Finite Group Databasebeta

← C2×#21458504 #30559625

Subgroups — C2×#21458504 #30559625

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic
2#21458504C2116yesmaximal, direct product factor
3C2×#16840119C212yesmaximal
4C2×#16840114C211yesmaximal, characteristic, complemented
5C2×#16840066C212yesmaximal, complemented
6C2×#16840039C211yesmaximal, characteristic
7C2×#16839984C212yesmaximal
8C2×#16839972C211yesmaximal, characteristic, complemented
9C2×Q8×#92418C211yesmaximal, characteristic, complemented
10C2×C4×#11758202C212yesmaximal, complemented
11C2×C4×#11758201C211yesmaximal, characteristic
12C2×C61×#557C211yesmaximal, characteristic, complemented
13C22×#11758202C2212yes—
14C22×#11758201C2211yescharacteristic
15#16840485—24no—
16#16840485C2218yes—
17C2×#14519777C2211yescharacteristic
18C2×#14519772—22no—
19C2×#14519765C2212yes—
20C2×#14519753—21no—
21C2×C4×Dic122C2212yes—
22C2×C4×D244C2211yescharacteristic
23C2×#14519735—21no—
24#16840119C22116yes—
25#16840114C2218yescomplemented
26#16840066C22116yescomplemented
27#16840039C2218yes—
28#16839984C22116yes—
29#16839972C2218yescomplemented
30Q8×#92418C2218yescomplemented
31C4×#11758202C22116yescomplemented
32C4×#11758201C2218yes—
33C2×#14519710C2212yes—
34C2×#14519708C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×C4⋊#92418C2212yes—
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2212yes—
39C2×#14519700C2212yes—
40C2×#14519700C2212yes—
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2212yes—
43C2×C4×#92418C2211yescharacteristic
44C2×C4×#92418C2212yes—
45C61×#557—24no—
46C61×#557C2218yescomplemented
47C2×C4⋊Q8×C61—21no—
48C2×C4⋊Q8×C61C2211yescharacteristic
49C2×#125×C61—22no—
50C2×#125×C61C2212yes—
51C2×C4×Q8×C61—21no—
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×Q8×C61C2212yes—
54C2×C4×Q8×C61C2211yescharacteristic
55C22×Dic122C2312yes—
56C22×D244C2311yescharacteristic
57C22×C4×D61—21no—
58C2×#11758202—28no—
59C2×#11758202C2318yes—
60C2×#11758201—24no—
61C2×#11758201C2314yes—
62C22×#92418C2311yescharacteristic
63C22×#92418C2312yes—
64C22×#92418C2311yescharacteristic
65#14519777—22no—
66#14519777C2314yes—
67#14519772—216no—
68#14519765—24no—
69#14519765C2318yes—
70#14519753—28no—
71C4×Dic122—24no—
72C4×Dic122C2318yes—
73C4×D244—22no—
74C4×D244C2314yes—
75#14519735—28no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—22no—
80C2×#11758198—22no—
81C2×#11758198—21no—
82C2×#11758198—22no—
83C2×C4×Dic61—22no—
84#14519710C2318yes—
85#14519708C2314yes—
86C4⋊#92418C2314yes—
87C4⋊#92418C2318yes—
88#14519701C2314yes—
89#14519700C2318yes—
90#14519700C2318yes—
91#14519700C2318yes—
92#14519697C2318yes—
93#14519697C2314yes—
94C4×#92418C2314yes—
95C4×#92418C2318yes—
96C22×Q8×C61—21no—
97C22×Q8×C61D411yescharacteristic
98C22×Q8×C61C2311yescharacteristic
99C4⋊Q8×C61—28no—
100C4⋊Q8×C61—22no—
101C4⋊Q8×C61C2314yes—
102#125×C61—216no—
103#125×C61—24no—
