Finite Group Databasebeta

← C2×#21429474 #28758916

Subgroups — C2×#21429474 #28758916

Order 15104.

3094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273705C211yesmaximal, characteristic
2C22×C4⋊C4×D59C211yesmaximal, characteristic
3#21429474C2116yesmaximal, direct product factor
4C2×#16837336C211yesmaximal, characteristic, complemented
5C2×#16837335C211yesmaximal, characteristic, complemented
6C2×#16837323C211yesmaximal, characteristic, complemented
7C2×#16837322C211yesmaximal, characteristic, complemented
8C2×#16837300C211yesmaximal, characteristic, complemented
9C2×#16837297C211yesmaximal, characteristic, complemented
10C2×#16837297C211yesmaximal, characteristic, complemented
11C2×#16837276C211yesmaximal, characteristic
12C2×#16837276C211yesmaximal, characteristic
13C2×#16837273C211yesmaximal, characteristic
14C2×#16837273C211yesmaximal, characteristic
15C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
16C2×C59×#389C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21C2×#14273705—28no—
22C2×#14273705C2218yes—
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
34C2×C4⋊C4×D59—28no—
35C2×C4⋊C4×D59C2218yes—
36C22×(C2×D59)⋊C4C2211yescharacteristic
37C22×(C2×D59)⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41#16837336C2218yescomplemented
42#16837335C2218yescomplemented
43#16837323C2218yescomplemented
44#16837322C2218yescomplemented
45#16837300C2218yescomplemented
46#16837297C2218yescomplemented
47#16837297C2218yescomplemented
48#16837276C2218yes—
49#16837276C2218yes—
50#16837273C2218yes—
51#16837273C2218yes—
52C4×(C2×D59)⋊C4C2218yes—
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
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×C4⋊C4×C59C2211yescharacteristic
65C22×C42×C59C2211yescharacteristic
66C59×#389C2218yescomplemented
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C22×Dic118—24no—
71C22×Dic118—42no—
72C22×Dic118—42no—
73C22×Dic118C2314yes—
74C23×Dic59C2311yescharacteristic
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×D59—24no—
85C22×C4×D59—42no—
86C22×C4×D59—42no—
87C22×C4×D59—42no—
88C22×C4×D59—42no—
89C22×C4×D59D418yes—
90C22×C4×D59C2314yes—
91C22×C4×D59C2314yes—
92C22×C4×D59C2314yes—
93#14273705—232no—
94C2×C4⋊Dic59—24no—
95C2×C4⋊Dic59—24no—
96C2×C4⋊Dic59—42no—
97C2×C4⋊Dic59C2314yes—
98C2×C4⋊Dic59C2314yes—
99C2×C4⋊Dic59C2314yes—
100C2×Dic59⋊C4—24no—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4—24no—
103C2×Dic59⋊C4—24no—
104C2×Dic59⋊C4—24no—
105C2×Dic59⋊C4—24no—
106C2×Dic59⋊C4—42no—
107C2×Dic59⋊C4—42no—
108C2×Dic59⋊C4C2314yes—
109C2×Dic59⋊C4C2314yes—
110C2×Dic59⋊C4C2314yes—
111C2×Dic59⋊C4C2314yes—
112C2×Dic59⋊C4C2314yes—
113C2×Dic59⋊C4C2314yes—
114C2×Dic59⋊C4C2314yes—
115C2×Dic59⋊C4C2314yes—
116C4⋊C4×D59—232no—
117C2×(C2×D59)⋊C4—24no—
118C2×(C2×D59)⋊C4—24no—
119C2×(C2×D59)⋊C4Q818yescomplemented
