Finite Group Databasebeta

← C2×#21434942 #29459336

Subgroups — C2×#21434942 #29459336

Order 15104.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837966C211yesmaximal, characteristic, complemented
2#21434942C2116yesmaximal, direct product factor
3C2×#16837720C211yesmaximal, characteristic, complemented
4C2×#16837740C211yesmaximal, characteristic, complemented
5C2×#16837723C211yesmaximal, characteristic, complemented
6C2×#16837715C211yesmaximal, characteristic, complemented
7C2×#16837653C211yesmaximal, characteristic, complemented
8C2×#16837650C211yesmaximal, characteristic, complemented
9C2×#16837636C211yesmaximal, characteristic, complemented
10C2×#16837633C211yesmaximal, characteristic, complemented
11C2×#16837547C211yesmaximal, characteristic, complemented
12C2×#16837547C211yesmaximal, characteristic, complemented
13C2×#16837552C211yesmaximal, characteristic, complemented
14C2×#16837535C211yesmaximal, characteristic, complemented
15C2×#16837369C211yesmaximal, characteristic, complemented
16C2×C59×#537C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22C22×#11745664C2211yescharacteristic, complemented
23C23×C59⋊C8C2211yescharacteristic, complemented
24#16837966—24no—
25#16837966C2218yescomplemented
26C2×#14273723—21no—
27C2×#14273716—21no—
28C2×#14273701C2211yescharacteristic
29C2×#14273701C2211yescharacteristic
30C2×#14273701C2211yescharacteristic
31C2×#14273701C2211yescharacteristic
32C2×#14273695—21no—
33C2×#14273695—21no—
34C2×#14273686C2211yescharacteristic
35#16837740C2218yescomplemented
36#16837723C2218yescomplemented
37#16837720C2218yescomplemented
38#16837715C2218yescomplemented
39#16837653C2218yescomplemented
40#16837650C2218yescomplemented
41#16837636C2218yescomplemented
42#16837633C2218yescomplemented
43#16837552C2218yescomplemented
44#16837547C2218yescomplemented
45#16837547C2218yescomplemented
46#16837535C2218yescomplemented
47C2×#14273660C2211yescharacteristic, complemented
48C2×#14273660C2211yescharacteristic, complemented
49C2×#14273658C2211yescharacteristic, complemented
50C2×#14273658C2211yescharacteristic, complemented
51C2×#14273651C2211yescharacteristic, complemented
52C2×#14273651C2211yescharacteristic, complemented
53C2×#14273648C2211yescharacteristic, complemented
54C2×#14273648C2211yescharacteristic, complemented
55C2×#14273647C2211yescharacteristic
56C2×#14273647C2211yescharacteristic
57C2×#14273647C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59#16837369C2218yescomplemented
60C2×C22⋊(C59⋊C8)C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
64C22×#41×C59C2211yescharacteristic
65C22×#41×C59C2211yescharacteristic, complemented
66C59×#537—24no—
67C59×#537C2218yescomplemented
68C2×C22⋊Q8×C59—21no—
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×C22⋊Q8×C59C2211yescharacteristic, complemented
71C2×#121×C59—21no—
72C2×#121×C59—21no—
73C2×#121×C59—21no—
74C2×#121×C59C2211yescharacteristic
75C2×#121×C59C2211yescharacteristic, complemented
76C22×C4⋊C4×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C22×D236—21no—
79C22×D236—22no—
80C22×D236—42no—
81C22×D236—42no—
82C22×D236C2311yescharacteristic
83C22×D236C2311yescharacteristic
84C22×D236C2314yes—
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C2×#11745671—42no—
