Finite Group Databasebeta

← C2×#21445005 #29655693

Subgroups — C2×#21445005 #29655693

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840108C211yesmaximal, characteristic
2C2×#16840047C211yesmaximal, characteristic, complemented
3C2×#16839972C211yesmaximal, characteristic, complemented
4#21445005C218yesmaximal, direct product factor
5C2×#16839506C211yesmaximal, characteristic
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
8C2×C61×#559C211yesmaximal, characteristic
9C22×#11758202—21no—
10C2×#14519777C2211yescharacteristic
11#16840108—22no—
12#16840108C2214yes—
13#16840047—22no—
14#16840047C2214yescomplemented
15#16839972—22no—
16#16839972C2214yescomplemented
17C2×#14519708—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519701—21no—
21C2×#14519700—21no—
22C2×#14519698—22no—
23C2×C4×#92418C2211yescharacteristic
24#16839506C2214yes—
25Q8⋊#92418C2214yescomplemented
26Q8⋊#92418C2214yescomplemented
27C61×#559—22no—
28C61×#559—22no—
29C61×#559—22no—
30C61×#559C2214yes—
31C2×#127×C61C2211yescharacteristic
32C2×#124×C61—21no—
33C2×#124×C61—21no—
34C2×#123×C61—22no—
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4×Q8×C61C2211yescharacteristic
37C2×C4×D4×C61—21no—
38C2×C4×D4×C61—21no—
39C22×Dic122—21no—
40C2×#11758202—24no—
41C2×#11758202—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#14519708—24no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418C2312yes—
55C4⋊#92418C2312yes—
56#14519701—24no—
57#14519700—24no—
58#14519698—28no—
59C4×#92418—21no—
60C4×#92418C2312yes—
61C22×Q8×C61D411yescharacteristic
62C22×Q8×C61D411yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61D412yes—
66C23×C4×C61—22no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61D412yes—
70#127×C61C2312yes—
71#124×C61—24no—
72#124×C61—24no—
73#124×C61—24no—
74#124×C61—24no—
75#123×C61—28no—
76#123×C61—28no—
77C4×Q8×C61—21no—
78C4×Q8×C61—21no—
79C4×Q8×C61—21no—
80C4×Q8×C61—21no—
81C4×Q8×C61D412yes—
82C4×Q8×C61D412yes—
83C4×Q8×C61C2312yes—
84C4×Q8×C61C2312yes—
85C4×D4×C61—24no—
86C4×D4×C61—24no—
87C4×D4×C61—24no—
88C4×D4×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—22no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C24×C61—22no—
100C2×Q8×C61—21no—
101C2×Q8×C61—21no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—22no—
105C2×Q8×C61—22no—
106C2×Q8×C61C2×D412yes—
107C2×Q8×C61C2×D412yes—
108C2×D4×C61—22no—
109C2×D4×C61—22no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—44no—
114C2×D4×C61—42no—
115C2×D4×C61—42no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61C2×D414yes—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—28no—
124C22×C4×C61—84no—
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—28no—
144C42×C61—22no—
145C42×C61—22no—
146C42×C61—22no—
147C42×C61—22no—
148C42×C61C2×D411yescharacteristic
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61C2411yescharacteristic
152#11758202—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—24no—
164C23×C61—44no—
165C23×C61—44no—
166C23×C61—44no—
167C23×C61#12011yescharacteristic
168Q8×C61—22no—
169Q8×C61—22no—
170Q8×C61—22no—
171Q8×C61—22no—
172Q8×C61—42no—
173Q8×C61—42no—
174D4×C61—44no—
175D4×C61—42no—
176D4×C61—42no—
177D4×C61—42no—
178D4×C61—42no—
179D4×C61—44no—
180D4×C61—44no—
181D4×C61—82no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—88no—
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#13512yes—
196C2×C4×C61#13512yes—
197C2×C4×C61AGL(1,ℤ/8)12yes—
198C2×C4×C61#13712yes—
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C2×Dic61—42no—
203C2×Dic61—82no—
204Dic122—42no—
205Dic122—42no—
206Dic122—82no—
207#92418—42no—
208#92418—42no—
209#92418—42no—
210C2×#1640—611nomaximal, Sylow
211C22×C61—44no—
212C22×C61—44no—
213C22×C61—44no—
214C22×C61—88no—
215C22×C61#44912yes—
216C22×C61#45212yes—
217C22×C61#45512yes—
218C22×C61C2×#12011yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61—42no—
223C4×C61—42no—
224C4×C61—42no—
225C4×C61#44912yes—
226C4×C61#45212yes—
227C4×C61C2×#13511yescharacteristic
228C4×C61C2×#13511yescharacteristic
229C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C61C2×#13711yescharacteristic
231Dic61—82no—
232C2×#559D6111yescharacteristic
233C2×#486—611no—
234C2×#475—611no—
235C2×#462—611no—
236#1640—618no—
237C2×#331—611no—
238C2×Q8⋊C8—611no—
239C2×Q8⋊C8—611no—
240C2×C61—84no—
241C2×C61#164014yescomplemented
242C2×C61C2×#44911yescharacteristic
243C2×C61C2×#45211yescharacteristic
244C2×C61C2×#45511yescharacteristic
245C22×Q16—1221no—
246#559—22no—
247#559—22no—
248#559—22no—
249#559C2×D6114yes—
250C2×C4⋊Q8—611no—
