Finite Group Databasebeta

← C2×#21444824 #29652232

Subgroups — C2×#21444824 #29652232

Order 15616.

1308 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1308 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×#16840076C212yesmaximal, complemented
3C2×#16839692C211yesmaximal, characteristic, complemented
4#21444824C218yesmaximal, direct product factor
5C2×#16839497C212yesmaximal, complemented
6C2×C61×#324C211yesmaximal, characteristic, complemented
7C22×#11758222—21no—
8#16840343—24no—
9#16840343—22no—
10#16840343C2214yes—
11C2×#14519757—22no—
12C2×#14519752—22no—
13C2×#14519751—21no—
14C2×#14519751C2212yes—
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196—21no—
17#16840076—24no—
18#16840076C2218yescomplemented
19C2×#14519711—22no—
20C2×#14519699—22no—
21#16839692—22no—
22#16839692C2214yescomplemented
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—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244D412yes—
37C22×C22⋊D61—22no—
38C23×Dic61—21no—
39C23×Dic61—21no—
40C22×C4×D61—22no—
41#14519757—28no—
42#14519757—28no—
43#14519752—28no—
44#14519752—28no—
45#14519751—24no—
46#14519751—24no—
47#14519751—22no—
48#14519751—22no—
49#14519751D414yes—
50#14519751C2314yes—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61D412yes—
56C2×C4⋊Dic61C2312yes—
57C2×#11758196—24no—
58C2×#11758196—44no—
59C2×#11758198—22no—
60C2×#11758198—22no—
61#14519711—28no—
62#14519699—28no—
63#14519684—21no—
64#14519684—24no—
65#14519684C2312yes—
66C23×C4×C61D411yescharacteristic
67C23×C4×C61D411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—22no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61D412yes—
73C2×C4⋊C4×C61C2312yes—
74C22⋊C8×C61—22no—
75C22⋊C8×C61C2314yes—
76C24×C61C2×D411yescharacteristic
77C23×D61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61D814yes—
86C22×C4×C61C2×D412yes—
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D412yes—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2411yescharacteristic
92C2×C22⋊D61—24no—
93C2×C22⋊D61—24no—
94C2×C22⋊D61—44no—
95C2×C22⋊D61—44no—
96C22×Dic61—24no—
97C22×Dic61—22no—
98C22×Dic61—22no—
99C22×Dic61—22no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106#11758222—48no—
107#11758222—416no—
108#11758222—48no—
109C2×D244—24no—
110C2×D244—24no—
111C2×D244—22no—
112C2×D244—44no—
113C2×D244—44no—
114C2×D244—82no—
115C2×D244C2×D414yes—
116C2×C4×D61—28no—
117C2×C4×D61—48no—
118C2×Dic122—24no—
119C2×Dic122—44no—
120C2×C8×C61—24no—
121C2×C8×C61—44no—
122C4⋊C4×C61—24no—
123C4⋊C4×C61—24no—
124#11758198—28no—
125#11758198—24no—
126#11758198—24no—
127C4⋊Dic61—24no—
128C4⋊Dic61—22no—
129C4⋊Dic61—24no—
130C4⋊Dic61—42no—
131C4⋊Dic61C2×D414yes—
132#11758196—48no—
133C23×C61—22no—
134C23×C61—22no—
135C23×C61#12011yescharacteristic
136C23×C61#12011yescharacteristic
137C23×C61C2×D812yes—
138C23×C61AGL(1,ℤ/8)12yes—
139C23×C61C22×D411yescharacteristic
140C22×D61—24no—
141C22×D61—44no—
142C22×D61—44no—
143C22×D61—44no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—24no—
147C2×C4×C61—24no—
148C2×C4×C61—24no—
149C2×C4×C61—22no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—81no—
156C2×C4×C61#12012yes—
157C2×C4×C61C2×D814yes—
158C2×C4×C61C22×D412yes—
159C22⋊D61—44no—
160C22⋊D61—44no—
161C22⋊D61—48no—
162C2×Dic61—24no—
163C2×Dic61—24no—
164C2×Dic61—48no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—44no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—42no—
171C2×Dic61—82no—
172C2×Dic61—82no—
173D244—44no—
174D244—48no—
175D244—82no—
176D244—84no—
177C4×D61—416no—
178Dic122—48no—
179C8×C61—44no—
180C2×#1610—611nomaximal, Sylow
181C22×C61—24no—
182C22×C61—24no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61#44712yes—
188C22×C61#44712yes—
189C22×C61#45612yes—
190C22×C61#45812yes—
191C22×C61C2×#12011yescharacteristic
192C22×C61C22×D811yescharacteristic
193C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
194C2×D61—44no—
195C2×D61—44no—
196C2×D61—44no—
197C2×D61—88no—
198C4×C61—24no—
199C4×C61—22no—
200C4×C61—22no—
201C4×C61—42no—
202Dic61—44no—
203Dic61—44no—
204Dic61—82no—
205C2×#537—611no—
206C2×#480—612no—
207C2×#398—611no—
208#1610—618no—
209C2×#327—612no—
210C2×#324D6111yescharacteristic, complemented
211C2×C61—21no—
212C2×C61—21no—
213C2×C61—22no—
214C2×C61#161014yescomplemented
215C2×C61C2×#44711yescharacteristic
