Finite Group Databasebeta

← C2×#21436375 #29465570

Subgroups — C2×#21436375 #29465570

Order 15104.

2082 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×#16838120C211yesmaximal, characteristic
2C2×Q8×C22⋊D59C211yesmaximal, characteristic
3#21436375C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837743C211yesmaximal, characteristic, complemented
6C2×#16837741C211yesmaximal, characteristic, complemented
7C2×#16837685C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837659C211yesmaximal, characteristic, complemented
10C2×#16837611C211yesmaximal, characteristic, complemented
11C2×#16837559C211yesmaximal, characteristic, complemented
12C2×#16837558C211yesmaximal, characteristic, complemented
13C2×#16837494C211yesmaximal, characteristic, complemented
14C2×#16837478C211yesmaximal, characteristic
15C2×#16837409C211yesmaximal, characteristic, complemented
16C2×C59×#419C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22#16838120—24no—
23#16838120C2218yes—
24Q8×C22⋊D59—24no—
25Q8×C22⋊D59C2218yes—
26C2×#14273726C2211yescharacteristic
27C2×#14273725—21no—
28C2×#14273725C2211yescharacteristic
29C2×#14273721—21no—
30C2×#14273720—21no—
31C2×#14273713—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273706—21no—
34C2×#14273706C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36C2×#14273703—21no—
37C2×#14273703C2211yescharacteristic
38C2×Q8×Dic59C2211yescharacteristic
39C2×C4×Dic118—21no—
40C2×#14273692C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×#14273685C2211yescharacteristic
44#16837751C2218yescomplemented
45#16837743C2218yescomplemented
46#16837741C2218yescomplemented
47#16837685C2218yescomplemented
48#16837660C2218yescomplemented
49#16837659C2218yescomplemented
50#16837611C2218yescomplemented
51#16837559C2218yescomplemented
52#16837558C2218yescomplemented
53#16837494C2218yescomplemented
54#16837478C2218yes—
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59#16837409C2218yescomplemented
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C23×Q8×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#419C2218yescomplemented
73C2×#103×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59—42no—
84C2×Q8×D59C2314yes—
85C22×C22⋊D59D411yescharacteristic
86C22×C4×D59—21no—
87C22×C4×D59C2311yescharacteristic
88C2×Dic236—42no—
89C2×Dic236C2314yes—
90C2×#11745672—24no—
91C2×#11745672—42no—
92C2×#11745672C2314yes—
93C2×#11745672C2314yes—
94C2×#11745659—42no—
95C2×#11745659C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273726—22no—
99#14273726C2314yes—
100#14273725—28no—
101#14273725—22no—
102#14273725C2314yes—
103#14273721—28no—
104#14273720—28no—
105#14273713—28no—
106#14273707—22no—
107#14273707C2314yes—
108#14273706—22no—
109#14273706—22no—
110#14273706—28no—
111#14273706C2314yes—
112#14273706C2314yes—
113#14273703—22no—
114#14273703—28no—
115#14273703C2314yes—
116Q8×Dic59—22no—
117Q8×Dic59C2314yes—
118C4×Dic118—28no—
119#14273692—22no—
120#14273692C2314yes—
121C4×C22⋊D59—28no—
122C4×C22⋊D59D414yes—
123C4×C22⋊D59C2314yes—
124#14273685—22no—
125#14273685C2314yes—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2311yescharacteristic
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⋊C4—21no—
137C2×Dic59⋊C4D411yescharacteristic
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4D411yescharacteristic
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273659C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273651C2314yes—
