Finite Group Databasebeta

← C2×#21426769 #28747421

Subgroups — C2×#21426769 #28747421

Order 15104.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273712C211yesmaximal, characteristic
2C22×C4×D236C211yesmaximal, characteristic
3C22×C4⋊C4×D59C211yesmaximal, characteristic, complemented
4#21426769C2116yesmaximal, direct product factor
5C2×#16837301C211yesmaximal, characteristic, complemented
6C2×#16837299C211yesmaximal, characteristic, complemented
7C2×#16837294C211yesmaximal, characteristic, complemented
8C2×#16837291C211yesmaximal, characteristic, complemented
9C2×#16837286C211yesmaximal, characteristic, complemented
10C2×#16837280C211yesmaximal, characteristic
11C2×#16837276C211yesmaximal, characteristic, complemented
12C2×#16837276C211yesmaximal, characteristic, complemented
13C2×#16837273C211yesmaximal, characteristic, complemented
14C2×#16837264C211yesmaximal, characteristic, complemented
15C2×#16837249C211yesmaximal, characteristic, complemented
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21C23×C4×D59C2211yescharacteristic
22C2×#14273712C4116yescomplemented
23C2×#14273712C2218yes—
24C2×C4×D236—28no—
25C2×C4×D236C2218yes—
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C4⋊Dic59C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C2×C4⋊C4×D59—28no—
34C2×C4⋊C4×D59C2218yescomplemented
35C22×(C2×D59)⋊C4C2211yescharacteristic
36C22×(C2×D59)⋊C4C2211yescharacteristic
37C22×(C2×D59)⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×(C2×D59)⋊C4C2211yescharacteristic
41C22×(C2×D59)⋊C4C2211yescharacteristic
42C22×(C2×D59)⋊C4C2211yescharacteristic
43C22×C4×Dic59C2211yescharacteristic
44C22×C4×Dic59C2211yescharacteristic
45#16837301C2218yescomplemented
46#16837299C2218yescomplemented
47#16837294C2218yescomplemented
48#16837291C2218yescomplemented
49#16837286C2218yescomplemented
50#16837280C2218yes—
51#16837276C2218yescomplemented
52#16837276C2218yescomplemented
53#16837273C2218yescomplemented
54#16837264C2218yescomplemented
55#16837249C2218yescomplemented
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C2×C59⋊#95C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×C42×C59C2211yescharacteristic
65C59×#387C2218yescomplemented
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C2×#95×C59C2211yescharacteristic
70C24×D59C2311yescharacteristic
71C24×D59C2311yescharacteristic
72C22×D236—24no—
73C22×D236—24no—
74C22×D236C2×C418yes—
75C22×D236C2314yes—
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C22×C4×D59—24no—
83C22×C4×D59—24no—
84C22×C4×D59—24no—
85C22×C4×D59—24no—
86C22×C4×D59—42no—
87C22×C4×D59—42no—
88C22×C4×D59—42no—
89C22×C4×D59—42no—
90C22×C4×D59—42no—
91C22×C4×D59—42no—
92C22×C4×D59C2×C418yescomplemented
93C22×C4×D59D418yes—
94C22×C4×D59C2314yes—
95C22×C4×D59C2314yes—
96C22×C4×D59C2314yes—
97C22×C4×D59C2314yes—
98#14273712C2×C4164yescomplemented
99C4×D236—232no—
100C2×C4⋊Dic59—24no—
