Finite Group Databasebeta

← C2×#21444790 #29652187

Subgroups — C2×#21444790 #29652187

Order 15616.

1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16840343C211yesmaximal, characteristic
2C2×#16839903C212yesmaximal, complemented
3C2×#16839682C211yesmaximal, characteristic, complemented
4#21444790C218yesmaximal, direct product factor
5C2×#16839497C212yesmaximal, complemented
6C2×C61×#324C211yesmaximal, characteristic, complemented
7C22×#11758222—21no—
8C23×Dic122C2211yescharacteristic
9C22×#11758190—22no—
10#16840343—24no—
11#16840343—22no—
12#16840343C2214yes—
13C2×#14519757—22no—
14C2×#14519752—22no—
15C2×#14519751—21no—
16C2×#14519751C2212yes—
17C22×#11758196—21no—
18#16839903—24no—
19#16839903C2218yescomplemented
20C2×#14519702—22no—
21#16839682—22no—
22#16839682C2214yescomplemented
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839497C2218yescomplemented
26C22×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2212yes—
28C61×#324C2214yescomplemented
29C2×#11758222—24no—
30C2×#11758222—24no—
31C2×#11758222—44no—
32C2×#11758222—44no—
33C22×Dic122—22no—
34C22×Dic122—21no—
35C22×Dic122—22no—
36C22×Dic122—21no—
37C22×Dic122—44no—
38C22×Dic122C2312yes—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244D412yes—
42C22×C22⋊D61—22no—
43C23×Dic61—21no—
44C23×Dic61—21no—
45C22×C4×D61—22no—
46C2×#11758190—28no—
47C2×#11758190—48no—
48#14519757—28no—
49#14519757—28no—
50#14519752—28no—
51#14519752—28no—
52#14519751—24no—
53#14519751—24no—
54#14519751—22no—
55#14519751—22no—
56#14519751D414yes—
57#14519751C2314yes—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61D412yes—
60C2×#11758196—24no—
61C2×#11758196—44no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64#14519702—28no—
65#14519684—21no—
66#14519684—24no—
67#14519684C2312yes—
68C23×C4×C61D411yescharacteristic
69C23×C4×C61D411yescharacteristic
70C23×C4×C61C2311yescharacteristic
71C22×C8×C61—22no—
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61D412yes—
75C2×C4⋊C4×C61C2312yes—
76C22⋊C8×C61—22no—
77C22⋊C8×C61C2314yes—
78C24×C61C2×D411yescharacteristic
79C23×D61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61SD1614yescomplemented
88C22×C4×C61C2×D412yes—
89C22×C4×C61C2×D412yes—
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D412yes—
93C22×C4×C61C2411yescharacteristic
94C2×C22⋊D61—24no—
95C2×C22⋊D61—24no—
96C2×C22⋊D61—44no—
97C2×C22⋊D61—44no—
98C22×Dic61—24no—
99C22×Dic61—24no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61—42no—
108#11758222—48no—
109#11758222—416no—
110#11758222—48no—
111C2×D244—24no—
112C2×D244—24no—
113C2×D244—22no—
114C2×D244—44no—
115C2×D244—44no—
116C2×D244—82no—
117C2×D244C2×D414yes—
118C2×C4×D61—28no—
119C2×C4×D61—48no—
120C2×Dic122—28no—
121C2×Dic122—24no—
122C2×Dic122—24no—
123C2×Dic122—44no—
124C2×Dic122—48no—
125C2×Dic122—44no—
126C2×Dic122—44no—
127C2×Dic122—44no—
128C2×Dic122—42no—
129C2×C8×C61—24no—
130C2×C8×C61—44no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—24no—
133#11758198—28no—
134#11758198—24no—
135#11758198—24no—
136C4⋊Dic61—24no—
137C4⋊Dic61—22no—
138C4⋊Dic61C2×D414yes—
139#11758196—48no—
140#11758190—416no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61#12011yescharacteristic
