Finite Group Databasebeta

← C2×#21436140 #29465288

Subgroups — C2×#21436140 #29465288

Order 15104.

2094 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
1C2×#16838086C211yesmaximal, characteristic
2C2×Q8×C22⋊D59C211yesmaximal, characteristic
3#21436140C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837731C211yesmaximal, characteristic, complemented
7C2×#16837711C211yesmaximal, characteristic, complemented
8C2×#16837658C211yesmaximal, characteristic, complemented
9C2×#16837640C211yesmaximal, characteristic, complemented
10C2×#16837610C211yesmaximal, characteristic, complemented
11C2×#16837556C211yesmaximal, characteristic, complemented
12C2×#16837509C211yesmaximal, characteristic, complemented
13C2×#16837476C211yesmaximal, characteristic
14C2×#16837411C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#451C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838086—24no—
22#16838086C2218yes—
23Q8×C22⋊D59—24no—
24Q8×C22⋊D59C2218yes—
25C2×#14273725—21no—
26C2×#14273725C2211yescharacteristic
27C2×#14273720—21no—
28C2×#14273718C2211yescharacteristic
29C2×#14273717—21no—
30C2×#14273709—21no—
31C2×#14273706—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273703—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273703C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×#14273686C2211yescharacteristic
41C2×#14273685—21no—
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837769C2218yescomplemented
44#16837744C2218yescomplemented
45#16837731C2218yescomplemented
46#16837711C2218yescomplemented
47#16837658C2218yescomplemented
48#16837640C2218yescomplemented
49#16837610C2218yescomplemented
50#16837556C2218yescomplemented
51#16837509C2218yescomplemented
52#16837476C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837411C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66#103×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
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×Dic118C2311yescharacteristic
79C2×Q8×D59—22no—
80C2×Q8×D59—24no—
81C2×Q8×D59—42no—
82C2×Q8×D59C2314yes—
83C22×C22⋊D59D411yescharacteristic
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59C2311yescharacteristic
87C2×#11745672—42no—
88C2×#11745672C2314yes—
89C2×#11745664—42no—
90C2×#11745664C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C2×C8×D59—42no—
94C2×C8×D59C2314yes—
95#14273725—28no—
96#14273725—22no—
97#14273725C2314yes—
98#14273720—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273717—28no—
102#14273709—28no—
103#14273706—22no—
104#14273706—28no—
105#14273706C2314yes—
106#14273703—22no—
107#14273703—22no—
108#14273703—28no—
109#14273703C2314yes—
110#14273703C2314yes—
111Q8×Dic59—22no—
112Q8×Dic59—22no—
113Q8×Dic59C2314yes—
114Q8×Dic59C2314yes—
115C4×C22⋊D59—28no—
116C4×C22⋊D59D414yes—
117C4×C22⋊D59C2314yes—
118#14273686—22no—
119#14273686C2314yes—
120#14273685—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59D411yescharacteristic
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4D411yescharacteristic
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273637C2314yes—
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⋊D59—24no—
217C2×C22⋊D59C2×D414yes—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59C2×D411yescharacteristic
223C22×Dic59C2×D411yescharacteristic
224C22×Dic59C2×D411yescharacteristic
225Q8×D59—28no—
226Q8×D59—44no—
227Q8×D59—48no—
228C2×C4×D59—22no—
