Finite Group Databasebeta

← #28484933

Subgroups — #28484933

Order 15104.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837602C211yesmaximal, characteristic
2#21424902C211yesmaximal, characteristic
3#21424101C211yesmaximal, characteristic, complemented
4C2×#16837145C211yesmaximal, characteristic
5#21421980C211yesmaximal, characteristic, complemented
6#21421931C211yesmaximal, characteristic, complemented
7C2×C59×#446C211yesmaximal, characteristic, complemented
8C22×#11745671—21no—
9C2×#14273724C2211yescharacteristic
10#16837602—22no—
11#16837602C414yescomplemented
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273651—21no—
15C2×#14273649—21no—
16C2×#14273649—21no—
17C2×#14273647—21no—
18#16837272C2211yescharacteristic
19#16837164—21no—
20#16837145—22no—
21C2×C4×Q8×C59C2211yescharacteristic
22C59×#446—22no—
23C59×#446—22no—
24C2×C4⋊C8×C59—21no—
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×#97×C59—21no—
27C2×C4×C8×C59C2211yescharacteristic
28C22×D236—21no—
29C22×D236—21no—
30C22×D236—21no—
31C2×#11745671—24no—
32C2×#11745671—42no—
33C2×#11745671—42no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36#14273724—21no—
37#14273724—21no—
38#14273724—21no—
39#14273724C2×C412yes—
40C2×C4⋊Dic59—21no—
41C2×C4⋊Dic59—21no—
42C2×C4⋊Dic59—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)C2×C412yes—
47#14273651—42no—
48#14273649—42no—
49#14273649—42no—
50#14273647—24no—
51C22×Q8×C59D411yescharacteristic
52C22×C8×C59—21no—
53C22×C8×C59D411yescharacteristic
54C22×C8×C59D411yescharacteristic
55C4×Q8×C59—21no—
56C4×Q8×C59—21no—
57C4×Q8×C59C2×C412yes—
58C4×Q8×C59D412yes—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59D411yescharacteristic
61C2×C42×C59—21no—
62C2×C42×C59C2311yescharacteristic
63C4⋊C8×C59—24no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59D412yes—
66#97×C59—24no—
67C4×C8×C59—21no—
68C4×C8×C59—21no—
69C23×D59—41no—
70C2×Q8×C59—21no—
71C2×Q8×C59—21no—
72C2×Q8×C59—21no—
73C2×Q8×C59—21no—
74C2×Q8×C59—21no—
75C2×Q8×C59C22⋊C412yes—
76C22×C4×C59—21no—
77C22×C4×C59—21no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C22×Dic59—41no—
82C2×D236—22no—
83C2×D236—22no—
84C2×D236—22no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—41no—
94C2×D236—41no—
95C2×D236—41no—
96C2×D236—81no—
97C2×D236—81no—
98C2×C8×C59—21no—
99C2×C8×C59—21no—
100C2×C8×C59—21no—
101C2×C8×C59—22no—
102C2×C8×C59—21no—
103C2×C8×C59—21no—
104C2×C8×C59—41no—
105C2×C8×C59—41no—
106C2×C8×C59SD1612yescomplemented
107C4⋊C4×C59—22no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—22no—
110C4⋊C4×C59C22⋊C412yes—
111C42×C59—22no—
112C42×C59—22no—
113C42×C59C22×C411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59#4111yescharacteristic
117#11745671—48no—
118C4⋊Dic59—41no—
119C4⋊Dic59—41no—
120C4⋊Dic59—41no—
121C4⋊Dic59—41no—
122C4⋊Dic59—81no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8—41no—
126C2×C59⋊C8—41no—
127C2×C59⋊C8—41no—
128C2×C59⋊C8—41no—
129C23×C59#12111yescharacteristic
130C22×D59—42no—
131C22×D59—81no—
132C22×D59—81no—
133C22×D59—81no—
134C22×D59—81no—
135C22×D59—81no—
136C22×D59—81no—
137Q8×C59—22no—
138Q8×C59—22no—
139Q8×C59—41no—
140Q8×C59—41no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—22no—
144C2×C4×C59—22no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59C2×C22⋊C411yescharacteristic
150C2×C4×C59C4×D411yescharacteristic
151C2×C4×C59C4×D411yescharacteristic
