Finite Group Databasebeta

← C2×#21435965 #29465077

Subgroups — C2×#21435965 #29465077

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838110C211yesmaximal, characteristic
2C2×Q8×C22⋊D59C211yesmaximal, characteristic
3#21435965C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837738C211yesmaximal, characteristic, complemented
6C2×#16837736C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837640C211yesmaximal, characteristic, complemented
10C2×#16837610C211yesmaximal, characteristic, complemented
11C2×#16837556C211yesmaximal, characteristic, complemented
12C2×Q16×Dic59C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic
14C22×#14273651C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#451C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838110—24no—
22#16838110C2218yes—
23Q8×C22⋊D59—24no—
24Q8×C22⋊D59C2218yes—
25C2×#14273726C2211yescharacteristic
26C2×#14273725—21no—
27C2×#14273725C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273707—21no—
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273704—21no—
33C2×#14273703—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273703C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×(C22⋊D59)⋊C4—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837751C2218yescomplemented
44#16837738C2218yescomplemented
45#16837736C2218yescomplemented
46#16837695C2218yescomplemented
47#16837641C2218yescomplemented
48#16837640C2218yescomplemented
49#16837610C2218yescomplemented
50#16837556C2218yescomplemented
51Q16×Dic59C2218yescomplemented
52(C22⋊D59)⋊C8C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2218yescomplemented
65C2×#14273650C2211yescharacteristic
66#103×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C23×Q8×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×Q16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#451C2218yescomplemented
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C2×Q8×D59—22no—
81C2×Q8×D59—24no—
82C2×Q8×D59—42no—
83C2×Q8×D59C2314yes—
84C22×C22⋊D59D411yescharacteristic
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C2×#11745672—42no—
90C2×#11745672C2314yes—
91C22×C59⋊C8—42no—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2314yes—
95C2×C8×D59—42no—
96C2×C8×D59C2314yes—
97#14273726—22no—
98#14273726C2314yes—
99#14273725—28no—
100#14273725—22no—
101#14273725C2314yes—
102#14273717—28no—
103#14273707—28no—
104#14273706—22no—
105#14273706—28no—
106#14273706C2314yes—
107#14273704—28no—
108#14273703—22no—
109#14273703—22no—
110#14273703—28no—
111#14273703C2314yes—
112#14273703C2314yes—
113Q8×Dic59—22no—
114Q8×Dic59—22no—
115Q8×Dic59C2314yes—
116Q8×Dic59C2314yes—
117C4×C22⋊D59—28no—
118C4×C22⋊D59D414yes—
119C4×C22⋊D59C2314yes—
120(C22⋊D59)⋊C4—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—22no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2314yes—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C4⋊C4×D59—22no—
138C4⋊C4×D59C2314yes—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273661C2314yes—
149#14273660C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159(C2×D59)⋊C8C2314yes—
160C8×Dic59C2314yes—
161C22×Q8×C59—21no—
162C22×Q8×C59—22no—
163C22×Q8×C59—24no—
164C22×Q8×C59—42no—
165C22×Q8×C59C2311yescharacteristic
166C22×Q8×C59C2311yescharacteristic
167C22×Q8×C59C2314yes—
168C22×Q8×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C2×Q16×C59—24no—
172C2×Q16×C59—42no—
173C2×Q16×C59C2314yes—
174C2×Q16×C59C2314yes—
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2311yescharacteristic
177C22⋊Q8×C59—22no—
178C22⋊Q8×C59C2314yes—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182#103×C59C2314yes—
183#103×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—24no—
190C2×Q8×C59—21no—
191C2×Q8×C59—22no—
192C2×Q8×C59—28no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59—44no—
198C2×Q8×C59—44no—
