Finite Group Databasebeta

← C2×#21458209 #30558472

Subgroups — C2×#21458209 #30558472

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C212yesmaximal
2#21458209C2116yesmaximal, direct product factor
3C2×#16840166C211yesmaximal, characteristic, complemented
4C2×#16840099C212yesmaximal, complemented
5C2×#16840097C212yesmaximal, complemented
6C2×#16840056C212yesmaximal, complemented
7C2×#16840004C211yesmaximal, characteristic, complemented
8C2×#16840003C211yesmaximal, characteristic, complemented
9C2×#16839856C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D61C211yesmaximal, characteristic
11C2×#107×D61C211yesmaximal, characteristic, complemented
12C22×#107×C61C211yesmaximal, characteristic, complemented
13C22×Dic244C2211yescharacteristic
14C22×C8×D61C2211yescharacteristic
15#16840467—28no—
16#16840467C22116yes—
17C2×#14519776C2212yes—
18C2×#14519767—22no—
19C2×#14519757C2212yes—
20C2×#14519756—22no—
21C2×#14519756C2212yes—
22C2×#14519755—22no—
23C2×#14519742C2212yes—
24C2×C4×C22⋊D61—22no—
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×C4⋊C4×D61C2212yes—
27#16840166C2218yescomplemented
28#16840099C22116yescomplemented
29#16840097C22116yescomplemented
30#16840056C22116yescomplemented
31#16840004C2218yescomplemented
32#16840003C2218yescomplemented
33#16839856C2218yescomplemented
34C8×C22⋊D61C2218yes—
35C2×#14519711C2211yescharacteristic
36C2×#14519710C2212yes—
37C2×#14519710C2212yes—
38#107×D61C2218yescomplemented
39C2×#14519706C2211yescharacteristic
40C2×#14519702C2212yes—
41C2×#14519700C2212yes—
42C2×#14519700C2212yes—
43C2×C22⋊#92418C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46C23×C8×C61C2211yescharacteristic
47C22×C4⋊C4×C61C2212yes—
48C2×#107×C61C2211yescharacteristic
49C2×#107×C61C2211yescharacteristic
50C2×#107×C61C2212yes—
51C2×#107×C61C2218yescomplemented
52C22×Dic122—22no—
53C22×Dic122C2312yes—
54C22×C22⋊D61D411yescharacteristic
55C22×C4×D61—22no—
56C22×C4×D61C2311yescharacteristic
57C2×Dic244—24no—
58C2×Dic244C2314yes—
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C2×C8×D61—24no—
62C2×C8×D61C2314yes—
63#14519776—24no—
64#14519776C2318yes—
65#14519767—216no—
66#14519757—24no—
67#14519757C2318yes—
68#14519756—24no—
69#14519756—216no—
70#14519756C2318yes—
71#14519755—216no—
72#14519742—24no—
73#14519742C2318yes—
74C4×C22⋊D61—216no—
75C4×C22⋊D61D414yes—
76C4×C22⋊D61C2314yes—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61C2312yes—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196D411yescharacteristic
84C4⋊C4×D61—24no—
85C4⋊C4×D61C2318yes—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61D411yescharacteristic
88C2×#11758198—22no—
89C2×#11758198D411yescharacteristic
90C2×C4×Dic61—22no—
91C2×C4×Dic61C2311yescharacteristic
92#14519711C2314yes—
93#14519710C2318yes—
94#14519710C2318yes—
95#14519706C2314yes—
96#14519702C2318yes—
97#14519700C2318yes—
98#14519700C2318yes—
99C22⋊#92418C2314yes—
100#14519689C2314yes—
101C8×Dic61C2314yes—
102C23×C4×C61—22no—
103C23×C4×C61C2311yescharacteristic
