Finite Group Databasebeta

← C2×#21432974 #29452847

Subgroups — C2×#21432974 #29452847

Order 15104.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273748C211yesmaximal, characteristic
2C2×#16837884C211yesmaximal, characteristic, complemented
3C2×#16837881C211yesmaximal, characteristic, complemented
4#21432974C2116yesmaximal, direct product factor
5C2×#16837512C211yesmaximal, characteristic, complemented
6C2×#16837511C211yesmaximal, characteristic, complemented
7C2×#16837507C211yesmaximal, characteristic, complemented
8C2×#16837506C211yesmaximal, characteristic, complemented
9C2×C4×#11745660C211yesmaximal, characteristic, complemented
10C2×SD16×Dic59C211yesmaximal, characteristic, complemented
11C2×#16837489C211yesmaximal, characteristic, complemented
12C2×#106×D59C211yesmaximal, characteristic, complemented
13C2×#16837402C211yesmaximal, characteristic, complemented
14C2×#16837400C211yesmaximal, characteristic, complemented
15C2×#16837356C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745687C2211yescharacteristic
19C2×#14273748C4116yescomplemented
20C2×#14273748C2218yes—
21C22×#11745672C2211yescharacteristic
22C22×#11745660C2211yescharacteristic
23C22×#11745669C2211yescharacteristic
24C22×#11745659C2211yescharacteristic
25C22×C8×D59C2211yescharacteristic
26#16837884—24no—
27#16837884C2218yescomplemented
28#16837881—24no—
29#16837881C2218yescomplemented
30C2×Q8×Dic59C2211yescharacteristic
31C2×C4×Dic118C2211yescharacteristic
32C2×#14273692C2211yescharacteristic
33C2×C4×D236—21no—
34C2×C4×D236C2211yescharacteristic
35C2×D4×Dic59C2211yescharacteristic
36C2×#14273689—21no—
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×(C22⋊D59)⋊C4—21no—
40C2×#14273684—21no—
41C2×#14273684C2211yescharacteristic
42C2×#14273683—21no—
43C22×Dic59⋊C4—21no—
44C2×C4⋊C4×D59—21no—
45C2×C4⋊C4×D59C2211yescharacteristic
46C2×C4⋊C4×D59C2211yescharacteristic
47#16837512C2218yescomplemented
48#16837511C2218yescomplemented
49#16837507C2218yescomplemented
50#16837506C2218yescomplemented
51C4×#11745660C2218yescomplemented
52SD16×Dic59C2218yescomplemented
53#16837489C2218yescomplemented
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57#106×D59C2218yescomplemented
58#16837402C2218yescomplemented
59#16837400C2218yescomplemented
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66#16837356C2218yescomplemented
67C2×#14273638C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C2×C8×Dic59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C2×C4×D4×C59C2211yescharacteristic
73C4×SD16×C59C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×C4×C8×C59C2211yescharacteristic
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689C2×C418yescomplemented
81C2×#11745689C2314yes—
82C2×#11745687—22no—
83C2×#11745687—24no—
84C2×#11745687C2×C418yescomplemented
85C2×#11745687C2314yes—
86C22×Dic118C2311yescharacteristic
87C22×D236—21no—
88C22×D236C2311yescharacteristic
89C22×C22⋊D59—21no—
90C23×Dic59—21no—
91C23×Dic59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59C2311yescharacteristic
98#14273748C2×C4164yescomplemented
