Finite Group Databasebeta

← C2×#21458690 #30560448

Subgroups — C2×#21458690 #30560448

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×#16840472C211yesmaximal, characteristic
2#21458690C2116yesmaximal, direct product factor
3C2×#16840161C212yesmaximal, complemented
4C2×#16840158C211yesmaximal, characteristic, complemented
5C2×#16840069C212yesmaximal, complemented
6C2×#16840057C211yesmaximal, characteristic, complemented
7C2×#16840059C212yesmaximal
8C2×#16840039C211yesmaximal, characteristic
9C2×Q8×#92418C211yesmaximal, characteristic, complemented
10C2×C4×#11758201C211yesmaximal, characteristic
11C2×C4×#11758201C212yesmaximal
12C2×C61×#557C211yesmaximal, characteristic, complemented
13C22×#11758201C2211yescharacteristic
14#16840472—24no—
15#16840472C2218yes—
16C2×#14519777C2211yescharacteristic
17C2×#14519769C2212yes—
18C2×#14519755—22no—
19C2×#14519753—21no—
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2212yes—
22C2×C4⋊C4×D61—21no—
23#16840161C22116yescomplemented
24#16840158C2218yescomplemented
25#16840069C22116yescomplemented
26#16840059C22116yes—
27#16840057C2218yescomplemented
28#16840039C2218yes—
29Q8×#92418C2218yescomplemented
30C4×#11758201C2218yes—
31C4×#11758201C22116yes—
32C2×#14519710C2212yes—
33C2×#14519710C2212yes—
34C2×#14519708C2212yes—
35C2×#14519708C2212yes—
36C2×#14519708C2211yescharacteristic
37C2×C4⋊#92418C2211yescharacteristic
38C2×C4⋊#92418C2212yes—
39C2×#14519701C2212yes—
40C2×#14519701C2211yescharacteristic
41C2×#14519697C2212yes—
42C2×#14519697C2211yescharacteristic
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×Dic122—21no—
56C22×D244C2311yescharacteristic
57C22×C4×D61—21no—
58C22×C4×D61—22no—
59C2×#11758201Q818yescomplemented
60C2×#11758201C2314yes—
61C22×#92418C2311yescharacteristic
62C22×#92418C2312yes—
63C22×#92418C2311yescharacteristic
64#14519777—22no—
65#14519777C2314yes—
66#14519769—24no—
67#14519769C2318yes—
68#14519755—216no—
69#14519753—28no—
70C4×D244—22no—
71C4×D244—24no—
72C4×D244C2314yes—
73C4×D244C2318yes—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2312yes—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C4⋊C4×D61—28no—
80C2×#11758198—22no—
81C2×#11758198—21no—
82#14519710C2318yes—
83#14519710C2318yes—
84#14519708C2318yes—
85#14519708C2318yes—
86#14519708C2314yes—
87C4⋊#92418C2314yes—
88C4⋊#92418C2318yes—
89#14519701C2318yes—
90#14519701C2314yes—
91#14519697C2318yes—
92#14519697C2314yes—
93C4×#92418C2314yes—
94C4×#92418C2318yes—
95C22×Q8×C61—21no—
96C22×Q8×C61D411yescharacteristic
97C22×Q8×C61C2311yescharacteristic
98C4⋊Q8×C61—28no—
99C4⋊Q8×C61—22no—
100C4⋊Q8×C61C2314yes—
101#125×C61—216no—
102#125×C61—24no—
103#125×C61C2318yes—
104C4×Q8×C61—28no—
105C4×Q8×C61—24no—
106C4×Q8×C61—22no—
107C4×Q8×C61D414yes—
108C4×Q8×C61C2314yes—
109C4×Q8×C61C2318yes—
110C4×Q8×C61C2314yes—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—22no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61D411yescharacteristic
117C2×C4⋊C4×C61D412yes—
118C2×C4⋊C4×C61C2312yes—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61—22no—
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2312yes—
124C23×D61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61—21no—
127C2×Q8×C61—24no—
128C2×Q8×C61—22no—
129C2×Q8×C61—44no—
130C2×Q8×C61C2×D414yes—
131C2×Q8×C61C2×Q814yes—
