Finite Group Databasebeta

← C2×#21427802 #28757173

Subgroups — C2×#21427802 #28757173

Order 15104.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273717C211yesmaximal, characteristic, complemented
2C22×#14273683C211yesmaximal, characteristic
3#21427802C2116yesmaximal, direct product factor
4C2×#16837338C211yesmaximal, characteristic
5C2×#16837325C211yesmaximal, characteristic
6C2×#16837325C211yesmaximal, characteristic
7C2×#16837299C211yesmaximal, characteristic, complemented
8C2×#16837298C211yesmaximal, characteristic, complemented
9C2×#16837297C211yesmaximal, characteristic, complemented
10C2×#16837297C211yesmaximal, characteristic, complemented
11C2×#16837288C211yesmaximal, characteristic, complemented
12C2×#16837287C211yesmaximal, characteristic, complemented
13C2×#16837271C211yesmaximal, characteristic, complemented
14C2×#16837260C211yesmaximal, characteristic
15C2×C22⋊C4×Dic59C211yesmaximal, characteristic
16C2×C59×#399C211yesmaximal, characteristic
17C24×Dic59C2211yescharacteristic
18C2×#14273717—28no—
19C2×#14273717C2218yescomplemented
20C2×#14273683—28no—
21C2×#14273683C2218yes—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
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×Dic59⋊C4C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C22⋊Dic59C2211yescharacteristic
37C22×C22⋊Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41C22×C4×Dic59C2211yescharacteristic
42#16837338C2218yes—
43#16837325C2218yes—
44#16837325C2218yes—
45#16837299C2218yescomplemented
46#16837298C2218yescomplemented
47#16837297C2218yescomplemented
48#16837297C2218yescomplemented
49#16837288C2218yescomplemented
50#16837287C2218yescomplemented
51#16837271C2218yescomplemented
52#16837260C2218yes—
53C22⋊C4×Dic59C2218yes—
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×C22⋊C4×C59C2211yescharacteristic
65C22×C22⋊C4×C59C2211yescharacteristic
66C22×C22⋊C4×C59C2211yescharacteristic
67C59×#399C2218yes—
68C2×#95×C59C2211yescharacteristic
69C23×Dic59—24no—
70C23×Dic59—24no—
71C23×Dic59Q818yes—
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2314yes—
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81#14273717—232no—
82#14273683—232no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59—24no—
86C2×C4⋊Dic59C2314yes—
87C2×C4⋊Dic59C2314yes—
88C2×C4⋊Dic59C2314yes—
89C2×Dic59⋊C4—24no—
90C2×Dic59⋊C4—24no—
91C2×Dic59⋊C4—24no—
92C2×Dic59⋊C4—24no—
93C2×Dic59⋊C4—24no—
94C2×Dic59⋊C4—24no—
95C2×Dic59⋊C4—42no—
96C2×Dic59⋊C4—42no—
97C2×Dic59⋊C4—42no—
98C2×Dic59⋊C4D418yes—
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×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×C22⋊Dic59—24no—
110C2×C22⋊Dic59—24no—
111C2×C22⋊Dic59—42no—
112C2×C22⋊Dic59C2314yes—
113C2×C22⋊Dic59C2314yes—
114C2×C22⋊Dic59C2314yes—
115C2×C4×Dic59—24no—
116C2×C4×Dic59—24no—
117C2×C4×Dic59—24no—
118C2×C4×Dic59—24no—
119C2×C4×Dic59C2314yes—
120C2×C4×Dic59C2314yes—
121C2×C4×Dic59C2314yes—
122C2×C4×Dic59C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C25×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C2×C4⋊C4×C59—24no—
138C2×C4⋊C4×C59—24no—
139C2×C4⋊C4×C59—42no—
140C2×C4⋊C4×C59C2314yes—
141C2×C4⋊C4×C59C2314yes—
142C2×C4⋊C4×C59C2314yes—
143C2×C22⋊C4×C59—24no—
144C2×C22⋊C4×C59—24no—
145C2×C22⋊C4×C59—42no—
146C2×C22⋊C4×C59C2314yes—
147C2×C22⋊C4×C59C2314yes—
148C2×C22⋊C4×C59C2314yes—
149#95×C59C2314yes—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59C2×Q814yes—
