Finite Group Databasebeta

← C2×#21423093 #28560829

Subgroups — C2×#21423093 #28560829

Order 15104.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837730C211yesmaximal, characteristic, complemented
2C2×#16837713C211yesmaximal, characteristic
3C2×#16837332C211yesmaximal, characteristic, complemented
4#21423093C218yesmaximal, direct product factor
5C2×#16837139C211yesmaximal, characteristic, complemented
6C2×#16837136C211yesmaximal, characteristic
7C2×#16837128C211yesmaximal, characteristic, complemented
8C2×C59×#539C211yesmaximal, characteristic
9C22×C4⋊Dic59C2211yescharacteristic
10C22×Dic59⋊C4—21no—
11#16837730—22no—
12#16837730C2214yescomplemented
13#16837713—22no—
14#16837713C2214yes—
15C2×#14273660—21no—
16C2×#14273658—21no—
17C2×#14273651—21no—
18C2×#14273648—21no—
19C2×C22⋊(C59⋊C8)C2211yescharacteristic
20C2×C22⋊(C59⋊C8)C2211yescharacteristic
21#16837332—22no—
22#16837332C2214yescomplemented
23C2×C59⋊#95—21no—
24C2×C59⋊#95C2211yescharacteristic
25#16837139C2214yescomplemented
26#16837136C2214yes—
27#16837128C2214yescomplemented
28C59×#539—22no—
29C59×#539—22no—
30C59×#539—22no—
31C59×#539C2214yes—
32C2×#126×C59—21no—
33C2×#125×C59—21no—
34C2×#123×C59—21no—
35C2×#123×C59—21no—
36C2×C22⋊Q8×C59—21no—
37C2×C22⋊Q8×C59C2211yescharacteristic
38C2×#121×C59C2211yescharacteristic
39C2×C4×D4×C59—21no—
40C22×C4⋊C4×C59C2211yescharacteristic
41C23×Dic59—21no—
42C23×Dic59—21no—
43C22×C59⋊C8—21no—
44C22×C59⋊C8—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59—21no—
50C2×C4⋊Dic59C2312yes—
51C2×Dic59⋊C4—24no—
52C2×Dic59⋊C4—44no—
53#14273660—24no—
54#14273658—24no—
55#14273651—24no—
56#14273648—24no—
57C22⋊(C59⋊C8)—21no—
58C22⋊(C59⋊C8)—21no—
59C22⋊(C59⋊C8)C2312yes—
60C22⋊(C59⋊C8)C2312yes—
61C59⋊#95—24no—
62C59⋊#95—21no—
63C59⋊#95C2312yes—
64C22×Q8×C59D411yescharacteristic
65C22×D4×C59—21no—
66C22×D4×C59D411yescharacteristic
67C23×C4×C59—21no—
68C23×C4×C59D411yescharacteristic
69C23×C4×C59D411yescharacteristic
70C23×C4×C59C2311yescharacteristic
71#126×C59—24no—
72#126×C59—24no—
73#125×C59—24no—
74#125×C59—24no—
75#123×C59—24no—
76#123×C59—24no—
77#123×C59—24no—
78#123×C59—24no—
79C22⋊Q8×C59—24no—
80C22⋊Q8×C59—24no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59D412yes—
84C22⋊Q8×C59C2312yes—
85#121×C59—21no—
86#121×C59—21no—
87#121×C59D412yes—
88#121×C59C2312yes—
89C4×D4×C59—24no—
90C4×D4×C59—24no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59—21no—
93C2×C4⋊C4×C59—21no—
94C2×C4⋊C4×C59—21no—
95C2×C4⋊C4×C59—21no—
96C2×C4⋊C4×C59—21no—
97C2×C4⋊C4×C59—21no—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59D412yes—
100C2×C4⋊C4×C59D411yescharacteristic
101C2×C4⋊C4×C59D411yescharacteristic
102C2×C4⋊C4×C59C2312yes—
103C2×C22⋊C4×C59—21no—
104C2×C22⋊C4×C59—21no—
105C2×C22⋊C4×C59—21no—
106C2×C22⋊C4×C59—21no—
107C2×C22⋊C4×C59—21no—
108C2×C42×C59—21no—
109C24×C59—21no—
110C24×C59C2×D411yescharacteristic
111C2×Q8×C59—21no—
112C2×Q8×C59—42no—
113C2×Q8×C59C2×D412yes—
114C2×D4×C59—22no—
115C2×D4×C59—22no—
116C2×D4×C59—21no—
117C2×D4×C59—42no—
118C2×D4×C59—42no—
119C2×D4×C59—42no—
120C2×D4×C59C2×D412yes—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—21no—
125C22×C4×C59—21no—
126C22×C4×C59—21no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—24no—
130C22×C4×C59—21no—
131C22×C4×C59—42no—
132C22×C4×C59—42no—
133C22×C4×C59—82no—
134C22×C4×C59C2×D412yes—
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2×D412yes—
138C22×C4×C59C2×D411yescharacteristic
139C22×C4×C59C2×D411yescharacteristic
140C22×C4×C59C2×D411yescharacteristic
141C22×C4×C59C2411yescharacteristic
142C22×Dic59—24no—
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—42no—
