Finite Group Databasebeta

← C2×#21460910 #30606285

Subgroups — C2×#21460910 #30606285

Order 15616.

750 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840748C212yesmaximal
2#21460910C214yesmaximal, direct product factor
3C2×#16839728C211yesmaximal, characteristic
4C2×D61⋊M16—22no—
5#16840748—22no—
6#16840748—22no—
7#16840748C414yes—
8#16840748C2214yes—
9C2×#14519838—22no—
10C2×#14519837C414yes—
11C22×#11758222C2211yescharacteristic
12C22×#11758194C411yescharacteristic
13#16839728—22no—
14#16839728C412yes—
15#16839728C2212yes—
16C2×#14519689—22no—
17C23×C8×C61C411yescharacteristic
18C2×#11758213—42no—
19D61⋊M16—24no—
20D61⋊M16—24no—
21D61⋊M16—42no—
22D61⋊M16—42no—
23C2×#11758217—24no—
24C2×D61⋊C8—42no—
25#14519838—24no—
26#14519838—24no—
27#14519837—24no—
28#14519837C2×C418yes—
29C2×#11758222—41no—
30C2×#11758222—41no—
31C2×#11758222—41no—
32C2×#11758222—41no—
33C2×#11758222C2×C412yes—
34C2×#11758222C2×C411yescharacteristic
35C2×#11758222D412yes—
36C2×#11758222D411yescharacteristic
37C2×#11758222Q811yescharacteristic
38C2×#11758222C2311yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×D244Q811yescharacteristic
41C22×C22⋊D61C2×C412yes—
42C22×C4×D61D412yes—
43C2×#11758194—21no—
44C2×#11758194—41no—
45C2×#11758194—41no—
46C2×#11758194C2×C412yes—
47C22×#92418—21no—
48#14519689—24no—
49#14519689—24no—
50C23×C4×C61C2×C411yescharacteristic
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C22×C8×C61—41no—
54C22×C8×C61—41no—
55C22×C8×C61C2×C412yes—
56C24×C61C4211yescharacteristic
57C23×D61C4⋊C412yes—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C4211yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C4⋊C411yescharacteristic
66C22×C4×C61C4⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61C4212yes—
71C2×C22⋊D61C22⋊C412yes—
72C2×C22⋊D61C4⋊C412yes—
73C2×C22⋊D61C22×C412yes—
74C22×Dic61C22⋊C412yes—
75#11758222—42no—
76#11758222—42no—
77#11758222—41no—
78#11758222—41no—
79#11758222—42no—
80#11758222—42no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244C4⋊C412yes—
90C2×D244C4⋊C411yescharacteristic
91C2×D244C2×Q811yescharacteristic
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61C22⋊C412yes—
97C2×C4×D61C22⋊C412yes—
98C2×C4×D61C4⋊C412yes—
99C2×C4×D61C2×D412yes—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×Dic122C22⋊C412yes—
103C2×Dic122C4⋊C411yescharacteristic
104C2×Dic122C2×D411yescharacteristic
105#11758217—28no—
106#11758217—44no—
107C2×#92420—44no—
108#11758213—44no—
109#11758213—44no—
110D61⋊C8—44no—
111D61⋊C8—44no—
112C2×C8×C61—22no—
113C2×C8×C61—42no—
114C2×C8×C61—41no—
115C2×C8×C61—41no—
116C2×C8×C61—42no—
117#11758194—42no—
118#11758194—42no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—42no—
125C23×C61#9511yescharacteristic
126C23×C61#9511yescharacteristic
127C23×C61C2×C4211yescharacteristic
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—44no—
131C22×D61#9512yes—
132C22×D61C2×C4⋊C412yes—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61#9511yescharacteristic
144C2×C4×C61#9511yescharacteristic
145C2×C4×C61#9911yescharacteristic
146C2×C4×C61#9911yescharacteristic
147C2×C4×C61#9911yescharacteristic
148C2×C4×C61#9911yescharacteristic
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C2×C4×C61C2×C4⋊C411yescharacteristic
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C2×Dic61—22no—
156C2×Dic61—22no—
157C2×Dic61#9512yes—
158C2×Dic61C2×C22⋊C412yes—
159D244—42no—
160D244—41no—
161D244—41no—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—22no—
167C4×D61—22no—
168C4×D61—22no—
169C4×D61—22no—
170Dic122—42no—
171Dic122—41no—
172Dic122—41no—
173#92420—48no—
174C8×C61—42no—
175#92418—42no—
176C2×#1392—611nomaximal, Sylow
177C22×C61—22no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—42no—
183C22×C61—42no—
184C22×C61#34211yescharacteristic
185C22×C61#34211yescharacteristic
186C22×C61C2×#9511yescharacteristic
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—44no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—82no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61#34211yescharacteristic
196C4×C61#34211yescharacteristic
197C4×C61C2×#9911yescharacteristic
198C4×C61C2×#9911yescharacteristic
199Dic61—22no—
200Dic61—22no—
201C2×#413—612no—
