Finite Group Databasebeta

← C2×#21444419 #29647918

Subgroups — C2×#21444419 #29647918

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D61C211yesmaximal, characteristic
2C2×#16839817C211yesmaximal, characteristic
3C2×#16839714C211yesmaximal, characteristic
4#21444419C218yesmaximal, direct product factor
5C2×#16839504C211yesmaximal, characteristic, complemented
6C2×#16839503C211yesmaximal, characteristic, complemented
7C2×#16839503C211yesmaximal, characteristic, complemented
8C2×C61×#330C211yesmaximal, characteristic, complemented
9C22×#11758189—21no—
10C2×#14519769C2211yescharacteristic
11C2×#14519768C411yescharacteristic
12C2×#14519768C411yescharacteristic
13C2×#14519767—21no—
14C2×#14519767—21no—
15#125×D61—22no—
16#125×D61—22no—
17#125×D61C414yes—
18#125×D61C2214yes—
19C2×C4⋊C4×D61—21no—
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61C411yescharacteristic
22C2×C4⋊C4×D61C411yescharacteristic
23C2×C42×D61C2211yescharacteristic
24#16839817—22no—
25#16839817C2214yes—
26C2×#14519706—21no—
27C2×#14519689—21no—
28#16839714—22no—
29#16839714C2214yes—
30C2×#14519688C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C8×Dic61—21no—
33#16839504C2214yescomplemented
34#16839503C2214yescomplemented
35#16839503C2214yescomplemented
36C2×#125×C61C2211yescharacteristic
37C2×#97×C61C2211yescharacteristic
38C2×#97×C61C2211yescharacteristic
39C61×#330C2214yescomplemented
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×#11758189—28no—
46C2×#11758189—24no—
47C22×#92418—21no—
48C22×#92418—21no—
49#14519769—21no—
50#14519769—21no—
51#14519769C2×C412yes—
52#14519769C2312yes—
53#14519768—22no—
54#14519768—22no—
55#14519768C2×C414yes—
56#14519768C2×C414yes—
57#14519767—24no—
58#14519767—24no—
59#14519767—24no—
60#14519767—24no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758196—21no—
70C2×#11758196—21no—
71C4⋊C4×D61—24no—
72C4⋊C4×D61—24no—
73C4⋊C4×D61—22no—
74C4⋊C4×D61—22no—
75C4⋊C4×D61—24no—
76C4⋊C4×D61—24no—
77C4⋊C4×D61C2×C414yes—
78C4⋊C4×D61C2×C414yes—
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D411yescharacteristic
82C42×D61C2×C412yes—
83C42×D61D412yes—
84C42×D61D412yes—
85C42×D61C2312yes—
86#14519706—24no—
87#14519689—24no—
88#14519688—21no—
89#14519688—21no—
90#14519688C2312yes—
91#14519688C2312yes—
92C8×Dic61—24no—
93C22×C8×C61—21no—
94C22×C8×C61—21no—
95#125×C61—21no—
96#125×C61—21no—
97#125×C61C2×C412yes—
98#125×C61C2312yes—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C4⋊C4×C61C2×C411yescharacteristic
103C2×C42×C61C2311yescharacteristic
104#97×C61—21no—
105#97×C61—21no—
106#97×C61C2312yes—
107#97×C61C2312yes—
108C23×D61C22⋊C411yescharacteristic
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C22⋊C411yescharacteristic
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—24no—
122C2×C4×D61—24no—
123C2×C4×D61—42no—
124C2×C4×D61—44no—
125C2×C4×D61—44no—
126C2×C4×D61C22⋊C412yes—
127C2×C4×D61C22⋊C412yes—
128C2×C4×D61C22⋊C412yes—
129C2×C4×D61C22×C412yes—
130C2×C4×D61C2×D412yes—
131C2×C4×D61C2×D412yes—
132C2×C8×C61—24no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—42no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—22no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61C22×C412yes—
143C4⋊C4×C61C22×C412yes—
144C42×C61C22×C411yescharacteristic
145C42×C61C2×D411yescharacteristic
