊C4—791no—
379C22×C22⋊C4—791no—
380C22×C22⋊C4—791no—
381C22×C22⋊C4—791no—
382C22×C22⋊C4—791no—
383C22×C42—791no—
384C22×C42—791no—
385C22×C42—791no—
386#400—798no—
387#400—798no—
388#400C2×D7918yescomplemented
389#397—798no—
390#397—798no—
391#396—798no—
392#395—798no—
393#393—798no—
394#391—798no—
395#388—798no—
396#388—798no—
397#388—798no—
398#387—798no—
399#387—798no—
400C4×C4⋊C4—798no—
401C2×#95—791no—
402C2×#95—791no—
403C2×#95—791no—
404C2×#95—791no—
405C2×#95—791no—
406C2×#95—791no—
407C2×#95—791no—
408C2×#95—791no—
409C2×#95—791no—
410C2×#95—791no—
411C2×#95—791no—
412C2×#95C2×D7911yescharacteristic
413C2×#95C2×D7911yescharacteristic
414C2×#95C2×D7911yescharacteristic
415C2×#95C2×D7911yescharacteristic
416C2×#95C2×D7911yescharacteristic
417C25—791no—
418C22×Q8—3162no—
419C22×Q8—3162no—
420C22×Q8—794no—
421C22×Q8—1584no—
422C23×C4—791no—
423C23×C4—791no—
424C23×C4—791no—
425C23×C4—791no—
426C23×C4—791no—
427C23×C4—791no—
428C23×C4—791no—
429C23×C4C22×D7911yescharacteristic
430C23×C4C22×D7911yescharacteristic
431C23×C4C22×D7911yescharacteristic
432C23×C4C22×D7911yescharacteristic
433C23×C4C22×D7911yescharacteristic
434C23×C4C22×D7911yescharacteristic
435C23×C4C22×D7911yescharacteristic
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—3162no—
439C2×C4⋊C4—3162no—
440C2×C4⋊C4—794no—
441C2×C4⋊C4—794no—
442C2×C4⋊C4—794no—
443C2×C4⋊C4—794no—
444C2×C4⋊C4—794no—
445C2×C4⋊C4—794no—
446C2×C4⋊C4—1584no—
447C2×C4⋊C4—1584no—
448C2×C4⋊C4—1584no—
449C2×C4⋊C4—1584no—
450C2×C4⋊C4C22×D7914yes—
451C2×C4⋊C4C22×D7914yes—
452C2×C22⋊C4—3162no—
453C2×C22⋊C4—3162no—
454C2×C22⋊C4—3162no—
455C2×C22⋊C4—3162no—
456C2×C22⋊C4—794no—
457C2×C22⋊C4—794no—
458C2×C22⋊C4—794no—
459C2×C22⋊C4—794no—
460C2×C22⋊C4—794no—
461C2×C22⋊C4—794no—
462C2×C22⋊C4—794no—
463C2×C22⋊C4—1584no—
464C2×C22⋊C4—1584no—
465C2×C22⋊C4—1584no—
466C2×C42—3162no—
467C2×C42—3162no—
468C2×C42—794no—
469C2×C42—794no—
470C2×C42—794no—
471C2×C42—1584no—
472#95—794no—
473#95—794no—
474#95—794no—
475#95—794no—
476#95—794no—
477#95—794no—
478#95—794no—
479#95—794no—
480#95—794no—
481#95—794no—
482#95—794no—
483#95C22×D7914yes—
484#95C22×D7914yes—
485#95C22×D7914yes—
486#95C22×D7914yes—
487#95C22×D7914yes—
488C24—792no—
489C24—1582no—
490C24—1582no—
491C24—1582no—
492C24—1582no—
493C24—1582no—
494C24—1582no—
495C24—1582no—
496C24C23×D7911yescharacteristic
497C2×Q8—3164no—
498C2×Q8—3164no—
499C2×Q8—31616no—
500C2×Q8—1588no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—794no—
523C22×C4—794no—
524C22×C4—794no—
525C22×C4—792no—
526C22×C4—792no—
527C22×C4—792no—
528C22×C4—792no—
529C22×C4—792no—
530C22×C4—792no—
531C22×C4—792no—
532C22×C4—1582no—
533C22×C4—1582no—
534C22×C4—1582no—
535C22×C4—1582no—
536C22×C4—1582no—
537C22×C4—1582no—
538C22×C4—1582no—
539C22×C4—1582no—
540C22×C4—1582no—
541C22×C4—1582no—
542C22×C4—1582no—
543C22×C4—1582no—
544C22×C4—1582no—
545C22×C4—1582no—
546C22×C4—1582no—
547C22×C4—1582no—
548C22×C4—1582no—
549C22×C4—1582no—
550C22×C4C23×D7912yes—
551C22×C4C23×D7912yes—
552C22×C4C23×D7912yes—
553C22×C4C23×D7912yes—
554C22×C4C23×D7912yes—
555C22×C4C23×D7912yes—
556C22×C4C23×D7912yes—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—3164no—
560C4⋊C4—3164no—
561C4⋊C4—1588no—
562C4⋊C4—1588no—
