Finite Group Databasebeta

← C2×#21435956 #29465067

Subgroups — C2×#21435956 #29465067

Order 15104.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838065C211yesmaximal, characteristic, complemented
2C2×#16838052C211yesmaximal, characteristic
3#21435956C2116yesmaximal, direct product factor
4C2×#16837751C211yesmaximal, characteristic, complemented
5C2×#16837734C211yesmaximal, characteristic, complemented
6C2×#16837730C211yesmaximal, characteristic, complemented
7C2×#16837686C211yesmaximal, characteristic, complemented
8C2×#16837630C211yesmaximal, characteristic, complemented
9C2×#16837605C211yesmaximal, characteristic, complemented
10C2×#16837540C211yesmaximal, characteristic, complemented
11C2×#16837539C211yesmaximal, characteristic, complemented
12C2×#16837493C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
14C22×#14273652C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#465C211yesmaximal, characteristic, complemented
17C22×#11745687—21no—
18C23×Dic118C2211yescharacteristic
19C22×Q8×D59C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C22×C8×D59C2211yescharacteristic
23#16838065—24no—
24#16838065C2218yescomplemented
25#16838052—24no—
26#16838052C2218yes—
27C2×#14273726—21no—
28C2×#14273726C2211yescharacteristic
29C2×#14273725C2211yescharacteristic
30C2×#14273709—21no—
31C2×#14273708—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273705—21no—
34C2×#14273704—21no—
35C2×#14273704—21no—
36C2×#14273698C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×(C22⋊D59)⋊C4—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837751C2218yescomplemented
44#16837734C2218yescomplemented
45#16837730C2218yescomplemented
46#16837686C2218yescomplemented
47#16837630C2218yescomplemented
48#16837605C2218yescomplemented
49#16837540C2218yescomplemented
50#16837539C2218yescomplemented
51#16837493C2218yescomplemented
52C8×C22⋊D59C2218yescomplemented
53C2×#14273658C2211yescharacteristic
54C2×#14273658C2211yescharacteristic
55C2×Dic59⋊C8C2211yescharacteristic
56C2×#14273652C2211yescharacteristic
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2218yescomplemented
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65#103×D59C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#465C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×#11745687—28no—
78C2×#11745687—48no—
79C22×Dic118—24no—
80C22×Dic118—21no—
81C22×Dic118—22no—
82C22×Dic118—21no—
83C22×Dic118—21no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2314yes—
87C22×Dic118C2311yescharacteristic
88C2×Q8×D59—22no—
89C2×Q8×D59—24no—
90C2×Q8×D59—42no—
91C2×Q8×D59C2314yes—
92C22×C22⋊D59—21no—
93C22×C22⋊D59D411yescharacteristic
94C23×Dic59—21no—
95C23×Dic59—21no—
96C23×Dic59—21no—
97C22×C4×D59—21no—
98C22×C4×D59—21no—
99C22×C4×D59C2311yescharacteristic
100C2×#11745670—24no—
101C2×#11745670—42no—
102C2×#11745670C2314yes—
103C2×#11745670C2314yes—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—42no—
107C2×C8×D59C2314yes—
108#14273726—28no—
109#14273726—22no—
110#14273726C2314yes—
111#14273725—22no—
112#14273725C2314yes—
113#14273709—28no—
114#14273708—28no—
115#14273707—22no—
116#14273707C2314yes—
117#14273705—28no—
118#14273704—28no—
119#14273704—28no—
120#14273698—22no—
121#14273698C2314yes—
122#14273692—22no—
123#14273692C2314yes—
124D4×Dic59—22no—
125D4×Dic59C2314yes—
126C4×C22⋊D59D414yes—
127C4×C22⋊D59C2314yes—
