Finite Group Databasebeta

← C2×#21432169 #28795222

Subgroups — C2×#21432169 #28795222

Order 15104.

2502 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273722C211yesmaximal, characteristic, complemented
2C22×#14273720C211yesmaximal, characteristic, complemented
3#21432169C2116yesmaximal, direct product factor
4C2×#16837335C211yesmaximal, characteristic, complemented
5C2×#16837334C211yesmaximal, characteristic, complemented
6C2×#16837333C211yesmaximal, characteristic, complemented
7C2×#16837326C211yesmaximal, characteristic, complemented
8C2×#16837325C211yesmaximal, characteristic, complemented
9C2×#16837325C211yesmaximal, characteristic, complemented
10C2×#16837324C211yesmaximal, characteristic, complemented
11C2×#16837324C211yesmaximal, characteristic, complemented
12C2×#16837318C211yesmaximal, characteristic
13C2×#16837317C211yesmaximal, characteristic
14C2×#16837317C211yesmaximal, characteristic
15C2×#16837271C211yesmaximal, characteristic, complemented
16C2×C59×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D59C2211yescharacteristic
18C2×#14273722—28no—
19C2×#14273722C2218yescomplemented
20C2×#14273720—28no—
21C2×#14273720C2218yescomplemented
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
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×(C2×D59)⋊C4C2211yescharacteristic
41C22×(C2×D59)⋊C4C2211yescharacteristic
42C22×(C2×D59)⋊C4C2211yescharacteristic
43C22×C4×Dic59C2211yescharacteristic
44#16837335C2218yescomplemented
45#16837334C2218yescomplemented
46#16837333C2218yescomplemented
47#16837326C2218yescomplemented
48#16837325C2218yescomplemented
49#16837325C2218yescomplemented
50#16837324C2218yescomplemented
51#16837324C2218yescomplemented
52#16837318C2218yes—
53#16837317C2218yes—
54#16837317C2218yes—
55#16837271C2218yescomplemented
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C22×C22⋊C4×C59C2211yescharacteristic
66C22×C22⋊C4×C59C2211yescharacteristic
67C59×#396C2218yescomplemented
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C22×C22⋊D59—42no—
71C22×C22⋊D59—42no—
72C22×C22⋊D59—42no—
73C22×C22⋊D59C2314yes—
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81#14273722—232no—
82#14273720—232no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59—42no—
86C2×C4⋊Dic59—42no—
87C2×C4⋊Dic59C2314yes—
88C2×C4⋊Dic59C2314yes—
89C2×C4⋊Dic59C2314yes—
90C2×C4⋊Dic59C2314yes—
91C2×Dic59⋊C4—24no—
92C2×Dic59⋊C4—24no—
93C2×Dic59⋊C4—24no—
94C2×Dic59⋊C4—42no—
95C2×Dic59⋊C4—42no—
96C2×Dic59⋊C4—42no—
97C2×Dic59⋊C4—42no—
98C2×Dic59⋊C4—42no—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×C22⋊Dic59—24no—
108C2×C22⋊Dic59—24no—
109C2×C22⋊Dic59—42no—
110C2×C22⋊Dic59C2314yes—
111C2×C22⋊Dic59C2314yes—
112C2×C22⋊Dic59C2314yes—
113C2×(C2×D59)⋊C4—24no—
114C2×(C2×D59)⋊C4—24no—
115C2×(C2×D59)⋊C4—24no—
116C2×(C2×D59)⋊C4—42no—
117C2×(C2×D59)⋊C4—42no—
118C2×(C2×D59)⋊C4—42no—
119C2×(C2×D59)⋊C4C2314yes—
120C2×(C2×D59)⋊C4C2314yes—
121C2×(C2×D59)⋊C4C2314yes—
122C2×(C2×D59)⋊C4C2314yes—
123C2×(C2×D59)⋊C4C2314yes—
124C2×(C2×D59)⋊C4C2314yes—
125C2×C4×Dic59D418yescomplemented
126C2×C4×Dic59C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C25×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C2×C4⋊C4×C59—24no—
140C2×C4⋊C4×C59—42no—
141C2×C4⋊C4×C59—42no—
142C2×C4⋊C4×C59C2314yes—
143C2×C4⋊C4×C59C2314yes—
144C2×C4⋊C4×C59C2314yes—
145C2×C22⋊C4×C59—24no—
146C2×C22⋊C4×C59—42no—
147C2×C22⋊C4×C59—42no—
148C2×C22⋊C4×C59C2314yes—
149C2×C22⋊C4×C59C2314yes—
150C2×C22⋊C4×C59C2314yes—
