Finite Group Databasebeta

← #28484913

Subgroups — #28484913

Order 15104.

562 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
1C2×#16837683C211yesmaximal, characteristic
2C2×#16837479C211yesmaximal, characteristic
3#21424897C211yesmaximal, characteristic, complemented
4#21424093C211yesmaximal, characteristic
5C2×#16837149C211yesmaximal, characteristic, complemented
6#21421930C211yesmaximal, characteristic, complemented
7C59×#1296C211yesmaximal, characteristic, complemented
8C22×#11745659—21no—
9C2×#14273727C2211yescharacteristic
10C2×C4×D236C2211yescharacteristic
11#16837683—22no—
12#16837683C414yescomplemented
13#16837479—22no—
14#16837479—22no—
15C2×#14273661—21no—
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17C2×#14273650—21no—
18C2×#14273650—21no—
19C2×#14273649—21no—
20C2×#14273647—21no—
21C2×(C2×D59)⋊C8—21no—
22C2×C4×C59⋊C8C2211yescharacteristic
23#16837164—21no—
24#16837149—22no—
25C2×C4⋊C8×C59C2211yescharacteristic
26C2×C4⋊C8×C59C2211yescharacteristic
27C59×#384C2211yescharacteristic
28C22×Dic118—21no—
29C22×D236D411yescharacteristic
30C22×C4×D59—21no—
31C2×#11745659—24no—
32C2×#11745659—42no—
33C2×#11745659—42no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8D411yescharacteristic
36C22×C59⋊C8D411yescharacteristic
37#14273727—21no—
38#14273727—21no—
39#14273727—21no—
40#14273727C2×C412yes—
41C4×D236—21no—
42C4×D236—21no—
43C4×D236C2×C412yes—
44C4×D236D412yes—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59—21no—
47C2×C4⋊Dic59D411yescharacteristic
48C2×(C2×D59)⋊C4—21no—
49#14273661—24no—
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)—21no—
52#14273650—42no—
53#14273650—42no—
54#14273649—24no—
55#14273647—42no—
56(C2×D59)⋊C8—24no—
57C4×C59⋊C8—21no—
58C4×C59⋊C8—21no—
59C22×C8×C59—21no—
60C22×C8×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C42×C59C2311yescharacteristic
65C4⋊C8×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59C2×C412yes—
68C4⋊C8×C59D412yes—
69C23×D59—21no—
70C22×C4×C59—41no—
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59#4111yescharacteristic
74C22×Dic59—21no—
75C22×Dic59—41no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236—21no—
79C2×D236—21no—
80C2×D236—21no—
81C2×D236C22⋊C412yes—
82C2×C4×D59—22no—
83C2×C4×D59—22no—
84C2×C4×D59—41no—
85C2×C4×D59—41no—
86C2×C4×D59—41no—
87C2×C4×D59—41no—
88C2×Dic118—22no—
89C2×Dic118—41no—
90C2×Dic118—41no—
91C2×Dic118—41no—
92C2×Dic118—41no—
93C2×Dic118—41no—
94C2×C8×C59—22no—
95C2×C8×C59—22no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—81no—
105C42×C59C22×C411yescharacteristic
106C42×C59C2×D411yescharacteristic
107C42×C59C2×D411yescharacteristic
108C42×C59#4111yescharacteristic
109(C2×D59)⋊C4—22no—
110(C2×D59)⋊C4—22no—
111C4⋊Dic59—21no—
112C4⋊Dic59—22no—
113C4⋊Dic59—22no—
114C4⋊Dic59—41no—
115C4⋊Dic59—41no—
116C4⋊Dic59C22⋊C412yes—
117C2×C59⋊C8—21no—
118C2×C59⋊C8—21no—
119C2×C59⋊C8—21no—
120C2×C59⋊C8—21no—
121C2×C59⋊C8—21no—
122C2×C59⋊C8—41no—
123C2×C59⋊C8—41no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8D812yes—
126#11745659—48no—
127C23×C59#12111yescharacteristic
128C22×D59—22no—
129C22×D59—41no—
130C22×D59—41no—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—81no—
138C2×C4×C59—81no—
139C2×C4×C59—81no—
140C2×C4×C59C2×C22⋊C411yescharacteristic
141C2×C4×C59C4×D411yescharacteristic
142C2×C4×C59C4×D411yescharacteristic
