Finite Group Databasebeta

← C2×#20290909 #28320579

Subgroups — C2×#20290909 #28320579

Order 13568.

1126 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811626C211yesmaximal, characteristic
2C2×C4×#11719940C211yesmaximal, characteristic
3#20290909C218yesmaximal, direct product factor
4C2×#16811503C212yesmaximal
5C2×#16811503C212yesmaximal
6C22×#13133207C211yesmaximal, characteristic
7C22×#11719940C2212yes—
8C22×#11719940C2212yes—
9#16811626—22no—
10#16811626C2214yes—
11C2×#13133284—21no—
12C2×C4⋊#88324—21no—
13C4×#11719940—22no—
14C4×#11719940C2214yes—
15C2×#13133272—21no—
16C2×C4×#88324—21no—
17#16811503C2218yes—
18#16811503C2218yes—
19C2×#13133207—21no—
20C2×#13133207—21no—
21C2×#13133207—22no—
22C2×#13133207—21no—
23C2×#13133207—21no—
24C2×#13133207—22no—
25C2×#13133207C414yes—
26C2×#13133207C2214yes—
27C22×C4⋊Dic53C411yescharacteristic
28C22×#11719919C411yescharacteristic
29C22×#11719919C411yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4⋊C4×C53C411yescharacteristic
34C2×#11719940—22no—
35C2×#11719940—24no—
36C2×#11719940—22no—
37C2×#11719940—28no—
38C2×#11719940Q818yes—
39C2×#11719940C2314yes—
40C2×#11719940C2314yes—
41C22×#88324—22no—
42C22×#88324—22no—
43#13133284—24no—
44C4⋊#88324—24no—
45#13133272—24no—
46C4×#88324—24no—
47C23×Dic53C2×C411yescharacteristic
48C23×Dic53C2×C411yescharacteristic
49C23×Dic53C2×C411yescharacteristic
50C23×Dic53C2311yescharacteristic
51#13133207—24no—
52#13133207—24no—
53#13133207—24no—
54#13133207—24no—
55#13133207—24no—
56#13133207—24no—
57#13133207—24no—
58#13133207—24no—
59C2×C4⋊Dic53—21no—
60C2×C4⋊Dic53—21no—
61C2×C4⋊Dic53—22no—
62C2×C4⋊Dic53C2×C414yes—
63C2×#11719919—21no—
64C2×#11719919—21no—
65C2×#11719919—22no—
66C2×#11719919—21no—
67C2×#11719919—21no—
68C2×#11719919—22no—
69C2×#11719919—21no—
70C2×#11719919—21no—
71C2×#11719919—21no—
72C2×#11719919—21no—
73C2×#11719919—21no—
74C2×#11719919—21no—
75C2×#11719919—21no—
76C2×#11719919—21no—
77C2×#11719919C2×C414yes—
78C2×#11719919C2×C414yes—
79C2×#11719919C2×C412yes—
80C2×#11719919C2×C412yes—
81C2×#11719919C2312yes—
82C2×#11719919C2312yes—
83C2×C4×Dic53C2×C412yes—
84C2×C4×Dic53D411yescharacteristic
85C2×C4×Dic53D411yescharacteristic
86C2×C4×Dic53D412yes—
87C2×C4×Dic53D411yescharacteristic
88C2×C4×Dic53D411yescharacteristic
89C2×C4×Dic53D412yes—
90C2×C4×Dic53C2312yes—
91C23×C4×C53C2×C411yescharacteristic
92C23×C4×C53C2×C411yescharacteristic
93C23×C4×C53C2×C411yescharacteristic
94C2×C4⋊C4×C53—21no—
95C2×C4⋊C4×C53—21no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53C2×C414yes—
98C24×C53C22×C411yescharacteristic
99C22×C4×C53—21no—
100C22×C4×C53—21no—
101C22×C4×C53—21no—
102C22×C4×C53—21no—
103C22×C4×C53—42no—
104C22×C4×C53—42no—
