Finite Group Databasebeta

← C2×#21444150 #29645856

Subgroups — C2×#21444150 #29645856

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519733C211yesmaximal, characteristic
2C2×#16839816C212yesmaximal, complemented
3#21444150C218yesmaximal, direct product factor
4C2×#16839487C212yesmaximal, complemented
5C2×#16839486C211yesmaximal, characteristic
6C2×C61×#323C211yesmaximal, characteristic
7C24×Dic61C411yescharacteristic
8C2×#14519733—22no—
9C2×#14519733—22no—
10C2×#14519733—24no—
11C2×#14519733C414yes—
12C2×#14519733C2214yes—
13C22×#11758196C411yescharacteristic
14C22×#11758196C2211yescharacteristic
15C22×C22⋊Dic61C411yescharacteristic
16C22×C4×Dic61C411yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839816—24no—
19#16839816C2218yescomplemented
20C2×#14519706—22no—
21C2×C22⋊#92418C2212yes—
22C2×#14519687—22no—
23#16839487C2218yescomplemented
24#16839486C2214yes—
25C22×C22⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2212yes—
27C61×#323C2214yes—
28C23×Dic61—24no—
29C23×Dic61—22no—
30C23×Dic61—21no—
31C23×Dic61—21no—
32C23×Dic61—24no—
33C23×Dic61C2×C414yes—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C22×#92418—22no—
39#14519733—28no—
40#14519733—28no—
41#14519733—28no—
42#14519733—28no—
43C2×#11758196—22no—
44C2×#11758196—22no—
45C2×#11758196—22no—
46C2×#11758196—22no—
47C2×#11758196C2×C414yes—
48C2×#11758196C2×C412yes—
49C2×#11758196C2312yes—
50C2×C22⋊Dic61—22no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61C2×C414yes—
53C2×C4×Dic61—22no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61—21no—
56C2×C4×Dic61C2×C414yes—
57C2×C4×Dic61C2×C412yes—
58C2×C4×Dic61D412yes—
59C2×C4×Dic61D412yes—
60C2×C4×Dic61D414yes—
61C2×C4×Dic61C2312yes—
62#14519706—28no—
63C22⋊#92418—22no—
64C22⋊#92418C2314yes—
65#14519687—28no—
66C25×C61C2×C411yescharacteristic
67C23×C4×C61C2×C411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61C2×C412yes—
73C2×C22⋊C4×C61C2312yes—
74C22⋊C8×C61—22no—
75C22⋊C8×C61C2314yes—
76C24×C61—21no—
77C24×C61—21no—
78C24×C61—22no—
79C24×C61—42no—
80C24×C61—42no—
81C24×C61M1614yes—
82C24×C61C22×C411yescharacteristic
83C24×C61C22×C412yes—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61C22×C412yes—
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2×D412yes—
92C22×C4×C61C2411yescharacteristic
93C22×Dic61—216no—
94C22×Dic61—28no—
95C22×Dic61—28no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—28no—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—24no—
103C22×Dic61—24no—
104C22×Dic61—28no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C22×Dic61C22⋊C412yes—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C412yes—
113C22×Dic61C22⋊C412yes—
114C22×Dic61M1614yes—
115C22×Dic61C22×C412yes—
116C22×Dic61C22×C412yes—
117C22×Dic61C22×C412yes—
118C22×Dic61C22×C412yes—
119C2×C8×C61—24no—
120C2×C8×C61—44no—
121C22⋊C4×C61—24no—
122C22⋊C4×C61—24no—
123C22⋊Dic61—28no—
124#11758196—24no—
125#11758196—24no—
126#11758196—28no—
127C4×Dic61—24no—
128C4×Dic61—24no—
129C4×Dic61C22⋊C414yes—
130C4×Dic61C22⋊C414yes—
131C4×Dic61C2×D414yes—
132C4×Dic61C2×D414yes—
133C2×#92418—24no—
