Finite Group Databasebeta

← C2×#21447255 #29708841

Subgroups — C2×#21447255 #29708841

Order 15616.

1270 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
1C22×#14519708C211yesmaximal, characteristic, complemented
2C22×C22⋊#92418C211yesmaximal, characteristic
3C2×#16839622C211yesmaximal, characteristic
4#21447255C218yesmaximal, direct product factor
5C2×#16839524C211yesmaximal, characteristic, complemented
6C2×#16839524C211yesmaximal, characteristic, complemented
7C2×#16839524C211yesmaximal, characteristic, complemented
8C2×C61×#380C211yesmaximal, characteristic
9C23×#92418C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C22⋊Dic61—21no—
14C2×#14519708—24no—
15C2×#14519708C2214yescomplemented
16C2×C22⋊#92418—24no—
17C2×C22⋊#92418C2214yes—
18#16839622—22no—
19#16839622C2214yes—
20C2×#14519684—21no—
21#16839524C2214yescomplemented
22#16839524C2214yescomplemented
23#16839524C2214yescomplemented
24C24×C4×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61—21no—
28C61×#380—22no—
29C61×#380C2214yes—
30C2×#95×C61—21no—
31C23×Dic61—21no—
32C23×Dic61—21no—
33C22×#92418—22no—
34C22×#92418—22no—
35C22×#92418—22no—
36C22×#92418—22no—
37C22×#92418—22no—
38C22×#92418D414yes—
39C22×#92418C2312yes—
40C22×#92418C2312yes—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61—22no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61C2312yes—
48C2×C4⋊Dic61C2312yes—
49C2×C22⋊Dic61—24no—
50C2×C22⋊Dic61—44no—
51#14519708—28no—
52C22⋊#92418—28no—
53#14519684—24no—
54C25×C61D411yescharacteristic
55C23×C4×C61—22no—
56C23×C4×C61—22no—
57C23×C4×C61—22no—
58C23×C4×C61—22no—
59C23×C4×C61—22no—
60C23×C4×C61—22no—
61C23×C4×C61—21no—
62C23×C4×C61—21no—
63C23×C4×C61D411yescharacteristic
64C23×C4×C61D412yes—
65C23×C4×C61C2312yes—
66C23×C4×C61C2311yescharacteristic
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61—22no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61C2312yes—
74C2×C4⋊C4×C61C2312yes—
75C2×C22⋊C4×C61—24no—
76C2×C22⋊C4×C61—44no—
77#95×C61—24no—
78C24×C61—22no—
79C24×C61—22no—
80C24×C61—22no—
81C24×C61—22no—
82C24×C61—22no—
83C24×C61—22no—
84C24×C61SD1614yes—
85C24×C61C2×D412yes—
86C24×C61C2×D411yescharacteristic
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—24no—
91C22×C4×C61—24no—
92C22×C4×C61—24no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—44no—
102C22×C4×C61—44no—
103C22×C4×C61—44no—
104C22×C4×C61—44no—
105C22×C4×C61—42no—
106C22×C4×C61—42no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D412yes—
114C22×C4×C61#4112yes—
115C22×C4×C61#4112yes—
116C22×C4×C61#4112yes—
117C22×C4×C61#4112yes—
118C22×C4×C61#4112yes—
119C22×C4×C61C2411yescharacteristic
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—42no—
123C22×Dic61—42no—
124C22×Dic61—42no—
125C22×Dic61—42no—
126C22×Dic61—42no—
127C22×Dic61—42no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—42no—
133C4⋊C4×C61—42no—
134C22⋊C4×C61—48no—
135C22⋊Dic61—48no—
136C4⋊Dic61—22no—
137C4⋊Dic61—22no—
138C4⋊Dic61—22no—
139C4⋊Dic61—22no—
140C4⋊Dic61—42no—
141C4⋊Dic61—42no—
142C2×#92418—28no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—22no—
146C2×#92418—22no—
147C2×#92418—22no—
148C2×#92418—44no—
149C2×#92418C2×D414yes—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—28no—
157C23×C61—28no—
158C23×C61—28no—
159C23×C61—44no—
160C23×C61—44no—
161C23×C61—44no—
162C23×C61—44no—
163C23×C61#12112yes—
164C23×C61#12312yes—
165C23×C61#12312yes—
166C23×C61C2×SD1614yes—