146C22×Dic59—42no—
147C22×Dic59—41no—
148C22×Dic59—41no—
149C22×Dic59—42no—
150C22×Dic59—42no—
151C4⋊C4×C59—24no—
152C4⋊C4×C59—24no—
153C4⋊C4×C59—24no—
154C4⋊C4×C59—22no—
155C4⋊C4×C59—22no—
156C4⋊C4×C59—22no—
157C4⋊C4×C59—21no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59C2×D412yes—
163C4⋊C4×C59C2×D412yes—
164C22⋊C4×C59—24no—
165C22⋊C4×C59—24no—
166C22⋊C4×C59—24no—
167C22⋊C4×C59—22no—
168C22⋊C4×C59—22no—
169C22⋊C4×C59—22no—
170C22⋊C4×C59—22no—
171C42×C59—24no—
172C4⋊Dic59—22no—
173C4⋊Dic59—22no—
174C4⋊Dic59—41no—
175C4⋊Dic59—41no—
176Dic59⋊C4—48no—
177C2×C59⋊C8—22no—
178C2×C59⋊C8—22no—
179C2×C59⋊C8—42no—
180C2×C59⋊C8—42no—
181C23×C59—22no—
182C23×C59—22no—
183C23×C59—22no—
184C23×C59—42no—
185C23×C59—42no—
186C23×C59—42no—
187C23×C59#12011yescharacteristic
188C23×C59#12011yescharacteristic
189C23×C59#13512yes—
190C23×C59AGL(1,ℤ/8)12yes—
191C23×C59C22×D411yescharacteristic
192Q8×C59—42no—
193Q8×C59—81no—
194D4×C59—42no—
195D4×C59—42no—
196D4×C59—42no—
197D4×C59—44no—
198D4×C59—81no—
199C2×C4×C59—22no—
200C2×C4×C59—22no—
201C2×C4×C59—22no—
202C2×C4×C59—22no—
203C2×C4×C59—22no—
204C2×C4×C59—22no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59—42no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—42no—
218C2×C4×C59—42no—
219C2×C4×C59—81no—
220C2×C4×C59—84no—
221C2×C4×C59#12011yescharacteristic
222C2×C4×C59#12011yescharacteristic
223C2×C4×C59C22×D411yescharacteristic
224C2×C4×C59C22×D411yescharacteristic
225C2×Dic59—24no—
226C2×Dic59—48no—
227C2×Dic59—42no—
228C2×Dic59—42no—
229C2×Dic59—42no—
230C2×Dic59—42no—
231C2×Dic59—42no—
232C2×Dic59—82no—
233C2×Dic59—82no—
234C59⋊C8—42no—
235C59⋊C8—42no—
236C2×#1609—591nomaximal, Sylow
237C22×C59—24no—
238C22×C59—24no—
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—21no—
242C22×C59—21no—
243C22×C59—42no—
244C22×C59—42no—
245C22×C59—42no—
246C22×C59—84no—
247C22×C59#44912yes—
248C22×C59#44912yes—
249C22×C59#45612yes—
250C22×C59#45812yes—
251C22×C59C2×#12011yescharacteristic
252C22×C59C2×#13511yescharacteristic
253C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C59—21no—
255C4×C59—21no—
256C4×C59—21no—
257C4×C59—21no—
258C4×C59—42no—
259C4×C59—42no—
260C4×C59—42no—
261C4×C59—42no—
262C4×C59—42no—
263Dic59—44no—
264Dic59—82no—
265C2×#539D5911yescharacteristic
266C2×#483—591no—
267C2×#480—591no—
268C2×#398—591no—
269#1609—598no—
270C2×#328—591no—
271C2×#327—591no—
272C2×#324—591no—
273C2×C59—21no—
274C2×C59—21no—
275C2×C59—22no—
276C2×C59—82no—
277C2×C59#160914yescomplemented
278C2×C59C2×#44911yescharacteristic
279C2×C59C2×#45611yescharacteristic
280C2×C59C2×#45811yescharacteristic
281#539—22no—
282#539—22no—
283#539—22no—
284#539C2×D5914yes—
285C2×#126—21no—
286C2×#125—21no—
287C2×#123—21no—
288C2×#123—21no—
289C2×C22⋊Q8—21no—
290C2×C22⋊Q8C2×D5911yescharacteristic
291C2×#121C2×D5911yescharacteristic
292C2×C4×D4—21no—
293C22×C4⋊C4—591no—
294C22×C4⋊C4—1181no—
295C22×C4⋊C4C2×D5911yescharacteristic
296#483—594no—
297#483—1182no—
298#480—594no—
299#480—1182no—
300C2×#107—1181no—
301C2×#106—1181no—
302C2×#103—1181no—
303C2×#102—1181no—
304C2×C22⋊C8—591no—
305C2×C22⋊C8—591no—
306#398—594no—
307#398—1182no—
308C2×#95—591no—
309C2×#95—1181no—
310#328—594no—
311#327—594no—
312#324—594no—
313C59C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8C22⋊D5911yescharacteristic
315C22×D4—21no—
316C22×D4C22⋊D5911yescharacteristic
317C23×C4—21no—
318C23×C4—1181no—
319C23×C4—1181no—
320C23×C4C22⋊D5911yescharacteristic
321C23×C4C22⋊D5911yescharacteristic
322C23×C4C22×D5911yescharacteristic
323C22×C8—1181no—
324C22×C8—1181no—
325#126—24no—
326#126—24no—
327#125—24no—
328#125—24no—
