Finite Group Databasebeta

← C2×#21436582 #29467269

Subgroups — C2×#21436582 #29467269

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838107C211yesmaximal, characteristic, complemented
2C2×#16838096C211yesmaximal, characteristic
3#21436582C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837722C211yesmaximal, characteristic, complemented
7C2×#16837743C211yesmaximal, characteristic, complemented
8C2×#16837715C211yesmaximal, characteristic, complemented
9C2×#16837712C211yesmaximal, characteristic, complemented
10C2×#16837681C211yesmaximal, characteristic, complemented
11C2×#16837648C211yesmaximal, characteristic, complemented
12C2×#16837632C211yesmaximal, characteristic, complemented
13C2×#16837501C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#428C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838107—24no—
20#16838107C2218yescomplemented
21#16838096—24no—
22#16838096C2218yes—
23C2×#14273726C2211yescharacteristic
24C2×#14273721—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273709—21no—
28C2×#14273707C2211yescharacteristic
29C2×#14273706—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273705—21no—
32C2×#14273702C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273700—21no—
35C2×#14273692C2211yescharacteristic
36C2×C4×D236—21no—
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837809C2218yescomplemented
43#16837743C2218yescomplemented
44#16837739C2218yescomplemented
45#16837722C2218yescomplemented
46#16837715C2218yescomplemented
47#16837712C2218yescomplemented
48#16837681C2218yescomplemented
49#16837648C2218yescomplemented
50#16837632C2218yescomplemented
51#16837501C2218yescomplemented
52#16837471C2218yescomplemented
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57#107×D59C2218yescomplemented
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C59×#428C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#107×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59D411yescharacteristic
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59C2311yescharacteristic
87C2×#11745660—24no—
88C2×#11745660C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—24no—
92C2×C8×D59C2314yes—
93#14273726—22no—
94#14273726C2314yes—
95#14273721—28no—
96#14273718—22no—
97#14273718C2314yes—
98#14273717—28no—
99#14273709—28no—
100#14273707—22no—
101#14273707C2314yes—
102#14273706—22no—
103#14273706—28no—
104#14273706C2314yes—
105#14273705—28no—
106#14273702—22no—
107#14273702C2314yes—
108#14273701—22no—
109#14273701C2314yes—
110#14273700—28no—
111#14273692—22no—
112#14273692C2314yes—
113C4×D236—28no—
114#14273689—22no—
115#14273689C2314yes—
116C4×C22⋊D59—28no—
117C4×C22⋊D59D414yes—
118C4×C22⋊D59C2314yes—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C4⋊C4×D59—22no—
131C4⋊C4×D59—22no—
132C4⋊C4×D59C2314yes—
133C4⋊C4×D59C2314yes—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59D411yescharacteristic
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273650C2314yes—
151#14273650C2314yes—
152#14273649C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273637C2314yes—
158C23×C4×C59—21no—
159C23×C4×C59C2311yescharacteristic
160C2×M16×C59—24no—
161C2×M16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#117×C59—22no—
165#117×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—22no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175#107×C59C2314yes—
176#107×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59—21no—
181C23×D59C2×D411yescharacteristic
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—24no—
189C22×C4×C59—82no—
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2411yescharacteristic
194C2×C22⋊D59—24no—
195C2×C22⋊D59—24no—
196C2×C22⋊D59—82no—
197C2×C22⋊D59C2×D414yes—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C2×D236—22no—
205C2×D236—22no—
206C2×D236—24no—
207C2×D236—21no—
208C2×D236—44no—
209C2×D236C2412yes—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—24no—
213C2×C4×D59—24no—
214C2×C4×D59—24no—
215C2×C4×D59—82no—
216C2×C4×D59—82no—
217C2×C4×D59—82no—
218C2×C4×D59C2×D412yes—
219C2×C4×D59C2412yes—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—82no—
225C2×Dic118C2412yes—
226M16×C59—28no—
227C2×C8×C59—22no—
228C2×C8×C59#4114yes—
229C2×C8×C59C2412yes—
230C2×C8×C59C2412yes—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C22⋊C4×C59—24no—
241C42×C59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59C2×D414yes—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4C2×D414yes—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59C2×D412yes—
