Finite Group Databasebeta

← C2×#21427690 #28756706

Subgroups — C2×#21427690 #28756706

Order 15104.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273726C211yesmaximal, characteristic, complemented
2C22×#14273705C211yesmaximal, characteristic
3C22×#14273705C211yesmaximal, characteristic
4C22×#14273692C211yesmaximal, characteristic, complemented
5#21427690C2116yesmaximal, direct product factor
6C2×#16837336C211yesmaximal, characteristic, complemented
7C2×#16837326C211yesmaximal, characteristic
8C2×#16837324C211yesmaximal, characteristic
9C2×#16837306C211yesmaximal, characteristic, complemented
10C2×#16837299C211yesmaximal, characteristic, complemented
11C2×#16837298C211yesmaximal, characteristic, complemented
12C2×#16837297C211yesmaximal, characteristic, complemented
13C2×#16837294C211yesmaximal, characteristic
14C2×#16837292C211yesmaximal, characteristic
15C2×#16837249C211yesmaximal, characteristic
16C2×C59×#398C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273726—28no—
21C2×#14273726C2218yescomplemented
22C2×#14273705—28no—
23C2×#14273705—28no—
24C2×#14273705C2218yes—
25C2×#14273705C2218yes—
26C2×#14273692—28no—
27C2×#14273692C2218yescomplemented
28C22×C4⋊Dic59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊C4C2211yescharacteristic
34C22×Dic59⋊C4C2211yescharacteristic
35C22×Dic59⋊C4C2211yescharacteristic
36C22×Dic59⋊C4C2211yescharacteristic
37C22×Dic59⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×(C2×D59)⋊C4C2211yescharacteristic
41C22×(C2×D59)⋊C4C2211yescharacteristic
42C22×(C2×D59)⋊C4C2211yescharacteristic
43C22×(C2×D59)⋊C4C2211yescharacteristic
44C22×C4×Dic59C2211yescharacteristic
45C22×C4×Dic59C2211yescharacteristic
46C22×C4×Dic59C2211yescharacteristic
47C22×C4×Dic59C2211yescharacteristic
48#16837336C2218yescomplemented
49#16837326C2218yes—
50#16837324C2218yes—
51#16837306C2218yescomplemented
52#16837299C2218yescomplemented
53#16837298C2218yescomplemented
54#16837297C2218yescomplemented
55#16837294C2218yes—
56#16837292C2218yes—
57#16837249C2218yes—
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C2×C59⋊#95C2211yescharacteristic
62C2×C59⋊#95C2211yescharacteristic
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×C4⋊C4×C59C2211yescharacteristic
65C22×C4⋊C4×C59C2211yescharacteristic
66C22×C4⋊C4×C59C2211yescharacteristic
67C59×#398C2218yescomplemented
68C2×#95×C59C2211yescharacteristic
69C2×#95×C59C2211yescharacteristic
70C2×#95×C59C2211yescharacteristic
71C24×D59C2311yescharacteristic
72C22×Dic118—24no—
73C22×Dic118—24no—
74C22×Dic118—24no—
75C22×Dic118—24no—
76C22×Dic118—24no—
77C22×Dic118D418yes—
78C22×Dic118C2314yes—
79C22×Dic118C2314yes—
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2311yescharacteristic
87C22×C4×D59—24no—
88C22×C4×D59—24no—
89C22×C4×D59—24no—
90C22×C4×D59C2314yes—
91#14273726—232no—
92#14273705—232no—
93#14273705—232no—
94#14273692—232no—
95C2×C4⋊Dic59—24no—
96C2×C4⋊Dic59—24no—
97C2×C4⋊Dic59C2314yes—
98C2×C4⋊Dic59C2314yes—
99C2×Dic59⋊C4—24no—
100C2×Dic59⋊C4—24no—
101C2×Dic59⋊C4—24no—
102C2×Dic59⋊C4—24no—