104#125×C61C2318yes—
105C4×Q8×C61—28no—
106C4×Q8×C61—24no—
107C4×Q8×C61—22no—
108C4×Q8×C61D414yes—
109C4×Q8×C61C2314yes—
110C4×Q8×C61C2318yes—
111C4×Q8×C61C2314yes—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D412yes—
119C2×C4⋊C4×C61C2312yes—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C42×C61—21no—
122C2×C42×C61—22no—
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2312yes—
125C23×D61—21no—
126C2×Q8×C61—24no—
127C2×Q8×C61—21no—
128C2×Q8×C61—24no—
129C2×Q8×C61—22no—
130C2×Q8×C61—44no—
131C2×Q8×C61C2×D414yes—
132C2×Q8×C61#4114yes—
133C2×Q8×C61C2412yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—22no—
144C2×D244—22no—
145C2×D244—22no—
146C2×D244—21no—
147C2×D244C2412yes—
148C2×C4×D61—24no—
149C2×C4×D61—44no—
150C2×Dic122—24no—
151C2×Dic122—24no—
152C2×Dic122—22no—
153C2×Dic122C2414yes—
154C4⋊C4×C61—28no—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—28no—
157C4⋊C4×C61—24no—
158C4⋊C4×C61—28no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61C2×D414yes—
162C4⋊C4×C61C2×D418yes—
163C4⋊C4×C61C2412yes—
164C4⋊C4×C61C2414yes—
165C42×C61—28no—
166C42×C61—24no—
167C42×C61C2×D414yes—
168C42×C61C2×D412yes—
169C42×C61C2414yes—
170C42×C61C2412yes—
171#11758202—216no—
172#11758201—28no—
173#11758198—28no—
174#11758198—24no—
175#11758198—28no—
176C4⋊Dic61—24no—
177C4⋊Dic61—24no—
178C4⋊Dic61—21no—
179C4⋊Dic61C2412yes—
180#11758196—28no—
181C4×Dic61—28no—
182C2×#92418—22no—
183C2×#92418—24no—
184C2×#92418—22no—
185C2×#92418C2412yes—
186C2×#92418C2414yes—
187C2×#92418C2412yes—
188C23×C61C22×D411yescharacteristic
189C22×D61—22no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193Q8×C61—24no—
194Q8×C61—28no—
195Q8×C61—22no—
196Q8×C61—48no—
197Q8×C61C2×#4114yes—
198C2×C4×C61—24no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—24no—
205C2×C4×C61—44no—
206C2×C4×C61—42no—
207C2×C4×C61#13514yes—
208C2×C4×C61C22×D414yes—
209C2×C4×C61C22×D414yes—
210C2×C4×C61C22×D412yes—
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D412yes—
213C2×C4×C61C2×#4112yes—
214C2×C4×C612−1+412yes—
215C2×C4×C61C2511yescharacteristic
216C2×Dic61—22no—
217C2×Dic61—24no—
218C2×Dic61—44no—
219C2×Dic61—42no—
220D244—22no—
221D244—22no—
222D244—42no—
223C4×D61—48no—
224Dic122—24no—
225Dic122—24no—
226Dic122—44no—
227#92418—22no—
228#92418—24no—
229#92418—22no—
230C2×#3364—611nomaximal, Sylow
231C22×C61#54812yes—
232C22×C61C2×#13512yes—
233C22×C61#57812yes—
234C22×C61C23×D411yescharacteristic
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—84no—
239C4×C61—24no—
240C4×C61—24no—
241C4×C61—24no—
242C4×C61—22no—
243C4×C61—44no—
244C4×C61—42no—
245C4×C61#54812yes—
246C4×C61C2×#13514yes—
247C4×C61C22×#4111yescharacteristic
248C4×C61C2×2−1+411yescharacteristic
249Dic61—44no—
250Dic61—42no—
251C2×#557D6111yescharacteristic, complemented
252C2×#556—611no—
253#3364—6116no—
254C2×#488—612no—
255C2×#487—611no—
