Finite Group Databasebeta

← C2×#20290178 #28315519

Subgroups — C2×#20290178 #28315519

Order 13568.

1050 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811646C211yesmaximal, characteristic
2C2×C4×#11719936C211yesmaximal, characteristic
3#20290178C218yesmaximal, direct product factor
4C2×#16811480C212yesmaximal, complemented
5C2×#16811480C212yesmaximal, complemented
6C2×#125×D53C211yesmaximal, characteristic
7C22×#11719936—21no—
8#16811646—22no—
9#16811646C2214yes—
10C2×#13133284—21no—
11C2×#13133274—21no—
12C4×#11719936—22no—
13C4×#11719936C2214yes—
14C2×#13133272C2212yes—
15C2×#13133272C2212yes—
16C2×C4×#88324—21no—
17#16811480C2218yescomplemented
18#16811480C2218yescomplemented
19C2×#13133209C411yescharacteristic
20C2×#13133208C2211yescharacteristic
21C2×#13133208C2211yescharacteristic
22C2×#13133207—21no—
23C2×#13133207—21no—
24#125×D53—22no—
25#125×D53—22no—
26#125×D53C414yes—
27#125×D53C2214yes—
28C2×C4⋊C4×D53—21no—
29C2×C4⋊C4×D53—21no—
30C2×C4⋊C4×D53C411yescharacteristic
31C2×C4⋊C4×D53C411yescharacteristic
32C2×C42×D53C2211yescharacteristic
33C2×#125×C53C411yescharacteristic
34C2×#11719936—28no—
35C2×#11719936—24no—
36C22×#88324—22no—
37C22×#88324—22no—
38#13133284—24no—
39#13133274—24no—
40#13133272—22no—
41#13133272—22no—
42#13133272C2314yes—
43#13133272C2314yes—
44C4×#88324—24no—
45C22×C4×D53—21no—
46C22×C4×D53—21no—
47C22×C4×D53C2×C411yescharacteristic
48C22×C4×D53D411yescharacteristic
49C22×C4×D53D411yescharacteristic
50#13133209—22no—
51#13133209C2×C414yes—
52#13133208—21no—
53#13133208—21no—
54#13133208—21no—
55#13133208—21no—
56#13133208C2×C412yes—
57#13133208C2×C412yes—
58#13133208C2312yes—
59#13133208C2312yes—
60#13133207—24no—
61#13133207—24no—
62#13133207—24no—
63#13133207—24no—
64C2×C4⋊Dic53—21no—
65C2×C4⋊Dic53—21no—
66C2×C4⋊Dic53C2×C411yescharacteristic
67C2×C4⋊Dic53C2×C411yescharacteristic
68C2×#11719919—21no—
69C2×#11719919—21no—
70C2×#11719919—21no—
71C2×#11719919—21no—
72C2×#11719919—21no—
73C2×#11719919—21no—
74C4⋊C4×D53—24no—
75C4⋊C4×D53—24no—
76C4⋊C4×D53—22no—
77C4⋊C4×D53—22no—
78C4⋊C4×D53—24no—
79C4⋊C4×D53—24no—
80C4⋊C4×D53C2×C414yes—
81C4⋊C4×D53C2×C414yes—
82C2×C4×Dic53D411yescharacteristic
83C2×C4×Dic53D411yescharacteristic
84C2×C4×Dic53C2311yescharacteristic
85C42×D53C2×C412yes—
86C42×D53D412yes—
87C42×D53D412yes—
88C42×D53C2312yes—
89#125×C53—22no—
90#125×C53C2×C414yes—
91C2×C4⋊C4×C53—21no—
92C2×C4⋊C4×C53—21no—
93C2×C4⋊C4×C53C2×C411yescharacteristic
94C2×C4⋊C4×C53C2×C411yescharacteristic
