Finite Group Databasebeta

← C2×#21426777 #28747430

Subgroups — C2×#21426777 #28747430

Order 15104.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273705C211yesmaximal, characteristic
2C22×C4×Dic118C211yesmaximal, characteristic, complemented
3C22×#14273685C211yesmaximal, characteristic
4#21426777C2116yesmaximal, direct product factor
5C2×#16837306C211yesmaximal, characteristic, complemented
6C2×#16837301C211yesmaximal, characteristic, complemented
7C2×#16837299C211yesmaximal, characteristic, complemented
8C2×#16837299C211yesmaximal, characteristic, complemented
9C2×#16837294C211yesmaximal, characteristic
10C2×#16837294C211yesmaximal, characteristic
11C2×#16837293C211yesmaximal, characteristic
12C2×#16837291C211yesmaximal, characteristic
13C2×#16837283C211yesmaximal, characteristic, complemented
14C2×#16837261C211yesmaximal, characteristic
15C2×#16837253C211yesmaximal, characteristic, complemented
16C2×C59×#387C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C2×#14273705C4116yescomplemented
20C2×#14273705C2218yes—
21C2×C4×Dic118—28no—
22C2×C4×Dic118C2218yescomplemented
23C2×#14273685—28no—
24C2×#14273685C2218yes—
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×C4⋊Dic59C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊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×C4×Dic59C2211yescharacteristic
41C22×C4×Dic59C2211yescharacteristic
42C22×C4×Dic59C2211yescharacteristic
43C22×C4×Dic59C2211yescharacteristic
44C22×C4×Dic59C2211yescharacteristic
45#16837306C2218yescomplemented
46#16837301C2218yescomplemented
47#16837299C2218yescomplemented
48#16837299C2218yescomplemented
49#16837294C2218yes—
50#16837294C2218yes—
51#16837293C2218yes—
52#16837291C2218yes—
53#16837283C2218yescomplemented
54#16837261C2218yes—
55#16837253C2218yescomplemented
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C2×C59⋊#95C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×C42×C59C2211yescharacteristic
65C59×#387C2218yescomplemented
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C2×#95×C59C2211yescharacteristic
70C24×D59C2311yescharacteristic
71C22×Dic118—24no—
72C22×Dic118—24no—
73C22×Dic118C2×C418yes—
74C22×Dic118C2314yes—
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C22×C4×D59—24no—
83C22×C4×D59—24no—
84C22×C4×D59C2×C418yes—
85C22×C4×D59C2314yes—
86#14273705C2×C4164yescomplemented
87C4×Dic118—232no—
88#14273685—232no—
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59—24no—
91C2×C4⋊Dic59—42no—
92C2×C4⋊Dic59C2314yes—
93C2×C4⋊Dic59C2314yes—
94C2×C4⋊Dic59C2314yes—
95C2×Dic59⋊C4—24no—
96C2×Dic59⋊C4—24no—
97C2×Dic59⋊C4—24no—
98C2×Dic59⋊C4—42no—
99C2×Dic59⋊C4C2×C418yes—
100C2×Dic59⋊C4C2×C418yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×(C2×D59)⋊C4—24no—
108C2×(C2×D59)⋊C4—24no—
109C2×(C2×D59)⋊C4—42no—
110C2×(C2×D59)⋊C4—42no—
111C2×(C2×D59)⋊C4C2×C418yes—
112C2×(C2×D59)⋊C4C2×C418yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
119C2×C4×Dic59—24no—
120C2×C4×Dic59—24no—
121C2×C4×Dic59—42no—
122C2×C4×Dic59—42no—
123C2×C4×Dic59D418yes—
124C2×C4×Dic59C2314yes—
125C2×C4×Dic59C2314yes—
126C2×C4×Dic59C2314yes—
127C2×C4×Dic59C2314yes—
128C2×C4×Dic59C2314yes—
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×C59C2×C418yes—
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×D59C22×C414yes—
160C23×D59C2412yes—
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×C59—22no—
178C22×C4×C59C22×C414yes—
179C22×C4×C59C22×C414yes—
180C22×C4×C59C22×C414yes—
