Finite Group Databasebeta

← C2×#21458694 #30560452

Subgroups — C2×#21458694 #30560452

Order 15616.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840490C211yesmaximal, characteristic, complemented
2#21458694C2116yesmaximal, direct product factor
3C2×#16840161C212yesmaximal, complemented
4C2×#16840158C211yesmaximal, characteristic, complemented
5C2×#16840066C212yesmaximal, complemented
6C2×#16840054C211yesmaximal, characteristic, complemented
7C2×#16840062C212yesmaximal
8C2×#16840042C211yesmaximal, characteristic
9C2×Q8×#92418C211yesmaximal, characteristic, complemented
10C2×C4×#11758200C211yesmaximal, characteristic
11C2×C4×#11758200C212yesmaximal
12C2×C61×#554C211yesmaximal, characteristic
13C22×#11758200C2211yescharacteristic
14#16840490—24no—
15#16840490C2218yescomplemented
16C2×#14519777C2211yescharacteristic
17C2×#14519775—21no—
18C2×#14519769C2212yes—
19C2×#14519767—22no—
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2212yes—
22C2×#14519742—21no—
23#16840161C22116yescomplemented
24#16840158C2218yescomplemented
25#16840066C22116yescomplemented
26#16840062C22116yes—
27#16840054C2218yescomplemented
28#16840042C2218yes—
29Q8×#92418C2218yescomplemented
30C4×#11758200C2218yes—
31C4×#11758200C22116yes—
32C2×#14519710C2212yes—
33C2×#14519710C2212yes—
34C2×#14519708C2212yes—
35C2×#14519708C2212yes—
36C2×#14519708C2211yescharacteristic
37C2×C4⋊#92418C2211yescharacteristic
38C2×C4⋊#92418C2212yes—
39C2×#14519700C2212yes—
40C2×#14519700C2211yescharacteristic
41C2×#14519698C2212yes—
42C2×#14519698C2211yescharacteristic
43C2×C4×#92418C2211yescharacteristic
44C2×C4×#92418C2212yes—
45C61×#554—24no—
46C61×#554C2218yes—
47C2×C4⋊Q8×C61C2211yescharacteristic
48C2×#125×C61C2212yes—
49C2×C22⋊Q8×C61—21no—
50C2×C22⋊Q8×C61—22no—
51C2×C4×Q8×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2212yes—
54C22×C4⋊C4×C61—21no—
55C22×Dic122—21no—
56C22×Dic122C2311yescharacteristic
57C2×#11758200Q818yescomplemented
58C2×#11758200C2314yes—
59C22×#92418C2311yescharacteristic
60C22×#92418C2312yes—
61C22×#92418C2311yescharacteristic
62#14519777—22no—
63#14519777C2314yes—
64#14519775—28no—
65#14519769—24no—
66#14519769C2318yes—
67#14519767—216no—
68C4×Dic122—24no—
69C4×Dic122—22no—
70C4×Dic122C2314yes—
71C4×Dic122C2318yes—
72#14519742—28no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2312yes—
76C2×#11758196—22no—
77C2×#11758196—21no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—21no—
82#14519710C2318yes—
83#14519710C2318yes—
84#14519708C2318yes—
85#14519708C2318yes—
86#14519708C2314yes—
87C4⋊#92418C2314yes—
88C4⋊#92418C2318yes—
89#14519700C2318yes—
90#14519700C2314yes—
91#14519698C2318yes—
92#14519698C2314yes—
93C4×#92418C2314yes—
94C4×#92418C2318yes—
95C22×Q8×C61—21no—
96C22×Q8×C61D411yescharacteristic
97C22×D4×C61C2311yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61—22no—
100C4⋊Q8×C61—22no—
101C4⋊Q8×C61C2314yes—
102#125×C61—24no—