216C2×C61C2×#45611yescharacteristic
217C2×C61C2×#45811yescharacteristic
218D61—84no—
219C22×#41—1221no—
220#537—614no—
221#537—1224no—
222#537—1222no—
223C2×C22⋊Q8—1222no—
224C2×#121—612no—
225C2×#121—1222no—
226C2×#121—1221no—
227C22×C4⋊C4—611no—
228C22×C4⋊C4—1221no—
229C22×C4⋊C4C2×D6111yescharacteristic
230#480—618no—
231#480—1224no—
232C2×#107—1222no—
233C2×#102—1222no—
234C2×C22⋊C8C2×D6112yes—
235#398—614no—
236#398—1222no—
237C2×#95—611no—
238C2×#95—1221no—
239#327—618no—
240#324C2×D6114yescomplemented
241C61C2×#161011yescharacteristic, complemented, Sylow
242C2×#41—1224no—
243C2×#41—1224no—
244C2×#41—2444no—
245C2×#41—2444no—
246C22×Q8—1221no—
247C22×D4—612no—
248C22×D4—1221no—
249C22×D4—1221no—
250C22×D4—1222no—
251C23×C4—1222no—
252C23×C4—1221no—
253C23×C4—1221no—
254C23×C4D24411yescharacteristic
255C23×C4D24411yescharacteristic
256C23×C4C22×D6111yescharacteristic
257C22×C8—22no—
258C22⋊Q8—1228no—
259C22⋊Q8—1228no—
260#121—614no—
261#121—614no—
262#121—1228no—
263#121—1228no—
264#121—1224no—
265#121—1222no—
266#121—1224no—
267#121—1222no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—612no—
271C2×C4⋊C4—612no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1222no—
274C2×C4⋊C4—1222no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1224no—
277C2×C4⋊C4—2444no—
278C2×C4⋊C4D24412yes—
279C2×C4⋊C4C22×D6112yes—
280C2×C22⋊C4—1222no—
281C2×C22⋊C4—1222no—
282#107—1228no—
283#102—1228no—
284C22⋊C8—22no—
285C22⋊C8C22×D6114yes—
286#95—612no—
287#95—1221no—
288#95—1224no—
289C24—1222no—
290C24C2×D24411yescharacteristic
291#41—2448no—
292#41—24416no—
293#41—2448no—
294C2×Q8—1224no—
295C2×Q8—2444no—
296C2×D4—614no—
297C2×D4—1224no—
298C2×D4—1224no—
299C2×D4—1224no—
300C2×D4—1224no—
301C2×D4—1222no—
302C2×D4—4882no—
303C2×D4—2444no—
304C2×D4—2444no—
305C2×D4—2444no—
306C2×D4—2444no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—1228no—
315C22×C4—1224no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—2448no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4D48814yes—
327C22×C4C2×D24412yes—
328C22×C4C2×D24412yes—
329C22×C4C2×D24411yescharacteristic
330C22×C4D4×D6112yes—
331C22×C4D4×D6112yes—
332C22×C4C23×D6111yescharacteristic
333C2×C8—24no—
334C2×C8—44no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—614no—
338C4⋊C4—1224no—
339C4⋊C4—1222no—
340C4⋊C4—1224no—
341C4⋊C4—2442no—
342C4⋊C4—2448no—
343C22⋊C4—1228no—
344C22⋊C4—1224no—
345C22⋊C4—1224no—
346C23—22no—
347C23—22no—
348C23—1224no—
349C23—2444no—
350C23—2444no—
351C23—2444no—
352C23#1451974711yescharacteristic
353C23#1451974711yescharacteristic
354C23C2×D48812yes—
355C23#1451980512yes—
356C23C22×D24411yescharacteristic
357Q8—2448no—
358D4—4882no—
359D4—4884no—
360D4—2444no—
361D4—2448no—
362D4—2444no—
363D4—2444no—
364D4—2448no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—1224no—
378C2×C4—1224no—
379C2×C4—4882no—
380C2×C4—4882no—
381C2×C4—24416no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2442no—
386C2×C4—2448no—
387C2×C4—2442no—
388C2×C4—2444no—
389C2×C4#1451974712yes—
390C2×C4C2×D48814yes—
391C2×C4C2×D4×D6112yes—
392C8—44no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—24no—
398C22—24no—
399C22—4888no—
400C22—2444no—
401C22—2444no—
402C22—2444no—
403C22#1683989812yes—
404C22#1683989812yes—
405C22#1683994712yes—
406C22#1683995312yes—
407C22C2×#1451974711yescharacteristic
408C22C22×D48811yescharacteristic
409C22C2×#1451980511yescharacteristic
410C4—22no—
411C4—22no—
412C4—24no—
413C4—42no—
414C4—4882no—
415C4—2444no—
416C4—2444no—
417C2—21no—
418C2—21no—
419C2—22no—
420C2—4884no—
421C2#2144482414yesdirect product factor
422C2C2×#1683989811yescharacteristic
423C2C2×#1683994711yescharacteristic
424C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC2×#16840343C2
hypercenterC2×#324D61
hypocenterC61C2×#1610
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×#16840076C2semidirect
3. C2×#16839692C2semidirect
4. #21444824C2direct (N × H)
5. C2×#16839497C2semidirect
6. C2×C61×#324C2semidirect
18. #16840076C22semidirect
22. #16839692C22semidirect
25. #16839497C22semidirect
28. C61×#324C22semidirect
210. C2×#324D61semidirect
214. C2×C61#1610semidirect
240. #324C2×D61semidirect
241. C61C2×#1610semidirect
421. C2#21444824direct (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×#168400762
C2×#168396922
#214448242
C2×#168394972
C2×C61×#3242
C2×#161061