181C22×C4×C59C2×D414yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
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×Dic59—22no—
204C22×Dic59C22×C414yes—
205C22×Dic59C22×C414yes—
206C22×Dic59C22×C414yes—
207C22×Dic59C2×D414yes—
208C22×Dic59C2×D414yes—
209C22×Dic59#4114yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C2×C4×D59—232no—
218C2×C4×D59—28no—
219C2×C4×D59—28no—
220C2×C4×D59C22×C4116yes—
221C2×Dic118—232no—
222C2×Dic118—28no—
223C2×Dic118—28no—
224C2×Dic118C22×C4116yes—
225C4⋊C4×C59—28no—
226C4⋊C4×C59C22×C4116yes—
227C42×C59—28no—
228(C2×D59)⋊C4—28no—
229(C2×D59)⋊C4—28no—
230(C2×D59)⋊C4—44no—
231(C2×D59)⋊C4—44no—
232(C2×D59)⋊C4C22×C4116yes—
233(C2×D59)⋊C4C22×C4116yes—
234C4⋊Dic59—28no—
235C4⋊Dic59—28no—
236C4⋊Dic59—44no—
237Dic59⋊C4—28no—
238Dic59⋊C4—28no—
239Dic59⋊C4—28no—
240Dic59⋊C4—44no—
241Dic59⋊C4C22×C4116yes—
242Dic59⋊C4C22×C4116yes—
243C4×Dic59—28no—
244C4×Dic59—28no—
245C4×Dic59—44no—
246C4×Dic59—44no—
247C4×Dic59C2×D4116yes—
248C23×C59C23×C412yes—
249C23×C59C22×D412yes—
250C23×C59C2×#4112yes—
251C23×C59H(5,𝔽2)12yes—
252C23×C592−1+412yes—
253C23×C592−1+412yes—
254C23×C592−1+412yes—
255C23×C59C2511yescharacteristic
256C22×D59—28no—
257C22×D59—28no—
258C22×D59—28no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59—22no—
265C22×D59—44no—
266C22×D59—44no—
267C22×D59—44no—
268C22×D59—44no—
269C22×D59C23×C414yes—
270C2×C4×C59—28no—
271C2×C4×C59—28no—
272C2×C4×C59—28no—
273C2×C4×C59—28no—
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—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—44no—
292C2×C4×C59—44no—
293C2×C4×C59—44no—
294C2×C4×C59C23×C414yes—
295C2×C4×C59C23×C414yes—
296C2×C4×C59C23×C414yes—
297C2×C4×C59C22×D414yes—
298C2×Dic59—28no—
299C2×Dic59—28no—
300C2×Dic59—28no—
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—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—44no—
317C2×Dic59—44no—
318C2×Dic59—44no—
319C2×Dic59C4×D4116yes—
320C2×Dic59C23×C414yes—
321C2×Dic59C23×C414yes—
322C2×Dic59C23×C414yes—
323C2×Dic59C22×D414yes—
324C2×Dic59C22×D414yes—
325C2×Dic59C2×#4114yes—
326C4×D59—232no—
327Dic118—232no—
328C2×#2323—591nomaximal, Sylow
329C22×C59C2×C4×D414yes—
330C22×C59#51914yes—
331C22×C59#52014yes—
332C22×C59#53614yes—
333C22×C59#53714yes—
334C22×C59#54114yes—
335C22×C59#54214yes—
336C22×C59C24×C411yescharacteristic
337C22×C59C23×D411yescharacteristic
338C22×C59C22×#4111yescharacteristic
339C22×C59C2×H(5,𝔽2)11yescharacteristic
340C22×C59C2×2−1+411yescharacteristic
341C22×C59C2×2−1+411yescharacteristic
342C22×C59C2×2−1+411yescharacteristic
343C2×D59—24no—
344C2×D59—24no—
345C2×D59—24no—
346C2×D59—416no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C4×C59—24no—
352C4×C59—24no—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59—42no—
358Dic59—24no—
359Dic59—24no—
360Dic59—24no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59C2×C4×D418yes—
365C22×C22⋊Q8—591no—
366C22×C4×Q8—591no—
367C22×#117—591no—
368#2323—5916no—
369C2×#391—591no—
370C2×#389—591no—
371C2×#389—591no—
372C2×#389—591no—
373C2×#388—591no—
374C2×#388—591no—
375C2×#388—591no—
376C2×#388—591no—
377C2×#387—591no—
378C2×#387D5911yescharacteristic, complemented
379C2×#380—591no—
380C2×C4×C4⋊C4—591no—
381C2×C59#232318yescomplemented
382C2×C59C22×C4×D411yescharacteristic
383C2×C59C2×#51911yescharacteristic
384C2×C59C2×#52011yescharacteristic
385C2×C59C2×#53611yescharacteristic
386C2×C59C2×#53711yescharacteristic
387C2×C59C2×#54111yescharacteristic
388C2×C59C2×#54211yescharacteristic
389D59—44no—
390C23×Q8—591no—