103#125×C61C2318yes—
104C22⋊Q8×C61—28no—
105C22⋊Q8×C61—216no—
106C4×Q8×C61D414yes—
107C4×Q8×C61C2314yes—
108C4×D4×C61—24no—
109C4×D4×C61—22no—
110C4×D4×C61C2314yes—
111C4×D4×C61C2318yes—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—28no—
116C2×C4⋊C4×C61D411yescharacteristic
117C2×C4⋊C4×C61D412yes—
118C2×C4⋊C4×C61C2312yes—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—22no—
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2312yes—
124C24×C61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61—24no—
127C2×Q8×C61—82no—
128C2×Q8×C61C2×D414yes—
129C2×D4×C61—21no—
130C2×D4×C61—22no—
131C2×D4×C61C2×Q814yes—
132C2×D4×C61C2412yes—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—24no—
136C22×C4×C61—28no—
137C22×C4×C61—44no—
138C22×C4×C61—84no—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D412yes—
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—21no—
147C2×Dic122—21no—
148C2×Dic122—22no—
149C2×Dic122—24no—
150C2×Dic122—44no—
151C2×Dic122C2×Q814yes—
152C2×Dic122C2412yes—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—28no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61C2×D414yes—
159C4⋊C4×C61C2×D418yes—
160C4⋊C4×C61C2412yes—
161C4⋊C4×C61C2414yes—
162C22⋊C4×C61—24no—
163C22⋊C4×C61—28no—
164C42×C61C2×D414yes—
165C42×C61C2×D412yes—
166C42×C61C2414yes—
167C42×C61C2412yes—
168#11758200C2×Q8116yescomplemented
169C4⋊Dic61—24no—
170C4⋊Dic61—21no—
171C4⋊Dic61—22no—
172C4⋊Dic61C2414yes—
173C4⋊Dic61C2412yes—
174#11758196—28no—
175#11758196—24no—
176#11758196—28no—
177#11758196—28no—
178C4×Dic61—28no—
179C4×Dic61—24no—
180C2×#92418—22no—
181C2×#92418—24no—
182C2×#92418C2×Q814yes—
183C2×#92418C2412yes—
184C2×#92418C2414yes—
185C2×#92418C2412yes—
186C23×C61—24no—
187C23×C61—22no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61C22×D411yescharacteristic
191Q8×C61—28no—
192Q8×C61—84no—
193D4×C61—24no—
194D4×C61—22no—
195D4×C61C22×Q814yes—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—24no—
201C2×C4×C61—42no—
202C2×C4×C61—44no—
203C2×C4×C61—48no—
204C2×C4×C61—88no—
205C2×C4×C61#13514yes—
206C2×C4×C61C22×D414yes—
207C2×C4×C61C22×D414yes—
208C2×C4×C61C22×D412yes—
209C2×C4×C61C22×D411yescharacteristic
210C2×C4×C61C22×D412yes—
211C2×C4×C61C22×Q812yes—
212C2×C4×C612−1+412yes—
213C2×C4×C61C2511yescharacteristic
214C2×Dic61—24no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—24no—
218C2×Dic61—44no—
219C2×Dic61—42no—
220Dic122—24no—
221Dic122—22no—
222Dic122—48no—
223Dic122C22×Q814yes—
224#92418—22no—
225#92418—24no—
226#92418C22×Q814yes—
227C2×#3381—611nomaximal, Sylow
228C22×C61—24no—
229C22×C61—48no—
230C22×C61—42no—
231C22×C61—42no—
232C22×C61D4×Q812yes—
233C22×C61C2×#13512yes—
234C22×C61#57712yes—
235C22×C61C23×D411yescharacteristic
236C4×C61—24no—
237C4×C61—24no—
238C4×C61—22no—
239C4×C61—42no—
240C4×C61—44no—
241C4×C61D4×Q812yes—
242C4×C61C2×#13514yes—
243C4×C61C23×Q811yescharacteristic