103C2×Dic59⋊C4—24no—
104C2×Dic59⋊C4—24no—
105C2×Dic59⋊C4—24no—
106C2×Dic59⋊C4D418yes—
107C2×Dic59⋊C4C2314yes—
108C2×Dic59⋊C4C2314yes—
109C2×Dic59⋊C4C2314yes—
110C2×Dic59⋊C4C2314yes—
111C2×Dic59⋊C4C2314yes—
112C2×Dic59⋊C4C2314yes—
113C2×Dic59⋊C4C2314yes—
114C2×Dic59⋊C4C2314yes—
115C2×(C2×D59)⋊C4—24no—
116C2×(C2×D59)⋊C4—24no—
117C2×(C2×D59)⋊C4—24no—
118C2×(C2×D59)⋊C4—24no—
119C2×(C2×D59)⋊C4—24no—
120C2×(C2×D59)⋊C4Q818yescomplemented
121C2×(C2×D59)⋊C4C2314yes—
122C2×(C2×D59)⋊C4C2314yes—
123C2×(C2×D59)⋊C4C2314yes—
124C2×(C2×D59)⋊C4C2314yes—
125C2×(C2×D59)⋊C4C2314yes—
126C2×(C2×D59)⋊C4C2314yes—
127C2×C4×Dic59—24no—
128C2×C4×Dic59—24no—
129C2×C4×Dic59—24no—
130C2×C4×Dic59—24no—
131C2×C4×Dic59C2314yes—
132C2×C4×Dic59C2314yes—
133C2×C4×Dic59C2314yes—
134C2×C4×Dic59C2314yes—
135C59⋊#95C2314yes—
136C59⋊#95C2314yes—
137C59⋊#95C2314yes—
138C59⋊#95C2314yes—
139C59⋊#95C2314yes—
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C2×C4⋊C4×C59—24no—
148C2×C4⋊C4×C59—24no—
149C2×C4⋊C4×C59—24no—
150C2×C4⋊C4×C59—24no—
151C2×C4⋊C4×C59C2314yes—
152C2×C4⋊C4×C59C2314yes—
153C2×C4⋊C4×C59C2314yes—
154C2×C4⋊C4×C59C2314yes—
155#95×C59C2314yes—
156#95×C59C2314yes—
157#95×C59C2314yes—
158C24×C59C2411yescharacteristic
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59C2×Q814yes—
166C23×D59C2412yes—
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×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59C2×D414yes—
186C22×C4×C59C2×D414yes—
187C22×C4×C59C2×Q814yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
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×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59C2×D414yes—
210C22×Dic59C2×D414yes—
211C22×Dic59C2×D414yes—
212C22×Dic59C2×D414yes—
213C22×Dic59C2×Q814yes—
214C22×Dic59#4114yes—
215C22×Dic59#4114yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C2×C4×D59—28no—
224C2×C4×D59—28no—
225C2×C4×D59—28no—
226C2×C4×D59—416no—
227C2×Dic118—232no—
228C2×Dic118—28no—
229C2×Dic118—28no—
230C2×Dic118—28no—
231C2×Dic118—28no—
232C2×Dic118—28no—
233C2×Dic118—416no—
234C2×Dic118C2×D4116yes—
235C4⋊C4×C59—28no—
236C4⋊C4×C59—28no—
237C4⋊C4×C59—28no—
238C4⋊C4×C59—28no—
239(C2×D59)⋊C4—28no—
240(C2×D59)⋊C4—28no—
241(C2×D59)⋊C4—28no—
242(C2×D59)⋊C4—28no—
243(C2×D59)⋊C4—28no—
244(C2×D59)⋊C4C2×Q8116yescomplemented
245C4⋊Dic59—28no—
246C4⋊Dic59—28no—
247Dic59⋊C4—28no—
248Dic59⋊C4—28no—
249Dic59⋊C4—28no—
250Dic59⋊C4—28no—
251Dic59⋊C4—28no—
252Dic59⋊C4—28no—
253Dic59⋊C4—28no—
254Dic59⋊C4C2×D4116yes—
255C4×Dic59—28no—
256C4×Dic59—28no—
257C4×Dic59—28no—
258C4×Dic59—28no—
259C23×C59C22×D412yes—
260C23×C59C22×D412yes—
261C23×C59C22×Q812yes—
262C23×C59C2×#4112yes—
263C23×C59C2×#4112yes—
264C23×C592−1+412yes—
265C23×C592−1+412yes—
266C23×C59C2511yescharacteristic
267C22×D59—28no—
268C22×D59—28no—
269C22×D59—28no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—44no—
277C22×D59—44no—
278C22×D59—44no—
279C22×D59—44no—
280C22×D59C22×Q814yes—
281C2×C4×C59—28no—
282C2×C4×C59—28no—
283C2×C4×C59—28no—
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—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—44no—
