Finite Group Databasebeta

← C2×#21428325 #28757246

Subgroups — C2×#21428325 #28757246

Order 15104.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273722C211yesmaximal, characteristic, complemented
2C22×#14273685C211yesmaximal, characteristic, complemented
3#21428325C2116yesmaximal, direct product factor
4C2×#16837339C211yesmaximal, characteristic, complemented
5C2×#16837339C211yesmaximal, characteristic, complemented
6C2×#16837334C211yesmaximal, characteristic, complemented
7C2×#16837319C211yesmaximal, characteristic
8C2×#16837304C211yesmaximal, characteristic
9C2×#16837301C211yesmaximal, characteristic, complemented
10C2×#16837294C211yesmaximal, characteristic, complemented
11C2×#16837294C211yesmaximal, characteristic, complemented
12C2×#16837294C211yesmaximal, characteristic, complemented
13C2×#16837280C211yesmaximal, characteristic
14C2×#16837276C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊Dic59C211yesmaximal, characteristic, complemented
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C2×#14273722—28no—
20C2×#14273722C2218yescomplemented
21C2×#14273685—28no—
22C2×#14273685C2218yescomplemented
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C4⋊Dic59C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×(C2×D59)⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
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×C4×Dic59C2211yescharacteristic
43C22×C4×Dic59C2211yescharacteristic
44C22×C4×Dic59C2211yescharacteristic
45#16837339C2218yescomplemented
46#16837339C2218yescomplemented
47#16837334C2218yescomplemented
48#16837319C2218yes—
49#16837304C2218yes—
50#16837301C2218yescomplemented
51#16837294C2218yescomplemented
52#16837294C2218yescomplemented
53#16837294C2218yescomplemented
54#16837280C2218yes—
55#16837276C2218yescomplemented
56C4×C4⋊Dic59C2218yescomplemented
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C59×#387C2218yescomplemented
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C24×D59C2311yescharacteristic
71C22×D236—24no—
72C22×D236—24no—
73C22×D236—42no—
74C22×D236C2314yes—
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C22×C4×D59—24no—
82C22×C4×D59—24no—
83C22×C4×D59—24no—
84C22×C4×D59C2314yes—
85#14273722—232no—
86#14273685—232no—
87C2×C4⋊Dic59—24no—
88C2×C4⋊Dic59—24no—
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59—24no—
91C2×C4⋊Dic59—42no—
92C2×C4⋊Dic59—42no—
93C2×C4⋊Dic59—42no—
94C2×C4⋊Dic59C2314yes—
95C2×C4⋊Dic59C2314yes—
96C2×C4⋊Dic59C2314yes—
97C2×C4⋊Dic59C2314yes—
98C2×C4⋊Dic59C2314yes—
99C2×C4⋊Dic59C2314yes—
100C2×C4⋊Dic59C2314yes—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4C2314yes—
103C2×(C2×D59)⋊C4—24no—
104C2×(C2×D59)⋊C4—24no—
105C2×(C2×D59)⋊C4—24no—
106C2×(C2×D59)⋊C4—24no—
107C2×(C2×D59)⋊C4—24no—
108C2×(C2×D59)⋊C4—24no—
109C2×(C2×D59)⋊C4—24no—
110C2×(C2×D59)⋊C4—24no—
111C2×(C2×D59)⋊C4—24no—
112C2×(C2×D59)⋊C4—42no—
113C2×(C2×D59)⋊C4—42no—
114C2×(C2×D59)⋊C4C2314yes—
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
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×Dic59—24no—
126C2×C4×Dic59—24no—
127C2×C4×Dic59—24no—
128C2×C4×Dic59C2314yes—
129C2×C4×Dic59C2314yes—
130C2×C4×Dic59C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C59⋊#95C2314yes—
134C59⋊#95C2314yes—
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59—24no—
143C2×C4⋊C4×C59D418yescomplemented
144C2×C4⋊C4×C59C2314yes—
145C2×C4⋊C4×C59C2314yes—
146C2×C42×C59—24no—
147C2×C42×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150#95×C59C2314yes—
151#95×C59C2314yes—
152C24×C59C2411yescharacteristic
