Finite Group Databasebeta

← C2×#21461078 #30609959

Subgroups — C2×#21461078 #30609959

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C212yesmaximal, complemented
2#21461078C218yesmaximal, direct product factor
3C2×#16840606C212yesmaximal, complemented
4C2×#16840605C212yesmaximal, complemented
5C22×C4×C22⋊D61C211yesmaximal, characteristic
6#16840783—24no—
7#16840783C2218yescomplemented
8C2×C4⋊#92420—22no—
9C2×C22⋊#92420C2214yes—
10C2×#14519832—22no—
11#16840606C2218yescomplemented
12#16840605C2218yescomplemented
13C23×C22⋊D61C411yescharacteristic
14C23×C4×D61C411yescharacteristic
15C2×C4×C22⋊D61—22no—
16C2×C4×C22⋊D61—22no—
17C2×C4×C22⋊D61—24no—
18C2×C4×C22⋊D61C414yes—
19C2×C4×C22⋊D61C2214yes—
20C22×#11758196C411yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C24×C4×C61C411yescharacteristic
25C22×#92420—24no—
26C4⋊#92420—28no—
27C22⋊#92420—24no—
28C22⋊#92420C2318yes—
29#14519832—28no—
30C24×D61C2×C411yescharacteristic
31C22×C22⋊D61—24no—
32C22×C22⋊D61—24no—
33C22×C22⋊D61—22no—
34C22×C22⋊D61—22no—
35C22×C22⋊D61C2×C414yes—
36C23×Dic61C2×C411yescharacteristic
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2311yescharacteristic
39C22×C4×D61—22no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—44no—
43C22×C4×D61C2×C414yes—
44C4×C22⋊D61—28no—
45C4×C22⋊D61—28no—
46C4×C22⋊D61—28no—
47C4×C22⋊D61—28no—
48C2×#11758196—22no—
49C2×#11758196—22no—
50C2×#11758196C2×C414yes—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—22no—
53C2×C22⋊Dic61C2×C412yes—
54C2×C22⋊Dic61C2312yes—
55C2×#11758198—22no—
56C2×#11758198—22no—
57C2×#11758198C2×C412yes—
58C2×#11758198C2312yes—
59C2×C4×Dic61C2×C412yes—
60C2×C4×Dic61D412yes—
61C2×C4×Dic61D412yes—
62C2×C4×Dic61D414yes—
63C2×C4×Dic61C2312yes—
64C25×C61C2×C411yescharacteristic
65C23×C4×C61—22no—
66C23×C4×C61—21no—
67C23×C4×C61—21no—
68C23×C4×C61—44no—
69C23×C4×C61C2×C411yescharacteristic
70C23×C4×C61C2×C414yes—
71C23×C4×C61C2×C411yescharacteristic
72C24×C61—21no—
73C24×C61—21no—
74C24×C61—22no—
75C24×C61—42no—
76C24×C61—42no—
77C24×C61M1614yes—
78C24×C61C22×C411yescharacteristic
79C24×C61C22×C412yes—
80C23×D61—21no—
81C23×D61—21no—
82C23×D61—22no—
83C23×D61—42no—
84C23×D61—42no—
85C23×D61M1614yes—
86C23×D61C22×C412yes—
87C22×C4×C61—24no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—24no—
91C22×C4×C61—24no—
92C22×C4×C61—44no—
93C22×C4×C61—48no—
94C22×C4×C61—48no—
95C22×C4×C61—44no—
96C22×C4×C61—42no—
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C22⋊C412yes—
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C22×C412yes—
101C22×C4×C61C22×C412yes—
102C2×C22⋊D61—216no—
103C2×C22⋊D61—216no—
104C2×C22⋊D61—28no—
105C2×C22⋊D61—28no—
106C2×C22⋊D61—28no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C22×Dic61C22⋊C412yes—
114C22×Dic61C22⋊C412yes—
115C22×Dic61C22×C412yes—
116C22×Dic61C22×C412yes—
117C22×Dic61C22×C411yescharacteristic
118C22×Dic61C2×D412yes—
119C22×Dic61C2×D412yes—
120C22×Dic61C2411yescharacteristic
121C2×C4×D61—24no—
122C2×C4×D61—24no—
123C2×C4×D61—44no—
124C2×C4×D61—48no—
125C2×C4×D61—44no—
126C2×C4×D61—48no—
127C2×#92420—28no—
128C2×#92420—48no—
129C22⋊Dic61—24no—
130C22⋊Dic61—24no—
131#11758198—24no—
132#11758198—24no—
133#11758196—28no—
134C4×Dic61C22⋊C414yes—
135C4×Dic61C22⋊C414yes—
136C4×Dic61C2×D414yes—
137C4×Dic61C2×D414yes—
138C23×C61—22no—
139C23×C61—22no—
140C23×C61—22no—
141C23×C61—22no—
142C23×C61—24no—
143C23×C61—24no—
144C23×C61—42no—
145C23×C61—42no—
146C23×C61—48no—
147C23×C61—42no—