120C2×(C2×D59)⋊C4Q818yescomplemented
121C2×(C2×D59)⋊C4C2314yes—
122C2×(C2×D59)⋊C4C2314yes—
123C2×(C2×D59)⋊C4C2314yes—
124C2×(C2×D59)⋊C4C2314yes—
125C2×C4×Dic59—42no—
126C2×C4×Dic59C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
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×C59—24no—
144C2×C4⋊C4×C59—24no—
145C2×C4⋊C4×C59—42no—
146C2×C4⋊C4×C59C2314yes—
147C2×C4⋊C4×C59C2314yes—
148C2×C4⋊C4×C59C2314yes—
149C2×C4⋊C4×C59C2314yes—
150C2×C42×C59—42no—
151C2×C42×C59C2314yes—
152#95×C59C2314yes—
153#95×C59C2314yes—
154C24×C59C2411yescharacteristic
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59C2×D414yes—
160C23×D59C2×Q814yes—
161C23×D59C2×Q814yes—
162C23×D59C2412yes—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
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×C59C2×D414yes—
181C22×C4×C59C2×Q814yes—
182C22×C4×C59C2×Q814yes—
183C22×C4×C59#4114yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
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×Dic59C2×D414yes—
209C22×Dic59C2×Q814yes—
210C22×Dic59C2×Q814yes—
211C22×Dic59#4114yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C2×C4×D59—232no—
220C2×C4×D59—28no—
221C2×C4×D59—28no—
222C2×C4×D59—28no—
223C2×C4×D59—28no—
224C2×C4×D59—416no—
225C2×C4×D59—44no—
226C2×C4×D59—44no—
227C2×C4×D59—44no—
228C2×C4×D59—44no—
229C2×C4×D59—416no—
230C2×C4×D59C2×D4116yes—
231C2×Dic118—28no—
232C2×Dic118—44no—
233C2×Dic118—44no—
234C2×Dic118—416no—
235C4⋊C4×C59—28no—
236C4⋊C4×C59—28no—
237C4⋊C4×C59—28no—
238C4⋊C4×C59—44no—
239C42×C59—44no—
240(C2×D59)⋊C4—28no—
241(C2×D59)⋊C4—28no—
242(C2×D59)⋊C4C2×Q8116yescomplemented
243(C2×D59)⋊C4C2×Q8116yescomplemented
244C4⋊Dic59—28no—
245C4⋊Dic59—28no—
246C4⋊Dic59—44no—
247Dic59⋊C4—28no—
248Dic59⋊C4—28no—
249Dic59⋊C4—28no—
250Dic59⋊C4—28no—
251Dic59⋊C4—28no—
252Dic59⋊C4—28no—
253Dic59⋊C4—44no—
254Dic59⋊C4—44no—
255C4×Dic59—44no—
256C23×C59C22×D412yes—
257C23×C59C22×Q812yes—
258C23×C59C22×Q812yes—
259C23×C59C2×#4112yes—
260C23×C59C2×#4112yes—
261C23×C59H(5,𝔽2)12yes—
262C23×C59H(5,𝔽2)12yes—
263C23×C59C2511yescharacteristic
264C22×D59—28no—
265C22×D59—28no—
266C22×D59—28no—
267C22×D59—28no—
268C22×D59—28no—
269C22×D59—28no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59C4⋊Q8116yes—
275C22×D59C22×D414yes—
276C22×D59C22×Q814yes—
277C22×D59C22×Q814yes—
278C2×C4×C59—28no—
279C2×C4×C59—28no—
280C2×C4×C59—28no—
281C2×C4×C59—28no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
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—44no—
300C2×C4×C59—44no—
301C2×C4×C59—44no—
302C2×C4×C59C22×D414yes—
303C2×C4×C59C22×Q814yes—
304C2×C4×C59C22×Q814yes—
305C2×C4×C59C2×#4114yes—
306C2×Dic59—28no—
307C2×Dic59—28no—
308C2×Dic59—28no—
309C2×Dic59—28no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
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—44no—
328C2×Dic59—44no—
329C2×Dic59—44no—
