Finite Group Databasebeta

← C2×#21462114 #30624007

Subgroups — C2×#21462114 #30624007

Order 15616.

1198 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519838C212yesmaximal, complemented
2#21462114C218yesmaximal, direct product factor
3C2×#16840672C212yesmaximal, complemented
4C2×#16840670C212yesmaximal, complemented
5C2×#16840333C211yesmaximal, characteristic
6C22×#11758217—22no—
7C2×#14519838—22no—
8C2×#14519838—24no—
9C2×#14519838C2214yes—
10C2×#14519838C2218yescomplemented
11#16840672C2218yescomplemented
12#16840670C2218yescomplemented
13C23×Dic122C2211yescharacteristic
14#16840333—24no—
15#16840333C414yes—
16#16840333C2214yes—
17C2×#14519775C411yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519764C411yescharacteristic
20C2×#14519764C2211yescharacteristic
21C2×#14519758—22no—
22C2×#14519756—22no—
23C2×#14519736C411yescharacteristic
24C22×#41×C61C411yescharacteristic
25C2×#11758217—24no—
26C2×#11758217—28no—
27C2×#11758217—42no—
28C2×#11758217—44no—
29C22×#92420—42no—
30#14519838—24no—
31#14519838—28no—
32#14519838C2318yes—
33C22×Dic122—42no—
34C22×Dic122—42no—
35C22×Dic122C2×C411yescharacteristic
36C22×Dic122C2×C412yes—
37C22×Dic122D412yes—
38C22×Dic122D414yes—
39C22×Dic122C2311yescharacteristic
40C22×Dic122C2312yes—
41C23×Dic61D412yes—
42#14519775—22no—
43#14519775—22no—
44#14519775C2×C414yes—
45#14519775C2×C412yes—
46#14519775C2312yes—
47#14519764—22no—
48#14519764—22no—
49#14519764C2×C414yes—
50#14519764C2×C412yes—
51#14519764C2312yes—
52#14519758—28no—
53#14519758—28no—
54#14519756—28no—
55#14519756—28no—
56#14519736—22no—
57#14519736C2×C414yes—
58C2×C4⋊Dic61—21no—
59C2×#11758196—22no—
60C2×#11758196—22no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C4×Dic61C2×C411yescharacteristic
65C2×C4×Dic61C2×C411yescharacteristic
66C2×#41×C61—22no—
67C2×#41×C61—42no—
68C2×#41×C61—42no—
69C2×#41×C61C2×C414yes—
70C22×Q8×C61C2×C411yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61C2×C411yescharacteristic
73C23×C4×C61—21no—
74C23×C4×C61C2×C411yescharacteristic
75C24×C61—21no—
76C24×C61C22⋊C411yescharacteristic
77#41×C61—48no—
78#41×C61—48no—
79C2×Q8×C61—21no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C2×Q8×C61C22×C412yes—
83C2×D4×C61—24no—
84C2×D4×C61—21no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61C22×C412yes—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—21no—
93C22×C4×C61—24no—
94C22×C4×C61—42no—
95C22×C4×C61—42no—
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C22⋊C412yes—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C22×C412yes—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—24no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61C22⋊C412yes—
106C22×Dic61C22⋊C414yes—
107C22×Dic61C2×D412yes—
108C22×Dic61C2×D414yes—
109C2×Dic122—41no—
110C2×Dic122—41no—
111C2×Dic122—44no—
112C2×Dic122—42no—
113C2×Dic122—44no—
114C2×Dic122—42no—
115C2×Dic122—44no—
116C2×Dic122—41no—
117C2×Dic122—44no—
118C2×Dic122—41no—
119C2×Dic122C22⋊C414yes—
120C2×Dic122C22⋊C412yes—
121C2×Dic122C22×C412yes—
122C2×Dic122C22×C411yescharacteristic
123C2×Dic122C2×D414yes—
124C2×Dic122C2×D412yes—
125C2×Dic122C2411yescharacteristic
126#11758217—28no—
127#11758217—44no—