152C2×C4×C59#12011yescharacteristic
153C2×C4×C59#12111yescharacteristic
154C2×C4×C59#12311yescharacteristic
155C2×C4×C59C2×SD1611yescharacteristic
156C2×C4×C59#13511yescharacteristic
157C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C59#13711yescharacteristic
162C2×C4×C59#13711yescharacteristic
163C2×Dic59—81no—
164C2×Dic59—81no—
165C2×Dic59—81no—
166D236—42no—
167D236—42no—
168D236—42no—
169D236—42no—
170D236—82no—
171D236—82no—
172D236—81no—
173D236—81no—
174D236—81no—
175D236—81no—
176C8×C59—22no—
177C8×C59—41no—
178C8×C59—42no—
179C59⋊C8—42no—
180C59⋊C8—81no—
181#9230—591nomaximal, Sylow
182C22×C59#38611yescharacteristic
183C22×C59#46011yescharacteristic
184C22×C59#46411yescharacteristic
185C22×C59#46811yescharacteristic
186C22×C59#46911yescharacteristic
187C22×C59#47111yescharacteristic
188C22×C59#47211yescharacteristic
189C2×D59—82no—
190C2×D59—82no—
191C2×D59—82no—
192C2×D59—161no—
193C2×D59—161no—
194C2×D59—161no—
195C2×D59—161no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—42no—
199C4×C59—42no—
200C4×C59#41711yescharacteristic
201C4×C59#41811yescharacteristic
202C4×C59C4×SD1611yescharacteristic
203C4×C59#44011yescharacteristic
204C4×C59#44811yescharacteristic
205C4×C59#44911yescharacteristic
206C4×C59#46811yescharacteristic
207C4×C59#46911yescharacteristic
208Dic59—161no—
209C2×#460—591no—
210C2×#446D5911yescharacteristic, complemented
211#1957—591no—
212#1803—591no—
213C2×#331—591no—
214#1296—591no—
215#1277—591no—
216C2×C59#168611yescharacteristic
217C2×C59#168811yescharacteristic
218C2×C59#169811yescharacteristic
219C2×C59#170211yescharacteristic
220C2×C59#188011yescharacteristic
221C2×C59#189511yescharacteristic
222C2×C59#190711yescharacteristic
223D59—162no—
224C22×SD16—1181no—
225C2×#127—591no—
226C2×C4×Q8C2×D5911yescharacteristic
227#460—594no—
228#460—1182no—
229#446—22no—
230#446—22no—
231C2×C4⋊C8—21no—
232C2×C4⋊C8—591no—
233C2×C4⋊C8—591no—
234C2×C4⋊C8C2×D5911yescharacteristic
235C2×#103—1181no—
236C2×#102—1181no—
237C2×#102—1181no—
238C2×#102—1181no—
239C2×#97—21no—
240C2×C4×C8C2×D5911yescharacteristic
241#384—591no—
242#340—1181no—
243#331—1182no—
244C59#923011yescharacteristic, complemented, Sylow
245C22×Q8D23611yescharacteristic
246C22×D4—1181no—
247C22×D4—1181no—
248C22×D4—1181no—
249C2×SD16—1184no—
250C2×SD16—2362no—
251C2×SD16—2362no—
252C22×C8—21no—
253C22×C8—1181no—
254C22×C8—1181no—
255C22×C8C22⋊D5911yescharacteristic
256C22×C8C22⋊D5911yescharacteristic
257#127—592no—
258#127—1181no—
259#127—1181no—
260#127—1181no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8C4×D5912yes—
264C4×Q8C22⋊D5912yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—1181no—
267C2×C4⋊C4—1181no—
268C2×C4⋊C4—1181no—
269C2×C4⋊C4D23611yescharacteristic
270C2×C42—21no—
271C2×C42C22×D5911yescharacteristic
272C4⋊C8—24no—
273C4⋊C8—21no—
274C4⋊C8—592no—
275C4⋊C8—1181no—
276C4⋊C8—1181no—
277C4⋊C8—1181no—
278C4⋊C8C22⋊D5912yes—
279#103—2362no—
280#102—1184no—
281#102—2362no—
282#102—2362no—
283#97—24no—
284C4×C8—21no—
285C4×C8—21no—
286C24—2361no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8(C2×D59)⋊C412yes—
293C2×D4—1182no—
294C2×D4—1182no—
295C2×D4—1182no—
296C2×D4—4721no—
297C2×D4—4721no—
298C2×D4—2361no—
299C2×D4—2361no—
300C2×D4—2361no—
301C2×D4—2361no—
302C2×D4—2361no—
303C2×D4—2361no—
304C2×D4—2361no—
305C2×D4—2361no—
306C2×D4—2361no—
307C2×D4—2361no—
