Finite Group Databasebeta

← #27280205

Subgroups — #27280205

Order 13568.

536 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13133224C211yesmaximal, characteristic, complemented
2#20273307C211yesmaximal, characteristic, complemented
3#20273166C211yesmaximal, characteristic, complemented
4#20273154C211yesmaximal, characteristic, complemented
5#20272606C211yesmaximal, characteristic, complemented
6#20272551C211yesmaximal, characteristic, complemented
7C53×#3106C211yesmaximal, characteristic
8C2×#13133224—21no—
9#16810647C2211yescharacteristic
10#16810579—22no—
11#16810579—21no—
12C4×#11719917—21no—
13C4×#11719917C2211yescharacteristic
14C4×#11719917C2211yescharacteristic
15C2×C4×#88322—21no—
16C2×C4×#88322C2211yescharacteristic
17#16810363—22no—
18Q8⋊#88322—21no—
19D4⋊#88322—21no—
20D4⋊#88322—21no—
21D4⋊#88322—21no—
22C53×#532C2211yescharacteristic
23C4×#41×C53C2211yescharacteristic
24C53×#482—21no—
25C53×#477C411yescharacteristic
26C53×#476C411yescharacteristic
27C53×#460C411yescharacteristic
28C53×#459C411yescharacteristic
29C53×#449—21no—
30C4×SD16×C53—21no—
31C4×D8×C53—21no—
32C53×#431C2211yescharacteristic
33#13133224—24no—
34#13133224—24no—
35C2×#11719917—22no—
36C2×#11719917—21no—
37C2×#11719917—21no—
38C2×#11719917—21no—
39C22×#88322—22no—
40C22×#88322—21no—
41C4⋊#88322—21no—
42C4⋊#88322—21no—
43#13133128—22no—
44#13133128—21no—
45#13133128D412yes—
46C4×#88322—22no—
47C4×#88322—21no—
48C4×#88322—21no—
49C4×#88322—21no—
50C4×#88322D411yescharacteristic
51C4×#88322D411yescharacteristic
52C2×#41×C53—21no—
53C2×#41×C53D411yescharacteristic
54C2×SD16×C53—21no—
55C2×D8×C53—21no—
56C4⋊Q8×C53C2×C411yescharacteristic
57#127×C53C2×C411yescharacteristic
58#124×C53—21no—
59#121×C53—21no—
60#121×C53—21no—
61C4×Q8×C53C2×C411yescharacteristic
62C4×Q8×C53D411yescharacteristic
63C4×D4×C53—21no—
64C4×D4×C53—21no—
65C4×D4×C53—21no—
66C4×D4×C53—21no—
67C4×D4×C53C2×C411yescharacteristic
68C4×D4×C53D411yescharacteristic
69#117×C53—21no—
70#117×C53D411yescharacteristic
71C2×C42×C53—21no—
72C2×C42×C53C2311yescharacteristic
73#107×C53—21no—
74#106×C53—21no—
75C4⋊C8×C53C2×C411yescharacteristic
76C4⋊C8×C53C2×C411yescharacteristic
77#103×C53—21no—
78#102×C53—21no—
79#102×C53—21no—
80#102×C53—21no—
81C22⋊C8×C53—21no—
82C4×C8×C53—21no—
83#41×C53—22no—
84#41×C53—22no—
85#41×C53—81no—
86#41×C53—81no—
87C2×Q8×C53—21no—
88C2×Q8×C53C22⋊C411yescharacteristic
89C2×D4×C53—21no—
90C2×D4×C53—21no—
91C2×D4×C53—21no—
92C2×D4×C53—21no—
93C2×D4×C53—41no—
94C2×D4×C53C22⋊C411yescharacteristic
95C22×C4×C53—21no—
96C22×C4×C53—21no—
97C22×C4×C53—21no—
98C22×C4×C53—41no—
99C22×C4×C53C2×D411yescharacteristic
100C22×C4×C53#4111yescharacteristic
101C22×C4×C53#4111yescharacteristic
102SD16×C53—42no—
103D8×C53—42no—
104C2×C8×C53—21no—
105C2×C8×C53—21no—
106C4⋊C4×C53—21no—
107C4⋊C4×C53—21no—
108C4⋊C4×C53—21no—
109C4⋊C4×C53—21no—
110C4⋊C4×C53C22⋊C411yescharacteristic
111C4⋊C4×C53C22⋊C411yescharacteristic
112C22⋊C4×C53—21no—
113C22⋊C4×C53—21no—
114C22⋊C4×C53—21no—
115C22⋊C4×C53—41no—
116C22⋊C4×C53—41no—
117C42×C53—21no—
118C42×C53—21no—
119C42×C53—21no—
120C42×C53C22×C411yescharacteristic