90C2×#11745671—42no—
91C2×#11745671C2314yes—
92C2×#11745671C2314yes—
93C2×#11745669—42no—
94C2×#11745669—42no—
95C2×#11745669C2314yes—
96C2×#11745669C2314yes—
97C2×#11745664—42no—
98C2×#11745664C2314yescomplemented
99C22×C59⋊C8—42no—
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2314yescomplemented
105#14273723—28no—
106#14273716—28no—
107#14273701—22no—
108#14273701—22no—
109#14273701—22no—
110#14273701—22no—
111#14273701C2314yes—
112#14273701C2314yes—
113#14273701C2314yes—
114#14273701C2314yes—
115#14273695—28no—
116#14273695—28no—
117#14273686—22no—
118#14273686C2314yes—
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C22⋊Dic59—21no—
122C2×(C2×D59)⋊C4—21no—
123C2×(C2×D59)⋊C4—21no—
124C2×(C2×D59)⋊C4—21no—
125C2×(C2×D59)⋊C4—21no—
126C2×C4×Dic59—21no—
127#14273660C2314yescomplemented
128#14273660C2314yescomplemented
129#14273658C2314yescomplemented
130#14273658C2314yescomplemented
131#14273651C2314yescomplemented
132#14273651C2314yescomplemented
133#14273648C2314yescomplemented
134#14273648C2314yescomplemented
135#14273647C2314yes—
136#14273647C2314yes—
137#14273647C2314yes—
138#14273647C2314yes—
139C22⋊(C59⋊C8)C2314yes—
140C22⋊(C59⋊C8)C2314yes—
141C22⋊(C59⋊C8)C2314yescomplemented
142C22⋊(C59⋊C8)C2314yescomplemented
143C2×#41×C59—22no—
144C2×#41×C59—42no—
145C2×#41×C59—42no—
146C2×#41×C59—42no—
147C2×#41×C59—42no—
148C2×#41×C59D414yes—
149C2×#41×C59C2314yes—
150C2×#41×C59C2314yescomplemented
151C22×Q8×C59D411yescharacteristic
152C22×Q8×C59C2311yescharacteristic
153C22×D4×C59—21no—
154C22×D4×C59—21no—
155C22×D4×C59—21no—
156C22×D4×C59D411yescharacteristic
157C22×D4×C59D411yescharacteristic
158C22×D4×C59D411yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C23×C4×C59—21no—
162C23×C4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C22⋊Q8×C59—28no—
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C22⋊Q8×C59C2314yescomplemented
170#121×C59—28no—
171#121×C59—28no—
172#121×C59—28no—
173#121×C59—22no—
174#121×C59—22no—
175#121×C59C2314yes—
176#121×C59C2314yescomplemented
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59—22no—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59—21no—
181C2×C4⋊C4×C59C2311yescharacteristic
182C2×C4⋊C4×C59C2311yescharacteristic
183C2×C4⋊C4×C59C2314yescomplemented
184C2×C22⋊C4×C59—21no—
185C2×C22⋊C4×C59—21no—
186C2×C22⋊C4×C59—21no—
187C2×C22⋊C4×C59—21no—
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C24×C59C2×D411yescharacteristic
191C24×C59C2×D411yescharacteristic
192C23×D59—21no—
193C23×D59—21no—
194C23×D59—24no—
195C23×D59—44no—
196C23×D59—82no—
197C23×D59—82no—
198#41×C59—48no—
199#41×C59—44no—
200#41×C59—44no—
201#41×C59—44no—
202#41×C59—44no—
203#41×C59—48no—
204C2×Q8×C59—21no—
205C2×Q8×C59—22no—
206C2×Q8×C59—22no—
207C2×Q8×C59—42no—
208C2×Q8×C59C2×D414yes—
209C2×Q8×C59C2412yes—
210C2×D4×C59—24no—
211C2×D4×C59—24no—
212C2×D4×C59—24no—
213C2×D4×C59—21no—
214C2×D4×C59—22no—
215C2×D4×C59—22no—
216C2×D4×C59—42no—
217C2×D4×C59—42no—
218C2×D4×C59—42no—
219C2×D4×C59—44no—
220C2×D4×C59—82no—
221C2×D4×C59—82no—
222C2×D4×C59C2×D414yes—
223C2×D4×C59C2×D414yes—
224C2×D4×C59C2×D414yes—
225C2×D4×C59C2412yes—
226C22×C4×C59—22no—
227C22×C4×C59—22no—
