Finite Group Databasebeta

← C2×#21458734 #30560507

Subgroups — C2×#21458734 #30560507

Order 15616.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840492C211yesmaximal, characteristic, complemented
2C2×#16840473C211yesmaximal, characteristic
3#21458734C2116yesmaximal, direct product factor
4C2×#16840170C212yesmaximal, complemented
5C2×#16840068C212yesmaximal, complemented
6C2×#16840054C211yesmaximal, characteristic, complemented
7C2×#16840049C211yesmaximal, characteristic
8C2×#16840041C212yesmaximal
9C2×#16839892C211yesmaximal, characteristic, complemented
10C2×#16839861C212yesmaximal
11C2×C4×#11758190C211yesmaximal, characteristic
12C2×C61×#500C211yesmaximal, characteristic, complemented
13C22×#11758190C2211yescharacteristic
14#16840492—24no—
15#16840492C2218yescomplemented
16#16840473—24no—
17#16840473C2218yes—
18C2×#14519776—21no—
19C2×#14519776C2212yes—
20C2×#14519775—22no—
21C2×#14519768C2212yes—
22C2×#14519757—21no—
23C2×#14519753—22no—
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519742—21no—
27C2×#14519742C2212yes—
28C2×C4×D244C2211yescharacteristic
29C2×#14519739C2212yes—
30C2×C4⋊C4×D61—21no—
31#16840170C22116yescomplemented
32#16840068C22116yescomplemented
33#16840054C2218yescomplemented
34#16840049C2218yes—
35#16840041C22116yes—
36#16839892C2218yescomplemented
37#16839861C22116yes—
38C4×#11758190C2218yes—
39C2×#14519710C2212yes—
40C2×#14519709C2211yescharacteristic
41C2×#14519708C2212yes—
42C2×C4⋊#92418C2211yescharacteristic
43C2×#14519706C2212yes—
44C2×#14519702C2211yescharacteristic
45C2×#14519700C2212yes—
46C2×#14519699C2211yescharacteristic
47C2×#14519697C2212yes—
48C2×#14519687C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4⋊Q8×C61C2211yescharacteristic
51C61×#500C2218yescomplemented
52C2×#107×C61C2212yes—
53C2×#107×C61C2212yes—
54C2×C4×C8×C61C2211yescharacteristic
55C22×Dic122—22no—
56C22×Dic122D411yescharacteristic
57C22×Dic122C2311yescharacteristic
58C22×D244C2311yescharacteristic
59C22×C4×D61—21no—
60C22×C4×D61—22no—
61C2×#11758190Q818yescomplemented
62C2×#11758190C2314yes—
63C22×#92418C2312yes—
64#14519776—28no—
65#14519776—24no—
66#14519776C2318yes—
67#14519775—216no—
68#14519768—24no—
69#14519768C2318yes—
70#14519757—28no—
71#14519753—216no—
72C4×Dic122—22no—
73C4×Dic122D414yes—
74C4×Dic122C2314yes—
75C4×Dic122C2314yes—
76#14519742—28no—
77#14519742—24no—
78#14519742C2318yes—
79C4×D244—22no—
80C4×D244C2314yes—
81#14519739—24no—
82#14519739C2318yes—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61D411yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196D412yes—
92C4⋊C4×D61—28no—
93C2×#11758198—21no—
94C2×#11758198—22no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519710C2318yes—
99#14519709C2314yes—
100#14519708C2318yes—
101C4⋊#92418C2314yes—
102#14519706C2318yes—
103#14519702C2314yes—
104#14519700C2318yes—
105#14519699C2314yes—
106#14519697C2318yes—
107#14519687C2318yes—
108C22×Q8×C61—21no—
109C22×Q8×C61—21no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C4⋊Q8×C61—22no—
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61C2314yes—
115C4⋊Q8×C61C2314yes—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61C2312yes—
119C2×C4⋊C4×C61C2312yes—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2318yes—
122#107×C61C2318yes—
123C4×C8×C61C2314yes—
124C23×D61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61—24no—
127C2×Q8×C61—82no—
128C2×Q8×C61—82no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D412yes—
138C22×Dic61C2×D412yes—
139C2×D244—21no—
140C2×D244—22no—
141C2×D244C2×Q814yes—
142C2×D244C2412yes—
143C2×C4×D61—24no—
144C2×C4×D61—28no—
145C2×C4×D61—44no—
146C2×C4×D61—84no—
147C2×Dic122—24no—
148C2×Dic122—21no—
149C2×Dic122—22no—
150C2×Dic122—28no—
151C2×Dic122—84no—
152C2×Dic122C2×D414yes—
153C2×Dic122C2×Q814yes—
154C2×Dic122C2412yes—
155C2×C8×C61—22no—
156C2×C8×C61C2×Q814yes—
157C2×C8×C61C2412yes—