146C42×C61C2×D411yescharacteristic
147C42×C61C2411yescharacteristic
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—24no—
151C4⋊Dic61—24no—
152C4⋊Dic61C22×C412yes—
153C4⋊Dic61C22×C412yes—
154#11758196—22no—
155#11758196—22no—
156#11758196—22no—
157#11758196—22no—
158#11758196—24no—
159#11758196—24no—
160#11758196—24no—
161#11758196—24no—
162C4×Dic61C22⋊C412yes—
163C4×Dic61C22⋊C412yes—
164C4×Dic61C22⋊C412yes—
165C4×Dic61C22×C412yes—
166C4×Dic61C2×D412yes—
167C4×Dic61C2×D412yes—
168C2×#92418—24no—
169C2×#92418—22no—
170C2×#92418—22no—
171C2×#92418—42no—
172#11758189—216no—
173C23×C61C2×C22⋊C411yescharacteristic
174C22×D61—22no—
175C22×D61—22no—
176C22×D61#10414yes—
177C22×D61C2×C22⋊C412yes—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61C2×C22⋊C411yescharacteristic
188C2×C4×C61C23×C411yescharacteristic
189C2×C4×C61C22×D411yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—22no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61#10114yes—
198C2×Dic61C2×C22⋊C412yes—
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C2×C22⋊C412yes—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—24no—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—48no—
208C4×D61—48no—
209C8×C61—24no—
210C8×C61—42no—
211#92418—24no—
212#92418—42no—
213C2×#1528—611nomaximal, Sylow
214C22×C61C2×#10112yes—
215C22×C61C2×#10412yes—
216C22×C61#42112yes—
217C22×C61C22×C22⋊C411yescharacteristic
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—28no—
221C2×D61C2×#10414yes—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—42no—
229C4×C61—42no—
230Dic61—22no—
231Dic61—22no—
232Dic61—42no—
233Dic61—42no—
234Dic61C2×#10114yes—
235C22×#125—611no—
236C2×#432—611no—
237C2×C4×M16—611no—
238#1528—618no—
239C2×#330—611no—
240C2×#330—611no—
241C2×#330—611no—
242C2×#330D6111yescharacteristic, complemented
243C2×C61#152814yescomplemented
244C2×C61C22×#10111yescharacteristic
245C2×C61C22×#10411yescharacteristic
246C2×C61C2×#42111yescharacteristic
247D61—24no—
248C22×M16—1221no—
249C2×#125—614no—
250C2×#125—614no—
251C2×#125—611no—
252C2×#125—611no—
253C2×#125—611no—
254C2×#125—1221no—
255C2×#125—1221no—
256C2×#125—1222no—
257C2×#125—1222no—
258C2×#125C2×D6111yescharacteristic
259C22×C4⋊C4—611no—
260C22×C4⋊C4—611no—
261C22×C4⋊C4—1221no—
262C22×C4⋊C4—1221no—
263C22×C42—611no—
264#432—614no—
265#432—1222no—
266C2×C4⋊C8—1221no—
267C2×C22⋊C8—1221no—
268C4×M16—614no—
269C4×M16—1222no—
270C2×#97—611no—
271C2×#97—611no—
272C2×#97C2×D6111yescharacteristic
273C2×#97C2×D6111yescharacteristic
274C2×C4×C8—1221no—
275#330—614no—
276#330—614no—
277#330—614no—
278#330C2×D6114yescomplemented
279C61C2×#152811yescharacteristic, complemented, Sylow
280C23×C4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C23×C4—1221no—
284C23×C4—1221no—
285C2×M16—1224no—
286C2×M16—1228no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—1221no—
290C22×C8—1221no—
291#125—21no—
292#125—21no—
293#125—614no—
294#125—614no—
295#125—612no—
296#125—612no—
297#125—1224no—
298#125—1224no—
299#125—1224no—
300#125—1224no—
301#125—1222no—
302#125—1222no—
303#125—1221no—
304#125—1221no—
305#125C4×D6112yes—
306#125C22×D6112yes—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—614no—
312C2×C4⋊C4—614no—
313C2×C4⋊C4—1222no—
314C2×C4⋊C4—1222no—
315C2×C4⋊C4—1224no—
316C2×C4⋊C4—1224no—
317C2×C4⋊C4—1224no—