229C2×C4×D59—22no—
230C2×C4×D59—24no—
231C2×C4×D59—24no—
232C2×C4×D59—44no—
233C2×C4×D59—44no—
234C2×C4×D59C2×D412yes—
235C2×C4×D59C2412yes—
236C2×Dic118—22no—
237C2×Dic118—22no—
238C2×Dic118—21no—
239C2×Dic118—24no—
240C2×Dic118—44no—
241C2×Dic118C2412yes—
242Q16×C59—28no—
243Q16×C59—44no—
244C2×C8×C59—22no—
245C2×C8×C59—22no—
246C2×C8×C59C2412yes—
247C2×C8×C59C2412yes—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59C2412yes—
251C22⋊C4×C59—24no—
252C22⋊Dic59—24no—
253C22⋊Dic59—24no—
254C22⋊Dic59C2×D414yes—
255#11745672—44no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4C2×D414yes—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—21no—
262C4⋊Dic59—24no—
263C4⋊Dic59—24no—
264C4⋊Dic59—24no—
265C4⋊Dic59C2412yes—
266C4⋊Dic59C2412yes—
267C4⋊Dic59C2412yes—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4C2×D414yes—
276C4×Dic59—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C4×Dic59C2×D412yes—
280C4×Dic59C2412yes—
281#11745664—44no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C8×D59—44no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59C22×D412yes—
291C23×C59C22×D411yescharacteristic
292C22×D59—22no—
293C22×D59—22no—
294C22×D59#13714yes—
295C22×D59C22×D412yes—
296Q8×C59—24no—
297Q8×C59—22no—
298Q8×C59—22no—
299Q8×C59—22no—
300Q8×C59—22no—
301Q8×C59—22no—
302Q8×C59—48no—
303Q8×C59—42no—
304Q8×C59—42no—
305Q8×C59C2×#4114yes—
306C2×C4×C59—24no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—24no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—48no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D411yescharacteristic
321C2×C4×C59C2×#4112yes—
322C2×C4×C59H(5,𝔽2)12yes—
323C2×C4×C59C2511yescharacteristic
324C22⋊D59—28no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—42no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59C22×D412yes—
337C2×Dic59C22×D412yes—
338C2×Dic59C22×D412yes—
339C4×D59—24no—
340C4×D59—22no—
341C4×D59—22no—
342C4×D59—48no—
343C4×D59—48no—
344Dic118—22no—
345Dic118—22no—
346Dic118—48no—
347Dic118—42no—
348C8×C59—22no—
349C8×C59—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3312—591nomaximal, Sylow
353C22×C59—22no—
354C22×C59—22no—
355C22×C59—22no—
356C22×C59—44no—
357C22×C59#54612yes—
358C22×C59C2×#13712yes—
359C22×C59#57812yes—
360C22×C59C23×D411yescharacteristic
361C2×D59—22no—
362C2×D59—28no—
363C2×D59—22no—
364C2×D59C2×#13714yes—
365C4×C59—24no—
366C4×C59—22no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59#54612yes—
371C4×C59C22×#4111yescharacteristic
372C4×C59C2×H(5,𝔽2)11yescharacteristic
373Dic59—22no—
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380C2×#552—591no—
381C2×D4×Q8—591no—
382#3312—5916no—
383C2×#491—591no—
384C2×#485—591no—
385C2×#483—591no—
386C2×#479—591no—
387C2×#470—591no—
388C2×#467—591no—
389C2×#462—591no—
390C2×#451—591no—
391C2×#451D5911yescharacteristic, complemented
392C2×#441—591no—
393C2×#435—591no—
394C2×#419—591no—
395C22×#103—591no—
396C2×C59—42no—
397C2×C59#331214yescomplemented
398C2×C59C2×#54611yescharacteristic
399C2×C59C22×#13711yescharacteristic
400C2×C59C2×#57811yescharacteristic
401D59—24no—
402C23×Q8—591no—
403C23×Q8C2×D5911yescharacteristic
404C22×Q16—591no—
405C22×Q16C2×D5911yescharacteristic
406C22×Q16C2×D5911yescharacteristic
407C22×M16—591no—
408C23×C8—591no—
409#552—598no—
410#552—1184no—
411D4×Q8—598no—
412D4×Q8—1184no—
413C2×C4⋊Q8—591no—
414C2×C4⋊Q8—1181no—
415C2×#126—1181no—
