Finite Group Databasebeta

← C2×#21444951 #29655636

Subgroups — C2×#21444951 #29655636

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×#16840469C211yesmaximal, characteristic
2C2×#16840141C211yesmaximal, characteristic, complemented
3C2×#16840054C211yesmaximal, characteristic, complemented
4#21444951C218yesmaximal, direct product factor
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×#16839492C211yesmaximal, characteristic, complemented
7C2×D4⋊#92418C211yesmaximal, characteristic
8C2×C61×#476C211yesmaximal, characteristic
9C22×#11758202—22no—
10#16840469—22no—
11#16840469—22no—
12#16840469—22no—
13#16840469C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519768—21no—
16C2×#14519756—21no—
17C2×#14519754—22no—
18C2×C4×Dic122C2211yescharacteristic
19C2×D4×Dic61—21no—
20C22×C4⋊Dic61—21no—
21#16840141—22no—
22#16840141C2214yescomplemented
23#16840054—22no—
24#16840054C2214yescomplemented
25C2×#14519710—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519700—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839510C2214yescomplemented
30#16839492C2214yescomplemented
31D4⋊#92418C2214yes—
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C61×#476—22no—
35C61×#476C2214yes—
36C2×#106×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C22×Dic122D411yescharacteristic
40C22×Dic122D412yes—
41C23×Dic61—22no—
42C2×#11758202—28no—
43C2×#11758202—48no—
44C22×#92418—21no—
45C22×#92418—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777D412yes—
49#14519777C2312yes—
50#14519768—24no—
51#14519768—24no—
52#14519756—24no—
53#14519756—24no—
54#14519754—28no—
55#14519754—28no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122D412yes—
59C4×Dic122C2312yes—
60D4×Dic61—24no—
61D4×Dic61—24no—
62C2×C4⋊Dic61—24no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×#11758196—22no—
69C2×#11758196—21no—
70C2×C22⋊Dic61—22no—
71C2×C4×Dic61—21no—
72#14519710—24no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75#14519700—24no—
76C4×#92418—21no—
77C4×#92418C2312yes—
78C22×Q8×C61—21no—
79C22×D4×C61D411yescharacteristic
80C23×C4×C61—21no—
81C22×C8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61D412yes—
89C4×D4×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C22⋊C4×C61—21no—
94C2×C42×C61C2311yescharacteristic
95#106×C61—24no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#102×C61—24no—
99C24×C61—21no—
100C2×Q8×C61—22no—
101C2×Q8×C61—44no—
102C2×Q8×C61—41no—
103C2×D4×C61—21no—
104C2×D4×C61—22no—
105C2×D4×C61Q1614yescomplemented
106C2×D4×C61C2×D412yes—
107C22×C4×C61—21no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61—41no—
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×Dic61—21no—
117C22×Dic61—22no—
118C22×Dic61—21no—
119C22×Dic61—28no—
120C22×Dic61—84no—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—21no—
124C2×Dic122—22no—
125C2×Dic122—44no—
126C2×Dic122C2×D412yes—
127C2×Dic122C2×D414yes—
128C2×C8×C61—22no—
129C2×C8×C61—42no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61C2×D412yes—
136C22⋊C4×C61—22no—
137C22⋊C4×C61—22no—
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61C2411yescharacteristic
142C22⋊Dic61—28no—
143#11758202—416no—
144C4⋊Dic61—28no—
145C4⋊Dic61—21no—
146C4⋊Dic61—22no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61—22no—
150C4⋊Dic61C2×D412yes—
151#11758196—28no—
152#11758196—22no—
153#11758196—22no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C2×#92418—24no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—42no—
160C23×C61—22no—
161C23×C61—24no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61#12011yescharacteristic
165Q8×C61—44no—
166Q8×C61—82no—
167D4×C61—22no—
168D4×C61—24no—
169D4×C61C2×Q1614yescomplemented
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—44no—
176C2×C4×C61—42no—
177C2×C4×C61—82no—
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61C2×Q1612yes—
182C2×C4×C61#13512yes—
183C2×C4×C61#13712yes—
184C2×C4×C61#13712yes—
185C2×C4×C61C22×D411yescharacteristic
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—24no—
191C2×Dic61—42no—
192C2×Dic61—44no—
193C2×Dic61—42no—
194C2×Dic61—88no—
195Dic122—22no—
196Dic122—22no—
197Dic122—42no—
198Dic122—44no—
199Dic122—82no—
200C8×C61—42no—
201#92418—24no—
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—82no—
216C4×C61#45112yes—
217C4×C61#45212yes—
218C4×C61C22×Q1611yescharacteristic
219C4×C61C2×#13511yescharacteristic
220C4×C61C2×#13711yescharacteristic
221C4×C61C2×#13711yescharacteristic
222Dic61—42no—
223Dic61—44no—
224Dic61—42no—
225C2×#554—611no—
226C2×#494—611no—
227C2×#477—611no—
228C2×#476D6111yescharacteristic
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—614no—
240#554—1222no—
241#554—1222no—
242#554—1222no—
243C2×C4⋊Q8—611no—
244C2×C4⋊Q8C2×D6111yescharacteristic
245C2×#125—1221no—
246C2×C22⋊Q8—1222no—
247C2×C22⋊Q8—1221no—