95C2×C42×C53C2×C411yescharacteristic
96C23×D53C22⋊C411yescharacteristic
97C22×C4×C53—21no—
98C22×C4×C53—21no—
99C22×C4×C53C22⋊C411yescharacteristic
100C22×C4×C53C22⋊C411yescharacteristic
101C22×C4×C53C22×C411yescharacteristic
102C22×Dic53—21no—
103C22×Dic53—21no—
104C22×Dic53C22⋊C411yescharacteristic
105C22×Dic53C2×D411yescharacteristic
106C22×Dic53C2×D411yescharacteristic
107C2×C4×D53—24no—
108C2×C4×D53—24no—
109C2×C4×D53—24no—
110C2×C4×D53—24no—
111C2×C4×D53—42no—
112C2×C4×D53—44no—
113C2×C4×D53—44no—
114C2×C4×D53C22⋊C412yes—
115C2×C4×D53C22⋊C412yes—
116C2×C4×D53C22⋊C412yes—
117C2×C4×D53C22×C412yes—
118C2×C4×D53C2×D412yes—
119C2×C4×D53C2×D412yes—
120C2×#88324—28no—
121C2×#88324—24no—
122C2×#88324—24no—
123C2×#88324—44no—
124#11719936—216no—
125C4⋊C4×C53—24no—
126C4⋊C4×C53—24no—
127C4⋊C4×C53—21no—
128C4⋊C4×C53—21no—
129C4⋊C4×C53C22×C412yes—
130C4⋊C4×C53C22×C412yes—
131C42×C53C22⋊C412yes—
132C42×C53C22×C412yes—
133C4⋊Dic53—21no—
134C4⋊Dic53—21no—
135C4⋊Dic53—22no—
136C4⋊Dic53—22no—
137C4⋊Dic53—22no—
138C4⋊Dic53—22no—
139C4⋊Dic53C22×C412yes—
140C4⋊Dic53C22×C412yes—
141#11719919—24no—
142#11719919—24no—
143#11719919—22no—
144#11719919—22no—
145#11719919—24no—
146#11719919—24no—
147#11719919—22no—
148#11719919—22no—
149C4×Dic53C22⋊C412yes—
150C4×Dic53C22⋊C412yes—
151C4×Dic53C22×C411yescharacteristic
152C4×Dic53C2×D411yescharacteristic
153C4×Dic53C2×D411yescharacteristic
154C4×Dic53C2×D412yes—
155C4×Dic53C2×D412yes—
156C4×Dic53C2411yescharacteristic
157C23×C53C2×C22⋊C411yescharacteristic
158C22×D53—22no—
159C22×D53—22no—
160C22×D53#10414yes—
161C22×D53C2×C22⋊C412yes—
162C2×C4×C53—22no—
163C2×C4×C53—22no—
164C2×C4×C53—22no—
165C2×C4×C53—22no—
166C2×C4×C53—22no—
167C2×C4×C53—42no—
168C2×C4×C53—42no—
169C2×C4×C53C2×C22⋊C411yescharacteristic
170C2×C4×C53C2×C22⋊C412yes—
171C2×C4×C53C2×C22⋊C412yes—
172C2×C4×C53C23×C411yescharacteristic
173C2×Dic53—22no—
174C2×Dic53—22no—
175C2×Dic53—22no—
176C2×Dic53—22no—
177C2×Dic53—42no—
178C2×Dic53—42no—
179C2×Dic53#10114yes—
180C2×Dic53C2×C22⋊C411yescharacteristic
181C2×Dic53C2×C22⋊C411yescharacteristic
182C2×Dic53C2×C22⋊C412yes—
183C2×Dic53C22×D411yescharacteristic
184C2×Dic53C22×D411yescharacteristic
185C4×D53—24no—
186C4×D53—24no—
187C4×D53—24no—
188C4×D53—24no—
189C4×D53—42no—
190C4×D53—42no—
191C4×D53—48no—
192C4×D53—48no—
193#88324—28no—
194#88324—44no—
195C2×#1528—531nomaximal, Sylow
196C22×C53C2×#10112yes—
197C22×C53C2×#10412yes—
198C22×C53#42112yes—
199C22×C53C22×C22⋊C411yescharacteristic
200C2×D53—22no—
201C2×D53—22no—
