Finite Group Databasebeta

← C2×#21458515 #30559637

Subgroups — C2×#21458515 #30559637

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic
2#21458515C2116yesmaximal, direct product factor
3C2×#16840119C212yesmaximal, complemented
4C2×#16840110C211yesmaximal, characteristic
5C2×#16840044C211yesmaximal, characteristic, complemented
6C2×#16840059C212yesmaximal, complemented
7C2×#16839984C212yesmaximal, complemented
8C2×#16839962C211yesmaximal, characteristic
9C2×Q8×#92418C211yesmaximal, characteristic, complemented
10C2×C4×#11758202C211yesmaximal, characteristic, complemented
11C2×C4×#11758201C212yesmaximal, complemented
12C2×C61×#557C211yesmaximal, characteristic, complemented
13C22×#11758202C2211yescharacteristic
14C22×#11758201C2212yes—
15#16840497—24no—
16#16840497C2218yes—
17C2×#14519774C2211yescharacteristic
18C2×#14519766—21no—
19C2×#14519765C2212yes—
20C2×#14519762—22no—
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×D244C2212yes—
23C2×#14519739—21no—
24#16840119C22116yescomplemented
25#16840110C2218yes—
26#16840059C22116yescomplemented
27#16840044C2218yescomplemented
28#16839984C22116yescomplemented
29#16839962C2218yes—
30Q8×#92418C2218yescomplemented
31C4×#11758202C2218yescomplemented
32C4×#11758201C22116yescomplemented
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2212yes—
35C2×C4⋊#92418C2211yescharacteristic
36C2×C4⋊#92418C2212yes—
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2212yes—
40C2×#14519697C2212yes—
41C2×#14519697C2212yes—
42C2×#14519697C2212yes—
43C2×C4×#92418C2212yes—
44C2×C4×#92418C2211yescharacteristic
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×Dic122C2311yescharacteristic
56C22×D244—21no—
57C22×D244—21no—
58C22×D244C2312yes—
59C22×C4×D61—22no—
60C2×#11758202—24no—
61C2×#11758202C2314yes—
62C2×#11758201—28no—
63C2×#11758201C2318yes—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2312yes—
67#14519774—22no—
68#14519774C2314yes—
69#14519766—28no—
70#14519765—24no—
71#14519765C2318yes—
72#14519762—216no—
73C4×Dic122—22no—
74C4×Dic122C2314yes—
75C4×D244—24no—
76C4×D244C2318yes—
77#14519739—28no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758198—22no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×C4×Dic61—21no—
84#14519710C2314yes—
85#14519708C2318yes—
86C4⋊#92418C2314yes—
87C4⋊#92418C2318yes—
88#14519701C2314yes—
89#14519700C2318yes—
90#14519700C2314yes—
91#14519697C2318yes—
92#14519697C2318yes—
93#14519697C2318yes—
94C4×#92418C2318yes—
95C4×#92418C2314yes—
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—22no—
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—21no—
144C2×D244—24no—
145C2×D244—24no—
146C2×D244—24no—
147C2×D244—22no—
148C2×D244—24no—
149C2×D244—44no—
150C2×D244—82no—
151C2×D244C2414yes—
152C2×C4×D61—28no—
153C2×C4×D61—84no—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—21no—
157C2×Dic122C2412yes—
158C4⋊C4×C61—28no—
159C4⋊C4×C61—24no—
160C4⋊C4×C61—28no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—28no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61C2×D414yes—
166C4⋊C4×C61C2×D418yes—
167C4⋊C4×C61C2412yes—
168C4⋊C4×C61C2414yes—
169C42×C61—28no—
170C42×C61—24no—
171C42×C61C2×D414yes—
172C42×C61C2×D412yes—
173C42×C61C2414yes—
174C42×C61C2412yes—
175#11758202—28no—
176#11758201—216no—
177#11758198—28no—
178#11758198—28no—
179#11758198—28no—
180C4⋊Dic61—21no—
181C4⋊Dic61C2412yes—
182#11758196—24no—
183C4×Dic61—24no—
184C2×#92418—24no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418C2412yes—
188C2×#92418C2412yes—
189C2×#92418C2414yes—
190C23×C61C22×D411yescharacteristic
191C22×D61—24no—
192C22×D61—44no—