248C2×C4×Q8—611no—
249C2×C4×D4—1221no—
250C2×C4×D4C2×D6111yescharacteristic
251C22×C4⋊C4—1221no—
252#494—614no—
253#494—1222no—
254#477—614no—
255#477—1222no—
256#476—22no—
257#476C2×D6114yes—
258C2×#107—1221no—
259C2×#106—21no—
260C2×C4⋊C8—611no—
261C2×C4⋊C8C2×D6111yescharacteristic
262C2×#103—1221no—
263C2×#102—21no—
264C2×C4×C8—611no—
265#333—614no—
266Q8⋊C8—614no—
267D4⋊C8—614no—
268C61C2×#163211yescharacteristic, complemented, Sylow
269C22×Q8—21no—
270C22×Q8—611no—
271C22×Q8—612no—
272C22×D4C22⋊D6111yescharacteristic
273C23×C4—21no—
274C23×C4—1222no—
275C2×Q16—1228no—
276C2×Q16—2448no—
277C22×C8—21no—
278C22×C8—1221no—
279C22×C8—1221no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—612no—
284C4⋊Q8—612no—
285C4⋊Q8—1221no—
286C4⋊Q8—1221no—
287C4⋊Q8C22×D6112yes—
288#125—1224no—
289#125—1224no—
290C22⋊Q8—1228no—
291C22⋊Q8—1228no—
292C22⋊Q8—1224no—
293C22⋊Q8—1224no—
294C4×Q8—612no—
295C4×Q8—612no—
296C4×Q8—1221no—
297C4×Q8—1221no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—1224no—
301C4×D4—1224no—
302C4×D4C22⋊D6112yes—
303C4×D4C22×D6112yes—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—1224no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1224no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4C22⋊D6111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—1222no—
317C2×C42—1221no—
318C2×C42C22×D6111yescharacteristic
319#107—1224no—
320#106—24no—
321C4⋊C8—21no—
322C4⋊C8—612no—
323C4⋊C8—1221no—
324C4⋊C8C22×D6112yes—
325#103—1224no—
326#102—24no—
327C4×C8—612no—
328C4×C8—1221no—
329C24—21no—
330C2×Q8—22no—
331C2×Q8—44no—
332C2×Q8—41no—
333C2×Q8—612no—
334C2×Q8—614no—
335C2×Q8—1222no—
336C2×Q8—1221no—
337C2×Q8—1222no—
338C2×Q8—1222no—
339C2×Q8—2444no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4#1175820214yescomplemented
343C2×D4C2×C22⋊D6112yes—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—1228no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1222no—
354C22×C4—4884no—
355C22×C4D4×D6111yescharacteristic
356C22×C4D4×D6111yescharacteristic
357C22×C4C2×C22⋊D6111yescharacteristic
358Q16—24416no—
359C2×C8—22no—
360C2×C8—42no—
361C2×C8—1224no—
362C2×C8—1222no—
363C2×C8—1222no—
364C2×C8—2442no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—612no—
371C4⋊C4—1228no—
372C4⋊C4—1228no—
373C4⋊C4—1222no—
374C4⋊C4—1222no—
375C4⋊C4—1222no—
376C4⋊C4—1221no—
377C4⋊C4—1222no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4C2×C22⋊D6112yes—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—1228no—
384C42—1222no—
385C42—1222no—
386C42D4×D6111yescharacteristic
387C42D4×D6111yescharacteristic
388C42C2×C22⋊D6111yescharacteristic
389C42C23×D6111yescharacteristic
390C23—22no—
391C23—24no—
392C23—42no—
393C23—42no—
394C23#1451974511yescharacteristic
395Q8—44no—
396Q8—82no—
397Q8—1222no—
398Q8—1222no—
399Q8—4882no—
400Q8—2444no—
401Q8—2442no—
402D4—22no—
403D4—24no—
404D4C2×#1175820214yescomplemented
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—82no—
413C2×C4—1222no—
414C2×C4—1222no—
415C2×C4—1224no—
416C2×C4—4888no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2444no—
420C2×C4#1451974511yescharacteristic
421C2×C4#1451974511yescharacteristic
422C2×C4#1451974511yescharacteristic
423C2×C4C2×#1175820212yes—
424C2×C4#1451979812yes—
425C2×C4#1451980612yes—
426C2×C4#1451980712yes—
427C2×C4C2×D4×D6111yescharacteristic
428C2×C4C2×D4×D6111yescharacteristic
429C2×C4C22×C22⋊D6111yescharacteristic
430C8—42no—
431C8—1224no—
432C8—2442no—
433C22—24no—
434C22—42no—
435C22—48no—
436C22—42no—
437C22#1683991712yes—
438C22#1683992112yes—
439C22#1683992812yes—
440C22C2×#1451974511yescharacteristic
441C4—21no—
442C4—21no—
443C4—42no—
444C4—82no—
445C4—2442no—
446C4—2444no—
447C4—2442no—
448C4#1683991712yes—
449C4#1683992112yes—
450C4C22×#1175820211yescharacteristic
451C4C2×#1451979811yescharacteristic
452C4C2×#1451980611yescharacteristic
453C4C2×#1451980711yescharacteristic
454C2—44no—
455C2#2144495114yesdirect product factor
456C2C2×#1683991711yescharacteristic
457C2C2×#1683992111yescharacteristic
458C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#476C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenterC2×#476D61
hypocenterC61C2×#1632
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#16840141C2semidirect
3. C2×#16840054C2semidirect
4. #21444951C2direct (N × H)
5. C2×#16839510C2semidirect
6. C2×#16839492C2semidirect
22. #16840141C22semidirect
24. #16840054C22semidirect
29. #16839510C22semidirect
30. #16839492C22semidirect
105. C2×D4×C61Q16semidirect
169. D4×C61C2×Q16semidirect
234. C2×C61#1632semidirect
268. C61C2×#1632semidirect
342. C2×D4#11758202semidirect
404. D4C2×#11758202semidirect
455. C2#21444951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404692
C2×#168401412
C2×#168400542
#214449512
C2×#168395102
C2×#168394922
C2×D4⋊#924182
C2×C61×#4762
C2×#163261