416C2×#125—591no—
417C2×#125—1181no—
418C2×#123—1181no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—591no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—1181no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8C2×D5911yescharacteristic
425C2×C4×Q8—591no—
426C2×C4×Q8—591no—
427C2×C4×D4—591no—
428C2×C4×D4—1181no—
429C2×#117—591no—
430C2×#117—1181no—
431C22×C4⋊C4—591no—
432#491—598no—
433#485—598no—
434#483—598no—
435#479—598no—
436#470—598no—
437#467—598no—
438#462—598no—
439#451—598no—
440#451C2×D5918yescomplemented
441#441—598no—
442#435—598no—
443C2×#107—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447#419—598no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#103—598no—
457C2×#103C2×D5911yescharacteristic
458C2×#103C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8C2×D5911yescharacteristic
461C2×#97—591no—
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—594no—
468C22×Q8—591no—
469C22×Q8—1181no—
470C22×Q8—1182no—
471C22×Q8—1184no—
472C22×Q8—2362no—
473C22×Q8C22×D5911yescharacteristic
474C22×Q8C22×D5911yescharacteristic
475C22×Q8C22×D5914yes—
476C22×Q8C22×D5911yescharacteristic
477C22×D4—591no—
478C23×C4—21no—
479C23×C4—591no—
480C23×C4—1181no—
481C23×C4—1181no—
482C23×C4C22×D5911yescharacteristic
483C2×Q16—24no—
484C2×Q16—42no—
485C2×Q16—594no—
486C2×Q16—2362no—
487C2×Q16C22×D5914yes—
488C2×Q16C22×D5914yes—
489C2×M16—594no—
490C2×M16—2362no—
491C22×C8—591no—
492C22×C8—591no—
493C22×C8—594no—
494C22×C8—2362no—
495C22×C8C22×D5911yescharacteristic
496C22×C8C22×D5911yescharacteristic
497C4⋊Q8—594no—
498C4⋊Q8—1182no—
499C4⋊Q8—1188no—
500#126—1188no—
501#125—594no—
502#125—1182no—
503#125—1188no—
504#123—1188no—
505C22⋊Q8—22no—
506C22⋊Q8—594no—
507C22⋊Q8—594no—
508C22⋊Q8—594no—
509C22⋊Q8—1188no—
510C22⋊Q8—1188no—
511C22⋊Q8—1182no—
512C22⋊Q8—1182no—
513C22⋊Q8—1182no—
514C22⋊Q8C22×D5914yes—
515C4×Q8—594no—
516C4×Q8—594no—
517C4×Q8—1182no—
518C4×Q8—1182no—
519C4×D4—594no—
520C4×D4—594no—
521C4×D4—1188no—
522#117—594no—
523#117—1188no—
524#117—1182no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—591no—
527C2×C4⋊C4—591no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C4⋊C4—594no—
531C2×C4⋊C4—1182no—
532C2×C4⋊C4—1181no—
533C2×C4⋊C4—1181no—
534C2×C4⋊C4—1181no—
535C2×C4⋊C4—1181no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—591no—
545C2×C22⋊C4—591no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C42—591no—
551C2×C42—1181no—
552C2×C42—1181no—
553C2×C42—1181no—
554#107—594no—
555#106—594no—
556#106—594no—
557C4⋊C8—594no—
558#103—594no—
559#103—594no—
560#103—594no—
561#103—594no—
562#103—594no—
563#103—594no—
564#103—594no—
565#103—594no—
566#103C22×D5914yes—
567#103C22×D5914yes—
568C22⋊C8—594no—
569C22⋊C8C22×D5914yes—
570#97—594no—
571C24—591no—
572C24D4×D5911yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—28no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—48no—
586C2×Q8—592no—
587C2×Q8—1184no—
588C2×Q8—1181no—
589C2×Q8—1188no—
590C2×Q8—1182no—
591C2×Q8—1182no—
592C2×Q8—2364no—
593C2×Q8—2364no—
594C2×Q8—2368no—
595C2×Q8#1174568714yes—
596C2×Q8C23×D5912yes—
597C2×Q8C23×D5912yes—
598C2×Q8C23×D5912yes—
599C2×D4—594no—
600C2×D4—1184no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—44no—
609C22×C4—591no—
610C22×C4—591no—
611C22×C4—591no—
612C22×C4—592no—
613C22×C4—592no—
614C22×C4—1184no—