202C2×#408—611no—
203#1392—614no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61—41no—
207C2×C61—41no—
208C2×C61#139212yescomplemented
209C2×C61C2×#34211yescharacteristic
210D61—42no—
211D61—42no—
212C22×#41—611no—
213C22×M16—611no—
214C22×M16—1222no—
215C23×C8#692311yescharacteristic
216#413—614no—
217#413—614no—
218#413—1222no—
219#413—1222no—
220C2×#101—1222no—
221C2×#100—614no—
222#408—612no—
223#408—612no—
224#408—1222no—
225C2×C22⋊C8—1222no—
226C61C2×#139211yescharacteristic, complemented, Sylow
227C2×#41—612no—
228C2×#41—611no—
229C2×#41—611no—
230C2×#41—612no—
231C2×#41—611no—
232C2×#41—611no—
233C2×#41—2441no—
234C2×#41—2441no—
235C2×#41—2441no—
236C2×#41—2441no—
237C22×Q8—611no—
238C22×D4—612no—
239C22×D4—611no—
240C23×C4—612no—
241C23×C4C2×#692311yescharacteristic
242C2×M16—612no—
243C2×M16—1221no—
244C2×M16—1224no—
245C2×M16—1224no—
246C2×M16—1224no—
247C2×M16—2442no—
248C2×M16—2442no—
249C2×M16—2442no—
250C2×M16—2441no—
251C2×M16—2441no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—41no—
255C22×C8—41no—
256C22×C8—1221no—
257C22×C8—2442no—
258C22×C8C2×#692312yes—
259#101—1224no—
260#101—1224no—
261#100—618no—
262#100—1224no—
263C22⋊C8—1224no—
264C22⋊C8—1224no—
265C24—612no—
266C24C4×#692311yescharacteristic
267#41—2442no—
268#41—2441no—
269#41—2441no—
270#41—2442no—
271#41—2441no—
272#41—2441no—
273#41—2442no—
274#41—2442no—
275#41—2441no—
276#41—2441no—
277#41—2441no—
278#41—2441no—
279C2×Q8—612no—
280C2×Q8—611no—
281C2×Q8—611no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C2×D4—612no—
285C2×D4—612no—
286C2×D4—612no—
287C2×D4—612no—
288C2×D4—612no—
289C2×D4—611no—
290C2×D4—611no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2442no—
294C2×D4—2442no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—612no—
300C22×C4—612no—
301C22×C4—612no—
302C22×C4—612no—
303C22×C4—612no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4C4×#692311yescharacteristic
309C22×C4C4⋊#692311yescharacteristic
310C22×C4C4⋊#692311yescharacteristic
311C22×C4C22⋊#692311yescharacteristic
312C22×C4C22⋊#692311yescharacteristic
313C22×C4C22×#692311yescharacteristic
314M16—1228no—
315M16—2442no—
316M16—2444no—
317M16—2444no—
318M16—2444no—
319M16—2442no—
320C2×C8—22no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—42no—
325C2×C8—1222no—
326C2×C8—2444no—
327C2×C8—2444no—
328C2×C8—2444no—
329C2×C8—2441no—
330C2×C8—2441no—
331C23—21no—
332C23—21no—
333C23—42no—
334C23—612no—
335C23—612no—
336C23—1222no—
337C23—1222no—
338C23—2444no—
339C23(C2×#6923)⋊C411yescharacteristic
340C23(C2×#6923)⋊C411yescharacteristic
341C23C2×C4×#692311yescharacteristic
342Q8—2442no—
343Q8—2441no—
344Q8—2441no—
345D4—2442no—
346D4—2441no—
347D4—2441no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351D4—2442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4(C2×#6923)⋊C411yescharacteristic
375C2×C4(C2×#6923)⋊C411yescharacteristic
376C2×C4#1451983511yescharacteristic
377C2×C4#1451983511yescharacteristic
378C2×C4#1451983611yescharacteristic
379C2×C4#1451983611yescharacteristic
380C2×C4C2×C22⋊#692311yescharacteristic
381C2×C4C2×C4⋊#692311yescharacteristic
382C8—42no—
383C8—2448no—
384C8—2442no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—1222no—
393C22—1222no—
394C22—4882no—
395C22—2442no—
396C22—2442no—
397C22—2444no—
398C22#1684064011yescharacteristic
399C22#1684064011yescharacteristic
400C22C2×(C2×#6923)⋊C411yescharacteristic
401C4—21no—
402C4—21no—
403C4—1222no—
404C4—1222no—
405C4#1684064011yescharacteristic
406C4#1684064011yescharacteristic
407C4C2×#1451983511yescharacteristic
408C4C2×#1451983611yescharacteristic
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—2442no—
414C2—2442no—
415C2#2146091012yesdirect product factor
416C2C2×#1684064011yescharacteristic
subgroupG/H
centerC2×C4#14519835
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC22×C61#342
prime radicalC22×#11758222C22
cosocleC2×#11758222C23
hypercenterC23×C8#6923
hypocenterC61C2×#1392
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #21460910C2direct (N × H)
208. C2×C61#1392semidirect
226. C61C2×#1392semidirect
415. C2#21460910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407482
#214609102
C2×#168397282
C2×#139261