Finite Group Databasebeta

← C2×#21427793 #28756517

Subgroups — C2×#21427793 #28756517

Order 15104.

3550 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273726C211yesmaximal, characteristic, complemented
2C22×#14273707C211yesmaximal, characteristic
3C22×#14273705C211yesmaximal, characteristic
4C22×C4⋊C4×D59C211yesmaximal, characteristic
5#21427793C2116yesmaximal, direct product factor
6C2×#16837334C211yesmaximal, characteristic, complemented
7C2×#16837323C211yesmaximal, characteristic, complemented
8C2×#16837322C211yesmaximal, characteristic, complemented
9C2×#16837299C211yesmaximal, characteristic, complemented
10C2×#16837297C211yesmaximal, characteristic, complemented
11C2×#16837276C211yesmaximal, characteristic
12C2×#16837273C211yesmaximal, characteristic
13C2×#16837271C211yesmaximal, characteristic, complemented
14C2×#16837261C211yesmaximal, characteristic
15C2×#16837249C211yesmaximal, characteristic
16C2×C59×#398C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C23×C4×D59C2211yescharacteristic
21C23×C4×D59C2211yescharacteristic
22C2×#14273726—28no—
23C2×#14273726C2218yescomplemented
24C2×#14273707—28no—
25C2×#14273707C2218yes—
26C2×#14273705—28no—
27C2×#14273705C2218yes—
28C22×C4⋊Dic59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C22×C4⋊Dic59C2211yescharacteristic
31C22×C4⋊Dic59C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×Dic59⋊C4C2211yescharacteristic
34C22×Dic59⋊C4C2211yescharacteristic
35C22×Dic59⋊C4C2211yescharacteristic
36C22×Dic59⋊C4C2211yescharacteristic
37C22×Dic59⋊C4C2211yescharacteristic
38C22×Dic59⋊C4C2211yescharacteristic
39C22×Dic59⋊C4C2211yescharacteristic
40C2×C4⋊C4×D59—28no—
41C2×C4⋊C4×D59C2218yes—
42C22×(C2×D59)⋊C4C2211yescharacteristic
43C22×(C2×D59)⋊C4C2211yescharacteristic
44C22×(C2×D59)⋊C4C2211yescharacteristic
45C22×(C2×D59)⋊C4C2211yescharacteristic
46C22×C4×Dic59C2211yescharacteristic
47C22×C4×Dic59C2211yescharacteristic
48#16837334C2218yescomplemented
49#16837323C2218yescomplemented
50#16837322C2218yescomplemented
51#16837299C2218yescomplemented
52#16837297C2218yescomplemented
53#16837276C2218yes—
54#16837273C2218yes—
55#16837271C2218yescomplemented
56#16837261C2218yes—
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—42no—
77C22×Dic118—42no—
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×D59—24no—
91C22×C4×D59—24no—
92C22×C4×D59—24no—
93C22×C4×D59—42no—
94C22×C4×D59—42no—
95C22×C4×D59Q818yescomplemented
96C22×C4×D59C2314yes—
97C22×C4×D59C2314yes—
98C22×C4×D59C2314yes—
99#14273726—232no—
100#14273707—232no—
101#14273705—232no—
102C2×C4⋊Dic59—24no—
103C2×C4⋊Dic59—24no—
104C2×C4⋊Dic59—24no—
105C2×C4⋊Dic59—24no—
106C2×C4⋊Dic59C2314yes—
