Finite Group Databasebeta

← C2×#21427126 #28748233

Subgroups — C2×#21427126 #28748233

Order 15104.

3310 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×#14273704C211yesmaximal, characteristic
2C22×C4×Dic118C211yesmaximal, characteristic, complemented
3C22×#14273683C211yesmaximal, characteristic
4#21427126C2116yesmaximal, direct product factor
5C2×#16837306C211yesmaximal, characteristic, complemented
6C2×#16837297C211yesmaximal, characteristic, complemented
7C2×#16837296C211yesmaximal, characteristic
8C2×#16837296C211yesmaximal, characteristic
9C2×#16837295C211yesmaximal, characteristic
10C2×#16837289C211yesmaximal, characteristic, complemented
11C2×#16837287C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
13C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
14C2×#16837253C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic59C211yesmaximal, characteristic
16C2×C59×#388C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C2×#14273704C4116yescomplemented
20C2×#14273704C2218yes—
21C2×C4×Dic118—28no—
22C2×C4×Dic118C2218yescomplemented
23C2×#14273683—28no—
24C2×#14273683C2218yes—
25C22×C4⋊Dic59C2211yescharacteristic
26C22×C4⋊Dic59C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×C22⋊Dic59C2211yescharacteristic
34C22×C22⋊Dic59C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41C22×C4×Dic59C2211yescharacteristic
42C22×C4×Dic59C2211yescharacteristic
43#16837306C2218yescomplemented
44#16837297C2218yescomplemented
45#16837296C2218yes—
46#16837296C2218yes—
47#16837295C2218yes—
48#16837289C2218yescomplemented
49#16837287C2218yescomplemented
50C4⋊C4×Dic59C2218yescomplemented
51C4×Dic59⋊C4C2218yescomplemented
52#16837253C2218yescomplemented
53C22⋊C4×Dic59C2218yes—
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C2×C59⋊#95C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C22×C22⋊C4×C59C2211yescharacteristic
66C22×C42×C59C2211yescharacteristic
67C59×#388C2218yes—
68C2×#95×C59C2211yescharacteristic
69C2×#95×C59C2211yescharacteristic
70C22×Dic118—24no—
71C22×Dic118—24no—
72C22×Dic118C2×C418yes—
73C22×Dic118C2314yes—
74C23×Dic59—24no—
75C23×Dic59—24no—
76C23×Dic59C2×C418yes—
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2314yes—
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86#14273704C2×C4164yescomplemented
87C4×Dic118—232no—
88#14273683—232no—
89C2×C4⋊Dic59—24no—
90C2×C4⋊Dic59C2×C418yes—
91C2×C4⋊Dic59C2314yes—
92C2×C4⋊Dic59C2314yes—
93C2×Dic59⋊C4—24no—
94C2×Dic59⋊C4—24no—
95C2×Dic59⋊C4—24no—
96C2×Dic59⋊C4C2×C418yes—
97C2×Dic59⋊C4C2×C418yes—
98C2×Dic59⋊C4D418yes—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×C22⋊Dic59—24no—
106C2×C22⋊Dic59—24no—
107C2×C22⋊Dic59C2×C418yes—
108C2×C22⋊Dic59C2314yes—
109C2×C22⋊Dic59C2314yes—
110C2×C22⋊Dic59C2314yes—
111C2×C4×Dic59—24no—
112C2×C4×Dic59—24no—
113C2×C4×Dic59—24no—
114C2×C4×Dic59—24no—
115C2×C4×Dic59—24no—
116C2×C4×Dic59—24no—
117C2×C4×Dic59—24no—
118C2×C4×Dic59C2314yes—
119C2×C4×Dic59C2314yes—
120C2×C4×Dic59C2314yes—
121C2×C4×Dic59C2314yes—
122C2×C4×Dic59C2314yes—
123C2×C4×Dic59C2314yes—
124C2×C4×Dic59C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C25×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×C59C2314yes—
142C2×C22⋊C4×C59—24no—