228C22×C4×C59—22no—
229C22×C4×C59—22no—
230C22×C4×C59—22no—
231C22×C4×C59—22no—
232C22×C4×C59—21no—
233C22×C4×C59—21no—
234C22×C4×C59—21no—
235C22×C4×C59—24no—
236C22×C4×C59—24no—
237C22×C4×C59—44no—
238C22×C4×C59—82no—
239C22×C4×C59C2×D411yescharacteristic
240C22×C4×C59C2×D411yescharacteristic
241C22×C4×C59C2×D411yescharacteristic
242C22×C4×C59C2×D412yes—
243C22×C4×C59C2×D412yes—
244C22×C4×C59C2×D412yes—
245C22×C4×C59C2412yes—
246C22×C4×C59C2412yes—
247C22×C4×C59C2412yes—
248C22×C4×C59C2411yescharacteristic
249C2×C22⋊D59—24no—
250C2×C22⋊D59—24no—
251C2×C22⋊D59—24no—
252C2×C22⋊D59—24no—
253C2×C22⋊D59—82no—
254C2×C22⋊D59—82no—
255C2×C22⋊D59—82no—
256C2×C22⋊D59—82no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C2×D236—22no—
260C2×D236—22no—
261C2×D236—22no—
262C2×D236—22no—
263C2×D236—21no—
264C2×D236—21no—
265C2×D236—24no—
266C2×D236—44no—
267C2×D236—44no—
268C2×D236—44no—
269C2×D236—48no—
270C2×D236C2412yes—
271C2×D236C2412yes—
272C4⋊C4×C59—21no—
273C4⋊C4×C59—21no—
274C4⋊C4×C59—24no—
275C4⋊C4×C59—24no—
276C4⋊C4×C59—24no—
277C4⋊C4×C59C2412yes—
278C4⋊C4×C59C2412yes—
279C22⋊C4×C59—24no—
280C22⋊C4×C59—24no—
281C22⋊C4×C59—24no—
282C22⋊C4×C59—24no—
283C22⋊Dic59—24no—
284#11745671—44no—
285#11745671—44no—
286#11745669—44no—
287#11745669—44no—
288(C2×D59)⋊C4—24no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292C4⋊Dic59—21no—
293C4⋊Dic59—21no—
294C4⋊Dic59C2412yes—
295C4⋊Dic59C2412yes—
296C4×Dic59—24no—
297#11745664—44no—
298C2×C59⋊C8—22no—
299C2×C59⋊C8—22no—
300C2×C59⋊C8—22no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—44no—
303C2×C59⋊C8C2412yes—
304C2×C59⋊C8C2412yes—
305C2×C59⋊C8C2412yes—
306C2×C59⋊C8C2412yes—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—22no—
313C23×C59—22no—
314C23×C59—22no—
315C23×C59—22no—
316C23×C59—22no—
317C23×C59—42no—
318C23×C59—42no—
319C23×C59—42no—
320C23×C59C22×D412yes—
321C23×C59C22×D412yes—
322C23×C59C22×D412yes—
323C23×C59C22×D411yescharacteristic
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—48no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—84no—
334C22×D59—84no—
335C22×D59—816no—
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—44no—
339Q8×C59—42no—
340D4×C59—22no—
341D4×C59—22no—
342D4×C59—44no—
343D4×C59—44no—
344D4×C59—44no—
345D4×C59—48no—
346D4×C59—42no—
347D4×C59—84no—
348D4×C59—84no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—24no—
353C2×C4×C59—24no—
354C2×C4×C59—24no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—22no—
363C2×C4×C59—22no—
364C2×C4×C59—48no—
365C2×C4×C59—42no—
366C2×C4×C59—42no—
367C2×C4×C59—42no—
368C2×C4×C59—84no—
369C2×C4×C59C22×D412yes—
370C2×C4×C59C22×D412yes—
371C2×C4×C59C22×D412yes—
372C2×C4×C59C22×D411yescharacteristic
373C2×C4×C59H(5,𝔽2)12yes—
374C2×C4×C59H(5,𝔽2)12yes—
375C2×C4×C59C2511yescharacteristic
376C22⋊D59—84no—
377C22⋊D59—84no—
378C22⋊D59—84no—
379C22⋊D59—84no—
380C2×Dic59—22no—
381C2×Dic59—22no—
382C2×Dic59—42no—
383C2×Dic59—42no—
384D236—22no—
385D236—22no—
386D236—22no—
387D236—22no—
388D236—48no—
389D236—42no—
390D236—42no—
391C59⋊C8—22no—
392C59⋊C8—22no—
393C59⋊C8—22no—
394C59⋊C8—22no—
395C2×#3198—591nomaximal, Sylow
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—22no—
400C22×C59—22no—
401C22×C59—22no—