391C24×C4—591no—
392C2×C22⋊Q8—5916no—
393C2×C22⋊Q8—598no—
394C2×C4×Q8—598no—
395C2×C4×Q8—1188no—
396C2×#117—598no—
397C2×#117—1188no—
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⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4C2×D5911yescharacteristic
408C22×C4⋊C4C2×D5911yescharacteristic
409C22×C22⋊C4—591no—
410C22×C22⋊C4—591no—
411C22×C22⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C22⋊C4—591no—
414C22×C22⋊C4—591no—
415C22×C42—591no—
416C22×C42—591no—
417C22×C42—591no—
418C22×C42—591no—
419C22×C42—591no—
420C22×C42C2×D5911yescharacteristic
421#391—598no—
422#389—598no—
423#389—598no—
424#389—598no—
425#388—598no—
426#388—598no—
427#388—598no—
428#388—598no—
429#387—598no—
430#387C2×D5918yescomplemented
431#380—598no—
432C4×C4⋊C4—598no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—591no—
437C2×#95—591no—
438C2×#95—591no—
439C2×#95C2×D5911yescharacteristic
440C2×#95C2×D5911yescharacteristic
441C2×#95C2×D5911yescharacteristic
442C2×#95C2×D5911yescharacteristic
443C59C2×#232311yescharacteristic, complemented, Sylow
444C25—591no—
445C22×Q8—598no—
446C22×Q8—594no—
447C22×Q8—1184no—
448C22×Q8—1184no—
449C23×C4—591no—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—591no—
453C23×C4—598no—
454C23×C4—594no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—1184no—
459C23×C4—1184no—
460C23×C4C22×D5911yescharacteristic
461C23×C4C22×D5911yescharacteristic
462C23×C4C22×D5911yescharacteristic
463C23×C4C22×D5911yescharacteristic
464C23×C4C22×D5911yescharacteristic
465C23×C4C22×D5911yescharacteristic
466C23×C4C22×D5911yescharacteristic
467C22⋊Q8—5964no—
468C4×Q8—11832no—
469#117—11832no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—598no—
472C2×C4⋊C4—598no—
473C2×C4⋊C4—594no—
474C2×C4⋊C4—594no—
475C2×C4⋊C4—594no—
476C2×C4⋊C4—594no—
477C2×C4⋊C4—594no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—594no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—1184no—
483C2×C4⋊C4—1184no—
484C2×C4⋊C4—1184no—
485C2×C4⋊C4—1184no—
486C2×C4⋊C4—1184no—
487C2×C4⋊C4—2362no—
488C2×C4⋊C4—2362no—
489C2×C4⋊C4C4×D5918yes—
490C2×C4⋊C4C22×D5914yes—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—598no—
493C2×C22⋊C4—598no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—594no—
500C2×C22⋊C4—1184no—
501C2×C22⋊C4—1184no—
502C2×C22⋊C4—2362no—
503C2×C22⋊C4—2362no—
504C2×C42—24no—
505C2×C42—598no—
506C2×C42—594no—
507C2×C42—594no—
508C2×C42—594no—
509C2×C42—594no—
510C2×C42—594no—
511C2×C42—1184no—
512C2×C42—1184no—
513C2×C42—2362no—
514C2×C42—2362no—
515C2×C42C22×D5914yes—
516#95—594no—
517#95—594no—
518#95—594no—
519#95—594no—
520#95—594no—
521#95—594no—
522#95C22×D5914yes—
523#95C22×D5914yes—
524#95C22×D5914yes—
525#95C22×D5914yes—
526C24—594no—
527C24—592no—
528C24—1182no—
529C24—1182no—
530C24—1182no—
531C24—1182no—
532C24—1182no—
533C24—1182no—
534C24C23×D5911yescharacteristic
535C2×Q8—5916no—
536C2×Q8—1188no—
537C2×Q8—1188no—
538C2×Q8—11832no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—594no—
557C22×C4—594no—
558C22×C4—594no—
559C22×C4—592no—
560C22×C4—594no—
561C22×C4—594no—
562C22×C4—594no—
563C22×C4—592no—
564C22×C4—592no—
565C22×C4—592no—
566C22×C4—5916no—
567C22×C4—592no—
568C22×C4—592no—
569C22×C4—592no—
570C22×C4—1188no—
571C22×C4—1188no—
572C22×C4—11832no—
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×C4—1182no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4C2×C4×D5914yes—
589C22×C4C2×C4×D5914yes—
590C22×C4C2×C4×D5914yes—
591C22×C4D4×D5914yes—
