Finite Group Databasebeta

← C2×#21443821 #29590205

Subgroups — C2×#21443821 #29590205

Order 15616.

824 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839679C211yesmaximal, characteristic
2C2×#16839488C211yesmaximal, characteristic, complemented
3#21443821C214yesmaximal, direct product factor
4C2×C61×#343C211yesmaximal, characteristic, complemented
5C23×D244C411yescharacteristic
6C22×#11758198—21no—
7C22×#11758198—21no—
8C2×C22⋊#92418—21no—
9#16839679—21no—
10#16839679—21no—
11#16839679C412yes—
12#16839679C2212yes—
13C2×#14519684C411yescharacteristic
14#16839488—21no—
15#16839488C2212yescomplemented
16C22×M16×C61—21no—
17C22×C4⋊C4×C61C2211yescharacteristic
18C61×#343—21no—
19C61×#343C2212yescomplemented
20C24×D61—21no—
21C22×D244—21no—
22C22×D244—41no—
23C22×D244—41no—
24C22×D244—44no—
25C22×D244C2×C412yes—
26C23×Dic61—21no—
27C22×#92418—41no—
28C2×#11758198—22no—
29C2×#11758198—22no—
30C2×#11758198—22no—
31C2×#11758198—22no—
32C2×#11758198—44no—
33C2×#11758198—42no—
34C2×#11758198—42no—
35C22⋊#92418—22no—
36C22⋊#92418—41no—
37#14519684—21no—
38#14519684C2×C412yes—
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C23×C4×C61D411yescharacteristic
42C2×M16×C61—24no—
43C2×M16×C61—22no—
44C2×M16×C61—41no—
45C2×M16×C61—42no—
46C22×C8×C61—41no—
47C2×C4⋊C4×C61—41no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61C2311yescharacteristic
53C24×C61C22⋊C411yescharacteristic
54C23×D61—24no—
55C23×D61—22no—
56C23×D61—42no—
57C23×D61—42no—
58C23×D61—42no—
59C23×D61—41no—
60C23×D61—41no—
61C23×D61—42no—
62C23×D61—42no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61—42no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61D812yes—
76C22×C4×C61SD1612yes—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—22no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—44no—
87C2×D244—48no—
88C2×D244—44no—
89C2×D244—44no—
90C2×D244—44no—
91M16×C61—24no—
92M16×C61—44no—
93M16×C61—42no—
94C2×C8×C61—44no—
95C2×C8×C61—42no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100#11758198—44no—
101#11758198—44no—
102#11758198—44no—
103#11758198—42no—
104#11758198—42no—
105C2×#92418—42no—
106C2×#92418—82no—
107C23×C61—22no—
108C23×C61—22no—
109C23×C61#9911yescharacteristic
110C23×C61#9911yescharacteristic
111C23×C61#10212yes—
112C23×C61#10412yes—
113C23×C61C2×C22⋊C411yescharacteristic
114C22×D61—24no—
115C22×D61—42no—
116C22×D61—44no—
117C22×D61—48no—
118C22×D61—48no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—44no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—84no—
126C22×D61—84no—
127C22×D61—82no—
128C22×D61—82no—
129C22×D61—82no—
130C22×D61—82no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
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—42no—
144C2×C4×C61—42no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—81no—
151C2×C4×C61#10212yes—
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C2×SD1611yescharacteristic
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—84no—
158D244—44no—
159D244—48no—
160D244—44no—
161C8×C61—44no—
162#92418—82no—
163C2×#1345—611nomaximal, Sylow
164C22×C61—24no—
165C22×C61—24no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61#32712yes—
171C22×C61#32712yes—
172C22×C61AΣL(1,𝔽16)12yes—
173C22×C61#35512yes—
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C2×D61—44no—
178C2×D61—44no—
179C2×D61—44no—
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—88no—
183C2×D61—88no—
184C2×D61—82no—
185C2×D61—82no—
186C4×C61—21no—
187C4×C61—22no—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—41no—
193Dic61—82no—
194C2×#394—611no—
195C2×#343D6111yescharacteristic, complemented
196C2×#324—611no—
197#1345—614no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—22no—
201C2×C61#134514yescomplemented
202C2×C61C2×#32711yescharacteristic
203C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
204C2×C61C2×#35511yescharacteristic
205D61—84no—
206C23×D4—611no—
207C22×M16—21no—
208C22×C4⋊C4C2×D6111yescharacteristic