330C2×Dic59C22×D414yes—
331C2×Dic59C22×Q814yes—
332C2×Dic59C22×Q814yes—
333C2×Dic59C2×#4114yes—
334C4×D59—232no—
335C4×D59—416no—
336C4×D59—416no—
337Dic118—416no—
338C2×#2583—591nomaximal, Sylow
339C22×C59#52514yes—
340C22×C59C2×C4⋊Q814yes—
341C22×C59#53414yes—
342C22×C59#55414yes—
343C22×C59#55414yes—
344C22×C59#55414yes—
345C22×C59#55414yes—
346C22×C59C23×D411yescharacteristic
347C22×C59C23×Q811yescharacteristic
348C22×C59C23×Q811yescharacteristic
349C22×C59C22×#4111yescharacteristic
350C22×C59C22×#4111yescharacteristic
351C22×C59C2×H(5,𝔽2)11yescharacteristic
352C22×C59C2×H(5,𝔽2)11yescharacteristic
353C2×D59—232no—
354C2×D59—24no—
355C2×D59—24no—
356C2×D59—24no—
357C2×D59—24no—
358C2×D59—24no—
359C2×D59—24no—
360C2×D59C2×C4⋊Q818yes—
361C4×C59—24no—
362C4×C59—24no—
363C4×C59—24no—
364C4×C59—24no—
365C4×C59—42no—
366C4×C59—42no—
367C4×C59—42no—
368Dic59—24no—
369Dic59—24no—
370Dic59—24no—
371Dic59—24no—
372Dic59—42no—
373Dic59—42no—
374Dic59—42no—
375C22×C22⋊Q8—591no—
376C23×C4⋊C4—591no—
377#2583—5916no—
378C2×#398—591no—
379C2×#398—591no—
380C2×#395—591no—
381C2×#395—591no—
382C2×#389—591no—
383C2×#389—591no—
384C2×#389—591no—
385C2×#389D5911yescharacteristic, complemented
386C2×#385—591no—
387C2×#385—591no—
388C2×#385—591no—
389C2×#385—591no—
390C2×C4×C22⋊C4—591no—
391C2×C59#258318yescomplemented
392C2×C59C2×#52511yescharacteristic
393C2×C59C22×C4⋊Q811yescharacteristic
394C2×C59C2×#53411yescharacteristic
395C2×C59C2×#55411yescharacteristic
396C2×C59C2×#55411yescharacteristic
397C2×C59C2×#55411yescharacteristic
398C2×C59C2×#55411yescharacteristic
399D59—28no—
400C23×Q8—591no—
401C24×C4—591no—
402C24×C4—591no—
403C24×C4—591no—
404C2×C22⋊Q8—598no—
405C2×C22⋊Q8—1188no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4—591no—
408C22×C4⋊C4—591no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—591no—
412C22×C4⋊C4—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4—598no—
418C22×C4⋊C4—1188no—
419C22×C4⋊C4C2×D5911yescharacteristic
420C22×C4⋊C4C2×D5911yescharacteristic
421C22×C4⋊C4C2×D5911yescharacteristic
422C22×C4⋊C4C2×D5911yescharacteristic
423C22×C22⋊C4—591no—
424C22×C22⋊C4—591no—
425C22×C22⋊C4—591no—
426C22×C22⋊C4—591no—
427C22×C42—591no—
428C22×C42C2×D5911yescharacteristic
429#398—598no—
430#398—598no—
431#395—598no—
432#395—598no—
433#389—598no—
434#389—598no—
435#389—598no—
436#389C2×D5918yescomplemented
437#385—598no—
438#385—598no—
439#385—598no—
440#385—598no—
441C4×C22⋊C4—598no—
442C2×#95—591no—
443C2×#95—591no—
444C2×#95—591no—
445C2×#95—591no—
446C2×#95—591no—
447C2×#95—591no—
448C2×#95—591no—
449C2×#95—591no—
450C2×#95C2×D5911yescharacteristic
451C2×#95C2×D5911yescharacteristic
452C59C2×#258311yescharacteristic, complemented, Sylow
453C25—591no—
454C22×Q8—594no—
455C22×Q8—1184no—
456C22×Q8—2362no—
457C22×Q8—2362no—
458C23×C4—591no—
459C23×C4—591no—