251C2×#127C2×D6111yescharacteristic
252C2×#124—21no—
253C2×#124—21no—
254C2×#123—22no—
255C2×C4×Q8C2×D6111yescharacteristic
256C2×C4×Q8C2×D6111yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259#486—614no—
260#486—1222no—
261#475—614no—
262#475—1222no—
263#462—614no—
264#462—1222no—
265C2×#106—1221no—
266C2×C4⋊C8—611no—
267C2×C4⋊C8—611no—
268C2×#103—1221no—
269C2×#103—1221no—
270C2×#102—1222no—
271C2×C4×C8—611no—
272#331—614no—
273Q8⋊C8—614no—
274Q8⋊C8—614no—
275C61C2×#164011yescharacteristic, complemented, Sylow
276C22×Q8—1221no—
277C22×Q8C22⋊D6111yescharacteristic
278C22×Q8C22⋊D6111yescharacteristic
279C22×D4—21no—
280C22×D4—21no—
281C22×D4C22⋊D6112yes—
282C23×C4—22no—
283C2×Q16—1224no—
284C2×Q16—2444no—
285C22×C8—1221no—
286C22×C8—1221no—
287C22×C8—1221no—
288C4⋊Q8—612no—
289C4⋊Q8—1221no—
290C4⋊Q8—1221no—
291C4⋊Q8—1221no—
292#127—21no—
293#127—21no—
294#127C22⋊D6112yes—
295#127C22×D6112yes—
296#124—24no—
297#124—24no—
298#124—24no—
299#124—24no—
300#123—28no—
301#123—28no—
302C4×Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8C22⋊D6112yes—
307C4×Q8C22⋊D6112yes—
308C4×Q8C22×D6112yes—
309C4×Q8C22×D6112yes—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—24no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4C22⋊D6111yescharacteristic
319C2×C4⋊C4C22⋊D6111yescharacteristic
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42C22×D6111yescharacteristic
326#106—1224no—
327C4⋊C8—612no—
328C4⋊C8—612no—
329C4⋊C8—1221no—
330C4⋊C8—1221no—
331#103—1224no—
332#103—1224no—
333#102—1228no—
334C4×C8—612no—
335C4×C8—1221no—
336C24—22no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—1222no—
344C2×Q8—2442no—
345C2×Q8—2442no—
346C2×Q8—2441no—
347C2×Q8C2×C22⋊D6112yes—
348C2×Q8C2×C22⋊D6112yes—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—44no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4C2×C22⋊D6114yes—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—28no—
365C22×C4—84no—
366C22×C4—2441no—
367C22×C4C2×C22⋊D6111yescharacteristic
368C22×C4C2×C22⋊D6111yescharacteristic
369C22×C4C2×C22⋊D6111yescharacteristic
370Q16—2448no—
371C2×C8—1222no—
372C2×C8—1222no—
373C2×C8—1222no—
374C2×C8—2442no—
375C2×C8—2442no—
376C2×C8—2442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—1222no—
384C4⋊C4—1222no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4C2×C22⋊D6112yes—
388C4⋊C4C2×C22⋊D6112yes—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—22no—
396C42C2×C22⋊D6111yescharacteristic
397C42C2×C22⋊D6111yescharacteristic
398C42C2×C22⋊D6111yescharacteristic
399C42C23×D6111yescharacteristic
400C23—24no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23#1451974611yescharacteristic
405Q8—22no—
406Q8—22no—
407Q8—22no—
408Q8—22no—
409Q8—42no—
410Q8—42no—
411Q8—4882no—
412Q8—2442no—
413Q8—2442no—
414D4—44no—
415D4—42no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—44no—
420D4—44no—
421D4—82no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—88no—
432C2×C4—4882no—
433C2×C4—2442no—
434C2×C4#1451974611yescharacteristic
435C2×C4#1451974611yescharacteristic
436C2×C4#1451974611yescharacteristic
437C2×C4#1451979712yes—
438C2×C4#1451979712yes—
439C2×C4#1451980212yes—
440C2×C4#1451980712yes—
441C2×C4C22×C22⋊D6111yescharacteristic
442C2×C4C22×C22⋊D6111yescharacteristic
443C2×C4C22×C22⋊D6111yescharacteristic
444C8—2442no—
445C8—2442no—
446C8—2442no—
447C22—44no—
448C22—44no—
449C22—44no—
450C22—88no—
451C22#1683990712yes—
452C22#1683992412yes—
453C22#1683994012yes—
454C22C2×#1451974611yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—4882no—
462C4#1683990712yes—
463C4#1683992412yes—
464C4C2×#1451979711yescharacteristic
465C4C2×#1451979711yescharacteristic
466C4C2×#1451980211yescharacteristic
467C4C2×#1451980711yescharacteristic
468C2—84no—
469C2#2144500514yesdirect product factor
470C2C2×#1683990711yescharacteristic
471C2C2×#1683992411yescharacteristic
472C2C2×#1683994011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#559C2
socleC23×C61#120
prime radicalC2×#127×C61C22
hypercenterC2×#559D61
hypocenterC61C2×#1640
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×#16840047C2semidirect
3. C2×#16839972C2semidirect
4. #21445005C2direct (N × H)
6. C2×Q8⋊#92418C2semidirect
7. C2×Q8⋊#92418C2semidirect
14. #16840047C22semidirect
16. #16839972C22semidirect
25. Q8⋊#92418C22semidirect
26. Q8⋊#92418C22semidirect
241. C2×C61#1640semidirect
275. C61C2×#1640semidirect
469. C2#21445005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401082
C2×#168400472
C2×#168399722
#214450052
C2×#168395062
C2×Q8⋊#924182
C2×C61×#5592
C2×#164061