209C22×C22⋊C4—1221no—
210C22×C22⋊C4—1221no—
211C2×C22⋊C8—1221no—
212#394—612no—
213#394—612no—
214#394—1221no—
215#394—1221no—
216C2×#95—611no—
217#343—21no—
218#343C2×D6112yescomplemented
219#324—612no—
220#324—1221no—
221C61C2×#134511yescharacteristic, complemented, Sylow
222C25—1221no—
223C22×D4—612no—
224C22×D4—1221no—
225C22×D4—2441no—
226C22×D4—2441no—
227C22×D4—2444no—
228C23×C4—1221no—
229C23×C4C4×D6111yescharacteristic
230C23×C4D24411yescharacteristic
231C23×C4C22⋊D6111yescharacteristic
232C2×M16—24no—
233C2×M16—22no—
234C2×M16—41no—
235C2×M16—42no—
236C22×C8—41no—
237C22×C8—2441no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C4⋊C4D24411yescharacteristic
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C4⋊C4C22×D6111yescharacteristic
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1222no—
246C2×C22⋊C4—1222no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—2444no—
249C2×C22⋊C4—2442no—
250C2×C22⋊C4—2442no—
251C22⋊C8—1222no—
252C22⋊C8—2441no—
253#95—612no—
254#95—1221no—
255C24—1224no—
256C24—1222no—
257C24—2442no—
258C24—2442no—
259C24—2442no—
260C24—2441no—
261C24—2441no—
262C24—2442no—
263C24—2442no—
264C24#1175819811yescharacteristic
265C2×D4—2442no—
266C2×D4—2442no—
267C2×D4—2444no—
268C2×D4—2444no—
269C2×D4—2448no—
270C2×D4—2444no—
271C2×D4—2444no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—1222no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4#1175819811yescharacteristic
286C22×C4#1175819811yescharacteristic
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819912yes—
289C22×C4#1175820112yes—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4C2×D24411yescharacteristic
292C22×C4C2×C22⋊D6111yescharacteristic
293M16—24no—
294M16—44no—
295M16—42no—
296C2×C8—42no—
297C2×C8—44no—
298C2×C8—4882no—
299C2×C8—2442no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—2444no—
305C22⋊C4—2444no—
306C22⋊C4—2444no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C23—22no—
310C23—22no—
311C23—1224no—
312C23—4882no—
313C23—4884no—
314C23—4884no—
315C23—4882no—
316C23—4882no—
317C23—4882no—
318C23—2442no—
319C23—2444no—
320C23—2442no—
321C23—2442no—
322C23—2448no—
323C23—2448no—
324C23—2442no—
325C23—2442no—
326C23—2442no—
327C23—2444no—
328C23#1451969111yescharacteristic
329C23#1451969111yescharacteristic
330C23#1451969712yes—
331C23#1451970512yes—
332C23C2×#1175819811yescharacteristic
333D4—2444no—
334D4—2444no—
335D4—2448no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—4884no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4#1451969712yes—
361C2×C4C2×#1175819911yescharacteristic
362C2×C4C2×#1175820111yescharacteristic
363C8—44no—
364C8—4882no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—24no—
370C22—24no—
371C22—4882no—
372C22—4888no—
373C22—4882no—
374C22—4882no—
375C22—4882no—
376C22—4888no—
377C22—2444no—
378C22—2444no—
379C22—2444no—
380C22#1683949512yes—
381C22#1683949512yes—
382C22#1683955012yes—
383C22#1683955812yes—
384C22C2×#1451969111yescharacteristic
385C22C2×#1451969711yescharacteristic
386C22C2×#1451970511yescharacteristic
387C4—21no—
388C4—22no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—4882no—
395C2—21no—
396C2—22no—
397C2—21no—
398C2—4884no—
399C2#2144382114yesdirect product factor
400C2C2×#1683949511yescharacteristic
401C2C2×#1683955011yescharacteristic
402C2C2×#1683955811yescharacteristic
subgroupG/H
centerC23#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#343C2
socleC23×C61#99
prime radicalC23×D244C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#343D61
hypocenterC61C2×#1345
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C2×#16839488C2semidirect
3. #21443821C2direct (N × H)
4. C2×C61×#343C2semidirect
15. #16839488C22semidirect
19. C61×#343C22semidirect
195. C2×#343D61semidirect
201. C2×C61#1345semidirect
218. #343C2×D61semidirect
221. C61C2×#1345semidirect
399. C2#21443821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168396792
C2×#168394882
#214438212
C2×C61×#3432
C2×#134561