143C2×C4×C59#12011yescharacteristic
144C2×C4×C59#12111yescharacteristic
145C2×C4×C59#12311yescharacteristic
146C2×C4×C59C2×D811yescharacteristic
147C2×C4×C59#13511yescharacteristic
148C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C59#13711yescharacteristic
152C2×C4×C59#13711yescharacteristic
153C2×C4×C59#13711yescharacteristic
154C2×Dic59—22no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—42no—
158C2×Dic59—81no—
159C2×Dic59—81no—
160D236—22no—
161D236—22no—
162D236—41no—
163D236—41no—
164C4×D59—42no—
165C4×D59—42no—
166C4×D59—42no—
167C4×D59—42no—
168Dic118—42no—
169Dic118—42no—
170Dic118—81no—
171Dic118—81no—
172C8×C59—42no—
173C8×C59—42no—
174C59⋊C8—22no—
175C59⋊C8—41no—
176C59⋊C8—81no—
177#9227—591nomaximal, Sylow
178C22×C59#38611yescharacteristic
179C22×C59#45911yescharacteristic
180C22×C59#46311yescharacteristic
181C22×C59#46811yescharacteristic
182C22×C59#47011yescharacteristic
183C22×C59#47111yescharacteristic
184C22×C59#47311yescharacteristic
185C2×D59—42no—
186C2×D59—42no—
187C2×D59—42no—
188C2×D59—81no—
189C2×D59—81no—
190C2×D59—81no—
191C2×D59—81no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—161no—
195C4×C59#41711yescharacteristic
196C4×C59#41911yescharacteristic
197C4×C59C4×D811yescharacteristic
198C4×C59#44211yescharacteristic
199C4×C59#44711yescharacteristic
200C4×C59#44911yescharacteristic
201C4×C59#46811yescharacteristic
202C4×C59#47011yescharacteristic
203Dic59—42no—
204Dic59—82no—
205C2×#474—591no—
206C2×#436—591no—
207#1956—591no—
208#1802—591no—
209C2×#332—591no—
210#1296D5911yescharacteristic, complemented
211#1277—591no—
212C2×C59#168511yescharacteristic
213C2×C59#168911yescharacteristic
214C2×C59#169911yescharacteristic
215C2×C59#170311yescharacteristic
216C2×C59#187911yescharacteristic
217C2×C59#189411yescharacteristic
218C2×C59#190811yescharacteristic
219D59—82no—
220C22×M16—1181no—
221C2×C4⋊Q8—591no—
222C2×C4×D4—591no—
223#474—594no—
224#474—1182no—
225#436—1182no—
226#436—1182no—
227C2×#107—1181no—
228C2×C4⋊C8—591no—
229C2×C4⋊C8C2×D5911yescharacteristic
230C2×C4⋊C8C2×D5911yescharacteristic
231C2×#103—1181no—
232C2×#103—1181no—
233C2×#102—1181no—
234C2×#102—1181no—
235C2×C22⋊C8—1181no—
236C2×C4×C8—591no—
237#384C2×D5911yescharacteristic
238#340—1181no—
239#332—1182no—
240C59#922711yescharacteristic, complemented, Sylow
241C22×Q8—1181no—
242C22×D4—591no—
243C23×C4—1181no—
244C2×M16—1184no—
245C2×M16—2362no—
246C2×M16—2362no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—591no—
250C22×C8—591no—
251C22×C8—1181no—
252C4⋊Q8—592no—
253C4⋊Q8—1181no—
254C4⋊Q8—1181no—
255C4⋊Q8—1181no—
256C4×D4—592no—
257C4×D4—592no—
258C4×D4—1181no—
259C4×D4—1181no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—591no—
264C2×C4⋊C4—1181no—
265C2×C4⋊C4—1181no—
266C2×C22⋊C4—1181no—
267C2×C42C22×D5911yescharacteristic
268#107—1184no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—1181no—
272C4⋊C8—1181no—
273C4⋊C8C4×D5912yes—
274C4⋊C8D23612yes—
275#103—2362no—
276#103—2362no—
277#102—1184no—
278#102—2362no—
279C22⋊C8—1184no—
280C4×C8—1181no—
281C4×C8—1181no—
282C24—1181no—
283C2×Q8—1182no—
284C2×Q8—2361no—
285C2×Q8—2361no—
286C2×Q8—2361no—
287C2×Q8—2361no—
288C2×Q8—2361no—
289C2×D4—592no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C22×C4—41no—
296C22×C4—1181no—
297C22×C4—1182no—
298C22×C4—1182no—