143C2×C22⋊C4×C59—24no—
144C2×C22⋊C4×C59C2×C418yes—
145C2×C22⋊C4×C59C2314yes—
146C2×C22⋊C4×C59C2314yes—
147C2×C22⋊C4×C59C2314yes—
148C2×C42×C59—24no—
149C2×C42×C59C2314yes—
150#95×C59C2314yes—
151#95×C59C2314yes—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59—22no—
157C24×C59—22no—
158C24×C59C22×C414yes—
159C24×C59C2412yes—
160C24×C59C2411yescharacteristic
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×C59C22×C414yes—
176C22×C4×C59C22×C414yes—
177C22×C4×C59C2×D414yes—
178C22×C4×C59#4114yes—
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
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—232no—
196C22×Dic59—28no—
197C22×Dic59—28no—
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×Dic59C22×C4116yes—
208C22×Dic59C22×C414yes—
209C22×Dic59C2×D414yes—
210C22×Dic59C2×D414yes—
211C22×Dic59#4114yes—
212C22×Dic59#4114yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C2×Dic118—232no—
222C2×Dic118—28no—
223C2×Dic118—28no—
224C2×Dic118C22×C4116yes—
225C4⋊C4×C59—28no—
226C22⋊C4×C59—28no—
227C22⋊C4×C59—28no—
228C22⋊C4×C59C22×C4116yes—
229C42×C59—28no—
230C22⋊Dic59—28no—
231C22⋊Dic59—28no—
232C22⋊Dic59C22×C4116yes—
233C4⋊Dic59—28no—
234C4⋊Dic59C22×C4116yes—
235Dic59⋊C4—28no—
236Dic59⋊C4—28no—
237Dic59⋊C4—28no—
238Dic59⋊C4C22×C4116yes—
239Dic59⋊C4C22×C4116yes—
240Dic59⋊C4C2×D4116yes—
241C4×Dic59—28no—
242C4×Dic59—28no—
243C4×Dic59—28no—
244C4×Dic59—28no—
245C4×Dic59—28no—
246C4×Dic59—28no—
247C4×Dic59—28no—
248C23×C59—28no—
249C23×C59—28no—
250C23×C59—28no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59—22no—
257C23×C59—44no—
258C23×C59—44no—
259C23×C59—44no—
260C23×C59—44no—
261C23×C59C23×C414yes—
262C23×C59C23×C412yes—
263C23×C59C22×D412yes—
264C23×C59C2×#4112yes—
265C23×C59C2×#4112yes—
266C23×C59C2×#4112yes—
267C23×C592−1+412yes—
268C23×C592−1+412yes—
269C23×C59C2511yescharacteristic
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—44no—
289C2×C4×C59—44no—
290C2×C4×C59C23×C414yes—
291C2×C4×C59C23×C414yes—
292C2×C4×C59C22×D414yes—
293C2×C4×C59C2×#4114yes—
294C2×Dic59—28no—
295C2×Dic59—28no—
296C2×Dic59—28no—
297C2×Dic59—28no—
298C2×Dic59—28no—
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—232no—
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×Dic59C4×D4116yes—
319C2×Dic59C23×C414yes—
320C2×Dic59C23×C414yes—
321C2×Dic59C23×C414yes—
322C2×Dic59C23×C414yes—
323C2×Dic59C22×D414yes—
324C2×Dic59C22×D414yes—
325C2×Dic59C2×#4114yes—
326C2×Dic59C2×#4114yes—
327Dic118—232no—
328C2×#2362—591nomaximal, Sylow
329C22×C59—24no—
330C22×C59—24no—
331C22×C59—24no—
332C22×C59—416no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59C2×C4×D414yes—
338C22×C59C4×#4114yes—
339C22×C59#51914yes—
340C22×C59#54714yes—
341C22×C59#54814yes—
342C22×C59#55214yes—
343C22×C59#55614yes—
344C22×C59C24×C411yescharacteristic
345C22×C59C23×D411yescharacteristic
346C22×C59C22×#4111yescharacteristic
347C22×C59C22×#4111yescharacteristic
348C22×C59C22×#4111yescharacteristic
349C22×C59C2×2−1+411yescharacteristic
350C22×C59C2×2−1+411yescharacteristic
351C4×C59—24no—
352C4×C59—24no—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—42no—
356C4×C59—42no—
357Dic59—24no—
358Dic59—24no—
359Dic59—24no—
360Dic59—24no—
361Dic59—24no—