128(C22⋊D59)⋊C4—28no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—22no—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2314yes—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4D411yescharacteristic
141C4⋊C4×D59—22no—
142C4⋊C4×D59C2314yes—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59D411yescharacteristic
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4D411yescharacteristic
148C2×C4×Dic59—21no—
149C2×C4×Dic59C2311yescharacteristic
150#14273658C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273651C2314yes—
158#14273651C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161C22⋊(C59⋊C8)C2314yes—
162(C2×D59)⋊C8C2314yes—
163C8×Dic59C2314yes—
164C22×Q8×C59C2311yescharacteristic
165C22×D4×C59—21no—
166C22×D4×C59C2311yescharacteristic
167C23×C4×C59C2311yescharacteristic
168C2×SD16×C59—42no—
169C2×SD16×C59C2314yes—
170C22×C8×C59—42no—
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2314yes—
174C22⋊Q8×C59—22no—
175C22⋊Q8×C59C2314yes—
176#121×C59—22no—
177#121×C59C2314yes—
178C2×C4⋊C4×C59—21no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59—21no—
183#106×C59C2314yes—
184#103×C59C2314yes—
185#102×C59C2314yes—
186C24×C59—21no—
187C24×C59C2×D411yescharacteristic
188C23×D59C2×D411yescharacteristic
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59C2412yes—
193C2×D4×C59—24no—
194C2×D4×C59—21no—
195C2×D4×C59—22no—
196C2×D4×C59—22no—
197C2×D4×C59—44no—
198C2×D4×C59C2412yes—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2412yes—
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—24no—
209C2×C22⋊D59—44no—
210C2×C22⋊D59SD1618yescomplemented
211C2×C22⋊D59C2×D414yes—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—24no—
218C22×Dic59—24no—
219C22×Dic59—44no—
220C22×Dic59—44no—
221C22×Dic59—44no—
222C22×Dic59C2×D411yescharacteristic
223C22×Dic59C2×D411yescharacteristic
224C22×Dic59C2×D411yescharacteristic
225Q8×D59—28no—
226Q8×D59—44no—
227Q8×D59—48no—
228#11745687—432no—
229C2×C4×D59—22no—
230C2×C4×D59—22no—
231C2×C4×D59—24no—
232C2×C4×D59—24no—
233C2×C4×D59—44no—
234C2×C4×D59—44no—
235C2×C4×D59C2×D412yes—
236C2×C4×D59C2412yes—
237C2×Dic118—21no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—22no—
241C2×Dic118—28no—
242C2×Dic118—24no—
243C2×Dic118—21no—
244C2×Dic118—24no—
245C2×Dic118—24no—
246C2×Dic118—44no—
247C2×Dic118—48no—
248C2×Dic118—44no—
249C2×Dic118—44no—
250C2×Dic118—44no—
251C2×Dic118#4114yescomplemented
252C2×Dic118C2412yes—
253C2×Dic118C2412yes—
254SD16×C59—44no—
255C2×C8×C59—22no—
256C2×C8×C59—22no—
257C2×C8×C59—44no—
258C2×C8×C59C2412yes—
259C2×C8×C59C2412yes—
260C4⋊C4×C59—24no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59C2412yes—
264C4⋊C4×C59C2412yes—
265C22⋊C4×C59—24no—
266C22⋊C4×C59—24no—
267C22⋊Dic59—24no—
268C22⋊Dic59—24no—
269C22⋊Dic59C2×D414yes—
270#11745670—28no—
271#11745670—44no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4C2×D414yes—
274C4⋊Dic59—21no—
275C4⋊Dic59—21no—
276C4⋊Dic59—24no—
277C4⋊Dic59—24no—
278C4⋊Dic59C2412yes—
279C4⋊Dic59C2412yes—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285Dic59⋊C4C2×D414yes—
286C4×Dic59—24no—
287C4×Dic59C2×D412yes—
288C4×Dic59C2412yes—
289C2×C59⋊C8—22no—
290C2×C59⋊C8—22no—
291C2×C59⋊C8C2412yes—
292C2×C59⋊C8C2412yes—
293C8×D59—44no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59C2×SD1614yes—
301C23×C59C22×D412yes—
302C23×C59C22×D411yescharacteristic
303C22×D59—22no—
304C22×D59—22no—
305C22×D59C2×SD1614yes—
306C22×D59C22×D412yes—
307Q8×C59—22no—
308Q8×C59—22no—
309Q8×C59—42no—
