Finite Group Databasebeta

← C2×#21427089 #28748193

Subgroups — C2×#21427089 #28748193

Order 15104.

3830 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×#14273709C211yesmaximal, characteristic
2C22×C4×C22⋊D59C211yesmaximal, characteristic
3C22×#14273684C211yesmaximal, characteristic, complemented
4#21427089C2116yesmaximal, direct product factor
5C2×#16837300C211yesmaximal, characteristic, complemented
6C2×#16837295C211yesmaximal, characteristic, complemented
7C2×#16837290C211yesmaximal, characteristic, complemented
8C2×#16837286C211yesmaximal, characteristic, complemented
9C2×#16837285C211yesmaximal, characteristic, complemented
10C2×#16837278C211yesmaximal, characteristic
11C2×#16837276C211yesmaximal, characteristic, complemented
12C2×#16837275C211yesmaximal, characteristic, complemented
13C2×#16837253C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D59C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C59C211yesmaximal, characteristic, complemented
17C23×C22⋊D59C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21C2×#14273709C4116yescomplemented
22C2×#14273709C2218yes—
23C2×C4×C22⋊D59—28no—
24C2×C4×C22⋊D59C2218yes—
25C2×#14273684—28no—
26C2×#14273684C2218yescomplemented
27C22×C4⋊Dic59C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊C4C2211yescharacteristic
34C22×C22⋊Dic59C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C22⋊Dic59C2211yescharacteristic
37C22×(C2×D59)⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41C22×C4×Dic59C2211yescharacteristic
42C22×C4×Dic59C2211yescharacteristic
43#16837300C2218yescomplemented
44#16837295C2218yescomplemented
45#16837290C2218yescomplemented
46#16837286C2218yescomplemented
47#16837285C2218yescomplemented
48#16837278C2218yes—
49#16837276C2218yescomplemented
50#16837275C2218yescomplemented
51#16837253C2218yescomplemented
52C4×(C2×D59)⋊C4C2218yescomplemented
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61#95×D59C2218yescomplemented
62C24×C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C22×C42×C59C2211yescharacteristic
66C22×C42×C59C2211yescharacteristic
67C4×C22⋊C4×C59C2218yescomplemented
68C2×#95×C59C2211yescharacteristic
69C2×#95×C59C2211yescharacteristic
70C24×D59C2311yescharacteristic
71C22×C22⋊D59—24no—
72C22×C22⋊D59—24no—
73C22×C22⋊D59C2×C418yes—
74C22×C22⋊D59C2314yes—
75C23×Dic59C2311yescharacteristic
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—24no—
87C22×C4×D59—24no—
88C22×C4×D59—42no—
89C22×C4×D59—42no—
90C22×C4×D59C2×C418yescomplemented
91C22×C4×D59C2314yes—
92C22×C4×D59C2314yes—
93C22×C4×D59C2314yes—
94#14273709C2×C4164yescomplemented
95C4×C22⋊D59—232no—
96#14273684—232no—
97C2×C4⋊Dic59—42no—
98C2×C4⋊Dic59C2×C418yescomplemented
99C2×C4⋊Dic59C2314yes—
100C2×C4⋊Dic59C2314yes—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4—24no—
103C2×Dic59⋊C4—24no—