318C2×C4⋊C4—1224no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4—1221no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4C4×D6111yescharacteristic
328C2×C4⋊C4C4×D6111yescharacteristic
329C2×C42—611no—
330C2×C42—611no—
331C2×C42—611no—
332C2×C42—612no—
333C2×C42—612no—
334C2×C42—612no—
335C2×C42—612no—
336C2×C42C22×D6111yescharacteristic
337C4⋊C8—1224no—
338C22⋊C8—1224no—
339#97—21no—
340#97—21no—
341#97—612no—
342#97—612no—
343#97—1221no—
344#97—1221no—
345#97C22×D6112yes—
346#97C22×D6112yes—
347C4×C8—1224no—
348C24—611no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—1224no—
361C22×C4—1224no—
362C22×C4—1224no—
363C22×C4—1224no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—2442no—
367C22×C4—2444no—
368C22×C4—2444no—
369C22×C4C2×C4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372M16—12216no—
373C2×C8—24no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C2×C8—1224no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—2442no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—612no—
388C4⋊C4—612no—
389C4⋊C4—1224no—
390C4⋊C4—1224no—
391C4⋊C4—1224no—
392C4⋊C4—1224no—
393C4⋊C4—1224no—
394C4⋊C4—1224no—
395C4⋊C4—1222no—
396C4⋊C4—1222no—
397C4⋊C4—1221no—
398C4⋊C4—1221no—
399C4⋊C4—1222no—
400C4⋊C4—1222no—
401C4⋊C4C2×C4×D6112yes—
402C4⋊C4C2×C4×D6112yes—
403C42—612no—
404C42—612no—
405C42—612no—
406C42—612no—
407C42—612no—
408C42—612no—
409C42C2×C4×D6111yescharacteristic
410C42D4×D6111yescharacteristic
411C42D4×D6111yescharacteristic
412C42C23×D6111yescharacteristic
413C23—612no—
414C23—614no—
415C23—1222no—
416C23—1222no—
417C23C22⋊C4×D6111yescharacteristic
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—612no—
426C2×C4—614no—
427C2×C4—612no—
428C2×C4—612no—
429C2×C4—1224no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—2442no—
438C2×C4—2442no—
439C2×C4—2448no—
440C2×C4—2448no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4C22⋊C4×D6111yescharacteristic
444C2×C4C22⋊C4×D6111yescharacteristic
445C2×C4C22⋊C4×D6111yescharacteristic
446C2×C4C22×C4×D6111yescharacteristic
447C2×C4C2×D4×D6111yescharacteristic
448C2×C4C2×D4×D6111yescharacteristic
449C8—24no—
450C8—42no—
451C8—1224no—
452C8—2442no—
453C22—614no—
454C22—1222no—
455C22—1228no—
456C22—1222no—
457C22#101×D6112yes—
458C22#104×D6112yes—
459C22#1683977712yes—
460C22C2×C22⋊C4×D6111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—614no—
470C4—1222no—
471C4—1222no—
472C4—2442no—
473C4—2442no—
474C2—1224no—
475C2#2144441914yesdirect product factor
476C2C2×#101×D6111yescharacteristic
477C2C2×#104×D6111yescharacteristic
478C2C2×#1683977711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC2×C61×#330C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenterC2×#330D61
hypocenterC61C2×#1528
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. #21444419C2direct (N × H)
5. C2×#16839504C2semidirect
6. C2×#16839503C2semidirect
7. C2×#16839503C2semidirect
8. C2×C61×#330C2semidirect
33. #16839504C22semidirect
34. #16839503C22semidirect
35. #16839503C22semidirect
39. C61×#330C22semidirect
242. C2×#330D61semidirect
243. C2×C61#1528semidirect
278. #330C2×D61semidirect
279. C61C2×#1528semidirect
475. C2#21444419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D612
C2×#168398172
C2×#168397142
#214444192
C2×#168395042
C2×#168395032
C2×C61×#3302
C2×#152861