Finite Group Databasebeta

← #27280408

Subgroups — #27280408

Order 13568.

452 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283373C211yesmaximal, characteristic
2#20274814C211yesmaximal, characteristic
3#20273235C211yesmaximal, characteristic
4#20273079C211yesmaximal, characteristic
5#20272592C211yesmaximal, characteristic
6#20272562C211yesmaximal, characteristic
7C2×C53×#485C211yesmaximal, characteristic
8#16810684—22no—
9#16810680—21no—
10#16810676—21no—
11#16810650—21no—
12#16810587C2211yescharacteristic
13#16810587C2211yescharacteristic
14C2×C22⋊#88322C2211yescharacteristic
15#16810579—21no—
16C4×C22⋊Dic53C2211yescharacteristic
17#16810382—21no—
18#16810382—21no—
19#16810360—22no—
20#16810349—21no—
21#16810349—21no—
22C2×C22⋊Q8×C53C2211yescharacteristic
23C2×#117×C53C2211yescharacteristic
24C53×#485—21no—
25C53×#485—21no—
26C53×#485—21no—
27C53×#485—21no—
28C2×#107×C53C411yescharacteristic, complemented
29C2×#106×C53C411yescharacteristic, complemented
30C2×#103×C53C411yescharacteristic, complemented
31C2×#103×C53C411yescharacteristic, complemented
32C2×C22⋊C8×C53C2211yescharacteristic
33C2×#11719917—21no—
34C2×#11719917—21no—
35C22×#88322—21no—
36C2×C22⋊Dic53—21no—
37C2×C4×Dic53—21no—
38C4⋊#88322—22no—
39C4⋊#88322—22no—
40C22⋊#88322—21no—
41C22⋊#88322—21no—
42C22⋊#88322—21no—
43C22⋊#88322—21no—
44C22⋊#88322D411yescharacteristic
45C22⋊#88322D411yescharacteristic
46C22⋊#88322D412yes—
47#13133128—22no—
48C4×#88322—22no—
49#13133124—21no—
50C22×Q8×C53C2×C411yescharacteristic
51C23×C4×C53C2311yescharacteristic
52C22×C8×C53C2×C411yescharacteristic
53C22×C8×C53C2×C411yescharacteristic
54C22⋊Q8×C53—21no—
55C22⋊Q8×C53—21no—
56C22⋊Q8×C53—21no—
57C22⋊Q8×C53—21no—
58#117×C53—21no—
59#117×C53—21no—
60#117×C53D411yescharacteristic
61#117×C53D411yescharacteristic
62#117×C53D411yescharacteristic
63#117×C53D411yescharacteristic
64C2×C4⋊C4×C53—21no—
65C2×C4⋊C4×C53C2×C411yescharacteristic
66C2×C4⋊C4×C53C2×C411yescharacteristic
67C2×C4⋊C4×C53C2×C411yescharacteristic
68C2×C22⋊C4×C53—21no—
69C2×C22⋊C4×C53—21no—
70C2×C42×C53—21no—
71#107×C53—21no—
72#107×C53—21no—
73#106×C53—21no—
74#106×C53—21no—
75#103×C53—21no—
76#103×C53—21no—
77#103×C53—21no—
78#103×C53—21no—
79C22⋊C8×C53—21no—
80C22⋊C8×C53—21no—
81C24×C53#4111yescharacteristic
82C2×Q8×C53—21no—
83C2×Q8×C53—21no—
84C2×Q8×C53—41no—
85C2×Q8×C53—41no—
86C22×C4×C53—21no—
87C22×C4×C53—21no—
88C22×C4×C53—21no—
89C22×C4×C53—21no—
90C22×C4×C53—41no—
91C22×C4×C53—41no—
92C22×C4×C53C22×C411yescharacteristic
93C22×C4×C53C2×D411yescharacteristic
94C22×C4×C53C2×D411yescharacteristic
95C22×C4×C53C2×D411yescharacteristic
96C22×C4×C53C2×D411yescharacteristic
97C22×C4×C53#4111yescharacteristic
98C22×Dic53—41no—
99C2×C8×C53—21no—
100C2×C8×C53—21no—
101C2×C8×C53—41no—
102C2×C8×C53—41no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C4⋊C4×C53—21no—
106C4⋊C4×C53—21no—
107C4⋊C4×C53—41no—
108C4⋊C4×C53—41no—
109C4⋊C4×C53C22⋊C411yescharacteristic
110C4⋊C4×C53C22⋊C411yescharacteristic
111C4⋊C4×C53C22⋊C411yescharacteristic
112C4⋊C4×C53C22⋊C411yescharacteristic
113C22⋊C4×C53—21no—