134C2×#92418—44no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61—22no—
138C23×C61—22no—
139C23×C61—24no—
140C23×C61—24no—
141C23×C61—42no—
142C23×C61—42no—
143C23×C61—48no—
144C23×C61—48no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61C2×C22⋊C411yescharacteristic
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61C2×M1612yes—
152C23×C61C2×M1612yes—
153C23×C61C2×M1614yes—
154C23×C61C23×C411yescharacteristic
155C2×C4×C61—24no—
156C2×C4×C61—22no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61C2×C22⋊C412yes—
164C2×C4×C61C22×D412yes—
165C2×Dic61—216no—
166C2×Dic61—216no—
167C2×Dic61—22no—
168C2×Dic61—22no—
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—24no—
172C2×Dic61—22no—
173C2×Dic61—22no—
174C2×Dic61—24no—
175C2×Dic61—24no—
176C2×Dic61—24no—
177C2×Dic61—22no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61C2×C22⋊C412yes—
184C2×Dic61C2×C22⋊C412yes—
185C2×Dic61C2×C22⋊C414yes—
186C2×Dic61C2×M1614yes—
187C8×C61—44no—
188#92418—44no—
189C2×#1464—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—24no—
195C22×C61—24no—
196C22×C61—24no—
197C22×C61—44no—
198C22×C61—44no—
199C22×C61—48no—
200C22×C61—42no—
201C22×C61—42no—
202C22×C61—48no—
203C22×C61#40712yes—
204C22×C61#40712yes—
205C22×C61#41012yes—
206C22×C61#41312yes—
207C22×C61C22×C22⋊C411yescharacteristic
208C22×C61C22×M1611yescharacteristic
209C22×C61C22×M1611yescharacteristic
210C4×C61—22no—
211C4×C61—22no—
212C4×C61—42no—
213Dic61—22no—
214Dic61—22no—
215Dic61—24no—
216Dic61—24no—
217Dic61—42no—
218C22×#117—611no—
219C2×#432—612no—
220#1464—618no—
221C2×#324—612no—
222C2×#323—611no—
223C2×#323D6111yescharacteristic
224C2×C61—21no—
225C2×C61—21no—
226C2×C61—22no—
227C2×C61—44no—
228C2×C61#146414yescomplemented
229C2×C61C2×#40711yescharacteristic
230C2×C61C2×#41011yescharacteristic
231C2×C61C2×#41311yescharacteristic
232C24×C4—611no—
233C2×#117—614no—
234C2×#117—614no—
235C2×#117—1222no—
236C2×#117—1222no—
237C2×#117—1224no—
238C22×C4⋊C4—611no—
239C22×C4⋊C4—611no—
240C22×C22⋊C4—611no—
241C22×C22⋊C4C2×D6111yescharacteristic
242C22×C42—611no—
243C22×C42—611no—
244#432—618no—
245#432—1224no—
246C2×C4⋊C8—1222no—
247C2×C22⋊C8—612no—
248C2×C22⋊C8C2×D6112yes—
249C2×#97—1222no—
250#324—618no—
251#323—614no—
252#323C2×D6114yes—
253C61C2×#146411yescharacteristic, complemented, Sylow
254C25C4×D6111yescharacteristic
255C23×C4—611no—
256C23×C4—611no—
257C23×C4—611no—
258C23×C4—614no—
259C23×C4—611no—
260C23×C4—1222no—
261C23×C4—1221no—
262C23×C4—1221no—
263C23×C4—1224no—
264C23×C4—1224no—
265C23×C4C4×D6111yescharacteristic
266C23×C4C22×D6111yescharacteristic
267C22×C8—22no—
268C22×C8—1222no—
269#117—1228no—
270#117—1228no—
271#117—1228no—
272#117—1228no—
273C2×C4⋊C4—614no—
274C2×C4⋊C4—612no—
275C2×C4⋊C4—612no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4—1222no—
278C2×C4⋊C4—1222no—
279C2×C4⋊C4—1222no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—614no—
283C2×C22⋊C4—1222no—
284C2×C22⋊C4—1222no—
285C2×C22⋊C4C4×D6112yes—
286C2×C22⋊C4C22×D6112yes—
287C2×C42—612no—
288C2×C42—612no—
289C2×C42—612no—
290C2×C42—614no—
291C2×C42—612no—
