Finite Group Databasebeta

← C2×#21427211 #28748372

Subgroups — C2×#21427211 #28748372

Order 15104.

2726 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273720C211yesmaximal, characteristic
2#21427211C2116yesmaximal, direct product factor
3C2×#16837299C211yesmaximal, characteristic, complemented
4C2×#16837296C211yesmaximal, characteristic
5C2×#16837295C211yesmaximal, characteristic
6C2×#16837290C211yesmaximal, characteristic
7C2×#16837285C211yesmaximal, characteristic, complemented
8C2×#16837283C211yesmaximal, characteristic, complemented
9C2×#16837283C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
12C2×#16837253C211yesmaximal, characteristic, complemented
13C2×C4×C22⋊Dic59C211yesmaximal, characteristic
14C2×C4×C22⋊Dic59C211yesmaximal, characteristic
15C2×#16837247C211yesmaximal, characteristic, complemented
16C2×C59×#385C211yesmaximal, characteristic
17C2×#14273720C4116yescomplemented
18C2×#14273720C2218yes—
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37#16837299C2218yescomplemented
38#16837296C2218yes—
39#16837295C2218yes—
40#16837290C2218yes—
41#16837285C2218yescomplemented
42#16837283C2218yescomplemented
43#16837283C2218yescomplemented
44C4⋊C4×Dic59C2218yescomplemented
45C4⋊C4×Dic59C2218yescomplemented
46#16837253C2218yescomplemented
47C4×C22⋊Dic59C2218yes—
48C4×C22⋊Dic59C2218yes—
49#16837247C2218yescomplemented
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C24×C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C59×#385C2218yes—
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76#14273720C2×C4164yescomplemented
77C2×C4⋊Dic59—24no—
78C2×C4⋊Dic59C2×C418yescomplemented
79C2×C4⋊Dic59C2314yes—
80C2×C4⋊Dic59C2314yes—
81C2×Dic59⋊C4—24no—
82C2×Dic59⋊C4—42no—
83C2×Dic59⋊C4C2×C418yescomplemented
84C2×Dic59⋊C4C2×C418yescomplemented
85C2×Dic59⋊C4C2314yes—
86C2×Dic59⋊C4C2314yes—
87C2×Dic59⋊C4C2314yes—
88C2×Dic59⋊C4C2314yes—
89C2×C22⋊Dic59—24no—
90C2×C22⋊Dic59—24no—
91C2×C22⋊Dic59C2×C418yes—
92C2×C22⋊Dic59C2×C418yes—
93C2×C22⋊Dic59C2314yes—
94C2×C22⋊Dic59C2314yes—
95C2×C22⋊Dic59C2314yes—
96C2×C22⋊Dic59C2314yes—
97C2×C4×Dic59—24no—
98C2×C4×Dic59—24no—
99C2×C4×Dic59—24no—
100C2×C4×Dic59—24no—
101C2×C4×Dic59—42no—
102C2×C4×Dic59—42no—
103C2×C4×Dic59—42no—
104C2×C4×Dic59C2×C418yescomplemented
105C2×C4×Dic59C2314yes—
106C2×C4×Dic59C2314yes—
107C2×C4×Dic59C2314yes—
108C2×C4×Dic59C2314yes—
109C2×C4×Dic59C2314yes—
110C2×C4×Dic59C2314yes—
111C2×C4×Dic59C2314yes—
112C2×C4×Dic59C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C25×C59C2311yescharacteristic
124C23×C4×C59—24no—
125C23×C4×C59—24no—
126C23×C4×C59—42no—
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2314yes—
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59—24no—
135C2×C4⋊C4×C59—24no—
136C2×C4⋊C4×C59C2314yes—
137C2×C4⋊C4×C59C2314yes—
138C2×C22⋊C4×C59—42no—
139C2×C22⋊C4×C59C2×C418yes—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2314yes—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59C22×C414yes—
151C24×C59C2412yes—
152C24×C59C2411yescharacteristic
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
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—28no—
168C22×C4×C59—28no—
169C22×C4×C59—44no—
170C22×C4×C59—416no—
171C22×C4×C59C22×C414yes—
172C22×C4×C59C22×C414yes—
173C22×C4×C59#4114yes—
174C22×C4×C59#4114yes—
175C22×C4×C59C2412yes—
176C22×C4×C59C2412yes—
177C22×C4×C59C2412yes—
178C22×C4×C59C2412yes—
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
