Finite Group Databasebeta

← C2×#21444787 #29652184

Subgroups — C2×#21444787 #29652184

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×#16839901C212yesmaximal, complemented
3#21444787C218yesmaximal, direct product factor
4C2×#16839495C212yesmaximal, complemented
5C2×#16839488C211yesmaximal, characteristic, complemented
6C2×C61×#395C211yesmaximal, characteristic, complemented
7C22×#11758222—21no—
8C22×#11758201—22no—
9#16840343—24no—
10#16840343—22no—
11#16840343C2214yes—
12C2×#14519757—22no—
13C2×#14519752—22no—
14C2×#14519751—21no—
15C2×#14519751C2212yes—
16#16839901—24no—
17#16839901C2218yescomplemented
18C2×#14519701—22no—
19C2×C22⋊#92418C2212yes—
20#16839495C2218yescomplemented
21#16839488C2214yescomplemented
22C23×Q8×C61C2211yescharacteristic
23C22×C4⋊C4×C61—21no—
24C22×C4⋊C4×C61C2211yescharacteristic
25C61×#395—22no—
26C61×#395C2214yescomplemented
27C2×#95×C61—21no—
28C2×#95×C61C2211yescharacteristic
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—
38C22×C4×D61—22no—
39C2×#11758201—28no—
40C2×#11758201—48no—
41C22×#92418—22no—
42#14519757—28no—
43#14519757—28no—
44#14519752—28no—
45#14519752—28no—
46#14519751—24no—
47#14519751—24no—
48#14519751—22no—
49#14519751—22no—
50#14519751D414yes—
51#14519751C2314yes—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61D412yes—
54C2×#11758198—22no—
55C2×#11758198—22no—
56#14519701—28no—
57C22⋊#92418—22no—
58C22⋊#92418C2314yes—
59C22×Q8×C61—21no—
60C22×Q8×C61—22no—
61C22×Q8×C61—22no—
62C22×Q8×C61—44no—
63C22×Q8×C61C2312yes—
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61D411yescharacteristic
67C23×C4×C61D411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×C4⋊C4×C61—22no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—24no—
72C2×C4⋊C4×C61—44no—
73C2×C4⋊C4×C61D412yes—
74C2×C4⋊C4×C61C2312yes—
75#95×C61—24no—
76#95×C61—21no—
77#95×C61C2312yes—
78C24×C61C2×D411yescharacteristic
79C23×D61—22no—
80C2×Q8×C61—28no—
81C2×Q8×C61—24no—
82C2×Q8×C61—44no—
83C2×Q8×C61—44no—
84C2×Q8×C61—44no—
85C2×Q8×C61—48no—
86C2×Q8×C61—42no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61—24no—
91C22×C4×C61—24no—
92C22×C4×C61—21no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—21no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—42no—
102C22×C4×C61—42no—
103C22×C4×C61SD1614yescomplemented
104C22×C4×C61C2×D412yes—
105C22×C4×C61C2×D412yes—
106C22×C4×C61C2×D412yes—
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D412yes—
109C22×C4×C61C2411yescharacteristic
110C2×C22⋊D61—24no—
111C2×C22⋊D61—24no—
112C2×C22⋊D61—44no—
113C2×C22⋊D61—44no—
114C22×Dic61—22no—
115#11758222—48no—
116#11758222—416no—
117#11758222—48no—
118C2×D244—24no—
119C2×D244—24no—
120C2×D244—22no—
121C2×D244—44no—
122C2×D244—44no—
123C2×D244—82no—
124C2×D244C2×D414yes—
125C2×C4×D61—28no—
126C2×C4×D61—48no—
127C2×Dic122—24no—
128C2×Dic122—44no—
129C4⋊C4×C61—24no—
130C4⋊C4×C61—24no—
131C4⋊C4×C61—48no—
132#11758201—416no—
133#11758198—28no—
134#11758198—24no—
135#11758198—24no—
136C4⋊Dic61—24no—
137C4⋊Dic61—22no—
138C4⋊Dic61C2×D414yes—
139C2×#92418—24no—
140C2×#92418—44no—
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—
152Q8×C61—28no—
153Q8×C61—44no—
154Q8×C61—48no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—24no—
158C2×C4×C61—24no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—48no—
168C2×C4×C61—42no—
169C2×C4×C61—44no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—44no—
174C2×C4×C61—42no—
175C2×C4×C61—81no—
176C2×C4×C61#12012yes—
177C2×C4×C61C2×SD1614yescomplemented
178C2×C4×C61C22×D412yes—
179C22⋊D61—44no—
180C22⋊D61—44no—
181C22⋊D61—48no—
182C2×Dic61—24no—
183C2×Dic61—44no—
184D244—44no—
185D244—48no—
186D244—82no—
187D244—84no—
188C4×D61—416no—
189Dic122—48no—
190#92418—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—44no—
213C4×C61—42no—
214C4×C61—44no—
215Dic61—44no—
216C2×#537—611no—
217C2×#448—612no—
218C2×#395D6111yescharacteristic, complemented
219#1604—618no—
220C2×#327—612no—
221C2×#324—611no—
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×Q8C2×D6111yescharacteristic