202C2×D53—28no—
203C2×D53C2×#10414yes—
204C4×C53—21no—
205C4×C53—21no—
206C4×C53—22no—
207C4×C53—22no—
208C4×C53—42no—
209C4×C53—42no—
210Dic53—21no—
211Dic53—21no—
212Dic53—21no—
213Dic53—21no—
214Dic53—42no—
215Dic53—42no—
216Dic53C2×#10114yes—
217C22×#125—531no—
218C2×#432—531no—
219C2×C4×M16—531no—
220#1528—538no—
221C2×#330—532no—
222C2×#330—532no—
223C2×C53#152814yescomplemented
224C2×C53C22×#10111yescharacteristic
225C2×C53C22×#10411yescharacteristic
226C2×C53C2×#42111yescharacteristic
227D53—24no—
228C22×M16—1061no—
229C2×#125—534no—
230C2×#125—534no—
231C2×#125—531no—
232C2×#125—531no—
233C2×#125—531no—
234C2×#125—1061no—
235C2×#125—1061no—
236C2×#125—1062no—
237C2×#125—1062no—
238C2×#125#615711yescharacteristic
239C22×C4⋊C4—531no—
240C22×C4⋊C4—531no—
241C22×C4⋊C4—1061no—
242C22×C4⋊C4—1061no—
243C22×C42—531no—
244#432—534no—
245#432—1062no—
246C2×C4⋊C8—1061no—
247C2×C22⋊C8—1061no—
248C4×M16—534no—
249C4×M16—1062no—
250C2×#97—532no—
251C2×#97—532no—
252C2×C4×C8—1061no—
253#330—538no—
254#330—538no—
255C53C2×#152811yescharacteristic, complemented, Sylow
256C23×C4—531no—
257C23×C4—531no—
258C23×C4—531no—
259C23×C4—1061no—
260C23×C4—1061no—
261C2×M16—1064no—
262C2×M16—1068no—
263C22×C8—1062no—
264C22×C8—1062no—
265#125—22no—
266#125—532no—
267#125—532no—
268#125—532no—
269#125—532no—
270#125—534no—
271#125—1064no—
272#125—1064no—
273#125—1064no—
274#125—1064no—
275#125—1061no—
276#125—1061no—
277#125—1061no—
278#125—1061no—
279#125—1062no—
280#125C2×#615714yes—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—531no—
284C2×C4⋊C4—531no—
285C2×C4⋊C4—534no—
286C2×C4⋊C4—534no—
287C2×C4⋊C4—1062no—
288C2×C4⋊C4—1062no—
289C2×C4⋊C4—1064no—
290C2×C4⋊C4—1064no—
291C2×C4⋊C4—1064no—
292C2×C4⋊C4—1064no—
293C2×C4⋊C4—1061no—
294C2×C4⋊C4—1061no—
295C2×C4⋊C4—1061no—
296C2×C4⋊C4—1061no—
297C2×C4⋊C4—1061no—
298C2×C4⋊C4—1061no—
299C2×C4⋊C4—1061no—
300C2×C4⋊C4—1061no—
301C2×C4⋊C4C2×#615711yescharacteristic
302C2×C4⋊C4C2×#615711yescharacteristic
303C2×C42—531no—
304C2×C42—531no—
305C2×C42—531no—
306C2×C42—532no—
307C2×C42—532no—
308C2×C42—532no—
309C2×C42—532no—
310C2×C42C2×#615711yescharacteristic
311C4⋊C8—1064no—
312C22⋊C8—1064no—
313#97—534no—
314#97—534no—
315#97—1062no—
316#97—1062no—
317C4×C8—1064no—
318C24—531no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—531no—
322C22×C4—531no—
323C22×C4—531no—
324C22×C4—532no—
325C22×C4—532no—
326C22×C4—532no—
327C22×C4—532no—
328C22×C4—532no—
329C22×C4—532no—
330C22×C4—1064no—
331C22×C4—1064no—
332C22×C4—1064no—