105C22×C4×C53—42no—
106C22×C4×C53C22⋊C411yescharacteristic
107C22×C4×C53C22⋊C411yescharacteristic
108C22×C4×C53C22⋊C412yes—
109C22×C4×C53C22×C412yes—
110C22×C4×C53C22×C412yes—
111C22×C4×C53C22×C412yes—
112C22×Dic53—21no—
113C22×Dic53—21no—
114C22×Dic53—21no—
115C22×Dic53—21no—
116C22×Dic53—42no—
117C22×Dic53—42no—
118C22×Dic53—42no—
119C22×Dic53C22⋊C411yescharacteristic
120C22×Dic53C22⋊C411yescharacteristic
121C22×Dic53C22⋊C412yes—
122C22×Dic53C22×C412yes—
123C22×Dic53C22×C412yes—
124C22×Dic53C22×C412yes—
125C22×Dic53C22×C411yescharacteristic
126C22×Dic53C2×D411yescharacteristic
127C22×Dic53C2×D411yescharacteristic
128C22×Dic53C2×D411yescharacteristic
129C22×Dic53C2×D411yescharacteristic
130C22×Dic53C2×Q814yes—
131C22×Dic53#4114yes—
132C22×Dic53C2411yescharacteristic
133#11719940—28no—
134#11719940—24no—
135#11719940—28no—
136#11719940—44no—
137#11719940C2×Q818yes—
138C2×#88324—28no—
139C2×#88324—24no—
140C2×#88324—24no—
141C2×#88324—44no—
142C4⋊C4×C53—24no—
143C4⋊C4×C53—24no—
144C4⋊Dic53—24no—
145C4⋊Dic53—24no—
146#11719919—24no—
147#11719919—24no—
148#11719919—24no—
149#11719919—24no—
150#11719919—22no—
151#11719919—22no—
152#11719919—22no—
153#11719919—22no—
154#11719919—22no—
155#11719919—22no—
156#11719919—22no—
157#11719919—22no—
158C4×Dic53C22⋊C412yes—
159C4×Dic53C22⋊C412yes—
160C4×Dic53C22⋊C412yes—
161C4×Dic53C22⋊C412yes—
162C4×Dic53C2×D412yes—
163C4×Dic53C2×D412yes—
164C4×Dic53C2×D412yes—
165C4×Dic53C2×D412yes—
166C23×C53—22no—
167C23×C53—22no—
168C23×C53C2×C22⋊C411yescharacteristic
169C23×C53C2×C22⋊C411yescharacteristic
170C23×C53C4×Q814yes—
171C23×C53C23×C411yescharacteristic
172C2×C4×C53—22no—
173C2×C4×C53—22no—
174C2×C4×C53—22no—
175C2×C4×C53—22no—
176C2×C4×C53—42no—
177C2×C4×C53—42no—
178C2×C4×C53—42no—
179C2×C4×C53—42no—
180C2×C4×C53—42no—
181C2×C4×C53—42no—
182C2×C4×C53—42no—
183C2×C4×C53—42no—
184C2×C4×C53C2×C22⋊C412yes—
185C2×C4×C53C2×C22⋊C412yes—
186C2×Dic53—22no—
187C2×Dic53—22no—
188C2×Dic53—22no—
189C2×Dic53—22no—
190C2×Dic53—42no—
191C2×Dic53—42no—
192C2×Dic53—42no—
193C2×Dic53—42no—
194C2×Dic53—42no—
195C2×Dic53—42no—
196C2×Dic53—42no—
197C2×Dic53—42no—
198C2×Dic53C2×C22⋊C412yes—
199C2×Dic53C2×C22⋊C412yes—
200C2×Dic53C2×C22⋊C411yescharacteristic
201C2×Dic53C2×C22⋊C411yescharacteristic
202C2×Dic53C4×Q814yes—
203C2×Dic53C22⋊Q814yes—
204C2×Dic53C22⋊Q814yes—
205C2×Dic53#12412yes—
206C2×Dic53#12412yes—
207C2×Dic53C4⋊Q812yes—
208C2×Dic53C4⋊Q812yes—
209C2×Dic53C22×D411yescharacteristic
210C2×Dic53C22×D411yescharacteristic
211C2×Dic53C22×Q812yes—
212C2×Dic53C2×#4112yes—
213#88324—28no—
214#88324—44no—
215C2×#1998—531nomaximal, Sylow
216C22×C53—21no—
217C22×C53—21no—
218C22×C53—21no—
219C22×C53—21no—
220C22×C53—28no—
221C22×C53#39112yes—