310D4×C59—22no—
311D4×C59—22no—
312D4×C59—48no—
313D4×C59—42no—
314C2×C4×C59—22no—
315C2×C4×C59—24no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D411yescharacteristic
326C2×C4×C59C2×#4112yes—
327C2×C4×C59H(5,𝔽2)12yes—
328C2×C4×C59C2511yescharacteristic
329C22⋊D59—48no—
330C22⋊D59C2×SD16116yescomplemented
331C2×Dic59—24no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—48no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—48no—
343C2×Dic59—48no—
344C2×Dic59C2×SD1614yes—
345C2×Dic59C22×D412yes—
346C2×Dic59C22×D412yes—
347C2×Dic59C22×D412yes—
348C4×D59—24no—
349C4×D59—22no—
350C4×D59—22no—
351C4×D59—48no—
352C4×D59—48no—
353Dic118—24no—
354Dic118—22no—
355Dic118—22no—
356Dic118—22no—
357Dic118—48no—
358Dic118—48no—
359Dic118—42no—
360Dic118—48no—
361Dic118C2×#4114yescomplemented
362C8×C59—22no—
363C8×C59—22no—
364C59⋊C8—22no—
365C59⋊C8—22no—
366C2×#3298—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—28no—
369C22×C59—22no—
370C22×C59—42no—
371C22×C59—42no—
372C22×C59—42no—
373C22×C59—84no—
374C22×C59#54612yes—
375C22×C59C22×SD1614yes—
376C22×C59C22×SD1612yes—
377C22×C59#57812yes—
378C22×C59C23×D411yescharacteristic
379C2×D59—22no—
380C2×D59—28no—
381C2×D59—22no—
382C2×D59C22×SD1614yes—
383C4×C59—22no—
384C4×C59—42no—
385C4×C59—42no—
386C4×C59—42no—
387C4×C59#54612yes—
388C4×C59C22×#4111yescharacteristic
389C4×C59C2×H(5,𝔽2)11yescharacteristic
390Dic59—24no—
391Dic59—22no—
392Dic59—22no—
393Dic59—42no—
394Dic59—42no—
395Dic59—42no—
396Dic59C22×SD1614yes—
397C2×D4×Q8—591no—
398C2×#547—591no—
399#3298—5916no—
400C2×#487—591no—
401C2×#483—591no—
402C2×#483—591no—
403C2×#475—591no—
404C2×#465—591no—
405C2×#465D5911yescharacteristic, complemented
406C2×#461—591no—
407C2×#448—591no—
408C2×#448—591no—
409C2×C4×SD16—591no—
410C2×C8×D4—591no—
411C22×#103—591no—
412C22×#103—591no—
413C2×C59—24no—
414C2×C59—82no—
415C2×C59#329814yescomplemented
416C2×C59C2×#54611yescharacteristic
417C2×C59C23×SD1611yescharacteristic
418C2×C59C2×#57811yescharacteristic
419D59—24no—
420C22×#41—1181no—
421C23×Q8—591no—
422C23×Q8—591no—
423C22×SD16—591no—
424C22×SD16—591no—
425C22×SD16C2×D5911yescharacteristic
426C23×C8—591no—
427C23×C8C2×D5911yescharacteristic
428D4×Q8—598no—
429D4×Q8—1184no—
430#547—598no—
431#547—1184no—
432C2×C4⋊Q8—591no—
433C2×C4⋊Q8—591no—
434C2×C4⋊Q8—1181no—
435C2×#123—1181no—
436C2×#123—1181no—
437C2×C22⋊Q8—591no—
438C2×C22⋊Q8—1181no—
439C2×C22⋊Q8—1181no—
440C2×C22⋊Q8—1181no—
441C2×C22⋊Q8C2×D5911yescharacteristic
442C2×#121—591no—
443C2×#121C2×D5911yescharacteristic
444C2×C4×Q8—591no—
445C2×C4×D4—591no—
446C2×C4×D4—591no—
447C2×C4×D4—1181no—
448C22×C4⋊C4—591no—
449C22×C4⋊C4—591no—
450#487—598no—
451#483—598no—
452#483—598no—
453#475—598no—
454#465—598no—
455#465C2×D5918yescomplemented
456#461—598no—
457#448—598no—
458#448—598no—
459C4×SD16—598no—
460C8×D4—598no—
461C2×#106—591no—
462C2×#106—591no—
463C2×#106C2×D5911yescharacteristic
464C2×C4⋊C8—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103—591no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—598no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103—598no—
475C2×#103C2×D5911yescharacteristic
476C2×#102C2×D5911yescharacteristic
477C2×C22⋊C8—591no—
478C2×C22⋊C8—591no—
479C2×C4×C8—591no—
480C59C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—1188no—
482C2×#41—2368no—
483C22×Q8—594no—
484C22×Q8—591no—
485C22×Q8—591no—
486C22×Q8—594no—
487C22×Q8—1181no—
488C22×Q8—1181no—