144C23×C61#12011yescharacteristic
145C23×C61C2×SD1612yes—
146C23×C61AGL(1,ℤ/8)12yes—
147C23×C61C22×D411yescharacteristic
148C22×D61—24no—
149C22×D61—44no—
150C22×D61—44no—
151C22×D61—44no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—24no—
155C2×C4×C61—24no—
156C2×C4×C61—24no—
157C2×C4×C61—22no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—81no—
164C2×C4×C61#12012yes—
165C2×C4×C61C2×SD1614yescomplemented
166C2×C4×C61C22×D412yes—
167C22⋊D61—44no—
168C22⋊D61—44no—
169C22⋊D61—48no—
170C2×Dic61—24no—
171C2×Dic61—24no—
172C2×Dic61—24no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—44no—
176C2×Dic61—48no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—44no—
180C2×Dic61—44no—
181D244—44no—
182D244—48no—
183D244—82no—
184D244—84no—
185C4×D61—416no—
186Dic122—28no—
187Dic122—44no—
188Dic122—48no—
189Dic122—48no—
190C8×C61—44no—
191C2×#1604—611nomaximal, Sylow
192C22×C61—24no—
193C22×C61—24no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61#45012yes—
199C22×C61#45012yes—
200C22×C61#45612yes—
201C22×C61B(4,𝔽2)12yes—
202C22×C61C2×#12011yescharacteristic
203C22×C61C22×SD1611yescharacteristic
204C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
205C2×D61—44no—
206C2×D61—44no—
207C2×D61—44no—
208C2×D61—88no—
209C4×C61—24no—
210C4×C61—22no—
211C4×C61—22no—
212C4×C61—42no—
213Dic61—44no—
214Dic61—44no—
215Dic61—44no—
216C2×#537—611no—
217C2×#448—612no—
218C2×#395—611no—
219#1604—618no—
220C2×#327—612no—
221C2×#324D6111yescharacteristic, complemented
222C2×C61—21no—
223C2×C61—21no—
224C2×C61—22no—
225C2×C61#160414yescomplemented
226C2×C61C2×#45011yescharacteristic
227C2×C61C2×#45611yescharacteristic
228C2×C61C2×B(4,𝔽2)11yescharacteristic
229D61—84no—
230C22×#41—1221no—
231C23×Q8—611no—
232C22×SD16—1222no—
233#537—614no—
234#537—1224no—
235#537—1222no—
236C2×C22⋊Q8—1222no—
237C2×#121—612no—
238C2×#121—1222no—
239C2×#121—1221no—
240C22×C4⋊C4—1221no—
241C22×C4⋊C4C2×D6111yescharacteristic
242#448—618no—
243#448—1224no—
244C2×#103—1222no—
245C2×C22⋊C8C2×D6112yes—
246#395—614no—
247#395—1222no—
248C2×#95—611no—
249C2×#95—1221no—
250#327—618no—
251#324C2×D6114yescomplemented
252C61C2×#160411yescharacteristic, complemented, Sylow
253C2×#41—1224no—
254C2×#41—1224no—
255C2×#41—2444no—
256C2×#41—2444no—
257C22×Q8—612no—
258C22×Q8—1221no—
259C22×Q8—1221no—
260C22×Q8—1222no—
261C22×Q8—1222no—
262C22×Q8—2444no—
263C22×D4—612no—
264C22×D4—1221no—
265C22×D4—1221no—
266C22×D4—1222no—
267C23×C4—1222no—
268C23×C4—1221no—
269C23×C4—1221no—
270C23×C4D24411yescharacteristic
271C23×C4D24411yescharacteristic
272C23×C4C22×D6111yescharacteristic
273C2×SD16—1228no—
274C2×SD16—2448no—
275C22×C8—22no—
276C22⋊Q8—1228no—
277C22⋊Q8—1228no—
278#121—614no—
279#121—614no—
280#121—1228no—
281#121—1228no—
282#121—1224no—
283#121—1222no—
284#121—1224no—
285#121—1222no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—612no—
289C2×C4⋊C4—1221no—
290C2×C4⋊C4—1224no—
291C2×C4⋊C4—2444no—
292C2×C4⋊C4D24412yes—
293C2×C4⋊C4C22×D6112yes—
294C2×C22⋊C4—1222no—
295C2×C22⋊C4—1222no—
296#103—1228no—
297C22⋊C8—22no—
298C22⋊C8C22×D6114yes—
299#95—612no—
300#95—1221no—
301#95—1224no—
302C24—1222no—
303C24C2×D24411yescharacteristic
304#41—2448no—
