Finite Group Databasebeta

← C2×#21427797 #28756518

Subgroups — C2×#21427797 #28756518

Order 15104.

3550 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×#14273726C211yesmaximal, characteristic, complemented
2C22×#14273706C211yesmaximal, characteristic
3C22×#14273704C211yesmaximal, characteristic
4C23×Dic59⋊C4C211yesmaximal, characteristic
5#21427797C2116yesmaximal, direct product factor
6C2×#16837336C211yesmaximal, characteristic, complemented
7C2×#16837335C211yesmaximal, characteristic, complemented
8C2×#16837323C211yesmaximal, characteristic, complemented
9C2×#16837322C211yesmaximal, characteristic, complemented
10C2×#16837299C211yesmaximal, characteristic, complemented
11C2×#16837299C211yesmaximal, characteristic, complemented
12C2×#16837277C211yesmaximal, characteristic
13C2×#16837271C211yesmaximal, characteristic, complemented
14C2×#16837260C211yesmaximal, characteristic
15C2×C22⋊C4×Dic59C211yesmaximal, characteristic
16C2×C59×#385C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C24×Dic59C2211yescharacteristic
20C24×Dic59C2211yescharacteristic
21C2×#14273726—28no—
22C2×#14273726C2218yescomplemented
23C2×#14273706—28no—
24C2×#14273706C2218yes—
25C2×#14273704—28no—
26C2×#14273704C2218yes—
27C22×C4⋊Dic59C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C22×C4⋊Dic59C2211yescharacteristic
31C22×Dic59⋊C4—28no—
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊C4C2211yescharacteristic
34C22×Dic59⋊C4C2211yescharacteristic
35C22×Dic59⋊C4C2211yescharacteristic
36C22×Dic59⋊C4C2211yescharacteristic
37C22×Dic59⋊C4C2218yes—
38C22×Dic59⋊C4C2211yescharacteristic
39C22×Dic59⋊C4C2211yescharacteristic
40C22×Dic59⋊C4C2211yescharacteristic
41C22×Dic59⋊C4C2211yescharacteristic
42C22×Dic59⋊C4C2211yescharacteristic
43C22×C22⋊Dic59C2211yescharacteristic
44C22×C22⋊Dic59C2211yescharacteristic
45C22×C4×Dic59C2211yescharacteristic
46C22×C4×Dic59C2211yescharacteristic
47#16837336C2218yescomplemented
48#16837335C2218yescomplemented
49#16837323C2218yescomplemented
50#16837322C2218yescomplemented
51#16837299C2218yescomplemented
52#16837299C2218yescomplemented
53#16837277C2218yes—
54#16837271C2218yescomplemented
55#16837260C2218yes—
56C22⋊C4×Dic59C2218yes—
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C2×C59⋊#95C2211yescharacteristic
62C2×C59⋊#95C2211yescharacteristic
63C24×C4×C59C2211yescharacteristic
64C22×C4⋊C4×C59C2211yescharacteristic
65C22×C4⋊C4×C59C2211yescharacteristic
66C22×C22⋊C4×C59C2211yescharacteristic
67C22×C22⋊C4×C59C2211yescharacteristic
68C59×#385C2218yes—
69C2×#95×C59C2211yescharacteristic
70C2×#95×C59C2211yescharacteristic
71C22×Dic118—24no—
72C22×Dic118—24no—
73C22×Dic118—24no—
74C22×Dic118—24no—
75C22×Dic118—42no—
76C22×Dic118—42no—
77C22×Dic118C2314yes—
78C22×Dic118C2314yes—
79C23×Dic59—24no—
80C23×Dic59—24no—
81C23×Dic59—24no—
82C23×Dic59—24no—
83C23×Dic59—42no—