128#11758217—48no—
129C2×#92420—44no—
130C2×#92420—48no—
131C22⋊Dic61—24no—
132C22⋊Dic61—28no—
133C22⋊Dic61—24no—
134C22⋊Dic61—24no—
135C4⋊Dic61—24no—
136#11758196—28no—
137#11758196—24no—
138#11758196—24no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61C22×C412yes—
142C4×Dic61C22×C412yes—
143C23×C61—22no—
144C23×C61—42no—
145C23×C61—44no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61#9912yes—
149C23×C61#9912yes—
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61C2×C22⋊C412yes—
152Q8×C61—42no—
153Q8×C61—42no—
154D4×C61—42no—
155D4×C61—42no—
156D4×C61—48no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—24no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—24no—
163C2×C4×C61—22no—
164C2×C4×C61—48no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61C2×C22⋊C411yescharacteristic
168C2×C4×C61C2×C22⋊C412yes—
169C2×C4×C61C23×C411yescharacteristic
170C2×Dic61—24no—
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—24no—
174C2×Dic61—22no—
175C2×Dic61—24no—
176C2×Dic61—24no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61C2×C22⋊C412yes—
183C2×Dic61C2×C22⋊C414yes—
184C2×Dic61C22×D412yes—
185Dic122—44no—
186Dic122—42no—
187Dic122—42no—
188Dic122—41no—
189Dic122—44no—
190Dic122—42no—
191Dic122—41no—
192#92420—48no—
193C2×#2133—611nomaximal, Sylow
194C22×C61—22no—
195C22×C61—24no—
196C22×C61—42no—
197C22×C61—42no—
198C22×C61—44no—
199C22×C61—42no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61C2×#9911yescharacteristic
203C22×C61C2×#9914yes—
204C22×C61C2×#9911yescharacteristic
205C22×C61C22×C22⋊C411yescharacteristic
206C4×C61—22no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210Dic61—22no—
211Dic61—24no—
212Dic61—22no—
213Dic61—42no—
214Dic61—42no—
215C2×#536—611no—
216C22×#101—612no—
217#2133—618no—
218C2×#356—612no—
219C2×#355—612no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—24no—
223C2×C61—82no—
224C2×C61#213312yescomplemented
225C2×C61C22×#9911yescharacteristic
226C22×#41#692311yescharacteristic
227C23×Q8—611no—
228C22×M16—1222no—
229#536—614no—
230#536—614no—
231#536—1224no—
232C2×C4⋊Q8—611no—
233C2×C4⋊Q8—611no—
234C2×#124—611no—
235C2×#124—611no—
236C2×#123—1222no—
237C2×C22⋊Q8—1222no—
238C2×#117—611no—
239C2×#101—614no—
240C2×#101—618no—
241C2×#101—1222no—
242C2×#101—1224no—
243#356—618no—
244#355—618no—
245C61C2×#213311yescharacteristic, complemented, Sylow
246C2×#41—22no—
247C2×#41—42no—
248C2×#41—42no—
249C2×#41C2×#692314yes—
250C22×Q8—612no—
251C22×Q8—614no—
252C22×Q8—611no—
253C22×Q8—612no—
254C22×Q8—611no—
255C22×Q8—612no—
256C22×Q8—2442no—
257C22×Q8—2442no—
258C22×Q8C2×#692311yescharacteristic
259C22×D4—21no—
260C22×D4C2×#692311yescharacteristic
261C23×C4—21no—
262C23×C4—612no—
263C23×C4C2×#692311yescharacteristic
264C2×M16—1224no—
265C2×M16—1228no—
266C2×M16—2444no—
267C2×M16—2442no—
268C22×C8—2442no—
269C4⋊Q8—612no—
270C4⋊Q8—612no—
271C4⋊Q8—614no—
272C4⋊Q8—1222no—
273C4⋊Q8—1222no—
274#124—612no—
275#124—612no—
276#124—614no—
277#124—1222no—
278#124—1222no—
279#123—1228no—
280#123—1228no—
281C22⋊Q8—1228no—
282C22⋊Q8—1228no—
283#117—614no—
284#117—1222no—
285C2×C4⋊C4—1222no—
286C2×C4⋊C4—1222no—