402C22×C59—22no—
403C22×C59—22no—
404C22×C59—22no—
405C22×C59—44no—
406C22×C59—44no—
407C22×C59—44no—
408C22×C59—42no—
409C22×C59—42no—
410C22×C59—42no—
411C22×C59—84no—
412C22×C59#53412yes—
413C22×C59#57612yes—
414C22×C59#57712yes—
415C22×C59C23×D411yescharacteristic
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—816no—
423C2×D59—84no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—22no—
427C4×C59—22no—
428C4×C59—42no—
429C4×C59—42no—
430C4×C59—42no—
431C4×C59#53412yes—
432C4×C59C2×H(5,𝔽2)11yescharacteristic
433C4×C59C2×H(5,𝔽2)11yescharacteristic
434Dic59—42no—
435Dic59—42no—
436C2×#537D5911yescharacteristic, complemented
437C2×#535—591no—
438#3198—5916no—
439C2×#481—591no—
440C2×#485—591no—
441C2×#482—591no—
442C2×#480—591no—
443C2×#469—591no—
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450—591no—
450C2×#447—591no—
451C2×#408—591no—
452C2×C59—42no—
453C2×C59—42no—
454C2×C59—42no—
455C2×C59—82no—
456C2×C59#319814yescomplemented
457C2×C59C2×#53411yescharacteristic
458C2×C59C2×#57611yescharacteristic
459C2×C59C2×#57711yescharacteristic
460D59—82no—
461D59—82no—
462C22×#41C2×D5911yescharacteristic
463C22×#41C2×D5911yescharacteristic, complemented
464C23×D4—591no—
465C22×SD16—591no—
466C22×SD16—591no—
467C22×D8—591no—
468C22×D8—591no—
469C22×M16—591no—
470C23×C8—591no—
471#537—24no—
472#537C2×D5918yescomplemented
473#535—598no—
474#535—1184no—
475C2×#127—1181no—
476C2×#124—1181no—
477C2×C22⋊Q8—21no—
478C2×C22⋊Q8C2×D5911yescharacteristic
479C2×C22⋊Q8C2×D5911yescharacteristic, complemented
480C2×#121—21no—
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—591no—
486C2×#121—591no—
487C2×#121C2×D5911yescharacteristic
488C2×#121C2×D5911yescharacteristic, complemented
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117—591no—
492C22×C4⋊C4C2×D5911yescharacteristic, complemented
493#485—598no—
494#482—598no—
495#481—598no—
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
507C2×#106—591no—
508C2×#106—591no—
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102—591no—
516C2×#102—591no—
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8—591no—
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—1181no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D5914yes—
530C2×#41C22×D5914yes—
531C2×#41C22×D5914yescomplemented
532C22×Q8C22⋊D5911yescharacteristic
533C22×Q8C22×D5911yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—591no—
538C22×D4—591no—
539C22×D4—594no—
540C22×D4—1181no—
541C22×D4—1181no—
542C22×D4—1181no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1182no—
546C22×D4—2362no—
547C22×D4—2362no—
548C22×D4C22⋊D5911yescharacteristic
549C22×D4C22⋊D5911yescharacteristic
550C22×D4C22⋊D5911yescharacteristic
551C22×D4C22×D5911yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D5911yescharacteristic
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5911yescharacteristic
557C2×SD16—594no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16—2362no—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—594no—
566C2×M16—2362no—
567C22×C8—591no—
568C22×C8—591no—
569C22×C8—591no—
570C22×C8—591no—
571C22×C8—594no—
572C22×C8—2362no—
573#127—1188no—
574#124—1188no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D5914yes—
