Finite Group Databasebeta

← C2×#21436706 #29467422

Subgroups — C2×#21436706 #29467422

Order 15104.

1866 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838123C211yesmaximal, characteristic
2C2×#16838110C211yesmaximal, characteristic
3#21436706C2116yesmaximal, direct product factor
4C2×#16837799C211yesmaximal, characteristic, complemented
5C2×#16837742C211yesmaximal, characteristic, complemented
6C2×#16837740C211yesmaximal, characteristic, complemented
7C2×#16837731C211yesmaximal, characteristic, complemented
8C2×#16837730C211yesmaximal, characteristic, complemented
9C2×#16837695C211yesmaximal, characteristic, complemented
10C2×#16837685C211yesmaximal, characteristic, complemented
11C2×#16837657C211yesmaximal, characteristic, complemented
12C2×Q16×Dic59C211yesmaximal, characteristic, complemented
13C2×#16837478C211yesmaximal, characteristic
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#16837441C211yesmaximal, characteristic, complemented
16C2×C59×#470C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18#16838123—24no—
19#16838123C2218yes—
20#16838110—24no—
21#16838110C2218yes—
22C2×#14273726C2211yescharacteristic
23C2×#14273726C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273720—21no—
26C2×#14273717—21no—
27C2×#14273713—21no—
28C2×#14273707—21no—
29C2×#14273704—21no—
30C2×#14273703C2211yescharacteristic
31C2×#14273703C2211yescharacteristic
32C2×Q8×Dic59C2211yescharacteristic
33C2×Q8×Dic59C2211yescharacteristic
34C2×#14273692—21no—
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273686C2211yescharacteristic
38C2×#14273685C2211yescharacteristic
39C22×C4⋊Dic59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41#16837799C2218yescomplemented
42#16837742C2218yescomplemented
43#16837740C2218yescomplemented
44#16837731C2218yescomplemented
45#16837730C2218yescomplemented
46#16837695C2218yescomplemented
47#16837685C2218yescomplemented
48#16837657C2218yescomplemented
49Q16×Dic59C2218yescomplemented
50#16837478C2218yes—
51#16837444C2218yescomplemented
52#16837441C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#470C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×C22⋊D59D411yescharacteristic
80C23×Dic59—21no—
81C22×C4×D59—21no—
82C22×C4×D59C2311yescharacteristic
83C2×#11745659—24no—
84C2×#11745659C2314yes—
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87#14273726—22no—
88#14273726—22no—
89#14273726C2314yes—
90#14273726C2314yes—
91#14273722—28no—
92#14273720—28no—
93#14273717—28no—
94#14273713—28no—
95#14273707—28no—
96#14273704—28no—
97#14273703—22no—
98#14273703—22no—
99#14273703C2314yes—
100#14273703C2314yes—
101Q8×Dic59—22no—
102Q8×Dic59—22no—
103Q8×Dic59C2314yes—
104Q8×Dic59C2314yes—
105#14273692—28no—
106C4×C22⋊D59D414yes—
107C4×C22⋊D59C2314yes—
108(C22⋊D59)⋊C4—28no—
109#14273686—22no—
110#14273686C2314yes—
111#14273685—22no—
112#14273685C2314yes—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—22no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2314yes—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4D411yescharacteristic
128C4⋊C4×D59—22no—
129C4⋊C4×D59C2314yes—
130C2×C22⋊Dic59—21no—
131C2×C22⋊Dic59D411yescharacteristic
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4D411yescharacteristic
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273661C2314yes—
143#14273660C2314yes—
144#14273659C2314yes—
145#14273659C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154C22⋊(C59⋊C8)C2314yes—