489C22×Q8—1184no—
490C22×Q8—1182no—
491C22×Q8—1181no—
492C22×Q8—1182no—
493C22×Q8—1184no—
494C22×Q8—2362no—
495C22×Q8—2362no—
496C22×Q8C22×D5911yescharacteristic
497C22×D4—21no—
498C22×D4—591no—
499C22×D4—1181no—
500C22×D4C22×D5911yescharacteristic
501C23×C4—591no—
502C23×C4—1181no—
503C23×C4—1181no—
504C23×C4—1181no—
505C23×C4—1181no—
506C23×C4—1181no—
507C23×C4C22×D5911yescharacteristic
508C2×SD16—42no—
509C2×SD16—594no—
510C2×SD16—594no—
511C2×SD16—1184no—
512C2×SD16—2362no—
513C2×SD16C22×D5914yes—
514C22×C8—42no—
515C22×C8—591no—
516C22×C8—591no—
517C22×C8—594no—
518C22×C8—2362no—
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5911yescharacteristic
521C22×C8C22×D5914yes—
522C4⋊Q8—594no—
523C4⋊Q8—594no—
524C4⋊Q8—1182no—
525C4⋊Q8—1182no—
526C4⋊Q8—1188no—
527#123—1188no—
528#123—1188no—
529C22⋊Q8—22no—
530C22⋊Q8—594no—
531C22⋊Q8—1188no—
532C22⋊Q8—1188no—
533C22⋊Q8—1188no—
534C22⋊Q8—1182no—
535C22⋊Q8C22×D5914yes—
536#121—22no—
537#121—594no—
538#121—1182no—
539#121C22×D5914yes—
540C4×Q8—594no—
541C4×Q8—1182no—
542C4×D4—594no—
543C4×D4—594no—
544C4×D4—594no—
545C4×D4—1182no—
546C4×D4—1188no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—591no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—594no—
552C2×C4⋊C4—594no—
553C2×C4⋊C4—1182no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4—1181no—
561C2×C4⋊C4—1182no—
562C2×C4⋊C4C22×D5911yescharacteristic
563C2×C4⋊C4C22×D5911yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—591no—
567C2×C22⋊C4—591no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C42—591no—
572C2×C42—1181no—
573#106—594no—
574#106—594no—
575#106C22×D5914yes—
576C4⋊C8—594no—
577#103—594no—
578#103—594no—
579#103—594no—
580#103—594no—
581#103—594no—
582#103—594no—
583#103—594no—
584#103—594no—
585#103C22×D5914yes—
586#102C22×D5914yes—
587C22⋊C8—594no—
588C22⋊C8—594no—
589C4×C8—594no—
590C24—21no—
591C24—591no—
592C24D4×D5911yescharacteristic
593#41—23632no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—594no—
598C2×Q8—592no—
599C2×Q8—592no—
600C2×Q8—1184no—
601C2×Q8—1184no—
602C2×Q8—1188no—
603C2×Q8—1181no—
604C2×Q8—1184no—
605C2×Q8—1181no—
606C2×Q8—1182no—
607C2×Q8—1188no—
608C2×Q8—1182no—
609C2×Q8—1182no—
610C2×Q8—2364no—
611C2×Q8—2364no—
612C2×Q8—2368no—
613C2×Q8—2364no—
614C2×Q8—2364no—
615C2×Q8—2364no—
616C2×Q8—2368no—
617C2×Q8C23×D5912yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—598no—
624C2×D4—594no—
625C2×D4—1184no—
626C2×D4—2364no—
627C2×D4C23×D5912yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—591no—
634C22×C4—591no—
635C22×C4—591no—
636C22×C4—592no—
637C22×C4—592no—
638C22×C4—1184no—
639C22×C4—1184no—
640C22×C4—1184no—
641C22×C4—1181no—
642C22×C4—1182no—
643C22×C4—1182no—
644C22×C4—1184no—
645C22×C4—1184no—
646C22×C4—1181no—
647C22×C4—1181no—
648C22×C4—1181no—
649C22×C4—2364no—
650C22×C4—2364no—
651C22×C4—2364no—
652C22×C4—2364no—
653C22×C4—2364no—
654C22×C4D4×D5912yes—
655C22×C4D4×D5911yescharacteristic
656C22×C4C23×D5912yes—
657C22×C4C23×D5911yescharacteristic
658SD16—44no—
659SD16—1188no—
660SD16—2364no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—592no—
665C2×C8—592no—
666C2×C8—1182no—
667C2×C8—1182no—
668C2×C8—2364no—
669C2×C8C23×D5912yes—
670C2×C8C23×D5912yes—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—594no—
675C4⋊C4—592no—
676C4⋊C4—592no—
677C4⋊C4—1184no—
678C4⋊C4—1184no—
679C4⋊C4—1184no—
680C4⋊C4—1184no—
681C4⋊C4—1184no—
682C4⋊C4—1184no—
683C4⋊C4—1181no—