104C22×C8×C61—24no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2314yes—
107C22×C8×C61C2311yescharacteristic
108C2×C4⋊C4×C61—24no—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61C2312yes—
111C2×C4⋊C4×C61C2318yes—
112C2×C4⋊C4×C61C2312yes—
113#107×C61C2314yes—
114#107×C61C2314yes—
115#107×C61C2318yes—
116C24×C61C2×D411yescharacteristic
117C23×D61C2×D411yescharacteristic
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—28no—
123C22×C4×C61—84no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D412yes—
126C22×C4×C61C2412yes—
127C22×C4×C61C2411yescharacteristic
128C2×C22⋊D61Q1618yescomplemented
129C2×C22⋊D61C2×D414yes—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—28no—
138C2×C4×D61—84no—
139C2×C4×D61C2×D412yes—
140C2×C4×D61C2412yes—
141C2×Dic122—24no—
142C2×Dic122—24no—
143C2×Dic122—22no—
144C2×Dic122—28no—
145C2×Dic122—84no—
146C2×Dic122C2414yes—
147C2×C8×C61—22no—
148C2×C8×C61—28no—
149C2×C8×C61#4114yes—
150C2×C8×C61C2412yes—
151C2×C8×C61C2412yes—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—28no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61C2414yes—
156C4⋊C4×C61C2414yes—
157C22⋊Dic61—28no—
158C22⋊Dic61C2×D414yes—
159#11758198—28no—
160#11758198C2×D414yes—
161C4⋊Dic61—22no—
162C4⋊Dic61—28no—
163C4⋊Dic61C2414yes—
164#11758196—28no—
165#11758196—28no—
166#11758196—28no—
167#11758196—28no—
168#11758196C2×D414yes—
169C4×Dic61—28no—
170C4×Dic61C2×D412yes—
171C4×Dic61C2412yes—
172C2×#92418—22no—
173C2×#92418—22no—
174C2×#92418C2412yes—
175C2×#92418C2412yes—
176Dic244—28no—
177C8×D61—28no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61C2×Q1614yes—
181C23×C61C22×D412yes—
182C23×C61C22×D411yescharacteristic
183C22×D61—22no—
184C22×D61—22no—
185C22×D61C2×Q1614yes—
186C22×D61C22×D412yes—
187C2×C4×C61—22no—
188C2×C4×C61—24no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—24no—
192C2×C4×C61—24no—
193C2×C4×C61—44no—
194C2×C4×C61—44no—
195C2×C4×C61—88no—
196C2×C4×C61C22×D412yes—
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C2×#4112yes—
199C2×C4×C612−1+412yes—
200C2×C4×C61C2511yescharacteristic
201C22⋊D61C2×Q16116yescomplemented
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—24no—
205C2×Dic61—24no—
206C2×Dic61—44no—
207C2×Dic61—44no—
208C2×Dic61C2×Q1614yes—
209C2×Dic61C22×D412yes—
210C2×Dic61C22×D412yes—
211C2×Dic61C22×D412yes—
212C4×D61—24no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—88no—
216Dic122—24no—
217Dic122—24no—
218Dic122—44no—
219Dic122—88no—
220C8×C61—22no—
221C8×C61C2×#4114yes—
222#92418—22no—
223#92418—22no—
224C2×#3338—611nomaximal, Sylow
225C22×C61—28no—
226C22×C61—22no—
227C22×C61—22no—
228C22×C61#54712yes—
229C22×C61C22×Q1614yes—
230C22×C61C22×Q1612yes—
231C22×C61#57612yes—
232C22×C61C23×D411yescharacteristic
233C2×D61—28no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61C22×Q1614yes—
237C4×C61—22no—
238C4×C61—44no—
239C4×C61—44no—
240C4×C61#54712yes—
241C4×C61C22×#4111yescharacteristic
242C4×C61C2×2−1+411yescharacteristic
243Dic61—22no—