287C2×C4⋊C4—1221no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1221no—
291C2×C42—611no—
292C2×C42—611no—
293#101—618no—
294#101—1228no—
295#101—1224no—
296C24—21no—
297C24C22⋊#692311yescharacteristic
298#41—48no—
299#41—48no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—614no—
304C2×Q8—612no—
305C2×Q8—614no—
306C2×Q8—612no—
307C2×Q8—611no—
308C2×Q8—612no—
309C2×Q8—611no—
310C2×Q8—2442no—
311C2×Q8—2444no—
312C2×Q8—2444no—
313C2×Q8—2441no—
314C2×Q8—2441no—
315C2×Q8—2444no—
316C2×Q8—2444no—
317C2×Q8—2442no—
318C2×Q8—2441no—
319C2×Q8—2441no—
320C2×Q8C22×#692312yes—
321C2×D4—24no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4C22×#692312yes—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—612no—
335C22×C4—612no—
336C22×C4—614no—
337C22×C4—614no—
338C22×C4—1222no—
339C22×C4—1224no—
340C22×C4—1222no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4C22⋊#692311yescharacteristic
344C22×C4C22⋊#692312yes—
345C22×C4C22×#692311yescharacteristic
346C22×C4C22×#692312yes—
347M16—1228no—
348M16—2444no—
349M16—2448no—
350C2×C8—2448no—
351C2×C8—2444no—
352C4⋊C4—1224no—
353C4⋊C4—1228no—
354C4⋊C4—1224no—
355C4⋊C4—1224no—
356C22⋊C4—1224no—
357C22⋊C4—1228no—
358C22⋊C4—1224no—
359C22⋊C4—1224no—
360C42—612no—
361C42—612no—
362C42—1221no—
363C42—1221no—
364C23—22no—
365C23—42no—
366C23—44no—
367C23—41no—
368C23—41no—
369C23#1451983512yes—
370C23#1451983512yes—
371C23C2×C22⋊#692311yescharacteristic
372C23C2×C22⋊#692312yes—
373Q8—42no—
374Q8—42no—
375Q8—2444no—
376Q8—2444no—
377Q8—2442no—
378Q8—2442no—
379Q8—2441no—
380Q8—2442no—
381Q8—2441no—
382D4—42no—
383D4—42no—
384D4—48no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—21no—
388C2×C4—24no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—48no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—612no—
396C2×C4—614no—
397C2×C4—612no—
398C2×C4—1224no—
399C2×C4—1222no—
400C2×C4—1224no—
401C2×C4—1222no—
402C2×C4—1224no—
403C2×C4—1224no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—1222no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4C2×C22⋊#692311yescharacteristic
411C2×C4C2×C22⋊#692312yes—
412C2×C4C23×#692311yescharacteristic
413C8—2448no—
414C22—22no—
415C22—24no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22C2×#1451983511yescharacteristic
423C22C2×#1451983514yes—
424C22C2×#1451983511yescharacteristic
425C22C22×C22⋊#692311yescharacteristic
426C4—22no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—1222no—
431C4—1224no—
432C4—1222no—
433C4—2442no—
434C4—2442no—
435C2—21no—
436C2—21no—
437C2—24no—
438C2—82no—
439C2#2146211412yesdirect product factor
440C2C22×#1451983511yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC22×#41×C61C4
socleC22×C61C2×#99
cosocleC2×Dic122C24
hypercenterC22×#41#6923
hypocenterC61C2×#2133
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#14519838C2semidirect
2. #21462114C2direct (N × H)
3. C2×#16840672C2semidirect
4. C2×#16840670C2semidirect
10. C2×#14519838C22semidirect
11. #16840672C22semidirect
12. #16840670C22semidirect
224. C2×C61#2133semidirect
245. C61C2×#2133semidirect
439. C2#21462114direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198382
#214621142
C2×#168406722
C2×#168406702
C2×#168403332
C2×#213361