264C4×Dic59C2412yes—
265C2×C59⋊C8—22no—
266C2×C59⋊C8—22no—
267C2×C59⋊C8C2412yes—
268C2×C59⋊C8C2412yes—
269#11745660—28no—
270C8×D59—28no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59C22×D412yes—
275C23×C59C22×D411yescharacteristic
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59—42no—
282C22×D59#13714yes—
283C22×D59C22×D412yes—
284C2×C4×C59—22no—
285C2×C4×C59—24no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59—84no—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C2×#4112yes—
300C2×C4×C592−1+412yes—
301C2×C4×C59C2511yescharacteristic
302C22⋊D59—28no—
303C22⋊D59—84no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315C2×Dic59C22×D412yes—
316D236—22no—
317D236—22no—
318D236—48no—
319D236—42no—
320C4×D59—24no—
321C4×D59—22no—
322C4×D59—22no—
323C4×D59—84no—
324C4×D59—84no—
325C4×D59—84no—
326Dic118—22no—
327Dic118—22no—
328Dic118—42no—
329Dic118—84no—
330C8×C59—22no—
331C8×C59C2×#4114yes—
332C59⋊C8—22no—
333C59⋊C8—22no—
334C2×#3346—591nomaximal, Sylow
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—44no—
339C22×C59#54712yes—
340C22×C59C2×#13712yes—
341C22×C59#57612yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—28no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—42no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—84no—
350C2×D59C2×#13714yes—
351C4×C59—22no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59—42no—
356C4×C59#54712yes—
357C4×C59C22×#4111yescharacteristic
358C4×C59C2×2−1+411yescharacteristic
359Dic59—22no—
360Dic59—22no—
361Dic59—22no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#554—591no—
366C2×#553—591no—
367#3346—5916no—
368C2×#501—591no—
369C2×#484—591no—
370C2×#481—591no—
371C2×#485—591no—
372C2×#480—591no—
373C2×#479—591no—
374C2×#474—591no—
375C2×#468—591no—
376C2×#465—591no—
377C2×#440—591no—
378C2×#435—591no—
379C2×#428D5911yescharacteristic, complemented
380C22×#107—591no—
381C2×C59—42no—
382C2×C59#334614yescomplemented
383C2×C59C2×#54711yescharacteristic
384C2×C59C22×#13711yescharacteristic
385C2×C59C2×#57611yescharacteristic
386D59—24no—
387D59—82no—
388C22×SD16—591no—
389C22×M16C2×D5911yescharacteristic
390C23×C8—591no—
391#554—598no—
392#554—1184no—
393#553—598no—
394#553—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#125—591no—
398C2×#125—1181no—
399C2×#123—1181no—
400C2×C22⋊Q8—591no—
401C2×C22⋊Q8—591no—
402C2×C22⋊Q8—1181no—
403C2×C22⋊Q8—1181no—
404C2×#121—591no—
405C2×#121—591no—
406C2×#121—1181no—
407C2×C4×Q8—591no—
408C2×C4×D4—591no—
409C2×C4×D4—591no—
410C2×C4×D4—1181no—
411C2×C4×D4—1181no—
412C2×#117C2×D5911yescharacteristic
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4C2×D5911yescharacteristic
416#501—598no—
417#485—598no—
418#484—598no—
419#481—598no—
420#480—598no—
421#479—598no—
422#474—598no—
423#468—598no—
424#465—598no—
425#440—598no—
426#435—598no—
427#428C2×D5918yescomplemented
428C2×#107—591no—
429C2×#107—591no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—598no—
433C2×#107C2×D5911yescharacteristic
434C2×#107C2×D5911yescharacteristic
435C2×#106—591no—
436C2×#106C2×D5911yescharacteristic
437C2×#106C2×D5911yescharacteristic
438C2×C4⋊C8—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×#102—591no—
445C2×C22⋊C8—591no—
446C2×C22⋊C8—591no—
447C2×#97—591no—
448C59C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—591no—
450C22×Q8—1181no—
451C22×D4—591no—
452C22×D4—591no—
453C22×D4—1181no—
454C22×D4—1181no—
455C23×C4—21no—
456C23×C4—591no—
457C23×C4—1181no—
458C23×C4—1181no—
459C23×C4—1181no—
460C23×C4C22×D5911yescharacteristic
461C2×SD16—594no—
462C2×SD16—1184no—
463C2×M16—24no—
464C2×M16C22×D5914yes—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8—594no—
468C22×C8—1184no—
469C22×C8C22×D5911yescharacteristic
470C22×C8C22×D5911yescharacteristic
471C4⋊Q8—594no—
472C4⋊Q8—1182no—
473#126—1188no—
474#125—594no—
475#125—1182no—
476#125—1188no—
477#123—1188no—
478C22⋊Q8—594no—
479C22⋊Q8—594no—
480C22⋊Q8—1188no—
481C22⋊Q8—1188no—
482C22⋊Q8—1182no—
483C22⋊Q8—1182no—
484#121—594no—
485#121—594no—
486#121—1188no—
487#121—1182no—
488#121—1182no—
489C4×Q8—594no—
490C4×Q8—1182no—
491C4×D4—594no—
492C4×D4—594no—
493C4×D4—594no—
494C4×D4—1188no—
495C4×D4—1182no—
496C4×D4—1188no—
497#117—22no—
498#117C22×D5914yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—594no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—1182no—
507C2×C4⋊C4—1182no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4C22×D5911yescharacteristic