121C42×C53C2×D411yescharacteristic
122C42×C53C2×D411yescharacteristic
123C42×C53C2×D411yescharacteristic
124#11719917—28no—
125#11719917—22no—
126#11719917—22no—
127#11719917—22no—
128#11719917—41no—
129#11719917—81no—
130C2×#88322—28no—
131C2×#88322—22no—
132C2×#88322—22no—
133C2×#88322—21no—
134C2×#88322—22no—
135C2×#88322—21no—
136C2×#88322—41no—
137C2×#88322—41no—
138C23×C53—21no—
139C23×C53—41no—
140C23×C53#12311yescharacteristic
141Q8×C53—21no—
142Q8×C53—81no—
143Q8×C53#10412yes—
144D4×C53—24no—
145D4×C53—21no—
146D4×C53—41no—
147D4×C53—41no—
148D4×C53—41no—
149D4×C53—41no—
150D4×C53—81no—
151D4×C53—82no—
152D4×C53#10412yes—
153C2×C4×C53—24no—
154C2×C4×C53—21no—
155C2×C4×C53—21no—
156C2×C4×C53—21no—
157C2×C4×C53—21no—
158C2×C4×C53—21no—
159C2×C4×C53—21no—
160C2×C4×C53—21no—
161C2×C4×C53—21no—
162C2×C4×C53—21no—
163C2×C4×C53—41no—
164C2×C4×C53—41no—
165C2×C4×C53—41no—
166C2×C4×C53—41no—
167C2×C4×C53—41no—
168C2×C4×C53—81no—
169C2×C4×C53—81no—
170C2×C4×C53C2×C22⋊C411yescharacteristic
171C2×C4×C53C4×D411yescharacteristic
172C2×C4×C53C4×D411yescharacteristic
173C2×C4×C53#12011yescharacteristic
174C2×C4×C53#12111yescharacteristic
175C2×C4×C53#12111yescharacteristic
176C8×C53—41no—
177C8×C53—41no—
178#88322—22no—
179#88322—24no—
180#88322—22no—
181#88322—42no—
182#88322—81no—
183#9211—531nomaximal, Sylow
184C22×C53—21no—
185C22×C53—21no—
186C22×C53—22no—
187C22×C53—21no—
188C22×C53—41no—
189C22×C53—41no—
190C22×C53—81no—
191C22×C53—81no—
192C22×C53—81no—
193C22×C53#38611yescharacteristic
194C4×C53—21no—
195C4×C53—21no—
196C4×C53—22no—
197C4×C53—21no—
198C4×C53—41no—
199C4×C53—41no—
200C4×C53—81no—
201C4×C53C2×#10411yescharacteristic
202C4×C53C2×#10411yescharacteristic
203C4×C53#44311yescharacteristic
204C4×C53#44411yescharacteristic
205C4×C53#47111yescharacteristic
206C4×C53#47211yescharacteristic
207#3106D5311yescharacteristic
208C4×#131—531no—
209#1525—531no—
210#1492—531no—
211#1489—531no—
212#1299—531no—
213#1278—531no—
214C2×C53—41no—
215C2×C53—42no—
216C2×C53—161no—
217C2×C53#187611yescharacteristic
218C2×C53#189611yescharacteristic
219C2×C53#190711yescharacteristic
220C2×#131—1061no—
221#532C2×D5311yescharacteristic
222C4×#41C2×D5311yescharacteristic
223#482—21no—
224#477Dic5311yescharacteristic
225#476Dic5311yescharacteristic
226#460Dic5311yescharacteristic
227#459Dic5311yescharacteristic
228#449—21no—
229C4×SD16—21no—
230C4×D8—21no—
231#431C2×D5311yescharacteristic
232#423—531no—
233#405—1062no—
234#405—1061no—
235C4×M16—531no—
236C4×M16—531no—
237C4×M16—1061no—
238C2×C4×C8—531no—
239C2×C4×C8—1061no—
240#329—1062no—
241Q8⋊C8—1061no—
242D4⋊C8—1061no—
243D4⋊C8—1061no—
244D4⋊C8—1061no—
245C53#921111yescharacteristic, complemented, Sylow
246C2×#41—21no—
247C2×#41C22⋊D5311yescharacteristic
248C2×SD16—21no—
249C2×D8—21no—
250#131—1064no—
251#131—1064no—
252C2×M16—1062no—
253C2×M16—1061no—
254C2×M16—1061no—
255C2×M16—1061no—
256C22×C8—1062no—
257C22×C8—1061no—
258C4⋊Q8C2×Dic5311yescharacteristic
259#127C2×Dic5311yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×Q8C2×Dic5311yescharacteristic
264C4×Q8C22⋊D5311yescharacteristic
