Finite Group Databasebeta

← C2×#21445103 #29655797

Subgroups — C2×#21445103 #29655797

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840158C211yesmaximal, characteristic, complemented
2C2×#16840042C211yesmaximal, characteristic, complemented
3C2×#16839967C211yesmaximal, characteristic, complemented
4#21445103C218yesmaximal, direct product factor
5C2×#16839508C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic, complemented
8C2×C61×#547C211yesmaximal, characteristic
9C22×#11758200—21no—
10C2×#14519777C2211yescharacteristic
11#16840158—22no—
12#16840158C2214yescomplemented
13#16840042—22no—
14#16840042C2214yescomplemented
15#16839967—22no—
16#16839967C2214yescomplemented
17C2×#14519710—21no—
18C2×#14519708—22no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519700—21no—
22C2×#14519698—21no—
23C2×C4×#92418C2211yescharacteristic
24#16839508C2214yescomplemented
25D4⋊#92418C2214yescomplemented
26D4⋊#92418C2214yescomplemented
27C22×#41×C61—21no—
28C61×#547—22no—
29C61×#547—22no—
30C61×#547—22no—
31C61×#547C2214yes—
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×#123×C61—22no—
34C2×C22⋊Q8×C61—21no—
35C2×#121×C61—21no—
36C2×C4×D4×C61C2211yescharacteristic
37C2×C4×D4×C61C2211yescharacteristic
38C22×C4⋊C4×C61—21no—
39C22×Dic122—21no—
40C2×#11758200—24no—
41C2×#11758200—44no—
42C22×#92418—21no—
43C22×#92418—21no—
44C22×#92418—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777C2312yes—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51#14519710—24no—
52#14519708—28no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418C2312yes—
56C4⋊#92418C2312yes—
57#14519700—24no—
58#14519698—24no—
59C4×#92418—21no—
60C4×#92418C2312yes—
61C2×#41×C61—24no—
62C2×#41×C61—24no—
63C2×#41×C61—44no—
64C2×#41×C61—44no—
65C22×Q8×C61—21no—
66C22×D4×C61—22no—
67C22×D4×C61D411yescharacteristic
68C22×D4×C61D411yescharacteristic
69C23×C4×C61—22no—
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C4⋊Q8×C61—21no—
73C4⋊Q8×C61—21no—
74C4⋊Q8×C61D412yes—
75C4⋊Q8×C61C2312yes—
76#123×C61—28no—
77#123×C61—28no—
78C22⋊Q8×C61—24no—
79C22⋊Q8×C61—24no—
80#121×C61—24no—
81#121×C61—24no—
82C4×D4×C61—21no—
83C4×D4×C61—21no—
84C4×D4×C61—21no—
85C4×D4×C61—21no—
86C4×D4×C61D412yes—
87C4×D4×C61D412yes—
88C4×D4×C61C2312yes—
89C4×D4×C61C2312yes—
90C2×C4⋊C4×C61—24no—
91C2×C4⋊C4×C61—22no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61D412yes—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C22⋊C4×C61—22no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C42×C61C2311yescharacteristic
101C24×C61—21no—
102C24×C61—21no—
103#41×C61—48no—
104#41×C61—416no—
105#41×C61—48no—
106C2×Q8×C61—22no—
107C2×Q8×C61—22no—
108C2×Q8×C61—42no—
109C2×Q8×C61—42no—
110C2×D4×C61—28no—
111C2×D4×C61—21no—
112C2×D4×C61—21no—
113C2×D4×C61—22no—
114C2×D4×C61—22no—
115C2×D4×C61—22no—
116C2×D4×C61—48no—
117C2×D4×C61SD1614yescomplemented
118C2×D4×C61C2×D412yes—
119C2×D4×C61C2×D412yes—
120C22×C4×C61—28no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—48no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×Dic61—41no—
137C2×Dic122—22no—
138C2×Dic122—42no—
139C2×Dic122—42no—
140C2×Dic122—41no—
141C4⋊C4×C61—28no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—22no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61C2×D412yes—
148C4⋊C4×C61C2×D412yes—
149C4⋊C4×C61C2×D414yes—
150C22⋊C4×C61—28no—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C22⋊C4×C61—22no—
154C22⋊C4×C61—22no—
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C42×C61C2411yescharacteristic
159#11758200—48no—
160C4⋊Dic61—22no—
161C4⋊Dic61—22no—
