Finite Group Databasebeta

← C2×#21445047 #29655943

Subgroups — C2×#21445047 #29655943

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840112C211yesmaximal, characteristic, complemented
2C2×#16840042C211yesmaximal, characteristic, complemented
3C2×#16839967C211yesmaximal, characteristic, complemented
4#21445047C218yesmaximal, direct product factor
5C2×#16839511C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic, complemented
8C2×C61×#555C211yesmaximal, characteristic
9C22×#11758200—21no—
10C2×#14519777C2211yescharacteristic
11#16840112—22no—
12#16840112C2214yescomplemented
13#16840042—22no—
14#16840042C2214yescomplemented
15#16839967—22no—
16#16839967C2214yescomplemented
17C2×#14519710—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701—22no—
21C2×#14519700—21no—
22C2×#14519698—21no—
23C2×C4×#92418C2211yescharacteristic
24#16839511C2214yescomplemented
25D4⋊#92418C2214yescomplemented
26D4⋊#92418C2214yescomplemented
27C61×#555—22no—
28C61×#555—22no—
29C61×#555—22no—
30C61×#555C2214yes—
31C2×C4⋊Q8×C61C2211yescharacteristic
32C2×#124×C61—22no—
33C2×#121×C61—21no—
34C2×#121×C61—21no—
35C2×C4×D4×C61C2211yescharacteristic
36C2×C4×D4×C61C2211yescharacteristic
37C2×#117×C61—21no—
38C2×#117×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—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418C2312yes—
55C4⋊#92418C2312yes—
56#14519701—28no—
57#14519700—24no—
58#14519698—24no—
59C4×#92418—21no—
60C4×#92418C2312yes—
61C22×Q8×C61D412yes—
62C22×D4×C61—22no—
63C22×D4×C61D411yescharacteristic
64C22×D4×C61D411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61D412yes—
70C4⋊Q8×C61C2312yes—
71#124×C61—28no—
72#124×C61—28no—
73#121×C61—24no—
74#121×C61—24no—
75#121×C61—24no—
76#121×C61—24no—
77C4×D4×C61—21no—
78C4×D4×C61—21no—
79C4×D4×C61—21no—
80C4×D4×C61—21no—
81C4×D4×C61D412yes—
82C4×D4×C61D412yes—
83C4×D4×C61C2312yes—
84C4×D4×C61C2312yes—
85#117×C61—24no—
86#117×C61—24no—
87#117×C61—24no—
88#117×C61—24no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61D411yescharacteristic
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—22no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C42×C61—22no—
98C2×C42×C61C2311yescharacteristic
99C24×C61—21no—
100C24×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—44no—
103C2×Q8×C61C2×D414yes—
104C2×D4×C61—28no—
105C2×D4×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61—22no—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—84no—
112C2×D4×C61C2×D412yes—
113C2×D4×C61C2×D412yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61—42no—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×Dic61—41no—
129C2×Dic122—22no—
130C2×Dic122—42no—
131C2×Dic122—42no—
132C2×Dic122—41no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61C2×D412yes—
140C4⋊C4×C61C2×D412yes—
141C22⋊C4×C61—28no—
142C22⋊C4×C61—28no—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C22⋊C4×C61—22no—
146C22⋊C4×C61—22no—
147C42×C61—28no—
148C42×C61C2×D411yescharacteristic
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2411yescharacteristic
152#11758200—48no—
153C4⋊Dic61—22no—
154C4⋊Dic61—22no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—22no—
160C2×#92418—42no—
161C2×#92418—42no—
162C2×#92418—42no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61#12011yescharacteristic
172Q8×C61—44no—
173Q8×C61—82no—
174D4×C61—22no—
175D4×C61—22no—
176D4×C61—22no—
177D4×C61—22no—
178D4×C61—42no—
179D4×C61—42no—
180D4×C61—88no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—24no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—44no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—44no—
193C2×C4×C61—44no—
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12011yescharacteristic
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#13512yes—
198C2×C4×C61#13512yes—
199C2×C4×C61AGL(1,ℤ/8)12yes—
200C2×C4×C61#13712yes—
201C2×C4×C61C22×D411yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C2×Dic61—42no—
205C2×Dic61—82no—
206Dic122—42no—
207Dic122—42no—
208Dic122—82no—
209#92418—42no—
210#92418—42no—
211#92418—42no—
212C2×#1646—611nomaximal, Sylow
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—42no—
216C22×C61—42no—
217C22×C61—42no—
218C22×C61—42no—
219C22×C61—84no—
220C22×C61—84no—
221C22×C61#44912yes—
222C22×C61#45212yes—
223C22×C61#45512yes—
224C22×C61C2×#12011yescharacteristic
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—42no—
228C4×C61—42no—
229C4×C61—44no—
230C4×C61#44912yes—
231C4×C61#45212yes—
232C4×C61C2×#13511yescharacteristic
233C4×C61C2×#13511yescharacteristic
234C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
235C4×C61C2×#13711yescharacteristic
236Dic61—82no—
237C2×#555D6111yescharacteristic
238C2×#487—611no—
239C2×#474—611no—
240C2×#461—611no—
241#1646—618no—
242C2×#333—611no—
243C2×D4⋊C8—611no—
244C2×D4⋊C8—611no—