148C23×C61—48no—
149C23×C61—42no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61C2×C22⋊C411yescharacteristic
153C23×C61C2×C22⋊C411yescharacteristic
154C23×C61C2×M1612yes—
155C23×C61C2×M1612yes—
156C23×C61C2×M1614yes—
157C23×C61C23×C411yescharacteristic
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—24no—
161C22×D61—24no—
162C22×D61—42no—
163C22×D61—42no—
164C22×D61—48no—
165C22×D61—42no—
166C22×D61—42no—
167C22×D61—42no—
168C22×D61—48no—
169C22×D61—42no—
170C22×D61C2×M1614yes—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—24no—
174C2×C4×C61—22no—
175C2×C4×C61—48no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—48no—
179C2×C4×C61—42no—
180C2×C4×C61#10014yes—
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C2×C22⋊C412yes—
183C22⋊D61—232no—
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—22no—
190C2×Dic61—41no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61C2×C22⋊C412yes—
197C2×Dic61C2×C22⋊C414yes—
198C2×Dic61C22×D412yes—
199C4×D61—48no—
200C4×D61—48no—
201#92420—48no—
202C2×#1466—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—24no—
208C22×C61—24no—
209C22×C61—24no—
210C22×C61—44no—
211C22×C61—44no—
212C22×C61—48no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—48no—
216C22×C61#40712yes—
217C22×C61#40712yes—
218C22×C61#41012yes—
219C22×C61C2×#10012yes—
220C22×C61C22×C22⋊C411yescharacteristic
221C22×C61C22×M1611yescharacteristic
222C22×C61C22×M1611yescharacteristic
223C2×D61—24no—
224C2×D61—44no—
225C2×D61—48no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—48no—
229C2×D61—44no—
230C4×C61—22no—
231C4×C61—42no—
232C4×C61C2×#10014yes—
233Dic61—24no—
234Dic61—22no—
235Dic61—22no—
236Dic61—42no—
237C22×C4×D4—611no—
238C2×#432—612no—
239#1466—618no—
240C2×#323—612no—
241C2×#323—612no—
242C2×C61—21no—
243C2×C61—21no—
244C2×C61—22no—
245C2×C61—44no—
246C2×C61#146614yescomplemented
247C2×C61C2×#40711yescharacteristic
248C2×C61C2×#41011yescharacteristic
249C2×C61C22×#10011yescharacteristic
250D61—44no—
251C23×D4—611no—
252C24×C4—611no—
253C24×C4#692311yescharacteristic
254C2×C4×D4—614no—
255C2×C4×D4—614no—
256C2×C4×D4—1222no—
257C2×C4×D4—1222no—
258C2×C4×D4—1224no—
259C22×C4⋊C4—611no—
260C22×C22⋊C4—611no—
261C22×C22⋊C4—611no—
262C22×C42—611no—
263#432—618no—
264#432—1224no—
265C2×C4⋊C8—1222no—
266C2×C22⋊C8—614no—
267C2×#97—1222no—
268#323—618no—
269#323—618no—
270C61C2×#146611yescharacteristic, complemented, Sylow
271C25—611no—
272C25C2×#692311yescharacteristic
273C22×D4—614no—
274C22×D4—1222no—
275C22×D4—1222no—
276C22×D4—1224no—
277C22×D4—1224no—
278C23×C4—22no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—44no—
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—614no—
286C23×C4—1222no—
287C23×C4—1221no—
288C23×C4—1221no—
289C23×C4—2444no—
290C23×C4C2×#692311yescharacteristic
291C23×C4C2×#692314yes—
292C23×C4C2×#692311yescharacteristic
293C22×C8—1224no—
294C4×D4—1228no—
295C4×D4—1228no—
296C4×D4—1228no—
297C4×D4—1228no—
298C2×C4⋊C4—614no—
299C2×C4⋊C4—1222no—
300C2×C4⋊C4—1222no—
301C2×C22⋊C4—612no—
302C2×C22⋊C4—612no—
303C2×C22⋊C4—612no—
304C2×C22⋊C4—612no—
305C2×C22⋊C4—1222no—
306C2×C22⋊C4—1222no—
307C2×C22⋊C4—1222no—
308C2×C22⋊C4—1222no—
309C2×C42—612no—
310C2×C42—612no—
311C2×C42—614no—
312C2×C42—612no—
313C2×C42—612no—
314C4⋊C8—1228no—
315C22⋊C8—618no—
316C22⋊C8—1224no—
317#97—1228no—
318C24—21no—
319C24—21no—
320C24—22no—
321C24—42no—
322C24—42no—
323C24—614no—
324C24—612no—
325C24—1221no—
326C24—1221no—