303C2×C4×C59—44no—
304C2×C4×C59—44no—
305C2×C4×C59—44no—
306C2×C4×C59C22×D414yes—
307C2×C4×C59C22×D414yes—
308C2×C4×C59C22×Q814yes—
309C2×Dic59—28no—
310C2×Dic59—28no—
311C2×Dic59—28no—
312C2×Dic59—28no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—44no—
328C2×Dic59—44no—
329C2×Dic59#121116yes—
330C2×Dic59C22×D414yes—
331C2×Dic59C22×D414yes—
332C2×Dic59C22×D414yes—
333C2×Dic59C22×D414yes—
334C2×Dic59C22×Q814yes—
335C2×Dic59C2×#4114yes—
336C2×Dic59C2×#4114yes—
337C4×D59—416no—
338Dic118—232no—
339Dic118—416no—
340C2×#2429—591nomaximal, Sylow
341C22×C59C2×#12114yes—
342C22×C59#53314yes—
343C22×C59#54114yes—
344C22×C59#54714yes—
345C22×C59#54814yes—
346C22×C59D4×Q814yes—
347C22×C59D4×Q814yes—
348C22×C59C23×D411yescharacteristic
349C22×C59C23×D411yescharacteristic
350C22×C59C23×Q811yescharacteristic
351C22×C59C22×#4111yescharacteristic
352C22×C59C22×#4111yescharacteristic
353C22×C59C2×2−1+411yescharacteristic
354C22×C59C2×2−1+411yescharacteristic
355C2×D59—24no—
356C2×D59—24no—
357C2×D59—24no—
358C2×D59—42no—
359C2×D59—416no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—42no—
363C4×C59—24no—
364C4×C59—24no—
365C4×C59—24no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370Dic59—24no—
371Dic59—24no—
372Dic59—24no—
373Dic59—24no—
374Dic59—42no—
375Dic59—42no—
376Dic59C2×#12118yes—
377C22×C4⋊Q8—591no—
378C22×C22⋊Q8—591no—
379C22×C22⋊Q8—591no—
380C22×C4×Q8—591no—
381#2429—5916no—
382C2×#398—591no—
383C2×#398D5911yescharacteristic, complemented
384C2×#396—591no—
385C2×#396—591no—
386C2×#391—591no—
387C2×#389—591no—
388C2×#389—591no—
389C2×#389—591no—
390C2×#388—591no—
391C2×#388—591no—
392C2×C4×C22⋊C4—591no—
393C2×C59#242918yescomplemented
394C2×C59C22×#12111yescharacteristic
395C2×C59C2×#53311yescharacteristic
396C2×C59C2×#54111yescharacteristic
397C2×C59C2×#54711yescharacteristic
398C2×C59C2×#54811yescharacteristic
399C2×C59C2×D4×Q811yescharacteristic
400C2×C59C2×D4×Q811yescharacteristic
401D59—44no—
402C23×Q8—591no—
403C23×Q8—591no—
404C24×C4—591no—
405C2×C4⋊Q8—598no—
406C2×C4⋊Q8—1188no—
407C2×C22⋊Q8—598no—
408C2×C22⋊Q8—598no—
409C2×C22⋊Q8—1188no—
410C2×C22⋊Q8—1188no—
411C2×C4×Q8—598no—
412C2×C4×Q8—1188no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4—591no—
418C22×C4⋊C4—591no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—591no—
422C22×C4⋊C4—591no—
423C22×C4⋊C4C2×D5911yescharacteristic
424C22×C4⋊C4C2×D5911yescharacteristic
425C22×C4⋊C4C2×D5911yescharacteristic
426C22×C4⋊C4C2×D5911yescharacteristic
427C22×C22⋊C4—591no—
428C22×C22⋊C4—591no—
429C22×C22⋊C4—591no—
430C22×C22⋊C4—591no—
431C22×C22⋊C4—591no—
432C22×C22⋊C4—591no—
433C22×C42—591no—
434C22×C42—591no—
435C22×C42—591no—
436C22×C42—591no—
437#398—598no—
438#398C2×D5918yescomplemented
439#396—598no—
440#396—598no—
441#391—598no—
442#389—598no—
443#389—598no—
444#389—598no—
445#388—598no—
446#388—598no—
447C4×C22⋊C4—598no—
448C2×#95—591no—
449C2×#95—591no—
450C2×#95—591no—
451C2×#95—591no—
452C2×#95—591no—
453C2×#95C2×D5911yescharacteristic