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59#4114yes—
167C23×D59C2412yes—
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×C59C2×D414yes—
186C22×C4×C59C2×D414yes—
187C22×C4×C59C2×D414yes—
188C22×C4×C59#4114yes—
189C22×C4×C59#4114yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
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#4114yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C2×D236—28no—
222C2×D236—28no—
223C2×D236—44no—
224C2×D236—416no—
225C2×C4×D59—232no—
226C2×C4×D59—28no—
227C2×C4×D59—28no—
228C2×C4×D59—28no—
229C4⋊C4×C59—28no—
230C4⋊C4×C59C2×D4116yescomplemented
231C42×C59—28no—
232(C2×D59)⋊C4—28no—
233(C2×D59)⋊C4—28no—
234(C2×D59)⋊C4—28no—
235(C2×D59)⋊C4—28no—
236(C2×D59)⋊C4—28no—
237(C2×D59)⋊C4—28no—
238(C2×D59)⋊C4—28no—
239(C2×D59)⋊C4—28no—
240(C2×D59)⋊C4—28no—
241(C2×D59)⋊C4—44no—
242(C2×D59)⋊C4—44no—
243C4⋊Dic59—28no—
244C4⋊Dic59—28no—
245C4⋊Dic59—28no—
246C4⋊Dic59—28no—
247C4⋊Dic59—44no—
248C4⋊Dic59—44no—
249C4⋊Dic59—44no—
250Dic59⋊C4—28no—
251C4×Dic59—28no—
252C4×Dic59—28no—
253C4×Dic59—28no—
254C23×C59C22×D412yes—
255C23×C59C2×#4112yes—
256C23×C59C2×#4112yes—
257C23×C59C2×#4112yes—
258C23×C59C2×#4112yes—
259C23×C59H(5,𝔽2)12yes—
260C23×C592−1+412yes—
261C23×C59C2511yescharacteristic
262C22×D59—28no—
263C22×D59—28no—
264C22×D59—28no—
265C22×D59—22no—
266C22×D59—22no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—44no—
279C22×D59—44no—
280C22×D59—44no—
281C22×D59—44no—
282C22×D59—44no—
283C22×D59—44no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59—44no—
289C22×D59C2×#4114yes—
290C2×C4×C59—28no—
291C2×C4×C59—28no—
292C2×C4×C59—28no—
293C2×C4×C59—28no—
294C2×C4×C59—28no—
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—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—44no—
312C2×C4×C59—44no—
313C2×C4×C59C22×D414yes—
314C2×C4×C59C22×D414yes—
315C2×C4×C59C22×D414yes—
316C2×C4×C59C2×#4114yes—
317C2×C4×C59C2×#4114yes—
318C2×Dic59—28no—
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—22no—
336C2×Dic59—44no—
337C2×Dic59—44no—
338C2×Dic59—44no—
339C2×Dic59—44no—
340C2×Dic59—44no—
341C2×Dic59C2×#4114yes—
342D236—416no—
343C4×D59—232no—
344C2×#2479—591nomaximal, Sylow
345C22×C59#52514yes—
346C22×C59#52914yes—
347C22×C59#54214yes—
348C22×C59#54714yes—
349C22×C59#55014yes—
350C22×C59#55114yes—
351C22×C59#55214yes—
352C22×C59C23×D411yescharacteristic
353C22×C59C22×#4111yescharacteristic
354C22×C59C22×#4111yescharacteristic
355C22×C59C22×#4111yescharacteristic
356C22×C59C22×#4111yescharacteristic
357C22×C59C2×H(5,𝔽2)11yescharacteristic
358C22×C59C2×2−1+411yescharacteristic
359C2×D59—24no—
360C2×D59—24no—
361C2×D59—24no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—416no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—88no—
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—24no—
378C4×C59—24no—
379C4×C59—24no—
380C4×C59—42no—
381C4×C59—42no—
382Dic59—24no—
383Dic59—42no—
384Dic59—42no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388C22×#126—591no—
389C22×#117—591no—
390#2479—5916no—
391C2×#399—591no—
392C2×#399—591no—
393C2×#398—591no—
394C2×#394—591no—
395C2×#390—591no—
396C2×#389—591no—
397C2×#388—591no—
398C2×#388—591no—
399C2×#388—591no—
400C2×#387D5911yescharacteristic, complemented
401C2×#386—591no—
402C2×#385—591no—
403C2×C4×C4⋊C4—591no—
404C2×C59#247918yescomplemented
405C2×C59C2×#52511yescharacteristic
406C2×C59C2×#52911yescharacteristic
407C2×C59C2×#54211yescharacteristic
408C2×C59C2×#54711yescharacteristic
409C2×C59C2×#55011yescharacteristic
410C2×C59C2×#55111yescharacteristic