101C2×C4⋊Dic59—24no—
102C2×C4⋊Dic59—42no—
103C2×C4⋊Dic59C2314yes—
104C2×C4⋊Dic59C2314yes—
105C2×C4⋊Dic59C2314yes—
106C2×Dic59⋊C4—24no—
107C2×Dic59⋊C4—24no—
108C2×Dic59⋊C4—42no—
109C2×Dic59⋊C4C2×C418yescomplemented
110C2×Dic59⋊C4C2314yes—
111C2×Dic59⋊C4C2314yes—
112C2×Dic59⋊C4C2314yes—
113C2×Dic59⋊C4C2314yes—
114C4⋊C4×D59—232no—
115C2×(C2×D59)⋊C4—24no—
116C2×(C2×D59)⋊C4—24no—
117C2×(C2×D59)⋊C4—24no—
118C2×(C2×D59)⋊C4—42no—
119C2×(C2×D59)⋊C4—42no—
120C2×(C2×D59)⋊C4C2×C418yescomplemented
121C2×(C2×D59)⋊C4C2×C418yescomplemented
122C2×(C2×D59)⋊C4C2×C418yescomplemented
123C2×(C2×D59)⋊C4C2314yes—
124C2×(C2×D59)⋊C4C2314yes—
125C2×(C2×D59)⋊C4C2314yes—
126C2×(C2×D59)⋊C4C2314yes—
127C2×(C2×D59)⋊C4C2314yes—
128C2×(C2×D59)⋊C4C2314yes—
129C2×(C2×D59)⋊C4C2314yes—
130C2×(C2×D59)⋊C4C2314yes—
131C2×C4×Dic59—42no—
132C2×C4×Dic59—42no—
133C2×C4×Dic59C2314yes—
134C2×C4×Dic59C2314yes—
135C59⋊#95C2314yes—
136C59⋊#95C2314yes—
137C59⋊#95C2314yes—
138C59⋊#95C2314yes—
139C59⋊#95C2314yes—
140C59⋊#95C2314yes—
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C2×C4⋊C4×C59—24no—
149C2×C4⋊C4×C59C2×C418yescomplemented
150C2×C4⋊C4×C59C2314yes—
151C2×C4⋊C4×C59C2314yes—
152C2×C42×C59—24no—
153C2×C42×C59C2314yes—
154#95×C59C2314yes—
155#95×C59C2314yes—
156#95×C59C2314yes—
157#95×C59C2314yes—
158C24×C59C2411yescharacteristic
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59—22no—
167C23×D59—22no—
168C23×D59—22no—
169C23×D59C22×C414yes—
170C23×D59C22×C414yes—
171C23×D59C2×D414yes—
172C23×D59#4114yes—
173C23×D59C2412yes—
174C23×D59C2412yes—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59C22×C414yes—
193C22×C4×C59C22×C414yes—
194C22×C4×C59C22×C414yes—
195C22×C4×C59C2×D414yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2412yes—
203C22×Dic59—22no—
204C22×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—22no—
213C22×Dic59—22no—
214C22×Dic59—22no—
215C22×Dic59—22no—
216C22×Dic59—22no—
217C22×Dic59—22no—
218C22×Dic59C22×C414yes—
219C22×Dic59C22×C414yes—
220C22×Dic59C2×D414yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C22×Dic59C2412yes—
226C22×Dic59C2412yes—
227C2×D236—232no—
228C2×D236—28no—
229C2×D236—28no—
230C2×D236C22×C4116yes—
231C2×C4×D59—232no—
232C2×C4×D59—28no—
233C2×C4×D59—28no—
234C2×C4×D59—28no—
235C2×C4×D59—28no—
236C2×C4×D59—416no—
237C2×C4×D59—44no—
238C2×C4×D59—44no—
239C2×C4×D59—44no—
240C2×C4×D59—44no—
241C2×C4×D59—44no—
242C2×C4×D59—44no—
243C2×C4×D59—416no—
244C2×C4×D59—416no—
245C2×C4×D59C22×C4116yescomplemented
246C2×C4×D59C2×D4116yes—
247C4⋊C4×C59—28no—
248C4⋊C4×C59C22×C4116yescomplemented
249C42×C59—28no—
250(C2×D59)⋊C4—28no—
251(C2×D59)⋊C4—28no—
252(C2×D59)⋊C4—28no—
253(C2×D59)⋊C4—44no—
254(C2×D59)⋊C4—44no—
255(C2×D59)⋊C4C22×C4116yescomplemented
256(C2×D59)⋊C4C22×C4116yescomplemented
257(C2×D59)⋊C4C22×C4116yescomplemented
258C4⋊Dic59—28no—
259C4⋊Dic59—28no—
260C4⋊Dic59—44no—
261Dic59⋊C4—28no—
262Dic59⋊C4—28no—