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—21no—
241C22×C4⋊C4C2×D6111yescharacteristic
242#448—618no—
243#448—1224no—
244C2×#103—1222no—
245C2×C22⋊C8—612no—
246#395—22no—
247#395C2×D6114yescomplemented
248C2×#95—21no—
249C2×#95C2×D6111yescharacteristic
250#327—618no—
251#324—614no—
252C61C2×#160411yescharacteristic, complemented, Sylow
253C2×#41—1224no—
254C2×#41—1224no—
255C2×#41—2444no—
256C2×#41—2444no—
257C22×Q8—21no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—44no—
261C22×Q8—1221no—
262C22×Q8C22×D6112yes—
263C22×D4—612no—
264C22×D4—1221no—
265C22×D4—1221no—
266C22×D4—1222no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—1222no—
270C23×C4C22⋊D6111yescharacteristic
271C23×C4C22⋊D6111yescharacteristic
272C23×C4C22×D6111yescharacteristic
273C2×SD16—1228no—
274C2×SD16—2448no—
275C22×C8—1222no—
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—1222no—
285#121—1224no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—612no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4C22⋊D6112yes—
293C2×C4⋊C4C22×D6112yes—
294C2×C22⋊C4—1222no—
295C2×C22⋊C4—1222no—
296#103—1228no—
297C22⋊C8—614no—
298C22⋊C8—1222no—
299#95—24no—
300#95—21no—
301#95C22×D6112yes—
302C24—1222no—
303C24C2×C22⋊D6111yescharacteristic
304#41—2448no—
305#41—24416no—
306#41—2448no—
307C2×Q8—28no—
308C2×Q8—24no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—48no—
313C2×Q8—42no—
314C2×Q8—1224no—
315C2×Q8—2444no—
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—24no—
331C22×C4—24no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—1228no—
344C22×C4—1222no—
345C22×C4—2448no—
346C22×C4#1175820114yescomplemented
347C22×C4D4×D6112yes—
348C22×C4D4×D6112yes—
349C22×C4C2×C22⋊D6112yes—
350C22×C4C2×C22⋊D6112yes—
351C22×C4C2×C22⋊D6111yescharacteristic
352C22×C4C23×D6111yescharacteristic
353SD16—24416no—
354C2×C8—1224no—
355C2×C8—2444no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—48no—
359C4⋊C4—614no—
360C4⋊C4—1224no—
361C4⋊C4—1222no—
362C22⋊C4—1228no—
363C22⋊C4—1224no—
364C22⋊C4—1224no—
365C23—22no—
366C23—22no—
367C23—1224no—
368C23—2444no—
369C23—2444no—
370C23—2444no—
371C23#1451974511yescharacteristic
372C23#1451974511yescharacteristic
373C23C2×#1175820112yes—
374C23#1451980212yes—
375C23C22×C22⋊D6111yescharacteristic
376Q8—28no—
377Q8—44no—
378Q8—48no—
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—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—48no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—81no—
408C2×C4—1224no—
409C2×C4—24416no—
410C2×C4—2444no—
411C2×C4#1451974512yes—
412C2×C4C2×#1175820114yescomplemented
413C2×C4C2×D4×D6112yes—
414C8—2444no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—24no—
421C22—4888no—
422C22—2444no—
423C22—2444no—
424C22—2444no—
425C22#1683991212yes—
426C22#1683991212yes—
427C22#1683994412yes—
428C22#1683994812yes—
429C22C2×#1451974511yescharacteristic
430C22C22×#1175820111yescharacteristic
431C22C2×#1451980211yescharacteristic
432C4—22no—
433C4—22no—
434C4—24no—
435C4—44no—
436C4—44no—
437C4—42no—
438C4—2444no—
439C2—21no—
440C2—21no—
441C2—22no—
442C2—4884no—
443C2#2144478714yesdirect product factor
444C2C2×#1683991211yescharacteristic
445C2C2×#1683994411yescharacteristic
446C2C2×#1683994811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#395C2
socleC23×C61#120
prime radicalC2×#16840343C2
hypercenterC2×#395D61
hypocenterC61C2×#1604
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C2×#16839901C2semidirect
3. #21444787C2direct (N × H)
4. C2×#16839495C2semidirect
5. C2×#16839488C2semidirect
6. C2×C61×#395C2semidirect
17. #16839901C22semidirect
20. #16839495C22semidirect
21. #16839488C22semidirect
26. C61×#395C22semidirect
103. C22×C4×C61SD16semidirect
177. C2×C4×C61C2×SD16semidirect
218. C2×#395D61semidirect
225. C2×C61#1604semidirect
247. #395C2×D61semidirect
252. C61C2×#1604semidirect
346. C22×C4#11758201semidirect
412. C2×C4C2×#11758201semidirect
443. C2#21444787direct (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×#168399012
#214447872
C2×#168394952
C2×#168394882
C2×C61×#3952
C2×#160461