Finite Group Databasebeta

← C2×#21435970 #29465082

Subgroups — C2×#21435970 #29465082

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×#16838107C211yesmaximal, characteristic
2C2×#16838065C211yesmaximal, characteristic
3#21435970C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837696C211yesmaximal, characteristic, complemented
7C2×#16837644C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837611C211yesmaximal, characteristic, complemented
10C2×#16837560C211yesmaximal, characteristic, complemented
11C2×#16837559C211yesmaximal, characteristic, complemented
12C2×#16837496C211yesmaximal, characteristic, complemented
13C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic
14C22×#14273650C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#484C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745672C2211yescharacteristic
22C23×C59⋊C8C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16838107—24no—
25#16838107C2218yes—
26#16838065—24no—
27#16838065C2218yes—
28C2×#14273726—21no—
29C2×#14273726C2211yescharacteristic
30C2×#14273725C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273707C2211yescharacteristic
34C2×#14273706—21no—
35C2×#14273706C2211yescharacteristic
36C2×#14273705—21no—
37C2×#14273705—21no—
38C2×#14273704—21no—
39C2×#14273692C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×(C22⋊D59)⋊C4—21no—
44C2×C4⋊C4×D59C2211yescharacteristic
45#16837751C2218yescomplemented
46#16837739C2218yescomplemented
47#16837696C2218yescomplemented
48#16837644C2218yescomplemented
49#16837641C2218yescomplemented
50#16837611C2218yescomplemented
51#16837560C2218yescomplemented
52#16837559C2218yescomplemented
53#16837496C2218yescomplemented
54(C22⋊D59)⋊C8C2218yes—
55C2×#14273660C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2218yescomplemented
66#103×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#484C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—24no—
78C22×Dic118—21no—
79C22×Dic118—22no—
80C22×Dic118—21no—
81C22×Dic118—21no—
82C22×Dic118—42no—
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2311yescharacteristic
85C22×Dic118C2314yes—
86C22×Dic118C2311yescharacteristic
87C2×Q8×D59—22no—
88C2×Q8×D59—24no—
89C2×Q8×D59—42no—
90C2×Q8×D59C2314yes—
91C22×C22⋊D59D411yescharacteristic
92C23×Dic59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59C2311yescharacteristic
96C2×Dic236—24no—
97C2×Dic236—42no—
98C2×Dic236C2314yes—
99C2×Dic236C2314yes—
100C2×#11745672—42no—
101C2×#11745672C2314yes—
102C22×C59⋊C8—42no—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2314yes—
106C2×C8×D59—42no—
107C2×C8×D59C2314yes—
108#14273726—28no—
109#14273726—22no—
110#14273726C2314yes—
111#14273725—22no—
112#14273725C2314yes—
113#14273717—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707C2314yes—
117#14273707C2314yes—
118#14273706—22no—
119#14273706—28no—
120#14273706C2314yes—
121#14273705—28no—
122#14273705—28no—
123#14273704—28no—
124#14273692—22no—
125#14273692—22no—
126#14273692C2314yes—
127#14273692C2314yes—
128C4×C22⋊D59—28no—
129C4×C22⋊D59D414yes—
130C4×C22⋊D59C2314yes—
131(C22⋊D59)⋊C4—28no—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59C2311yescharacteristic
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4D411yescharacteristic
143C4⋊C4×D59—22no—
144C4⋊C4×D59C2314yes—
145C2×C22⋊Dic59—21no—
146C2×C22⋊Dic59D411yescharacteristic
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59C2311yescharacteristic
153#14273660C2314yes—
154Dic59⋊C8C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162#14273650C2314yes—
163(C2×D59)⋊C8C2314yes—
164C8×Dic59C2314yes—
165C22×Q8×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—22no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2314yes—
179C2×C22⋊C4×C59—21no—
180#107×C59C2314yes—
181#107×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59C2412yes—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—24no—
198C22×C4×C59—82no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C2×C22⋊D59Q1618yescomplemented