263Dic59⋊C4—44no—
264Dic59⋊C4C22×C4116yescomplemented
265C4×Dic59—44no—
266C4×Dic59—44no—
267C23×C59C23×C412yes—
268C23×C59C22×D412yes—
269C23×C59C2×#4112yes—
270C23×C59H(5,𝔽2)12yes—
271C23×C59H(5,𝔽2)12yes—
272C23×C592−1+412yes—
273C23×C592−1+412yes—
274C23×C59C2511yescharacteristic
275C22×D59—28no—
276C22×D59—28no—
277C22×D59—28no—
278C22×D59—28no—
279C22×D59—28no—
280C22×D59—28no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—28no—
286C22×D59—28no—
287C22×D59—28no—
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—44no—
295C22×D59—44no—
296C22×D59—44no—
297C22×D59—44no—
298C22×D59C4×D4116yes—
299C22×D59C23×C414yes—
300C22×D59C23×C414yes—
301C22×D59C22×D414yes—
302C22×D59C2×#4114yes—
303C2×C4×C59—28no—
304C2×C4×C59—28no—
305C2×C4×C59—28no—
306C2×C4×C59—28no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—44no—
325C2×C4×C59—44no—
326C2×C4×C59—44no—
327C2×C4×C59C23×C414yes—
328C2×C4×C59C23×C414yes—
329C2×C4×C59C23×C414yes—
330C2×C4×C59C22×D414yes—
331C2×Dic59—28no—
332C2×Dic59—28no—
333C2×Dic59—28no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—44no—
350C2×Dic59—44no—
351C2×Dic59—44no—
352C2×Dic59C23×C414yes—
353C2×Dic59C23×C414yes—
354C2×Dic59C22×D414yes—
355D236—232no—
356C4×D59—232no—
357C4×D59—416no—
358C4×D59—416no—
359C4×D59—416no—
360C2×#2322—591nomaximal, Sylow
361C22×C59C2×C4×D414yes—
362C22×C59#52014yes—
363C22×C59#52014yes—
364C22×C59#53414yes—
365C22×C59#53614yes—
366C22×C59#53914yes—
367C22×C59#53914yes—
368C22×C59C24×C411yescharacteristic
369C22×C59C23×D411yescharacteristic
370C22×C59C22×#4111yescharacteristic
371C22×C59C2×H(5,𝔽2)11yescharacteristic
372C22×C59C2×H(5,𝔽2)11yescharacteristic
373C22×C59C2×2−1+411yescharacteristic
374C22×C59C2×2−1+411yescharacteristic
375C2×D59—232no—
376C2×D59—24no—
377C2×D59—24no—
378C2×D59—24no—
379C2×D59—24no—
380C2×D59—24no—
381C2×D59—24no—
382C2×D59—24no—
383C2×D59—24no—
384C2×D59—24no—
385C2×D59—416no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—42no—
390C2×D59C2×C4×D418yes—
391C4×C59—24no—
392C4×C59—24no—
393C4×C59—24no—
394C4×C59—24no—
395C4×C59—42no—
396C4×C59—42no—
397C4×C59—42no—
398Dic59—24no—
399Dic59—24no—
400Dic59—24no—
401Dic59—42no—
402Dic59—42no—
403Dic59—42no—
404C22×#123—591no—
405C22×C4×D4—591no—
406C23×C4⋊C4—591no—
407#2322—5916no—
408C2×#389—591no—
409C2×#389—591no—
410C2×#388—591no—
411C2×#388—591no—
412C2×#387—591no—
413C2×#387D5911yescharacteristic, complemented
414C2×#386—591no—
415C2×#385—591no—
416C2×#385—591no—
417C2×#385—591no—
418C2×#381—591no—
419C2×C4×C22⋊C4—591no—
420C2×C59#232218yescomplemented
421C2×C59C22×C4×D411yescharacteristic
422C2×C59C2×#52011yescharacteristic
423C2×C59C2×#52011yescharacteristic
424C2×C59C2×#53411yescharacteristic
425C2×C59C2×#53611yescharacteristic
426C2×C59C2×#53911yescharacteristic
427C2×C59C2×#53911yescharacteristic
428D59—28no—
429D59—44no—
430C23×D4—591no—
431C24×C4—591no—