563C4⋊C4—1588no—
564C4⋊C4—1588no—
565C22⋊C4—3164no—
566C22⋊C4—3164no—
567C22⋊C4—3164no—
568C22⋊C4—3164no—
569C22⋊C4—1588no—
570C22⋊C4—1588no—
571C22⋊C4—1588no—
572C42—3164no—
573C42—3164no—
574C42—1588no—
575C23—3164no—
576C23—3164no—
577C23—3164no—
578C23—3164no—
579C23—3164no—
580C23—3164no—
581C23—3164no—
582C23—1582no—
583C23—1582no—
584C23—1582no—
585C23—1582no—
586C23—1582no—
587C23—1582no—
588C23—1582no—
589C23#41×D7912yes—
590C23#41×D7912yes—
591C23#41×D7912yes—
592C23#1457920612yes—
593C23#1457920712yes—
594C23#1457920812yes—
595C23#1457920912yes—
596C23C24×D7911yescharacteristic
597Q8—31616no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—3164no—
627C2×C4—3164no—
628C2×C4—3164no—
629C2×C4—3164no—
630C2×C4—794no—
631C2×C4—794no—
632C2×C4—794no—
633C2×C4—1582no—
634C2×C4—1582no—
635C2×C4—1582no—
636C2×C4—1582no—
637C2×C4—1582no—
638C2×C4—1582no—
639C2×C4—1582no—
640C2×C4—1582no—
641C2×C4—1582no—
642C2×C4—1582no—
643C2×C4—1582no—
644C2×C4—1582no—
645C2×C4—1582no—
646C2×C4—1582no—
647C2×C4—1582no—
648C2×C4—1582no—
649C2×C4—1588no—
650C2×C4—1588no—
651C2×C4—1588no—
652C2×C4—1582no—
653C2×C4—1582no—
654C22—3162no—
655C22—3162no—
656C22—3162no—
657C22—3162no—
658C22—3162no—
659C22—3162no—
660C22—3162no—
661C22—6328no—
662C22#1909909614yes—
663C22#1909914714yes—
664C22#1909916114yes—
665C22#1909917214yes—
666C22#1909917914yes—
667C22#1909918114yes—
668C22#1909918314yes—
669C22C2×#41×D7911yescharacteristic
670C22C2×#41×D7911yescharacteristic
671C22C2×#41×D7911yescharacteristic
672C22C2×#1457920611yescharacteristic
673C22C2×#1457920711yescharacteristic
674C22C2×#1457920811yescharacteristic
675C22C2×#1457920911yescharacteristic
676C4—42no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—3162no—
684C4—3162no—
685C4—3162no—
686C4—3162no—
687C4—1584no—
688C4—1584no—
689C4—1584no—
690C2—6322no—
691C2#2376942518yesdirect product factor
692C2C2×#1909909611yescharacteristic
693C2C2×#1909914711yescharacteristic
694C2C2×#1909916111yescharacteristic
695C2C2×#1909917211yescharacteristic
696C2C2×#1909917911yescharacteristic
697C2C2×#1909918111yescharacteristic
698C2C2×#1909918311yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#400×C79C2
socleC24×C79C24
prime radicalC24×D79C23
hypercenterC2×#400D79
hypocenterC79C2×#2650
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #23769425C2direct (N × H)
2. C2×#19098504C2semidirect
3. C2×#19098501C2semidirect
7. C2×#19098483C2semidirect
9. C2×#19098467C2semidirect
13. C2×#19098450C2semidirect
14. C2×#19098448C2semidirect
15. C2×#19098414C2semidirect
16. C2×#400×C79C2semidirect
34. #19098504C22semidirect
35. #19098501C22semidirect
39. #19098483C22semidirect
41. #19098467C22semidirect
45. #19098450C22semidirect
46. #19098448C22semidirect
47. #19098414C22semidirect
61. #400×C79C22semidirect
341. C2×C79#2650semidirect
353. C2×#400D79semidirect
366. C79C2×#2650semidirect
388. #400C2×D79semidirect
691. C2#23769425direct (N × H)

Maximal subgroups

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

subgroupindex
#237694252
C2×#190985042
C2×#190985012
C2×#190984922
C2×#190984872
C2×#190984832
C2×#190984762
C2×#190984672
C2×#190984552
C2×#190984532
C2×#190984502
C2×#190984482
C2×#190984142
C2×#400×C792
C2×#265079