256C2×#479—612no—
257C2×#474—611no—
258C2×#464—612no—
259C2×#462—611no—
260C2×C8×Q8—611no—
261C2×C4×Q16—612no—
262C2×C4×SD16—611no—
263C2×C61#336414yescomplemented
264C2×C61C2×#54811yescharacteristic
265C2×C61C22×#13511yescharacteristic
266C2×C61C2×#57811yescharacteristic
267D61—82no—
268C22×Q16—612no—
269C22×SD16—611no—
270#557—24no—
271#557C2×D6118yescomplemented
272#556—618no—
273#556—1224no—
274C2×C4⋊Q8—21no—
275C2×C4⋊Q8—611no—
276C2×C4⋊Q8C2×D6111yescharacteristic
277C2×#126—1222no—
278C2×#125—22no—
279C2×#125C2×D6112yes—
280C2×#124—612no—
281C2×C22⋊Q8—1221no—
282C2×C4×Q8—21no—
283C2×C4×Q8—612no—
284C2×C4×Q8C2×D6111yescharacteristic
285C2×C4×Q8C2×D6112yes—
286C2×C4×Q8C2×D6111yescharacteristic
287C2×C4×D4—611no—
288C2×#117—1221no—
289#488—6116no—
290#487—618no—
291#479—6116no—
292#474—618no—
293#464—6116no—
294#462—618no—
295C8×Q8—618no—
296C4×Q16—6116no—
297C4×SD16—618no—
298C2×#107—612no—
299C2×#106—611no—
300C2×C4⋊C8—612no—
301C2×C4⋊C8—611no—
302C2×#103—611no—
303C2×#103—612no—
304C2×#103—612no—
305C2×#103—612no—
306C2×#102—611no—
307C2×#102—612no—
308C2×C4×C8—611no—
309C2×C4×C8—612no—
310C61C2×#336411yescharacteristic, complemented, Sylow
311C22×Q8—21no—
312C22×Q8—612no—
313C22×Q8C22⋊D6111yescharacteristic
314C22×Q8C22×D6111yescharacteristic
315C22×D4—611no—
316C23×C4—1221no—
317C2×Q16—618no—
318C2×Q16—1228no—
319C2×SD16—614no—
320C2×SD16—1224no—
321C22×C8—611no—
322C22×C8—612no—
323C22×C8—611no—
324C4⋊Q8—28no—
325C4⋊Q8—22no—
326C4⋊Q8—614no—
327C4⋊Q8—1222no—
328C4⋊Q8C22×D6114yes—
329#126—12216no—
330#125—216no—
331#125—24no—
332#125C22×D6118yes—
333#124—618no—
334#124—1224no—
335C22⋊Q8—1228no—
336C4×Q8—28no—
337C4×Q8—24no—
338C4×Q8—22no—
339C4×Q8—618no—
340C4×Q8—1224no—
341C4×Q8C22⋊D6114yes—
342C4×Q8C22×D6114yes—
343C4×Q8C22×D6118yes—
344C4×Q8C22×D6114yes—
345C4×D4—614no—
346C4×D4—1222no—
347#117—1228no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4C22⋊D6111yescharacteristic
358C2×C4⋊C4C22⋊D6112yes—
359C2×C4⋊C4C22×D6111yescharacteristic
360C2×C4⋊C4C22×D6112yes—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1221no—
363C2×C22⋊C4—1222no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42—1222no—
367C2×C42C22×D6111yescharacteristic
368C2×C42C22×D6112yes—
369#107—618no—
370#106—614no—
371C4⋊C8—614no—
372C4⋊C8—618no—
373#103—614no—
374#103—618no—
375#103—618no—
376#103—618no—
377#102—614no—
378#102—618no—
379C4×C8—614no—
380C4×C8—618no—
381C24—1221no—
382C2×Q8—21no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—24no—
386C2×Q8—44no—
387C2×Q8—614no—
388C2×Q8—1222no—
389C2×Q8—1224no—
390C2×Q8—1224no—
391C2×Q8#1175822614yes—
392C2×Q8C2×C22⋊D6114yes—
393C2×Q8C23×D6112yes—
394C2×D4—612no—
395C2×D4—1221no—
396C2×D4—1222no—
397C2×D4—1222no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—1221no—
402C22×C4—1222no—
403C22×C4—1224no—
404C22×C4—2444no—
405C22×C4C2×C22⋊D6112yes—