454C2×#95C2×D5911yescharacteristic
455C2×#95C2×D5911yescharacteristic
456C59C2×#242911yescharacteristic, complemented, Sylow
457C25—591no—
458C22×Q8—598no—
459C22×Q8—594no—
460C22×Q8—594no—
461C22×Q8—1184no—
462C22×Q8—1184no—
463C22×Q8—1184no—
464C22×Q8—1184no—
465C22×Q8—1184no—
466C23×C4—591no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4—591no—
471C23×C4—591no—
472C23×C4—591no—
473C23×C4—594no—
474C23×C4—1184no—
475C23×C4—1184no—
476C23×C4—1184no—
477C23×C4C22×D5911yescharacteristic
478C23×C4C22×D5911yescharacteristic
479C23×C4C22×D5911yescharacteristic
480C23×C4C22×D5911yescharacteristic
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483C23×C4C22×D5911yescharacteristic
484C4⋊Q8—11832no—
485C22⋊Q8—11832no—
486C22⋊Q8—11832no—
487C4×Q8—11832no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—598no—
493C2×C4⋊C4—594no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—594no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—594no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—594no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—1184no—
504C2×C4⋊C4—1184no—
505C2×C4⋊C4—1184no—
506C2×C4⋊C4—1184no—
507C2×C4⋊C4—1184no—
508C2×C4⋊C4—1184no—
509C2×C4⋊C4—1184no—
510C2×C4⋊C4—1184no—
511C2×C4⋊C4—1184no—
512C2×C4⋊C4C22×D5914yes—
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5914yes—
515C2×C4⋊C4C22×D5914yes—
516C2×C22⋊C4—598no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—594no—
520C2×C22⋊C4—594no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—594no—
523C2×C22⋊C4—1184no—
524C2×C22⋊C4—1184no—
525C2×C22⋊C4—1184no—
526C2×C22⋊C4—1184no—
527C2×C22⋊C4—1184no—
528C2×C42—594no—
529C2×C42—594no—
530C2×C42—594no—
531C2×C42—594no—
532C2×C42—1184no—
533C2×C42—1184no—
534C2×C42—1184no—
535C2×C42—1184no—
536#95—594no—
537#95—594no—
538#95—594no—
539#95—594no—
540#95—594no—
541#95C22×D5914yes—
542#95C22×D5914yes—
543#95C22×D5914yes—
544C24—594no—
545C24—592no—
546C24—1182no—
547C24—1182no—
548C24—1182no—
549C24—1182no—
550C24—1182no—
551C24—1182no—
552C24C23×D5911yescharacteristic
553C2×Q8—5916no—
554C2×Q8—1188no—
555C2×Q8—11832no—
556C2×Q8—1188no—
557C2×Q8—1188no—
558C2×Q8—1188no—
559C2×Q8—1188no—
560C2×Q8—23616no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—594no—
580C22×C4—594no—
581C22×C4—594no—
582C22×C4—592no—
583C22×C4—594no—
584C22×C4—594no—
585C22×C4—594no—
586C22×C4—594no—
587C22×C4—592no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—1188no—
594C22×C4—1188no—
595C22×C4—1188no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—23616no—
611C22×C4D4×D5914yes—
612C22×C4D4×D5914yes—
613C22×C4Q8×D5914yes—
614C22×C4C23×D5912yes—
615C22×C4C23×D5912yes—
616C22×C4C23×D5912yes—
617C22×C4C23×D5912yes—
618C22×C4C23×D5912yes—
619C22×C4C23×D5912yes—
620C22×C4C23×D5912yes—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—5916no—
626C4⋊C4—1188no—
627C4⋊C4—1188no—
628C4⋊C4—1188no—
629C4⋊C4—1188no—
630C4⋊C4—1188no—
631C4⋊C4—1188no—
632C4⋊C4—1188no—
633C4⋊C4—1188no—
634C4⋊C4—1188no—
635C22⋊C4—5916no—
636C22⋊C4—1188no—
637C22⋊C4—1188no—
638C22⋊C4—1188no—