107C2×C4⋊Dic59C2314yes—
108C2×C4⋊Dic59C2314yes—
109C2×C4⋊Dic59C2314yes—
110C2×Dic59⋊C4—24no—
111C2×Dic59⋊C4—24no—
112C2×Dic59⋊C4—24no—
113C2×Dic59⋊C4—24no—
114C2×Dic59⋊C4—24no—
115C2×Dic59⋊C4—42no—
116C2×Dic59⋊C4—42no—
117C2×Dic59⋊C4D418yes—
118C2×Dic59⋊C4C2314yes—
119C2×Dic59⋊C4C2314yes—
120C2×Dic59⋊C4C2314yes—
121C2×Dic59⋊C4C2314yes—
122C2×Dic59⋊C4C2314yes—
123C2×Dic59⋊C4C2314yes—
124C2×Dic59⋊C4C2314yes—
125C2×Dic59⋊C4C2314yes—
126C4⋊C4×D59—232no—
127C2×(C2×D59)⋊C4—24no—
128C2×(C2×D59)⋊C4—24no—
129C2×(C2×D59)⋊C4D418yes—
130C2×(C2×D59)⋊C4Q818yescomplemented
131C2×(C2×D59)⋊C4C2314yes—
132C2×(C2×D59)⋊C4C2314yes—
133C2×(C2×D59)⋊C4C2314yes—
134C2×(C2×D59)⋊C4C2314yes—
135C2×C4×Dic59—24no—
136C2×C4×Dic59—24no—
137C2×C4×Dic59C2314yes—
138C2×C4×Dic59C2314yes—
139C59⋊#95C2314yes—
140C59⋊#95C2314yes—
141C59⋊#95C2314yes—
142C59⋊#95C2314yes—
143C59⋊#95C2314yes—
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149C23×C4×C59C2311yescharacteristic
150C23×C4×C59C2311yescharacteristic
151C2×C4⋊C4×C59—24no—
152C2×C4⋊C4×C59—24no—
153C2×C4⋊C4×C59—24no—
154C2×C4⋊C4×C59—24no—
155C2×C4⋊C4×C59C2314yes—
156C2×C4⋊C4×C59C2314yes—
157C2×C4⋊C4×C59C2314yes—
158C2×C4⋊C4×C59C2314yes—
159#95×C59C2314yes—
160#95×C59C2314yes—
161#95×C59C2314yes—
162C24×C59C2411yescharacteristic
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59—22no—
167C23×D59C2×D414yes—
168C23×D59C2×Q814yes—
169C23×D59C2×Q814yes—
170C23×D59C2412yes—
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×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59C2×D414yes—
189C22×C4×C59C2×D414yes—
190C22×C4×C59C2×Q814yes—
191C22×C4×C59C2×Q814yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2412yes—
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×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—22no—
213C22×Dic59—22no—
214C22×Dic59C2×D414yes—
215C22×Dic59C2×D414yes—
216C22×Dic59C2×D414yes—
217C22×Dic59C2×Q814yes—
218C22×Dic59C2×Q814yes—
219C22×Dic59#4114yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C22×Dic59C2412yes—
226C22×Dic59C2412yes—
227C2×C4×D59—232no—
228C2×C4×D59—28no—
229C2×C4×D59—28no—
230C2×C4×D59—28no—
231C2×C4×D59—28no—
232C2×C4×D59—28no—
233C2×C4×D59—28no—
234C2×C4×D59—44no—
235C2×C4×D59—44no—
236C2×C4×D59—416no—
237C2×C4×D59—416no—
238C2×C4×D59C2×Q8116yescomplemented
239C2×Dic118—28no—
240C2×Dic118—28no—
241C2×Dic118—28no—
242C2×Dic118—28no—
243C2×Dic118—44no—
244C2×Dic118—44no—
245C2×Dic118—416no—
246C2×Dic118—416no—
247C4⋊C4×C59—28no—
248C4⋊C4×C59—28no—
249C4⋊C4×C59—28no—
250C4⋊C4×C59—28no—
251(C2×D59)⋊C4—28no—
252(C2×D59)⋊C4—28no—
253(C2×D59)⋊C4C2×D4116yes—
254(C2×D59)⋊C4C2×Q8116yescomplemented
255C4⋊Dic59—28no—
256C4⋊Dic59—28no—
257C4⋊Dic59—28no—