114C22⋊C4×C53—21no—
115C22⋊C4×C53—21no—
116C22⋊C4×C53—21no—
117C22⋊C4×C53—41no—
118C22⋊C4×C53—41no—
119C42×C53—21no—
120C42×C53—21no—
121C42×C53—21no—
122C42×C53—21no—
123C22⋊Dic53—22no—
124C22⋊Dic53—41no—
125C4×Dic53—41no—
126C4×Dic53—41no—
127#11719917—41no—
128#11719917—41no—
129#11719917—41no—
130#11719917—41no—
131C2×#88322—21no—
132C2×#88322—22no—
133C2×#88322—21no—
134C2×#88322—41no—
135C2×#88322—41no—
136C2×#88322—41no—
137C23×C53—21no—
138C23×C53—21no—
139C23×C53—41no—
140C23×C53—41no—
141C23×C53C4×D411yescharacteristic
142C23×C53#12111yescharacteristic
143C23×C53#12311yescharacteristic
144Q8×C53—41no—
145Q8×C53—41no—
146Q8×C53—81no—
147C2×C4×C53—21no—
148C2×C4×C53—21no—
149C2×C4×C53—21no—
150C2×C4×C53—21no—
151C2×C4×C53—21no—
152C2×C4×C53—21no—
153C2×C4×C53—21no—
154C2×C4×C53—21no—
155C2×C4×C53—21no—
156C2×C4×C53—21no—
157C2×C4×C53—41no—
158C2×C4×C53—41no—
159C2×C4×C53—41no—
160C2×C4×C53—41no—
161C2×C4×C53—41no—
162C2×C4×C53—41no—
163C2×C4×C53—41no—
164C2×C4×C53—41no—
165C2×C4×C53—41no—
166C2×C4×C53—81no—
167C2×C4×C53—81no—
168C2×C4×C53C2×C22⋊C411yescharacteristic
169C2×C4×C53C4×D411yescharacteristic
170C2×C4×C53#12011yescharacteristic
171C2×C4×C53#12111yescharacteristic
172C2×Dic53—42no—
173C2×Dic53—81no—
174C2×Dic53—81no—
175C8×C53—41no—
176C8×C53—41no—
177#88322—41no—
178#88322—41no—
179#88322—42no—
180#88322—81no—
181#9240—531nomaximal, Sylow
182C22×C53—21no—
183C22×C53—21no—
184C22×C53—21no—
185C22×C53—21no—
186C22×C53—21no—
187C22×C53—21no—
188C22×C53—21no—
189C22×C53—21no—
190C22×C53—81no—
191C22×C53—81no—
192C22×C53#38611yescharacteristic
193C22×C53#44311yescharacteristic
194C22×C53#44411yescharacteristic
195C4×C53—21no—
196C4×C53—21no—
197C4×C53—21no—
198C4×C53—41no—
199C4×C53—41no—
200C4×C53—41no—
201C4×C53—41no—
202C4×C53—81no—
203C4×C53—81no—
204C4×C53#41011yescharacteristic
205C4×C53#41011yescharacteristic
206Dic53—82no—
207C2×#485D5311yescharacteristic
208#2924—531no—
209#1826—531no—
210#1508—531no—
211#1472—531no—
212#1293—531no—
213#1282—531no—
214C2×C53—21no—
215C2×C53—21no—
216C2×C53—41no—
217C2×C53—41no—
218C2×C53#187611yescharacteristic
219C2×C53#189911yescharacteristic
220C2×C53#190211yescharacteristic
221C2×C22⋊Q8C2×D5311yescharacteristic
222C2×#117C2×D5311yescharacteristic
223#485—21no—
224#485—21no—
225#485—21no—
226#485—21no—
227#433—1062no—
228#432—1061no—
229#431—1061no—
230C2×#107Dic5311yescharacteristic, complemented
231C2×#106Dic5311yescharacteristic, complemented
232#424—1061no—
233C2×#103Dic5311yescharacteristic, complemented
234C2×#103Dic5311yescharacteristic, complemented
235#407—531no—
236#407—531no—
237C2×C22⋊C8—531no—
238C2×C22⋊C8C2×D5311yescharacteristic
239#405—1061no—
240C4×C22⋊C4—531no—
241#339—1061no—
242#339—1061no—
243#328—1062no—
244#324—1061no—
245#324—1061no—
246C53#924011yescharacteristic, complemented, Sylow
247C22×Q8C2×Dic5311yescharacteristic
248C23×C4C22×D5311yescharacteristic
249C2×M16—1061no—
250C2×M16—1061no—
251C22×C8—1061no—
252C22×C8C2×Dic5311yescharacteristic
253C22×C8C2×Dic5311yescharacteristic
