Finite Group Databasebeta

← C2×#21427808 #28757178

Subgroups — C2×#21427808 #28757178

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×#14273684C211yesmaximal, characteristic
3#21427808C2116yesmaximal, direct product factor
4C2×#16837339C211yesmaximal, characteristic
5C2×#16837337C211yesmaximal, characteristic
6C2×#16837326C211yesmaximal, characteristic
7C2×#16837324C211yesmaximal, characteristic
8C2×#16837300C211yesmaximal, characteristic, complemented
9C2×#16837299C211yesmaximal, characteristic, complemented
10C2×#16837299C211yesmaximal, characteristic, complemented
11C2×#16837299C211yesmaximal, characteristic, complemented
12C2×#16837285C211yesmaximal, characteristic, complemented
13C2×#16837271C211yesmaximal, characteristic, complemented
14C2×#16837261C211yesmaximal, characteristic
15C2×#16837249C211yesmaximal, characteristic
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×C4×D59C2211yescharacteristic
18C2×#14273717—28no—
19C2×#14273717C2218yescomplemented
20C2×#14273684—28no—
21C2×#14273684C2218yes—
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×Dic59⋊C4C2211yescharacteristic
35C22×Dic59⋊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#16837339C2218yes—
46#16837337C2218yes—
47#16837326C2218yes—
48#16837324C2218yes—
49#16837300C2218yescomplemented
50#16837299C2218yescomplemented
51#16837299C2218yescomplemented
52#16837299C2218yescomplemented
53#16837285C2218yescomplemented
54#16837271C2218yescomplemented
55#16837261C2218yes—
56#16837249C2218yes—
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
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C22×C4×D59—24no—
78C22×C4×D59—24no—
79C22×C4×D59Q818yes—
80C22×C4×D59C2314yes—
81#14273717—232no—
82#14273684—232no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59—24no—
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—24no—
95C2×Dic59⋊C4—24no—
96C2×Dic59⋊C4—24no—
97C2×Dic59⋊C4—42no—
98C2×Dic59⋊C4—42no—
99C2×Dic59⋊C4—42no—
100C2×Dic59⋊C4D418yes—
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×Dic59⋊C4C2314yes—
110C2×Dic59⋊C4C2314yes—
111C2×(C2×D59)⋊C4—24no—
112C2×(C2×D59)⋊C4—24no—
113C2×(C2×D59)⋊C4—24no—
114C2×(C2×D59)⋊C4—24no—
115C2×(C2×D59)⋊C4—42no—
116C2×(C2×D59)⋊C4—42no—
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×C4×Dic59—24no—
124C2×C4×Dic59—24no—
125C2×C4×Dic59—24no—
126C2×C4×Dic59C2314yes—
127C2×C4×Dic59C2314yes—
128C2×C4×Dic59C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59—24no—
141C2×C4⋊C4×C59—24no—
142C2×C4⋊C4×C59C2314yes—
143C2×C4⋊C4×C59C2314yes—
144C2×C42×C59—24no—
145C2×C42×C59C2314yes—
146#95×C59C2314yes—
147#95×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150C24×C59C2411yescharacteristic
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59C2×Q814yes—
158C23×D59C2412yes—
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×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59C2×D414yes—
178C22×C4×C59C2×Q814yes—
179C22×C4×C59#4114yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
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×Dic59C2×D414yes—
204C22×Dic59C2×D414yes—
205C22×Dic59C2×Q814yes—
206C22×Dic59#4114yes—
207C22×Dic59#4114yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C2×C4×D59—232no—
216C2×C4×D59—28no—
217C2×C4×D59—28no—
218C2×C4×D59C2×Q8116yes—
219C4⋊C4×C59—28no—
220C4⋊C4×C59—28no—
221C42×C59—28no—
222(C2×D59)⋊C4—28no—
223(C2×D59)⋊C4—28no—
224(C2×D59)⋊C4—28no—
225(C2×D59)⋊C4—28no—
226(C2×D59)⋊C4—44no—
227(C2×D59)⋊C4—44no—
228C4⋊Dic59—28no—
229C4⋊Dic59—28no—
230C4⋊Dic59—28no—
231C4⋊Dic59—44no—
232Dic59⋊C4—28no—
233Dic59⋊C4—28no—
234Dic59⋊C4—28no—
235Dic59⋊C4—28no—
236Dic59⋊C4—28no—
237Dic59⋊C4—28no—
238Dic59⋊C4—44no—
239Dic59⋊C4—44no—
240Dic59⋊C4—44no—
241Dic59⋊C4C2×D4116yes—
242C4×Dic59—28no—
243C4×Dic59—28no—
244C4×Dic59—28no—
245C23×C59C22×D412yes—
246C23×C59C22×Q812yes—