84C23×Dic59Q818yescomplemented
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87C23×Dic59C2311yescharacteristic
88C23×Dic59C2314yes—
89C23×Dic59C2311yescharacteristic
90C23×Dic59C2311yescharacteristic
91C23×Dic59C2311yescharacteristic
92C23×Dic59C2311yescharacteristic
93C23×Dic59C2314yes—
94C23×Dic59C2311yescharacteristic
95#14273726—232no—
96#14273706—232no—
97#14273704—232no—
98C2×C4⋊Dic59—24no—
99C2×C4⋊Dic59—24no—
100C2×C4⋊Dic59—24no—
101C2×C4⋊Dic59—42no—
102C2×C4⋊Dic59C2314yes—
103C2×C4⋊Dic59C2314yes—
104C2×C4⋊Dic59C2314yes—
105C2×C4⋊Dic59C2314yes—
106C2×Dic59⋊C4—24no—
107C2×Dic59⋊C4—24no—
108C2×Dic59⋊C4—24no—
109C2×Dic59⋊C4—24no—
110C2×Dic59⋊C4—24no—
111C2×Dic59⋊C4—24no—
112C2×Dic59⋊C4—24no—
113C2×Dic59⋊C4—24no—
114C2×Dic59⋊C4—24no—
115C2×Dic59⋊C4—232no—
116C2×Dic59⋊C4D418yes—
117C2×Dic59⋊C4C2314yes—
118C2×Dic59⋊C4C2314yes—
119C2×Dic59⋊C4C2314yes—
120C2×Dic59⋊C4C2314yes—
121C2×Dic59⋊C4C2314yes—
122C2×Dic59⋊C4C2314yes—
123C2×Dic59⋊C4C2314yes—
124C2×Dic59⋊C4C2314yes—
125C2×Dic59⋊C4C2314yes—
126C2×Dic59⋊C4C2314yes—
127C2×C22⋊Dic59—24no—
128C2×C22⋊Dic59D418yes—
129C2×C22⋊Dic59C2314yes—
130C2×C22⋊Dic59C2314yes—
131C2×C4×Dic59—24no—
132C2×C4×Dic59—24no—
133C2×C4×Dic59C2314yes—
134C2×C4×Dic59C2314yes—
135C59⋊#95C2314yes—
136C59⋊#95C2314yes—
137C59⋊#95C2314yes—
138C59⋊#95C2314yes—
139C59⋊#95C2314yes—
140C59⋊#95C2314yes—
141C25×C59C2311yescharacteristic
142C23×C4×C59—24no—
143C23×C4×C59—24no—
144C23×C4×C59—42no—
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2314yes—
149C23×C4×C59C2311yescharacteristic
150C23×C4×C59C2311yescharacteristic
151C23×C4×C59C2311yescharacteristic
152C2×C4⋊C4×C59—24no—
153C2×C4⋊C4×C59—42no—
154C2×C4⋊C4×C59C2314yes—
155C2×C4⋊C4×C59C2314yes—
156C2×C22⋊C4×C59—24no—
157C2×C22⋊C4×C59Q818yescomplemented
158C2×C22⋊C4×C59C2314yes—
159C2×C22⋊C4×C59C2314yes—
160#95×C59C2314yes—
161#95×C59C2314yes—
162C24×C59—22no—
163C24×C59—22no—
164C24×C59—22no—
165C24×C59—22no—
166C24×C59C2×D414yes—
167C24×C59C2×Q814yes—
168C24×C59C2×Q814yes—
169C24×C59C2412yes—
170C24×C59C2411yescharacteristic
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—28no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—28no—
188C22×C4×C59—44no—
189C22×C4×C59—416no—
190C22×C4×C59C2×D414yes—
191C22×C4×C59C2×Q814yes—
192C22×C4×C59C2×Q814yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2412yes—
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—232no—
208C22×Dic59—28no—
209C22×Dic59—28no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—22no—
213C22×Dic59—22no—
214C22×Dic59—22no—
215C22×Dic59—28no—
216C22×Dic59—22no—
217C22×Dic59—22no—
218C22×Dic59—22no—
219C22×Dic59—22no—
220C22×Dic59—28no—
221C22×Dic59—44no—
222C22×Dic59—416no—
223C22×Dic59C2×D414yes—
224C22×Dic59C2×D414yes—
225C22×Dic59C2×D414yes—
226C22×Dic59C2×D414yes—
227C22×Dic59C2×Q814yes—
228C22×Dic59C2×Q814yes—
229C22×Dic59C2×Q8116yescomplemented