155(C2×D59)⋊C8C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×Q8×C59C2311yescharacteristic
159C23×C4×C59C2311yescharacteristic
160C2×Q16×C59—24no—
161C2×Q16×C59C2314yes—
162C2×M16×C59—24no—
163C2×M16×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C22⋊Q8×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176#106×C59C2314yes—
177#103×C59C2314yes—
178#103×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59C2×D411yescharacteristic
181C2×Q8×C59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×Q8×C59C2412yes—
189C22×C4×C59—22no—
190C22×C4×C59—22no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—24no—
200C2×C22⋊D59C2×D414yes—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—24no—
206C22×Dic59—82no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—24no—
213C2×C4×D59—82no—
214C2×C4×D59C2×D412yes—
215C2×C4×D59C2412yes—
216C2×Dic118—24no—
217C2×Dic118—24no—
218C2×Dic118—44no—
219C2×Dic118—82no—
220Q16×C59—28no—
221M16×C59—28no—
222C2×C8×C59—22no—
223C2×C8×C59#4114yes—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—21no—
230C4⋊C4×C59C2412yes—
231C4⋊C4×C59C2412yes—
232C22⋊C4×C59—24no—
233C22⋊C4×C59—24no—
234C22⋊Dic59—24no—
235C22⋊Dic59C2×D414yes—
236(C2×D59)⋊C4—24no—
237(C2×D59)⋊C4—24no—
238(C2×D59)⋊C4—24no—
239(C2×D59)⋊C4C2×D414yes—
240C4⋊Dic59—21no—
241C4⋊Dic59—21no—
242C4⋊Dic59—24no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—24no—
246C4⋊Dic59—24no—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267#11745659—28no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59C22×D412yes—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59C22×D412yes—
277Q8×C59—22no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—22no—
281Q8×C59—42no—
282Q8×C59—42no—
283C2×C4×C59—22no—
284C2×C4×C59—24no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C592−1+412yes—
299C2×C4×C59C2511yescharacteristic
300C22⋊D59—28no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—84no—
312C2×Dic59#13714yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315C2×Dic59C22×D412yes—
316C4×D59—24no—
317C4×D59—22no—
318C4×D59—22no—
319C4×D59—84no—
320Dic118—48no—
321Dic118—84no—
322C8×C59—22no—
323C8×C59C2×#4114yes—
324C59⋊C8—22no—
325C59⋊C8—22no—
326C2×#3356—591nomaximal, Sylow
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—44no—
331C22×C59#54712yes—
332C22×C59C2×#13712yes—
333C22×C59#57712yes—
334C22×C59C23×D411yescharacteristic
335C2×D59—22no—
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—44no—
339C4×C59—22no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59#54712yes—
345C4×C59C22×#4111yescharacteristic
346C4×C59C2×2−1+411yescharacteristic
347Dic59—22no—
348Dic59—22no—
349Dic59—42no—
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
353Dic59C2×#13714yes—
354C2×#556—591no—
355C2×#554—591no—
356#3356—5916no—
357C2×#498—591no—
358C2×#485—591no—
359C2×#485—591no—
360C2×#483—591no—
361C2×#483—591no—
362C2×#477—591no—
363C2×#475—591no—
364C2×#470—591no—
365C2×#470D5911yescharacteristic, complemented
366C2×C4×Q16—591no—
367C2×#436—591no—
368C2×#428—591no—
369C2×#428—591no—
370C2×C59—42no—
371C2×C59#335614yescomplemented
372C2×C59C2×#54711yescharacteristic
373C2×C59C22×#13711yescharacteristic
374C2×C59C2×#57711yescharacteristic
375D59—42no—
376C22×Q16C2×D5911yescharacteristic
377C22×M16—591no—
378C22×M16C2×D5911yescharacteristic
379#556—598no—
380#556—1184no—
381#554—598no—
382#554—1184no—
