Finite Group Databasebeta

← C2×#21453953 #29886340

Subgroups — C2×#21453953 #29886340

Order 15616.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453953C2116yesmaximal, direct product factor
2C2×#16839699C211yesmaximal, characteristic, complemented
3C2×#16839695C211yesmaximal, characteristic, complemented
4C2×#16839691C211yesmaximal, characteristic, complemented
5C2×#16839688C211yesmaximal, characteristic, complemented
6C2×#16839684C211yesmaximal, characteristic, complemented
7C2×#16839679C211yesmaximal, characteristic, complemented
8C2×#16839678C211yesmaximal, characteristic, complemented
9C2×#16839678C211yesmaximal, characteristic, complemented
10C2×#16839677C211yesmaximal, characteristic, complemented
11C2×#16839677C211yesmaximal, characteristic, complemented
12C2×#16839671C211yesmaximal, characteristic
13C2×#16839663C211yesmaximal, characteristic, complemented
14C2×#16839655C211yesmaximal, characteristic, complemented
15C2×#16839648C211yesmaximal, characteristic, complemented
16C2×C61×#396C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C22⋊D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839699C2218yescomplemented
39#16839695C2218yescomplemented
40#16839691C2218yescomplemented
41#16839688C2218yescomplemented
42#16839684C2218yescomplemented
43#16839679C2218yescomplemented
44#16839678C2218yescomplemented
45#16839678C2218yescomplemented
46#16839677C2218yescomplemented
47#16839677C2218yescomplemented
48#16839671C2218yes—
49#16839663C2218yescomplemented
50#16839655C2218yescomplemented
51#16839648C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#396C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C24×D61C2311yescharacteristic
69C22×D244—24no—
70C22×D244—42no—
71C22×D244—42no—
72C22×D244C2314yes—
73C22×C22⋊D61—42no—
74C22×C22⋊D61—42no—
75C22×C22⋊D61—42no—
76C22×C22⋊D61—42no—
77C22×C22⋊D61—42no—
78C22×C22⋊D61—42no—
79C22×C22⋊D61C2314yes—
80C22×C22⋊D61C2314yes—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C2×C4⋊Dic61—42no—
88C2×C4⋊Dic61—42no—
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61C2314yes—
91C2×C4⋊Dic61C2314yes—
92C2×C4⋊Dic61C2314yes—
93C2×#11758196—42no—
94C2×#11758196—42no—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×C22⋊Dic61—42no—
98C2×C22⋊Dic61—42no—
99C2×C22⋊Dic61C2314yes—
100C2×C22⋊Dic61C2314yes—
101C2×#11758198—42no—
102C2×#11758198—42no—
103C2×#11758198—42no—
104C2×#11758198—42no—
105C2×#11758198—42no—
106C2×#11758198—42no—
107C2×#11758198—42no—
108C2×#11758198—42no—
109C2×#11758198—42no—
110C2×#11758198—42no—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×C4×Dic61—42no—
122C2×C4×Dic61C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130C25×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61—24no—
138C2×C4⋊C4×C61—42no—
139C2×C4⋊C4×C61—42no—
140C2×C4⋊C4×C61C2314yes—
141C2×C4⋊C4×C61C2314yes—
142C2×C4⋊C4×C61C2314yes—
143C2×C22⋊C4×C61—24no—
144C2×C22⋊C4×C61—42no—
145C2×C22⋊C4×C61—42no—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61C2412yes—
158C24×C61C2411yescharacteristic
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C2412yes—
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×C61—22no—
191C22×C4×C61—22no—
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—44no—
200C2×C22⋊D61—44no—
201C2×C22⋊D61—44no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—44no—
205C2×C22⋊D61—416no—
206C2×C22⋊D61—416no—
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—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C2×D244—28no—
232C2×D244—44no—
233C2×D244—44no—
234C2×D244—416no—
235C4⋊C4×C61—28no—
236C4⋊C4×C61—44no—
237C4⋊C4×C61—44no—
238C22⋊C4×C61—28no—
239C22⋊C4×C61—44no—
240C22⋊C4×C61—44no—
241C22⋊Dic61—44no—
242C22⋊Dic61—44no—
243#11758198—44no—
244#11758198—44no—
245#11758198—44no—
246#11758198—44no—
247#11758198—44no—
248#11758198—44no—
249#11758198—44no—
250#11758198—44no—
251#11758198—44no—
252#11758198—44no—
253C4⋊Dic61—44no—
254C4⋊Dic61—44no—
255C4⋊Dic61—44no—
256#11758196—44no—
257#11758196—44no—
258C4×Dic61—44no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—44no—
269C23×C61—44no—
270C23×C61—44no—
271C23×C61—44no—
272C23×C61—44no—
273C23×C61C2×#4112yes—
274C23×C61H(5,𝔽2)12yes—
275C23×C61H(5,𝔽2)12yes—
276C23×C61H(5,𝔽2)12yes—
277C23×C61H(5,𝔽2)12yes—
278C23×C61H(5,𝔽2)12yes—