99C2×#11745672C2×C418yescomplemented
100C2×#11745672C2314yes—
101C2×#11745660C2×C418yescomplemented
102C2×#11745660C2314yes—
103C2×#11745669C2×C418yescomplemented
104C2×#11745669C2314yes—
105C2×#11745659—24no—
106C2×#11745659C2314yes—
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C2×C8×D59C2×C418yescomplemented
110C2×C8×D59C2314yes—
111Q8×Dic59—22no—
112Q8×Dic59C2314yes—
113C4×Dic118—22no—
114C4×Dic118C2314yes—
115#14273692—22no—
116#14273692C2314yes—
117C4×D236—22no—
118C4×D236—28no—
119C4×D236C2314yes—
120D4×Dic59—22no—
121D4×Dic59C2314yes—
122#14273689—28no—
123#14273689—22no—
124#14273689C2314yes—
125C4×C22⋊D59—28no—
126(C22⋊D59)⋊C4—28no—
127#14273684—28no—
128#14273684D414yes—
129#14273684C2314yes—
130#14273683—28no—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—28no—
139C2×Dic59⋊C4D411yescharacteristic
140C2×Dic59⋊C4D411yescharacteristic
141C4⋊C4×D59—22no—
142C4⋊C4×D59—22no—
143C4⋊C4×D59—28no—
144C4⋊C4×D59C2314yes—
145C4⋊C4×D59C2314yes—
146C2×C22⋊Dic59—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×(C2×D59)⋊C4D411yescharacteristic
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153C2×C4×Dic59—21no—
154C2×C4×Dic59C2311yescharacteristic
155#14273659C2314yes—
156#14273658C2314yes—
157#14273658C2314yes—
158#14273652C2314yes—
159#14273651C2314yes—
160#14273650C2314yes—
161#14273649C2314yes—
162#14273648C2314yes—
163#14273647C2314yes—
164#14273638C2314yes—
165#14273637C2314yes—
166C8×Dic59C2314yes—
167C22×Q8×C59C2311yescharacteristic
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C2×SD16×C59C2×C418yescomplemented
171C2×SD16×C59C2314yes—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C4×Q8×C59—22no—
175C4×Q8×C59C2314yes—
176C4×D4×C59—22no—
177C4×D4×C59C2314yes—
178C2×C4⋊C4×C59—21no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183C2×C42×C59C2311yescharacteristic
184#106×C59C2314yes—
185#103×C59C2314yes—
186#102×C59C2314yes—
187C4×C8×C59C2314yes—
188C24×C59—21no—
189C23×D59—21no—
190C23×D59C2×D411yescharacteristic
191C2×Q8×C59—21no—
192C2×Q8×C59—22no—
193C2×Q8×C59C22×C414yes—
194C2×Q8×C59C2412yes—
195C2×D4×C59—21no—
196C2×D4×C59—22no—
197C2×D4×C59C22×C414yes—
198C2×D4×C59C2412yes—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—24no—
203C22×C4×C59—82no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2411yescharacteristic
207C2×C22⋊D59—28no—
208C2×C22⋊D59—24no—
209C22×Dic59—21no—
210C22×Dic59—28no—
211C22×Dic59—24no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—82no—
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C22×Dic59C2×D411yescharacteristic
219#11745689—216no—
220#11745689—28no—
221#11745689C22×C4116yescomplemented
222#11745687—216no—
223#11745687—28no—
224#11745687C22×C4116yescomplemented
225C2×D236—28no—
226C2×D236—24no—
227C2×D236—21no—
228C2×D236—22no—
229C2×D236C22×C414yes—
230C2×D236C2412yes—
231C2×C4×D59—28no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—24no—
235C2×C4×D59—24no—
236C2×C4×D59—24no—
237C2×C4×D59—82no—
238C2×C4×D59—82no—
239C2×C4×D59—82no—
240C2×C4×D59—82no—
241C2×C4×D59C22×C414yes—