247C23×C59C2×#4112yes—
248C23×C59C2×#4112yes—
249C23×C59C2×#4112yes—
250C23×C59H(5,𝔽2)12yes—
251C23×C592−1+412yes—
252C23×C59C2511yescharacteristic
253C22×D59—28no—
254C22×D59—28no—
255C22×D59—28no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—44no—
263C22×D59—44no—
264C22×D59—44no—
265C22×D59—44no—
266C22×D59C22×Q814yes—
267C2×C4×C59—28no—
268C2×C4×C59—28no—
269C2×C4×C59—28no—
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—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—44no—
289C2×C4×C59—44no—
290C2×C4×C59—44no—
291C2×C4×C59—44no—
292C2×C4×C59C22×D414yes—
293C2×C4×C59C22×Q814yes—
294C2×C4×C59C2×#4114yes—
295C2×Dic59—28no—
296C2×Dic59—28no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
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×Dic59C2×#4114yes—
322C2×Dic59C2×#4114yes—
323C4×D59—232no—
324C2×#2441—591nomaximal, Sylow
325C22×C59C2×C22⋊Q814yes—
326C22×C59#53314yes—
327C22×C59#54414yes—
328C22×C59#54714yes—
329C22×C59#55014yes—
330C22×C59#55214yes—
331C22×C59#55314yes—
332C22×C59C23×D411yescharacteristic
333C22×C59C23×Q811yescharacteristic
334C22×C59C22×#4111yescharacteristic
335C22×C59C22×#4111yescharacteristic
336C22×C59C22×#4111yescharacteristic
337C22×C59C2×H(5,𝔽2)11yescharacteristic
338C22×C59C2×2−1+411yescharacteristic
339C2×D59—24no—
340C2×D59—24no—
341C2×D59—24no—
342C2×D59—42no—
343C2×D59—416no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C4×C59—24no—
348C4×C59—24no—
349C4×C59—24no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59—42no—
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×#399—591no—
366C2×#396—591no—
367C2×#396—591no—
368C2×#389—591no—
369C2×#389—591no—
370C2×#389—591no—
371C2×#389—591no—
372C2×#387—591no—
373C2×#387D5911yescharacteristic, complemented
374C2×#384—591no—
375C2×#380—591no—
376C2×C4×C22⋊C4—591no—
377C2×C59#244118yescomplemented
378C2×C59C22×C22⋊Q811yescharacteristic
379C2×C59C2×#53311yescharacteristic
380C2×C59C2×#54411yescharacteristic
381C2×C59C2×#54711yescharacteristic
382C2×C59C2×#55011yescharacteristic
383C2×C59C2×#55211yescharacteristic
384C2×C59C2×#55311yescharacteristic
385D59—44no—
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⋊C4—591no—
405C22×C4⋊C4C2×D5911yescharacteristic
406C22×C4⋊C4C2×D5911yescharacteristic
407C22×C22⋊C4—591no—
408C22×C22⋊C4—591no—
409C22×C22⋊C4—591no—
410C22×C22⋊C4—591no—
411C22×C22⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C42—591no—
414C22×C42—591no—
415C22×C42—591no—
416C22×C42C2×D5911yescharacteristic
417#399—598no—
418#399—598no—
419#396—598no—
420#396—598no—
421#389—598no—
422#389—598no—
423#389—598no—
424#389—598no—
425#387—598no—
426#387C2×D5918yescomplemented
427#384—598no—
428#380—598no—
429C4×C22⋊C4—598no—
430C2×#95—591no—
431C2×#95—591no—
432C2×#95—591no—
433C2×#95—591no—
434C2×#95C2×D5911yescharacteristic
435C2×#95C2×D5911yescharacteristic
436C2×#95C2×D5911yescharacteristic
437C2×#95C2×D5911yescharacteristic
438C59C2×#244111yescharacteristic, complemented, Sylow
439C25—591no—
440C23×C4—591no—
441C23×C4—591no—
442C23×C4—591no—
443C23×C4—598no—
444C23×C4—594no—
445C23×C4—591no—
446C23×C4—591no—
447C23×C4—591no—
448C23×C4—591no—
449C23×C4—1184no—
450C23×C4—1184no—
451C23×C4C22×D5911yescharacteristic
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—598no—
463C2×C4⋊C4—594no—
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⋊C4—2362no—
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—594no—
493C2×C22⋊C4—594no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—1184no—
499C2×C22⋊C4—1184no—
500C2×C22⋊C4—1184no—
501C2×C22⋊C4—1184no—
502C2×C22⋊C4—2362no—
503C2×C22⋊C4—2362no—
504C2×C42—24no—
505C2×C42—594no—
506C2×C42—594no—
507C2×C42—594no—
508C2×C42—1184no—
509C2×C42—1184no—
510C2×C42—1184no—
511C2×C42C22×D5914yes—
512#95—594no—
513#95—594no—
514#95—594no—
515#95—594no—
516#95C22×D5914yes—