204C2×C22⋊D59C2×D414yes—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—44no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214Q8×D59—28no—
215Q8×D59—44no—
216Q8×D59—48no—
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59—24no—
220C2×C4×D59—24no—
221C2×C4×D59—44no—
222C2×C4×D59—82no—
223C2×C4×D59C2×D412yes—
224C2×C4×D59C2412yes—
225C2×Dic118—21no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—28no—
232C2×Dic118—21no—
233C2×Dic118—24no—
234C2×Dic118—21no—
235C2×Dic118—24no—
236C2×Dic118—24no—
237C2×Dic118—44no—
238C2×Dic118—48no—
239C2×Dic118—44no—
240C2×Dic118—44no—
241C2×Dic118—82no—
242C2×Dic118#4114yes—
243C2×Dic118C2412yes—
244C2×Dic118C2412yes—
245C2×Dic118C2412yes—
246C2×C8×C59—22no—
247C2×C8×C59—22no—
248C2×C8×C59C2412yes—
249C2×C8×C59C2412yes—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C22⋊C4×C59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59C2×D414yes—
261#11745672—44no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4C2×D414yes—
265C4⋊Dic59—21no—
266C4⋊Dic59—24no—
267C4⋊Dic59—24no—
268C4⋊Dic59C2412yes—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4C2×D414yes—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C4×Dic59C2×D412yes—
280C4×Dic59C2412yes—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—44no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286Dic236—28no—
287Dic236—44no—
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—22no—
299Q8×C59—22no—
300Q8×C59—42no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59—42no—
313C2×C4×C59—84no—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D411yescharacteristic
316C2×C4×C59C2×#4112yes—
317C2×C4×C59H(5,𝔽2)12yes—
318C2×C4×C59C2511yescharacteristic
319C22⋊D59C2×Q16116yescomplemented
320C2×Dic59—24no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—48no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59C2×Q1614yes—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334C2×Dic59C22×D412yes—
335C4×D59—24no—
336C4×D59—22no—
337C4×D59—22no—
338C4×D59—48no—
339C4×D59—84no—
340Dic118—24no—
341Dic118—22no—
342Dic118—22no—
343Dic118—22no—
344Dic118—22no—
345Dic118—22no—
346Dic118—48no—
347Dic118—48no—
348Dic118—42no—
349Dic118—42no—
350Dic118—84no—
351Dic118C2×#4114yes—
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—22no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59#54612yes—
375C4×C59C22×#4111yescharacteristic
376C4×C59C2×H(5,𝔽2)11yescharacteristic
377Dic59—24no—
378Dic59—22no—
379Dic59—22no—
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×#484D5911yescharacteristic, complemented
390C2×#477—591no—
391C2×#467—591no—
392C2×#467—591no—
393C2×#462—591no—
394C2×#451—591no—
395C2×#451—591no—
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×Q8—591no—
408C22×Q16—591no—
409C22×Q16—591no—
410C22×Q16—591no—
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⋊C4C2×D5911yescharacteristic
436#487—598no—
437#484—598no—
438#484C2×D5918yescomplemented
439#477—598no—
440#467—598no—
441#467—598no—
442#462—598no—
443#451—598no—
444#451—598no—
445C4×Q16—598no—
446C8×D4—598no—
447C2×#107—591no—
448C2×#107C2×D5911yescharacteristic
449C2×#107C2×D5911yescharacteristic
450C2×C4⋊C8—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#103—591no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—598no—
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—594no—
468C22×Q8—591no—
469C22×Q8—591no—
470C22×Q8—591no—
471C22×Q8—594no—
472C22×Q8—1181no—
473C22×Q8—1181no—
474C22×Q8—1184no—
475C22×Q8—1182no—
476C22×Q8—1181no—
477C22×Q8—1182no—
478C22×Q8—1184no—
479C22×Q8—2362no—
480C22×Q8—2362no—
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—594no—
490C2×Q16—594no—
491C2×Q16—594no—
492C2×Q16—1184no—
493C2×Q16—2362no—
494C2×Q16—2362no—
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—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—594no—
535C2×C4⋊C4—1182no—
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⋊C4—1181no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4C22×D5911yescharacteristic
546C2×C4⋊C4C22×D5911yescharacteristic
547C2×C4⋊C4C22×D5914yes—