460C23×C4—591no—
461C23×C4—591no—
462C23×C4—598no—
463C23×C4—594no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—591no—
467C23×C4—594no—
468C23×C4—594no—
469C23×C4—1184no—
470C23×C4—1184no—
471C23×C4—1184no—
472C23×C4—1184no—
473C23×C4—2362no—
474C23×C4—2362no—
475C23×C4—2362no—
476C23×C4—2362no—
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5911yescharacteristic
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483C23×C4C22×D5911yescharacteristic
484C22⋊Q8—11832no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
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—11832no—
501C2×C4⋊C4—1184no—
502C2×C4⋊C4—1184no—
503C2×C4⋊C4—1184no—
504C2×C4⋊C4—1184no—
505C2×C4⋊C4—1184no—
506C2×C4⋊C4—1184no—
507C2×C4⋊C4—1184no—
508C2×C4⋊C4—1184no—
509C2×C4⋊C4—2362no—
510C2×C4⋊C4—2362no—
511C2×C4⋊C4—2362no—
512C2×C4⋊C4C22×D5914yes—
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5914yes—
515C2×C4⋊C4C22×D5914yes—
516C2×C22⋊C4—598no—
517C2×C22⋊C4—598no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—594no—
520C2×C22⋊C4—594no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—1184no—
523C2×C22⋊C4—1184no—
524C2×C42—42no—
525C2×C42—594no—
526C2×C42—2362no—
527C2×C42C22×D5914yes—
528#95—594no—
529#95—594no—
530#95—594no—
531#95—594no—
532#95—594no—
533#95—594no—
534#95—594no—
535#95—594no—
536#95C22×D5914yes—
537#95C22×D5914yes—
538C24—594no—
539C24—594no—
540C24—594no—
541C24—592no—
542C24—1182no—
543C24—1182no—
544C24—1182no—
545C24—1182no—
546C24C23×D5911yescharacteristic
547C2×Q8—1188no—
548C2×Q8—2364no—
549C2×Q8—2364no—
550C2×Q8—23616no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—594no—
569C22×C4—594no—
570C22×C4—594no—
571C22×C4—594no—
572C22×C4—592no—
573C22×C4—592no—
574C22×C4—592no—
575C22×C4—592no—
576C22×C4—5916no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—1188no—
581C22×C4—1188no—
582C22×C4—11832no—
583C22×C4—1188no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1188no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—23616no—
603C22×C4—2364no—
604C22×C4—2364no—
605C22×C4—2364no—
606C22×C4—2364no—
607C22×C4—23616no—
608C22×C4#1174568514yes—
609C22×C4D4×D5914yes—
610C22×C4Q8×D5914yes—
611C22×C4Q8×D5914yes—
612C22×C4C23×D5912yes—
613C22×C4C23×D5912yes—
614C22×C4C23×D5912yes—
615C22×C4C23×D5912yes—
616C22×C4C23×D5912yes—
617C22×C4C23×D5912yes—
618C22×C4C23×D5912yes—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—1188no—
624C4⋊C4—1188no—
625C4⋊C4—1188no—
626C4⋊C4—1188no—
627C4⋊C4—1188no—
628C4⋊C4—1188no—
629C4⋊C4—1188no—
630C4⋊C4—1188no—
631C4⋊C4—2364no—
632C4⋊C4—2364no—
633C4⋊C4—2364no—
634C22⋊C4—5916no—
635C22⋊C4—5916no—
636C22⋊C4—1188no—
637C22⋊C4—1188no—
638C42—44no—
639C42—2364no—
640C23—5916no—
641C23—594no—
642C23—594no—
643C23—594no—
644C23—1188no—
645C23—1188no—
646C23—1182no—
647C23—1182no—
648C23—1182no—
649C23—1182no—