104C2×Dic59⋊C4—24no—
105C2×Dic59⋊C4C2×C418yescomplemented
106C2×Dic59⋊C4C2314yes—
107C2×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×Dic59⋊C4C2314yes—
110C2×Dic59⋊C4C2314yes—
111C2×C22⋊Dic59—24no—
112C2×C22⋊Dic59—42no—
113C2×C22⋊Dic59C2×C418yescomplemented
114C2×C22⋊Dic59C2314yes—
115C2×C22⋊Dic59C2314yes—
116C2×C22⋊Dic59C2314yes—
117C2×(C2×D59)⋊C4—24no—
118C2×(C2×D59)⋊C4C2×C418yescomplemented
119C2×(C2×D59)⋊C4D418yes—
120C2×(C2×D59)⋊C4C2314yes—
121C2×(C2×D59)⋊C4C2314yes—
122C2×(C2×D59)⋊C4C2314yes—
123C2×C4×Dic59—24no—
124C2×C4×Dic59—24no—
125C2×C4×Dic59—24no—
126C2×C4×Dic59C2314yes—
127C2×C4×Dic59C2314yes—
128C2×C4×Dic59C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C59⋊#95C2314yes—
134C59⋊#95C2314yes—
135C59⋊#95C2314yes—
136C59⋊#95C2314yes—
137C25×C59C2311yescharacteristic
138C23×C4×C59—24no—
139C23×C4×C59—24no—
140C23×C4×C59—42no—
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2314yes—
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C2×C22⋊C4×C59—24no—
149C2×C22⋊C4×C59C2×C418yescomplemented
150C2×C22⋊C4×C59C2314yes—
151C2×C22⋊C4×C59C2314yes—
152C2×C42×C59—24no—
153C2×C42×C59—42no—
154C2×C42×C59C2314yes—
155C2×C42×C59C2314yes—
156#95×C59C2314yes—
157#95×C59C2314yes—
158C24×C59—22no—
159C24×C59—22no—
160C24×C59—22no—
161C24×C59—22no—
162C24×C59—22no—
163C24×C59—22no—
164C24×C59C22×C414yes—
165C24×C59C2412yes—
166C24×C59C2411yescharacteristic
167C23×D59—22no—
168C23×D59—22no—
169C23×D59—22no—
170C23×D59—22no—
171C23×D59C22×C414yes—
172C23×D59C2×D414yes—
173C23×D59#4114yes—
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—28no—
189C22×C4×C59—28no—
190C22×C4×C59—44no—
191C22×C4×C59—416no—
192C22×C4×C59C22×C414yes—
193C22×C4×C59C22×C414yes—
194C22×C4×C59C2×D414yes—
195C22×C4×C59#4114yes—
196C22×C4×C59#4114yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2412yes—
203C2×C22⋊D59—232no—
204C2×C22⋊D59—28no—
205C2×C22⋊D59—28no—
206C2×C22⋊D59C22×C4116yes—
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×Dic59—22no—
219C22×Dic59—22no—
220C22×Dic59—22no—
221C22×Dic59—22no—
222C22×Dic59—22no—
223C22×Dic59—22no—
224C22×Dic59C22×C414yes—
225C22×Dic59C22×C414yes—
226C22×Dic59C22×C414yes—
227C22×Dic59C2×D414yes—
228C22×Dic59C2412yes—
229C22×Dic59C2412yes—
230C22×Dic59C2412yes—
231C22×Dic59C2412yes—
232C22×Dic59C2412yes—
233C22×Dic59C2412yes—
234C22×Dic59C2412yes—
235C2×C4×D59—232no—
236C2×C4×D59—28no—
237C2×C4×D59—28no—
238C2×C4×D59—28no—
239C2×C4×D59—28no—
240C2×C4×D59—28no—
241C2×C4×D59—28no—
242C2×C4×D59—44no—
243C2×C4×D59—44no—
244C2×C4×D59—416no—
245C2×C4×D59—416no—
246C2×C4×D59C22×C4116yescomplemented
247C22⋊C4×C59—28no—
248C22⋊C4×C59C22×C4116yescomplemented
249C42×C59—28no—
250C42×C59—44no—
251C22⋊Dic59—28no—
252C22⋊Dic59—44no—
253C22⋊Dic59C22×C4116yescomplemented
254(C2×D59)⋊C4—28no—
255(C2×D59)⋊C4C22×C4116yescomplemented