517#95C22×D5914yes—
518#95C22×D5914yes—
519#95C22×D5914yes—
520C24—594no—
521C24—592no—
522C24—1182no—
523C24—1182no—
524C24—1182no—
525C24—1182no—
526C24—1182no—
527C24—1182no—
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—22no—
546C22×C4—22no—
547C22×C4—594no—
548C22×C4—594no—
549C22×C4—594no—
550C22×C4—592no—
551C22×C4—594no—
552C22×C4—594no—
553C22×C4—592no—
554C22×C4—592no—
555C22×C4—5916no—
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#1174568514yes—
580C22×C4D4×D5914yes—
581C22×C4Q8×D5914yes—
582C22×C4C23×D5912yes—
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—5916no—
592C4⋊C4—1188no—
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—2364no—
602C4⋊C4—2364no—
603C4⋊C4—2364no—
604C4⋊C4—2364no—
605C22⋊C4—1188no—
606C22⋊C4—1188no—
607C22⋊C4—1188no—
608C22⋊C4—1188no—
609C22⋊C4—2364no—
610C22⋊C4—2364no—
611C42—28no—
612C42—1188no—
613C42—1188no—
614C42—1188no—
615C23—594no—
616C23—1188no—
617C23—1188no—
618C23—1182no—
619C23—1182no—
620C23—1182no—
621C23—1182no—
622C23—1182no—
623C23—1182no—
624C23—1188no—
625C23—2364no—
626C23—2364no—
627C23—2364no—
628C23—2364no—
629C23C2×D4×D5912yes—
630C23C2×Q8×D5912yes—
631C23#41×D5912yes—
632C23#41×D5912yes—
633C23C2×#1174568512yes—
634C23#1427377312yes—
635C23#1427377412yes—
636C23C24×D5911yescharacteristic
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—28no—
645C2×C4—28no—
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—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—5916no—
663C2×C4—594no—
664C2×C4—594no—
665C2×C4—594no—
666C2×C4—594no—
667C2×C4—594no—
668C2×C4—11832no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1188no—
674C2×C4—1188no—
675C2×C4—1182no—
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—2364no—
688C2×C4—2364no—
689C2×C4—2364no—
690C2×C4—2364no—
691C2×C4C2×D4×D5914yes—
692C2×C4C2×Q8×D5914yes—
693C2×C4C2×#1174568514yes—
694C22—1184no—
695C22—1184no—
696C22—1184no—
697C22—23616no—
698C22—2362no—
699C22—2362no—
700C22—2362no—
701C22—2362no—
702C22C22⋊Q8×D5914yes—
703C22#1683795614yes—
704C22#1683803214yes—
705C22#1683805014yes—
706C22#1683807314yes—
707C22#1683808514yes—
708C22#1683810314yes—
709C22C22×D4×D5911yescharacteristic
710C22C22×Q8×D5911yescharacteristic
711C22C2×#41×D5911yescharacteristic
712C22C2×#41×D5911yescharacteristic
713C22C22×#1174568511yescharacteristic
714C22C2×#1427377311yescharacteristic
715C22C2×#1427377411yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—598no—
724C4—1184no—
725C4—1184no—
726C4—2362no—
727C4—2362no—
728C4—2362no—
729C4—2362no—
730C2—2364no—
731C2#2142780818yesdirect product factor
732C2C2×C22⋊Q8×D5911yescharacteristic
733C2C2×#1683795611yescharacteristic
734C2C2×#1683803211yescharacteristic
735C2C2×#1683805011yescharacteristic
736C2C2×#1683807311yescharacteristic
737C2C2×#1683808511yescharacteristic
738C2C2×#1683810311yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#387D59
hypocenterC59C2×#2441
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14273717C2semidirect
3. #21427808C2direct (N × H)
8. C2×#16837300C2semidirect
9. C2×#16837299C2semidirect
10. C2×#16837299C2semidirect
11. C2×#16837299C2semidirect
12. C2×#16837285C2semidirect
13. C2×#16837271C2semidirect
16. C2×C59×#387C2semidirect
19. C2×#14273717C22semidirect
49. #16837300C22semidirect
50. #16837299C22semidirect
51. #16837299C22semidirect
52. #16837299C22semidirect
53. #16837285C22semidirect
54. #16837271C22semidirect
64. C59×#387C22semidirect
373. C2×#387D59semidirect
377. C2×C59#2441semidirect
426. #387C2×D59semidirect
438. C59C2×#2441semidirect
731. C2#21427808direct (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×#142736842
#214278082
C2×#168373392
C2×#168373372
C2×#168373262
C2×#168373242
C2×#168373002
C2×#168372992
C2×#168372852
C2×#168372712
C2×#168372612
C2×#168372492
C2×C59×#3872
C2×#244159