615C22×C4—1184no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1181no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—2364no—
623C22×C4—2364no—
624C22×C4D4×D5912yes—
625C22×C4D4×D5911yescharacteristic
626C22×C4C23×D5912yes—
627C22×C4C23×D5911yescharacteristic
628Q16—28no—
629Q16—44no—
630Q16—2364no—
631M16—2364no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—1182no—
637C2×C8—1182no—
638C2×C8—2364no—
639C2×C8C23×D5912yes—
640C2×C8C23×D5912yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—594no—
644C4⋊C4—592no—
645C4⋊C4—592no—
646C4⋊C4—592no—
647C4⋊C4—1184no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1181no—
659C4⋊C4—1184no—
660C4⋊C4C23×D5912yes—
661C22⋊C4—24no—
662C22⋊C4—594no—
663C22⋊C4—594no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C42—592no—
669C42—592no—
670C42—1184no—
671C42—1184no—
672C42—1184no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—594no—
677C23—592no—
678C23—1182no—
679C23—1182no—
680C23C2×D4×D5912yes—
681C23C2×D4×D5911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—1182no—
692Q8—1182no—
693Q8—2368no—
694Q8—2362no—
695Q8C2×#1174568714yes—
696D4—1188no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—592no—
711C2×C4—592no—
712C2×C4—592no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1184no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—2368no—
724C2×C4—2368no—
725C2×C4—2362no—
726C2×C4—2362no—
727C2×C4—2362no—
728C2×C4—2362no—
729C2×C4C2×D4×D5912yes—
730C2×C4C2×D4×D5911yescharacteristic
731C2×C4C2×#1174568712yes—
732C2×C4#1427377212yes—
733C2×C4C24×D5911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1182no—
737C8—1182no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—594no—
743C22—1182no—
744C22—1182no—
745C22—1188no—
746C22#1683803912yes—
747C22#137×D5912yes—
748C22#1683821512yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1182no—
756C4—1182no—
757C4—1182no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683803912yes—
763C4C22×#1174568711yescharacteristic
764C4C2×#1427377211yescharacteristic
765C2—42no—
766C2—1184no—
767C2#2143614014yesdirect product factor
768C2C2×#1683803911yescharacteristic
769C2C2×#137×D5911yescharacteristic
770C2C2×#1683821511yescharacteristic
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×#3312
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. #21436140C2direct (N × H)
4. C2×#16837769C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837731C2semidirect
7. C2×#16837711C2semidirect
8. C2×#16837658C2semidirect
9. C2×#16837640C2semidirect
10. C2×#16837610C2semidirect
11. C2×#16837556C2semidirect
12. C2×#16837509C2semidirect
14. C2×#16837411C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#451C2semidirect
43. #16837769C22semidirect
44. #16837744C22semidirect
45. #16837731C22semidirect
46. #16837711C22semidirect
47. #16837658C22semidirect
48. #16837640C22semidirect
49. #16837610C22semidirect
50. #16837556C22semidirect
51. #16837509C22semidirect
57. #16837411C22semidirect
66. #103×D59C22semidirect
73. C59×#451C22semidirect
391. C2×#451D59semidirect
397. C2×C59#3312semidirect
440. #451C2×D59semidirect
462. C59C2×#3312semidirect
767. C2#21436140direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380862
C2×Q8×C22⋊D592
#214361402
C2×#168377692
C2×#168377442
C2×#168377312
C2×#168377112
C2×#168376582
C2×#168376402
C2×#168376102
C2×#168375562
C2×#168375092
C2×#168374762
C2×#168374112
C2×#103×D592
C2×C59×#4512
C2×#331259