230C22×Dic59#4114yes—
231C22×Dic59C2412yes—
232C22×Dic59C2412yes—
233C22×Dic59C2412yes—
234C22×Dic59C2412yes—
235C22×Dic59C2412yes—
236C22×Dic59C2412yes—
237C22×Dic59C2412yes—
238C22×Dic59C2412yes—
239C2×Dic118—28no—
240C2×Dic118—28no—
241C2×Dic118—28no—
242C2×Dic118—28no—
243C2×Dic118—44no—
244C2×Dic118—44no—
245C2×Dic118—416no—
246C2×Dic118—416no—
247C4⋊C4×C59—28no—
248C4⋊C4×C59—44no—
249C22⋊C4×C59—28no—
250C22⋊C4×C59C2×Q8116yescomplemented
251C22⋊Dic59—28no—
252C22⋊Dic59C2×D4116yes—
253C4⋊Dic59—28no—
254C4⋊Dic59—28no—
255C4⋊Dic59—28no—
256C4⋊Dic59—44no—
257Dic59⋊C4—28no—
258Dic59⋊C4—28no—
259Dic59⋊C4—28no—
260Dic59⋊C4—28no—
261Dic59⋊C4—28no—
262Dic59⋊C4—28no—
263Dic59⋊C4—28no—
264Dic59⋊C4—28no—
265Dic59⋊C4—28no—
266Dic59⋊C4C2×D4116yes—
267C4×Dic59—28no—
268C4×Dic59—28no—
269C23×C59—28no—
270C23×C59—28no—
271C23×C59—28no—
272C23×C59—28no—
273C23×C59—28no—
274C23×C59—28no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59C4⋊Q8116yescomplemented
280C23×C59C22×D414yes—
281C23×C59C22×D412yes—
282C23×C59C22×D412yes—
283C23×C59C22×Q814yes—
284C23×C59C22×Q812yes—
285C23×C59C22×Q814yes—
286C23×C59C22×Q812yes—
287C23×C59C2×#4112yes—
288C23×C59H(5,𝔽2)12yes—
289C23×C592−1+412yes—
290C23×C59C2511yescharacteristic
291C2×C4×C59—28no—
292C2×C4×C59—28no—
293C2×C4×C59—28no—
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—22no—
308C2×C4×C59—22no—
309C2×C4×C59—416no—
310C2×C4×C59—44no—
311C2×C4×C59—44no—
312C2×C4×C59—44no—
313C2×C4×C59C22×D414yes—
314C2×C4×C59C22×Q814yes—
315C2×C4×C59C22×Q814yes—
316C2×Dic59—28no—
317C2×Dic59—28no—
318C2×Dic59—28no—
319C2×Dic59—28no—
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—232no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—416no—
339C2×Dic59—44no—
340C2×Dic59—44no—
341C2×Dic59—44no—
342C2×Dic59C22⋊Q8116yescomplemented
343C2×Dic59C22×D414yes—
344C2×Dic59C22×D414yes—
345C2×Dic59C22×D414yes—
346C2×Dic59C22×D414yes—
347C2×Dic59C22×Q814yes—
348C2×Dic59C22×Q814yes—
349C2×Dic59C2×#4114yes—
350Dic118—416no—
351Dic118—416no—
352C2×#2440—591nomaximal, Sylow
353C22×C59—24no—
354C22×C59—24no—
355C22×C59—24no—
356C22×C59—232no—
357C22×C59—24no—
358C22×C59—24no—
359C22×C59—24no—
360C22×C59C2×C22⋊Q814yes—
361C22×C59C2×C4⋊Q814yes—
362C22×C59C2×C4⋊Q818yescomplemented
363C22×C59#54414yes—
364C22×C59D4214yes—
365C22×C59#54714yes—
366C22×C59D4×Q814yes—
367C22×C59#55414yes—
368C22×C59C23×D411yescharacteristic
369C22×C59C23×D411yescharacteristic
370C22×C59C23×Q811yescharacteristic
371C22×C59C23×Q811yescharacteristic
372C22×C59C22×#4111yescharacteristic
373C22×C59C2×H(5,𝔽2)11yescharacteristic
374C22×C59C2×2−1+411yescharacteristic
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—24no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59—42no—
381Dic59—24no—
382Dic59—24no—
383Dic59—24no—
384Dic59—24no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59C2×C22⋊Q818yescomplemented