383C2×C4⋊Q8—591no—
384C2×C4⋊Q8—591no—
385C2×#126—1181no—
386C2×#126—1181no—
387C2×#125—1181no—
388C2×#124—1181no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391C2×C22⋊Q8—1181no—
392C2×C22⋊Q8—1181no—
393C2×C22⋊Q8C2×D5911yescharacteristic
394C2×C22⋊Q8C2×D5911yescharacteristic
395C2×C4×Q8—591no—
396C2×C4×Q8—591no—
397C2×C4×Q8—1181no—
398C2×C4×D4—591no—
399C2×C4×D4—1181no—
400C2×#117—591no—
401C2×#117—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404#498—598no—
405#485—598no—
406#485—598no—
407#483—598no—
408#483—598no—
409#477—598no—
410#475—598no—
411#470—598no—
412#470C2×D5918yescomplemented
413C4×Q16—598no—
414#436—598no—
415#428—598no—
416#428—598no—
417C2×#107—591no—
418C2×#107—591no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×#106—591no—
423C2×#106—591no—
424C2×#106—591no—
425C2×#106C2×D5911yescharacteristic
426C2×C4⋊C8—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103—591no—
431C2×#103C2×D5911yescharacteristic
432C2×#103C2×D5911yescharacteristic
433C2×C22⋊C8—591no—
434C2×C22⋊C8—591no—
435C2×C4×C8—591no—
436C59C2×#335611yescharacteristic, complemented, Sylow
437C22×Q8—1181no—
438C22×Q8—1181no—
439C22×Q8C22×D5911yescharacteristic
440C22×Q8C22×D5911yescharacteristic
441C22×D4—591no—
442C23×C4—591no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C2×Q16—24no—
447C2×Q16C22×D5914yes—
448C2×M16—24no—
449C2×M16—594no—
450C2×M16—1184no—
451C2×M16C22×D5914yes—
452C22×C8—591no—
453C22×C8—591no—
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456C4⋊Q8—594no—
457C4⋊Q8—594no—
458C4⋊Q8—1182no—
459C4⋊Q8—1182no—
460#126—1188no—
461#126—1188no—
462#125—1188no—
463#124—1188no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—594no—
467C22⋊Q8—594no—
468C22⋊Q8—1188no—
469C22⋊Q8—1188no—
470C22⋊Q8—1182no—
471C22⋊Q8—1182no—
472C22⋊Q8C22×D5914yes—
473C22⋊Q8C22×D5914yes—
474C4×Q8—594no—
475C4×Q8—594no—
476C4×Q8—1182no—
477C4×Q8—1182no—
478C4×Q8—1188no—
479C4×D4—594no—
480C4×D4—594no—
481C4×D4—1188no—
482#117—594no—
483#117—594no—
484#117—1182no—
485#117—1182no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—594no—
492C2×C4⋊C4—591no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—594no—
495C2×C4⋊C4—1182no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1182no—
505C2×C4⋊C4C22×D5911yescharacteristic
506C2×C4⋊C4C22×D5911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—591no—
510C2×C22⋊C4—591no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C42—591no—
516C2×C42—1181no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42—1181no—
520#107—594no—
521#107—594no—
522#107—594no—
523#106—594no—
524#106—594no—
525#106—594no—
526#106—594no—
527#106—594no—
528#106C22×D5914yes—
529C4⋊C8—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103C22×D5914yes—
535#103C22×D5914yes—
536C22⋊C8—594no—
537C22⋊C8—594no—
538C4×C8—594no—
539C24—591no—
540C24D4×D5911yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—1184no—
548C2×Q8—1184no—
549C2×Q8—4722no—
550C2×Q8—2364no—
551C2×Q8C23×D5912yes—
552C2×Q8C23×D5912yes—
553C2×D4—594no—
554C2×D4—1184no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—591no—
562C22×C4—591no—
563C22×C4—591no—
564C22×C4—592no—
565C22×C4—592no—
566C22×C4—1184no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1184no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1181no—
574C22×C4—4722no—
575C22×C4—4722no—
576C22×C4D4×D5912yes—
577C22×C4D4×D5911yescharacteristic