157C24×C59C2412yes—
158C24×C59C2411yescharacteristic
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
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×C59C2×D414yes—
176C22×C4×C59#4114yes—
177C22×C4×C59C2412yes—
178C22×C4×C59C2412yes—
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—232no—
190C22×Dic59—28no—
191C22×Dic59—28no—
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×Dic59C2×D414yes—
205C22×Dic59C2×D414yes—
206C22×Dic59C2×Q814yes—
207C22×Dic59C2×Q8116yes—
208C22×Dic59C2×Q814yes—
209C22×Dic59#4114yes—
210C22×Dic59#4114yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C4⋊C4×C59—28no—
220C4⋊C4×C59—28no—
221C4⋊C4×C59—44no—
222C22⋊C4×C59—28no—
223C22⋊C4×C59—28no—
224C22⋊C4×C59—44no—
225C22⋊Dic59—28no—
226C22⋊Dic59—28no—
227C22⋊Dic59—44no—
228C4⋊Dic59—28no—
229C4⋊Dic59—28no—
230C4⋊Dic59—28no—
231Dic59⋊C4—28no—
232Dic59⋊C4—28no—
233Dic59⋊C4—28no—
234Dic59⋊C4—28no—
235Dic59⋊C4—28no—
236Dic59⋊C4—28no—
237Dic59⋊C4—44no—
238Dic59⋊C4—44no—
239Dic59⋊C4—44no—
240Dic59⋊C4C2×D4116yes—
241C4×Dic59—28no—
242C4×Dic59—28no—
243C4×Dic59—28no—
244C4×Dic59—28no—
245C23×C59—28no—
246C23×C59—28no—
247C23×C59—28no—
248C23×C59—22no—
249C23×C59—22no—
250C23×C59—22no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—44no—
255C23×C59—44no—
256C23×C59—44no—
257C23×C59—44no—
258C23×C59C22×D412yes—
259C23×C59C22×Q814yes—
260C23×C59C22×Q812yes—
261C23×C59C2×#4112yes—
262C23×C59C2×#4112yes—
263C23×C59C2×#4112yes—
264C23×C59H(5,𝔽2)12yes—
265C23×C592−1+412yes—
266C23×C59C2511yescharacteristic
267C2×C4×C59—28no—
268C2×C4×C59—28no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—44no—
286C2×C4×C59—44no—
287C2×C4×C59—44no—
288C2×C4×C59—44no—
289C2×C4×C59C22×D414yes—
290C2×C4×C59C2×#4114yes—
291C2×Dic59—28no—
292C2×Dic59—28no—
293C2×Dic59—28no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—232no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—44no—
314C2×Dic59—44no—
315C2×Dic59—44no—
316C2×Dic59—44no—
317C2×Dic59C22⋊Q8116yes—
318C2×Dic59C22×D414yes—
319C2×Dic59C22×D414yes—
320C2×Dic59C22×Q814yes—
321C2×Dic59C22×Q814yes—
322C2×Dic59C2×#4114yes—
323C2×Dic59C2×#4114yes—
324C2×#2441—591nomaximal, Sylow
325C22×C59—24no—
326C22×C59—24no—
327C22×C59—24no—
328C22×C59—42no—
329C22×C59—416no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59C2×C22⋊Q814yes—
334C22×C59#53314yes—
335C22×C59#54414yes—
336C22×C59#54714yes—
337C22×C59#55014yes—
338C22×C59#55214yes—
339C22×C59#55314yes—
340C22×C59C23×D411yescharacteristic
341C22×C59C23×Q811yescharacteristic
342C22×C59C22×#4111yescharacteristic
343C22×C59C22×#4111yescharacteristic
344C22×C59C22×#4111yescharacteristic
345C22×C59C2×H(5,𝔽2)11yescharacteristic
346C22×C59C2×2−1+411yescharacteristic
347C4×C59—24no—
348C4×C59—24no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59—42no—
353Dic59—24no—
354Dic59—24no—
355Dic59—24no—
356Dic59—42no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59C2×C22⋊Q818yes—
361C22×#125—591no—
362C22×#117—591no—
363#2441—5916no—
364C2×#399—591no—
365C2×#399D5911yescharacteristic
366C2×#396—591no—
367C2×#396—591no—
368C2×#389—591no—
369C2×#389—591no—
370C2×#389—591no—
371C2×#389—591no—
372C2×#387—591no—
373C2×#387—591no—
374C2×#384—591no—
375C2×#380—591no—
376C2×C4×C22⋊C4—591no—
377C2×C59—44no—
378C2×C59#244118yescomplemented
379C2×C59C22×C22⋊Q811yescharacteristic
380C2×C59C2×#53311yescharacteristic