333C22×C4—1064no—
334C22×C4—1061no—
335C22×C4—1061no—
336C22×C4—2122no—
337C22×C4—2124no—
338C22×C4—2124no—
339C22×C4C22⋊#615711yescharacteristic
340C22×C4C22⋊#615711yescharacteristic
341C22×C4C22×#615711yescharacteristic
342M16—10616no—
343C2×C8—1064no—
344C2×C8—1068no—
345C2×C8—1064no—
346C2×C8—2124no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—532no—
352C4⋊C4—532no—
353C4⋊C4—1064no—
354C4⋊C4—1064no—
355C4⋊C4—1062no—
356C4⋊C4—1062no—
357C4⋊C4—1062no—
358C4⋊C4—1062no—
359C4⋊C4—1062no—
360C4⋊C4—1062no—
361C4⋊C4—1062no—
362C4⋊C4—1062no—
363C4⋊C4—1061no—
364C4⋊C4—1061no—
365C4⋊C4—1064no—
366C4⋊C4—1064no—
367C4⋊C4C22×#615712yes—
368C4⋊C4C22×#615712yes—
369C42—532no—
370C42—531no—
371C42—531no—
372C42—532no—
373C42—532no—
374C42—532no—
375C42—531no—
376C42—531no—
377C42C22⋊#615712yes—
378C42C22×#615712yes—
379C23—534no—
380C23—532no—
381C23—1062no—
382C23—1062no—
383C23C2×C22⋊#615711yescharacteristic
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—534no—
392C2×C4—532no—
393C2×C4—531no—
394C2×C4—531no—
395C2×C4—531no—
396C2×C4—531no—
397C2×C4—1064no—
398C2×C4—1064no—
399C2×C4—1064no—
400C2×C4—1064no—
401C2×C4—1062no—
402C2×C4—1062no—
403C2×C4—1062no—
404C2×C4—1062no—
405C2×C4—2122no—
406C2×C4—2122no—
407C2×C4—2128no—
408C2×C4—2128no—
409C2×C4—2122no—
410C2×C4—2122no—
411C2×C4C2×C22⋊#615711yescharacteristic
412C2×C4C2×C22⋊#615712yes—
413C2×C4C2×C22⋊#615712yes—
414C2×C4C23×#615711yescharacteristic
415C8—1068no—
416C8—2124no—
417C22—534no—
418C22—1062no—
419C22—1068no—
420C22—1062no—
421C22D53⋊#10112yes—
422C22D53⋊#10412yes—
423C22#1681162012yes—
424C22C22×C22⋊#615711yescharacteristic
425C4—22no—
426C4—22no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—534no—
432C4—1061no—
433C4—1061no—
434C4—1061no—
435C4—1061no—
436C4—2122no—
437C4—2122no—
438C2—1064no—
439C2#2029017814yesdirect product factor
440C2C2×D53⋊#10111yescharacteristic
441C2C2×D53⋊#10411yescharacteristic
442C2C2×#1681162011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×#125×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC4×Dic53C24
hypercenterC2×#125#6157
hypocenterC53C2×#1528
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #20290178C2direct (N × H)
4. C2×#16811480C2semidirect
5. C2×#16811480C2semidirect
17. #16811480C22semidirect
18. #16811480C22semidirect
223. C2×C53#1528semidirect
255. C53C2×#1528semidirect
439. C2#20290178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168116462
C2×C4×#117199362
#202901782
C2×#168114802
C2×#125×D532
C2×#152853