167C23×C61C2×SD1612yes—
168C23×C61#13512yes—
169C23×C61AGL(1,ℤ/8)12yes—
170C23×C61#13712yes—
171C23×C61C22×D411yescharacteristic
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—44no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—48no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—84no—
188C2×C4×C61—84no—
189C2×C4×C61#12112yes—
190C2×C4×C61#12314yes—
191C2×C4×C61#12312yes—
192C2×C4×C61#12312yes—
193C2×C4×C61#12414yes—
194C2×C4×C61#12614yes—
195C2×C4×C61#12614yes—
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C2×#4111yescharacteristic
198C2×C4×C61C2×#4111yescharacteristic
199C2×C4×C61C2×#4111yescharacteristic
200C2×C4×C61C2×#4111yescharacteristic
201C2×C4×C61C2×#4111yescharacteristic
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—84no—
209C2×Dic61—84no—
210#92418—24no—
211#92418—42no—
212C2×#2077—611nomaximal, Sylow
213C22×C61—24no—
214C22×C61—24no—
215C22×C61—24no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—416no—
219C22×C61—42no—
220C22×C61—42no—
221C22×C61#39714yes—
222C22×C61#46514yes—
223C22×C61#46814yes—
224C22×C61#48114yes—
225C22×C61#48214yes—
226C22×C61#48314yes—
227C22×C61#48514yes—
228C22×C61C2×#12111yescharacteristic
229C22×C61C2×#12311yescharacteristic
230C22×C61C2×#12311yescharacteristic
231C22×C61C22×SD1611yescharacteristic
232C22×C61C2×#13511yescharacteristic
233C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C61C2×#13711yescharacteristic
235C4×C61—42no—
236C4×C61—82no—
237C4×C61—82no—
238C4×C61#39714yes—
239C4×C61C2×#12311yescharacteristic
240C4×C61C2×#12411yescharacteristic
241C4×C61C2×#12611yescharacteristic
242C4×C61C2×#12611yescharacteristic
243Dic61—82no—
244Dic61—82no—
245C22×#106—611no—
246C22×C22⋊C8—611no—
247C2×#380—611no—
248C2×#380D6111yescharacteristic
249#2077—618no—
250C2×#340—611no—
251C2×#340—611no—
252C2×#340—611no—
253C2×C61—44no—
254C2×C61#207718yescomplemented
255C2×C61C2×#39711yescharacteristic
256C2×C61C2×#46511yescharacteristic
257C2×C61C2×#46811yescharacteristic
258C2×C61C2×#48311yescharacteristic
259C2×C61C2×#48211yescharacteristic
260C2×C61C2×#48511yescharacteristic
261C2×C61C2×#48111yescharacteristic
262C24×C4C2×D6111yescharacteristic
263C23×C8—611no—
264C23×C8—611no—
265C22×C4⋊C4—611no—
266C22×C4⋊C4—611no—
267C22×C4⋊C4C2×D6111yescharacteristic
268C22×C4⋊C4C2×D6111yescharacteristic
269C22×C22⋊C4—21no—
270C22×C22⋊C4—1221no—
271C2×#106—614no—
272C2×#106—1224no—
273C2×C22⋊C8—614no—
274C2×C22⋊C8—1224no—
275#380—22no—
276#380—614no—
277#380—1222no—
278#380C2×D6114yes—
279C2×#95—21no—
280C2×#95—1221no—
281#340—614no—
282#340—614no—
283#340—614no—
284C61C2×#207711yescharacteristic, complemented, Sylow
285C25C22⋊D6111yescharacteristic
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—1221no—
295C23×C4—1221no—
296C23×C4C22⋊D6112yes—
297C23×C4C22⋊D6111yescharacteristic
298C23×C4C22×D6112yes—
299C23×C4C22×D6111yescharacteristic
300C22×C8—614no—
301C22×C8—612no—
302C22×C8—612no—
303C22×C8—1222no—
304C22×C8—1222no—
305C22×C8—1222no—
306C22×C8—1222no—
307C22×C8—1222no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—612no—
315C2×C4⋊C4—612no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1222no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1222no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4C22×D6112yes—
323C2×C4⋊C4C22×D6112yes—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—1224no—
327C2×C22⋊C4—2444no—
328#106—1228no—
329C22⋊C8—1228no—
330#95—24no—