156#14273651C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161C8×Dic59C2314yes—
162C22×Q8×C59—21no—
163C22×Q8×C59—22no—
164C22×Q8×C59—24no—
165C22×Q8×C59—42no—
166C22×Q8×C59C2311yescharacteristic
167C22×Q8×C59C2314yes—
168C22×Q8×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C2×M16×C59—42no—
172C2×M16×C59C2314yes—
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175#117×C59—22no—
176#117×C59C2314yes—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181#103×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—24no—
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—28no—
192C2×Q8×C59—22no—
193C2×Q8×C59—22no—
194C2×Q8×C59—44no—
195C2×Q8×C59—44no—
196C2×Q8×C59—48no—
197C2×Q8×C59#4114yes—
198C2×Q8×C59C2412yes—
199C2×Q8×C59C2412yes—
200C22×C4×C59—21no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—24no—
207C22×C4×C59—44no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—24no—
213C2×C22⋊D59C2×D414yes—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220C22×Dic59C2×D411yescharacteristic
221Q8×D59—28no—
222Q8×D59—44no—
223Q8×D59—48no—
224C2×C4×D59—22no—
225C2×C4×D59—22no—
226C2×C4×D59—24no—
227C2×C4×D59—44no—
228C2×C4×D59C2×D412yes—
229C2×C4×D59C2412yes—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—22no—
233C2×Dic118—22no—
234C2×Dic118—21no—
235C2×Dic118—21no—
236C2×Dic118—24no—
237C2×Dic118—24no—
238C2×Dic118—44no—
239C2×Dic118—44no—
240C2×Dic118C2412yes—
241C2×Dic118C2412yes—
242M16×C59—44no—
243C2×C8×C59—22no—
244C2×C8×C59—22no—
245C2×C8×C59C2412yes—
246C2×C8×C59C2412yes—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59C2412yes—
250C4⋊C4×C59C2412yes—
251C22⋊C4×C59—24no—
252C42×C59—24no—
253C22⋊Dic59—24no—
254C22⋊Dic59—24no—
255C22⋊Dic59C2×D414yes—
256#11745672—28no—
257#11745672—44no—
258(C2×D59)⋊C4—24no—
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—24no—
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—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285Dic236—44no—
286#11745659—44no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59C22×D412yes—
291C23×C59C22×D411yescharacteristic
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59C22×D412yes—
296Q8×C59—24no—
297Q8×C59—22no—
298Q8×C59—22no—
299Q8×C59—22no—
300Q8×C59—48no—
301Q8×C59—42no—
302Q8×C59C2×#4114yes—
303C2×C4×C59—24no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—24no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—48no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C2×#4112yes—
319C2×C4×C59H(5,𝔽2)12yes—
320C2×C4×C59C2511yescharacteristic
321C22⋊D59—28no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59#13714yes—
333C2×Dic59C22×D412yes—
334C2×Dic59C22×D412yes—
335C2×Dic59C22×D412yes—
336C4×D59—24no—
337C4×D59—22no—
338C4×D59—22no—
339C4×D59—48no—
340Dic118—22no—
341Dic118—22no—
342Dic118—22no—
343Dic118—22no—
344Dic118—48no—
345Dic118—42no—
346Dic118—42no—
347Dic118—48no—
348C8×C59—22no—
349C8×C59—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3328—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—22no—
363C2×D59—22no—
364C2×D59—44no—
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—42no—
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379Dic59C2×#13714yes—
380C2×#556—591no—
381C2×D4×Q8—591no—
382#3328—5916no—
383C2×#487—591no—
384C2×#485—591no—
385C2×#485—591no—
386C2×#475—591no—
387C2×#470—591no—
388C2×#470—591no—
389C2×#462—591no—
390C2×#451—591no—
391C2×#451—591no—
392C2×C4×Q16—591no—
393C2×#436—591no—
394C2×#419—591no—
395C2×#419D5911yescharacteristic, complemented