411C2×C59C2×#55211yescharacteristic
412D59—44no—
413D59—82no—
414C23×D4—591no—
415C24×C4—591no—
416C2×#126—598no—
417C2×#126—1188no—
418C2×#117—598no—
419C2×#117—1188no—
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⋊C4C2×D5911yescharacteristic
429C22×C4⋊C4C2×D5911yescharacteristic
430C22×C22⋊C4—591no—
431C22×C22⋊C4—591no—
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×C42—591no—
442C22×C42—591no—
443C22×C42—591no—
444C22×C42C2×D5911yescharacteristic
445#399—598no—
446#399—598no—
447#398—598no—
448#394—598no—
449#390—598no—
450#389—598no—
451#388—598no—
452#388—598no—
453#388—598no—
454#387C2×D5918yescomplemented
455#386—598no—
456#385—598no—
457C4×C4⋊C4—598no—
458C2×#95—591no—
459C2×#95—591no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95C2×D5911yescharacteristic
463C2×#95C2×D5911yescharacteristic
464C2×#95C2×D5911yescharacteristic
465C2×#95C2×D5911yescharacteristic
466C59C2×#247911yescharacteristic, complemented, Sylow
467C25—591no—
468C25—591no—
469C22×D4—594no—
470C22×D4—1184no—
471C22×D4—1184no—
472C22×D4—2362no—
473C23×C4—591no—
474C23×C4—591no—
475C23×C4—591no—
476C23×C4—591no—
477C23×C4—591no—
478C23×C4—591no—
479C23×C4—594no—
480C23×C4—1184no—
481C23×C4—1184no—
482C23×C4—1184no—
483C23×C4C22×D5911yescharacteristic
484C23×C4C22×D5911yescharacteristic
485C23×C4C22×D5911yescharacteristic
486C23×C4C22×D5911yescharacteristic
487C23×C4C22×D5911yescharacteristic
488C23×C4C22×D5911yescharacteristic
489C23×C4C22×D5911yescharacteristic
490#126—11832no—
491#117—11832no—
492C2×C4⋊C4—24no—
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⋊C4D23618yescomplemented
510C2×C4⋊C4C22×D5914yes—
511C2×C4⋊C4C22×D5914yes—
512C2×C22⋊C4—594no—
513C2×C22⋊C4—594no—
514C2×C22⋊C4—594no—
515C2×C22⋊C4—594no—
516C2×C22⋊C4—594no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—594no—
520C2×C22⋊C4—594no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—594no—
523C2×C22⋊C4—1184no—
524C2×C22⋊C4—1184no—
525C2×C22⋊C4—1184no—
526C2×C22⋊C4—1184no—
527C2×C22⋊C4—1184no—
528C2×C22⋊C4—1184no—
529C2×C22⋊C4—1184no—
530C2×C22⋊C4—1184no—
531C2×C22⋊C4—1184no—
532C2×C22⋊C4—2362no—
533C2×C22⋊C4—2362no—
534C2×C42—24no—
535C2×C42—594no—
536C2×C42—594no—
537C2×C42—594no—
538C2×C42—1184no—
539C2×C42—1184no—
540C2×C42—1184no—
541C2×C42C22×D5914yes—
542#95—594no—
543#95—594no—
544#95—594no—
545#95—594no—
546#95C22×D5914yes—
547#95C22×D5914yes—
548#95C22×D5914yes—
549#95C22×D5914yes—
550C24—594no—
551C24—592no—
552C24—592no—
553C24—1182no—
554C24—1182no—
555C24—1182no—
556C24—1182no—
557C24—1182no—
558C24—1182no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24—1182no—
563C24—1182no—
564C24—1182no—
565C24—1182no—
566C24C23×D5911yescharacteristic
567C2×D4—1188no—
568C2×D4—1188no—
569C2×D4—2364no—
570C2×D4—23616no—
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—22no—
587C22×C4—594no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—592no—
594C22×C4—1188no—
595C22×C4—1188no—
596C22×C4—11832no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1188no—
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×C4—1182no—
615C22×C4C2×D23614yes—
616C22×C4C2×D23614yes—
617C22×C4C2×D23614yes—
618C22×C4#1174568714yes—
619C22×C4#1174568914yes—
620C22×C4C23×D5912yes—
621C22×C4C23×D5912yes—
622C22×C4C23×D5912yes—
623C22×C4C23×D5912yes—
624C22×C4C23×D5912yes—
625C22×C4C23×D5912yes—
626C22×C4C23×D5912yes—
627C4⋊C4—28no—
628C4⋊C4—1188no—
629C4⋊C4—1188no—
630C4⋊C4—1188no—
631C4⋊C4—1188no—
632C4⋊C4—1188no—
633C4⋊C4—2364no—
634C4⋊C4—2364no—
635C4⋊C4—2364no—
636C4⋊C4C2×D236116yescomplemented