256(C2×D59)⋊C4C2×D4116yes—
257C4⋊Dic59—44no—
258C4⋊Dic59C22×C4116yescomplemented
259Dic59⋊C4—28no—
260Dic59⋊C4—28no—
261Dic59⋊C4—28no—
262Dic59⋊C4—28no—
263Dic59⋊C4C22×C4116yescomplemented
264C4×Dic59—28no—
265C4×Dic59—28no—
266C4×Dic59—28no—
267C23×C59—28no—
268C23×C59—28no—
269C23×C59—28no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—44no—
277C23×C59—44no—
278C23×C59—44no—
279C23×C59—44no—
280C23×C59C23×C414yes—
281C23×C59C23×C412yes—
282C23×C59C22×D412yes—
283C23×C59C2×#4112yes—
284C23×C59C2×#4112yes—
285C23×C59C2×#4112yes—
286C23×C59H(5,𝔽2)12yes—
287C23×C592−1+412yes—
288C23×C59C2511yescharacteristic
289C22×D59—28no—
290C22×D59—28no—
291C22×D59—28no—
292C22×D59—28no—
293C22×D59—28no—
294C22×D59—28no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59C4×D4116yes—
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—28no—
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—416no—
322C2×C4×C59—44no—
323C2×C4×C59C23×C414yes—
324C2×C4×C59C23×C414yes—
325C2×C4×C59C22×D414yes—
326C2×C4×C59C2×#4114yes—
327C2×C4×C59C2×#4114yes—
328C22⋊D59—232no—
329C2×Dic59—28no—
330C2×Dic59—28no—
331C2×Dic59—28no—
332C2×Dic59—28no—
333C2×Dic59—22no—
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—22no—
350C2×Dic59—44no—
351C2×Dic59—44no—
352C2×Dic59—44no—
353C2×Dic59C23×C414yes—
354C2×Dic59C23×C414yes—
355C2×Dic59C23×C414yes—
356C2×Dic59C22×D414yes—
357C4×D59—232no—
358C4×D59—416no—
359C4×D59—416no—
360C2×#2359—591nomaximal, Sylow
361C22×C59—24no—
362C22×C59—24no—
363C22×C59—24no—
364C22×C59—416no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59C2×C4×D414yes—
370C22×C59C4×#4114yes—
371C22×C59#52014yes—
372C22×C59#54614yes—
373C22×C59#54714yes—
374C22×C59#55114yes—
375C22×C59#55214yes—
376C22×C59C24×C411yescharacteristic
377C22×C59C23×D411yescharacteristic
378C22×C59C22×#4111yescharacteristic
379C22×C59C22×#4111yescharacteristic
380C22×C59C22×#4111yescharacteristic
381C22×C59C2×H(5,𝔽2)11yescharacteristic
382C22×C59C2×2−1+411yescharacteristic
383C2×D59—232no—
384C2×D59—24no—
385C2×D59—24no—
386C2×D59—24no—
387C2×D59—24no—
388C2×D59—24no—
389C2×D59—24no—
390C2×D59C2×C4×D418yes—
391C4×C59—24no—
392C4×C59—24no—
393C4×C59—24no—
394C4×C59—24no—
395C4×C59—24no—
396C4×C59—42no—
397Dic59—24no—
398Dic59—24no—
399Dic59—24no—
400Dic59—24no—
401Dic59—42no—
402Dic59—42no—
403Dic59—42no—
404C22×#123—591no—
405C22×C4×D4—591no—
406C22×#117—591no—
407#2359—5916no—
408C2×#389—591no—
409C2×#388—591no—
410C2×#388—591no—
411C2×#387—591no—
412C2×#387—591no—
413C2×#386—591no—
414C2×#385—591no—
415C2×#385—591no—
416C2×C4×C4⋊C4—591no—
417C2×C4×C22⋊C4—591no—
418C2×C4×C22⋊C4D5911yescharacteristic, complemented
419C22×#95—591no—
420C2×C59—44no—
421C2×C59#235918yescomplemented
422C2×C59C22×C4×D411yescharacteristic
423C2×C59C2×C4×#4111yescharacteristic
424C2×C59C2×#52011yescharacteristic