244Dic61—22no—
245Dic61—44no—
246Dic61—44no—
247Dic61C22×Q1614yes—
248C2×#554—612no—
249#3338—6116no—
250C2×#500—611no—
251C2×#484—612no—
252C2×#484—612no—
253C2×#477—612no—
254C2×#467—611no—
255C2×#467—611no—
256C2×C4×Q16—611no—
257C2×C8×D4—611no—
258C22×#107—611no—
259C22×#107D6111yescharacteristic, complemented
260C2×C61—24no—
261C2×C61#333814yescomplemented
262C2×C61C2×#54711yescharacteristic
263C2×C61C23×Q1611yescharacteristic
264C2×C61C2×#57611yescharacteristic
265D61—24no—
266C22×Q16—611no—
267C23×C8—611no—
268C23×C8C2×D6111yescharacteristic
269#554—6116no—
270#554—1228no—
271C2×C4⋊Q8—612no—
272C2×#125—1222no—
273C2×C22⋊Q8—612no—
274C2×C22⋊Q8—612no—
275C2×C22⋊Q8—1222no—
276C2×C22⋊Q8—1222no—
277C2×C4×Q8—612no—
278C2×C4×D4—611no—
279C2×C4×D4—1222no—
280C22×C4⋊C4—612no—
281C22×C4⋊C4C2×D6112yes—
282#500—618no—
283#484—6116no—
284#484—6116no—
285#477—6116no—
286#467—618no—
287#467—618no—
288C4×Q16—618no—
289C8×D4—618no—
290C2×#107—611no—
291C2×#107—612no—
292C2×#107—612no—
293C2×#107—618no—
294C2×#107C2×D6112yes—
295C2×#107C2×D6111yescharacteristic
296C2×#107C2×D6111yescharacteristic
297C2×#107C2×D6118yescomplemented
298C2×C4⋊C8—611no—
299C2×#103—612no—
300C2×#103—612no—
301C2×#103—612no—
302C2×C22⋊C8—611no—
303C2×C22⋊C8—611no—
304C2×C4×C8—611no—
305C61C2×#333811yescharacteristic, complemented, Sylow
306C22×Q8—612no—
307C22×Q8—1222no—
308C22×D4—611no—
309C23×C4—22no—
310C23×C4—611no—
311C23×C4—1222no—
312C23×C4C22×D6111yescharacteristic
313C2×Q16—614no—
314C2×Q16—1224no—
315C22×C8—24no—
316C22×C8—611no—
317C22×C8—611no—
318C22×C8—614no—
319C22×C8—1224no—
320C22×C8C22×D6111yescharacteristic
321C22×C8C22×D6114yes—
322C22×C8C22×D6111yescharacteristic
323C4⋊Q8—618no—
324C4⋊Q8—1224no—
325#125—12216no—
326C22⋊Q8—618no—
327C22⋊Q8—618no—
328C22⋊Q8—12216no—
329C22⋊Q8—12216no—
330C22⋊Q8—1224no—
331C22⋊Q8—1224no—
332C4×Q8—618no—
333C4×Q8—1224no—
334C4×D4—614no—
335C4×D4—614no—
336C4×D4—12216no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—611no—
340C2×C4⋊C4—612no—
341C2×C4⋊C4—618no—
342C2×C4⋊C4—1224no—
343C2×C4⋊C4—1222no—
344C2×C4⋊C4—1222no—
345C2×C4⋊C4—1222no—
346C2×C4⋊C4—1222no—
347C2×C4⋊C4—1222no—
348C2×C4⋊C4C22×D6112yes—
349C2×C4⋊C4C22×D6112yes—
350C2×C4⋊C4C22×D6118yes—
351C2×C22⋊C4—611no—
352C2×C22⋊C4—611no—
353C2×C22⋊C4—1222no—
354C2×C22⋊C4—1222no—
355C2×C42—611no—
356C2×C42—1222no—
357#107—614no—
358#107—618no—
359#107—618no—
360#107C22×D6114yes—
361#107C22×D6114yes—
362#107C22×D6118yes—
363C4⋊C8—614no—
364#103—618no—
365#103—618no—
366#103—618no—
367C22⋊C8—614no—
368C22⋊C8—614no—
369C4×C8—614no—
370C24—611no—
371C24D4×D6111yescharacteristic
372C2×Q8—614no—
373C2×Q8—1228no—
374C2×Q8—1222no—
375C2×Q8—1224no—
376C2×Q8—1224no—
377C2×Q8—4884no—
378C2×D4—614no—
379C2×D4—618no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—28no—
385C22×C4—84no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—1228no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—4884no—
397C22×C4D4×D6112yes—
398C22×C4D4×D6111yescharacteristic