327C24—1222no—
328C24—2442no—
329C24—2442no—
330C24#1175821314yes—
331C24C22×#692311yescharacteristic
332C24C22×#692312yes—
333C2×D4—1228no—
334C2×D4—1228no—
335C2×D4—12216no—
336C2×D4—12216no—
337C2×D4—1228no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—44no—
344C22×C4—48no—
345C22×C4—48no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4—612no—
349C22×C4—612no—
350C22×C4—612no—
351C22×C4—612no—
352C22×C4—612no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—612no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1224no—
361C22×C4—1224no—
362C22×C4—2444no—
363C22×C4—2448no—
364C22×C4—2448no—
365C22×C4—2442no—
366C22×C4—2444no—
367C22×C4—2442no—
368C22×C4C22⋊#692312yes—
369C22×C4C22⋊#692311yescharacteristic
370C22×C4C22⋊#692311yescharacteristic
371C22×C4C22×#692312yes—
372C22×C4C22×#692312yes—
373C2×C8—1228no—
374C2×C8—2448no—
375C4⋊C4—1228no—
376C22⋊C4—1224no—
377C22⋊C4—1224no—
378C22⋊C4—1224no—
379C22⋊C4—1224no—
380C42—614no—
381C42—614no—
382C42—614no—
383C42—614no—
384C23—22no—
385C23—22no—
386C23—24no—
387C23—24no—
388C23—22no—
389C23—22no—
390C23—42no—
391C23—48no—
392C23—42no—
393C23—42no—
394C23—48no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—614no—
399C23—1224no—
400C23—1224no—
401C23—1222no—
402C23—1222no—
403C23—2442no—
404C23—2448no—
405C23—2442no—
406C23—2442no—
407C23—2448no—
408C23—2442no—
409C23—2442no—
410C23—2442no—
411C23C2×C22⋊#692311yescharacteristic
412C23C2×C22⋊#692311yescharacteristic
413C23D61⋊M1612yes—
414C23C2×#1175821312yes—
415C23C2×#1175821314yes—
416C23C23×#692311yescharacteristic
417D4—12232no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—48no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—48no—
426C2×C4—42no—
427C2×C4—612no—
428C2×C4—614no—
429C2×C4—612no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—1222no—
436C2×C4—2448no—
437C2×C4—2441no—
438C2×C4—2442no—
439C2×C4—2441no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2448no—
443C2×C4—2442no—
444C2×C4#1451983714yes—
445C2×C4C2×C22⋊#692312yes—
446C2×C4C2×C22⋊#692312yes—
447C8—2448no—
448C22—24no—
449C22—24no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—24no—
455C22—44no—
456C22—48no—
457C22—44no—
458C22—48no—
459C22—42no—
460C22—42no—
461C22—1224no—
462C22—2444no—
463C22—2448no—
464C22—2444no—
465C22—2448no—
466C22—2442no—
467C22—2442no—
468C22#1684073312yes—
469C22#1684073312yes—
470C22#1684074112yes—
471C22C2×#1451983712yes—
472C22C22×C22⋊#692311yescharacteristic
473C22C2×D61⋊M1611yescharacteristic
474C22C22×#1175821311yescharacteristic
475C4—22no—
476C4—42no—
477C4—1224no—
478C4—1222no—
479C4—1222no—
480C4—2442no—
481C4C2×#1451983714yes—
482C2—22no—
483C2—21no—
484C2—21no—
485C2—44no—
486C2—2444no—
487C2#2146107814yesdirect product factor
488C2C2×#1684073311yescharacteristic
489C2C2×#1684074111yescharacteristic
490C2C22×#1451983711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC24×C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×Dic61C24
hypercenterC24×C4#6923
hypocenterC61C2×#1466
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840783C2semidirect
2. #21461078C2direct (N × H)
3. C2×#16840606C2semidirect
4. C2×#16840605C2semidirect
7. #16840783C22semidirect
11. #16840606C22semidirect
12. #16840605C22semidirect
246. C2×C61#1466semidirect
270. C61C2×#1466semidirect
487. C2#21461078direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407832
#214610782
C2×#168406062
C2×#168406052
C22×C4×C22⋊D612
C2×#146661