158C2×C8×C61C2412yes—
159C4⋊C4×C61—24no—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61C2414yes—
164C4⋊C4×C61C2414yes—
165C42×C61C2×D412yes—
166C42×C61C2412yes—
167#11758198—24no—
168#11758198—28no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—28no—
172C4⋊Dic61C2×D414yes—
173C4⋊Dic61C2412yes—
174C4⋊Dic61C2412yes—
175#11758196—24no—
176#11758196—28no—
177#11758196—28no—
178#11758196—28no—
179#11758196C2×D418yes—
180C4×Dic61—24no—
181C4×Dic61—28no—
182C4×Dic61C2×D414yes—
183C4×Dic61C2414yes—
184C2×#92418—24no—
185C2×#92418C2414yes—
186#11758190C2×Q8116yescomplemented
187C23×C61C22×D411yescharacteristic
188C22×D61—24no—
189C22×D61—22no—
190C22×D61—42no—
191C22×D61—42no—
192Q8×C61—84no—
193Q8×C61—84no—
194C2×C4×C61—22no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—44no—
198C2×C4×C61—44no—
199C2×C4×C61#13714yes—
200C2×C4×C61C22×D412yes—
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D412yes—
203C2×C4×C61C22×Q812yes—
204C2×C4×C612−1+412yes—
205C2×C4×C61C2511yescharacteristic
206C2×Dic61—24no—
207C2×Dic61—24no—
208C2×Dic61—24no—
209C2×Dic61—22no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61C22×D414yes—
215C2×Dic61C22×D414yes—
216D244—24no—
217D244—22no—
218D244C22×Q814yes—
219C4×D61—48no—
220C4×D61—88no—
221Dic122—24no—
222Dic122—28no—
223Dic122—22no—
224Dic122—88no—
225Dic122C22×Q814yes—
226C8×C61—22no—
227C8×C61C22×Q814yes—
228#92418—24no—
229C2×#3385—611nomaximal, Sylow
230C22×C61D4×Q812yes—
231C22×C61C2×#13712yes—
232C22×C61#57612yes—
233C22×C61C23×D411yescharacteristic
234C2×D61—24no—
235C2×D61—48no—
236C2×D61—42no—
237C2×D61—42no—
238C4×C61—22no—
239C4×C61—44no—
240C4×C61—44no—
241C4×C61D4×Q812yes—
242C4×C61C2×#13714yes—
243C4×C61C23×Q811yescharacteristic
244C4×C61C2×2−1+411yescharacteristic
245Dic61—24no—
246Dic61—24no—
247Dic61—24no—
248Dic61—42no—
249Dic61—42no—
250C2×Q82—611no—
251C2×#554—611no—
252#3385—6116no—
253C2×#501—612no—
254C2×#500D6111yescharacteristic, complemented
255C2×#479—612no—
256C2×#477—611no—
257C2×#476—611no—
258C2×#474—612no—
259C2×#446—611no—
260C2×#440—612no—
261C2×C4×SD16—611no—
262C2×C61#338514yescomplemented
263C2×C61C2×D4×Q811yescharacteristic
264C2×C61C22×#13711yescharacteristic
265C2×C61C2×#57611yescharacteristic
266D61—44no—
267C22×SD16—611no—
268Q82—618no—
269Q82—1224no—
270#554—618no—
271#554—1224no—
272C2×C4⋊Q8—612no—
273C2×C4⋊Q8—1221no—
274C2×C4⋊Q8—1222no—
275C2×C4⋊Q8C2×D6111yescharacteristic
276C2×C4⋊Q8C2×D6111yescharacteristic
277C2×#125—612no—
278C2×C22⋊Q8—1221no—
279C2×C22⋊Q8—1222no—
280C2×C4×Q8—611no—
281C2×C4×Q8—612no—
282C2×C4×Q8—611no—
283C2×C4×Q8—1221no—
284C2×C4×D4—612no—
285C2×C4×D4—611no—
286C22×C4⋊C4—1221no—
287#501—6116no—
288#500C2×D6118yescomplemented
289#479—6116no—
290#477—618no—
291#476—618no—
292#474—6116no—
293#446—618no—
294#440—6116no—
295C4×SD16—618no—
296C2×#107—612no—
297C2×#107C2×D6112yes—
298C2×#107C2×D6112yes—
299C2×#106—611no—
300C2×#106—612no—
301C2×C4⋊C8—612no—
302C2×C4⋊C8—611no—
303C2×#103—611no—
304C2×#103—612no—
305C2×#102—611no—
306C2×#102—612no—
307C2×#97—612no—
308C2×C4×C8C2×D6111yescharacteristic
309C61C2×#338511yescharacteristic, complemented, Sylow
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—611no—
313C22×Q8—611no—
314C22×Q8—1222no—
315C22×D4—611no—
316C23×C4—1222no—
317C23×C4—1221no—
318C2×SD16—618no—
319C2×SD16—614no—
320C22×C8—612no—
321C22×C8C22×D6111yescharacteristic
322C22×C8C22×D6111yescharacteristic
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—618no—
326C4⋊Q8—1224no—
327C4⋊Q8—1228no—
328C4⋊Q8—12216no—
329C4⋊Q8C22×D6114yes—
330C4⋊Q8C22×D6114yes—
331#125—618no—
332#125—1224no—
333C22⋊Q8—1228no—
334C22⋊Q8—12216no—
335C4×Q8—614no—
336C4×Q8—614no—
337C4×Q8—618no—
338C4×Q8—614no—
339C4×Q8—1224no—
340C4×Q8—1228no—
341C4×Q8—1222no—
342C4×D4—618no—
343C4×D4—614no—
344C4×D4—1224no—