132C2×Q8×C61C2412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C22×Dic61—22no—
142C22×Dic61—21no—
143C2×D244—21no—
144C2×D244—22no—
145C2×D244C2×Q814yes—
146C2×D244C2412yes—
147C2×C4×D61—24no—
148C2×C4×D61—28no—
149C2×C4×D61—44no—
150C2×C4×D61—84no—
151C2×Dic122—24no—
152C2×Dic122—82no—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—28no—
156C4⋊C4×C61—24no—
157C4⋊C4×C61—28no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61C2×D414yes—
161C4⋊C4×C61C2×D418yes—
162C4⋊C4×C61C2412yes—
163C4⋊C4×C61C2414yes—
164C42×C61—28no—
165C42×C61—24no—
166C42×C61C2×D414yes—
167C42×C61C2×D412yes—
168C42×C61C2414yes—
169C42×C61C2412yes—
170#11758201C2×Q8116yescomplemented
171#11758198—28no—
172#11758198—24no—
173C4⋊Dic61—24no—
174C4⋊Dic61—21no—
175C4⋊Dic61—22no—
176C4⋊Dic61C2414yes—
177C4⋊Dic61C2412yes—
178#11758196—28no—
179#11758196—28no—
180C2×#92418—22no—
181C2×#92418—24no—
182C2×#92418C2×Q814yes—
183C2×#92418C2412yes—
184C2×#92418C2414yes—
185C2×#92418C2412yes—
186C23×C61C22×D411yescharacteristic
187C22×D61—24no—
188C22×D61—22no—
189C22×D61—42no—
190C22×D61—42no—
191Q8×C61—24no—
192Q8×C61—28no—
193Q8×C61—22no—
194Q8×C61—48no—
195Q8×C61C22×Q814yes—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—22no—
199C2×C4×C61—24no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—24no—
203C2×C4×C61—44no—
204C2×C4×C61—42no—
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—22no—
215C2×Dic61—24no—
216C2×Dic61—42no—
217C2×Dic61—44no—
218D244—24no—
219D244—22no—
220D244C22×Q814yes—
221C4×D61—48no—
222C4×D61—88no—
223Dic122—84no—
224#92418—22no—
225#92418—24no—
226#92418C22×Q814yes—
227C2×#3381—611nomaximal, Sylow
228C22×C61D4×Q812yes—
229C22×C61C2×#13512yes—
230C22×C61#57712yes—
231C22×C61C23×D411yescharacteristic
232C2×D61—24no—
233C2×D61—48no—
234C2×D61—42no—
235C2×D61—42no—
236C4×C61—24no—
237C4×C61—24no—
238C4×C61—22no—
239C4×C61—24no—
240C4×C61—44no—
241C4×C61—42no—
242C4×C61D4×Q812yes—
243C4×C61C2×#13514yes—
244C4×C61C23×Q811yescharacteristic
245C4×C61C2×2−1+411yescharacteristic
246Dic61—42no—
247Dic61—44no—
248C2×#557D6111yescharacteristic, complemented
249C2×#554—611no—
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#338114yescomplemented
261C2×C61C2×D4×Q811yescharacteristic
262C2×C61C22×#13511yescharacteristic
263C2×C61C2×#57711yescharacteristic
264D61—44no—
265C22×SD16—611no—
266#557—24no—
267#557C2×D6118yescomplemented
268#554—618no—
269#554—1224no—
270C2×C4⋊Q8—21no—
271C2×C4⋊Q8—611no—
272C2×C4⋊Q8C2×D6111yescharacteristic
273C2×#125—22no—
274C2×#125—612no—
275C2×#125C2×D6112yes—
276C2×C22⋊Q8—1221no—
277C2×C22⋊Q8—1222no—
278C2×C4×Q8—21no—
279C2×C4×Q8C2×D6111yescharacteristic
280C2×C4×Q8C2×D6112yes—
281C2×C4×Q8C2×D6111yescharacteristic
282C2×C4×D4—612no—
283C2×C4×D4—611no—
284C22×C4⋊C4—1221no—
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—1221no—
310C22×Q8C22⋊D6111yescharacteristic
311C22×Q8C22×D6111yescharacteristic
312C22×D4—611no—
313C23×C4—1222no—
314C23×C4—1221no—
315C2×SD16—618no—
316C2×SD16—614no—
317C22×C8—611no—
318C22×C8—611no—
319C22×C8—612no—
320C4⋊Q8—28no—
321C4⋊Q8—22no—
322C4⋊Q8—614no—
323C4⋊Q8—1222no—
324C4⋊Q8C22×D6114yes—
325#125—216no—
326#125—24no—
327#125—618no—
328#125—1224no—
329#125C22×D6118yes—
330C22⋊Q8—1228no—
331C22⋊Q8—12216no—
332C4×Q8—28no—
333C4×Q8—24no—
334C4×Q8—22no—
335C4×Q8C22⋊D6114yes—
336C4×Q8C22×D6114yes—
337C4×Q8C22×D6118yes—