199C2×Q8×C59—48no—
200C2×Q8×C59#4114yes—
201C2×Q8×C59C2412yes—
202C2×Q8×C59C2412yes—
203C2×Q8×C59C2412yes—
204C22×C4×C59—21no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—24no—
211C22×C4×C59—44no—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2412yes—
215C22×C4×C59C2411yescharacteristic
216C2×C22⋊D59Q1618yescomplemented
217C2×C22⋊D59C2×D414yes—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—24no—
223C22×Dic59—82no—
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D411yescharacteristic
226C22×Dic59C2×D411yescharacteristic
227Q8×D59—28no—
228Q8×D59—44no—
229Q8×D59—48no—
230C2×C4×D59—22no—
231C2×C4×D59—22no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—44no—
235C2×C4×D59—82no—
236C2×C4×D59C2×D412yes—
237C2×C4×D59C2412yes—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—21no—
241C2×Dic118—24no—
242C2×Dic118—24no—
243C2×Dic118—44no—
244C2×Dic118—82no—
245C2×Dic118C2412yes—
246Q16×C59—28no—
247Q16×C59—44no—
248C2×C8×C59—22no—
249C2×C8×C59—22no—
250C2×C8×C59C2412yes—
251C2×C8×C59C2412yes—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59C2412yes—
255C22⋊C4×C59—24no—
256C22⋊Dic59—24no—
257C22⋊Dic59C2×D414yes—
258#11745672—44no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4C2×D414yes—
262C4⋊Dic59—21no—
263C4⋊Dic59—21no—
264C4⋊Dic59—24no—
265C4⋊Dic59—21no—
266C4⋊Dic59—24no—
267C4⋊Dic59—24no—
268C4⋊Dic59C2412yes—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4C2×D414yes—
279C4×Dic59—24no—
280C4×Dic59—24no—
281C4×Dic59C2×D412yes—
282C4×Dic59C2412yes—
283C2×C59⋊C8—22no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—44no—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288C8×D59—44no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59C2×Q1614yes—
292C23×C59C22×D412yes—
293C23×C59C22×D411yescharacteristic
294C22×D59—22no—
295C22×D59—22no—
296C22×D59C2×Q1614yes—
297C22×D59C22×D412yes—
298Q8×C59—24no—
299Q8×C59—22no—
300Q8×C59—22no—
301Q8×C59—22no—
302Q8×C59—22no—
303Q8×C59—22no—
304Q8×C59—48no—
305Q8×C59—42no—
306Q8×C59—42no—
307Q8×C59C2×#4114yes—
308C2×C4×C59—24no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—24no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—48no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D411yescharacteristic
323C2×C4×C59C2×#4112yes—
324C2×C4×C59H(5,𝔽2)12yes—
325C2×C4×C59C2511yescharacteristic
326C22⋊D59C2×Q16116yescomplemented
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337C2×Dic59—84no—
338C2×Dic59C2×Q1614yes—
339C2×Dic59C22×D412yes—
340C2×Dic59C22×D412yes—
341C2×Dic59C22×D412yes—
342C4×D59—24no—
343C4×D59—22no—
344C4×D59—22no—
345C4×D59—48no—
346C4×D59—84no—
347Dic118—22no—
348Dic118—22no—
349Dic118—48no—
350Dic118—42no—
351Dic118—84no—
352C8×C59—22no—
353C8×C59—22no—
354C59⋊C8—22no—
355C59⋊C8—22no—
356C2×#3299—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—28no—
359C22×C59—22no—
360C22×C59#54612yes—
361C22×C59C22×Q1614yes—
362C22×C59C22×Q1612yes—
363C22×C59#57712yes—
364C22×C59C23×D411yescharacteristic
365C2×D59—22no—
366C2×D59—28no—
367C2×D59—22no—
368C2×D59C22×Q1614yes—
369C4×C59—24no—
370C4×C59—22no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59#54612yes—
375C4×C59C22×#4111yescharacteristic
376C4×C59C2×H(5,𝔽2)11yescharacteristic
377Dic59—22no—
378Dic59—22no—
379Dic59—42no—
380Dic59—42no—
381Dic59—42no—
382Dic59—42no—
383Dic59C22×Q1614yes—
384C2×#554—591no—
385C2×D4×Q8—591no—
386#3299—5916no—
387C2×#487—591no—
388C2×#484—591no—
389C2×#484—591no—
390C2×#477—591no—
391C2×#467—591no—
392C2×#467—591no—
393C2×#462—591no—
394C2×#451—591no—
395C2×#451D5911yescharacteristic, complemented
396C2×C4×Q16—591no—
397C2×C8×D4—591no—
398C22×#103—591no—
399C22×#103—591no—
400C2×C59—24no—
401C2×C59#329914yescomplemented
402C2×C59C2×#54611yescharacteristic
403C2×C59C23×Q1611yescharacteristic
404C2×C59C2×#57711yescharacteristic
405D59—24no—