242C2×C4×D59C2×D412yes—
243C2×C4×D59#4114yes—
244C2×C4×D59C2412yes—
245C2×Dic118—21no—
246C2×Dic118—22no—
247C2×Dic118C22×C414yes—
248C2×Dic118C2412yes—
249SD16×C59C22×C4116yescomplemented
250C2×C8×C59—22no—
251C2×C8×C59C22×C414yes—
252C2×C8×C59C2412yes—
253C2×C8×C59C2412yes—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59C2412yes—
258C4⋊C4×C59C2412yes—
259C22⋊C4×C59—24no—
260C42×C59—24no—
261C42×C59C2×D412yes—
262C42×C59C2412yes—
263C22⋊Dic59—24no—
264#11745672C22×C4116yescomplemented
265#11745669C22×C4116yescomplemented
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4C2×D414yes—
269(C2×D59)⋊C4C2×D414yes—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4C2×D414yes—
280Dic59⋊C4C2×D414yes—
281C4×Dic59—24no—
282C4×Dic59—24no—
283C4×Dic59—24no—
284C4×Dic59C2×D412yes—
285C4×Dic59C2412yes—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C22×C414yes—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290#11745660C22×C4116yescomplemented
291#11745659—28no—
292C8×D59C22×C4116yescomplemented
293C23×C59—24no—
294C23×C59—22no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59C22×D411yescharacteristic
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—24no—
301C22×D59—22no—
302C22×D59—42no—
303C22×D59—42no—
304C22×D59C4×D414yes—
305C22×D59C22×D412yes—
306Q8×C59—24no—
307Q8×C59—22no—
308Q8×C59C23×C414yes—
309D4×C59—24no—
310D4×C59—22no—
311D4×C59C23×C414yes—
312C2×C4×C59—24no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—84no—
321C2×C4×C59C23×C412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D411yescharacteristic
325C2×C4×C59C2×#4112yes—
326C2×C4×C59C2511yescharacteristic
327C22⋊D59—216no—
328C2×Dic59—24no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—216no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59—84no—
338C2×Dic59C4×D414yes—
339C2×Dic59C22×D412yes—
340C2×Dic59C22×D412yes—
341C2×Dic59C22×D412yes—
342D236—216no—
343D236—24no—
344D236—22no—
345D236C23×C414yes—
346C4×D59—216no—
347C4×D59—84no—
348C4×D59—84no—
349C4×D59—84no—
350C4×D59—84no—
351C4×D59C4×D418yes—
352C4×D59C23×C414yes—
353C4×D59C2×#4114yes—
354Dic118—24no—
355Dic118—22no—
356Dic118C23×C414yes—
357C8×C59—22no—
358C8×C59C23×C414yes—
359C59⋊C8—22no—
360C59⋊C8C23×C414yes—
361C2×#2952—591nomaximal, Sylow
362C22×C59—24no—
363C22×C59—48no—
364C22×C59—42no—
365C22×C59—42no—
366C22×C59C2×C4×D412yes—
367C22×C59#57712yes—
368C22×C59#57712yes—
369C22×C59C23×D411yescharacteristic
370C2×D59—28no—
371C2×D59—22no—
372C2×D59—22no—
373C2×D59—24no—
374C2×D59—48no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59C2×C4×D414yes—
378C4×C59—24no—
379C4×C59—22no—
380C4×C59—22no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59C2×C4×D412yes—
384C4×C59C24×C411yescharacteristic
385C4×C59C22×#4111yescharacteristic
386Dic59—24no—
387Dic59—22no—
388Dic59—22no—
389Dic59—42no—
390Dic59—42no—
391Dic59C2×C4×D414yes—
392C22×#135—591no—
393C2×#520—591no—
394C2×#520—591no—
395#2952—5916no—
396C2×#442—591no—
397C2×#442—591no—
398C2×#441—591no—
399C2×#441—591no—
400C2×C4×SD16—591no—
401C2×C4×SD16—591no—
402C2×C4×SD16—591no—