345C4×D4—1222no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—1228no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1222no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4C22×D6112yes—
359C2×C4⋊C4C22×D6112yes—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1221no—
362C2×C42—612no—
363C2×C42—1222no—
364C2×C42—1221no—
365C2×C42C22×D6111yescharacteristic
366#107—618no—
367#107C22×D6118yes—
368#107C22×D6118yes—
369#106—614no—
370#106—618no—
371C4⋊C8—618no—
372C4⋊C8—614no—
373#103—614no—
374#103—618no—
375#102—614no—
376#102—618no—
377#97—618no—
378C4×C8C22×D6114yes—
379C24—1221no—
380C2×Q8—24no—
381C2×Q8—24no—
382C2×Q8—82no—
383C2×Q8—82no—
384C2×Q8—614no—
385C2×Q8—614no—
386C2×Q8—612no—
387C2×Q8—1228no—
388C2×Q8—1224no—
389C2×Q8—1221no—
390C2×Q8—1222no—
391C2×Q8—4884no—
392C2×D4—614no—
393C2×D4—612no—
394C2×D4—1221no—
395C2×D4—1222no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—612no—
399C22×C4—612no—
400C22×C4—1228no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1224no—
405C22×C4—4884no—
406C22×C4—2444no—
407C22×C4D4×D6111yescharacteristic
408C22×C4D4×D6111yescharacteristic
409C22×C4C23×D6111yescharacteristic
410SD16—6116no—
411C2×C8—22no—
412C2×C8—614no—
413C2×C8—1224no—
414C2×C8Q8×D6114yes—
415C2×C8C23×D6112yes—
416C2×C8C23×D6112yes—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—614no—
422C4⋊C4—618no—
423C4⋊C4—612no—
424C4⋊C4—612no—
425C4⋊C4—1228no—
426C4⋊C4—1228no—
427C4⋊C4—1228no—
428C4⋊C4—1228no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1224no—
432C4⋊C4C23×D6114yes—
433C4⋊C4C23×D6114yes—
434C22⋊C4—1228no—
435C22⋊C4—1224no—
436C42—614no—
437C42—614no—
438C42—1228no—
439C42—1224no—
440C42D4×D6112yes—
441C42C23×D6112yes—
442C23—1222no—
443C23—1224no—
444C23—2442no—
445C23—2442no—
446C23C2×D4×D6111yescharacteristic
447Q8—84no—
448Q8—84no—
449Q8—614no—
450Q8—1228no—
451Q8—1222no—
452Q8—1224no—
453Q8—4888no—
454D4—614no—
455D4—1222no—
456D4—1224no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—614no—
463C2×C4—614no—
464C2×C4—1224no—
465C2×C4—1224no—
466C2×C4—1222no—
467C2×C4—1224no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—4888no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4—2448no—
474C2×C4#1451980914yes—
475C2×C4C2×D4×D6112yes—
476C2×C4C2×D4×D6112yes—
477C2×C4C2×D4×D6111yescharacteristic
478C2×C4C2×Q8×D6112yes—
479C2×C4#1451982512yes—
480C2×C4C24×D6111yescharacteristic
481C8—22no—
482C8—1224no—
483C8C2×Q8×D6114yes—
484C22—1224no—
485C22—2448no—
486C22—2442no—
487C22—2442no—
488C22#1684042712yes—
489C22C2×#1451980912yes—
490C22#1684056312yes—
491C22C22×D4×D6111yescharacteristic
492C4—22no—
493C4—44no—
494C4—44no—
495C4—1224no—
496C4—1224no—
497C4—1224no—
498C4—2442no—
499C4—2442no—
500C4#1684042712yes—
501C4C2×#1451980914yes—
502C4C22×Q8×D6111yescharacteristic
503C4C2×#1451982511yescharacteristic
504C2—2444no—
505C2#2145873414yesdirect product factor
506C2C2×#1684042711yescharacteristic
507C2C22×#1451980911yescharacteristic
508C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#500C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#500D61
hypocenterC61C2×#3385
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#16840492C2semidirect
3. #21458734C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840068C2semidirect
6. C2×#16840054C2semidirect
9. C2×#16839892C2semidirect
12. C2×C61×#500C2semidirect
15. #16840492C22semidirect
31. #16840170C22semidirect
32. #16840068C22semidirect
33. #16840054C22semidirect
36. #16839892C22semidirect
51. C61×#500C22semidirect
61. C2×#11758190Q8semidirect
186. #11758190C2×Q8semidirect
254. C2×#500D61semidirect
262. C2×C61#3385semidirect
288. #500C2×D61semidirect
309. C61C2×#3385semidirect
505. C2#21458734direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404922
C2×#168404732
#214587342
C2×#168401702
C2×#168400682
C2×#168400542
C2×#168400492
C2×#168400412
C2×#168398922
C2×#168398612
C2×C4×#117581902
C2×C61×#5002
C2×#338561