425C2×C59C2×#54611yescharacteristic
426C2×C59C2×#54711yescharacteristic
427C2×C59C2×#55111yescharacteristic
428C2×C59C2×#55211yescharacteristic
429D59—28no—
430C23×D4—591no—
431C24×C4—591no—
432C24×C4—591no—
433C24×C4—591no—
434C24×C4C2×D5911yescharacteristic
435C2×#123—5916no—
436C2×#123—598no—
437C2×C4×D4—598no—
438C2×C4×D4—1188no—
439C2×#117—598no—
440C2×#117—1188no—
441C22×C4⋊C4—591no—
442C22×C4⋊C4—591no—
443C22×C4⋊C4—591no—
444C22×C4⋊C4—591no—
445C22×C4⋊C4—591no—
446C22×C4⋊C4—591no—
447C22×C4⋊C4—591no—
448C22×C22⋊C4—591no—
449C22×C22⋊C4—591no—
450C22×C22⋊C4—591no—
451C22×C22⋊C4—591no—
452C22×C22⋊C4—591no—
453C22×C22⋊C4—591no—
454C22×C22⋊C4C2×D5911yescharacteristic
455C22×C22⋊C4C2×D5911yescharacteristic
456C22×C42—591no—
457C22×C42—591no—
458C22×C42—591no—
459C22×C42C2×D5911yescharacteristic
460C22×C42C2×D5911yescharacteristic
461#389—598no—
462#388—598no—
463#388—598no—
464#387—598no—
465#387—598no—
466#386—598no—
467#385—598no—
468#385—598no—
469C4×C4⋊C4—598no—
470C4×C22⋊C4—598no—
471C4×C22⋊C4C2×D5918yescomplemented
472C2×#95—591no—
473C2×#95—591no—
474C2×#95—591no—
475C2×#95—591no—
476C2×#95—591no—
477C2×#95—591no—
478C2×#95—591no—
479C2×#95—591no—
480C2×#95—598no—
481C2×#95C2×D5911yescharacteristic
482C2×#95C2×D5911yescharacteristic
483C59C2×#235911yescharacteristic, complemented, Sylow
484C25—591no—
485C25C22×D5911yescharacteristic
486C22×D4—598no—
487C22×D4—594no—
488C22×D4—1184no—
489C22×D4—1184no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—42no—
493C23×C4—591no—
494C23×C4—591no—
495C23×C4—591no—
496C23×C4—591no—
497C23×C4—598no—
498C23×C4—594no—
499C23×C4—591no—
500C23×C4—591no—
501C23×C4—591no—
502C23×C4—594no—
503C23×C4—594no—
504C23×C4—1184no—
505C23×C4—1184no—
506C23×C4—1184no—
507C23×C4—1184no—
508C23×C4—1184no—
509C23×C4—1184no—
510C23×C4—2362no—
511C23×C4—2362no—
512C23×C4C22×D5911yescharacteristic
513C23×C4C22×D5914yes—
514C23×C4C22×D5911yescharacteristic
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5911yescharacteristic
517C23×C4C22×D5911yescharacteristic
518C23×C4C22×D5911yescharacteristic
519#123—5964no—
520C4×D4—11832no—
521#117—11832no—
522C2×C4⋊C4—598no—
523C2×C4⋊C4—598no—
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—594no—
531C2×C4⋊C4—1184no—
532C2×C4⋊C4—1184no—
533C2×C4⋊C4—1184no—
534C2×C4⋊C4—1184no—
535C2×C4⋊C4—2362no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—598no—
538C2×C22⋊C4—594no—
539C2×C22⋊C4—598no—
540C2×C22⋊C4—598no—
541C2×C22⋊C4—594no—
542C2×C22⋊C4—594no—
543C2×C22⋊C4—594no—
544C2×C22⋊C4—594no—
545C2×C22⋊C4—594no—
546C2×C22⋊C4—1184no—
547C2×C22⋊C4—1184no—
548C2×C22⋊C4—2362no—
549C2×C22⋊C4C4×D5918yescomplemented
550C2×C22⋊C4C22×D5914yes—
551C2×C22⋊C4C22×D5914yes—
552C2×C42—24no—
553C2×C42—42no—
554C2×C42—594no—
555C2×C42—594no—
556C2×C42—594no—
557C2×C42—1184no—
558C2×C42—1184no—
559C2×C42—1184no—
