Finite Group Databasebeta

← C2×#21447492 #29832804

Subgroups — C2×#21447492 #29832804

Order 15616.

1230 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×#16840332C211yesmaximal, characteristic
2C2×#16839734C212yesmaximal
3#21447492C218yesmaximal, direct product factor
4C2×#16839557C211yesmaximal, characteristic, complemented
5C2×#16839556C212yesmaximal, complemented
6C2×C61×#354C211yesmaximal, characteristic, complemented
7C22×#11758224C2211yescharacteristic
8C22×Q8×D61C411yescharacteristic, complemented
9#16840332—24no—
10#16840332C414yescomplemented
11#16840332C2214yes—
12C2×#14519777C411yescharacteristic, complemented
13C2×#14519775C411yescharacteristic, complemented
14C2×#14519764C2211yescharacteristic
15C2×#14519759—22no—
16C2×#14519754—22no—
17C2×#14519734C411yescharacteristic, complemented
18C2×#14519733—22no—
19#16839734—24no—
20#16839734C2218yes—
21C2×#14519692C2212yes—
22C2×#14519691—22no—
23#16839557C2214yescomplemented
24#16839556C2218yescomplemented
25C2×#124×C61C2211yescharacteristic
26C2×#99×C61C2212yes—
27C61×#354C2214yescomplemented
28C2×#11758224—42no—
29C2×#11758224—42no—
30C2×#11758224C2×C412yes—
31C2×#11758224D414yes—
32C2×#11758224C2312yes—
33C22×Dic122—21no—
34C22×Dic122C2×C411yescharacteristic
35C22×Dic122C2×C411yescharacteristic
36C2×Q8×D61—22no—
37C2×Q8×D61—42no—
38C2×Q8×D61—42no—
39C2×Q8×D61C2×C414yescomplemented
40C22×C22⋊D61D412yes—
41C23×Dic61D412yes—
42C22×C4×D61—21no—
43C22×C4×D61C2×C411yescharacteristic
44#14519777—22no—
45#14519777C2×C414yescomplemented
46#14519775—22no—
47#14519775C2×C414yescomplemented
48#14519764—22no—
49#14519764C2×C412yes—
50#14519764C2312yes—
51#14519759—28no—
52#14519759—28no—
53#14519754—28no—
54#14519754—28no—
55#14519734—22no—
56#14519734C2×C414yescomplemented
57#14519733—28no—
58#14519733—44no—
59C2×C4⋊Dic61—22no—
60C2×#11758196—21no—
61C2×#11758196—22no—
62C2×#11758196—42no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×#11758198—21no—
66C2×C4×Dic61—42no—
67C2×C4×Dic61C2×C411yescharacteristic
68#14519692—22no—
69#14519692C2314yes—
70#14519691—28no—
71C22×Q8×C61C2×C411yescharacteristic
72C22×D4×C61C2311yescharacteristic
73#124×C61—22no—
74#124×C61C2×C412yes—
75#124×C61C2312yes—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—22no—
78C2×C42×C61C2×C411yescharacteristic
79#99×C61—22no—
80#99×C61C2314yes—
81C24×C61C2×D412yes—
82C23×D61C22⋊C411yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C2×Q8×C61C22×C412yes—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61C22×C411yescharacteristic
90C2×D4×C61C2×D412yes—
91C2×D4×C61C2411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C22×C411yescharacteristic
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C2×C22⋊D61C22⋊C414yes—
99C2×C22⋊D61C2×D414yes—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—24no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—42no—
106C22×Dic61C22⋊C412yes—
107C22×Dic61C22⋊C414yes—
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C2×D414yes—
110Q8×D61—48no—
111Q8×D61—48no—
112#11758224—44no—
113#11758224—44no—
114#11758224—44no—
115#11758224—44no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—24no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61C22⋊C412yes—
122C2×C4×D61C22×C412yes—
123C2×Dic122—21no—
124C2×Dic122—24no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122—42no—
128C2×Dic122—42no—
129C2×Dic122—41no—
130C2×Dic122—41no—