162C4⋊Dic61—41no—
163C4⋊Dic61—41no—
164C2×#92418—24no—
165C2×#92418—22no—
166C2×#92418—22no—
167C2×#92418—22no—
168C2×#92418—42no—
169C2×#92418—42no—
170C23×C61—22no—
171C23×C61—24no—
172C23×C61—22no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61#12011yescharacteristic
179Q8×C61—42no—
180Q8×C61—42no—
181Q8×C61—44no—
182D4×C61—22no—
183D4×C61—22no—
184D4×C61—22no—
185D4×C61—24no—
186D4×C61—416no—
187D4×C61—42no—
188D4×C61C2×SD1614yescomplemented
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—24no—
193C2×C4×C61—416no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—44no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—44no—
202C2×C4×C61—44no—
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12011yescharacteristic
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61C2×SD1612yes—
207C2×C4×C61#13512yes—
208C2×C4×C61AGL(1,ℤ/8)12yes—
209C2×C4×C61AGL(1,ℤ/8)12yes—
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×Dic61—42no—
214C2×Dic61—82no—
215Dic122—42no—
216Dic122—42no—
217Dic122—82no—
218#92418—24no—
219#92418—42no—
220#92418—42no—
221C2×#1654—611nomaximal, Sylow
222C22×C61—24no—
223C22×C61—48no—
224C22×C61—42no—
225C22×C61—42no—
226C22×C61—42no—
227C22×C61—42no—
228C22×C61—42no—
229C22×C61—84no—
230C22×C61#44912yes—
231C22×C61#45012yes—
232C22×C61#45612yes—
233C22×C61C2×#12011yescharacteristic
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—42no—
237C4×C61—44no—
238C4×C61—42no—
239C4×C61#44912yes—
240C4×C61#45012yes—
241C4×C61C22×SD1611yescharacteristic
242C4×C61C2×#13511yescharacteristic
243C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
245Dic61—82no—
246C2×#547D6111yescharacteristic
247C2×#498—611no—
248C2×#474—611no—
249C2×#461—611no—
250#1654—618no—
251C2×#332—611no—
252C2×D4⋊C8—611no—
253C2×D4⋊C8—611no—
254C2×C61—44no—
255C2×C61—82no—
256C2×C61#165414yescomplemented
257C2×C61C2×#45011yescharacteristic
258C2×C61C2×#44911yescharacteristic
259C2×C61C2×#45611yescharacteristic
260C22×#41—21no—
261C22×SD16—1221no—
262#547—22no—
263#547—22no—
264#547—22no—
265#547C2×D6114yes—
266C2×C4⋊Q8—611no—
267C2×C4⋊Q8C2×D6111yescharacteristic
268C2×#123—22no—
269C2×C22⋊Q8—21no—
270C2×#121—21no—
271C2×C4×D4C2×D6111yescharacteristic
272C2×C4×D4C2×D6111yescharacteristic
273C22×C4⋊C4—21no—
274#498—614no—
275#498—1222no—
276#474—614no—
277#474—1222no—
278#461—614no—
279#461—1222no—
280C2×#107—1221no—
281C2×#106—1222no—
282C2×C4⋊C8—611no—
283C2×C4⋊C8—611no—
284C2×#103—1221no—
285C2×#102—1221no—
286C2×C4×C8—611no—
287#332—614no—
288D4⋊C8—614no—
289D4⋊C8—614no—
290C61C2×#165411yescharacteristic, complemented, Sylow
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×Q8—1221no—
297C22×D4—22no—
298C22×D4C22⋊D6111yescharacteristic
299C22×D4C22⋊D6111yescharacteristic
300C23×C4—22no—
301C23×C4—21no—
302C23×C4—21no—
303C2×SD16—1224no—
304C2×SD16—2444no—
305C22×C8—1221no—
306C22×C8—1221no—
307C22×C8—1221no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—612no—
311C4⋊Q8—1221no—
312C4⋊Q8—1221no—
313C4⋊Q8—1221no—
314C4⋊Q8C22⋊D6112yes—
315C4⋊Q8C22×D6112yes—
316#123—28no—
317#123—28no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320#121—24no—
321#121—24no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4C22⋊D6112yes—
327C4×D4C22⋊D6112yes—
328C4×D4C22×D6112yes—
329C4×D4C22×D6112yes—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4C22⋊D6111yescharacteristic
337C2×C4⋊C4C22⋊D6111yescharacteristic
338C2×C4⋊C4C22⋊D6112yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C42C22×D6111yescharacteristic
343#107—1224no—
344#106—1228no—
345C4⋊C8—612no—
346C4⋊C8—612no—