406C23×Q8—591no—
407C23×Q8C2×D5911yescharacteristic
408C22×Q16—591no—
409C22×Q16C2×D5911yescharacteristic
410C22×Q16C2×D5911yescharacteristic
411C23×C8—591no—
412C23×C8—591no—
413#554—598no—
414#554—1184no—
415D4×Q8—598no—
416D4×Q8—1184no—
417C2×C4⋊Q8—591no—
418C2×C4⋊Q8—591no—
419C2×C4⋊Q8—1181no—
420C2×#125—1181no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—591no—
423C2×C22⋊Q8—591no—
424C2×C22⋊Q8—1181no—
425C2×C22⋊Q8—1181no—
426C2×C22⋊Q8—1181no—
427C2×C22⋊Q8—1181no—
428C2×C22⋊Q8C2×D5911yescharacteristic
429C2×C4×Q8—591no—
430C2×C4×Q8—591no—
431C2×C4×D4—591no—
432C2×C4×D4—1181no—
433C2×C4×D4—1181no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4—591no—
436#487—598no—
437#484—598no—
438#484—598no—
439#477—598no—
440#467—598no—
441#467—598no—
442#462—598no—
443#451—598no—
444#451C2×D5918yescomplemented
445C4×Q16—598no—
446C8×D4—598no—
447C2×#107—591no—
448C2×#107—591no—
449C2×#107—591no—
450C2×C4⋊C8—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#103—598no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—598no—
461C2×#103C2×D5911yescharacteristic
462C2×#103C2×D5911yescharacteristic
463C2×C22⋊C8—591no—
464C2×C22⋊C8C2×D5911yescharacteristic
465C2×C4×C8—591no—
466C59C2×#329911yescharacteristic, complemented, Sylow
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—594no—
472C22×Q8—591no—
473C22×Q8—1181no—
474C22×Q8—1181no—
475C22×Q8—1182no—
476C22×Q8—1184no—
477C22×Q8—2362no—
478C22×Q8C22×D5911yescharacteristic
479C22×Q8C22×D5911yescharacteristic
480C22×Q8C22×D5914yes—
481C22×Q8C22×D5911yescharacteristic
482C22×D4—591no—
483C23×C4—21no—
484C23×C4—591no—
485C23×C4—1181no—
486C23×C4—1181no—
487C23×C4—1181no—
488C23×C4C22×D5911yescharacteristic
489C2×Q16—24no—
490C2×Q16—42no—
491C2×Q16—594no—
492C2×Q16—2362no—
493C2×Q16C22×D5914yes—
494C2×Q16C22×D5914yes—
495C22×C8—591no—
496C22×C8—591no—
497C22×C8—594no—
498C22×C8—594no—
499C22×C8—2362no—
500C22×C8—2362no—
501C22×C8C22×D5911yescharacteristic
502C22×C8C22×D5911yescharacteristic
503C4⋊Q8—594no—
504C4⋊Q8—594no—
505C4⋊Q8—1182no—
506C4⋊Q8—1182no—
507C4⋊Q8—1188no—
508#125—1188no—
509C22⋊Q8—22no—
510C22⋊Q8—594no—
511C22⋊Q8—594no—
512C22⋊Q8—594no—
513C22⋊Q8—1188no—
514C22⋊Q8—1188no—
515C22⋊Q8—1188no—
516C22⋊Q8—1188no—
517C22⋊Q8—1182no—
518C22⋊Q8—1182no—
519C22⋊Q8—1182no—
520C22⋊Q8C22×D5914yes—
521C4×Q8—594no—
522C4×Q8—594no—
523C4×Q8—1182no—
524C4×Q8—1182no—
525C4×D4—594no—
526C4×D4—594no—
527C4×D4—1188no—
528C4×D4—1188no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—591no—
531C2×C4⋊C4—591no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—594no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—594no—
536C2×C4⋊C4—1182no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1182no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4C22×D5911yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—591no—
551C2×C22⋊C4—591no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C42—591no—
556C2×C42—1181no—
557C2×C42—1181no—
558#107—594no—
559#107—594no—
560#107—594no—
561C4⋊C8—594no—
562#103—594no—
563#103—594no—
564#103—594no—
565#103—594no—
566#103—594no—
567#103—594no—
568#103—594no—
569#103—594no—
570#103C22×D5914yes—
571#103C22×D5914yes—
572C22⋊C8—594no—
573C22⋊C8C22×D5914yes—
574C4×C8—594no—
575C24—591no—
576C24D4×D5911yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—592no—
591C2×Q8—1184no—
592C2×Q8—1184no—
593C2×Q8—1181no—
594C2×Q8—1188no—
595C2×Q8—1182no—
596C2×Q8—1182no—
597C2×Q8—4722no—
598C2×Q8—2364no—
599C2×Q8—2364no—
600C2×Q8—2368no—
601C2×Q8#1174568714yes—
602C2×Q8C23×D5912yes—
603C2×Q8C23×D5912yes—
604C2×Q8C23×D5912yes—
605C2×D4—598no—
606C2×D4—594no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—44no—
615C22×C4—591no—
616C22×C4—591no—
617C22×C4—591no—
618C22×C4—592no—
619C22×C4—592no—
620C22×C4—1184no—
621C22×C4—1184no—
622C22×C4—1182no—