151#95×C59C2314yes—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59—22no—
157C24×C59—22no—
158C24×C59—22no—
159C24×C59C2412yes—
160C24×C59C2411yescharacteristic
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59—22no—
167C23×D59—22no—
168C23×D59C2412yes—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
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×C59C2×D414yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C2×C22⋊D59—44no—
194C2×C22⋊D59—44no—
195C2×C22⋊D59—44no—
196C2×C22⋊D59—416no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59—22no—
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×Dic59C2×D414yes—
217C22×Dic59C2×D414yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C4⋊C4×C59—28no—
226C4⋊C4×C59—44no—
227C4⋊C4×C59—44no—
228C22⋊C4×C59—28no—
229C22⋊C4×C59—44no—
230C22⋊C4×C59—44no—
231C22⋊Dic59—28no—
232C22⋊Dic59—28no—
233C22⋊Dic59—44no—
234(C2×D59)⋊C4—28no—
235(C2×D59)⋊C4—28no—
236(C2×D59)⋊C4—28no—
237(C2×D59)⋊C4—44no—
238(C2×D59)⋊C4—44no—
239(C2×D59)⋊C4—44no—
240C4⋊Dic59—28no—
241C4⋊Dic59—28no—
242C4⋊Dic59—44no—
243C4⋊Dic59—44no—
244Dic59⋊C4—28no—
245Dic59⋊C4—28no—
246Dic59⋊C4—28no—
247Dic59⋊C4—44no—
248Dic59⋊C4—44no—
249Dic59⋊C4—44no—
250Dic59⋊C4—44no—
251Dic59⋊C4—44no—
252C4×Dic59C2×D4116yescomplemented
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—44no—
261C23×C59—44no—
262C23×C59—44no—
263C23×C59—44no—
264C23×C59—44no—
265C23×C59—44no—
266C23×C59—44no—
267C23×C59C22×D412yes—
268C23×C59H(5,𝔽2)12yes—
269C23×C59H(5,𝔽2)12yes—
270C23×C59H(5,𝔽2)12yes—
271C23×C592−1+412yes—
272C23×C592−1+412yes—
273C23×C592−1+412yes—
274C23×C59C2511yescharacteristic
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—44no—
283C22×D59—44no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59—44no—
289C2×C4×C59—28no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—44no—
308C2×C4×C59—44no—
309C2×C4×C59—44no—
310C2×C4×C59—44no—
311C2×C4×C59—44no—
312C2×C4×C59C22×D414yes—
313C22⋊D59—416no—
314C2×Dic59—28no—
315C2×Dic59—28no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—44no—
336C2×Dic59—44no—
337C2×Dic59—44no—
338C2×Dic59—44no—
339C2×Dic59—44no—
340C2×Dic59C22×D414yes—
341C2×Dic59C22×D414yes—
342C2×#2823—591nomaximal, Sylow
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—88no—
351C22×C59#53714yes—
352C22×C59#53714yes—
353C22×C59#53714yes—
354C22×C59#56014yes—
355C22×C59#56314yes—
356C22×C59#56314yes—
357C22×C59#56314yes—
358C22×C59C23×D411yescharacteristic
359C22×C59C2×H(5,𝔽2)11yescharacteristic
360C22×C59C2×H(5,𝔽2)11yescharacteristic
361C22×C59C2×H(5,𝔽2)11yescharacteristic
362C22×C59C2×2−1+411yescharacteristic
363C22×C59C2×2−1+411yescharacteristic
364C22×C59C2×2−1+411yescharacteristic
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—88no—
373C4×C59—24no—
374C4×C59—42no—
375C4×C59—42no—
376C4×C59—42no—
377C4×C59—42no—
378C4×C59—42no—
379Dic59—24no—
380Dic59—24no—
381Dic59—42no—
382Dic59—42no—
383Dic59—42no—
384Dic59—42no—
385Dic59—42no—
386C22×#126—591no—
387C22×#126—591no—
388#2823—5916no—
389C2×#398—591no—
390C2×#398—591no—
391C2×#398—591no—
392C2×#396—591no—
393C2×#396—591no—
394C2×#396—591no—
395C2×#396—591no—
396C2×#396—591no—
397C2×#396D5911yescharacteristic, complemented
398C2×#394—591no—
399C2×#394—591no—
400C2×#394—591no—
401C2×#384—591no—
402C2×C59—82no—
403C2×C59#282318yescomplemented
404C2×C59C2×#53711yescharacteristic
405C2×C59C2×#53711yescharacteristic
406C2×C59C2×#53711yescharacteristic
407C2×C59C2×#56011yescharacteristic
408C2×C59C2×#56311yescharacteristic