362Dic59—42no—
363Dic59—42no—
364Dic59C2×C4×D418yes—
365C22×C22⋊Q8—591no—
366C22×C4×Q8—591no—
367C22×#117—591no—
368#2362—5916no—
369C2×#391—591no—
370C2×#389—591no—
371C2×#388—591no—
372C2×#388—591no—
373C2×#388—591no—
374C2×#388D5911yescharacteristic
375C2×#387—591no—
376C2×#387—591no—
377C2×C4×C4⋊C4—591no—
378C2×C4×C4⋊C4—591no—
379C2×C4×C4⋊C4—591no—
380C2×C4×C22⋊C4—591no—
381C2×C59—44no—
382C2×C59#236218yescomplemented
383C2×C59C22×C4×D411yescharacteristic
384C2×C59C2×C4×#4111yescharacteristic
385C2×C59C2×#51911yescharacteristic
386C2×C59C2×#54711yescharacteristic
387C2×C59C2×#54811yescharacteristic
388C2×C59C2×#55211yescharacteristic
389C2×C59C2×#55611yescharacteristic
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⋊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—
417C22×C42—591no—
418C22×C42—591no—
419C22×C42—591no—
420C22×C42C2×D5911yescharacteristic
421#391—598no—
422#389—598no—
423#388—598no—
424#388—598no—
425#388—598no—
426#388C2×D5918yes—
427#387—598no—
428#387—598no—
429C4×C4⋊C4—598no—
430C4×C4⋊C4—598no—
431C4×C4⋊C4—598no—
432C4×C22⋊C4—598no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—591no—
437C2×#95—591no—
438C2×#95—591no—
439C2×#95—591no—
440C2×#95—591no—
441C2×#95C2×D5911yescharacteristic
442C2×#95C2×D5911yescharacteristic
443C59C2×#236211yescharacteristic, complemented, Sylow
444C25C22×D5911yescharacteristic
445C22×Q8—598no—
446C22×Q8—594no—
447C22×Q8—1184no—
448C22×Q8—1184no—
449C23×C4—591no—
450C23×C4—598no—
451C23×C4—594no—
452C23×C4—591no—
453C23×C4—591no—
454C23×C4—591no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—591no—
459C23×C4—1184no—
460C23×C4—1184no—
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—598no—
474C2×C4⋊C4—598no—
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—594no—
483C2×C4⋊C4—1184no—
484C2×C4⋊C4—1184no—
485C2×C4⋊C4—1184no—
486C2×C4⋊C4—1184no—
487C2×C4⋊C4C22×D5914yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—598no—
491C2×C22⋊C4—594no—
492C2×C22⋊C4—594no—
493C2×C22⋊C4—594no—
494C2×C22⋊C4—1184no—
495C2×C22⋊C4—1184no—
496C2×C22⋊C4C4×D5918yes—
497C2×C22⋊C4C22×D5914yes—
498C2×C22⋊C4C22×D5914yes—
499C2×C22⋊C4C22×D5914yes—
500C2×C42—24no—
501C2×C42—594no—
502C2×C42—594no—
503C2×C42—594no—
504C2×C42—594no—
505C2×C42—594no—
506C2×C42—594no—
507C2×C42—594no—
508C2×C42—1184no—
509C2×C42—1184no—
510C2×C42—1184no—
511C2×C42—1184no—
512C2×C42—1184no—
513C2×C42—1184no—
514C2×C42—1184no—
515C2×C42C22×D5914yes—
516#95—594no—
517#95—594no—
518#95—594no—
519#95—594no—
520#95—594no—
521#95—594no—
522#95—594no—
523#95—594no—
524#95C22×D5914yes—
525#95C22×D5914yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C4×D5914yes—
533C24C23×D5912yes—
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—594no—
554C22×C4—594no—
555C22×C4—594no—
556C22×C4—592no—
557C22×C4—594no—
558C22×C4—594no—
559C22×C4—594no—
560C22×C4—5916no—
561C22×C4—594no—
562C22×C4—594no—
563C22×C4—592no—
564C22×C4—592no—
565C22×C4—592no—
566C22×C4—592no—
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×C4—1182no—
589C22×C4C2×C4×D5914yes—
590C22×C4C2×C4×D5914yes—
591C22×C4D4×D5914yes—
592C22×C4#1174568714yes—
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—5916no—
603C4⋊C4—5916no—