244C4×C61C2×2−1+411yescharacteristic
245Dic61—24no—
246Dic61—44no—
247Dic61—42no—
248C2×#557—611no—
249C2×#554D6111yescharacteristic
250#3381—6116no—
251C2×#499—612no—
252C2×#498—611no—
253C2×#479—612no—
254C2×#477—611no—
255C2×#478—612no—
256C2×#474—611no—
257C2×C8×Q8—611no—
258C2×C4×SD16—612no—
259C2×C4×SD16—611no—
260C2×C61—44no—
261C2×C61#338114yescomplemented
262C2×C61C2×D4×Q811yescharacteristic
263C2×C61C22×#13511yescharacteristic
264C2×C61C2×#57711yescharacteristic
265C22×SD16—611no—
266#557—618no—
267#557—1224no—
268#554—24no—
269#554C2×D6118yes—
270C2×C4⋊Q8—611no—
271C2×C4⋊Q8—1221no—
272C2×C4⋊Q8C2×D6111yescharacteristic
273C2×#125—612no—
274C2×#125—1222no—
275C2×#125C2×D6112yes—
276C2×C22⋊Q8—21no—
277C2×C22⋊Q8—22no—
278C2×C4×Q8—611no—
279C2×C4×Q8—612no—
280C2×C4×Q8—1221no—
281C2×C4×Q8C2×D6111yescharacteristic
282C2×C4×D4C2×D6112yes—
283C2×C4×D4C2×D6111yescharacteristic
284C22×C4⋊C4—21no—
285#499—6116no—
286#498—618no—
287#479—6116no—
288#478—6116no—
289#477—618no—
290#474—618no—
291C8×Q8—618no—
292C4×SD16—618no—
293C4×SD16—6116no—
294C2×#107—612no—
295C2×#107—612no—
296C2×#106—612no—
297C2×#106—612no—
298C2×#106—611no—
299C2×C4⋊C8—612no—
300C2×C4⋊C8—611no—
301C2×#103—612no—
302C2×#103—611no—
303C2×#102—611no—
304C2×#102—612no—
305C2×C4×C8—611no—
306C2×C4×C8—612no—
307C61C2×#338111yescharacteristic, complemented, Sylow
308C22×Q8—21no—
309C22×Q8—611no—
310C22×Q8—1221no—
311C22×Q8C22⋊D6111yescharacteristic
312C22×D4C22×D6111yescharacteristic
313C23×C4—21no—
314C23×C4—22no—
315C2×SD16—618no—
316C2×SD16—614no—
317C22×C8—611no—
318C22×C8—611no—
319C22×C8—612no—
320C4⋊Q8—22no—
321C4⋊Q8—614no—
322C4⋊Q8—1228no—
323C4⋊Q8—1222no—
324C4⋊Q8C22×D6114yes—
325#125—24no—
326#125—618no—
327#125—12216no—
328#125—1224no—
329#125C22×D6118yes—
330C22⋊Q8—28no—
331C22⋊Q8—216no—
332C4×Q8—614no—
333C4×Q8—618no—
334C4×Q8—1228no—
335C4×Q8—1224no—
336C4×Q8—1222no—
337C4×Q8C22⋊D6114yes—
338C4×Q8C22×D6114yes—
339C4×D4—24no—
340C4×D4—22no—
341C4×D4C22×D6114yes—
342C4×D4C22×D6118yes—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—612no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4C22⋊D6111yescharacteristic
355C2×C4⋊C4C22⋊D6112yes—
356C2×C4⋊C4C22×D6111yescharacteristic
357C2×C4⋊C4C22×D6112yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C42—1222no—
361C2×C42—1221no—
362C2×C42C22×D6112yes—
363C2×C42C22×D6111yescharacteristic
364#107—618no—
365#107—618no—
366#106—618no—
367#106—614no—
368#106—618no—
369C4⋊C8—614no—
370C4⋊C8—618no—
371#103—618no—
372#103—614no—
373#102—618no—
374#102—614no—
375C4×C8—614no—
376C4×C8—618no—
377C24—21no—
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8—82no—
381C2×Q8—614no—
382C2×Q8—612no—
383C2×Q8—1221no—
384C2×Q8—1224no—
385C2×Q8—1222no—
386C2×Q8—2444no—
387C2×Q8C2×C22⋊D6114yes—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4Q8×D6114yes—
391C2×D4C23×D6112yes—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—28no—