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×Dic59C22×C414yes—
200C22×Dic59C22×C414yes—
201C22×Dic59C22×C414yes—
202C22×Dic59C22×C414yes—
203C22×Dic59#4114yes—
204C22×Dic59#4114yes—
205C22×Dic59C2412yes—
206C22×Dic59C2412yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C4⋊C4×C59—28no—
214C4⋊C4×C59—28no—
215C22⋊C4×C59—44no—
216C22⋊C4×C59C22×C4116yes—
217C22⋊Dic59—28no—
218C22⋊Dic59—28no—
219C22⋊Dic59C22×C4116yes—
220C22⋊Dic59C22×C4116yes—
221C4⋊Dic59—28no—
222C4⋊Dic59C22×C4116yescomplemented
223Dic59⋊C4—28no—
224Dic59⋊C4—44no—
225Dic59⋊C4C22×C4116yescomplemented
226Dic59⋊C4C22×C4116yescomplemented
227C4×Dic59—28no—
228C4×Dic59—28no—
229C4×Dic59—28no—
230C4×Dic59—28no—
231C4×Dic59—44no—
232C4×Dic59—44no—
233C4×Dic59—44no—
234C4×Dic59C22×C4116yescomplemented
235C23×C59—28no—
236C23×C59—28no—
237C23×C59—28no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—44no—
245C23×C59—44no—
246C23×C59—44no—
247C23×C59—44no—
248C23×C59C23×C414yes—
249C23×C59C23×C412yes—
250C23×C59C2×#4112yes—
251C23×C59C2×#4112yes—
252C23×C59C2×#4112yes—
253C23×C59C2×#4112yes—
254C23×C59H(5,𝔽2)12yes—
255C23×C592−1+412yes—
256C23×C59C2511yescharacteristic
257C2×C4×C59—28no—
258C2×C4×C59—28no—
259C2×C4×C59—28no—
260C2×C4×C59—28no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
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—416no—
276C2×C4×C59—44no—
277C2×C4×C59—44no—
278C2×C4×C59C23×C414yes—
279C2×C4×C59C23×C414yes—
280C2×C4×C59C2×#4114yes—
281C2×C4×C59C2×#4114yes—
282C2×Dic59—28no—
283C2×Dic59—28no—
284C2×Dic59—28no—
285C2×Dic59—28no—
286C2×Dic59—28no—
287C2×Dic59—28no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
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—44no—
307C2×Dic59—44no—
308C2×Dic59C23×C414yes—
309C2×Dic59C23×C414yes—
310C2×Dic59C23×C414yes—
311C2×Dic59C23×C414yes—
312C2×Dic59C2×#4114yes—
313C2×Dic59C2×#4114yes—
314C2×#2373—591nomaximal, Sylow
315C22×C59—24no—
316C22×C59—24no—
317C22×C59—24no—
318C22×C59—416no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59C4×#4114yes—
324C22×C59C4×#4114yes—
325C22×C59#52014yes—
326C22×C59#55114yes—
327C22×C59#55214yes—
328C22×C59#55314yes—
329C22×C59#55614yes—
330C22×C59C24×C411yescharacteristic
331C22×C59C22×#4111yescharacteristic
332C22×C59C22×#4111yescharacteristic
333C22×C59C22×#4111yescharacteristic
334C22×C59C22×#4111yescharacteristic
335C22×C59C2×H(5,𝔽2)11yescharacteristic
336C22×C59C2×2−1+411yescharacteristic
337C4×C59—24no—
338C4×C59—24no—
339C4×C59—24no—
340C4×C59—24no—
341C4×C59—42no—
342C4×C59—42no—
343Dic59—24no—
344Dic59—24no—
345Dic59—24no—
346Dic59—24no—
347Dic59—24no—
348Dic59—24no—
349Dic59—42no—
350Dic59—42no—
351C22×#126—591no—
352#2373—5916no—
353C2×#389—591no—
354C2×#388—591no—
355C2×#388—591no—
356C2×#388—591no—
357C2×#387—591no—
358C2×#387—591no—
359C2×#387—591no—
360C2×#385D5911yescharacteristic
361C2×C4×C4⋊C4—591no—
362C2×C4×C4⋊C4—591no—
363C2×C4×C4⋊C4—591no—
364C2×C4×C22⋊C4—591no—
365C2×C4×C22⋊C4—591no—
366C2×#376—591no—
367C2×C59—44no—
368C2×C59#237318yescomplemented
369C2×C59C2×C4×#4111yescharacteristic
370C2×C59C2×C4×#4111yescharacteristic
371C2×C59C2×#52011yescharacteristic
372C2×C59C2×#55111yescharacteristic
373C2×C59C2×#55211yescharacteristic
374C2×C59C2×#55311yescharacteristic
375C2×C59C2×#55611yescharacteristic
376C24×C4C2×D5911yescharacteristic
377C2×#126—5916no—
378C2×#126—598no—
379C22×C4⋊C4—591no—
380C22×C4⋊C4—591no—