578C22×C4C23×D5912yes—
579C22×C4C23×D5911yescharacteristic
580Q16—28no—
581M16—28no—
582M16—1188no—
583C2×C8—22no—
584C2×C8—592no—
585C2×C8—592no—
586C2×C8—1182no—
587C2×C8—1182no—
588C2×C8#1174568714yes—
589C2×C8C23×D5912yes—
590C2×C8C23×D5912yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—594no—
596C4⋊C4—592no—
597C4⋊C4—592no—
598C4⋊C4—592no—
599C4⋊C4—592no—
600C4⋊C4—1184no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1181no—
608C4⋊C4—1184no—
609C4⋊C4—1181no—
610C4⋊C4—1181no—
611C4⋊C4—1181no—
612C4⋊C4C23×D5912yes—
613C4⋊C4C23×D5912yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—594no—
617C22⋊C4—594no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C42—592no—
623C42—592no—
624C42—1184no—
625C42—1184no—
626C42—1184no—
627C42—1184no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—592no—
632C23—1182no—
633C23—1182no—
634C23—1182no—
635C23C2×D4×D5912yes—
636C23C2×D4×D5911yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—4724no—
644Q8—2368no—
645D4—1188no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—594no—
659C2×C4—592no—
660C2×C4—592no—
661C2×C4—592no—
662C2×C4—1182no—
663C2×C4—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1184no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—4724no—
672C2×C4—4724no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4—2362no—
677C2×C4C2×D4×D5912yes—
678C2×C4C2×D4×D5911yescharacteristic
679C2×C4C2×#1174568712yes—
680C2×C4#1427377412yes—
681C2×C4C24×D5911yescharacteristic
682C8—22no—
683C8—1182no—
684C8—1182no—
685C8C2×#1174568714yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—1182no—
691C22—1182no—
692C22—1182no—
693C22—2364no—
694C22#1683805212yes—
695C22#137×D5912yes—
696C22#1683821112yes—
697C22C22×D4×D5911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—594no—
704C4—1182no—
705C4—1182no—
706C4—2362no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C4#1683805212yes—
711C4C22×#1174568711yescharacteristic
712C4C2×#1427377411yescharacteristic
713C2—42no—
714C2—2362no—
715C2#2143670614yesdirect product factor
716C2C2×#1683805211yescharacteristic
717C2C2×#137×D5911yescharacteristic
718C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#470C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#470D59
hypocenterC59C2×#3356
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #21436706C2direct (N × H)
4. C2×#16837799C2semidirect
5. C2×#16837742C2semidirect
6. C2×#16837740C2semidirect
7. C2×#16837731C2semidirect
8. C2×#16837730C2semidirect
9. C2×#16837695C2semidirect
10. C2×#16837685C2semidirect
11. C2×#16837657C2semidirect
12. C2×Q16×Dic59C2semidirect
14. C2×#16837444C2semidirect
15. C2×#16837441C2semidirect
16. C2×C59×#470C2semidirect
41. #16837799C22semidirect
42. #16837742C22semidirect
43. #16837740C22semidirect
44. #16837731C22semidirect
45. #16837730C22semidirect
46. #16837695C22semidirect
47. #16837685C22semidirect
48. #16837657C22semidirect
49. Q16×Dic59C22semidirect
51. #16837444C22semidirect
52. #16837441C22semidirect
73. C59×#470C22semidirect
365. C2×#470D59semidirect
371. C2×C59#3356semidirect
412. #470C2×D59semidirect
436. C59C2×#3356semidirect
715. C2#21436706direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381232
C2×#168381102
#214367062
C2×#168377992
C2×#168377422
C2×#168377402
C2×#168377312
C2×#168377302
C2×#168376952
C2×#168376852
C2×#168376572
C2×Q16×Dic592
C2×#168374782
C2×#168374442
C2×#168374412
C2×C59×#4702
C2×#335659