Finite Group Databasebeta

← C2×#21445031 #29655684

Subgroups — C2×#21445031 #29655684

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840472C211yesmaximal, characteristic
2C2×#16840114C211yesmaximal, characteristic, complemented
3C2×#16840039C211yesmaximal, characteristic
4#21445031C218yesmaximal, direct product factor
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic
8C2×C61×#462C211yesmaximal, characteristic, complemented
9#16840472—22no—
10#16840472—22no—
11#16840472—22no—
12#16840472C2214yes—
13C2×#14519777C2211yescharacteristic
14C2×#14519769—21no—
15C2×#14519755—22no—
16C2×#14519753—21no—
17C2×C4×D244—21no—
18C2×C4×D244C2211yescharacteristic
19C2×C4⋊C4×D61—21no—
20#16840114—22no—
21#16840114C2214yescomplemented
22#16840039—22no—
23#16840039C2214yes—
24C2×#14519710—21no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519700—22no—
27C2×#14519697—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839510C2214yescomplemented
30Q8⋊#92418C2214yescomplemented
31#16839489C2214yes—
32C22×Q16×C61—21no—
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×C4×Q8×C61C2211yescharacteristic
35C61×#462—22no—
36C61×#462C2214yescomplemented
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#103×C61—21no—
39C22×Dic122D412yes—
40C22×D244D411yescharacteristic
41C22×C4×D61—21no—
42C22×C4×D61—22no—
43C22×#92418—21no—
44C22×#92418—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777D412yes—
48#14519777C2312yes—
49#14519769—24no—
50#14519769—24no—
51#14519755—28no—
52#14519755—28no—
53#14519753—24no—
54#14519753—24no—
55C4×D244—24no—
56C4×D244—24no—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244D412yes—
60C4×D244C2312yes—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61D411yescharacteristic
64C2×#11758196—22no—
65C2×#11758196—22no—
66C4⋊C4×D61—24no—
67C4⋊C4×D61—24no—
68C2×#11758198—22no—
69C2×#11758198—21no—
70#14519710—24no—
71C4⋊#92418—21no—
72C4⋊#92418C2312yes—
73#14519700—28no—
74#14519697—24no—
75C4×#92418—21no—
76C4×#92418C2312yes—
77C22×Q8×C61—21no—
78C22×Q8×C61D411yescharacteristic
79C2×Q16×C61—24no—
80C2×Q16×C61—44no—
81C22×C8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61D412yes—
89C4×Q8×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C42×C61—21no—
95C2×C42×C61C2311yescharacteristic
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#103×C61—24no—
99C23×D61—21no—
100C2×Q8×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—41no—
105C2×Q8×C61—42no—
106C2×Q8×C61—42no—
107C2×Q8×C61C2×D412yes—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—22no—
115C22×Dic61—21no—
116C2×D244—21no—
117C2×D244—22no—
118C2×D244Q1614yescomplemented
119C2×D244C2×D412yes—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—28no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—84no—
126C2×Dic122—22no—
127C2×Dic122—44no—
128C2×Dic122C2×D414yes—
129Q16×C61—48no—
130C2×C8×C61—22no—
131C2×C8×C61—42no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61C2×D412yes—
140C42×C61—22no—
141C42×C61—22no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2411yescharacteristic
146#11758198—28no—
147#11758198—22no—
148#11758198—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C4⋊Dic61—21no—
152C4⋊Dic61—22no—
153C4⋊Dic61—22no—
154C4⋊Dic61C2×D412yes—
155#11758196—28no—
156#11758196—28no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—42no—
160C2×#92418—42no—
161C23×C61#12011yescharacteristic
162C22×D61—22no—
163C22×D61—24no—
164C22×D61—42no—
165C22×D61—42no—
166Q8×C61—22no—
167Q8×C61—22no—
168Q8×C61—42no—
169Q8×C61—42no—
170Q8×C61—42no—
171Q8×C61—82no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—82no—
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61C2×Q1612yes—
183C2×C4×C61#13512yes—
184C2×C4×C61AGL(1,ℤ/8)12yes—
185C2×C4×C61#13712yes—
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×C4×C61C22×D411yescharacteristic
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—42no—
192C2×Dic61—44no—
193D244—22no—
194D244—24no—
195D244C2×Q1614yescomplemented
196C4×D61—42no—
197C4×D61—42no—
198C4×D61—44no—
199C4×D61—88no—
200Dic122—44no—
201Dic122—82no—
202C8×C61—42no—
203#92418—42no—
204#92418—42no—
205C2×#1644—611nomaximal, Sylow
206C22×C61#44912yes—
207C22×C61#45112yes—
208C22×C61#45512yes—
209C22×C61C2×#12011yescharacteristic
210C2×D61—24no—
211C2×D61—48no—
212C2×D61—42no—
213C2×D61—42no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—42no—
217C4×C61—42no—
218C4×C61—82no—
219C4×C61#44912yes—
220C4×C61#45112yes—
221C4×C61C22×Q1611yescharacteristic
222C4×C61C2×#13511yescharacteristic
223C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
224C4×C61C2×#13711yescharacteristic
225Dic61—42no—
226Dic61—44no—
227C2×#554—611no—
228C2×#487—611no—
229C2×#474—611no—
230C2×#462D6111yescharacteristic, complemented
231#1644—618no—
232C2×#333—611no—
233C2×Q8⋊C8—611no—
234C2×D4⋊C8—611no—
235C2×C61#164414yescomplemented
236C2×C61C2×#45111yescharacteristic
237C2×C61C2×#44911yescharacteristic