409C2×C59C2×#56311yescharacteristic
410C2×C59C2×#56311yescharacteristic
411D59—82no—
412C23×D4—591no—
413C2×#126—598no—
414C2×#126—598no—
415C2×#126—1188no—
416C2×#126—1188no—
417C22×C4⋊C4—591no—
418C22×C4⋊C4—591no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—591no—
422C22×C4⋊C4—591no—
423C22×C4⋊C4—591no—
424C22×C4⋊C4—591no—
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4C2×D5911yescharacteristic
430C22×C4⋊C4C2×D5911yescharacteristic
431C22×C4⋊C4C2×D5911yescharacteristic
432C22×C22⋊C4—591no—
433C22×C22⋊C4—591no—
434C22×C22⋊C4—591no—
435C22×C22⋊C4—591no—
436C22×C22⋊C4—591no—
437C22×C22⋊C4—591no—
438C22×C22⋊C4—591no—
439C22×C22⋊C4—591no—
440C22×C22⋊C4—591no—
441C22×C22⋊C4C2×D5911yescharacteristic
442C22×C22⋊C4C2×D5911yescharacteristic
443C22×C22⋊C4C2×D5911yescharacteristic
444C22×C42—591no—
445#398—598no—
446#398—598no—
447#398—598no—
448#396—598no—
449#396—598no—
450#396—598no—
451#396—598no—
452#396—598no—
453#396C2×D5918yescomplemented
454#394—598no—
455#394—598no—
456#394—598no—
457#384—598no—
458C2×#95—591no—
459C2×#95—591no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95—591no—
463C2×#95C2×D5911yescharacteristic
464C59C2×#282311yescharacteristic, complemented, Sylow
465C25—591no—
466C25C22×D5911yescharacteristic
467C22×D4—594no—
468C22×D4—2362no—
469C22×D4—2362no—
470C22×D4—2362no—
471C23×C4—591no—
472C23×C4—591no—
473C23×C4—591no—
474C23×C4—591no—
475C23×C4—591no—
476C23×C4—591no—
477C23×C4—591no—
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5911yescharacteristic
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483C23×C4C22×D5911yescharacteristic
484#126—11832no—
485#126—11832no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—594no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4—594no—
492C2×C4⋊C4—594no—
493C2×C4⋊C4—594no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—594no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—594no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—1184no—
502C2×C4⋊C4—1184no—
503C2×C4⋊C4—1184no—
504C2×C4⋊C4—1184no—
505C2×C4⋊C4—1184no—
506C2×C4⋊C4—2362no—
507C2×C4⋊C4—2362no—
508C2×C4⋊C4—2362no—
509C2×C4⋊C4—2362no—
510C2×C4⋊C4—2362no—
511C2×C4⋊C4—2362no—
512C2×C4⋊C4—2362no—
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5914yes—
515C2×C4⋊C4C22×D5914yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—594no—
520C2×C22⋊C4—594no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—594no—
523C2×C22⋊C4—594no—
524C2×C22⋊C4—594no—
525C2×C22⋊C4—594no—
526C2×C22⋊C4—594no—
527C2×C22⋊C4—594no—
528C2×C22⋊C4—1184no—
529C2×C22⋊C4—1184no—
530C2×C22⋊C4—1184no—
531C2×C22⋊C4—1184no—
532C2×C22⋊C4—1184no—
533C2×C22⋊C4—2362no—
534C2×C22⋊C4—2362no—
535C2×C22⋊C4—2362no—
536C2×C22⋊C4—2362no—
537C2×C22⋊C4C22×D5914yes—
538C2×C22⋊C4C22×D5914yes—
539C2×C22⋊C4C22×D5914yes—
540C2×C42—598no—
541C2×C42—594no—
542#95—594no—
543#95—594no—
544#95—594no—
545#95—594no—
546#95—594no—
547#95C22×D5914yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—592no—
556C24—1182no—
557C24—1182no—
558C24—1182no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24—1182no—
563C24C23×D5912yes—
564C24C23×D5911yescharacteristic
565C2×D4—2364no—
566C2×D4—2364no—
567C2×D4—2364no—
568C2×D4—23616no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—594no—
587C22×C4—594no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1182no—
614C22×C4D4×D5914yes—
615C22×C4C23×D5912yes—
616C22×C4C23×D5912yes—
617C22×C4C23×D5912yes—
618C22×C4C23×D5912yes—