258C4⋊Dic59—28no—
259Dic59⋊C4—28no—
260Dic59⋊C4—28no—
261Dic59⋊C4—28no—
262Dic59⋊C4—28no—
263Dic59⋊C4—28no—
264Dic59⋊C4—44no—
265Dic59⋊C4—44no—
266Dic59⋊C4C2×D4116yes—
267C4×Dic59—28no—
268C4×Dic59—28no—
269C23×C59C22×D412yes—
270C23×C59C22×D412yes—
271C23×C59C22×Q812yes—
272C23×C59C22×Q812yes—
273C23×C59C2×#4112yes—
274C23×C59H(5,𝔽2)12yes—
275C23×C592−1+412yes—
276C23×C59C2511yescharacteristic
277C22×D59—28no—
278C22×D59—28no—
279C22×D59—28no—
280C22×D59—28no—
281C22×D59—28no—
282C22×D59—28no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—22no—
286C22×D59—22no—
287C22×D59C4⋊Q8116yescomplemented
288C22×D59C22×D414yes—
289C22×D59C22×Q814yes—
290C22×D59C22×Q814yes—
291C2×C4×C59—28no—
292C2×C4×C59—28no—
293C2×C4×C59—28no—
294C2×C4×C59—28no—
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—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—44no—
313C2×C4×C59—44no—
314C2×C4×C59—44no—
315C2×C4×C59C22×D414yes—
316C2×C4×C59C22×D414yes—
317C2×C4×C59C22×Q814yes—
318C2×C4×C59C22×Q814yes—
319C2×Dic59—28no—
320C2×Dic59—28no—
321C2×Dic59—28no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—44no—
338C2×Dic59—44no—
339C2×Dic59—44no—
340C2×Dic59C22⋊Q8116yescomplemented
341C2×Dic59C22×D414yes—
342C2×Dic59C22×D414yes—
343C2×Dic59C22×D414yes—
344C2×Dic59C22×Q814yes—
345C2×Dic59C22×Q814yes—
346C2×Dic59C2×#4114yes—
347C4×D59—232no—
348C4×D59—416no—
349C4×D59—416no—
350Dic118—416no—
351Dic118—416no—
352C2×#2440—591nomaximal, Sylow
353C22×C59C2×C22⋊Q814yes—
354C22×C59C2×C4⋊Q814yes—
355C22×C59#54414yes—
356C22×C59D4214yes—
357C22×C59#54714yes—
358C22×C59D4×Q814yes—
359C22×C59#55414yes—
360C22×C59C23×D411yescharacteristic
361C22×C59C23×D411yescharacteristic
362C22×C59C23×Q811yescharacteristic
363C22×C59C23×Q811yescharacteristic
364C22×C59C22×#4111yescharacteristic
365C22×C59C2×H(5,𝔽2)11yescharacteristic
366C22×C59C2×2−1+411yescharacteristic
367C2×D59—24no—
368C2×D59—24no—
369C2×D59—24no—
370C2×D59—232no—
371C2×D59—24no—
372C2×D59—24no—
373C2×D59—24no—
374C2×D59C2×C4⋊Q818yescomplemented
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—24no—
378C4×C59—24no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382Dic59—24no—
383Dic59—24no—
384Dic59—24no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59C2×C22⋊Q818yescomplemented
389C22×C4⋊Q8—591no—
390C22×C22⋊Q8—591no—
391C22×C22⋊Q8—591no—
392C23×C4⋊C4—591no—
393#2440—5916no—
394C2×#398—591no—
395C2×#398D5911yescharacteristic, complemented
396C2×#395—591no—
397C2×#395—591no—
398C2×#389—591no—
399C2×#389—591no—
400C2×#385—591no—
401C2×#385—591no—
402C2×#384—591no—
403C2×#380—591no—
404C2×C4×C22⋊C4—591no—
405C2×C59#244018yescomplemented
406C2×C59C22×C22⋊Q811yescharacteristic