637C22⋊C4—1188no—
638C22⋊C4—1188no—
639C22⋊C4—1188no—
640C22⋊C4—1188no—
641C22⋊C4—1188no—
642C22⋊C4—1188no—
643C22⋊C4—1188no—
644C22⋊C4—1188no—
645C22⋊C4—1188no—
646C22⋊C4—2364no—
647C22⋊C4—2364no—
648C42—28no—
649C42—1188no—
650C42—1188no—
651C42—1188no—
652C23—594no—
653C23—1188no—
654C23—1182no—
655C23—1182no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1188no—
661C23—1188no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—2364no—
670C23—2364no—
671C23—2364no—
672C23—2364no—
673C23—2364no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23—2364no—
679C23—2364no—
680C23C22×D23612yes—
681C23#41×D5912yes—
682C23#41×D5912yes—
683C23C2×#1174568712yes—
684C23C2×#1174568912yes—
685C23#1427377312yes—
686C23#1427377412yes—
687C23C24×D5911yescharacteristic
688D4—23616no—
689C2×C4—28no—
690C2×C4—28no—
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—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—594no—
713C2×C4—11832no—
714C2×C4—1188no—
715C2×C4—1182no—
716C2×C4—1182no—
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×C4C22×D23614yes—
738C2×C4C22×D23614yes—
739C2×C4C22×D23614yes—
740C2×C4C2×#1174568714yes—
741C2×C4C2×#1174568914yes—
742C22—1184no—
743C22—1184no—
744C22—1184no—
745C22—4728no—
746C22—2362no—
747C22—2362no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—23616no—
755C22—2362no—
756C22—2362no—
757C22—2362no—
758C22#1683791414yes—
759C22#1683793814yes—
760C22#1683801814yes—
761C22#1683805614yes—
762C22#1683807414yes—
763C22#1683807514yes—
764C22#1683809014yes—
765C22C23×D23611yescharacteristic
766C22C2×#41×D5911yescharacteristic
767C22C2×#41×D5911yescharacteristic
768C22C22×#1174568711yescharacteristic
769C22C22×#1174568911yescharacteristic
770C22C2×#1427377311yescharacteristic
771C22C2×#1427377411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—1184no—
780C4—2362no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C2—4722no—
786C2—2364no—
787C2#2142832518yesdirect product factor
788C2C2×#1683791411yescharacteristic
789C2C2×#1683793811yescharacteristic
790C2C2×#1683801811yescharacteristic
791C2C2×#1683805611yescharacteristic
792C2C2×#1683807411yescharacteristic
793C2C2×#1683807511yescharacteristic
794C2C2×#1683809011yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC23×D236C22
hypercenterC2×#387D59
hypocenterC59C2×#2479
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14273722C2semidirect
2. C22×#14273685C2semidirect
3. #21428325C2direct (N × H)
4. C2×#16837339C2semidirect
5. C2×#16837339C2semidirect
6. C2×#16837334C2semidirect
9. C2×#16837301C2semidirect
10. C2×#16837294C2semidirect
11. C2×#16837294C2semidirect
12. C2×#16837294C2semidirect
14. C2×#16837276C2semidirect
15. C2×C4×C4⋊Dic59C2semidirect
16. C2×C59×#387C2semidirect
20. C2×#14273722C22semidirect
22. C2×#14273685C22semidirect
45. #16837339C22semidirect
46. #16837339C22semidirect
47. #16837334C22semidirect
50. #16837301C22semidirect
51. #16837294C22semidirect
52. #16837294C22semidirect
53. #16837294C22semidirect
55. #16837276C22semidirect
56. C4×C4⋊Dic59C22semidirect
64. C59×#387C22semidirect
143. C2×C4⋊C4×C59D4semidirect
230. C4⋊C4×C59C2×D4semidirect
400. C2×#387D59semidirect
404. C2×C59#2479semidirect
454. #387C2×D59semidirect
466. C59C2×#2479semidirect
509. C2×C4⋊C4D236semidirect
636. C4⋊C4C2×D236semidirect
787. C2#21428325direct (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×#142736852
#214283252
C2×#168373392
C2×#168373342
C2×#168373192
C2×#168373042
C2×#168373012
C2×#168372942
C2×#168372802
C2×#168372762
C2×C4×C4⋊Dic592
C2×C59×#3872
C2×#247959