222C22×C53#39112yes—
223C22×C53#41312yes—
224C22×C53#41312yes—
225C22×C53C22×C22⋊C411yescharacteristic
226C22×C53C2×C4×Q812yes—
227C4×C53—22no—
228C4×C53—22no—
229C4×C53—42no—
230C4×C53—42no—
231Dic53—22no—
232Dic53—22no—
233Dic53—42no—
234Dic53—42no—
235Dic53#39112yes—
236Dic53#39112yes—
237Dic53C2×C22⋊Q812yes—
238Dic53C2×#12411yescharacteristic
239Dic53C2×C4⋊Q811yescharacteristic
240C22×#125—531no—
241C2×#423—531no—
242C2×C4×M16—531no—
243#1998—538no—
244C2×#343—532no—
245C2×#343—532no—
246C2×C53—22no—
247C2×C53—22no—
248C2×C53#199814yescomplemented
249C2×C53C2×#39111yescharacteristic
250C2×C53C2×#41311yescharacteristic
251C2×C53C2×#41311yescharacteristic
252C22×M16—532no—
253C22×M16—532no—
254C2×#125—534no—
255C2×#125—534no—
256C2×#125—1061no—
257C2×#125—1061no—
258C2×#125—1062no—
259C2×#125—1061no—
260C2×#125—1061no—
261C2×#125—1062no—
262C22×C4⋊C4—531no—
263C22×C4⋊C4—531no—
264C22×C4⋊C4—531no—
265C22×C4⋊C4—531no—
266C22×C4⋊C4—531no—
267C22×C4⋊C4#615711yescharacteristic
268C22×C42—531no—
269#423—534no—
270#423—1062no—
271C2×C4⋊C8—1061no—
272C2×C4⋊C8—1061no—
273C4×M16—534no—
274C4×M16—1062no—
275C2×#97—1061no—
276C2×C4×C8—1061no—
277#343—538no—
278#343—538no—
279C53C2×#199811yescharacteristic, complemented, Sylow
280C23×C4—531no—
281C23×C4—531no—
282C23×C4—531no—
283C23×C4—531no—
284C23×C4C2×#615711yescharacteristic
285C23×C4C2×#615711yescharacteristic
286C23×C4C2×#615711yescharacteristic
287C2×M16—534no—
288C2×M16—538no—
289C2×M16—534no—
290C2×M16—1062no—
291C2×M16—1064no—
292C2×M16—1062no—
293C2×M16—1068no—
294C22×C8—1062no—
295C22×C8—1062no—
296#125—1064no—
297#125—1064no—
298#125—1064no—
299#125—1064no—
300#125—1064no—
301#125—1064no—
302#125—1064no—
303#125—1064no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—532no—
308C2×C4⋊C4—532no—
309C2×C4⋊C4—532no—
310C2×C4⋊C4—532no—
311C2×C4⋊C4—534no—
312C2×C4⋊C4—534no—
313C2×C4⋊C4—534no—
314C2×C4⋊C4—1061no—
315C2×C4⋊C4—1061no—
316C2×C4⋊C4—1061no—
317C2×C4⋊C4—1061no—
318C2×C4⋊C4—1062no—
319C2×C4⋊C4—1061no—
320C2×C4⋊C4—1061no—
321C2×C4⋊C4—1061no—
322C2×C4⋊C4—1061no—
323C2×C4⋊C4—1061no—
324C2×C4⋊C4—1061no—
325C2×C4⋊C4—1062no—
326C2×C4⋊C4—1061no—
327C2×C4⋊C4—1061no—
328C2×C4⋊C4—1062no—
329C2×C4⋊C4—1061no—
330C2×C4⋊C4—1061no—
331C2×C4⋊C4C2×#615714yes—
332C2×C42—531no—
333C2×C42—531no—
334C2×C42—532no—
335C2×C42—531no—
336C2×C42—531no—
337C2×C42—532no—
338C2×C42—532no—
339C2×C42—532no—
340C4⋊C8—1064no—
341C4⋊C8—1064no—
342#97—1064no—
343C4×C8—1064no—
344C24C22×#615711yescharacteristic
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—531no—
353C22×C4—531no—
354C22×C4—531no—
355C22×C4—531no—
356C22×C4—534no—
357C22×C4—534no—
358C22×C4—531no—
359C22×C4—531no—
360C22×C4—531no—