308C2×D4—2361no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—2361no—
312C22×C4C2×D23611yescharacteristic
313C22×C4#1174568511yescharacteristic
314C22×C4C2×C22⋊D5911yescharacteristic
315SD16—2368no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—22no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—1182no—
325C2×C8—2361no—
326C2×C8—2361no—
327C2×C8—2361no—
328C2×C8—2361no—
329C2×C8—2361no—
330C2×C8#1174567112yescomplemented
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—22no—
334C4⋊C4—4721no—
335C4⋊C4—2361no—
336C4⋊C4—2361no—
337C4⋊C4—2361no—
338C4⋊C4—2361no—
339C4⋊C4(C2×D59)⋊C412yes—
340C42—22no—
341C42—22no—
342C42C2×C4×D5911yescharacteristic
343C42#1174568511yescharacteristic
344C42C2×C22⋊D5911yescharacteristic
345C42C2×C22⋊D5911yescharacteristic
346C23—4721no—
347C23—4721no—
348C23—4721no—
349C23—4721no—
350C23—4721no—
351C23—4721no—
352C23—2362no—
353C23#1427370111yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358D4—4722no—
359D4—4722no—
360D4—4721no—
361D4—4721no—
362D4—4721no—
363D4—4721no—
364D4—2362no—
365D4—2362no—
366D4—2362no—
367D4—2362no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—4721no—
377C2×C4—4721no—
378C2×C4—4721no—
379C2×C4C2×(C2×D59)⋊C411yescharacteristic
380C2×C4C4×C22⋊D5911yescharacteristic
381C2×C4C4×C22⋊D5911yescharacteristic
382C2×C4#1427369611yescharacteristic
383C2×C4#1427370111yescharacteristic
384C2×C4#1427371011yescharacteristic
385C2×C4C2×#1174567111yescharacteristic
386C2×C4#1427374711yescharacteristic
387C2×C4#1427375211yescharacteristic
388C2×C4#1427375511yescharacteristic
389C2×C4#1427375511yescharacteristic
390C2×C4#1427375511yescharacteristic
391C2×C4#1427375811yescharacteristic
392C2×C4#1427376011yescharacteristic
393C8—22no—
394C8—41no—
395C8—42no—
396C8—4721no—
397C8—2362no—
398C22—9441no—
399C22—9441no—
400C22—9441no—
401C22—9441no—
402C22—4722no—
403C22—4722no—
404C22—4722no—
405C22#1683728111yescharacteristic
406C22#1683760211yescharacteristic
407C22#1683762411yescharacteristic
408C22#1683764811yescharacteristic
409C22#1683765511yescharacteristic
410C22#1683766511yescharacteristic
411C22#1683767211yescharacteristic
412C4—21no—
413C4—21no—
414C4—42no—
415C4—42no—
416C4—9441no—
417C4#1683740411yescharacteristic
418C4#1683740811yescharacteristic
419C4C4×#1174567111yescharacteristic
420C4#1683750011yescharacteristic
421C4#1683754111yescharacteristic
422C4#1683754711yescharacteristic
423C4#1683764811yescharacteristic
424C4#1683765511yescharacteristic
425C2—9442no—
426C2#2142356811yescharacteristic
427C2#2142358011yescharacteristic
428C2#2142363611yescharacteristic
429C2#2142366411yescharacteristic
430C2#2142445111yescharacteristic
431C2#2142453411yescharacteristic
432C2#2142460411yescharacteristic
subgroupG/H
centerC23#14273701
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#446C2
socleC23×C59#121
prime radicalC2×#14273724C22
cosocleC2×C42×C59C23
hypercenterC2×#446D59
hypocenterC59#9230
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
3. #21424101C2semidirect
5. #21421980C2semidirect
6. #21421931C2semidirect
7. C2×C59×#446C2semidirect
11. #16837602C4semidirect
106. C2×C8×C59SD16semidirect
210. C2×#446D59semidirect
244. C59#9230semidirect
330. C2×C8#11745671semidirect

Maximal subgroups

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

subgroupindex
C2×#168376022
#214249022
#214241012
C2×#168371452
#214219802
#214219312
C2×C59×#4462
#923059