560C2×C42C22×D5914yes—
561C2×C42C22×D5914yes—
562#95—594no—
563#95—594no—
564#95—594no—
565#95—594no—
566#95—594no—
567#95—594no—
568#95—594no—
569#95—594no—
570#95C22×D5914yes—
571#95C22×D5914yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—594no—
579C24—594no—
580C24—594no—
581C24—592no—
582C24—1182no—
583C24—1182no—
584C24—1182no—
585C24—1182no—
586C24C2×C4×D5914yes—
587C24C23×D5912yes—
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—28no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—416no—
610C22×C4—594no—
611C22×C4—594no—
612C22×C4—594no—
613C22×C4—594no—
614C22×C4—592no—
615C22×C4—592no—
616C22×C4—592no—
617C22×C4—592no—
618C22×C4—5916no—
619C22×C4—592no—
620C22×C4—592no—
621C22×C4—592no—
622C22×C4—1188no—
623C22×C4—1188no—
624C22×C4—11832no—
625C22×C4—1188no—
626C22×C4—1188no—
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—1182no—
641C22×C4—1182no—
642C22×C4—1182no—
643C22×C4—1182no—
644C22×C4—1188no—
645C22×C4—1188no—
646C22×C4—2364no—
647C22×C4—2364no—
648C22×C4—23616no—
649C22×C4—23616no—
650C22×C4C2×C4×D5914yes—
651C22×C4C2×C4×D5914yes—
652C22×C4#1174568514yes—
653C22×C4#1174568514yes—
654C22×C4D4×D5914yes—
655C22×C4C23×D5912yes—
656C22×C4C23×D5912yes—
657C22×C4C23×D5912yes—
658C22×C4C23×D5912yes—
659C22×C4C23×D5912yes—
660C22×C4C23×D5912yes—
661C4⋊C4—5916no—
662C4⋊C4—5916no—
663C4⋊C4—1188no—
664C4⋊C4—1188no—
665C4⋊C4—1188no—
666C4⋊C4—1188no—
667C4⋊C4—2364no—
668C22⋊C4—28no—
669C22⋊C4—5916no—
670C22⋊C4—5916no—
671C22⋊C4—5916no—
672C22⋊C4—1188no—
673C22⋊C4—1188no—
674C22⋊C4—2364no—
675C22⋊C4C2×C4×D59116yescomplemented
676C42—28no—
677C42—44no—
678C42—1188no—
679C42—1188no—
680C42—1188no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—594no—
695C23—594no—
696C23—594no—
697C23—5916no—
698C23—1182no—
699C23—1182no—
700C23—1182no—
701C23—1182no—
702C23—1188no—
703C23—1188no—
704C23—1188no—
705C23—1188no—
706C23—1188no—
707C23—1188no—
708C23C22×C4×D5914yes—
709C23C22×C4×D5912yes—
710C23C2×D4×D5912yes—
711C23#41×D5912yes—
712C23C2×#1174568512yes—
713C23C2×#1174568512yes—
714C23#1427377212yes—
715C23#1427377412yes—
716C23C24×D5911yescharacteristic
717D4—11832no—
718C2×C4—22no—
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—22no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—594no—
739C2×C4—594no—
740C2×C4—594no—
741C2×C4—594no—
742C2×C4—11832no—
743C2×C4—1182no—
744C2×C4—1182no—
745C2×C4—1182no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1188no—
752C2×C4—1188no—
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—2364no—
767C2×C4—2364no—
768C2×C4—2364no—
769C2×C4C22×C4×D5914yes—
770C2×C4C22×C4×D5914yes—
771C2×C4C2×D4×D5914yes—
772C2×C4C2×#1174568514yes—
773C2×C4C2×#1174568514yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—598no—
783C22—1184no—
784C22—1184no—
785C22—1184no—
786C22—1184no—
787C22—11832no—