361C22×C4—531no—
362C22×C4—532no—
363C22×C4—532no—
364C22×C4—532no—
365C22×C4—532no—
366C22×C4—1061no—
367C22×C4—1061no—
368C22×C4—1061no—
369C22×C4—1061no—
370C22×C4—2122no—
371C22×C4—2122no—
372C22×C4—2122no—
373C22×C4C22⋊#615711yescharacteristic
374C22×C4C22⋊#615711yescharacteristic
375C22×C4C22⋊#615712yes—
376C22×C4C22×#615712yes—
377C22×C4C22×#615712yes—
378C22×C4C22×#615712yes—
379M16—538no—
380M16—1068no—
381M16—1064no—
382M16—1068no—
383M16—2124no—
384C2×C8—1064no—
385C2×C8—1068no—
386C2×C8—1064no—
387C2×C8—2124no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—1062no—
391C4⋊C4—1062no—
392C4⋊C4—1062no—
393C4⋊C4—1062no—
394C4⋊C4—1062no—
395C4⋊C4—1062no—
396C4⋊C4—1062no—
397C4⋊C4—1062no—
398C4⋊C4—1064no—
399C4⋊C4—1064no—
400C4⋊C4—1064no—
401C4⋊C4—1064no—
402C4⋊C4—1064no—
403C4⋊C4—1064no—
404C42—532no—
405C42—532no—
406C42—532no—
407C42—532no—
408C42—532no—
409C42—532no—
410C42—532no—
411C42—532no—
412C23—22no—
413C23—22no—
414C23C2×C22⋊#615711yescharacteristic
415C23C2×C22⋊#615711yescharacteristic
416C23Q8×#615714yes—
417C23C23×#615711yescharacteristic
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—534no—
431C2×C4—534no—
432C2×C4—532no—
433C2×C4—532no—
434C2×C4—532no—
435C2×C4—532no—
436C2×C4—531no—
437C2×C4—531no—
438C2×C4—531no—
439C2×C4—531no—
440C2×C4—534no—
441C2×C4—532no—
442C2×C4—532no—
443C2×C4—532no—
444C2×C4—532no—
445C2×C4—1062no—
446C2×C4—1062no—
447C2×C4—1062no—
448C2×C4—1062no—
449C2×C4—2122no—
450C2×C4—2122no—
451C2×C4—2122no—
452C2×C4—2122no—
453C2×C4—2122no—
454C2×C4—2122no—
455C2×C4—2122no—
456C2×C4—2122no—
457C2×C4C2×C22⋊#615712yes—
458C2×C4C2×C22⋊#615712yes—
459C8—1068no—
460C8—2124no—
461C22—28no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22(C2×#6157)⋊Q812yes—
467C22(C2×#6157)⋊Q812yes—
468C22#1681160912yes—
469C22#1681161012yes—
470C22C22×C22⋊#615711yescharacteristic
471C22C2×Q8×#615712yes—
472C4—22no—
473C4—22no—
474C4—42no—
475C4—42no—
476C4—532no—
477C4—531no—
478C4—531no—
479C4—532no—
480C4—532no—
481C4—1062no—
482C4—1062no—
483C4—2122no—
484C4—2122no—
485C2—22no—
486C2—22no—
487C2#2029090914yesdirect product factor
488C2C2×(C2×#6157)⋊Q811yescharacteristic
489C2C2×#1681160911yescharacteristic
490C2C2×#1681161011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC23×C53C23×C4
FrattiniC23C23×#6157
FittingC22×C4⋊C4×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC22×Dic53C24
hypercenterC22×C4⋊C4#6157
hypocenterC53C2×#1998
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20290909C2direct (N × H)
248. C2×C53#1998semidirect
279. C53C2×#1998semidirect
487. C2#20290909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168116262
C2×C4×#117199402
#202909092
C2×#168115032
C22×#131332072
C2×#199853