639C22⋊C4—1188no—
640C22⋊C4—1188no—
641C42—1188no—
642C42—1188no—
643C42—1188no—
644C42—1188no—
645C23—594no—
646C23—1188no—
647C23—1182no—
648C23—1182no—
649C23—1182no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23—1188no—
654C23—1188no—
655C23—2364no—
656C23—2364no—
657C23—2364no—
658C23—2364no—
659C23C2×D4×D5912yes—
660C23C2×D4×D5912yes—
661C23C2×Q8×D5912yes—
662C23#41×D5912yes—
663C23#41×D5912yes—
664C23#1427377412yes—
665C23#1427377512yes—
666C23C24×D5911yescharacteristic
667Q8—11832no—
668Q8—23616no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—5916no—
695C2×C4—594no—
696C2×C4—594no—
697C2×C4—594no—
698C2×C4—594no—
699C2×C4—594no—
700C2×C4—594no—
701C2×C4—594no—
702C2×C4—1188no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1188no—
712C2×C4—1188no—
713C2×C4—1188no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—23616no—
721C2×C4—2364no—
722C2×C4—2364no—
723C2×C4C2×D4×D5914yes—
724C2×C4C2×D4×D5914yes—
725C2×C4C2×Q8×D5914yes—
726C22—1184no—
727C22—1184no—
728C22—1184no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—23616no—
734C22#121×D5914yes—
735C22#1683795814yes—
736C22#1683801114yes—
737C22#1683805014yes—
738C22#1683806214yes—
739C22#1683806514yes—
740C22#1683806714yes—
741C22C22×D4×D5911yescharacteristic
742C22C22×D4×D5911yescharacteristic
743C22C22×Q8×D5911yescharacteristic
744C22C2×#41×D5911yescharacteristic
745C22C2×#41×D5911yescharacteristic
746C22C2×#1427377411yescharacteristic
747C22C2×#1427377511yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—598no—
756C4—1184no—
757C4—1184no—
758C4—1184no—
759C4—1184no—
760C4—2362no—
761C4—2362no—
762C2—2364no—
763C2#2142769018yesdirect product factor
764C2C2×#121×D5911yescharacteristic
765C2C2×#1683795811yescharacteristic
766C2C2×#1683801111yescharacteristic
767C2C2×#1683805011yescharacteristic
768C2C2×#1683806211yescharacteristic
769C2C2×#1683806511yescharacteristic
770C2C2×#1683806711yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#398C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#398D59
hypocenterC59C2×#2429
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14273726C2semidirect
4. C22×#14273692C2semidirect
5. #21427690C2direct (N × H)
6. C2×#16837336C2semidirect
9. C2×#16837306C2semidirect
10. C2×#16837299C2semidirect
11. C2×#16837298C2semidirect
12. C2×#16837297C2semidirect
16. C2×C59×#398C2semidirect
21. C2×#14273726C22semidirect
27. C2×#14273692C22semidirect
48. #16837336C22semidirect
51. #16837306C22semidirect
52. #16837299C22semidirect
53. #16837298C22semidirect
54. #16837297C22semidirect
67. C59×#398C22semidirect
120. C2×(C2×D59)⋊C4Q8semidirect
244. (C2×D59)⋊C4C2×Q8semidirect
383. C2×#398D59semidirect
393. C2×C59#2429semidirect
438. #398C2×D59semidirect
456. C59C2×#2429semidirect
763. C2#21427690direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737262
C22×#142737052
C22×#142736922
#214276902
C2×#168373362
C2×#168373262
C2×#168373242
C2×#168373062
C2×#168372992
C2×#168372982
C2×#168372972
C2×#168372942
C2×#168372922
C2×#168372492
C2×C59×#3982
C2×#242959