331#95—1224no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24#1175820014yes—
339C24C2×C22⋊D6112yes—
340C24C2×C22⋊D6111yescharacteristic
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4—2442no—
373C22×C4#1175822212yes—
374C22×C4#1175822212yes—
375C22×C4D4×D6112yes—
376C22×C4#1175822412yes—
377C22×C4#1175822412yes—
378C22×C4#1175822412yes—
379C22×C4C2×C22⋊D6112yes—
380C22×C4C2×C22⋊D6111yescharacteristic
381C22×C4C23×D6111yescharacteristic
382C2×C8—614no—
383C2×C8—1222no—
384C2×C8—1222no—
385C2×C8—1228no—
386C2×C8—1222no—
387C2×C8—1222no—
388C2×C8—1222no—
389C2×C8—2444no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—1222no—
397C4⋊C4—1222no—
398C4⋊C4—1222no—
399C4⋊C4—1222no—
400C4⋊C4—2442no—
401C4⋊C4—2442no—
402C22⋊C4—48no—
403C22⋊C4—2448no—
404C23—28no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—28no—
412C23—28no—
413C23—44no—
414C23—44no—
415C23—44no—
416C23—44no—
417C23#1451974912yes—
418C23#1451975812yes—
419C23#1451976012yes—
420C23C2×#1175820014yes—
421C23C2×#1175820012yes—
422C23#1451979712yes—
423C23#1451980212yes—
424C23#1451980812yes—
425C23C22×C22⋊D6111yescharacteristic
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—84no—
442C2×C4—84no—
443C2×C4—4884no—
444C2×C4—4884no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4#1451974912yes—
452C2×C4#1451975812yes—
453C2×C4#1451975914yes—
454C2×C4#1451976012yes—
455C2×C4#1451976314yes—
456C2×C4#1451977014yes—
457C2×C4#1451977014yes—
458C2×C4C2×D4×D6111yescharacteristic
459C2×C4C2×#1175822411yescharacteristic
460C2×C4C2×#1175822411yescharacteristic
461C2×C4C2×#1175822411yescharacteristic
462C2×C4C2×#1175822211yescharacteristic
463C2×C4C2×#1175822211yescharacteristic
464C8—1224no—
465C8—2442no—
466C22—24no—
467C22—24no—
468C22—24no—
469C22—42no—
470C22—42no—
471C22—416no—
472C22—42no—
473C22—42no—
474C22#1683969014yes—
475C22#1683998914yes—
476C22#1684001014yes—
477C22#1684007814yes—
478C22#1684008614yes—
479C22#1684009214yes—
480C22#1684010014yes—
481C22C2×#1451974911yescharacteristic
482C22C2×#1451975811yescharacteristic
483C22C2×#1451976011yescharacteristic
484C22C22×#1175820011yescharacteristic
485C22C2×#1451979711yescharacteristic
486C22C2×#1451980211yescharacteristic
487C22C2×#1451980811yescharacteristic
488C4—42no—
489C4—82no—
490C4—82no—
491C4—4882no—
492C4—4882no—
493C4#1683969014yes—
494C4C2×#1451975911yescharacteristic
495C4C2×#1451976311yescharacteristic
496C4C2×#1451977011yescharacteristic
497C4C2×#1451977011yescharacteristic
498C2—44no—
499C2#2144725518yesdirect product factor
500C2C2×#1683969011yescharacteristic
501C2C2×#1683998911yescharacteristic
502C2C2×#1684001011yescharacteristic
503C2C2×#1684009211yescharacteristic
504C2C2×#1684008611yescharacteristic
505C2C2×#1684010011yescharacteristic
506C2C2×#1684007811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#380C2
socleC24×C61C2×D4
prime radicalC25×C61D4
hypercenterC2×#380D61
hypocenterC61C2×#2077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#14519708C2semidirect
4. #21447255C2direct (N × H)
5. C2×#16839524C2semidirect
6. C2×#16839524C2semidirect
7. C2×#16839524C2semidirect
15. C2×#14519708C22semidirect
21. #16839524C22semidirect
22. #16839524C22semidirect
23. #16839524C22semidirect
254. C2×C61#2077semidirect
284. C61C2×#2077semidirect
499. C2#21447255direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197082
C22×C22⋊#924182
C2×#168396222
#214472552
C2×#168395242
C2×C61×#3802
C2×#207761