Finite Group Databasebeta

← C2×#21461344 #30611759

Subgroups — C2×#21461344 #30611759

Order 15616.

974 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840785C211yesmaximal, characteristic
2C2×#16840780C211yesmaximal, characteristic
3#21461344C218yesmaximal, direct product factor
4C2×#16840622C212yesmaximal, complemented
5C2×#16840621C212yesmaximal, complemented
6C2×#16840316C211yesmaximal, characteristic
7#16840785—22no—
8#16840785C2214yes—
9#16840780—22no—
10#16840780C2214yes—
11C2×#14519844C2212yes—
12C2×#14519844C2212yes—
13C2×#14519834—21no—
14C2×#14519834—21no—
15C2×#14519832—21no—
16C2×C4×#92420—21no—
17#16840622C2218yescomplemented
18#16840621C2218yescomplemented
19#16840316—22no—
20#16840316—22no—
21#16840316C414yes—
22#16840316C2214yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519775C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519757C411yescharacteristic
27C2×#14519755—21no—
28C2×#14519753C411yescharacteristic
29C2×C4×Dic122—21no—
30C2×C4×Dic122C411yescharacteristic
31C2×#14519734—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×Q8×C61C411yescharacteristic
34C22×#92420—22no—
35C22×#92420—22no—
36#14519844—22no—
37#14519844—22no—
38#14519844C2314yes—
39#14519844C2314yes—
40#14519834—24no—
41#14519834—24no—
42#14519832—24no—
43C4×#92420—24no—
44C22×Dic122—21no—
45C22×Dic122C2×C411yescharacteristic
46C22×C4×D61C2×C411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49#14519776—21no—
50#14519776—21no—
51#14519776C2×C412yes—
52#14519776C2312yes—
53#14519775—21no—
54#14519775—21no—
55#14519775C2×C412yes—
56#14519775C2312yes—
57#14519767—24no—
58#14519767—24no—
59#14519757—22no—
60#14519757C2×C414yes—
61#14519755—24no—
62#14519755—24no—
63#14519753—22no—
64#14519753C2×C414yes—
65C4×Dic122—22no—
66C4×Dic122—24no—
67C4×Dic122—24no—
68C4×Dic122C2×C414yes—
69#14519734—24no—
70#14519734—24no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C42×D61C2×C412yes—
85C42×D61D412yes—
86C42×D61D412yes—
87C42×D61C2312yes—
88C22×Q8×C61C2×C411yescharacteristic
89C4×Q8×C61—22no—
90C4×Q8×C61C2×C414yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C42×C61—21no—
94C2×C42×C61C2×C411yescharacteristic
95C23×D61C22⋊C411yescharacteristic
96C2×Q8×C61—21no—
97C2×Q8×C61—42no—
98C2×Q8×C61C22×C412yes—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61C22⋊C411yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C2×D411yescharacteristic
108C22×Dic61C2×D411yescharacteristic
109C2×C4×D61—24no—
110C2×C4×D61—24no—
111C2×C4×D61—42no—
112C2×C4×D61C22⋊C412yes—
113C2×C4×D61C22⋊C412yes—
114C2×C4×D61C22⋊C412yes—
115C2×C4×D61C22×C412yes—
116C2×C4×D61C2×D412yes—
117C2×C4×D61C2×D412yes—
118C2×Dic122—21no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—44no—
122C2×Dic122—42no—
123C2×Dic122C22×C412yes—
124C2×#92420—24no—
125C2×#92420—24no—
126C2×#92420—44no—
127C2×#92420—44no—
128C4⋊C4×C61—24no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61C22×C412yes—
131C42×C61—24no—
132C42×C61C22⋊C412yes—
133C42×C61C22×C412yes—
134#11758198—24no—
135#11758198—24no—
136C4⋊Dic61—21no—
137C4⋊Dic61—24no—
138C4⋊Dic61C22×C412yes—