579C22⋊Q8C22×D5914yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—594no—
586#121—594no—
587#121—594no—
588#121—594no—
589#121—1182no—
590#121—1182no—
591#121—1182no—
592#121—1182no—
593#121C22×D5914yes—
594#121C22×D5914yescomplemented
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—591no—
604C2×C4⋊C4—591no—
605C2×C4⋊C4C22×D5911yescharacteristic
606C2×C4⋊C4C22×D5911yescharacteristic
607C2×C4⋊C4C22×D5914yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1181no—
613C2×C22⋊C4—1181no—
614C2×C22⋊C4—1181no—
615C2×C22⋊C4—1181no—
616C2×C22⋊C4—1181no—
617C2×C42—1181no—
618#107—594no—
619#107—594no—
620#106—594no—
621#106—594no—
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102—594no—
629#102—594no—
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8—594no—
634C24—21no—
635C24—1184no—
636C24—1181no—
637C24—1181no—
638C24—4722no—
639C24—4722no—
640C24—2364no—
641C24C2×C22⋊D5911yescharacteristic
642C24C2×C22⋊D5911yescharacteristic
643C24C2×C22⋊D5911yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D5914yes—
655C2×Q8C23×D5912yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—592no—
669C2×D4—592no—
670C2×D4—1184no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1184no—
674C2×D4—1181no—
675C2×D4—1181no—
676C2×D4—1184no—
677C2×D4—1182no—
678C2×D4—1182no—
679C2×D4—1182no—
680C2×D4—1182no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—4722no—
684C2×D4—4722no—
685C2×D4—2364no—
686C2×D4—2364no—
687C2×D4—2364no—
688C2×D4—2368no—
689C2×D4C2×C22⋊D5914yes—
690C2×D4C2×C22⋊D5914yes—
691C2×D4C2×C22⋊D5914yes—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4C2×C22⋊D5912yes—
709C22×C4C2×C22⋊D5912yes—
710C22×C4C2×C22⋊D5912yes—
711C22×C4C2×C22⋊D5911yescharacteristic
712C22×C4C2×C22⋊D5911yescharacteristic
713C22×C4C2×C22⋊D5911yescharacteristic
714C22×C4C23×D5912yes—
715C22×C4C23×D5912yes—
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—2364no—
719SD16—2364no—
720D8—2364no—
721D8—2364no—
722M16—2364no—
723C2×C8—592no—
724C2×C8—592no—
725C2×C8—592no—
726C2×C8—592no—
727C2×C8—1182no—
728C2×C8—1182no—
729C2×C8—1182no—
730C2×C8—1182no—
731C2×C8—2364no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—592no—
738C4⋊C4—592no—
739C4⋊C4—1181no—
740C4⋊C4—1181no—
741C4⋊C4C23×D5912yes—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1184no—
748C22⋊C4—1184no—
749C22⋊C4—1184no—
750C22⋊C4—1184no—
751C22⋊C4—1184no—
752C42—1184no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—1182no—
767C23—1182no—
768C23—4724no—
769C23—4724no—
770C23—47216no—
771C23—2368no—
772C23—2362no—
773C23—2362no—
774C23—2362no—
775C23—2362no—
776C23—2362no—
777C23—2362no—
778C23C22×C22⋊D5912yes—
779C23C22×C22⋊D5912yes—
780C23C22×C22⋊D5912yes—
781C23C22×C22⋊D5911yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—1182no—
796D4—1182no—
797D4—1182no—
798D4—1182no—
799D4—4724no—
800D4—4724no—
801D4—4724no—
802D4—4724no—
803D4—2368no—
804D4—2362no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—2362no—
829C2×C4—2362no—
830C2×C4C22×C22⋊D5912yes—
831C2×C4C22×C22⋊D5912yes—
832C2×C4C22×C22⋊D5912yes—
833C2×C4C22×C22⋊D5911yescharacteristic
834C2×C4#1427377212yes—
835C2×C4#1427377212yes—
836C2×C4C24×D5911yescharacteristic