403C2×C4×SD16D5911yescharacteristic, complemented
404C22×#106—591no—
405C2×#417—591no—
406C2×#417—591no—
407C2×#405—591no—
408C2×C59—44no—
409C2×C59#295214yescomplemented
410C2×C59C22×C4×D411yescharacteristic
411C2×C59C2×#57711yescharacteristic
412C2×C59C2×#57711yescharacteristic
413D59—24no—
414D59—44no—
415C22×#41—591no—
416C22×#41—591no—
417C2×#135—5916no—
418C2×#135—598no—
419C22×Q16—591no—
420C22×SD16—591no—
421C22×SD16C2×D5911yescharacteristic
422C22×D8—591no—
423C22×M16—591no—
424C23×C8—591no—
425#520—598no—
426#520—598no—
427#520—1184no—
428#520—1184no—
429C2×C4×Q8—591no—
430C2×C4×Q8—591no—
431C2×C4×Q8—591no—
432C2×C4×Q8C2×D5911yescharacteristic
433C2×C4×D4—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—1181no—
437C2×C4×D4—1181no—
438C2×C4×D4—1181no—
439C2×C4×D4—1181no—
440C2×C4×D4C2×D5911yescharacteristic
441C2×#117—591no—
442C2×#117—1181no—
443C2×#117—1181no—
444C22×C4⋊C4—591no—
445C22×C4⋊C4—591no—
446C22×C4⋊C4—1181no—
447C22×C4⋊C4—1181no—
448#442—598no—
449#442—598no—
450#441—598no—
451#441—598no—
452C4×SD16—598no—
453C4×SD16—598no—
454C4×SD16—598no—
455C4×SD16C2×D5918yescomplemented
456C2×#106—591no—
457C2×#106—591no—
458C2×#106—591no—
459C2×#106—598no—
460C2×#106C2×D5911yescharacteristic
461#417—598no—
462#417—598no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103C2×D5911yescharacteristic
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×#102C2×D5911yescharacteristic
471#405—598no—
472C2×#97—591no—
473C2×#97—591no—
474C2×C4×C8—591no—
475C2×C4×C8C2×D5911yescharacteristic
476C59C2×#295211yescharacteristic, complemented, Sylow
477C2×#41—598no—
478C2×#41—594no—
479C2×#41—598no—
480C2×#41—594no—
481C2×#41—1182no—
482C2×#41—1184no—
483C2×#41—1182no—
484C2×#41—1184no—
485C22×Q8—591no—
486C22×Q8C22×D5911yescharacteristic
487C22×D4—591no—
488C22×D4—1181no—
489C22×D4—1181no—
490C22×D4C22×D5911yescharacteristic
491C23×C4—21no—
492C23×C4—591no—
493C23×C4—1181no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4—1181no—
498C23×C4—1181no—
499C23×C4—1181no—
500#135—5964no—
501C2×Q16—598no—
502C2×Q16—594no—
503C2×SD16—598no—
504C2×SD16—594no—
505C2×SD16C4×D5918yescomplemented
506C2×SD16C22×D5914yes—
507C2×D8—598no—
508C2×D8—594no—
509C2×M16—594no—
510C2×M16—1184no—
511C22×C8—591no—
512C22×C8—598no—
513C22×C8—594no—
514C22×C8—591no—
515C22×C8C22×D5911yescharacteristic
516C22×C8C22×D5911yescharacteristic
517C4×Q8—22no—
518C4×Q8—594no—
519C4×Q8—594no—
520C4×Q8—594no—
521C4×Q8—1182no—
522C4×Q8—1182no—
523C4×Q8—1182no—
524C4×Q8C22×D5914yes—
525C4×D4—22no—
526C4×D4—594no—
527C4×D4—594no—
528C4×D4—594no—
529C4×D4—1188no—
530C4×D4—1182no—
531C4×D4—1182no—
532C4×D4—1188no—
533C4×D4—1188no—
534C4×D4—1188no—
535C4×D4—1182no—
536C4×D4C22×D5914yes—
537#117—594no—
538#117—594no—
539#117—1188no—
540#117—1188no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—591no—
546C2×C4⋊C4—594no—
547C2×C4⋊C4—594no—
548C2×C4⋊C4—1188no—
549C2×C4⋊C4—1182no—
550C2×C4⋊C4—1182no—
551C2×C4⋊C4—1188no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4—1181no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4C22×D5911yescharacteristic