407C2×C59C22×C4⋊Q811yescharacteristic
408C2×C59C2×#54411yescharacteristic
409C2×C59C2×D4211yescharacteristic
410C2×C59C2×#54711yescharacteristic
411C2×C59C2×D4×Q811yescharacteristic
412C2×C59C2×#55411yescharacteristic
413D59—28no—
414C23×Q8—591no—
415C23×Q8—591no—
416C24×C4—591no—
417C24×C4—591no—
418C24×C4—591no—
419C2×C4⋊Q8—598no—
420C2×C4⋊Q8—1188no—
421C2×C22⋊Q8—598no—
422C2×C22⋊Q8—598no—
423C2×C22⋊Q8—1188no—
424C2×C22⋊Q8—1188no—
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4—591no—
430C22×C4⋊C4—591no—
431C22×C4⋊C4—591no—
432C22×C4⋊C4—591no—
433C22×C4⋊C4—591no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4—591no—
436C22×C4⋊C4—591no—
437C22×C4⋊C4—598no—
438C22×C4⋊C4—1188no—
439C22×C4⋊C4C2×D5911yescharacteristic
440C22×C4⋊C4C2×D5911yescharacteristic
441C22×C4⋊C4C2×D5911yescharacteristic
442C22×C4⋊C4C2×D5911yescharacteristic
443C22×C22⋊C4—591no—
444C22×C22⋊C4—591no—
445C22×C22⋊C4—591no—
446C22×C22⋊C4—591no—
447C22×C42—591no—
448C22×C42—591no—
449#398—598no—
450#398C2×D5918yescomplemented
451#395—598no—
452#395—598no—
453#389—598no—
454#389—598no—
455#385—598no—
456#385—598no—
457#384—598no—
458#380—598no—
459C4×C22⋊C4—598no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95—591no—
463C2×#95—591no—
464C2×#95—591no—
465C2×#95C2×D5911yescharacteristic
466C2×#95C2×D5911yescharacteristic
467C2×#95C2×D5911yescharacteristic
468C59C2×#244011yescharacteristic, complemented, Sylow
469C25—591no—
470C22×Q8—594no—
471C22×Q8—594no—
472C22×Q8—1184no—
473C22×Q8—1184no—
474C22×Q8—1184no—
475C22×Q8—1184no—
476C22×Q8—2362no—
477C22×Q8—2362no—
478C23×C4—591no—
479C23×C4—591no—
480C23×C4—591no—
481C23×C4—591no—
482C23×C4—598no—
483C23×C4—594no—
484C23×C4—591no—
485C23×C4—591no—
486C23×C4—591no—
487C23×C4—594no—
488C23×C4—594no—
489C23×C4—1184no—
490C23×C4—1184no—
491C23×C4—1184no—
492C23×C4—1184no—
493C23×C4—1184no—
494C23×C4—1184no—
495C23×C4—2362no—
496C23×C4—2362no—
497C23×C4C22×D5911yescharacteristic
498C23×C4C22×D5911yescharacteristic
499C23×C4C22×D5911yescharacteristic
500C23×C4C22×D5911yescharacteristic
501C23×C4C22×D5911yescharacteristic
502C23×C4C22×D5911yescharacteristic
503C23×C4C22×D5911yescharacteristic
504C4⋊Q8—11832no—
505C22⋊Q8—11832no—
506C22⋊Q8—11832no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—598no—
512C2×C4⋊C4—594no—
513C2×C4⋊C4—594no—
514C2×C4⋊C4—594no—
515C2×C4⋊C4—594no—
516C2×C4⋊C4—594no—
517C2×C4⋊C4—594no—
518C2×C4⋊C4—594no—
519C2×C4⋊C4—594no—
520C2×C4⋊C4—594no—
521C2×C4⋊C4—594no—
522C2×C4⋊C4—594no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—11832no—
525C2×C4⋊C4—1184no—
526C2×C4⋊C4—1184no—
527C2×C4⋊C4—1184no—
528C2×C4⋊C4—1184no—
529C2×C4⋊C4—1184no—
530C2×C4⋊C4—1184no—