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4C2×Dic5311yescharacteristic
270C4×D4C22⋊D5311yescharacteristic
271#117—21no—
272#117C22⋊D5311yescharacteristic
273C2×C42—21no—
274C2×C42C22×D5311yescharacteristic
275#107—21no—
276#106—21no—
277C4⋊C8—1061no—
278C4⋊C8—1061no—
279C4⋊C8C2×Dic5311yescharacteristic
280C4⋊C8C2×Dic5311yescharacteristic
281#103—21no—
282#102—21no—
283#102—21no—
284#102—21no—
285C22⋊C8—21no—
286#97—532no—
287#97—1062no—
288#97—1061no—
289C4×C8—21no—
290C4×C8—531no—
291C4×C8—531no—
292C4×C8—1062no—
293C4×C8—1061no—
294C4×C8—1061no—
295C4×C8—1061no—
296#41—22no—
297#41—22no—
298#41—81no—
299#41—81no—
300C2×Q8—21no—
301C2×Q8C22⋊Dic5311yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4C22⋊Dic5311yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4#1171994711yescharacteristic
313C22×C4#1171994711yescharacteristic
314C22×C4C2×C22⋊D5311yescharacteristic
315SD16—42no—
316D8—42no—
317M16—1068no—
318M16—1062no—
319M16—1062no—
320M16—1062no—
321M16—4241no—
322M16—2121no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—1068no—
326C2×C8—1062no—
327C2×C8—1062no—
328C2×C8—1061no—
329C2×C8—1061no—
330C2×C8—1062no—
331C2×C8—2121no—
332C2×C8—2121no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4C22⋊Dic5311yescharacteristic
338C4⋊C4C22⋊Dic5311yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42D4×D5311yescharacteristic
348C42D4×D5311yescharacteristic
349C42C22×Dic5311yescharacteristic
350C42C2×C22⋊D5311yescharacteristic
351C23—21no—
352C23—41no—
353C23#1313319811yescharacteristic
354Q8—21no—
355Q8—81no—
356Q8#1313314412yes—
357D4—24no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—82no—
365D4#1313314412yes—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×C22⋊Dic5311yescharacteristic
384C2×C4D4×Dic5311yescharacteristic
385C2×C4D4×Dic5311yescharacteristic
386C2×C4#1313318511yescharacteristic
387C2×C4#1313318911yescharacteristic
388C2×C4#1313318911yescharacteristic
389C8—41no—
390C8—41no—
391C8—1062no—
392C8—1062no—
393C8—1064no—
394C8—4241no—
395C8—2122no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1681050311yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4C2×#1313314411yescharacteristic
414C4C2×#1313314411yescharacteristic
415C4#1681074011yescharacteristic
416C4#1681074511yescharacteristic
417C4#1681088411yescharacteristic
418C4#1681089111yescharacteristic
419C2—41no—
420C2—42no—
421C2—161no—
422C2#2027504411yescharacteristic
423C2#2027515911yescharacteristic
424C2#2027522511yescharacteristic
subgroupG/H
centerC2×C4#13133189
commutatorC42×C53C22×C4
FrattiniC2×C42C22×D53
Fitting, prime radicalC53×#3106C2
socleC22×C53#386
cosocleC2×C42×C53C23
hypercenter#3106D53
hypocenterC53#9211
LCSG ▷ C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. C4×#13133224C2semidirect
2. #20273307C2semidirect
3. #20273166C2semidirect
4. #20273154C2semidirect
5. #20272606C2semidirect
6. #20272551C2semidirect
245. C53#9211semidirect

Maximal subgroups

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

subgroupindex
C4×#131332242
#202733072
#202731662
#202731542
#202726062
#202725512
C53×#31062
#921153