432C24×C4—591no—
433C24×C4—591no—
434C24×C4—591no—
435C2×#123—5916no—
436C2×#123—598no—
437C2×C4×D4—598no—
438C2×C4×D4—1188no—
439C22×C4⋊C4—591no—
440C22×C4⋊C4—591no—
441C22×C4⋊C4—591no—
442C22×C4⋊C4—591no—
443C22×C4⋊C4—591no—
444C22×C4⋊C4—591no—
445C22×C4⋊C4—591no—
446C22×C4⋊C4—598no—
447C22×C4⋊C4—1188no—
448C22×C4⋊C4C2×D5911yescharacteristic
449C22×C4⋊C4C2×D5911yescharacteristic
450C22×C22⋊C4—591no—
451C22×C22⋊C4—591no—
452C22×C22⋊C4—591no—
453C22×C22⋊C4—591no—
454C22×C22⋊C4—591no—
455C22×C22⋊C4—591no—
456C22×C22⋊C4—591no—
457C22×C22⋊C4—591no—
458C22×C42—591no—
459C22×C42—591no—
460C22×C42C2×D5911yescharacteristic
461#389—598no—
462#389—598no—
463#388—598no—
464#388—598no—
465#387—598no—
466#387C2×D5918yescomplemented
467#386—598no—
468#385—598no—
469#385—598no—
470#385—598no—
471#381—598no—
472C4×C22⋊C4—598no—
473C2×#95—591no—
474C2×#95—591no—
475C2×#95—591no—
476C2×#95—591no—
477C2×#95—591no—
478C2×#95—591no—
479C2×#95C2×D5911yescharacteristic
480C2×#95C2×D5911yescharacteristic
481C2×#95C2×D5911yescharacteristic
482C2×#95C2×D5911yescharacteristic
483C59C2×#232211yescharacteristic, complemented, Sylow
484C25—591no—
485C25—591no—
486C22×D4—598no—
487C22×D4—594no—
488C22×D4—1184no—
489C22×D4—1184no—
490C23×C4—591no—
491C23×C4—591no—
492C23×C4—591no—
493C23×C4—598no—
494C23×C4—594no—
495C23×C4—598no—
496C23×C4—594no—
497C23×C4—591no—
498C23×C4—591no—
499C23×C4—591no—
500C23×C4—594no—
501C23×C4—594no—
502C23×C4—1184no—
503C23×C4—1184no—
504C23×C4—1184no—
505C23×C4—1184no—
506C23×C4—2362no—
507C23×C4—2362no—
508C23×C4—2362no—
509C23×C4—2362no—
510C23×C4—2362no—
511C23×C4—2362no—
512C23×C4C22×D5911yescharacteristic
513C23×C4C22×D5911yescharacteristic
514C23×C4C22×D5911yescharacteristic
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5911yescharacteristic
517C23×C4C22×D5911yescharacteristic
518C23×C4C22×D5911yescharacteristic
519#123—5964no—
520C4×D4—11832no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—598no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—594no—
525C2×C4⋊C4—594no—
526C2×C4⋊C4—594no—
527C2×C4⋊C4—594no—
528C2×C4⋊C4—594no—
529C2×C4⋊C4—594no—
530C2×C4⋊C4—11832no—
531C2×C4⋊C4—1184no—
532C2×C4⋊C4—1184no—
533C2×C4⋊C4—1184no—
534C2×C4⋊C4—1184no—
535C2×C4⋊C4—2362no—
536C2×C4⋊C4—2362no—
537C2×C4⋊C4C4×D5918yescomplemented
538C2×C4⋊C4C22×D5914yes—
539C2×C4⋊C4C22×D5914yes—
540C2×C22⋊C4—598no—
541C2×C22⋊C4—598no—
542C2×C22⋊C4—598no—
543C2×C22⋊C4—594no—
544C2×C22⋊C4—594no—
545C2×C22⋊C4—594no—
546C2×C22⋊C4—594no—
547C2×C22⋊C4—594no—
548C2×C22⋊C4—594no—
549C2×C22⋊C4—594no—
550C2×C22⋊C4—594no—
551C2×C22⋊C4—1184no—
552C2×C22⋊C4—1184no—
553C2×C22⋊C4—1184no—
554C2×C22⋊C4—2362no—
555C2×C22⋊C4—2362no—
556C2×C42—24no—
557C2×C42—594no—
558C2×C42—594no—
559C2×C42—2362no—
560C2×C42—2362no—
561C2×C42C22×D5914yes—
562#95—594no—
563#95—594no—
564#95—594no—
565#95—594no—
566#95—594no—
567#95—594no—
568#95C22×D5914yes—
569#95C22×D5914yes—