299C22×C4—2361no—
300C22×C4—2361no—
301C22×C4—2361no—
302C22×C4—2361no—
303C22×C4—2361no—
304C22×C4#1174568511yescharacteristic
305C22×C4D4×D5911yescharacteristic
306C22×C4D4×D5911yescharacteristic
307M16—2368no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—592no—
315C2×C8—1181no—
316C2×C8—1181no—
317C2×C8—1181no—
318C2×C8—1181no—
319C2×C8—1181no—
320C2×C8—2361no—
321C2×C8—2361no—
322C2×C8—2361no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—81no—
328C4⋊C4—592no—
329C4⋊C4—1181no—
330C4⋊C4—1182no—
331C4⋊C4—1182no—
332C4⋊C4—2361no—
333C4⋊C4—2361no—
334C22⋊C4—1182no—
335C22⋊C4—1182no—
336C42C2×C4×D5911yescharacteristic
337C42C2×D23611yescharacteristic
338C42D4×D5911yescharacteristic
339C42#1174568911yescharacteristic
340C23—1182no—
341C23—2361no—
342C23—2361no—
343C23—2361no—
344C23—2361no—
345C23—2361no—
346C23—2361no—
347C23#1427370011yescharacteristic
348Q8—4721no—
349Q8—4721no—
350Q8—2362no—
351Q8—2362no—
352D4—1182no—
353D4—1182no—
354D4—2361no—
355D4—2361no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—1182no—
362C2×C4—4721no—
363C2×C4—4721no—
364C2×C4—2362no—
365C2×C4—2361no—
366C2×C4—2361no—
367C2×C4—2362no—
368C2×C4—2362no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4C22⋊C4×D5911yescharacteristic
372C2×C4#1427368911yescharacteristic
373C2×C4C4×D23611yescharacteristic
374C2×C4#1427369711yescharacteristic
375C2×C4#1427370211yescharacteristic
376C2×C4#1427371211yescharacteristic
377C2×C4D8×D5911yescharacteristic
378C2×C4#1427375011yescharacteristic
379C2×C4#1427375111yescharacteristic
380C2×C4#1427375411yescharacteristic
381C2×C4#1427375411yescharacteristic
382C2×C4#1427375611yescharacteristic
383C2×C4#1427375611yescharacteristic
384C2×C4#1427375911yescharacteristic
385C8—42no—
386C8—42no—
387C8—1182no—
388C8—4721no—
389C8—2361no—
390C22—4721no—
391C22—4721no—
392C22—4721no—
393C22—4721no—
394C22—2362no—
395C22—2362no—
396C22—2362no—
397C22#1683728011yescharacteristic
398C22#1683759611yescharacteristic
399C22#1683762011yescharacteristic
400C22#1683764711yescharacteristic
401C22#1683765911yescharacteristic
402C22#1683766411yescharacteristic
403C22#1683767611yescharacteristic
404C4—21no—
405C4—21no—
406C4—161no—
407C4—4722no—
408C4—2362no—
409C4#1683740011yescharacteristic
410C4#1683740911yescharacteristic
411C4#1683748411yescharacteristic
412C4#1683751311yescharacteristic
413C4#1683753711yescharacteristic
414C4#1683755011yescharacteristic
415C4#1683764911yescharacteristic
416C4#1683766111yescharacteristic
417C2—4722no—
418C2#2142356011yescharacteristic
419C2#2142358411yescharacteristic
420C2#2142364611yescharacteristic
421C2#2142367411yescharacteristic
422C2#2142444511yescharacteristic
423C2#2142452811yescharacteristic
424C2#2142461211yescharacteristic
subgroupG/H
centerC23#14273700
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#121
prime radicalC22×D236D4
cosocleC2×C42×C59C23
hypercenter#1296D59
hypocenterC59#9227
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #21424897C2semidirect
5. C2×#16837149C2semidirect
6. #21421930C2semidirect
7. C59×#1296C2semidirect
12. #16837683C4semidirect
210. #1296D59semidirect
240. C59#9227semidirect

Maximal subgroups

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

subgroupindex
C2×#168376832
C2×#168374792
#214248972
#214240932
C2×#168371492
#214219302
C59×#12962
#922759