292C2×C42—614no—
293C2×C42—1222no—
294C2×C42—1221no—
295C2×C42—1221no—
296C4⋊C8—1228no—
297C22⋊C8—22no—
298C22⋊C8—614no—
299C22⋊C8—1222no—
300C22⋊C8C22×D6114yes—
301#97—1228no—
302C24—21no—
303C24—21no—
304C24—22no—
305C24—42no—
306C24—42no—
307C24#1175818914yes—
308C24C2×C4×D6111yescharacteristic
309C24C2×C4×D6112yes—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—612no—
315C22×C4—612no—
316C22×C4—612no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—612no—
320C22×C4—614no—
321C22×C4—612no—
322C22×C4—612no—
323C22×C4—612no—
324C22×C4—1224no—
325C22×C4—1224no—
326C22×C4—1228no—
327C22×C4—12216no—
328C22×C4—1228no—
329C22×C4—1228no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1222no—
333C22×C4—1228no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—2442no—
339C22×C4—2442no—
340C22×C4C2×C4×D6112yes—
341C22×C4C2×C4×D6111yescharacteristic
342C22×C4D4×D6112yes—
343C22×C4D4×D6112yes—
344C22×C4C23×D6111yescharacteristic
345C2×C8—24no—
346C2×C8—44no—
347C2×C8—1224no—
348C2×C8—2444no—
349C4⋊C4—1228no—
350C4⋊C4—1224no—
351C4⋊C4—1224no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—1228no—
355C42—614no—
356C42—614no—
357C42—614no—
358C42—614no—
359C42—1224no—
360C42—1224no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—24no—
366C23—22no—
367C23—48no—
368C23—42no—
369C23—42no—
370C23—48no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23C22⋊C4×D6111yescharacteristic
376C23C22⋊C4×D6111yescharacteristic
377C23M16×D6112yes—
378C23C2×#1175818912yes—
379C23C2×#1175818914yes—
380C23C22×C4×D6111yescharacteristic
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—614no—
392C2×C4—614no—
393C2×C4—12216no—
394C2×C4—12216no—
395C2×C4—1222no—
396C2×C4—1224no—
397C2×C4—1224no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—1224no—
401C2×C4—1224no—
402C2×C4—1222no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4C22⋊C4×D6112yes—
412C2×C4C2×D4×D6112yes—
413C8—44no—
414C8—2444no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—24no—
422C22—44no—
423C22—48no—
424C22—44no—
425C22—48no—
426C22—42no—
427C22—42no—
428C22#1683972412yes—
429C22#1683972412yes—
430C22#1683973412yes—
431C22#1683974312yes—
432C22C2×C22⋊C4×D6111yescharacteristic
433C22C2×M16×D6111yescharacteristic
434C22C22×#1175818911yescharacteristic
435C4—22no—
436C4—22no—
437C4—42no—
438C4—1222no—
439C4—1222no—
440C4—1224no—
441C4—1224no—
442C4—2442no—
443C2—22no—
444C2—21no—
445C2—21no—
446C2—44no—
447C2#2144415014yesdirect product factor
448C2C2×#1683972411yescharacteristic
449C2C2×#1683973411yescharacteristic
450C2C2×#1683974311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC22×C4×C61C24
hypercenterC2×#323D61
hypocenterC61C2×#1464
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#16839816C2semidirect
3. #21444150C2direct (N × H)
4. C2×#16839487C2semidirect
19. #16839816C22semidirect
23. #16839487C22semidirect
228. C2×C61#1464semidirect
253. C61C2×#1464semidirect
447. C2#21444150direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197332
C2×#168398162
#214441502
C2×#168394872
C2×#168394862
C2×C61×#3232
C2×#146461