131C2×Dic122C22⋊C412yes—
132C2×Dic122C22×C412yes—
133C2×Dic122C22×C412yes—
134C22⋊C4×C61—24no—
135C22⋊C4×C61—24no—
136C22⋊C4×C61—24no—
137C22⋊C4×C61—42no—
138C42×C61—21no—
139C42×C61C22×C412yes—
140C22⋊Dic61—24no—
141C22⋊Dic61—24no—
142C22⋊Dic61—24no—
143C22⋊Dic61—42no—
144#11758198—24no—
145C4⋊Dic61—28no—
146#11758196—24no—
147#11758196—28no—
148#11758196—48no—
149C4×Dic61—21no—
150C4×Dic61—48no—
151C4×Dic61C22×C412yes—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—44no—
155C23×C61C2×C22⋊C411yescharacteristic
156C23×C61C2×C22⋊C412yes—
157C23×C61C22×D412yes—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—42no—
161C22×D61C2×C22⋊C412yes—
162Q8×C61—42no—
163Q8×C61—42no—
164D4×C61—41no—
165D4×C61—42no—
166D4×C61—41no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—44no—
175C2×C4×C61—84no—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C23×C411yescharacteristic
178C22⋊D61—44no—
179C22⋊D61—44no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—42no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—44no—
192C2×Dic61—84no—
193C2×Dic61#9912yes—
194C2×Dic61#9912yes—
195C2×Dic61C2×C22⋊C414yes—
196C2×Dic61C2×C22⋊C412yes—
197C4×D61—24no—
198C4×D61—24no—
199C4×D61—48no—
200Dic122—42no—
201Dic122—42no—
202Dic122—42no—
203Dic122—48no—
204Dic122—42no—
205C2×#2129—611nomaximal, Sylow
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—44no—
212C22×C61—82no—
213C22×C61C2×#9911yescharacteristic
214C22×C61C2×#9911yescharacteristic
215C22×C61C22×C22⋊C411yescharacteristic
216C2×D61—22no—
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—42no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—42no—
223C4×C61—42no—
224C4×C61—84no—
225Dic61—24no—
226Dic61—42no—
227Dic61—42no—
228Dic61—84no—
229Dic61C2×#9914yes—
230C2×#536—611no—
231C2×#410—612no—
232#2129—618no—
233C2×#354—612no—
234C2×#354—611no—
235C2×#354D6111yescharacteristic, complemented
236C2×C61—21no—
237C2×C61—21no—
238C2×C61—42no—
239C2×C61—42no—
240C2×C61#212912yescomplemented
241C2×C61C22×#9911yescharacteristic
242D61—42no—
243C22×#41—611no—
244C23×Q8—611no—
245#536—614no—
246#536—614no—
247#536—1224no—
248C2×C4⋊Q8—611no—
249C2×C4⋊Q8—611no—
250C2×#124—611no—
251C2×#124C2×D6111yescharacteristic
252C2×#123—1222no—
253C2×C22⋊Q8—1222no—
254C2×#117—611no—
255C2×#117—1222no—
256#410—618no—
257#410—1224no—
258C2×#99—612no—
259C2×#99—1222no—
260C2×#99C2×D6112yes—
261#354—614no—
262#354—618no—
263#354C2×D6114yescomplemented
264C61C2×#212911yescharacteristic, complemented, Sylow
265C2×#41—612no—
266C2×#41—614no—
267C2×#41—612no—
268C2×#41—2442no—
269C2×#41—2442no—
270C22×Q8—611no—
271C22×Q8—614no—
272C22×Q8—611no—
273C22×Q8—1221no—
274C22×Q8—1222no—
275C22×Q8—2442no—
276C22×Q8—2442no—
277C22×Q8C4×D6111yescharacteristic
278C22×D4—612no—
279C22×D4C22×D6111yescharacteristic
280C23×C4—612no—
281C23×C4—611no—
282C23×C4—1221no—
283C4⋊Q8—614no—
284C4⋊Q8—614no—
285C4⋊Q8—1222no—
286C4⋊Q8—1222no—
287#124—22no—
288#124—612no—
289#124—612no—
290#124—1222no—
291#124C4×D6112yes—
292#124C22×D6112yes—
293#123—1228no—
294#123—1228no—
295C22⋊Q8—1228no—
296C22⋊Q8—1228no—
297#117—614no—
298#117—1222no—
299#117—1228no—
300#117—2444no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1222no—
303C2×C4⋊C4—1222no—
304C2×C4⋊C4—2442no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1222no—
309C2×C22⋊C4—1222no—
310C2×C42—611no—
311C2×C42—2442no—
312C2×C42C4×D6111yescharacteristic
313#99—22no—
