Finite Group Databasebeta

← C2×#21444953 #29655638

Subgroups — C2×#21444953 #29655638

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840141C211yesmaximal, characteristic, complemented
2C2×#16840057C211yesmaximal, characteristic, complemented
3C2×#16840052C211yesmaximal, characteristic
4#21444953C218yesmaximal, direct product factor
5C2×#16839511C211yesmaximal, characteristic, complemented
6C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic
8C2×C61×#554C211yesmaximal, characteristic
9C22×#11758202—22no—
10C2×#14519777C2211yescharacteristic
11#16840141—22no—
12#16840141C2214yescomplemented
13#16840057—22no—
14#16840057C2214yescomplemented
15#16840052—22no—
16#16840052C2214yes—
17C2×#14519710—21no—
18C2×#14519708—21no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519701—21no—
22C2×#14519698—21no—
23C2×C4×#92418C2211yescharacteristic
24#16839511C2214yescomplemented
25Q8⋊#92418C2214yescomplemented
26D4⋊#92418C2214yes—
27C61×#554—22no—
28C61×#554—22no—
29C61×#554—22no—
30C61×#554C2214yes—
31C2×C4⋊Q8×C61C2211yescharacteristic
32C2×#125×C61—21no—
33C2×C22⋊Q8×C61—21no—
34C2×C22⋊Q8×C61—22no—
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4×D4×C61—21no—
37C2×C4×D4×C61C2211yescharacteristic
38C22×C4⋊C4×C61—21no—
39C22×Dic122—21no—
40C2×#11758202—28no—
41C2×#11758202—48no—
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—24no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418C2312yes—
56C4⋊#92418C2312yes—
57#14519701—24no—
58#14519698—24no—
59C4×#92418—21no—
60C4×#92418C2312yes—
61C22×Q8×C61D411yescharacteristic
62C22×Q8×C61D412yes—
63C22×D4×C61D411yescharacteristic
64C23×C4×C61—22no—
65C23×C4×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61D412yes—
69C4⋊Q8×C61C2312yes—
70#125×C61—24no—
71#125×C61—24no—
72C22⋊Q8×C61—24no—
73C22⋊Q8×C61—28no—
74C22⋊Q8×C61—24no—
75C22⋊Q8×C61—28no—
76C4×Q8×C61—21no—
77C4×Q8×C61—21no—
78C4×Q8×C61D412yes—
79C4×Q8×C61C2312yes—
80C4×D4×C61—24no—
81C4×D4×C61—24no—
82C4×D4×C61—21no—
83C4×D4×C61—21no—
84C4×D4×C61D412yes—
85C4×D4×C61C2312yes—
86C2×C4⋊C4×C61—24no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—24no—
93C2×C4⋊C4×C61D411yescharacteristic
94C2×C4⋊C4×C61D411yescharacteristic
95C2×C22⋊C4×C61—22no—
96C2×C22⋊C4×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99C24×C61—21no—
100C2×Q8×C61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C2×Q8×C61—44no—
105C2×Q8×C61C2×D412yes—
106C2×Q8×C61C2×D414yes—
107C2×D4×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61Q1614yescomplemented
110C2×D4×C61C2×D412yes—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—28no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61—84no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×Dic61—41no—
125C2×Dic122—22no—
126C2×Dic122—44no—
127C2×Dic122—41no—
128C4⋊C4×C61—28no—
129C4⋊C4×C61—28no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61C2×D412yes—
139C4⋊C4×C61C2×D412yes—
140C22⋊C4×C61—28no—
141C22⋊C4×C61—22no—
142C22⋊C4×C61—22no—
143C42×C61—22no—
144C42×C61—22no—
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2411yescharacteristic
149#11758202—416no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—41no—
153C4⋊Dic61—41no—
154C2×#92418—24no—
155C2×#92418—22no—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—42no—