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#107C22×D5914yes—
560#107C22×D5914yes—
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—22no—
579C2×Q8—22no—
580C2×Q8—594no—
581C2×Q8—592no—
582C2×Q8—592no—
583C2×Q8—592no—
584C2×Q8—1184no—
585C2×Q8—1184no—
586C2×Q8—1188no—
587C2×Q8—1181no—
588C2×Q8—1181no—
589C2×Q8—1184no—
590C2×Q8—1181no—
591C2×Q8—1182no—
592C2×Q8—1188no—
593C2×Q8—1182no—
594C2×Q8—1182no—
595C2×Q8—1182no—
596C2×Q8—1182no—
597C2×Q8—4722no—
598C2×Q8—2364no—
599C2×Q8—2364no—
600C2×Q8—2368no—
601C2×Q8—2364no—
602C2×Q8—2364no—
603C2×Q8—2368no—
604C2×Q8C23×D5912yes—
605C2×D4—598no—
606C2×D4—594no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—82no—
615C22×C4—591no—
616C22×C4—591no—
617C22×C4—591no—
618C22×C4—592no—
619C22×C4—592no—
620C22×C4—1184no—
621C22×C4—1184no—
622C22×C4—1181no—
623C22×C4—1182no—
624C22×C4—1182no—
625C22×C4—1184no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—1181no—
629C22×C4—4722no—
630C22×C4—2364no—
631C22×C4—2364no—
632C22×C4D4×D5912yes—
633C22×C4D4×D5911yescharacteristic
634C22×C4C23×D5912yes—
635C22×C4C23×D5911yescharacteristic
636Q16—1188no—
637Q16—2364no—
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—21no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—594no—
655C4⋊C4—592no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4—1184no—
662C4⋊C4—1184no—
663C4⋊C4—1184no—
664C4⋊C4—1181no—
665C4⋊C4—1184no—
666C4⋊C4C23×D5912yes—
667C4⋊C4C23×D5912yes—
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—22no—
690Q8—42no—
691Q8—594no—
692Q8—1182no—
693Q8—1184no—
694Q8—1182no—
695Q8—1182no—
696Q8—1182no—
697Q8—1182no—
698Q8—4724no—
699Q8—2368no—
700Q8—2368no—
701Q8—2362no—
702Q8—2362no—
703D4—5916no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—594no—
718C2×C4—592no—
719C2×C4—592no—
720C2×C4—592no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1184no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1184no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—4724no—
732C2×C4—2368no—
733C2×C4—2368no—
734C2×C4—2362no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4C2×D4×D5912yes—
738C2×C4C2×D4×D5911yescharacteristic
739C2×C4#41×D5912yes—
740C2×C4#1427377312yes—
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#1683804412yes—
754C22C2×Q16×D5914yes—
755C22C2×Q16×D5912yes—
756C22#1683821212yes—
757C22C22×D4×D5911yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—594no—
764C4—1182no—
765C4—1184no—
766C4—1182no—
767C4—2362no—
768C4—2362no—
769C4—2362no—
770C4#1683804412yes—
771C4C2×#41×D5911yescharacteristic
772C4C2×#1427377311yescharacteristic
773C2—24no—
774C2—1184no—
775C2#2143597014yesdirect product factor
776C2C2×#1683804411yescharacteristic
777C2C22×Q16×D5911yescharacteristic
778C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#484C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#484D59
hypocenterC59C2×#3299
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #21435970C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837696C2semidirect
7. C2×#16837644C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837611C2semidirect
10. C2×#16837560C2semidirect
11. C2×#16837559C2semidirect
12. C2×#16837496C2semidirect
14. C22×#14273650C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#484C2semidirect
45. #16837751C22semidirect
46. #16837739C22semidirect
47. #16837696C22semidirect
48. #16837644C22semidirect
49. #16837641C22semidirect
50. #16837611C22semidirect
51. #16837560C22semidirect
52. #16837559C22semidirect
53. #16837496C22semidirect
65. C2×#14273650C22semidirect
66. #103×D59C22semidirect
71. C59×#484C22semidirect
203. C2×C22⋊D59Q16semidirect
319. C22⋊D59C2×Q16semidirect
389. C2×#484D59semidirect
401. C2×C59#3299semidirect
438. #484C2×D59semidirect
466. C59C2×#3299semidirect
775. C2#21435970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381072
C2×#168380652
#214359702
C2×#168377512
C2×#168377392
C2×#168376962
C2×#168376442
C2×#168376412
C2×#168376112
C2×#168375602
C2×#168375592
C2×#168374962
C2×(C22⋊D59)⋊C82
C22×#142736502
C2×#103×D592
C2×C59×#4842
C2×#329959