570#95C22×D5914yes—
571#95C22×D5914yes—
572C24—594no—
573C24—594no—
574C24—594no—
575C24—592no—
576C24—594no—
577C24—592no—
578C24—1182no—
579C24—1182no—
580C24—1182no—
581C24—1182no—
582C24—1182no—
583C24—1182no—
584C24—1182no—
585C24—1182no—
586C24—1182no—
587C24—1182no—
588C24C23×D5911yescharacteristic
589C2×D4—5916no—
590C2×D4—1188no—
591C2×D4—1188no—
592C2×D4—11832no—
593C22×C4—22no—
594C22×C4—22no—
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—594no—
611C22×C4—594no—
612C22×C4—594no—
613C22×C4—592no—
614C22×C4—592no—
615C22×C4—592no—
616C22×C4—5916no—
617C22×C4—5916no—
618C22×C4—592no—
619C22×C4—592no—
620C22×C4—592no—
621C22×C4—1188no—
622C22×C4—1188no—
623C22×C4—11832no—
624C22×C4—1188no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4—1182no—
630C22×C4—1182no—
631C22×C4—1182no—
632C22×C4—1182no—
633C22×C4—1182no—
634C22×C4—1182no—
635C22×C4—1182no—
636C22×C4—1182no—
637C22×C4—1182no—
638C22×C4—1182no—
639C22×C4—1182no—
640C22×C4—1188no—
641C22×C4—23616no—
642C22×C4—2364no—
643C22×C4—2364no—
644C22×C4—2364no—
645C22×C4—2364no—
646C22×C4—2364no—
647C22×C4—2364no—
648C22×C4—23616no—
649C22×C4—23616no—
650C22×C4C2×C4×D5914yes—
651C22×C4C2×C4×D5914yes—
652C22×C4C2×C4×D5914yes—
653C22×C4D4×D5914yes—
654C22×C4C23×D5912yes—
655C22×C4C23×D5912yes—
656C22×C4C23×D5912yes—
657C22×C4C23×D5912yes—
658C22×C4C23×D5912yes—
659C22×C4C23×D5912yes—
660C22×C4C23×D5912yes—
661C4⋊C4—28no—
662C4⋊C4—5916no—
663C4⋊C4—1188no—
664C4⋊C4—1188no—
665C4⋊C4—1188no—
666C4⋊C4—1188no—
667C4⋊C4—2364no—
668C4⋊C4—2364no—
669C4⋊C4C2×C4×D59116yescomplemented
670C22⋊C4—5916no—
671C22⋊C4—5916no—
672C22⋊C4—5916no—
673C22⋊C4—1188no—
674C22⋊C4—1188no—
675C22⋊C4—1188no—
676C22⋊C4—2364no—
677C22⋊C4—2364no—
678C42—28no—
679C42—2364no—
680C42—2364no—
681C23—594no—
682C23—594no—
683C23—594no—
684C23—5916no—
685C23—594no—
686C23—1188no—
687C23—1188no—
688C23—1182no—
689C23—1182no—
690C23—1182no—
691C23—1182no—
692C23—1188no—
693C23—1188no—
694C23—1188no—
695C23—1188no—
696C23—1182no—
697C23—1182no—
698C23—1182no—
699C23—1182no—
700C23—1182no—
701C23—1182no—
702C23—1188no—
703C23—1188no—
704C23—1188no—
705C23—2364no—
706C23—2364no—
707C23—2364no—
708C23—2364no—
709C23C22×C4×D5912yes—
710C23C2×D4×D5912yes—
711C23#41×D5912yes—
712C23#1427377312yes—
713C23#1427377312yes—
714C23#1427377412yes—
715C23#1427377512yes—
716C23C24×D5911yescharacteristic
717D4—11832no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—594no—
743C2×C4—594no—
744C2×C4—594no—
745C2×C4—11832no—
746C2×C4—1188no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1188no—
754C2×C4—1188no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—1182no—
759C2×C4—1182no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—23616no—
765C2×C4—23616no—
766C2×C4—23616no—
767C2×C4—2364no—
768C2×C4—2364no—
769C2×C4—2364no—
770C2×C4C22×C4×D5914yes—
771C2×C4C22×C4×D5914yes—
772C2×C4C22×C4×D5914yes—