396C22×C4—44no—
397C22×C4—84no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1222no—
401C22×C4C2×C22⋊D6112yes—
402C22×C4C2×C22⋊D6112yes—
403C22×C4C2×C22⋊D6111yescharacteristic
404C22×C4C2×C22⋊D6111yescharacteristic
405C22×C4C23×D6111yescharacteristic
406SD16—6116no—
407C2×C8—614no—
408C2×C8—612no—
409C2×C8—612no—
410C2×C8—614no—
411C2×C8—1222no—
412C2×C8—1224no—
413C4⋊C4—28no—
414C4⋊C4—24no—
415C4⋊C4—28no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—614no—
419C4⋊C4—612no—
420C4⋊C4—1221no—
421C4⋊C4—1222no—
422C4⋊C4—1224no—
423C4⋊C4—1228no—
424C4⋊C4—1228no—
425C4⋊C4—1228no—
426C4⋊C4—1224no—
427C4⋊C4C2×C22⋊D6114yes—
428C4⋊C4C2×C22⋊D6118yes—
429C4⋊C4C23×D6114yes—
430C4⋊C4C23×D6112yes—
431C22⋊C4—24no—
432C22⋊C4—28no—
433C42—1228no—
434C42—1224no—
435C42C2×C22⋊D6114yes—
436C42C2×C22⋊D6112yes—
437C42C23×D6114yes—
438C42C23×D6112yes—
439C23—22no—
440C23—24no—
441C23—42no—
442C23—42no—
443C23C22×C22⋊D6111yescharacteristic
444Q8—28no—
445Q8—84no—
446Q8—614no—
447Q8—1222no—
448Q8—1224no—
449Q8—2448no—
450D4—22no—
451D4—24no—
452D4C2×Q8×D6114yes—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—48no—
461C2×C4—88no—
462C2×C4—1222no—
463C2×C4—1224no—
464C2×C4—1222no—
465C2×C4—1224no—
466C2×C4—2444no—
467C2×C4—2442no—
468C2×C4#1451979714yes—
469C2×C4C22×C22⋊D6114yes—
470C2×C4C22×C22⋊D6114yes—
471C2×C4C22×C22⋊D6112yes—
472C2×C4C22×C22⋊D6112yes—
473C2×C4C22×C22⋊D6111yescharacteristic
474C2×C4C2×Q8×D6112yes—
475C2×C4#1451982512yes—
476C2×C4C24×D6111yescharacteristic
477C8—614no—
478C8—1222no—
479C8—1224no—
480C22—24no—
481C22—48no—
482C22—42no—
483C22—42no—
484C22Q8×C22⋊D6112yes—
485C22C2×#1451979712yes—
486C22#1684057312yes—
487C22C23×C22⋊D6111yescharacteristic
488C4—24no—
489C4—24no—
490C4—22no—
491C4—42no—
492C4—44no—
493C4—1224no—
494C4—2444no—
495C4—2442no—
496C4Q8×C22⋊D6112yes—
497C4C2×#1451979714yes—
498C4C22×Q8×D6111yescharacteristic
499C4C2×#1451982511yescharacteristic
500C2—44no—
501C2#2145869414yesdirect product factor
502C2C2×Q8×C22⋊D6111yescharacteristic
503C2C22×#1451979711yescharacteristic
504C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenterC2×#554D61
hypocenterC61C2×#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840490C2semidirect
2. #21458694C2direct (N × H)
3. C2×#16840161C2semidirect
4. C2×#16840158C2semidirect
5. C2×#16840066C2semidirect
6. C2×#16840054C2semidirect
9. C2×Q8×#92418C2semidirect
15. #16840490C22semidirect
23. #16840161C22semidirect
24. #16840158C22semidirect
25. #16840066C22semidirect
27. #16840054C22semidirect
29. Q8×#92418C22semidirect
57. C2×#11758200Q8semidirect
168. #11758200C2×Q8semidirect
261. C2×C61#3381semidirect
307. C61C2×#3381semidirect
501. C2#21458694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404902
#214586942
C2×#168401612
C2×#168401582
C2×#168400662
C2×#168400542
C2×#168400622
C2×#168400422
C2×Q8×#924182
C2×C4×#117582002
C2×C61×#5542
C2×#338161