837C8—1182no—
838C8—1182no—
839C8—1182no—
840C8—1182no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—47216no—
858C22—4724no—
859C22—4724no—
860C22—2362no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2362no—
865C22—2362no—
866C22#1683796112yes—
867C22#1683820512yes—
868C22#1683821012yes—
869C22C23×C22⋊D5911yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—2362no—
877C4—2362no—
878C4#1683796112yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—4722no—
886C2—4722no—
887C2#2143494214yesdirect product factor
888C2C2×#1683796111yescharacteristic
889C2C2×#1683820511yescharacteristic
890C2C2×#1683821011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#537C2
socleC23×C59C22×D4
hypercenterC2×#537D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16837966C2semidirect
2. #21434942C2direct (N × H)
3. C2×#16837720C2semidirect
4. C2×#16837740C2semidirect
5. C2×#16837723C2semidirect
6. C2×#16837715C2semidirect
7. C2×#16837653C2semidirect
8. C2×#16837650C2semidirect
9. C2×#16837636C2semidirect
10. C2×#16837633C2semidirect
11. C2×#16837547C2semidirect
12. C2×#16837547C2semidirect
13. C2×#16837552C2semidirect
14. C2×#16837535C2semidirect
15. C2×#16837369C2semidirect
16. C2×C59×#537C2semidirect
22. C22×#11745664C22semidirect
23. C23×C59⋊C8C22semidirect
25. #16837966C22semidirect
35. #16837740C22semidirect
36. #16837723C22semidirect
37. #16837720C22semidirect
38. #16837715C22semidirect
39. #16837653C22semidirect
40. #16837650C22semidirect
41. #16837636C22semidirect
42. #16837633C22semidirect
43. #16837552C22semidirect
44. #16837547C22semidirect
45. #16837547C22semidirect
46. #16837535C22semidirect
47. C2×#14273660C22semidirect
48. C2×#14273660C22semidirect
49. C2×#14273658C22semidirect
50. C2×#14273658C22semidirect
51. C2×#14273651C22semidirect
52. C2×#14273651C22semidirect
53. C2×#14273648C22semidirect
54. C2×#14273648C22semidirect
59. #16837369C22semidirect
62. C2×C22⋊(C59⋊C8)C22semidirect
63. C2×C22⋊(C59⋊C8)C22semidirect
65. C22×#41×C59C22semidirect
67. C59×#537C22semidirect
70. C2×C22⋊Q8×C59C22semidirect
75. C2×#121×C59C22semidirect
76. C22×C4⋊C4×C59C22semidirect
98. C2×#11745664C23semidirect
104. C22×C59⋊C8C23semidirect
127. #14273660C23semidirect
128. #14273660C23semidirect
129. #14273658C23semidirect
130. #14273658C23semidirect
131. #14273651C23semidirect
132. #14273651C23semidirect
133. #14273648C23semidirect
134. #14273648C23semidirect
141. C22⋊(C59⋊C8)C23semidirect
142. C22⋊(C59⋊C8)C23semidirect
150. C2×#41×C59C23semidirect
169. C22⋊Q8×C59C23semidirect
176. #121×C59C23semidirect
183. C2×C4⋊C4×C59C23semidirect
436. C2×#537D59semidirect
456. C2×C59#3198semidirect
463. C22×#41C2×D59semidirect
472. #537C2×D59semidirect
479. C2×C22⋊Q8C2×D59semidirect
488. C2×#121C2×D59semidirect
492. C22×C4⋊C4C2×D59semidirect
522. C59C2×#3198semidirect
531. C2×#41C22×D59semidirect
579. C22⋊Q8C22×D59semidirect
594. #121C22×D59semidirect
607. C2×C4⋊C4C22×D59semidirect
887. C2#21434942direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379662
#214349422
C2×#168377202
C2×#168377402
C2×#168377232
C2×#168377152
C2×#168376532
C2×#168376502
C2×#168376362
C2×#168376332
C2×#168375472
C2×#168375522
C2×#168375352
C2×#168373692
C2×C59×#5372
C2×#319859