159C2×#92418—42no—
160C23×C61—22no—
161C23×C61—24no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61#12011yescharacteristic
165Q8×C61—22no—
166Q8×C61—22no—
167Q8×C61—44no—
168Q8×C61—42no—
169Q8×C61—82no—
170D4×C61—22no—
171D4×C61—24no—
172D4×C61C2×Q1614yescomplemented
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—24no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—44no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—44no—
185C2×C4×C61—88no—
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#12011yescharacteristic
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61C2×Q1612yes—
190C2×C4×C61#13512yes—
191C2×C4×C61#13712yes—
192C2×C4×C61#13712yes—
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×Dic61—42no—
197C2×Dic61—82no—
198Dic122—44no—
199Dic122—82no—
200#92418—24no—
201#92418—42no—
202#92418—42no—
203C2×#1632—611nomaximal, Sylow
204C22×C61—24no—
205C22×C61—48no—
206C22×C61—42no—
207C22×C61—42no—
208C22×C61#45112yes—
209C22×C61#45212yes—
210C22×C61#45312yes—
211C22×C61C2×#12011yescharacteristic
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—42no—
215C4×C61—42no—
216C4×C61—42no—
217C4×C61—44no—
218C4×C61#45112yes—
219C4×C61#45212yes—
220C4×C61C22×Q1611yescharacteristic
221C4×C61C2×#13511yescharacteristic
222C4×C61C2×#13711yescharacteristic
223C4×C61C2×#13711yescharacteristic
224Dic61—82no—
225C2×#554D6111yescharacteristic
226C2×#494—611no—
227C2×#477—611no—
228C2×#476—611no—
229#1632—618no—
230C2×#333—611no—
231C2×Q8⋊C8—611no—
232C2×D4⋊C8—611no—
233C2×C61—44no—
234C2×C61#163214yescomplemented
235C2×C61C2×#45111yescharacteristic
236C2×C61C2×#45211yescharacteristic
237C2×C61C2×#45311yescharacteristic
238C22×Q16—1222no—
239#554—22no—
240#554—22no—
241#554—22no—
242#554C2×D6114yes—
243C2×C4⋊Q8—611no—
244C2×C4⋊Q8C2×D6111yescharacteristic
245C2×#125—21no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—22no—
248C2×C4×Q8C2×D6111yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4C2×D6111yescharacteristic
251C22×C4⋊C4—21no—
252#494—614no—
253#494—1222no—
254#477—614no—
255#477—1222no—
256#476—614no—
257#476—1222no—
258C2×#107—1221no—
259C2×#106—1221no—
260C2×C4⋊C8—611no—
261C2×C4⋊C8—611no—
262C2×#103—1221no—
263C2×#102—1221no—
264C2×C4×C8—611no—
265#333—614no—
266Q8⋊C8—614no—
267D4⋊C8—614no—
268C61C2×#163211yescharacteristic, complemented, Sylow
269C22×Q8—1221no—
270C22×Q8C22⋊D6111yescharacteristic
271C22×Q8C22⋊D6112yes—
272C22×D4C22⋊D6111yescharacteristic
273C23×C4—22no—
274C23×C4—21no—
275C2×Q16—1228no—
276C2×Q16—2448no—
277C22×C8—1221no—
278C22×C8—1221no—
279C22×C8—1221no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—612no—
283C4⋊Q8—1221no—
284C4⋊Q8—1221no—
285C4⋊Q8—1221no—
286C4⋊Q8C22⋊D6112yes—
287C4⋊Q8C22×D6112yes—
288#125—24no—
289#125—24no—
290C22⋊Q8—24no—
291C22⋊Q8—28no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8C22⋊D6112yes—
297C4×Q8C22×D6112yes—
298C4×D4—24no—
299C4×D4—24no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4C22⋊D6112yes—
303C4×D4C22×D6112yes—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4C22⋊D6111yescharacteristic
314C2×C4⋊C4C22⋊D6111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C42—21no—
318C2×C42C22×D6111yescharacteristic
319#107—1224no—
320#106—1224no—
321C4⋊C8—612no—
322C4⋊C8—612no—
323C4⋊C8—1221no—