338C4×Q8C22×D6114yes—
339C4×D4—614no—
340C4×D4—618no—
341C4×D4—1224no—
342C4×D4—1222no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—611no—
349C2×C4⋊C4—612no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1221no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1228no—
354C2×C4⋊C4C22⋊D6111yescharacteristic
355C2×C4⋊C4C22⋊D6112yes—
356C2×C4⋊C4C22×D6111yescharacteristic
357C2×C4⋊C4C22×D6112yes—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1222no—
360C2×C42—22no—
361C2×C42—21no—
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—1221no—
378C2×Q8—21no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—24no—
382C2×Q8—44no—
383C2×Q8—1224no—
384C2×Q8—4882no—
385C2×Q8Q8×D6114yes—
386C2×Q8C2×C22⋊D6114yes—
387C2×Q8C23×D6112yes—
388C2×D4—614no—
389C2×D4—612no—
390C2×D4—1221no—
391C2×D4—1222no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—1221no—
396C22×C4—1222no—
397C22×C4—1228no—
398C22×C4—1224no—
399C22×C4—4884no—
400C22×C4—2444no—
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—24no—
417C4⋊C4—28no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—614no—
421C4⋊C4—612no—
422C4⋊C4—1221no—
423C4⋊C4—1222no—
424C4⋊C4—1228no—
425C4⋊C4—1224no—
426C4⋊C4—1228no—
427C4⋊C4C2×C22⋊D6114yes—
428C4⋊C4C2×C22⋊D6118yes—
429C4⋊C4C23×D6114yes—
430C4⋊C4C23×D6112yes—
431C22⋊C4—1224no—
432C22⋊C4—1228no—
433C42—28no—
434C42—24no—
435C42C2×C22⋊D6114yes—
436C42C2×C22⋊D6112yes—
437C42C23×D6114yes—
438C42C23×D6112yes—
439C23—1222no—
440C23—1224no—
441C23—2442no—
442C23—2442no—
443C23C22×C22⋊D6111yescharacteristic
444Q8—28no—
445Q8—22no—
446Q8—24no—
447Q8—48no—
448Q8—4884no—
449Q8C2×Q8×D6114yes—
450D4—614no—
451D4—1222no—
452D4—1224no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—1222no—
463C2×C4—1224no—
464C2×C4—4888no—
465C2×C4—2442no—
466C2×C4—2444no—
467C2×C4—2448no—
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—1224no—
481C22—2448no—
482C22—2442no—
483C22—2442no—
484C22Q8×C22⋊D6112yes—
485C22C2×#1451979712yes—
486C22#1684057012yes—
487C22C23×C22⋊D6111yescharacteristic
488C4—24no—
489C4—24no—
490C4—24no—
491C4—22no—
492C4—44no—
493C4—42no—
494C4—2442no—
495C4—2444no—
496C4Q8×C22⋊D6112yes—
497C4C2×#1451979714yes—
498C4C22×Q8×D6111yescharacteristic
499C4C2×#1451982511yescharacteristic
500C2—2444no—
501C2#2145869014yesdirect product factor
502C2C2×Q8×C22⋊D6111yescharacteristic
503C2C22×#1451979711yescharacteristic
504C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#557C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenterC2×#557D61
hypocenterC61C2×#3381
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. #21458690C2direct (N × H)
3. C2×#16840161C2semidirect
4. C2×#16840158C2semidirect
5. C2×#16840069C2semidirect
6. C2×#16840057C2semidirect
9. C2×Q8×#92418C2semidirect
12. C2×C61×#557C2semidirect
23. #16840161C22semidirect
24. #16840158C22semidirect
25. #16840069C22semidirect
27. #16840057C22semidirect
29. Q8×#92418C22semidirect
46. C61×#557C22semidirect
59. C2×#11758201Q8semidirect
170. #11758201C2×Q8semidirect
248. C2×#557D61semidirect
260. C2×C61#3381semidirect
267. #557C2×D61semidirect
307. C61C2×#3381semidirect
501. C2#21458690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404722
#214586902
C2×#168401612
C2×#168401582
C2×#168400692
C2×#168400572
C2×#168400592
C2×#168400392
C2×Q8×#924182
C2×C4×#117582012
C2×C61×#5572
C2×#338161