389C22×C4⋊Q8—591no—
390C22×C22⋊Q8—591no—
391C22×C22⋊Q8—591no—
392C23×C4⋊C4—591no—
393#2440—5916no—
394C2×#398—591no—
395C2×#398—591no—
396C2×#395—591no—
397C2×#395—591no—
398C2×#389—591no—
399C2×#389—591no—
400C2×#385—591no—
401C2×#385D5911yescharacteristic
402C2×#384—591no—
403C2×#380—591no—
404C2×C4×C22⋊C4—591no—
405C2×C59—28no—
406C2×C59#244018yescomplemented
407C2×C59C22×C22⋊Q811yescharacteristic
408C2×C59C22×C4⋊Q811yescharacteristic
409C2×C59C2×#54411yescharacteristic
410C2×C59C2×D4211yescharacteristic
411C2×C59C2×#54711yescharacteristic
412C2×C59C2×D4×Q811yescharacteristic
413C2×C59C2×#55411yescharacteristic
414C23×Q8—591no—
415C23×Q8—591no—
416C24×C4—591no—
417C24×C4—591no—
418C24×C4C2×D5911yescharacteristic
419C2×C4⋊Q8—598no—
420C2×C4⋊Q8—1188no—
421C2×C22⋊Q8—598no—
422C2×C22⋊Q8—598no—
423C2×C22⋊Q8—1188no—
424C2×C22⋊Q8—1188no—
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4—591no—
430C22×C4⋊C4—591no—
431C22×C4⋊C4—591no—
432C22×C4⋊C4—591no—
433C22×C4⋊C4—591no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4—598no—
436C22×C4⋊C4—591no—
437C22×C4⋊C4—591no—
438C22×C4⋊C4—591no—
439C22×C4⋊C4—591no—
440C22×C4⋊C4—1188no—
441C22×C4⋊C4C2×D5911yescharacteristic
442C22×C4⋊C4C2×D5911yescharacteristic
443C22×C22⋊C4—591no—
444C22×C22⋊C4—591no—
445C22×C22⋊C4C2×D5911yescharacteristic
446C22×C22⋊C4C2×D5911yescharacteristic
447C22×C42—591no—
448C22×C42—591no—
449#398—598no—
450#398—598no—
451#395—598no—
452#395—598no—
453#389—598no—
454#389—598no—
455#385—598no—
456#385C2×D5918yes—
457#384—598no—
458#380—598no—
459C4×C22⋊C4—598no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95—591no—
463C2×#95—591no—
464C2×#95—591no—
465C2×#95—591no—
466C2×#95C2×D5911yescharacteristic
467C2×#95C2×D5911yescharacteristic
468C59C2×#244011yescharacteristic, complemented, Sylow
469C25C22×D5911yescharacteristic
470C22×Q8—594no—
471C22×Q8—594no—
472C22×Q8—1184no—
473C22×Q8—1184no—
474C22×Q8—1184no—
475C22×Q8—1184no—
476C22×Q8—2362no—
477C22×Q8—2362no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—591no—
482C23×C4—598no—
483C23×C4—594no—
484C23×C4—591no—
485C23×C4—591no—
486C23×C4—591no—
487C23×C4—591no—
488C23×C4—591no—
489C23×C4—591no—
490C23×C4—591no—
491C23×C4—594no—
492C23×C4—1184no—
493C23×C4—1184no—
494C23×C4—1184no—
495C23×C4—1184no—
496C23×C4—2362no—
497C23×C4C22×D5911yescharacteristic
498C23×C4C22×D5911yescharacteristic
499C23×C4C22×D5911yescharacteristic
500C23×C4C22×D5914yes—
501C23×C4C22×D5911yescharacteristic
502C23×C4C22×D5911yescharacteristic
503C23×C4C22×D5911yescharacteristic
504C4⋊Q8—11832no—
505C22⋊Q8—11832no—
506C22⋊Q8—11832no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—598no—
510C2×C4⋊C4—594no—
511C2×C4⋊C4—594no—
512C2×C4⋊C4—594no—
513C2×C4⋊C4—594no—
514C2×C4⋊C4—594no—
515C2×C4⋊C4—594no—
516C2×C4⋊C4—594no—
517C2×C4⋊C4—594no—
518C2×C4⋊C4—594no—
519C2×C4⋊C4—594no—