592C22×C4C23×D5912yes—
593C22×C4C23×D5912yes—
594C22×C4C23×D5912yes—
595C22×C4C23×D5912yes—
596C22×C4C23×D5912yes—
597C22×C4C23×D5912yes—
598C22×C4C23×D5912yes—
599C4⋊C4—28no—
600C4⋊C4—5916no—
601C4⋊C4—5916no—
602C4⋊C4—1188no—
603C4⋊C4—1188no—
604C4⋊C4—1188no—
605C4⋊C4—1188no—
606C4⋊C4—1188no—
607C4⋊C4—2364no—
608C4⋊C4—2364no—
609C4⋊C4C2×C4×D59116yes—
610C22⋊C4—5916no—
611C22⋊C4—5916no—
612C22⋊C4—1188no—
613C22⋊C4—1188no—
614C22⋊C4—2364no—
615C22⋊C4—2364no—
616C42—28no—
617C42—5916no—
618C42—1188no—
619C42—1188no—
620C42—2364no—
621C42—2364no—
622C23—594no—
623C23—1182no—
624C23—1182no—
625C23—1182no—
626C23—1182no—
627C23—1182no—
628C23—1182no—
629C23—1188no—
630C23—1188no—
631C23—1188no—
632C23—2364no—
633C23—2364no—
634C23—2364no—
635C23—2364no—
636C23C22×C4×D5912yes—
637C23C2×D4×D5912yes—
638C23#41×D5912yes—
639C23#1427377312yes—
640C23#1427377412yes—
641C23#1427377412yes—
642C23#1427377512yes—
643C23C24×D5911yescharacteristic
644Q8—11832no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—594no—
670C2×C4—594no—
671C2×C4—594no—
672C2×C4—5916no—
673C2×C4—594no—
674C2×C4—594no—
675C2×C4—594no—
676C2×C4—11832no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1188no—
684C2×C4—1188no—
685C2×C4—1188no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—2364no—
696C2×C4—2364no—
697C2×C4—2364no—
698C2×C4C22×C4×D5914yes—
699C2×C4C22×C4×D5914yes—
700C2×C4C22×C4×D5914yes—
701C2×C4C2×D4×D5914yes—
702C22—1184no—
703C22—1184no—
704C22—1184no—
705C22—2362no—
706C22—2362no—
707C22—23616no—
708C22—2362no—
709C22—2362no—
710C22C4×D4×D5914yes—
711C22#1683787814yes—
712C22#1683788214yes—
713C22#1683797414yes—
714C22#1683798214yes—
715C22#1683801114yes—
716C22#1683801814yes—
717C22C23×C4×D5911yescharacteristic
718C22C22×D4×D5911yescharacteristic
719C22C2×#41×D5911yescharacteristic
720C22C2×#1427377311yescharacteristic
721C22C2×#1427377411yescharacteristic
722C22C2×#1427377411yescharacteristic
723C22C2×#1427377511yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—598no—
732C4—1184no—
733C4—1184no—
734C4—1184no—
735C4—2362no—
736C4—2362no—
737C4—2362no—
738C2—2364no—
739C2#2142677718yesdirect product factor
740C2C2×C4×D4×D5911yescharacteristic
741C2C2×#1683787811yescharacteristic
742C2C2×#1683788211yescharacteristic
743C2C2×#1683797411yescharacteristic
744C2C2×#1683798211yescharacteristic
745C2C2×#1683801111yescharacteristic
746C2C2×#1683801811yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#387C2
socleC24×C59C24
prime radicalC24×D59C23
cosocleC23×C59C25
hypercenterC2×#387D59
hypocenterC59C2×#2323
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic118C2semidirect
4. #21426777C2direct (N × H)
5. C2×#16837306C2semidirect
6. C2×#16837301C2semidirect
7. C2×#16837299C2semidirect
8. C2×#16837299C2semidirect
13. C2×#16837283C2semidirect
15. C2×#16837253C2semidirect
16. C2×C59×#387C2semidirect
19. C2×#14273705C4semidirect
22. C2×C4×Dic118C22semidirect
45. #16837306C22semidirect
46. #16837301C22semidirect
47. #16837299C22semidirect
48. #16837299C22semidirect
53. #16837283C22semidirect
55. #16837253C22semidirect
65. C59×#387C22semidirect
86. #14273705C2×C4semidirect
378. C2×#387D59semidirect
381. C2×C59#2323semidirect
430. #387C2×D59semidirect
443. C59C2×#2323semidirect
739. C2#21426777direct (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×Dic1182
C22×#142736852
#214267772
C2×#168373062
C2×#168373012
C2×#168372992
C2×#168372942
C2×#168372932
C2×#168372912
C2×#168372832
C2×#168372612
C2×#168372532
C2×C59×#3872
C2×#232359