773C2×C4C2×D4×D5914yes—
774C22—598no—
775C22—1184no—
776C22—1184no—
777C22—11832no—
778C22—1184no—
779C22—1184no—
780C22—1184no—
781C22—1184no—
782C22—1184no—
783C22—1184no—
784C22—1184no—
785C22—2362no—
786C22—2362no—
787C22—23616no—
788C22—2362no—
789C22—2362no—
790C22C4×D4×D5914yes—
791C22#1683788214yes—
792C22#1683788414yes—
793C22#1683796314yes—
794C22#1683797514yes—
795C22#1683799314yes—
796C22#1683800014yes—
797C22C23×C4×D5911yescharacteristic
798C22C22×D4×D5911yescharacteristic
799C22C2×#41×D5911yescharacteristic
800C22C2×#1427377311yescharacteristic
801C22C2×#1427377311yescharacteristic
802C22C2×#1427377411yescharacteristic
803C22C2×#1427377511yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—1184no—
812C4—1184no—
813C4—1184no—
814C4—2362no—
815C4—2362no—
816C4—2362no—
817C2—1188no—
818C2—2364no—
819C2#2142676918yesdirect product factor
820C2C2×C4×D4×D5911yescharacteristic
821C2C2×#1683788211yescharacteristic
822C2C2×#1683788411yescharacteristic
823C2C2×#1683796311yescharacteristic
824C2C2×#1683797511yescharacteristic
825C2C2×#1683799311yescharacteristic
826C2C2×#1683800011yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC23×D236C22
cosocleC23×C59C25
hypercenterC2×#387D59
hypocenterC59C2×#2322
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D59C2semidirect
4. #21426769C2direct (N × H)
5. C2×#16837301C2semidirect
6. C2×#16837299C2semidirect
7. C2×#16837294C2semidirect
8. C2×#16837291C2semidirect
9. C2×#16837286C2semidirect
11. C2×#16837276C2semidirect
12. C2×#16837276C2semidirect
13. C2×#16837273C2semidirect
14. C2×#16837264C2semidirect
15. C2×#16837249C2semidirect
16. C2×C59×#387C2semidirect
22. C2×#14273712C4semidirect
34. C2×C4⋊C4×D59C22semidirect
45. #16837301C22semidirect
46. #16837299C22semidirect
47. #16837294C22semidirect
48. #16837291C22semidirect
49. #16837286C22semidirect
51. #16837276C22semidirect
52. #16837276C22semidirect
53. #16837273C22semidirect
54. #16837264C22semidirect
55. #16837249C22semidirect
65. C59×#387C22semidirect
92. C22×C4×D59C2×C4semidirect
98. #14273712C2×C4semidirect
109. C2×Dic59⋊C4C2×C4semidirect
120. C2×(C2×D59)⋊C4C2×C4semidirect
121. C2×(C2×D59)⋊C4C2×C4semidirect
122. C2×(C2×D59)⋊C4C2×C4semidirect
149. C2×C4⋊C4×C59C2×C4semidirect
245. C2×C4×D59C22×C4semidirect
248. C4⋊C4×C59C22×C4semidirect
255. (C2×D59)⋊C4C22×C4semidirect
256. (C2×D59)⋊C4C22×C4semidirect
257. (C2×D59)⋊C4C22×C4semidirect
264. Dic59⋊C4C22×C4semidirect
413. C2×#387D59semidirect
420. C2×C59#2322semidirect
466. #387C2×D59semidirect
483. C59C2×#2322semidirect
537. C2×C4⋊C4C4×D59semidirect
669. C4⋊C4C2×C4×D59semidirect
819. C2#21426769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737122
C22×C4×D2362
C22×C4⋊C4×D592
#214267692
C2×#168373012
C2×#168372992
C2×#168372942
C2×#168372912
C2×#168372862
C2×#168372802
C2×#168372762
C2×#168372732
C2×#168372642
C2×#168372492
C2×C59×#3872
C2×#232259