396C2×C59—42no—
397C2×C59#332814yescomplemented
398C2×C59C2×#54611yescharacteristic
399C2×C59C22×#13711yescharacteristic
400C2×C59C2×#57811yescharacteristic
401D59—42no—
402C23×Q8—591no—
403C23×Q8C2×D5911yescharacteristic
404C22×Q16—591no—
405C22×Q16—591no—
406C22×Q16—591no—
407C22×M16—591no—
408C22×M16C2×D5911yescharacteristic
409#556—598no—
410#556—1184no—
411D4×Q8—598no—
412D4×Q8—1184no—
413C2×C4⋊Q8—591no—
414C2×C4⋊Q8—591no—
415C2×C4⋊Q8—1181no—
416C2×#126—1181no—
417C2×#126—1181no—
418C2×#124—1181no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—591no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—591no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8—1181no—
425C2×C4×Q8—591no—
426C2×C4×Q8—591no—
427C2×C4×Q8—1181no—
428C2×C4×D4—591no—
429C2×C4×D4—1181no—
430C2×#117—591no—
431C2×#117C2×D5911yescharacteristic
432#487—598no—
433#485—598no—
434#485—598no—
435#475—598no—
436#470—598no—
437#470—598no—
438#462—598no—
439#451—598no—
440#451—598no—
441C4×Q16—598no—
442#436—598no—
443C2×#107—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447#419—598no—
448#419C2×D5918yescomplemented
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103C2×D5911yescharacteristic
456C2×#103C2×D5911yescharacteristic
457C2×#103C2×D5911yescharacteristic
458C2×#103C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×C4×C8—591no—
462C59C2×#332811yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—594no—
468C22×Q8—591no—
469C22×Q8—591no—
470C22×Q8—1181no—
471C22×Q8—1181no—
472C22×Q8—1182no—
473C22×Q8—1184no—
474C22×Q8—2362no—
475C22×Q8C22×D5911yescharacteristic
476C22×Q8C22×D5914yes—
477C22×Q8C22×D5911yescharacteristic
478C22×D4—591no—
479C23×C4—21no—
480C23×C4—591no—
481C23×C4—1181no—
482C23×C4C22×D5911yescharacteristic
483C2×Q16—594no—
484C2×Q16—594no—
485C2×Q16—594no—
486C2×Q16—1184no—
487C2×Q16—2362no—
488C2×Q16—2362no—
489C2×M16—42no—
490C2×M16—594no—
491C2×M16—2362no—
492C2×M16C22×D5914yes—
493C22×C8—591no—
494C22×C8—591no—
495C22×C8C22×D5911yescharacteristic
496C22×C8C22×D5911yescharacteristic
497C4⋊Q8—594no—
498C4⋊Q8—594no—
499C4⋊Q8—1182no—
500C4⋊Q8—1182no—
501C4⋊Q8—1188no—
502#126—1188no—
503#126—1188no—
504#124—1188no—
505C22⋊Q8—594no—
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⋊Q8—1182no—
515C4×Q8—594no—
516C4×Q8—594no—
517C4×Q8—1188no—
518C4×Q8—1182no—
519C4×Q8—1182no—
520C4×D4—594no—
521C4×D4—594no—
522C4×D4—1188no—
523#117—22no—
524#117—594no—
525#117—1182no—
526#117C22×D5914yes—
527C2×C4⋊C4—591no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
540C2×C4⋊C4C22×D5911yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—591no—
543C2×C22⋊C4—591no—
544C2×C22⋊C4—1181no—
545C2×C22⋊C4—1181no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C42—21no—
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#103C22×D5914yes—
565#103C22×D5914yes—
566#103C22×D5914yes—
567#103C22×D5914yes—
568C22⋊C8—594no—
569C22⋊C8—594no—
570C4×C8—594no—
571C24—591no—
572C24D4×D5911yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—28no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—592no—
584C2×Q8—592no—
585C2×Q8—1184no—
586C2×Q8—1184no—
587C2×Q8—1181no—
588C2×Q8—1181no—
589C2×Q8—1188no—
590C2×Q8—1182no—
591C2×Q8—1182no—
592C2×Q8—1182no—
593C2×Q8—1182no—
594C2×Q8—2364no—
595C2×Q8—2364no—
596C2×Q8—2364no—
597C2×Q8—2368no—
598C2×Q8#1174568514yes—
599C2×Q8C23×D5912yes—
600C2×Q8C23×D5912yes—
601C2×D4—594no—
602C2×D4—1184no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—591no—