238C2×C61C2×#45511yescharacteristic
239D61—44no—
240C22×Q16—21no—
241#554—614no—
242#554—1222no—
243#554—1222no—
244#554—1222no—
245C2×C4⋊Q8—611no—
246C2×C4⋊Q8C2×D6111yescharacteristic
247C2×#125—1221no—
248C2×C22⋊Q8—1222no—
249C2×C22⋊Q8—1221no—
250C2×C4×Q8C2×D6111yescharacteristic
251C2×C4×D4—611no—
252C2×C4×D4—1221no—
253C22×C4⋊C4—1221no—
254#487—614no—
255#487—1222no—
256#474—614no—
257#474—1222no—
258#462—22no—
259#462C2×D6114yescomplemented
260C2×#107—1221no—
261C2×C4⋊C8—611no—
262C2×C4⋊C8C2×D6111yescharacteristic
263C2×#103—21no—
264C2×#103—1222no—
265C2×#102—1221no—
266C2×C4×C8—611no—
267#333—614no—
268Q8⋊C8—614no—
269D4⋊C8—614no—
270C61C2×#164411yescharacteristic, complemented, Sylow
271C22×Q8—21no—
272C22×Q8—612no—
273C22×Q8C22⋊D6111yescharacteristic
274C22×D4—611no—
275C23×C4—1222no—
276C23×C4—1221no—
277C2×Q16—24no—
278C2×Q16—44no—
279C22×C8—21no—
280C22×C8—1221no—
281C22×C8—1221no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—612no—
286C4⋊Q8—612no—
287C4⋊Q8—1221no—
288C4⋊Q8—1221no—
289C4⋊Q8C22×D6112yes—
290#125—1224no—
291#125—1224no—
292C22⋊Q8—1228no—
293C22⋊Q8—1228no—
294C22⋊Q8—1224no—
295C22⋊Q8—1224no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C22⋊D6112yes—
299C4×Q8C22×D6112yes—
300C4×D4—612no—
301C4×D4—612no—
302C4×D4—1224no—
303C4×D4—1224no—
304C4×D4—1221no—
305C4×D4—1221no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—1224no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4—1222no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1224no—
316C2×C4⋊C4C22⋊D6111yescharacteristic
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1221no—
319C2×C42—21no—
320C2×C42C22×D6111yescharacteristic
321#107—1224no—
322C4⋊C8—21no—
323C4⋊C8—612no—
324C4⋊C8—1221no—
325C4⋊C8C22×D6112yes—
326#103—24no—
327#103—1228no—
328#102—1224no—
329C4×C8—612no—
330C4×C8—1221no—
331C24—1221no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—41no—
337C2×Q8—42no—
338C2×Q8—42no—
339C2×Q8—614no—
340C2×Q8—1222no—
341C2×Q8—2444no—
342C2×Q8C2×C22⋊D6112yes—
343C2×D4—612no—
344C2×D4—614no—
345C2×D4—1222no—
346C2×D4—1221no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—1228no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—4884no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4D4×D6111yescharacteristic
359C22×C4D4×D6111yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361Q16—48no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—1222no—
365C2×C8—1222no—
366C2×C8—2442no—
367C2×C8—2442no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—612no—
376C4⋊C4—1228no—
377C4⋊C4—1228no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4—1221no—
381C4⋊C4—1222no—
382C4⋊C4—1222no—
383C4⋊C4C2×C22⋊D6112yes—
384C22⋊C4—1228no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C42—22no—
388C42—22no—
389C42D4×D6111yescharacteristic
390C42D4×D6111yescharacteristic
391C42C2×C22⋊D6111yescharacteristic
392C42C23×D6111yescharacteristic
393C23—1222no—
394C23—1224no—
395C23—2442no—
396C23—2442no—
397C23#1451974511yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403Q8—82no—
404Q8—4882no—
405Q8—2444no—
406D4—614no—
407D4—1222no—
408D4—1224no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4—1222no—
417C2×C4—1224no—
418C2×C4—4888no—
419C2×C4—2444no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2444no—
424C2×C4#1451974511yescharacteristic
425C2×C4#1451974511yescharacteristic
426C2×C4#1451974511yescharacteristic
427C2×C4Q16×D6112yes—
428C2×C4#1451979712yes—
429C2×C4#1451980312yes—
430C2×C4#1451980912yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C22×C22⋊D6111yescharacteristic
434C8—42no—
435C8—2442no—
436C8—2442no—
437C22—1224no—
438C22—2442no—
439C22—2448no—
440C22—2442no—
441C22#1683990512yes—
442C22#1683991612yes—
443C22#1683993812yes—
444C22C2×#1451974511yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—82no—
450C4—2444no—
451C4—2442no—
452C4#1683990512yes—
453C4#1683991612yes—
454C4C2×Q16×D6111yescharacteristic
455C4C2×#1451979711yescharacteristic
456C4C2×#1451980311yescharacteristic
457C4C2×#1451980911yescharacteristic
458C2—2444no—
459C2#2144503114yesdirect product factor
460C2C2×#1683991611yescharacteristic
461C2C2×#1683990511yescharacteristic
462C2C2×#1683993811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#462C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#462D61
hypocenterC61C2×#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#16840114C2semidirect
4. #21445031C2direct (N × H)
5. C2×#16839510C2semidirect
6. C2×Q8⋊#92418C2semidirect
8. C2×C61×#462C2semidirect
21. #16840114C22semidirect
29. #16839510C22semidirect
30. Q8⋊#92418C22semidirect
36. C61×#462C22semidirect
118. C2×D244Q16semidirect
195. D244C2×Q16semidirect
230. C2×#462D61semidirect
235. C2×C61#1644semidirect
259. #462C2×D61semidirect
270. C61C2×#1644semidirect
459. C2#21445031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404722
C2×#168401142
C2×#168400392
#214450312
C2×#168395102
C2×Q8⋊#924182
C2×#168394892
C2×C61×#4622
C2×#164461