520C2×C4⋊C4—594no—
521C2×C4⋊C4—594no—
522C2×C4⋊C4—594no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—11832no—
525C2×C4⋊C4—1184no—
526C2×C4⋊C4—1184no—
527C2×C4⋊C4—1184no—
528C2×C4⋊C4—1184no—
529C2×C4⋊C4—1184no—
530C2×C4⋊C4—1184no—
531C2×C4⋊C4—1184no—
532C2×C4⋊C4—1184no—
533C2×C4⋊C4—1184no—
534C2×C4⋊C4—1184no—
535C2×C4⋊C4—1184no—
536C2×C4⋊C4—1184no—
537C2×C4⋊C4—2362no—
538C2×C4⋊C4C22×D5914yes—
539C2×C4⋊C4C22×D5914yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—598no—
542C2×C22⋊C4—594no—
543C2×C22⋊C4—594no—
544C2×C22⋊C4—1184no—
545C2×C22⋊C4Dic11818yescomplemented
546C2×C22⋊C4C22×D5914yes—
547C2×C22⋊C4C22×D5914yes—
548C2×C42—594no—
549C2×C42—594no—
550C2×C42—1184no—
551C2×C42—1184no—
552#95—594no—
553#95—594no—
554#95—594no—
555#95—594no—
556#95—594no—
557#95—594no—
558#95C22×D5914yes—
559#95C22×D5914yes—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24C2×Dic11814yes—
565C24D4×D5914yes—
566C24Q8×D5914yes—
567C24C23×D5912yes—
568C24C23×D5911yescharacteristic
569C2×Q8—1188no—
570C2×Q8—1188no—
571C2×Q8—1188no—
572C2×Q8—1188no—
573C2×Q8—2364no—
574C2×Q8—2364no—
575C2×Q8—23616no—
576C2×Q8—23616no—
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—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—594no—
597C22×C4—594no—
598C22×C4—594no—
599C22×C4—592no—
600C22×C4—594no—
601C22×C4—594no—
602C22×C4—594no—
603C22×C4—594no—
604C22×C4—5916no—
605C22×C4—592no—
606C22×C4—592no—
607C22×C4—592no—
608C22×C4—592no—
609C22×C4—592no—
610C22×C4—592no—
611C22×C4—592no—
612C22×C4—1188no—
613C22×C4—11832no—
614C22×C4—1188no—
615C22×C4—1188no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1182no—
620C22×C4—1182no—
621C22×C4—1182no—
622C22×C4—1182no—
623C22×C4—1182no—
624C22×C4—1182no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4—1188no—
630C22×C4—1182no—
631C22×C4—1182no—
632C22×C4—1182no—
633C22×C4—1182no—
634C22×C4—2364no—
635C22×C4—23616no—
636C22×C4C2×Dic11814yes—
637C22×C4C2×Dic11814yes—
638C22×C4D4×D5914yes—
639C22×C4C23×D5912yes—
640C22×C4C23×D5912yes—
641C22×C4C23×D5912yes—
642C22×C4C23×D5912yes—
643C22×C4C23×D5912yes—
644C22×C4C23×D5912yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—5916no—
648C4⋊C4—1188no—
649C4⋊C4—1188no—
650C4⋊C4—1188no—
651C4⋊C4—1188no—
652C4⋊C4—1188no—
653C4⋊C4—1188no—
654C4⋊C4—1188no—
655C4⋊C4—1188no—
656C4⋊C4—1188no—
657C4⋊C4—1188no—
658C4⋊C4—1188no—
659C4⋊C4—1188no—
660C4⋊C4—2364no—
661C22⋊C4—28no—
662C22⋊C4—5916no—
663C22⋊C4—1188no—
664C22⋊C4C2×Dic118116yescomplemented
665C42—1188no—
666C42—1188no—
667C23—28no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—28no—
673C23—28no—
674C23—28no—
675C23—28no—
676C23—28no—
677C23#14273726116yescomplemented
678C23C2×D4×D5914yes—
679C23C2×D4×D5912yes—
680C23C2×D4×D5912yes—
681C23C2×Q8×D5914yes—
682C23C2×Q8×D5912yes—
683C23C22×Dic11814yes—
684C23C22×Dic11812yes—
685C23#41×D5912yes—
686C23#1427377212yes—