381C22×C4⋊C4—591no—
382C22×C4⋊C4—591no—
383C22×C4⋊C4—591no—
384C22×C4⋊C4—591no—
385C22×C4⋊C4C2×D5911yescharacteristic
386C22×C4⋊C4C2×D5911yescharacteristic
387C22×C22⋊C4—591no—
388C22×C22⋊C4—591no—
389C22×C22⋊C4—591no—
390C22×C22⋊C4—591no—
391C22×C22⋊C4C2×D5911yescharacteristic
392C22×C22⋊C4C2×D5911yescharacteristic
393C22×C42—591no—
394C22×C42—591no—
395C22×C42—591no—
396C22×C42—591no—
397C22×C42—591no—
398C22×C42—591no—
399C22×C42—591no—
400C22×C42—591no—
401#389—598no—
402#388—598no—
403#388—598no—
404#388—598no—
405#387—598no—
406#387—598no—
407#387—598no—
408#385C2×D5918yes—
409C4×C4⋊C4—598no—
410C4×C4⋊C4—598no—
411C4×C4⋊C4—598no—
412C4×C22⋊C4—598no—
413C4×C22⋊C4—598no—
414#376—598no—
415C2×#95—591no—
416C2×#95—591no—
417C2×#95—591no—
418C2×#95—591no—
419C2×#95—591no—
420C2×#95—591no—
421C2×#95—591no—
422C2×#95—591no—
423C2×#95—591no—
424C2×#95—591no—
425C2×#95C2×D5911yescharacteristic
426C2×#95C2×D5911yescharacteristic
427C59C2×#237311yescharacteristic, complemented, Sylow
428C25C22×D5911yescharacteristic
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—591no—
433C23×C4—591no—
434C23×C4—591no—
435C23×C4—591no—
436C23×C4—591no—
437C23×C4—591no—
438C23×C4—591no—
439C23×C4—591no—
440C23×C4C22×D5911yescharacteristic
441C23×C4C22×D5911yescharacteristic
442C23×C4C22×D5914yes—
443C23×C4C22×D5911yescharacteristic
444C23×C4C22×D5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C23×C4C22×D5911yescharacteristic
447#126—5964no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—598no—
451C2×C4⋊C4—598no—
452C2×C4⋊C4—598no—
453C2×C4⋊C4—594no—
454C2×C4⋊C4—594no—
455C2×C4⋊C4—594no—
456C2×C4⋊C4—594no—
457C2×C4⋊C4—594no—
458C2×C4⋊C4—594no—
459C2×C4⋊C4—1184no—
460C2×C4⋊C4—1184no—
461C2×C4⋊C4—2362no—
462C2×C4⋊C4C22×D5914yes—
463C2×C4⋊C4C22×D5914yes—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—598no—
466C2×C22⋊C4—598no—
467C2×C22⋊C4—594no—
468C2×C22⋊C4—594no—
469C2×C22⋊C4—594no—
470C2×C22⋊C4—594no—
471C2×C22⋊C4—1184no—
472C2×C22⋊C4—1184no—
473C2×C22⋊C4C4×D5918yes—
474C2×C22⋊C4C22×D5914yes—
475C2×C22⋊C4C22×D5914yes—
476C2×C42—598no—
477C2×C42—594no—
478C2×C42—594no—
479C2×C42—594no—
480C2×C42—594no—
481C2×C42—594no—
482C2×C42—594no—
483C2×C42—594no—
484C2×C42—594no—
485C2×C42—1184no—
486C2×C42—1184no—
487C2×C42—1184no—
488C2×C42—1184no—
489C2×C42—2362no—
490C2×C42—2362no—
491C2×C42—2362no—
492#95—594no—
493#95—594no—
494#95—594no—
495#95—594no—
496#95—594no—
497#95—594no—
498#95—594no—
499#95—594no—
500#95—594no—
501#95—594no—
502#95C22×D5914yes—
503#95C22×D5914yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×C4×D5914yes—
511C24C23×D5912yes—
512C24C23×D5911yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—44no—
530C22×C4—416no—
531C22×C4—594no—
532C22×C4—594no—
533C22×C4—594no—
534C22×C4—594no—
535C22×C4—594no—
536C22×C4—594no—
537C22×C4—592no—
538C22×C4—592no—
539C22×C4—592no—
540C22×C4—592no—
541C22×C4—592no—
542C22×C4—592no—
543C22×C4—592no—
544C22×C4—592no—
545C22×C4—1182no—
546C22×C4—1182no—
547C22×C4—1182no—
548C22×C4—1182no—
549C22×C4—1182no—
550C22×C4—1182no—
551C22×C4—1182no—
552C22×C4—1182no—
553C22×C4—1182no—
554C22×C4—1182no—
555C22×C4—1182no—
556C22×C4—1182no—
557C22×C4—1182no—
558C22×C4—1182no—
559C22×C4—1182no—
560C22×C4—1182no—
561C22×C4—1182no—
562C22×C4—1182no—
563C22×C4C2×C4×D5914yes—
564C22×C4C2×C4×D5914yes—
565C22×C4#1174568714yes—
566C22×C4#1174568714yes—
567C22×C4C23×D5912yes—
568C22×C4C23×D5912yes—