314#99—614no—
315#99—1228no—
316#99—1222no—
317#99C22×D6114yes—
318C24—611no—
319C24D4×D6112yes—
320#41—2444no—
321#41—2444no—
322#41—2444no—
323#41—2444no—
324C2×Q8—21no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—612no—
328C2×Q8—612no—
329C2×Q8—612no—
330C2×Q8—1224no—
331C2×Q8—1221no—
332C2×Q8—2441no—
333C2×Q8—2441no—
334C2×Q8—2441no—
335C2×Q8—2441no—
336C2×Q8—2442no—
337C2×Q8—2442no—
338C2×Q8—2448no—
339C2×Q8—2448no—
340C2×Q8C2×C4×D6112yes—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—614no—
344C2×D4—614no—
345C2×D4—2442no—
346C2×D4—2442no—
347C2×D4C2×C4×D6111yescharacteristic
348C2×D4D4×D6112yes—
349C2×D4C23×D6111yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—42no—
353C22×C4—611no—
354C22×C4—614no—
355C22×C4—614no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1224no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1224no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4C2×C4×D6111yescharacteristic
371C4⋊C4—1224no—
372C4⋊C4—1228no—
373C4⋊C4—1228no—
374C4⋊C4—2448no—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—42no—
379C22⋊C4—1224no—
380C22⋊C4—1224no—
381C22⋊C4—1224no—
382C22⋊C4—1224no—
383C22⋊C4—2442no—
384C42—21no—
385C42—612no—
386C42—1221no—
387C42—2448no—
388C42C2×C4×D6112yes—
389C23—22no—
390C23—22no—
391C23—44no—
392C23—612no—
393C23—1221no—
394C23—1221no—
395C23—2442no—
396C23C22⋊C4×D6112yes—
397C23C22⋊C4×D6111yescharacteristic
398C23C2×D4×D6112yes—
399Q8—42no—
400Q8—42no—
401Q8—2442no—
402Q8—2442no—
403Q8—2442no—
404Q8—2442no—
405Q8—2448no—
406D4—41no—
407D4—42no—
408D4—41no—
409D4—2444no—
410D4—2444no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—84no—
420C2×C4—612no—
421C2×C4—612no—
422C2×C4—612no—
423C2×C4—614no—
424C2×C4—1224no—
425C2×C4—1224no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—4884no—
435C2×C4—2448no—
436C2×C4—2444no—
437C2×C4—2442no—
438C2×C4—2441no—
439C2×C4—2441no—
440C2×C4C22⋊C4×D6111yescharacteristic
441C2×C4C22×C4×D6111yescharacteristic
442C22—22no—
443C22—22no—
444C22—22no—
445C22—42no—
446C22—42no—
447C22—44no—
448C22—82no—
449C22—1222no—
450C22—2442no—
451C22—2442no—
452C22—2442no—
453C22#99×D6111yescharacteristic
454C22#99×D6111yescharacteristic
455C22C2×C22⋊C4×D6111yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—84no—
461C4—614no—
462C4—1224no—
463C4—4884no—
464C4—2442no—
465C4—2442no—
466C2—21no—
467C2—21no—
468C2—42no—
469C2—42no—
470C2—2442no—
471C2#2144749212yesdirect product factor
472C2C2×#99×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C23×C4
FrattiniC2×D4C23×D61
FittingC2×C61×#354C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC2×D4×C61C24
hypercenterC2×#354D61
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
3. #21447492C2direct (N × H)
4. C2×#16839557C2semidirect
5. C2×#16839556C2semidirect
6. C2×C61×#354C2semidirect
8. C22×Q8×D61C4semidirect
10. #16840332C4semidirect
12. C2×#14519777C4semidirect
13. C2×#14519775C4semidirect
17. C2×#14519734C4semidirect
23. #16839557C22semidirect
24. #16839556C22semidirect
27. C61×#354C22semidirect
39. C2×Q8×D61C2×C4semidirect
45. #14519777C2×C4semidirect
47. #14519775C2×C4semidirect
56. #14519734C2×C4semidirect
235. C2×#354D61semidirect
240. C2×C61#2129semidirect
263. #354C2×D61semidirect
264. C61C2×#2129semidirect
471. C2#21447492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403322
C2×#168397342
#214474922
C2×#168395572
C2×#168395562
C2×C61×#3542
C2×#212961