687C23#1427377412yes—
688C23C24×D5911yescharacteristic
689Q8—23616no—
690Q8—23616no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—5916no—
714C2×C4—594no—
715C2×C4—594no—
716C2×C4—594no—
717C2×C4—594no—
718C2×C4—594no—
719C2×C4—594no—
720C2×C4—594no—
721C2×C4—11832no—
722C2×C4—1188no—
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—1188no—
732C2×C4—1188no—
733C2×C4—1188no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—23616no—
744C2×C4—2364no—
745C2×C4—2364no—
746C2×C4—2364no—
747C2×C4C2×D4×D5914yes—
748C2×C4C22×Dic11814yes—
749C2×C4C22×Dic11814yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D5914yes—
758C22C2×#1427372614yes—
759C22C2×#1427372618yescomplemented
760C22#1683803114yes—
761C22#1683803414yes—
762C22#1683805014yes—
763C22D4×Dic11814yes—
764C22#1683811114yes—
765C22C22×D4×D5911yescharacteristic
766C22C22×D4×D5911yescharacteristic
767C22C22×Q8×D5911yescharacteristic
768C22C23×Dic11811yescharacteristic
769C22C2×#41×D5911yescharacteristic
770C22C2×#1427377211yescharacteristic
771C22C2×#1427377411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—598no—
779C4—1184no—
780C4—1184no—
781C4—1184no—
782C4—1184no—
783C4—2362no—
784C4—2362no—
785C4—2362no—
786C2—28no—
787C2#2142779718yesdirect product factor
788C2C2×C22⋊Q8×D5911yescharacteristic
789C2C22×#1427372611yescharacteristic
790C2C2×#1683803111yescharacteristic
791C2C2×#1683803411yescharacteristic
792C2C2×#1683805011yescharacteristic
793C2C2×D4×Dic11811yescharacteristic
794C2C2×#1683811111yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#385C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#385D59
hypocenterC59C2×#2440
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14273726C2semidirect
5. #21427797C2direct (N × H)
6. C2×#16837336C2semidirect
7. C2×#16837335C2semidirect
8. C2×#16837323C2semidirect
9. C2×#16837322C2semidirect
10. C2×#16837299C2semidirect
11. C2×#16837299C2semidirect
13. C2×#16837271C2semidirect
22. C2×#14273726C22semidirect
47. #16837336C22semidirect
48. #16837335C22semidirect
49. #16837323C22semidirect
50. #16837322C22semidirect
51. #16837299C22semidirect
52. #16837299C22semidirect
54. #16837271C22semidirect
84. C23×Dic59Q8semidirect
157. C2×C22⋊C4×C59Q8semidirect
229. C22×Dic59C2×Q8semidirect
250. C22⋊C4×C59C2×Q8semidirect
279. C23×C59C4⋊Q8semidirect
342. C2×Dic59C22⋊Q8semidirect
362. C22×C59C2×C4⋊Q8semidirect
388. Dic59C2×C22⋊Q8semidirect
406. C2×C59#2440semidirect
468. C59C2×#2440semidirect
545. C2×C22⋊C4Dic118semidirect
664. C22⋊C4C2×Dic118semidirect
677. C23#14273726semidirect
759. C22C2×#14273726semidirect
787. C2#21427797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737262
C22×#142737062
C22×#142737042
C23×Dic59⋊C42
#214277972
C2×#168373362
C2×#168373352
C2×#168373232
C2×#168373222
C2×#168372992
C2×#168372772
C2×#168372712
C2×#168372602
C2×C22⋊C4×Dic592
C2×C59×#3852
C2×#244059