650C23—1188no—
651C23—1188no—
652C23—1188no—
653C23—1188no—
654C23C2×D4×D5912yes—
655C23C2×Q8×D5912yes—
656C23C2×Q8×D5912yes—
657C23#41×D5912yes—
658C23C2×#1174568512yes—
659C23#1427377212yes—
660C23#1427377312yes—
661C23C24×D5911yescharacteristic
662Q8—23616no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—594no—
688C2×C4—594no—
689C2×C4—594no—
690C2×C4—594no—
691C2×C4—11832no—
692C2×C4—1188no—
693C2×C4—1188no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1188no—
703C2×C4—1188no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—23616no—
714C2×C4—23616no—
715C2×C4—2364no—
716C2×C4—2364no—
717C2×C4—2364no—
718C2×C4C2×D4×D5914yes—
719C2×C4C2×Q8×D5914yes—
720C2×C4C2×Q8×D5914yes—
721C2×C4C2×#1174568514yes—
722C22—598no—
723C22—1184no—
724C22—1184no—
725C22—1184no—
726C22—1184no—
727C22—1184no—
728C22—1184no—
729C22—11832no—
730C22#1683791114yes—
731C22C4⋊Q8×D5914yes—
732C22#1683796014yes—
733C22#1683810614yes—
734C22#1683810714yes—
735C22#1683810814yes—
736C22#1683811214yes—
737C22C22×D4×D5911yescharacteristic
738C22C22×Q8×D5911yescharacteristic
739C22C22×Q8×D5911yescharacteristic
740C22C2×#41×D5911yescharacteristic
741C22C22×#1174568511yescharacteristic
742C22C2×#1427377211yescharacteristic
743C22C2×#1427377311yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—1184no—
752C4—1184no—
753C4—1184no—
754C4—1184no—
755C4—2362no—
756C4—2362no—
757C4—2362no—
758C2—1188no—
759C2#2142947418yesdirect product factor
760C2C2×#1683791111yescharacteristic
761C2C2×C4⋊Q8×D5911yescharacteristic
762C2C2×#1683796011yescharacteristic
763C2C2×#1683810611yescharacteristic
764C2C2×#1683810711yescharacteristic
765C2C2×#1683810811yescharacteristic
766C2C2×#1683811211yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#389C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59C2×#2583
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #21429474C2direct (N × H)
4. C2×#16837336C2semidirect
5. C2×#16837335C2semidirect
6. C2×#16837323C2semidirect
7. C2×#16837322C2semidirect
8. C2×#16837300C2semidirect
9. C2×#16837297C2semidirect
10. C2×#16837297C2semidirect
16. C2×C59×#389C2semidirect
41. #16837336C22semidirect
42. #16837335C22semidirect
43. #16837323C22semidirect
44. #16837322C22semidirect
45. #16837300C22semidirect
46. #16837297C22semidirect
47. #16837297C22semidirect
66. C59×#389C22semidirect
119. C2×(C2×D59)⋊C4Q8semidirect
120. C2×(C2×D59)⋊C4Q8semidirect
242. (C2×D59)⋊C4C2×Q8semidirect
243. (C2×D59)⋊C4C2×Q8semidirect
385. C2×#389D59semidirect
391. C2×C59#2583semidirect
436. #389C2×D59semidirect
452. C59C2×#2583semidirect
759. C2#21429474direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737052
C22×C4⋊C4×D592
#214294742
C2×#168373362
C2×#168373352
C2×#168373232
C2×#168373222
C2×#168373002
C2×#168372972
C2×#168372762
C2×#168372732
C2×C4×(C2×D59)⋊C42
C2×C59×#3892
C2×#258359