139#11758196—24no—
140#11758196—22no—
141#11758196—22no—
142#11758196—24no—
143#11758196—22no—
144#11758196—22no—
145#11758196—22no—
146#11758196—22no—
147C4×Dic61—24no—
148C4×Dic61C22⋊C412yes—
149C4×Dic61C22⋊C412yes—
150C4×Dic61C22×C411yescharacteristic
151C4×Dic61C2×D412yes—
152C4×Dic61C2×D412yes—
153C4×Dic61C2×D411yescharacteristic
154C4×Dic61C2×D411yescharacteristic
155C4×Dic61C2411yescharacteristic
156C23×C61C2×C22⋊C411yescharacteristic
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61C2×C22⋊C412yes—
161Q8×C61—42no—
162Q8×C61—42no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61C2×C22⋊C412yes—
171C2×C4×C61C2×C22⋊C412yes—
172C2×C4×C61C2×C22⋊C411yescharacteristic
173C2×C4×C61C23×C411yescharacteristic
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61C2×C22⋊C412yes—
180C2×Dic61C2×C22⋊C411yescharacteristic
181C2×Dic61C2×C22⋊C411yescharacteristic
182C2×Dic61#13514yes—
183C2×Dic61#13714yes—
184C2×Dic61C22×D411yescharacteristic
185C2×Dic61C22×D411yescharacteristic
186C4×D61—24no—
187C4×D61—24no—
188C4×D61—24no—
189C4×D61—24no—
190C4×D61—42no—
191C4×D61—42no—
192Dic122—42no—
193Dic122—44no—
194Dic122—44no—
195Dic122—42no—
196#92420—44no—
197#92420—44no—
198C2×#1554—611nomaximal, Sylow
199C22×C61#41312yes—
200C22×C61#41612yes—
201C22×C61#41912yes—
202C22×C61C22×C22⋊C411yescharacteristic
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—44no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—22no—
210C4×C61—22no—
211C4×C61—42no—
212C4×C61—42no—
213Dic61—22no—
214Dic61—42no—
215Dic61—42no—
216Dic61#41612yes—
217Dic61#41912yes—
218Dic61C2×#13512yes—
219Dic61C2×#13712yes—
220C2×#533—611no—
221C2×#432—611no—
222C2×#431—611no—
223#1554—618no—
224C2×#333—612no—
225C2×#332—612no—
226C2×C61#155414yescomplemented
227C2×C61C2×#41311yescharacteristic
228C2×C61C2×#41611yescharacteristic
229C2×C61C2×#41911yescharacteristic
230D61—42no—
231#533—614no—
232#533—614no—
233#533—1222no—
234#533—1222no—
235C2×C4⋊Q8—611no—
236C2×C4⋊Q8—611no—
237C2×#125—1221no—
238C2×C22⋊Q8—611no—
239C2×C22⋊Q8—611no—
240C2×C22⋊Q8—1221no—
241C2×C4×Q8—611no—
242C2×C4×Q8—1221no—
243C2×C4×Q8#692311yescharacteristic
244C2×#117—1221no—
245C22×C42—611no—
246#432—614no—
247#432—1222no—
248#431—614no—
249#431—1222no—
250C2×C4⋊C8—612no—
251C2×C4⋊C8—612no—
252C2×C22⋊C8—1221no—
253C2×C22⋊C8—1221no—
254C2×#97—1221no—
255C2×C4×C8—1221no—
256#333—618no—
257#332—618no—
258C61C2×#155411yescharacteristic, complemented, Sylow
259C22×Q8—611no—
260C22×Q8—1221no—
261C22×Q8C2×#692311yescharacteristic
262C23×C4—611no—
263C23×C4—611no—
264C23×C4—611no—
265C22×C8—1222no—
266C22×C8—1222no—
267C4⋊Q8—612no—
268C4⋊Q8—612no—
269C4⋊Q8—612no—
270C4⋊Q8—612no—
271C4⋊Q8—1221no—
272C4⋊Q8—1221no—
273C4⋊Q8—1221no—
274C4⋊Q8—1221no—
275#125—1224no—
276#125—1224no—
277C22⋊Q8—614no—
278C22⋊Q8—614no—
279C22⋊Q8—1222no—
280C22⋊Q8—1224no—
281C22⋊Q8—1224no—
282C22⋊Q8—1222no—
283C4×Q8—22no—
284C4×Q8—614no—
285C4×Q8—1224no—
286C4×Q8—1224no—
287C4×Q8—1222no—
288C4×Q8C2×#692314yes—
289#117—1224no—
290#117—1224no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1221no—