381C2×C59C2×#54411yescharacteristic
382C2×C59C2×#54711yescharacteristic
383C2×C59C2×#55011yescharacteristic
384C2×C59C2×#55211yescharacteristic
385C2×C59C2×#55311yescharacteristic
386C24×C4—591no—
387C2×#125—598no—
388C2×#125—1188no—
389C2×#117—598no—
390C2×#117—1188no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4—591no—
393C22×C4⋊C4—591no—
394C22×C4⋊C4—591no—
395C22×C4⋊C4—591no—
396C22×C4⋊C4—591no—
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—591no—
400C22×C4⋊C4—591no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404C22×C4⋊C4C2×D5911yescharacteristic
405C22×C4⋊C4C2×D5911yescharacteristic
406C22×C4⋊C4C2×D5911yescharacteristic
407C22×C22⋊C4—591no—
408C22×C22⋊C4—591no—
409C22×C22⋊C4—591no—
410C22×C22⋊C4C2×D5911yescharacteristic
411C22×C22⋊C4C2×D5911yescharacteristic
412C22×C22⋊C4C2×D5911yescharacteristic
413C22×C42—591no—
414C22×C42—591no—
415C22×C42—591no—
416C22×C42—591no—
417#399—598no—
418#399C2×D5918yes—
419#396—598no—
420#396—598no—
421#389—598no—
422#389—598no—
423#389—598no—
424#389—598no—
425#387—598no—
426#387—598no—
427#384—598no—
428#380—598no—
429C4×C22⋊C4—598no—
430C2×#95—591no—
431C2×#95—591no—
432C2×#95—591no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—591no—
437C2×#95C2×D5911yescharacteristic
438C59C2×#244111yescharacteristic, complemented, Sylow
439C25C22×D5911yescharacteristic
440C23×C4—591no—
441C23×C4—598no—
442C23×C4—594no—
443C23×C4—591no—
444C23×C4—591no—
445C23×C4—591no—
446C23×C4—591no—
447C23×C4—591no—
448C23×C4—591no—
449C23×C4—591no—
450C23×C4—1184no—
451C23×C4—1184no—
452C23×C4C22×D5911yescharacteristic
453C23×C4C22×D5911yescharacteristic
454C23×C4C22×D5911yescharacteristic
455C23×C4C22×D5911yescharacteristic
456C23×C4C22×D5911yescharacteristic
457C23×C4C22×D5911yescharacteristic
458#125—11832no—
459#117—11832no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—598no—
464C2×C4⋊C4—594no—
465C2×C4⋊C4—594no—
466C2×C4⋊C4—594no—
467C2×C4⋊C4—594no—
468C2×C4⋊C4—594no—
469C2×C4⋊C4—594no—
470C2×C4⋊C4—594no—
471C2×C4⋊C4—594no—
472C2×C4⋊C4—594no—
473C2×C4⋊C4—594no—
474C2×C4⋊C4—594no—
475C2×C4⋊C4—594no—
476C2×C4⋊C4—594no—
477C2×C4⋊C4—1184no—
478C2×C4⋊C4—1184no—
479C2×C4⋊C4—1184no—
480C2×C4⋊C4—1184no—
481C2×C4⋊C4—1184no—
482C2×C4⋊C4—1184no—
483C2×C4⋊C4—1184no—
484C2×C4⋊C4—1184no—
485C2×C4⋊C4—1184no—
486C2×C4⋊C4—2362no—
487C2×C4⋊C4—2362no—
488C2×C4⋊C4—2362no—
489C2×C4⋊C4C22×D5914yes—
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—1184no—
499C2×C22⋊C4—1184no—
500C2×C22⋊C4—2362no—
501C2×C22⋊C4C22×D5914yes—
502C2×C22⋊C4C22×D5914yes—
503C2×C22⋊C4C22×D5914yes—
504C2×C42—594no—
505C2×C42—594no—
506C2×C42—594no—
507C2×C42—594no—
508C2×C42—1184no—
509C2×C42—1184no—
510C2×C42—1184no—
511C2×C42—1184no—
512#95—594no—
513#95—594no—
514#95—594no—
515#95—594no—
516#95—594no—
517#95—594no—
518#95—594no—
519#95C22×D5914yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D5914yes—
527C24C23×D5912yes—
528C24C23×D5911yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—594no—
546C22×C4—594no—
547C22×C4—594no—
548C22×C4—592no—
549C22×C4—594no—
550C22×C4—5916no—
551C22×C4—594no—
552C22×C4—594no—
553C22×C4—592no—
554C22×C4—592no—
555C22×C4—592no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—592no—
560C22×C4—1188no—
561C22×C4—11832no—
562C22×C4—1188no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—1182no—
572C22×C4—1182no—
573C22×C4—1182no—
574C22×C4—1182no—