517C2×C4⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5914yes—
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C42—21no—
530C2×C42—591no—
531C2×C42—1181no—
532#107—594no—
533#107—594no—
534#107—594no—
535#107—594no—
536#107C22×D5914yes—
537#107C22×D5914yes—
538#106—594no—
539#106C22×D5914yes—
540#106C22×D5914yes—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#102—594no—
546#102—594no—
547#102—594no—
548C22⋊C8—594no—
549C22⋊C8—594no—
550#97—594no—
551C24—591no—
552C24—1181no—
553C24D4×D5911yescharacteristic
554C2×Q8—592no—
555C2×Q8—1184no—
556C2×Q8—1181no—
557C2×Q8—1182no—
558C2×Q8—1182no—
559C2×Q8—4722no—
560C2×D4—594no—
561C2×D4—592no—
562C2×D4—1184no—
563C2×D4—1184no—
564C2×D4—1184no—
565C2×D4—1181no—
566C2×D4—1182no—
567C2×D4—1182no—
568C2×D4—4722no—
569C2×D4—2364no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—592no—
582C22×C4—592no—
583C22×C4—1184no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—4722no—
592C22×C4—4722no—
593C22×C4—4722no—
594C22×C4D4×D5912yes—
595C22×C4D4×D5911yescharacteristic
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598SD16—1188no—
599M16—28no—
600C2×C8—22no—
601C2×C8—592no—
602C2×C8—592no—
603C2×C8—1182no—
604C2×C8—1182no—
605C2×C8—1188no—
606C2×C8#1174568514yes—
607C2×C8C23×D5912yes—
608C2×C8C23×D5912yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—594no—
615C4⋊C4—592no—
616C4⋊C4—592no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1184no—
627C4⋊C4C23×D5912yes—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—594no—
633C22⋊C4—594no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—24no—
640C42—592no—
641C42—592no—
642C42—1184no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—594no—
647C23—592no—
648C23—1182no—
649C23—1182no—
650C23—1182no—
651C23—2362no—
652C23—2362no—
653C23—2362no—
654C23C2×D4×D5912yes—
655C23C2×D4×D5911yescharacteristic
656Q8—1182no—
657Q8—1182no—
658Q8—4724no—
659Q8—2362no—
660D4—1188no—
661D4—1182no—
662D4—1182no—
663D4—4724no—
664D4—2368no—
665D4—2362no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—592no—
680C2×C4—592no—
681C2×C4—592no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1184no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—4724no—
692C2×C4—4724no—
693C2×C4—4724no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4C2×D4×D5912yes—
698C2×C4C2×D4×D5911yescharacteristic
699C2×C4C2×#1174568512yes—
700C2×C4#1427377512yes—
701C2×C4C24×D5911yescharacteristic
702C8—22no—
703C8—1182no—
704C8—1182no—
705C8C2×#1174568514yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—594no—
711C22—1182no—
712C22—1182no—
713C22—1188no—
714C22—4724no—
715C22—2362no—
716C22—2362no—
717C22—2362no—
718C22#1683805312yes—
719C22#137×D5912yes—
720C22#1683820612yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1182no—
728C4—1182no—
729C4—1182no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4#1683805312yes—
734C4C22×#1174568511yescharacteristic
735C4C2×#1427377511yescharacteristic
736C2—42no—
737C2—1184no—
738C2—4722no—
739C2#2143658214yesdirect product factor
740C2C2×#1683805311yescharacteristic
741C2C2×#137×D5911yescharacteristic
742C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
prime radicalC2×#16838096C2
hypercenterC2×#428D59
hypocenterC59C2×#3346
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16838107C2semidirect
3. #21436582C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837722C2semidirect
7. C2×#16837743C2semidirect
8. C2×#16837715C2semidirect
9. C2×#16837712C2semidirect
10. C2×#16837681C2semidirect
11. C2×#16837648C2semidirect
12. C2×#16837632C2semidirect
13. C2×#16837501C2semidirect
14. C2×#16837471C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#428C2semidirect
20. #16838107C22semidirect
42. #16837809C22semidirect
43. #16837743C22semidirect
44. #16837739C22semidirect
45. #16837722C22semidirect
46. #16837715C22semidirect
47. #16837712C22semidirect
48. #16837681C22semidirect
49. #16837648C22semidirect
50. #16837632C22semidirect
51. #16837501C22semidirect
52. #16837471C22semidirect
57. #107×D59C22semidirect
72. C59×#428C22semidirect
379. C2×#428D59semidirect
382. C2×C59#3346semidirect
427. #428C2×D59semidirect
448. C59C2×#3346semidirect
739. C2#21436582direct (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×#168380962
#214365822
C2×#168378092
C2×#168377392
C2×#168377222
C2×#168377432
C2×#168377152
C2×#168377122
C2×#168376812
C2×#168376482
C2×#168376322
C2×#168375012
C2×#168374712
C2×#107×D592
C2×C59×#4282
C2×#334659