788C22—1184no—
789C22—1184no—
790C22C4×D4×D5914yes—
791C22C4×#1174568514yes—
792C22#1683788114yes—
793C22#1683804214yes—
794C22#1683805714yes—
795C22#1683808114yes—
796C22#1683809114yes—
797C22C23×C4×D5911yescharacteristic
798C22C22×D4×D5911yescharacteristic
799C22C2×#41×D5911yescharacteristic
800C22C22×#1174568511yescharacteristic
801C22C22×#1174568511yescharacteristic
802C22C2×#1427377211yescharacteristic
803C22C2×#1427377411yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—24no—
809C4—42no—
810C4—1184no—
811C4—1184no—
812C4—1184no—
813C4—1184no—
814C4—2362no—
815C4—2362no—
816C4—2362no—
817C2—44no—
818C2—1188no—
819C2#2142708918yesdirect product factor
820C2C2×C4×D4×D5911yescharacteristic
821C2C2×C4×#1174568511yescharacteristic
822C2C2×#1683788111yescharacteristic
823C2C2×#1683804211yescharacteristic
824C2C2×#1683805711yescharacteristic
825C2C2×#1683808111yescharacteristic
826C2C2×#1683809111yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C4×C22⋊C4×C59C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
cosocleC23×C59C25
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C2×#2359
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#14273684C2semidirect
4. #21427089C2direct (N × H)
5. C2×#16837300C2semidirect
6. C2×#16837295C2semidirect
7. C2×#16837290C2semidirect
8. C2×#16837286C2semidirect
9. C2×#16837285C2semidirect
11. C2×#16837276C2semidirect
12. C2×#16837275C2semidirect
13. C2×#16837253C2semidirect
14. C2×C4×(C2×D59)⋊C4C2semidirect
15. C2×#95×D59C2semidirect
16. C2×C4×C22⋊C4×C59C2semidirect
21. C2×#14273709C4semidirect
26. C2×#14273684C22semidirect
43. #16837300C22semidirect
44. #16837295C22semidirect
45. #16837290C22semidirect
46. #16837286C22semidirect
47. #16837285C22semidirect
49. #16837276C22semidirect
50. #16837275C22semidirect
51. #16837253C22semidirect
52. C4×(C2×D59)⋊C4C22semidirect
61. #95×D59C22semidirect
67. C4×C22⋊C4×C59C22semidirect
90. C22×C4×D59C2×C4semidirect
94. #14273709C2×C4semidirect
98. C2×C4⋊Dic59C2×C4semidirect
105. C2×Dic59⋊C4C2×C4semidirect
113. C2×C22⋊Dic59C2×C4semidirect
118. C2×(C2×D59)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C59C2×C4semidirect
246. C2×C4×D59C22×C4semidirect
248. C22⋊C4×C59C22×C4semidirect
253. C22⋊Dic59C22×C4semidirect
255. (C2×D59)⋊C4C22×C4semidirect
258. C4⋊Dic59C22×C4semidirect
263. Dic59⋊C4C22×C4semidirect
418. C2×C4×C22⋊C4D59semidirect
421. C2×C59#2359semidirect
471. C4×C22⋊C4C2×D59semidirect
483. C59C2×#2359semidirect
549. C2×C22⋊C4C4×D59semidirect
675. C22⋊C4C2×C4×D59semidirect
819. C2#21427089direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737092
C22×C4×C22⋊D592
C22×#142736842
#214270892
C2×#168373002
C2×#168372952
C2×#168372902
C2×#168372862
C2×#168372852
C2×#168372782
C2×#168372762
C2×#168372752
C2×#168372532
C2×C4×(C2×D59)⋊C42
C2×#95×D592
C2×C4×C22⋊C4×C592
C2×#235959