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117C22⋊D5311yescharacteristic
261#117C22⋊D5311yescharacteristic
262#117C22⋊D5311yescharacteristic
263#117C22⋊D5311yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×Dic5311yescharacteristic
266C2×C4⋊C4C2×Dic5311yescharacteristic
267C2×C4⋊C4C2×Dic5311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—1061no—
271C2×C42—21no—
272C2×C42—1061no—
273#107—21no—
274#107—21no—
275#106—21no—
276#106—21no—
277C4⋊C8—1062no—
278C4⋊C8—1062no—
279#103—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—531no—
286C22⋊C8—531no—
287C22⋊C8—532no—
288C22⋊C8—1061no—
289C22⋊C8—1061no—
290C22⋊C8—1061no—
291C22⋊C8—1061no—
292#97—1062no—
293C4×C8—1062no—
294#95—1061no—
295C24#1171994711yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—2121no—
307C22×C4D4×D5311yescharacteristic
308C22×C4D4×D5311yescharacteristic
309C22×C4#1171994711yescharacteristic
310C22×C4C22×Dic5311yescharacteristic
311C22×C4C2×C22⋊D5311yescharacteristic
312C22×C4C2×C22⋊D5311yescharacteristic
313M16—2121no—
314M16—2121no—
315M16—2121no—
316M16—2121no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—1061no—
322C2×C8—1062no—
323C2×C8—1061no—
324C2×C8—2121no—
325C2×C8—2121no—
326C2×C8—2121no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊Dic5311yescharacteristic
334C4⋊C4C22⋊Dic5311yescharacteristic
335C4⋊C4C22⋊Dic5311yescharacteristic
336C4⋊C4C22⋊Dic5311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—1062no—
344C22⋊C4—2121no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—2121no—
350C42—2121no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic5311yescharacteristic
356C23#1313318911yescharacteristic
357C23#1313319811yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—4241no—
383C2×C4—4241no—
384C2×C4—2122no—
385C2×C4C2×C22⋊Dic5311yescharacteristic
386C2×C4D4×Dic5311yescharacteristic
387C2×C4#1313318511yescharacteristic
388C2×C4#1313318911yescharacteristic
389C8—41no—
390C8—41no—
391C8—4241no—
392C8—2121no—
393C8—2121no—
394C8—2122no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1681050311yescharacteristic
406C22#1681074011yescharacteristic
407C22#1681074511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—4242no—
418C4#1681059711yescharacteristic
419C4#1681059711yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#2027504411yescharacteristic
425C2#2027517411yescharacteristic
426C2#2027519011yescharacteristic
subgroupG/H
centerC22#16810503
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
FittingC2×C53×#485C2
socleC22×C53#386
prime radicalC24×C53#41
cosocleC23×C4×C53C23
hypercenterC2×#485D53
hypocenterC53#9240
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
28. C2×#107×C53C4semidirect
29. C2×#106×C53C4semidirect
30. C2×#103×C53C4semidirect
31. C2×#103×C53C4semidirect
230. C2×#107Dic53semidirect
231. C2×#106Dic53semidirect
233. C2×#103Dic53semidirect
234. C2×#103Dic53semidirect
246. C53#9240semidirect

Maximal subgroups

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

subgroupindex
#202833732
#202748142
#202732352
#202730792
#202725922
#202725622
C2×C53×#4852
#924053