193C22×D61—44no—
194C22×D61—44no—
195Q8×C61—24no—
196Q8×C61—28no—
197Q8×C61—22no—
198Q8×C61—48no—
199Q8×C61C2×#4114yes—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—24no—
207C2×C4×C61—44no—
208C2×C4×C61—42no—
209C2×C4×C61#13514yes—
210C2×C4×C61C22×D412yes—
211C2×C4×C61C22×D414yes—
212C2×C4×C61C22×D414yes—
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C22×D412yes—
215C2×C4×C61C2×#4112yes—
216C2×C4×C612−1+412yes—
217C2×C4×C61C2511yescharacteristic
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—42no—
221C2×Dic61—42no—
222D244—24no—
223D244—24no—
224D244—44no—
225D244—48no—
226D244—84no—
227C4×D61—88no—
228Dic122—22no—
229Dic122—22no—
230Dic122—42no—
231#92418—24no—
232#92418—22no—
233#92418—22no—
234C2×#3365—611nomaximal, Sylow
235C22×C61#54812yes—
236C22×C61C2×#13512yes—
237C22×C61#57712yes—
238C22×C61C23×D411yescharacteristic
239C2×D61—44no—
240C2×D61—44no—
241C2×D61—44no—
242C2×D61—88no—
243C4×C61—24no—
244C4×C61—24no—
245C4×C61—24no—
246C4×C61—22no—
247C4×C61—44no—
248C4×C61—42no—
249C4×C61#54812yes—
250C4×C61C2×#13514yes—
251C4×C61C22×#4111yescharacteristic
252C4×C61C2×2−1+411yescharacteristic
253Dic61—42no—
254Dic61—42no—
255C2×#559—611no—
256C2×#557D6111yescharacteristic, complemented
257#3365—6116no—
258C2×#488—612no—
259C2×#486—611no—
260C2×#475—611no—
261C2×#478—612no—
262C2×#464—612no—
263C2×#460—611no—
264C2×C8×Q8—611no—
265C2×C4×Q16—611no—
266C2×C4×SD16—612no—
267C2×C61#336514yescomplemented
268C2×C61C2×#54811yescharacteristic
269C2×C61C22×#13511yescharacteristic
270C2×C61C2×#57711yescharacteristic
271D61—84no—
272C22×Q16—611no—
273C22×SD16—612no—
274#559—618no—
275#559—1224no—
276#557—24no—
277#557C2×D6118yescomplemented
278C2×C4⋊Q8—21no—
279C2×C4⋊Q8C2×D6111yescharacteristic
280C2×#127—611no—
281C2×#125—22no—
282C2×#125C2×D6112yes—
283C2×#124—612no—
284C2×#124—1221no—
285C2×#123—1222no—
286C2×C4×Q8—21no—
287C2×C4×Q8—611no—
288C2×C4×Q8C2×D6112yes—
289C2×C4×Q8C2×D6111yescharacteristic
290C2×C4×Q8C2×D6111yescharacteristic
291C2×C4×D4—612no—
292C2×C4×D4—1221no—
293#488—6116no—
294#486—618no—
295#478—6116no—
296#475—618no—
297#464—6116no—
298#460—618no—
299C8×Q8—618no—
300C4×Q16—618no—
301C4×SD16—6116no—
302C2×#107—611no—
303C2×#106—612no—
304C2×C4⋊C8—612no—
305C2×C4⋊C8—611no—
306C2×#103—611no—
307C2×#103—612no—
308C2×#103—611no—
309C2×#102—612no—
310C2×#102—612no—
311C2×#102—612no—
312C2×C4×C8—611no—
313C2×C4×C8—612no—
314C61C2×#336511yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8—611no—
317C22×Q8C22⋊D6111yescharacteristic
318C22×Q8C22×D6111yescharacteristic
319C22×D4—612no—
320C22×D4—1221no—
321C22×D4—1221no—
322C23×C4—1222no—
323C2×Q16—614no—
324C2×Q16—1224no—
325C2×SD16—618no—
326C2×SD16—1228no—
327C22×C8—612no—
328C22×C8—611no—
329C22×C8—611no—
330C4⋊Q8—28no—
331C4⋊Q8—22no—
332C4⋊Q8C22×D6114yes—
333#127—614no—
334#127—1222no—
335#125—216no—
336#125—24no—
337#125C22×D6118yes—
338#124—618no—
339#124—1228no—
340#124—1224no—
341#123—12216no—
342C4×Q8—28no—
343C4×Q8—24no—
344C4×Q8—22no—
345C4×Q8—614no—
346C4×Q8—1222no—
347C4×Q8C22⋊D6114yes—
348C4×Q8C22×D6118yes—
349C4×Q8C22×D6114yes—
350C4×Q8C22×D6114yes—
351C4×D4—618no—
352C4×D4—1228no—
353C4×D4—1224no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—611no—
360C2×C4⋊C4—1221no—
361C2×C4⋊C4C22⋊D6111yescharacteristic
362C2×C4⋊C4C22⋊D6112yes—
363C2×C4⋊C4C22×D6111yescharacteristic
364C2×C4⋊C4C22×D6112yes—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1222no—
367C2×C22⋊C4—1222no—
368C2×C42—22no—
369C2×C42—21no—
370C2×C42—1221no—
371C2×C42C22×D6112yes—
372C2×C42C22×D6111yescharacteristic
373#107—614no—
374#106—618no—
375C4⋊C8—614no—