279C23×C612−1+412yes—
280C23×C61C2511yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—44no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61—44no—
303C22×D61—44no—
304C22×D61—44no—
305C22×D61—44no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C2×C4×C61—28no—
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—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—44no—
328C2×C4×C61—44no—
329C2×C4×C61—44no—
330C2×C4×C61—44no—
331C2×C4×C61—44no—
332C2×C4×C61C2×#4114yes—
333C22⋊D61—416no—
334C22⋊D61—416no—
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—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—44no—
354C2×Dic61—44no—
355C2×Dic61—44no—
356C2×Dic61—44no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359D244—416no—
360C2×#2829—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—88no—
369C22×C61#53814yes—
370C22×C61#54014yes—
371C22×C61#54214yes—
372C22×C61#56014yes—
373C22×C61#56014yes—
374C22×C61#56214yes—
375C22×C61#56214yes—
376C22×C61C22×#4111yescharacteristic
377C22×C61C2×H(5,𝔽2)11yescharacteristic
378C22×C61C2×H(5,𝔽2)11yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C22×C61C2×H(5,𝔽2)11yescharacteristic
382C22×C61C2×2−1+411yescharacteristic
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—88no—
398C2×D61—88no—
399C4×C61—24no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405Dic61—42no—
406Dic61—42no—
407Dic61—42no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411#2829—6116no—
412C2×#399—611no—
413C2×#398—611no—
414C2×#397—611no—
415C2×#397—611no—
416C2×#396—611no—
417C2×#396D6111yescharacteristic, complemented
418C2×#394—611no—
419C2×#394—611no—
420C2×#394—611no—
421C2×#394—611no—
422C2×#394—611no—
423C2×#392—611no—
424C2×#390—611no—
425C2×#388—611no—
426C2×#387—611no—
427C2×C61—82no—
428C2×C61#282918yescomplemented
429C2×C61C2×#53811yescharacteristic
430C2×C61C2×#54011yescharacteristic
431C2×C61C2×#54211yescharacteristic
432C2×C61C2×#56011yescharacteristic
433C2×C61C2×#56011yescharacteristic
434C2×C61C2×#56211yescharacteristic
435C2×C61C2×#56211yescharacteristic
436D61—82no—
437D61—82no—
438C23×D4—611no—
439C23×D4—611no—
440C23×D4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C4⋊C4C2×D6111yescharacteristic
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4—611no—
457C22×C22⋊C4—611no—
458C22×C22⋊C4—611no—
459C22×C22⋊C4—611no—
460C22×C22⋊C4—611no—
461C22×C22⋊C4C2×D6111yescharacteristic
462C22×C22⋊C4C2×D6111yescharacteristic
463C22×C22⋊C4C2×D6111yescharacteristic
464C22×C42—611no—
465#399—618no—
466#398—618no—
467#397—618no—
468#397—618no—
469#396—618no—
470#396C2×D6118yescomplemented
471#394—618no—
472#394—618no—
473#394—618no—
474#394—618no—
475#394—618no—
476#392—618no—
477#390—618no—
478#388—618no—
479#387—618no—
480C2×#95—611no—
481C2×#95—611no—
482C2×#95—611no—
483C2×#95—611no—
484C2×#95—611no—
485C2×#95—611no—
486C2×#95—611no—
487C2×#95C2×D6111yescharacteristic
488C61C2×#282911yescharacteristic, complemented, Sylow
489C25—611no—
490C25—611no—
491C25C22×D6111yescharacteristic
492C22×D4—614no—
493C22×D4—614no—
494C22×D4—614no—
495C22×D4—1224no—
496C22×D4—2442no—
497C22×D4—2442no—
498C22×D4—2442no—
499C22×D4—2442no—
500C22×D4—2442no—
501C22×D4—2442no—
502C22×D4—2442no—
503C22×D4—2442no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C2×C4⋊C4—24no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—2442no—
525C2×C4⋊C4—2442no—
526C2×C4⋊C4—2442no—
527C2×C4⋊C4—2442no—
528C2×C4⋊C4—2442no—
529C2×C4⋊C4C22×D6114yes—
530C2×C4⋊C4C22×D6114yes—
531C2×C4⋊C4C22×D6114yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—614no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
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—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—2442no—
548C2×C22⋊C4—2442no—
549C2×C22⋊C4—2442no—
550C2×C22⋊C4—2442no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4—2442no—
556C2×C22⋊C4—2442no—
557C2×C22⋊C4—2442no—
558C2×C22⋊C4—2442no—
559C2×C22⋊C4C22×D6114yes—
560C2×C22⋊C4C22×D6114yes—
561C2×C22⋊C4C22×D6114yes—
562C2×C42—614no—
563C2×C42—2442no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95—614no—
571#95C22×D6114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—612no—