623C22×C4—1182no—
624C22×C4—1184no—
625C22×C4—1181no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—4722no—
630C22×C4—4722no—
631C22×C4—2364no—
632C22×C4D4×D5912yes—
633C22×C4D4×D5911yescharacteristic
634C22×C4C23×D5912yes—
635C22×C4C23×D5911yescharacteristic
636Q16—28no—
637Q16—44no—
638Q16—2364no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—592no—
642C2×C8—592no—
643C2×C8—1182no—
644C2×C8—1182no—
645C2×C8—2364no—
646C2×C8—2364no—
647C2×C8C23×D5912yes—
648C2×C8C23×D5912yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—594no—
652C4⋊C4—592no—
653C4⋊C4—592no—
654C4⋊C4—592no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4—1184no—
662C4⋊C4—1184no—
663C4⋊C4—1181no—
664C4⋊C4—1184no—
665C4⋊C4—1181no—
666C4⋊C4—1181no—
667C4⋊C4—1184no—
668C4⋊C4C23×D5912yes—
669C22⋊C4—24no—
670C22⋊C4—594no—
671C22⋊C4—594no—
672C22⋊C4—1184no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C42—592no—
676C42—592no—
677C42—1184no—
678C42—1184no—
679C23—22no—
680C23—22no—
681C23—594no—
682C23—592no—
683C23—1182no—
684C23—1182no—
685C23Q16×D5914yes—
686C23C2×D4×D5912yes—
687C23C2×D4×D5911yescharacteristic
688Q8—22no—
689Q8—24no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—48no—
695Q8—42no—
696Q8—42no—
697Q8—1182no—
698Q8—1182no—
699Q8—4724no—
700Q8—2368no—
701Q8—2362no—
702Q8C2×#1174568714yes—
703D4—5916no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—594no—
718C2×C4—592no—
719C2×C4—592no—
720C2×C4—592no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1184no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—4724no—
731C2×C4—4724no—
732C2×C4—2368no—
733C2×C4—2362no—
734C2×C4—2362no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4C2×D4×D5912yes—
738C2×C4C2×D4×D5911yescharacteristic
739C2×C4C2×#1174568712yes—
740C2×C4#1427377212yes—
741C2×C4C24×D5911yescharacteristic
742C8—22no—
743C8—22no—
744C8—1182no—
745C8—1182no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—594no—
750C22—1188no—
751C22—1182no—
752C22—1182no—
753C22#1683803912yes—
754C22C2×Q16×D5914yes—
755C22C2×Q16×D5912yes—
756C22#1683821112yes—
757C22C22×D4×D5911yescharacteristic
758C4—22no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—594no—
764C4—1182no—
765C4—1182no—
766C4—2362no—
767C4—2362no—
768C4—2362no—
769C4—2362no—
770C4#1683803912yes—
771C4C22×#1174568711yescharacteristic
772C4C2×#1427377211yescharacteristic
773C2—24no—
774C2—1184no—
775C2#2143596514yesdirect product factor
776C2C2×#1683803911yescharacteristic
777C2C22×Q16×D5911yescharacteristic
778C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#451C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#451D59
hypocenterC59C2×#3299
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #21435965C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837738C2semidirect
6. C2×#16837736C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837640C2semidirect
10. C2×#16837610C2semidirect
11. C2×#16837556C2semidirect
12. C2×Q16×Dic59C2semidirect
14. C22×#14273651C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#451C2semidirect
43. #16837751C22semidirect
44. #16837738C22semidirect
45. #16837736C22semidirect
46. #16837695C22semidirect
47. #16837641C22semidirect
48. #16837640C22semidirect
49. #16837610C22semidirect
50. #16837556C22semidirect
51. Q16×Dic59C22semidirect
64. C2×#14273651C22semidirect
66. #103×D59C22semidirect
73. C59×#451C22semidirect
216. C2×C22⋊D59Q16semidirect
326. C22⋊D59C2×Q16semidirect
395. C2×#451D59semidirect
401. C2×C59#3299semidirect
444. #451C2×D59semidirect
466. C59C2×#3299semidirect
775. C2#21435965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381102
C2×Q8×C22⋊D592
#214359652
C2×#168377512
C2×#168377382
C2×#168377362
C2×#168376952
C2×#168376412
C2×#168376402
C2×#168376102
C2×#168375562
C2×Q16×Dic592
C2×(C22⋊D59)⋊C82
C22×#142736512
C2×#103×D592
C2×C59×#4512
C2×#329959