245C2×C61—82no—
246C2×C61—82no—
247C2×C61#164614yescomplemented
248C2×C61C2×#44911yescharacteristic
249C2×C61C2×#45211yescharacteristic
250C2×C61C2×#45511yescharacteristic
251C22×SD16—1221no—
252#555—22no—
253#555—22no—
254#555—22no—
255#555C2×D6114yes—
256C2×C4⋊Q8—611no—
257C2×C4⋊Q8C2×D6111yescharacteristic
258C2×#124—22no—
259C2×#121—21no—
260C2×#121—21no—
261C2×C4×D4C2×D6111yescharacteristic
262C2×C4×D4C2×D6111yescharacteristic
263C2×#117—21no—
264C2×#117—21no—
265#487—614no—
266#487—1222no—
267#474—614no—
268#474—1222no—
269#461—614no—
270#461—1222no—
271C2×#107—1221no—
272C2×C4⋊C8—611no—
273C2×C4⋊C8—611no—
274C2×#103—1222no—
275C2×#103—1221no—
276C2×#102—1221no—
277C2×C4×C8—611no—
278#333—614no—
279D4⋊C8—614no—
280D4⋊C8—614no—
281C61C2×#164611yescharacteristic, complemented, Sylow
282C22×Q8—1221no—
283C22×Q8C22⋊D6112yes—
284C22×D4—22no—
285C22×D4C22⋊D6111yescharacteristic
286C22×D4C22⋊D6111yescharacteristic
287C23×C4—21no—
288C23×C4—21no—
289C2×SD16—1224no—
290C2×SD16—2444no—
291C22×C8—1221no—
292C22×C8—1221no—
293C22×C8—1221no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—612no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299C4⋊Q8—1221no—
300C4⋊Q8C22⋊D6112yes—
301C4⋊Q8C22×D6112yes—
302#124—28no—
303#124—28no—
304#121—24no—
305#121—24no—
306#121—24no—
307#121—24no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4C22⋊D6112yes—
313C4×D4C22⋊D6112yes—
314C4×D4C22×D6112yes—
315C4×D4C22×D6112yes—
316#117—24no—
317#117—24no—
318#117—24no—
319#117—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4C22⋊D6111yescharacteristic
325C2×C4⋊C4C22⋊D6111yescharacteristic
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C42—22no—
331C2×C42C22×D6111yescharacteristic
332#107—1224no—
333C4⋊C8—612no—
334C4⋊C8—612no—
335C4⋊C8—1221no—
336C4⋊C8—1221no—
337#103—1228no—
338#103—1224no—
339#102—1224no—
340C4×C8—612no—
341C4×C8—1221no—
342C24—21no—
343C24—21no—
344C2×Q8—22no—
345C2×Q8—44no—
346C2×Q8—1222no—
347C2×Q8—2442no—
348C2×Q8—2442no—
349C2×Q8—2441no—
350C2×Q8C2×C22⋊D6114yes—
351C2×D4—28no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—84no—
359C2×D4C2×C22⋊D6112yes—
360C2×D4C2×C22⋊D6112yes—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—2441no—
373C22×C4C2×C22⋊D6111yescharacteristic
374C22×C4C2×C22⋊D6111yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376SD16—2448no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—2442no—
381C2×C8—2442no—
382C2×C8—2442no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4C2×C22⋊D6112yes—
394C4⋊C4C2×C22⋊D6112yes—
395C22⋊C4—28no—
396C22⋊C4—28no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—28no—
402C42C2×C22⋊D6111yescharacteristic
403C42C2×C22⋊D6111yescharacteristic
404C42C2×C22⋊D6111yescharacteristic
405C42C23×D6111yescharacteristic
406C23—22no—
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23#1451974611yescharacteristic
415Q8—44no—
416Q8—82no—
417Q8—4882no—
418Q8—2442no—
419Q8—2442no—
420D4—22no—
421D4—22no—
422D4—22no—
423D4—22no—
424D4—42no—
425D4—42no—
426D4—88no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—4882no—
441C2×C4—2442no—
442C2×C4#1451974611yescharacteristic
443C2×C4#1451974611yescharacteristic
444C2×C4#1451974611yescharacteristic
445C2×C4#1451979712yes—
446C2×C4#1451979712yes—
447C2×C4#1451980212yes—
448C2×C4#1451980712yes—
449C2×C4C22×C22⋊D6111yescharacteristic
450C2×C4C22×C22⋊D6111yescharacteristic
451C2×C4C22×C22⋊D6111yescharacteristic
452C8—2442no—
453C8—2442no—
454C8—2442no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—84no—
462C22—84no—
463C22#1683990712yes—
464C22#1683992412yes—
465C22#1683994012yes—
466C22C2×#1451974611yescharacteristic
467C4—21no—
468C4—21no—
469C4—44no—
470C4—42no—
471C4—42no—
472C4—4882no—
473C4#1683990712yes—
474C4#1683992412yes—
475C4C2×#1451979711yescharacteristic
476C4C2×#1451979711yescharacteristic
477C4C2×#1451980211yescharacteristic
478C4C2×#1451980711yescharacteristic
479C2—82no—
480C2—82no—
481C2#2144504714yesdirect product factor
482C2C2×#1683990711yescharacteristic
483C2C2×#1683992411yescharacteristic
484C2C2×#1683994011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC2×C61×#555C2
socleC23×C61#120
hypercenterC2×#555D61
hypocenterC61C2×#1646
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#16840112C2semidirect
2. C2×#16840042C2semidirect
3. C2×#16839967C2semidirect
4. #21445047C2direct (N × H)
5. C2×#16839511C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×D4⋊#92418C2semidirect
12. #16840112C22semidirect
14. #16840042C22semidirect
16. #16839967C22semidirect
24. #16839511C22semidirect
25. D4⋊#92418C22semidirect
26. D4⋊#92418C22semidirect
247. C2×C61#1646semidirect
281. C61C2×#1646semidirect
481. C2#21445047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401122
C2×#168400422
C2×#168399672
#214450472
C2×#168395112
C2×D4⋊#924182
C2×C61×#5552
C2×#164661