580C24—612no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24—1222no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—1222no—
593C24—1222no—
594C24—1222no—
595C24C23×D6112yes—
596C24C23×D6111yescharacteristic
597C2×D4—1228no—
598C2×D4—2444no—
599C2×D4—2444no—
600C2×D4—24416no—
601C2×D4—2444no—
602C2×D4—2444no—
603C2×D4—2444no—
604C2×D4—2444no—
605C2×D4—2444no—
606C2×D4—2444no—
607C2×D4—24416no—
608C2×D4—24416no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
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—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4#1175822414yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C4⋊C4—28no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—2444no—
661C4⋊C4—2444no—
662C4⋊C4—2444no—
663C4⋊C4—2444no—
664C4⋊C4—2444no—
665C22⋊C4—28no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—2444no—
669C22⋊C4—2444no—
670C22⋊C4—2444no—
671C22⋊C4—2444no—
672C22⋊C4—2444no—
673C22⋊C4—2444no—
674C22⋊C4—2444no—
675C22⋊C4—2444no—
676C22⋊C4—2444no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C22⋊C4—2444no—
680C42—2444no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—2444no—
710C23—2444no—
711C23—2444no—
712C23—2444no—
713C23—2444no—
714C23—2444no—
715C23—2444no—
716C23—2444no—
717C23—2444no—
718C23—2444no—
719C23—2444no—
720C23—2444no—
721C23—2444no—
722C23—2444no—
723C23C2×#1175822412yes—
724C23#1451982212yes—
725C23#1451982212yes—
726C23#1451982312yes—
727C23#1451982312yes—
728C23#1451982312yes—
729C23#1451982512yes—
730C23C24×D6111yescharacteristic
731D4—24416no—
732D4—24416no—
733D4—24416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
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—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—2444no—
776C2×C4—2444no—
777C2×C4—2444no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4—2444no—
781C2×C4C2×#1175822414yes—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—88no—
790C22—4888no—
791C22—4888no—
792C22—2442no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22#1684034914yes—
807C22#1684036514yes—
808C22#1684038514yes—
809C22#1684050014yes—
810C22#1684050314yes—
811C22#1684050814yes—
812C22#1684050814yes—
813C22C22×#1175822411yescharacteristic
814C22C2×#1451982211yescharacteristic
815C22C2×#1451982211yescharacteristic
816C22C2×#1451982311yescharacteristic
817C22C2×#1451982311yescharacteristic
818C22C2×#1451982311yescharacteristic
819C22C2×#1451982511yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—2442no—
827C4—2442no—
828C4—2442no—
829C4—2442no—
830C4—2442no—
831C4—2442no—
832C2—82no—
833C2—4882no—
834C2—4882no—
835C2#2145395318yesdirect product factor
836C2C2×#1684034911yescharacteristic
837C2C2×#1684036511yescharacteristic
838C2C2×#1684038511yescharacteristic
839C2C2×#1684050011yescharacteristic
840C2C2×#1684050311yescharacteristic
841C2C2×#1684050811yescharacteristic
842C2C2×#1684050811yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#396C2
socleC24×C61C24
prime radicalC2×#16839671C2
hypercenterC2×#396D61
hypocenterC61C2×#2829
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #21453953C2direct (N × H)
2. C2×#16839699C2semidirect
3. C2×#16839695C2semidirect
4. C2×#16839691C2semidirect
5. C2×#16839688C2semidirect
6. C2×#16839684C2semidirect
7. C2×#16839679C2semidirect
8. C2×#16839678C2semidirect
9. C2×#16839678C2semidirect
10. C2×#16839677C2semidirect
11. C2×#16839677C2semidirect
13. C2×#16839663C2semidirect
14. C2×#16839655C2semidirect
15. C2×#16839648C2semidirect
16. C2×C61×#396C2semidirect
38. #16839699C22semidirect
39. #16839695C22semidirect
40. #16839691C22semidirect
41. #16839688C22semidirect
42. #16839684C22semidirect
43. #16839679C22semidirect
44. #16839678C22semidirect
45. #16839678C22semidirect
46. #16839677C22semidirect
47. #16839677C22semidirect
49. #16839663C22semidirect
50. #16839655C22semidirect
51. #16839648C22semidirect
65. C61×#396C22semidirect
417. C2×#396D61semidirect
428. C2×C61#2829semidirect
470. #396C2×D61semidirect
488. C61C2×#2829semidirect
835. C2#21453953direct (N × H)

Maximal subgroups

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

subgroupindex
#214539532
C2×#168396992
C2×#168396952
C2×#168396912
C2×#168396882
C2×#168396842
C2×#168396792
C2×#168396782
C2×#168396772
C2×#168396712
C2×#168396632
C2×#168396552
C2×#168396482
C2×C61×#3962
C2×#282961