399C22×C4C23×D6112yes—
400C22×C4C23×D6111yescharacteristic
401Q16—1228no—
402C2×C8—22no—
403C2×C8—28no—
404C2×C8—612no—
405C2×C8—612no—
406C2×C8—1222no—
407C2×C8—1222no—
408C2×C8—1228no—
409C2×C8#1175822214yes—
410C2×C8C23×D6112yes—
411C2×C8C23×D6112yes—
412C4⋊C4—22no—
413C4⋊C4—28no—
414C4⋊C4—22no—
415C4⋊C4—614no—
416C4⋊C4—614no—
417C4⋊C4—1228no—
418C4⋊C4—1228no—
419C4⋊C4—1228no—
420C4⋊C4—1228no—
421C4⋊C4—1222no—
422C4⋊C4—1228no—
423C4⋊C4C23×D6114yes—
424C4⋊C4C23×D6114yes—
425C22⋊C4—614no—
426C22⋊C4—614no—
427C22⋊C4—1228no—
428C22⋊C4—1228no—
429C42—612no—
430C42—612no—
431C42—1228no—
432C23—22no—
433C23—22no—
434C23—614no—
435C23—612no—
436C23—1222no—
437C23—1222no—
438C23Q16×D6114yes—
439C23C2×D4×D6112yes—
440C23C2×D4×D6111yescharacteristic
441Q8—1224no—
442Q8—1224no—
443Q8—4888no—
444Q8—2444no—
445D4—6116no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—88no—
455C2×C4—614no—
456C2×C4—612no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1224no—
464C2×C4—1224no—
465C2×C4—1224no—
466C2×C4—4888no—
467C2×C4—2444no—
468C2×C4—2444no—
469C2×C4C2×D4×D6112yes—
470C2×C4C2×D4×D6111yescharacteristic
471C2×C4C2×#1175822212yes—
472C2×C4#1451982512yes—
473C2×C4C24×D6111yescharacteristic
474C8—22no—
475C8—1222no—
476C8—1222no—
477C8C2×#1175822214yes—
478C22—28no—
479C22—22no—
480C22—22no—
481C22—614no—
482C22—1228no—
483C22—1222no—
484C22—1222no—
485C22#1684041312yes—
486C22C2×Q16×D6114yes—
487C22C2×Q16×D6112yes—
488C22#1684056312yes—
489C22C22×D4×D6111yescharacteristic
490C4—22no—
491C4—44no—
492C4—44no—
493C4—614no—
494C4—1222no—
495C4—1222no—
496C4—2444no—
497C4—2444no—
498C4#1684041312yes—
499C4C22×#1175822211yescharacteristic
500C4C2×#1451982511yescharacteristic
501C2—24no—
502C2—1224no—
503C2#2145820914yesdirect product factor
504C2C2×#1684041311yescharacteristic
505C2C22×Q16×D6111yescharacteristic
506C2C2×#1684056311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC22×#107×C61C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenterC22×#107D61
hypocenterC61C2×#3338
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #21458209C2direct (N × H)
3. C2×#16840166C2semidirect
4. C2×#16840099C2semidirect
5. C2×#16840097C2semidirect
6. C2×#16840056C2semidirect
7. C2×#16840004C2semidirect
8. C2×#16840003C2semidirect
9. C2×#16839856C2semidirect
11. C2×#107×D61C2semidirect
12. C22×#107×C61C2semidirect
27. #16840166C22semidirect
28. #16840099C22semidirect
29. #16840097C22semidirect
30. #16840056C22semidirect
31. #16840004C22semidirect
32. #16840003C22semidirect
33. #16839856C22semidirect
38. #107×D61C22semidirect
51. C2×#107×C61C22semidirect
128. C2×C22⋊D61Q16semidirect
201. C22⋊D61C2×Q16semidirect
259. C22×#107D61semidirect
261. C2×C61#3338semidirect
297. C2×#107C2×D61semidirect
305. C61C2×#3338semidirect
503. C2#21458209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
#214582092
C2×#168401662
C2×#168400992
C2×#168400972
C2×#168400562
C2×#168400042
C2×#168400032
C2×#168398562
C2×C8×C22⋊D612
C2×#107×D612
C22×#107×C612
C2×#333861