376C4⋊C8—618no—
377#103—614no—
378#103—614no—
379#103—618no—
380#102—618no—
381#102—618no—
382#102—618no—
383C4×C8—618no—
384C4×C8—614no—
385C24—1222no—
386C2×Q8—21no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—24no—
390C2×Q8—44no—
391C2×Q8—612no—
392C2×Q8—1221no—
393C2×Q8—1222no—
394C2×Q8—1222no—
395C2×Q8#1175822614yes—
396C2×Q8C2×C22⋊D6114yes—
397C2×Q8C23×D6112yes—
398C2×D4—614no—
399C2×D4—1224no—
400C2×D4—1224no—
401C2×D4—1222no—
402C2×D4—1224no—
403C2×D4—1224no—
404C2×D4—4882no—
405C2×D4—2444no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—1221no—
410C22×C4—1221no—
411C22×C4—1228no—
412C22×C4—4884no—
413C22×C4C2×C22⋊D6112yes—
414C22×C4C2×C22⋊D6112yes—
415C22×C4C2×C22⋊D6111yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417C22×C4C23×D6111yescharacteristic
418Q16—1228no—
419SD16—12216no—
420C2×C8—612no—
421C2×C8—612no—
422C2×C8—614no—
423C2×C8—1224no—
424C2×C8—1222no—
425C2×C8—1222no—
426C4⋊C4—28no—
427C4⋊C4—24no—
428C4⋊C4—28no—
429C4⋊C4—24no—
430C4⋊C4—28no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—612no—
434C4⋊C4—1221no—
435C4⋊C4—1224no—
436C4⋊C4C2×C22⋊D6114yes—
437C4⋊C4C2×C22⋊D6118yes—
438C4⋊C4C23×D6114yes—
439C4⋊C4C23×D6112yes—
440C22⋊C4—1228no—
441C22⋊C4—1228no—
442C22⋊C4—1228no—
443C42—28no—
444C42—24no—
445C42—1224no—
446C42C2×C22⋊D6114yes—
447C42C2×C22⋊D6112yes—
448C42C23×D6114yes—
449C42C23×D6112yes—
450C23—1224no—
451C23—2444no—
452C23—2444no—
453C23—2444no—
454C23C22×C22⋊D6111yescharacteristic
455Q8—28no—
456Q8—22no—
457Q8—24no—
458Q8—48no—
459Q8—1222no—
460Q8—1222no—
461Q8—2442no—
462Q8C2×#1175822614yes—
463D4—1224no—
464D4—1224no—
465D4—4884no—
466D4—2448no—
467D4—2444no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—4888no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4#1451979714yes—
483C2×C4C22×C22⋊D6114yes—
484C2×C4C22×C22⋊D6114yes—
485C2×C4C22×C22⋊D6112yes—
486C2×C4C22×C22⋊D6112yes—
487C2×C4C22×C22⋊D6111yescharacteristic
488C2×C4C2×#1175822612yes—
489C2×C4#1451982512yes—
490C2×C4C24×D6111yescharacteristic
491C8—1224no—
492C8—1222no—
493C8—1222no—
494C22—4888no—
495C22—2444no—
496C22—2444no—
497C22—2444no—
498C22#1684042312yes—
499C22C2×#1451979712yes—
500C22#1684057012yes—
501C22C23×C22⋊D6111yescharacteristic
502C4—24no—
503C4—24no—
504C4—24no—
505C4—22no—
506C4—44no—
507C4—42no—
508C4—2442no—
509C4—2442no—
510C4#1684042312yes—
511C4C2×#1451979714yes—
512C4C22×#1175822611yescharacteristic
513C4C2×#1451982511yescharacteristic
514C2—4884no—
515C2#2145851514yesdirect product factor
516C2C2×#1684042311yescharacteristic
517C2C22×#1451979711yescharacteristic
518C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#557C2
socleC23×C61C22×D4
prime radicalC2×#14519774C22
hypercenterC2×#557D61
hypocenterC61C2×#3365
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. #21458515C2direct (N × H)
3. C2×#16840119C2semidirect
5. C2×#16840044C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16839984C2semidirect
9. C2×Q8×#92418C2semidirect
10. C2×C4×#11758202C2semidirect
11. C2×C4×#11758201C2semidirect
12. C2×C61×#557C2semidirect
24. #16840119C22semidirect
26. #16840059C22semidirect
27. #16840044C22semidirect
28. #16839984C22semidirect
30. Q8×#92418C22semidirect
31. C4×#11758202C22semidirect
32. C4×#11758201C22semidirect
46. C61×#557C22semidirect
256. C2×#557D61semidirect
267. C2×C61#3365semidirect
277. #557C2×D61semidirect
314. C61C2×#3365semidirect
515. C2#21458515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
#214585152
C2×#168401192
C2×#168401102
C2×#168400442
C2×#168400592
C2×#168399842
C2×#168399622
C2×Q8×#924182
C2×C4×#117582022
C2×C4×#117582012
C2×C61×#5572
C2×#336561