684C4⋊C4—1181no—
685C4⋊C4—1184no—
686C4⋊C4C23×D5912yes—
687C4⋊C4C23×D5912yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—594no—
691C22⋊C4—594no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C22⋊C4—1184no—
695C42—592no—
696C42—592no—
697C42—1184no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—594no—
705C23—592no—
706C23—1182no—
707C23—1182no—
708C23SD16×D5914yes—
709C23C2×D4×D5912yes—
710C23C2×D4×D5911yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—594no—
715Q8—1182no—
716Q8—1184no—
717Q8—1182no—
718Q8—1182no—
719Q8—2368no—
720Q8—2368no—
721Q8—2368no—
722Q8—2362no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—42no—
727D4—5916no—
728D4—2368no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—594no—
740C2×C4—592no—
741C2×C4—592no—
742C2×C4—592no—
743C2×C4—1182no—
744C2×C4—1182no—
745C2×C4—1182no—
746C2×C4—1184no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1184no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—2368no—
754C2×C4—2368no—
755C2×C4—2368no—
756C2×C4—2368no—
757C2×C4—2362no—
758C2×C4—2362no—
759C2×C4—2368no—
760C2×C4—2362no—
761C2×C4C2×D4×D5912yes—
762C2×C4C2×D4×D5911yescharacteristic
763C2×C4#41×D5912yes—
764C2×C4#1427377212yes—
765C2×C4C24×D5911yescharacteristic
766C8—22no—
767C8—22no—
768C8—1182no—
769C8—1182no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—594no—
778C22—1188no—
779C22—1182no—
780C22—1182no—
781C22#1683804112yes—
782C22C2×SD16×D5914yes—
783C22C2×SD16×D5912yes—
784C22#1683821612yes—
785C22C22×D4×D5911yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—594no—
791C4—1182no—
792C4—1184no—
793C4—1182no—
794C4—2362no—
795C4—2362no—
796C4—2362no—
797C4#1683804112yes—
798C4C2×#41×D5911yescharacteristic
799C4C2×#1427377211yescharacteristic
800C2—24no—
801C2—82no—
802C2—1184no—
803C2#2143595614yesdirect product factor
804C2C2×#1683804111yescharacteristic
805C2C22×SD16×D5911yescharacteristic
806C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#465C2
socleC23×C59C22×D4
prime radicalC2×#16838052C2
hypercenterC2×#465D59
hypocenterC59C2×#3298
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16838065C2semidirect
3. #21435956C2direct (N × H)
4. C2×#16837751C2semidirect
5. C2×#16837734C2semidirect
6. C2×#16837730C2semidirect
7. C2×#16837686C2semidirect
8. C2×#16837630C2semidirect
9. C2×#16837605C2semidirect
10. C2×#16837540C2semidirect
11. C2×#16837539C2semidirect
12. C2×#16837493C2semidirect
13. C2×C8×C22⋊D59C2semidirect
14. C22×#14273652C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#465C2semidirect
24. #16838065C22semidirect
43. #16837751C22semidirect
44. #16837734C22semidirect
45. #16837730C22semidirect
46. #16837686C22semidirect
47. #16837630C22semidirect
48. #16837605C22semidirect
49. #16837540C22semidirect
50. #16837539C22semidirect
51. #16837493C22semidirect
52. C8×C22⋊D59C22semidirect
60. C2×#14273652C22semidirect
65. #103×D59C22semidirect
73. C59×#465C22semidirect
210. C2×C22⋊D59SD16semidirect
251. C2×Dic118#41semidirect
330. C22⋊D59C2×SD16semidirect
361. Dic118C2×#41semidirect
405. C2×#465D59semidirect
415. C2×C59#3298semidirect
455. #465C2×D59semidirect
480. C59C2×#3298semidirect
803. C2#21435956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380652
C2×#168380522
#214359562
C2×#168377512
C2×#168377342
C2×#168377302
C2×#168376862
C2×#168376302
C2×#168376052
C2×#168375402
C2×#168375392
C2×#168374932
C2×C8×C22⋊D592
C22×#142736522
C2×#103×D592
C2×C59×#4652
C2×#329859