324C4⋊C8—1221no—
325#103—1224no—
326#102—1224no—
327C4×C8—612no—
328C4×C8—1221no—
329C24—21no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—44no—
335C2×Q8—1222no—
336C2×Q8—2444no—
337C2×Q8—2441no—
338C2×Q8C2×C22⋊D6112yes—
339C2×Q8C2×C22⋊D6114yes—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4#1175820214yescomplemented
343C2×D4C2×C22⋊D6112yes—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—28no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—84no—
354C22×C4—2441no—
355C22×C4C2×C22⋊D6111yescharacteristic
356C22×C4C2×C22⋊D6111yescharacteristic
357C22×C4C2×C22⋊D6111yescharacteristic
358Q16—24416no—
359C2×C8—1224no—
360C2×C8—1222no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—2442no—
364C2×C8—2442no—
365C4⋊C4—28no—
366C4⋊C4—28no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—1222no—
376C4⋊C4—1222no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4C2×C22⋊D6112yes—
380C4⋊C4C2×C22⋊D6112yes—
381C22⋊C4—28no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C42—22no—
385C42—22no—
386C42C2×C22⋊D6111yescharacteristic
387C42C2×C22⋊D6111yescharacteristic
388C42C2×C22⋊D6111yescharacteristic
389C42C23×D6111yescharacteristic
390C23—22no—
391C23—24no—
392C23—42no—
393C23—42no—
394C23#1451974611yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—44no—
398Q8—42no—
399Q8—82no—
400Q8—4882no—
401Q8—2444no—
402D4—22no—
403D4—24no—
404D4C2×#1175820214yescomplemented
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—88no—
418C2×C4—4882no—
419C2×C4—2442no—
420C2×C4#1451974611yescharacteristic
421C2×C4#1451974611yescharacteristic
422C2×C4#1451974611yescharacteristic
423C2×C4C2×#1175820212yes—
424C2×C4#1451979712yes—
425C2×C4#1451980712yes—
426C2×C4#1451980812yes—
427C2×C4C22×C22⋊D6111yescharacteristic
428C2×C4C22×C22⋊D6111yescharacteristic
429C2×C4C22×C22⋊D6111yescharacteristic
430C8—1224no—
431C8—2442no—
432C8—2442no—
433C22—24no—
434C22—42no—
435C22—48no—
436C22—42no—
437C22#1683991812yes—
438C22#1683992412yes—
439C22#1683993012yes—
440C22C2×#1451974611yescharacteristic
441C4—21no—
442C4—21no—
443C4—42no—
444C4—44no—
445C4—42no—
446C4—42no—
447C4—4882no—
448C4#1683991812yes—
449C4#1683992412yes—
450C4C22×#1175820211yescharacteristic
451C4C2×#1451979711yescharacteristic
452C4C2×#1451980711yescharacteristic
453C4C2×#1451980811yescharacteristic
454C2—44no—
455C2#2144495314yesdirect product factor
456C2C2×#1683991811yescharacteristic
457C2C2×#1683992411yescharacteristic
458C2C2×#1683993011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#554C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenterC2×#554D61
hypocenterC61C2×#1632
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840141C2semidirect
2. C2×#16840057C2semidirect
4. #21444953C2direct (N × H)
5. C2×#16839511C2semidirect
6. C2×Q8⋊#92418C2semidirect
12. #16840141C22semidirect
14. #16840057C22semidirect
24. #16839511C22semidirect
25. Q8⋊#92418C22semidirect
109. C2×D4×C61Q16semidirect
172. D4×C61C2×Q16semidirect
234. C2×C61#1632semidirect
268. C61C2×#1632semidirect
342. C2×D4#11758202semidirect
404. D4C2×#11758202semidirect
455. C2#21444953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401412
C2×#168400572
C2×#168400522
#214449532
C2×#168395112
C2×Q8⋊#924182
C2×D4⋊#924182
C2×C61×#5542
C2×#163261