531C2×C4⋊C4—1184no—
532C2×C4⋊C4—1184no—
533C2×C4⋊C4—1184no—
534C2×C4⋊C4—2362no—
535C2×C4⋊C4—2362no—
536C2×C4⋊C4C22×D5914yes—
537C2×C4⋊C4C22×D5914yes—
538C2×C4⋊C4C22×D5914yes—
539C2×C4⋊C4C22×D5914yes—
540C2×C22⋊C4—598no—
541C2×C22⋊C4—598no—
542C2×C22⋊C4—594no—
543C2×C22⋊C4—594no—
544C2×C22⋊C4—594no—
545C2×C22⋊C4—594no—
546C2×C22⋊C4—1184no—
547C2×C22⋊C4—1184no—
548C2×C42—594no—
549C2×C42—594no—
550C2×C42—1184no—
551C2×C42—1184no—
552#95—594no—
553#95—594no—
554#95—594no—
555#95—594no—
556#95—594no—
557#95C22×D5914yes—
558#95C22×D5914yes—
559#95C22×D5914yes—
560C24—594no—
561C24—594no—
562C24—594no—
563C24—592no—
564C24—1182no—
565C24—1182no—
566C24—1182no—
567C24—1182no—
568C24C23×D5911yescharacteristic
569C2×Q8—1188no—
570C2×Q8—1188no—
571C2×Q8—1188no—
572C2×Q8—1188no—
573C2×Q8—2364no—
574C2×Q8—2364no—
575C2×Q8—23616no—
576C2×Q8—23616no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—594no—
595C22×C4—594no—
596C22×C4—594no—
597C22×C4—592no—
598C22×C4—594no—
599C22×C4—594no—
600C22×C4—594no—
601C22×C4—592no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—5916no—
605C22×C4—592no—
606C22×C4—592no—
607C22×C4—592no—
608C22×C4—1188no—
609C22×C4—11832no—
610C22×C4—1188no—
611C22×C4—1188no—
612C22×C4—1188no—
613C22×C4—1188no—
614C22×C4—1182no—
615C22×C4—1182no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1182no—
620C22×C4—1182no—
621C22×C4—1182no—
622C22×C4—1182no—
623C22×C4—1182no—
624C22×C4—1182no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4—1188no—
630C22×C4—2364no—
631C22×C4—2364no—
632C22×C4—23616no—
633C22×C4—23616no—
634C22×C4D4×D5914yes—
635C22×C4D4×D5914yes—
636C22×C4Q8×D5914yes—
637C22×C4Q8×D5914yes—
638C22×C4C23×D5912yes—
639C22×C4C23×D5912yes—
640C22×C4C23×D5912yes—
641C22×C4C23×D5912yes—
642C22×C4C23×D5912yes—
643C22×C4C23×D5912yes—
644C22×C4C23×D5912yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—5916no—
650C4⋊C4—1188no—
651C4⋊C4—1188no—
652C4⋊C4—1188no—
653C4⋊C4—1188no—
654C4⋊C4—1188no—
655C4⋊C4—1188no—
656C4⋊C4—1188no—
657C4⋊C4—1188no—
658C4⋊C4—1188no—
659C4⋊C4—2364no—
660C4⋊C4—2364no—
661C22⋊C4—5916no—
662C22⋊C4—5916no—
663C22⋊C4—1188no—
664C22⋊C4—1188no—
665C42—1188no—
666C42—1188no—
667C23—5916no—
668C23—594no—
669C23—594no—
670C23—594no—
671C23—1188no—
672C23—1182no—
673C23—1182no—
674C23—1182no—
675C23—1182no—
676C23—1188no—
677C23—1188no—
678C23—1188no—
679C23—1188no—
680C23—1188no—
681C23C2×D4×D5912yes—
682C23C2×D4×D5912yes—
683C23C2×Q8×D5912yes—
684C23C2×Q8×D5912yes—
685C23#41×D5912yes—
686C23#1427377312yes—
687C23#1427377412yes—
688C23C24×D5911yescharacteristic
689Q8—23616no—
690Q8—23616no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—5916no—