299C2×C4⋊C4C2×#692311yescharacteristic
300C2×C22⋊C4—1221no—
301C2×C22⋊C4—1221no—
302C2×C42—21no—
303C2×C42—611no—
304C2×C42—611no—
305C2×C42—611no—
306C2×C42—612no—
307C2×C42—612no—
308C2×C42—612no—
309C2×C42—612no—
310C2×C42—1221no—
311C2×C42C2×#692311yescharacteristic
312C4⋊C8—614no—
313C4⋊C8—614no—
314C4⋊C8—1222no—
315C4⋊C8—1222no—
316C22⋊C8—1224no—
317C22⋊C8—1224no—
318#97—1224no—
319C4×C8—1224no—
320C24—611no—
321C2×Q8—21no—
322C2×Q8—42no—
323C2×Q8—612no—
324C2×Q8—1222no—
325C2×Q8—1222no—
326C2×Q8—1221no—
327C2×Q8—2442no—
328C2×Q8—2444no—
329C2×Q8C22×#692312yes—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—612no—
336C22×C4—612no—
337C22×C4—612no—
338C22×C4—612no—
339C22×C4—612no—
340C22×C4—612no—
341C22×C4—1224no—
342C22×C4—1224no—
343C22×C4—1221no—
344C22×C4—1221no—
345C22×C4—2442no—
346C22×C4C22⋊#692311yescharacteristic
347C22×C4C22⋊#692311yescharacteristic
348C22×C4C22×#692311yescharacteristic
349C2×C8—1224no—
350C2×C8—1224no—
351C2×C8—2444no—
352C2×C8—2444no—
353C4⋊C4—24no—
354C4⋊C4—21no—
355C4⋊C4—612no—
356C4⋊C4—1222no—
357C4⋊C4—1222no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4—1224no—
361C4⋊C4—1222no—
362C4⋊C4—1222no—
363C4⋊C4—1224no—
364C4⋊C4—1221no—
365C4⋊C4—1224no—
366C4⋊C4C22×#692312yes—
367C22⋊C4—1224no—
368C22⋊C4—1224no—
369C42—24no—
370C42—612no—
371C42—612no—
372C42—611no—
373C42—611no—
374C42—612no—
375C42—612no—
376C42—611no—
377C42—611no—
378C42—1224no—
379C42C22⋊#692312yes—
380C42C22×#692312yes—
381C23—612no—
382C23—1222no—
383C23—1222no—
384C23—1222no—
385C23C2×C22⋊#692311yescharacteristic
386Q8—42no—
387Q8—42no—
388Q8—2442no—
389Q8—2442no—
390Q8—2444no—
391Q8—2444no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—614no—
400C2×C4—614no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—611no—
404C2×C4—611no—
405C2×C4—612no—
406C2×C4—1224no—
407C2×C4—1224no—
408C2×C4—1224no—
409C2×C4—1224no—
410C2×C4—1222no—
411C2×C4—1222no—
412C2×C4—1222no—
413C2×C4—2442no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4C2×C22⋊#692312yes—
418C2×C4C2×C22⋊#692311yescharacteristic
419C2×C4C2×C22⋊#692312yes—
420C2×C4C23×#692311yescharacteristic
421C8—2444no—
422C8—2444no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—2444no—
427C22#1684074812yes—
428C22#1684075212yes—
429C22#1684075512yes—
430C22C22×C22⋊#692311yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—22no—
435C4—42no—
436C4—42no—
437C4—612no—
438C4—612no—
439C4—612no—
440C4—612no—
441C4—1222no—
442C4—2442no—
443C4—2442no—
444C2—2442no—
445C2#2146134414yesdirect product factor
446C2C2×#1684074811yescharacteristic
447C2C2×#1684075211yescharacteristic
448C2C2×#1684075511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61C2×#1554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461344C2direct (N × H)
4. C2×#16840622C2semidirect
5. C2×#16840621C2semidirect
17. #16840622C22semidirect
18. #16840621C22semidirect
226. C2×C61#1554semidirect
258. C61C2×#1554semidirect
445. C2#21461344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407852
C2×#168407802
#214613442
C2×#168406222
C2×#168406212
C2×#168403162
C2×#155461