558C2×C4⋊C4C22×D5911yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—591no—
561C2×C22⋊C4—591no—
562C2×C22⋊C4—1181no—
563C2×C22⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C42—21no—
566C2×C42—591no—
567C2×C42—1181no—
568C2×C42—1181no—
569C2×C42—1181no—
570C2×C42C22×D5911yescharacteristic
571#106—594no—
572#106—594no—
573#106—594no—
574#106C22×D5914yes—
575#103—594no—
576#103—594no—
577#103—594no—
578#103C22×D5914yes—
579#102—594no—
580#102—594no—
581#102—594no—
582#102C22×D5914yes—
583#97—594no—
584#97—594no—
585C4×C8—594no—
586C4×C8C22×D5914yes—
587C24—21no—
588C24—591no—
589C24—1181no—
590#41—5916no—
591#41—5916no—
592#41—1188no—
593#41—11816no—
594#41—1188no—
595#41—11816no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—594no—
599C2×Q8—592no—
600C2×Q8—1181no—
601C2×Q8—1182no—
602C2×Q8C2×C4×D5914yes—
603C2×Q8C23×D5912yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—594no—
607C2×D4—592no—
608C2×D4—1184no—
609C2×D4—1188no—
610C2×D4—1184no—
611C2×D4—1188no—
612C2×D4—1181no—
613C2×D4—1182no—
614C2×D4C2×C4×D5914yes—
615C2×D4C23×D5912yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—591no—
622C22×C4—594no—
623C22×C4—592no—
624C22×C4—594no—
625C22×C4—592no—
626C22×C4—591no—
627C22×C4—591no—
628C22×C4—1184no—
629C22×C4—1188no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1184no—
633C22×C4—1184no—
634C22×C4—1188no—
635C22×C4—1184no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—1184no—
640C22×C4—4722no—
641C22×C4—4722no—
642C22×C4—4722no—
643C22×C4—4722no—
644C22×C4—4722no—
645C22×C4D4×D5911yescharacteristic
646C22×C4D4×D5911yescharacteristic
647C22×C4C23×D5911yescharacteristic
648Q16—5916no—
649SD16—5916no—
650SD16C2×C4×D59116yescomplemented
651D8—5916no—
652M16—1188no—
653C2×C8—22no—
654C2×C8—594no—
655C2×C8—592no—
656C2×C8—5916no—
657C2×C8—592no—
658C2×C8—1182no—
659C2×C8C2×C4×D5914yes—
660C2×C8C23×D5912yes—
661C2×C8C23×D5912yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—594no—
666C4⋊C4—594no—
667C4⋊C4—592no—
668C4⋊C4—592no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1184no—
672C4⋊C4—1184no—
673C4⋊C4—1181no—
674C4⋊C4—1181no—
675C4⋊C4—1184no—
676C4⋊C4C23×D5912yes—
677C4⋊C4C23×D5912yes—
678C22⋊C4—24no—
679C22⋊C4—594no—
680C22⋊C4—594no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—24no—
685C42—592no—
686C42—592no—
687C42—1184no—
688C42—1184no—
689C42—1184no—
690C42D4×D5912yes—
691C42C23×D5912yes—
692C23—22no—
693C23—24no—
694C23—42no—
695C23—42no—
696C23—592no—
697C23—594no—
698C23—1182no—
699C23—1182no—
700C23—1182no—
701C23—1184no—
702C23—2362no—
703C23—2362no—
704C23C2×D4×D5911yescharacteristic
705Q8—22no—
706Q8—24no—
707Q8—594no—
708Q8—1182no—
709Q8—1184no—
710Q8C22×C4×D5914yes—
711D4—22no—
712D4—24no—
713D4—594no—
714D4—11816no—
715D4—11816no—
716D4—1182no—
717D4—1184no—
718D4C22×C4×D5914yes—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—592no—
729C2×C4—594no—
730C2×C4—594no—
731C2×C4—594no—
732C2×C4—598no—
733C2×C4—592no—
734C2×C4—592no—
735C2×C4—11816no—