575C22×C4—1182no—
576C22×C4—1182no—
577C22×C4—1182no—
578C22×C4—1182no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4D4×D5914yes—
582C22×C4#1174568714yes—
583C22×C4C23×D5912yes—
584C22×C4C23×D5912yes—
585C22×C4C23×D5912yes—
586C22×C4C23×D5912yes—
587C22×C4C23×D5912yes—
588C22×C4C23×D5912yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—5916no—
593C4⋊C4—1188no—
594C4⋊C4—1188no—
595C4⋊C4—1188no—
596C4⋊C4—1188no—
597C4⋊C4—1188no—
598C4⋊C4—1188no—
599C4⋊C4—1188no—
600C4⋊C4—1188no—
601C4⋊C4—1188no—
602C4⋊C4—2364no—
603C4⋊C4—2364no—
604C4⋊C4—2364no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—1188no—
609C22⋊C4—1188no—
610C22⋊C4—2364no—
611C42—1188no—
612C42—1188no—
613C42—1188no—
614C42—1188no—
615C23—28no—
616C23—28no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—28no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D5912yes—
629C23C2×Q8×D5914yes—
630C23C2×Q8×D5912yes—
631C23#41×D5912yes—
632C23#41×D5912yes—
633C23C2×#1174568712yes—
634C23#1427377212yes—
635C23#1427377412yes—
636C23C24×D5911yescharacteristic
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—5916no—
660C2×C4—594no—
661C2×C4—594no—
662C2×C4—594no—
663C2×C4—594no—
664C2×C4—594no—
665C2×C4—594no—
666C2×C4—11832no—
667C2×C4—1188no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1188no—
675C2×C4—1188no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—2364no—
689C2×C4—2364no—
690C2×C4—2364no—
691C2×C4—2364no—
692C2×C4C2×D4×D5914yes—
693C2×C4C2×#1174568714yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C22⋊Q8×D5914yes—
703C22#1683795414yes—
704C22#1683803114yes—
705C22#1683805014yes—
706C22#1683807214yes—
707C22#1683808914yes—
708C22#1683809714yes—
709C22C22×D4×D5911yescharacteristic
710C22C22×Q8×D5911yescharacteristic
711C22C2×#41×D5911yescharacteristic
712C22C2×#41×D5911yescharacteristic
713C22C22×#1174568711yescharacteristic
714C22C2×#1427377211yescharacteristic
715C22C2×#1427377411yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—598no—
723C4—1184no—
724C4—1184no—
725C4—1184no—
726C4—2362no—
727C4—2362no—
728C4—2362no—
729C4—2362no—
730C2—44no—
731C2#2142780218yesdirect product factor
732C2C2×C22⋊Q8×D5911yescharacteristic
733C2C2×#1683795411yescharacteristic
734C2C2×#1683803111yescharacteristic
735C2C2×#1683805011yescharacteristic
736C2C2×#1683807211yescharacteristic
737C2C2×#1683808911yescharacteristic
738C2C2×#1683809711yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#399C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#399D59
hypocenterC59C2×#2441
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#14273717C2semidirect
3. #21427802C2direct (N × H)
7. C2×#16837299C2semidirect
8. C2×#16837298C2semidirect
9. C2×#16837297C2semidirect
10. C2×#16837297C2semidirect
11. C2×#16837288C2semidirect
12. C2×#16837287C2semidirect
13. C2×#16837271C2semidirect
19. C2×#14273717C22semidirect
45. #16837299C22semidirect
46. #16837298C22semidirect
47. #16837297C22semidirect
48. #16837297C22semidirect
49. #16837288C22semidirect
50. #16837287C22semidirect
51. #16837271C22semidirect
378. C2×C59#2441semidirect
438. C59C2×#2441semidirect
731. C2#21427802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737172
C22×#142736832
#214278022
C2×#168373382
C2×#168373252
C2×#168372992
C2×#168372982
C2×#168372972
C2×#168372882
C2×#168372872
C2×#168372712
C2×#168372602
C2×C22⋊C4×Dic592
C2×C59×#3992
C2×#244159