329#123—24no—
330#123—24no—
331#123—24no—
332#123—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8C22⋊D5912yes—
338C22⋊Q8C22×D5912yes—
339#121—21no—
340#121—21no—
341#121C22⋊D5912yes—
342#121C22×D5912yes—
343C4×D4—24no—
344C4×D4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—592no—
354C2×C4⋊C4—1181no—
355C2×C4⋊C4—1181no—
356C2×C4⋊C4—1181no—
357C2×C4⋊C4—1181no—
358C2×C4⋊C4—1181no—
359C2×C4⋊C4—1184no—
360C2×C4⋊C4—2364no—
361C2×C4⋊C4C22⋊D5912yes—
362C2×C4⋊C4C22⋊D5911yescharacteristic
363C2×C4⋊C4C22⋊D5911yescharacteristic
364C2×C4⋊C4C22×D5912yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42—21no—
371#107—1184no—
372#106—1184no—
373#103—1184no—
374#102—1184no—
375C22⋊C8—592no—
376C22⋊C8—592no—
377C22⋊C8—1181no—
378C22⋊C8—1181no—
379#95—592no—
380#95—1181no—
381#95—1184no—
382C24—21no—
383C24C2×C22⋊D5911yescharacteristic
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8C2×C22⋊D5912yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4C2×C22⋊D5912yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4—1184no—
408C22×C4—1182no—
409C22×C4—1182no—
410C22×C4—2361no—
411C22×C4—2361no—
412C22×C4—2362no—
413C22×C4—2362no—
414C22×C4—2362no—
415C22×C4—2362no—
416C22×C4C2×C22⋊D5912yes—
417C22×C4C2×C22⋊D5911yescharacteristic
418C22×C4C2×C22⋊D5911yescharacteristic
419C22×C4C2×C22⋊D5912yes—
420C22×C4C2×C22⋊D5911yescharacteristic
421C22×C4C2×C22⋊D5911yescharacteristic
422C22×C4C2×C22⋊D5911yescharacteristic
423C22×C4C23×D5911yescharacteristic
424C2×C8—1182no—
425C2×C8—1182no—
426C2×C8—2362no—
427C2×C8—2362no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—1182no—
440C4⋊C4—1182no—
441C4⋊C4—2368no—
442C4⋊C4—2361no—
443C4⋊C4—2361no—
444C4⋊C4C2×C22⋊D5912yes—
445C4⋊C4C2×C22⋊D5912yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C42—24no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23#1427369611yescharacteristic
461C23#1427369611yescharacteristic
462C23#1427374712yes—
463C23#1427375212yes—
464C23C22×C22⋊D5911yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—81no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—81no—
493C2×C4—84no—
494C2×C4—1184no—
495C2×C4—4722no—
496C2×C4—4722no—
497C2×C4—2362no—
498C2×C4—2362no—
499C2×C4—2362no—
500C2×C4—2362no—
501C2×C4—2368no—
502C2×C4—2362no—
503C2×C4#1427369611yescharacteristic
504C2×C4#1427369611yescharacteristic
505C2×C4C22×C22⋊D5911yescharacteristic
506C2×C4C22×C22⋊D5911yescharacteristic
507C8—2362no—
508C8—2362no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—84no—
519C22#1683754712yes—
520C22#1683754712yes—
521C22#1683758512yes—
522C22#1683759212yes—
523C22C2×#1427369611yescharacteristic
524C22C2×#1427374711yescharacteristic
525C22C2×#1427375211yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—4722no—
536C4—2364no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—82no—
541C2#2142309314yesdirect product factor
542C2C2×#1683754711yescharacteristic
543C2C2×#1683758511yescharacteristic
544C2C2×#1683759211yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#539C2
socleC23×C59#120
prime radicalC2×#121×C59C22
hypercenterC2×#539D59
hypocenterC59C2×#1609
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#16837730C2semidirect
3. C2×#16837332C2semidirect
4. #21423093C2direct (N × H)
5. C2×#16837139C2semidirect
7. C2×#16837128C2semidirect
12. #16837730C22semidirect
22. #16837332C22semidirect
25. #16837139C22semidirect
27. #16837128C22semidirect
277. C2×C59#1609semidirect
313. C59C2×#1609semidirect
541. C2#21423093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168377302
C2×#168377132
C2×#168373322
#214230932
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