612C22×C4—591no—
613C22×C4—591no—
614C22×C4—592no—
615C22×C4—592no—
616C22×C4—1184no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—2364no—
624C22×C4D4×D5912yes—
625C22×C4D4×D5911yescharacteristic
626C22×C4C23×D5912yes—
627C22×C4C23×D5911yescharacteristic
628Q16—1188no—
629Q16—2364no—
630Q16—2364no—
631M16—44no—
632M16—2364no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—592no—
636C2×C8—592no—
637C2×C8—1182no—
638C2×C8—1182no—
639C2×C8C23×D5912yes—
640C2×C8C23×D5912yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—594no—
644C4⋊C4—592no—
645C4⋊C4—592no—
646C4⋊C4—1184no—
647C4⋊C4—1184no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4C23×D5912yes—
658C4⋊C4C23×D5912yes—
659C22⋊C4—24no—
660C22⋊C4—594no—
661C22⋊C4—594no—
662C22⋊C4—1184no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C42—24no—
668C42—592no—
669C42—592no—
670C42—1184no—
671C42—1184no—
672C42—1184no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—592no—
677C23—1182no—
678C23—1182no—
679C23—1182no—
680C23C2×D4×D5912yes—
681C23C2×D4×D5911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—1182no—
689Q8—1182no—
690Q8—1182no—
691Q8—1182no—
692Q8—2368no—
693Q8—2368no—
694Q8—2362no—
695Q8—2362no—
696Q8C2×#1174568514yes—
697D4—1188no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—594no—
712C2×C4—592no—
713C2×C4—592no—
714C2×C4—592no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1184no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
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×#1174568512yes—
732C2×C4#1427377212yes—
733C2×C4C24×D5911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1182no—
737C8—1182no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—1182no—
743C22—1182no—
744C22—1182no—
745C22—2364no—
746C22#1683804212yes—
747C22#137×D5912yes—
748C22#1683821812yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—594no—
756C4—1182no—
757C4—1182no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683804212yes—
763C4C22×#1174568511yescharacteristic
764C4C2×#1427377211yescharacteristic
765C2—42no—
766C2—2362no—
767C2#2143637514yesdirect product factor
768C2C2×#1683804211yescharacteristic
769C2C2×#137×D5911yescharacteristic
770C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#419C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#419D59
hypocenterC59C2×#3328
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #21436375C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837743C2semidirect
6. C2×#16837741C2semidirect
7. C2×#16837685C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837659C2semidirect
10. C2×#16837611C2semidirect
11. C2×#16837559C2semidirect
12. C2×#16837558C2semidirect
13. C2×#16837494C2semidirect
15. C2×#16837409C2semidirect
16. C2×C59×#419C2semidirect
44. #16837751C22semidirect
45. #16837743C22semidirect
46. #16837741C22semidirect
47. #16837685C22semidirect
48. #16837660C22semidirect
49. #16837659C22semidirect
50. #16837611C22semidirect
51. #16837559C22semidirect
52. #16837558C22semidirect
53. #16837494C22semidirect
59. #16837409C22semidirect
72. C59×#419C22semidirect
395. C2×#419D59semidirect
397. C2×C59#3328semidirect
448. #419C2×D59semidirect
462. C59C2×#3328semidirect
767. C2#21436375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381202
C2×Q8×C22⋊D592
#214363752
C2×#168377512
C2×#168377432
C2×#168377412
C2×#168376852
C2×#168376602
C2×#168376592
C2×#168376112
C2×#168375592
C2×#168375582
C2×#168374942
C2×#168374782
C2×#168374092
C2×C59×#4192
C2×#332859