736C2×C4—11816no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1184no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—4724no—
744C2×C4—4724no—
745C2×C4—4724no—
746C2×C4—4724no—
747C2×C4—4724no—
748C2×C4—2362no—
749C2×C4—2362no—
750C2×C4C22×C4×D5912yes—
751C2×C4C2×D4×D5912yes—
752C2×C4C2×D4×D5912yes—
753C2×C4C2×D4×D5911yescharacteristic
754C2×C4#41×D5912yes—
755C2×C4C24×D5911yescharacteristic
756C8—22no—
757C8—594no—
758C8—1182no—
759C8C22×C4×D5914yes—
760C22—24no—
761C22—42no—
762C22—42no—
763C22—48no—
764C22—594no—
765C22—1182no—
766C22—1182no—
767C22—1188no—
768C22—1184no—
769C22—2362no—
770C22—2362no—
771C22—2368no—
772C22C4×D4×D5912yes—
773C22#1683820812yes—
774C22#1683820912yes—
775C22C22×D4×D5911yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—594no—
782C4—1184no—
783C4—1182no—
784C4—1182no—
785C4—2362no—
786C4—2362no—
787C4C4×D4×D5912yes—
788C4C23×C4×D5911yescharacteristic
789C4C2×#41×D5911yescharacteristic
790C2—44no—
791C2—1184no—
792C2—2364no—
793C2#2143297414yesdirect product factor
794C2C2×C4×D4×D5911yescharacteristic
795C2C2×#1683820811yescharacteristic
796C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC22×#14273748C2
cosocleC2×C4×C59C25
hypercenterC2×C4×SD16D59
hypocenterC59C2×#2952
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16837884C2semidirect
3. C2×#16837881C2semidirect
4. #21432974C2direct (N × H)
5. C2×#16837512C2semidirect
6. C2×#16837511C2semidirect
7. C2×#16837507C2semidirect
8. C2×#16837506C2semidirect
9. C2×C4×#11745660C2semidirect
10. C2×SD16×Dic59C2semidirect
11. C2×#16837489C2semidirect
12. C2×#106×D59C2semidirect
13. C2×#16837402C2semidirect
14. C2×#16837400C2semidirect
15. C2×#16837356C2semidirect
16. C2×C4×SD16×C59C2semidirect
19. C2×#14273748C4semidirect
27. #16837884C22semidirect
29. #16837881C22semidirect
47. #16837512C22semidirect
48. #16837511C22semidirect
49. #16837507C22semidirect
50. #16837506C22semidirect
51. C4×#11745660C22semidirect
52. SD16×Dic59C22semidirect
53. #16837489C22semidirect
57. #106×D59C22semidirect
58. #16837402C22semidirect
59. #16837400C22semidirect
66. #16837356C22semidirect
73. C4×SD16×C59C22semidirect
80. C2×#11745689C2×C4semidirect
84. C2×#11745687C2×C4semidirect
98. #14273748C2×C4semidirect
99. C2×#11745672C2×C4semidirect
101. C2×#11745660C2×C4semidirect
103. C2×#11745669C2×C4semidirect
109. C2×C8×D59C2×C4semidirect
170. C2×SD16×C59C2×C4semidirect
221. #11745689C22×C4semidirect
224. #11745687C22×C4semidirect
249. SD16×C59C22×C4semidirect
264. #11745672C22×C4semidirect
265. #11745669C22×C4semidirect
290. #11745660C22×C4semidirect
292. C8×D59C22×C4semidirect
403. C2×C4×SD16D59semidirect
409. C2×C59#2952semidirect
455. C4×SD16C2×D59semidirect
476. C59C2×#2952semidirect
505. C2×SD16C4×D59semidirect
650. SD16C2×C4×D59semidirect
793. C2#21432974direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737482
C2×#168378842
C2×#168378812
#214329742
C2×#168375122
C2×#168375112
C2×#168375072
C2×#168375062
C2×C4×#117456602
C2×SD16×Dic592
C2×#168374892
C2×#106×D592
C2×#168374022
C2×#168374002
C2×#168373562
C2×C4×SD16×C592
C2×#295259