305#41—24416no—
306#41—2448no—
307C2×Q8—1224no—
308C2×Q8—1228no—
309C2×Q8—1224no—
310C2×Q8—2444no—
311C2×Q8—2444no—
312C2×Q8—2444no—
313C2×Q8—2444no—
314C2×Q8—2448no—
315C2×Q8—2442no—
316C2×D4—614no—
317C2×D4—1224no—
318C2×D4—1224no—
319C2×D4—1224no—
320C2×D4—1224no—
321C2×D4—1222no—
322C2×D4—4882no—
323C2×D4—2444no—
324C2×D4—2444no—
325C2×D4—2444no—
326C2×D4—2444no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—1228no—
335C22×C4—1224no—
336C22×C4—1224no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—2448no—
341C22×C4—2442no—
342C22×C4—2442no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4—2442no—
346C22×C4#1175819014yescomplemented
347C22×C4C2×D24412yes—
348C22×C4C2×D24412yes—
349C22×C4C2×D24411yescharacteristic
350C22×C4D4×D6112yes—
351C22×C4D4×D6112yes—
352C22×C4C23×D6111yescharacteristic
353SD16—24416no—
354C2×C8—24no—
355C2×C8—44no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—614no—
359C4⋊C4—1224no—
360C4⋊C4—1222no—
361C4⋊C4—2448no—
362C22⋊C4—1228no—
363C22⋊C4—1224no—
364C22⋊C4—1224no—
365C23—22no—
366C23—22no—
367C23—1224no—
368C23—2444no—
369C23—2444no—
370C23—2444no—
371C23#1451974711yescharacteristic
372C23#1451974711yescharacteristic
373C23C2×#1175819012yes—
374C23#1451980512yes—
375C23C22×D24411yescharacteristic
376Q8—1228no—
377Q8—2444no—
378Q8—2448no—
379Q8—2448no—
380D4—4882no—
381D4—4884no—
382D4—2444no—
383D4—2448no—
384D4—2444no—
385D4—2444no—
386D4—2448no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—1224no—
400C2×C4—1224no—
401C2×C4—1224no—
402C2×C4—24416no—
403C2×C4—2442no—
404C2×C4—2448no—
405C2×C4—2442no—
406C2×C4—2444no—
407C2×C4—2444no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2444no—
411C2×C4#1451974712yes—
412C2×C4C2×#1175819014yescomplemented
413C2×C4C2×D4×D6112yes—
414C8—44no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—24no—
421C22—4888no—
422C22—2444no—
423C22—2444no—
424C22—2444no—
425C22#1683991512yes—
426C22#1683991512yes—
427C22#1683994712yes—
428C22#1683995012yes—
429C22C2×#1451974711yescharacteristic
430C22C22×#1175819011yescharacteristic
431C22C2×#1451980511yescharacteristic
432C4—22no—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—2444no—
437C4—2444no—
438C4—2444no—
439C2—21no—
440C2—21no—
441C2—22no—
442C2—4884no—
443C2#2144479014yesdirect product factor
444C2C2×#1683991511yescharacteristic
445C2C2×#1683994711yescharacteristic
446C2C2×#1683995011yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC2×#16840343C2
hypercenterC2×#324D61
hypocenterC61C2×#1604
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#16839903C2semidirect
3. C2×#16839682C2semidirect
4. #21444790C2direct (N × H)
5. C2×#16839497C2semidirect
6. C2×C61×#324C2semidirect
19. #16839903C22semidirect
22. #16839682C22semidirect
25. #16839497C22semidirect
28. C61×#324C22semidirect
87. C22×C4×C61SD16semidirect
165. C2×C4×C61C2×SD16semidirect
221. C2×#324D61semidirect
225. C2×C61#1604semidirect
251. #324C2×D61semidirect
252. C61C2×#1604semidirect
346. C22×C4#11758190semidirect
412. C2×C4C2×#11758190semidirect
443. C2#21444790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403432
C2×#168399032
C2×#168396822
#214447902
C2×#168394972
C2×C61×#3242
C2×#160461