347C4⋊C8—1221no—
348C4⋊C8—1221no—
349#103—1224no—
350#102—1224no—
351C4×C8—612no—
352C4×C8—1221no—
353C24—21no—
354C24—21no—
355#41—48no—
356#41—416no—
357#41—48no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—1222no—
363C2×Q8—2442no—
364C2×Q8—2442no—
365C2×Q8—2441no—
366C2×D4—28no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—48no—
373C2×D4#1175820014yescomplemented
374C2×D4C2×C22⋊D6112yes—
375C2×D4C2×C22⋊D6112yes—
376C22×C4—28no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—48no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—2441no—
390C22×C4C2×C22⋊D6111yescharacteristic
391C22×C4C2×C22⋊D6111yescharacteristic
392C22×C4C2×C22⋊D6111yescharacteristic
393SD16—2448no—
394C2×C8—1224no—
395C2×C8—1222no—
396C2×C8—1222no—
397C2×C8—1222no—
398C2×C8—2442no—
399C2×C8—2442no—
400C4⋊C4—28no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—1222no—
407C4⋊C4—1222no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C4⋊C4C2×C22⋊D6112yes—
411C4⋊C4C2×C22⋊D6114yes—
412C4⋊C4C2×C22⋊D6112yes—
413C22⋊C4—28no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C42C2×C22⋊D6111yescharacteristic
419C42C2×C22⋊D6111yescharacteristic
420C42C2×C22⋊D6111yescharacteristic
421C42C23×D6111yescharacteristic
422C23—22no—
423C23—24no—
424C23—22no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23#1451974611yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—44no—
434Q8—4882no—
435Q8—2442no—
436Q8—2442no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4—24no—
441D4—416no—
442D4—42no—
443D4C2×#1175820014yescomplemented
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—416no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—4882no—
459C2×C4—2442no—
460C2×C4#1451974611yescharacteristic
461C2×C4#1451974611yescharacteristic
462C2×C4#1451974611yescharacteristic
463C2×C4C2×#1175820012yes—
464C2×C4#1451979712yes—
465C2×C4#1451980212yes—
466C2×C4#1451980312yes—
467C2×C4C22×C22⋊D6111yescharacteristic
468C2×C4C22×C22⋊D6111yescharacteristic
469C2×C4C22×C22⋊D6111yescharacteristic
470C8—1224no—
471C8—2442no—
472C8—2442no—
473C22—24no—
474C22—42no—
475C22—42no—
476C22—48no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22#1683990712yes—
482C22#1683991312yes—
483C22#1683994512yes—
484C22C2×#1451974611yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—44no—
489C4—42no—
490C4—4882no—
491C4#1683990712yes—
492C4#1683991312yes—
493C4C22×#1175820011yescharacteristic
494C4C2×#1451979711yescharacteristic
495C4C2×#1451980211yescharacteristic
496C4C2×#1451980311yescharacteristic
497C2—44no—
498C2—82no—
499C2#2144510314yesdirect product factor
500C2C2×#1683991311yescharacteristic
501C2C2×#1683990711yescharacteristic
502C2C2×#1683994511yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC2×C61×#547C2
socleC23×C61#120
hypercenterC2×#547D61
hypocenterC61C2×#1654
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16840158C2semidirect
2. C2×#16840042C2semidirect
3. C2×#16839967C2semidirect
4. #21445103C2direct (N × H)
5. C2×#16839508C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×D4⋊#92418C2semidirect
12. #16840158C22semidirect
14. #16840042C22semidirect
16. #16839967C22semidirect
24. #16839508C22semidirect
25. D4⋊#92418C22semidirect
26. D4⋊#92418C22semidirect
117. C2×D4×C61SD16semidirect
188. D4×C61C2×SD16semidirect
256. C2×C61#1654semidirect
290. C61C2×#1654semidirect
373. C2×D4#11758200semidirect
443. D4C2×#11758200semidirect
499. C2#21445103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401582
C2×#168400422
C2×#168399672
#214451032
C2×#168395082
C2×D4⋊#924182
C2×C61×#5472
C2×#165461