406C22×C4C2×C22⋊D6111yescharacteristic
407C22×C4C2×C22⋊D6112yes—
408C22×C4C2×C22⋊D6111yescharacteristic
409C22×C4C23×D6111yescharacteristic
410Q16—12216no—
411SD16—1228no—
412C2×C8—612no—
413C2×C8—614no—
414C2×C8—612no—
415C2×C8—1222no—
416C2×C8—1224no—
417C2×C8—1222no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—28no—
421C4⋊C4—24no—
422C4⋊C4—28no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—612no—
426C4⋊C4—1221no—
427C4⋊C4—1228no—
428C4⋊C4—1224no—
429C4⋊C4—1224no—
430C4⋊C4C2×C22⋊D6114yes—
431C4⋊C4C2×C22⋊D6118yes—
432C4⋊C4C23×D6112yes—
433C4⋊C4C23×D6114yes—
434C22⋊C4—1228no—
435C22⋊C4—1224no—
436C22⋊C4—1228no—
437C42—28no—
438C42—24no—
439C42—1228no—
440C42C2×C22⋊D6112yes—
441C42C2×C22⋊D6114yes—
442C42C23×D6112yes—
443C42C23×D6114yes—
444C23—1222no—
445C23—2442no—
446C23—2442no—
447C23—2442no—
448C23C22×C22⋊D6111yescharacteristic
449Q8—28no—
450Q8—22no—
451Q8—24no—
452Q8—48no—
453Q8—1224no—
454Q8—1224no—
455Q8—2444no—
456Q8C2×#1175822614yes—
457D4—1222no—
458D4—1222no—
459D4—2442no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—1222no—
470C2×C4—1224no—
471C2×C4—2442no—
472C2×C4—2444no—
473C2×C4—2448no—
474C2×C4#1451979714yes—
475C2×C4C22×C22⋊D6114yes—
476C2×C4C22×C22⋊D6112yes—
477C2×C4C22×C22⋊D6114yes—
478C2×C4C22×C22⋊D6112yes—
479C2×C4C22×C22⋊D6111yescharacteristic
480C2×C4C2×#1175822612yes—
481C2×C4#1451982512yes—
482C2×C4C24×D6111yescharacteristic
483C8—1222no—
484C8—1224no—
485C8—1222no—
486C22—4884no—
487C22—2442no—
488C22—2442no—
489C22—2442no—
490C22#1684042312yes—
491C22C2×#1451979712yes—
492C22#1684057712yes—
493C22C23×C22⋊D6111yescharacteristic
494C4—24no—
495C4—24no—
496C4—24no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—2442no—
501C4—2444no—
502C4#1684042312yes—
503C4C2×#1451979714yes—
504C4C22×#1175822611yescharacteristic
505C4C2×#1451982511yescharacteristic
506C2—4882no—
507C2#2145850414yesdirect product factor
508C2C2×#1684042311yescharacteristic
509C2C22×#1451979711yescharacteristic
510C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#557C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#557D61
hypocenterC61C2×#3364
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #21458504C2direct (N × H)
4. C2×#16840114C2semidirect
5. C2×#16840066C2semidirect
8. C2×#16839972C2semidirect
9. C2×Q8×#92418C2semidirect
10. C2×C4×#11758202C2semidirect
12. C2×C61×#557C2semidirect
25. #16840114C22semidirect
26. #16840066C22semidirect
29. #16839972C22semidirect
30. Q8×#92418C22semidirect
31. C4×#11758202C22semidirect
46. C61×#557C22semidirect
251. C2×#557D61semidirect
263. C2×C61#3364semidirect
271. #557C2×D61semidirect
310. C61C2×#3364semidirect
507. C2#21458504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
#214585042
C2×#168401192
C2×#168401142
C2×#168400662
C2×#168400392
C2×#168399842
C2×#168399722
C2×Q8×#924182
C2×C4×#117582022
C2×C4×#117582012
C2×C61×#5572
C2×#336461