619C22×C4C23×D5912yes—
620C22×C4C23×D5912yes—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—1188no—
625C4⋊C4—1188no—
626C4⋊C4—1188no—
627C4⋊C4—1188no—
628C4⋊C4—1188no—
629C4⋊C4—2364no—
630C4⋊C4—2364no—
631C4⋊C4—2364no—
632C4⋊C4—2364no—
633C4⋊C4—2364no—
634C4⋊C4—2364no—
635C4⋊C4—2364no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—1188no—
640C22⋊C4—1188no—
641C22⋊C4—1188no—
642C22⋊C4—1188no—
643C22⋊C4—1188no—
644C22⋊C4—2364no—
645C22⋊C4—2364no—
646C22⋊C4—2364no—
647C22⋊C4—2364no—
648C42—5916no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—2364no—
671C23—2364no—
672C23—2364no—
673C23—2364no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23C2×D4×D5912yes—
678C23#1427377212yes—
679C23#1427377212yes—
680C23#1427377312yes—
681C23#1427377412yes—
682C23#1427377412yes—
683C23#1427377512yes—
684C23C24×D5911yescharacteristic
685D4—23616no—
686C2×C4—22no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—594no—
710C2×C4—594no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1188no—
716C2×C4—1188no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—2364no—
733C2×C4—2364no—
734C2×C4—2364no—
735C2×C4—2364no—
736C2×C4—2364no—
737C2×C4C2×D4×D5914yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—4728no—
747C22—2362no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22#1683797914yes—
755C22#1683798114yes—
756C22#1683798214yes—
757C22#1683814014yes—
758C22#1683815314yes—
759C22#1683815314yes—
760C22#1683815414yes—
761C22C22×D4×D5911yescharacteristic
762C22C2×#1427377211yescharacteristic
763C22C2×#1427377211yescharacteristic
764C22C2×#1427377311yescharacteristic
765C22C2×#1427377411yescharacteristic
766C22C2×#1427377411yescharacteristic
767C22C2×#1427377511yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—1184no—
775C4—1184no—
776C4—2362no—
777C4—2362no—
778C4—2362no—
779C4—2362no—
780C4—2362no—
781C2—82no—
782C2—4722no—
783C2#2143216918yesdirect product factor
784C2C2×#1683797911yescharacteristic
785C2C2×#1683798111yescharacteristic
786C2C2×#1683798211yescharacteristic
787C2C2×#1683814011yescharacteristic
788C2C2×#1683815311yescharacteristic
789C2C2×#1683815311yescharacteristic
790C2C2×#1683815411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#396C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#396D59
hypocenterC59C2×#2823
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14273722C2semidirect
2. C22×#14273720C2semidirect
3. #21432169C2direct (N × H)
4. C2×#16837335C2semidirect
5. C2×#16837334C2semidirect
6. C2×#16837333C2semidirect
7. C2×#16837326C2semidirect
8. C2×#16837325C2semidirect
9. C2×#16837325C2semidirect
10. C2×#16837324C2semidirect
11. C2×#16837324C2semidirect
15. C2×#16837271C2semidirect
16. C2×C59×#396C2semidirect
19. C2×#14273722C22semidirect
21. C2×#14273720C22semidirect
44. #16837335C22semidirect
45. #16837334C22semidirect
46. #16837333C22semidirect
47. #16837326C22semidirect
48. #16837325C22semidirect
49. #16837325C22semidirect
50. #16837324C22semidirect
51. #16837324C22semidirect
55. #16837271C22semidirect
67. C59×#396C22semidirect
125. C2×C4×Dic59D4semidirect
252. C4×Dic59C2×D4semidirect
397. C2×#396D59semidirect
403. C2×C59#2823semidirect
453. #396C2×D59semidirect
464. C59C2×#2823semidirect
783. C2#21432169direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737222
C22×#142737202
#214321692
C2×#168373352
C2×#168373342
C2×#168373332
C2×#168373262
C2×#168373252
C2×#168373242
C2×#168373182
C2×#168373172
C2×#168372712
C2×C59×#3962
C2×#282359