604C4⋊C4—1188no—
605C4⋊C4—1188no—
606C4⋊C4—1188no—
607C4⋊C4—1188no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—5916no—
611C22⋊C4—1188no—
612C22⋊C4—1188no—
613C22⋊C4C2×C4×D59116yes—
614C42—28no—
615C42—1188no—
616C42—1188no—
617C42—1188no—
618C42—1188no—
619C42—1188no—
620C42—1188no—
621C42—1188no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D5914yes—
636C23C22×C4×D5912yes—
637C23C2×D4×D5912yes—
638C23#41×D5912yes—
639C23#41×D5912yes—
640C23C2×#1174568712yes—
641C23#1427377412yes—
642C23#1427377412yes—
643C23C24×D5911yescharacteristic
644Q8—11832no—
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—28no—
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—44no—
664C2×C4—44no—
665C2×C4—594no—
666C2×C4—594no—
667C2×C4—594no—
668C2×C4—5916no—
669C2×C4—594no—
670C2×C4—594no—
671C2×C4—594no—
672C2×C4—594no—
673C2×C4—594no—
674C2×C4—11832no—
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—1188no—
686C2×C4—1188no—
687C2×C4—1188no—
688C2×C4—1188no—
689C2×C4—1188no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—2364no—
697C2×C4—2364no—
698C2×C4C22×C4×D5914yes—
699C2×C4C22×C4×D5914yes—
700C2×C4C2×D4×D5914yes—
701C2×C4C2×#1174568714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—416no—
709C22—42no—
710C22C4×D4×D5914yes—
711C22C4×#1174568714yes—
712C22#1683787914yes—
713C22#1683805014yes—
714C22#1683805814yes—
715C22#1683808814yes—
716C22#1683812114yes—
717C22C23×C4×D5911yescharacteristic
718C22C22×D4×D5911yescharacteristic
719C22C2×#41×D5911yescharacteristic
720C22C2×#41×D5911yescharacteristic
721C22C22×#1174568711yescharacteristic
722C22C2×#1427377411yescharacteristic
723C22C2×#1427377411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—598no—
731C4—1184no—
732C4—1184no—
733C4—1184no—
734C4—1184no—
735C4—1184no—
736C4—2362no—
737C4—2362no—
738C2—44no—
739C2#2142712618yesdirect product factor
740C2C2×C4×D4×D5911yescharacteristic
741C2C2×C4×#1174568711yescharacteristic
742C2C2×#1683787911yescharacteristic
743C2C2×#1683805011yescharacteristic
744C2C2×#1683805811yescharacteristic
745C2C2×#1683808811yescharacteristic
746C2C2×#1683812111yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#388C2
socleC24×C59C24
prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC2×#388D59
hypocenterC59C2×#2362
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic118C2semidirect
4. #21427126C2direct (N × H)
5. C2×#16837306C2semidirect
6. C2×#16837297C2semidirect
10. C2×#16837289C2semidirect
11. C2×#16837287C2semidirect
12. C2×C4⋊C4×Dic59C2semidirect
13. C2×C4×Dic59⋊C4C2semidirect
14. C2×#16837253C2semidirect
19. C2×#14273704C4semidirect
22. C2×C4×Dic118C22semidirect
43. #16837306C22semidirect
44. #16837297C22semidirect
48. #16837289C22semidirect
49. #16837287C22semidirect
50. C4⋊C4×Dic59C22semidirect
51. C4×Dic59⋊C4C22semidirect
52. #16837253C22semidirect
86. #14273704C2×C4semidirect
382. C2×C59#2362semidirect
443. C59C2×#2362semidirect
739. C2#21427126direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737042
C22×C4×Dic1182
C22×#142736832
#214271262
C2×#168373062
C2×#168372972
C2×#168372962
C2×#168372952
C2×#168372892
C2×#168372872
C2×C4⋊C4×Dic592
C2×C4×Dic59⋊C42
C2×#168372532
C2×C22⋊C4×Dic592
C2×C59×#3882
C2×#236259