569C22×C4C23×D5912yes—
570C22×C4C23×D5912yes—
571C22×C4C23×D5912yes—
572C22×C4C23×D5912yes—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—5916no—
576C4⋊C4—5916no—
577C4⋊C4—5916no—
578C4⋊C4—1188no—
579C4⋊C4—1188no—
580C4⋊C4—2364no—
581C22⋊C4—44no—
582C22⋊C4—5916no—
583C22⋊C4—5916no—
584C22⋊C4—1188no—
585C22⋊C4—1188no—
586C22⋊C4C2×C4×D59116yes—
587C42—5916no—
588C42—1188no—
589C42—1188no—
590C42—1188no—
591C42—1188no—
592C42—2364no—
593C42—2364no—
594C42—2364no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D5914yes—
609C23C22×C4×D5912yes—
610C23#41×D5912yes—
611C23#41×D5912yes—
612C23C2×#1174568712yes—
613C23C2×#1174568712yes—
614C23#1427377212yes—
615C23#1427377512yes—
616C23C24×D5911yescharacteristic
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—594no—
639C2×C4—594no—
640C2×C4—594no—
641C2×C4—594no—
642C2×C4—594no—
643C2×C4—594no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—1188no—
657C2×C4—1188no—
658C2×C4—1188no—
659C2×C4—1188no—
660C2×C4—1188no—
661C2×C4—1188no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—2364no—
669C2×C4—2364no—
670C2×C4C22×C4×D5914yes—
671C2×C4C22×C4×D5914yes—
672C2×C4C2×#1174568714yes—
673C2×C4C2×#1174568714yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22C4×#1174568714yes—
683C22C4×#1174568714yes—
684C22#1683788314yes—
685C22#1683808314yes—
686C22#1683808614yes—
687C22#1683809714yes—
688C22#1683812314yes—
689C22C23×C4×D5911yescharacteristic
690C22C2×#41×D5911yescharacteristic
691C22C2×#41×D5911yescharacteristic
692C22C22×#1174568711yescharacteristic
693C22C22×#1174568711yescharacteristic
694C22C2×#1427377211yescharacteristic
695C22C2×#1427377511yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—1184no—
703C4—1184no—
704C4—1184no—
705C4—1184no—
706C4—1184no—
707C4—1184no—
708C4—2362no—
709C4—2362no—
710C2—44no—
711C2#2142721118yesdirect product factor
712C2C2×C4×#1174568711yescharacteristic
713C2C2×C4×#1174568711yescharacteristic
714C2C2×#1683788311yescharacteristic
715C2C2×#1683808311yescharacteristic
716C2C2×#1683808611yescharacteristic
717C2C2×#1683809711yescharacteristic
718C2C2×#1683812311yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#385C2
socleC24×C59C24
prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC2×#385D59
hypocenterC59C2×#2373
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #21427211C2direct (N × H)
3. C2×#16837299C2semidirect
7. C2×#16837285C2semidirect
8. C2×#16837283C2semidirect
9. C2×#16837283C2semidirect
10. C2×C4⋊C4×Dic59C2semidirect
11. C2×C4⋊C4×Dic59C2semidirect
12. C2×#16837253C2semidirect
15. C2×#16837247C2semidirect
17. C2×#14273720C4semidirect
37. #16837299C22semidirect
41. #16837285C22semidirect
42. #16837283C22semidirect
43. #16837283C22semidirect
44. C4⋊C4×Dic59C22semidirect
45. C4⋊C4×Dic59C22semidirect
46. #16837253C22semidirect
49. #16837247C22semidirect
76. #14273720C2×C4semidirect
78. C2×C4⋊Dic59C2×C4semidirect
83. C2×Dic59⋊C4C2×C4semidirect
84. C2×Dic59⋊C4C2×C4semidirect
104. C2×C4×Dic59C2×C4semidirect
222. C4⋊Dic59C22×C4semidirect
225. Dic59⋊C4C22×C4semidirect
226. Dic59⋊C4C22×C4semidirect
234. C4×Dic59C22×C4semidirect
368. C2×C59#2373semidirect
427. C59C2×#2373semidirect
711. C2#21427211direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737202
#214272112
C2×#168372992
C2×#168372962
C2×#168372952
C2×#168372902
C2×#168372852
C2×#168372832
C2×C4⋊C4×Dic592
C2×#168372532
C2×C4×C22⋊Dic592
C2×#168372472
C2×C59×#3852
C2×#237359