716C2×C4—594no—
717C2×C4—594no—
718C2×C4—594no—
719C2×C4—594no—
720C2×C4—594no—
721C2×C4—594no—
722C2×C4—11832no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1188no—
730C2×C4—1188no—
731C2×C4—1188no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—23616no—
742C2×C4—23616no—
743C2×C4—2364no—
744C2×C4—2364no—
745C2×C4—2364no—
746C2×C4C2×D4×D5914yes—
747C2×C4C2×D4×D5914yes—
748C2×C4C2×Q8×D5914yes—
749C2×C4C2×Q8×D5914yes—
750C22—598no—
751C22—1184no—
752C22—11832no—
753C22—1184no—
754C22—1184no—
755C22—1184no—
756C22—1184no—
757C22—1184no—
758C22C22⋊Q8×D5914yes—
759C22C4⋊Q8×D5914yes—
760C22#1683803214yes—
761C22#1683803614yes—
762C22#1683805014yes—
763C22#1683806514yes—
764C22#1683810814yes—
765C22C22×D4×D5911yescharacteristic
766C22C22×D4×D5911yescharacteristic
767C22C22×Q8×D5911yescharacteristic
768C22C22×Q8×D5911yescharacteristic
769C22C2×#41×D5911yescharacteristic
770C22C2×#1427377311yescharacteristic
771C22C2×#1427377411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—598no—
780C4—1184no—
781C4—1184no—
782C4—1184no—
783C4—2362no—
784C4—2362no—
785C4—2362no—
786C2—1188no—
787C2#2142779318yesdirect product factor
788C2C2×C22⋊Q8×D5911yescharacteristic
789C2C2×C4⋊Q8×D5911yescharacteristic
790C2C2×#1683803211yescharacteristic
791C2C2×#1683803611yescharacteristic
792C2C2×#1683805011yescharacteristic
793C2C2×#1683806511yescharacteristic
794C2C2×#1683810811yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#398C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#398D59
hypocenterC59C2×#2440
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
5. #21427793C2direct (N × H)
6. C2×#16837334C2semidirect
7. C2×#16837323C2semidirect
8. C2×#16837322C2semidirect
9. C2×#16837299C2semidirect
10. C2×#16837297C2semidirect
13. C2×#16837271C2semidirect
16. C2×C59×#398C2semidirect
23. C2×#14273726C22semidirect
48. #16837334C22semidirect
49. #16837323C22semidirect
50. #16837322C22semidirect
51. #16837299C22semidirect
52. #16837297C22semidirect
55. #16837271C22semidirect
67. C59×#398C22semidirect
95. C22×C4×D59Q8semidirect
130. C2×(C2×D59)⋊C4Q8semidirect
238. C2×C4×D59C2×Q8semidirect
254. (C2×D59)⋊C4C2×Q8semidirect
287. C22×D59C4⋊Q8semidirect
340. C2×Dic59C22⋊Q8semidirect
374. C2×D59C2×C4⋊Q8semidirect
388. Dic59C2×C22⋊Q8semidirect
395. C2×#398D59semidirect
405. C2×C59#2440semidirect
450. #398C2×D59semidirect
468. C59C2×#2440semidirect
787. C2#21427793direct (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×#142737072
C22×#142737052
C22×C4⋊C4×D592
#214277932
C2×#168373342
C2×#168373232
C2×#168373222
C2×#168372992
C2×#168372972
C2×#168372762
C2×#168372732
C2×#168372712
C2×#168372612
C2×#168372492
C2×C59×#3982
C2×#244059