Finite Group Databasebeta

← #28484901

Subgroups — #28484901

Order 15104.

578 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
1C2×#16837604C211yesmaximal, characteristic
2C2×#16837481C211yesmaximal, characteristic
3#21424093C211yesmaximal, characteristic
4C2×#16837148C211yesmaximal, characteristic, complemented
5#21421979C211yesmaximal, characteristic, complemented
6#21421931C211yesmaximal, characteristic, complemented
7C59×#1990C211yesmaximal, characteristic, complemented
8C22×#11745671—21no—
9C22×#11745659—21no—
10C2×C4×D236C2211yescharacteristic
11#16837604—22no—
12#16837604C414yescomplemented
13#16837481—22no—
14#16837481—22no—
15C2×C4⋊(C59⋊C8)C2211yescharacteristic
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17C2×C4⋊(C59⋊C8)C2211yescharacteristic
18C2×#14273651—21no—
19C2×#14273647—21no—
20C2×(C2×D59)⋊C8—21no—
21#16837164—21no—
22#16837148—22no—
23C2×C4⋊Q8×C59C2211yescharacteristic
24C2×C4×C8×C59C2211yescharacteristic
25C59×#384C2211yescharacteristic
26C59×#340—21no—
27C59×#340—21no—
28C22×D236D411yescharacteristic
29C22×C4×D59—21no—
30C2×#11745671—24no—
31C2×#11745671—42no—
32C2×#11745671—42no—
33C2×#11745659—24no—
34C2×#11745659—42no—
35C2×#11745659—42no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—21no—
38C22×C59⋊C8—21no—
39C4×D236—21no—
40C4×D236—21no—
41C4×D236C2×C412yes—
42C4×D236D412yes—
43C2×C4⋊Dic59D411yescharacteristic
44C2×(C2×D59)⋊C4—21no—
45C4⋊(C59⋊C8)—21no—
46C4⋊(C59⋊C8)—21no—
47C4⋊(C59⋊C8)—21no—
48C4⋊(C59⋊C8)—21no—
49C4⋊(C59⋊C8)C2×C412yes—
50C4⋊(C59⋊C8)D412yes—
51#14273651—24no—
52#14273647—42no—
53(C2×D59)⋊C8—24no—
54C22×Q8×C59—21no—
55C22×C8×C59D411yescharacteristic
56C22×C8×C59D411yescharacteristic
57C4⋊Q8×C59—21no—
58C4⋊Q8×C59—21no—
59C4⋊Q8×C59—21no—
60C4⋊Q8×C59C2×C412yes—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—21no—
66C2×C42×C59C2311yescharacteristic
67C4×C8×C59—21no—
68C4×C8×C59—21no—
69C23×D59—21no—
70C2×Q8×C59—22no—
71C2×Q8×C59—41no—
72C2×Q8×C59—41no—
73C2×Q8×C59—41no—
74C2×Q8×C59—41no—
75C2×Q8×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59C2×D411yescharacteristic
80C22×C4×C59#4111yescharacteristic
81C22×Dic59—21no—
82C2×D236—21no—
83C2×D236—21no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236—21no—
87C2×D236C22⋊C412yes—
88C2×C4×D59—22no—
89C2×C4×D59—22no—
90C2×C4×D59—41no—
91C2×C4×D59—41no—
92C2×C4×D59—41no—
93C2×C4×D59—41no—
94C2×C8×C59—21no—
95C2×C8×C59—21no—
96C2×C8×C59—21no—
97C2×C8×C59—21no—
98C2×C8×C59—21no—
99C2×C8×C59SD1612yescomplemented
100C4⋊C4×C59—22no—
101C4⋊C4×C59—22no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—41no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—81no—
109C42×C59C22×C411yescharacteristic
110C42×C59C2×D411yescharacteristic
111C42×C59C2×D411yescharacteristic
112C42×C59#4111yescharacteristic
113#11745671—48no—
114(C2×D59)⋊C4—22no—
115(C2×D59)⋊C4—22no—
116C4⋊Dic59—21no—
117C4⋊Dic59C22⋊C412yes—
118C2×C59⋊C8—22no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8—41no—
123C2×C59⋊C8—41no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8—41no—
126C2×C59⋊C8—41no—
127#11745659—48no—
128C23×C59#12111yescharacteristic
129C22×D59—22no—
130C22×D59—41no—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135C22×D59—41no—
136Q8×C59—42no—
137Q8×C59—42no—
138Q8×C59—81no—
139Q8×C59—81no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—42no—
143C2×C4×C59—81no—
144C2×C4×C59—81no—
145C2×C4×C59—81no—
146C2×C4×C59—81no—
147C2×C4×C59—81no—
148C2×C4×C59C2×C22⋊C411yescharacteristic
149C2×C4×C59C4×D411yescharacteristic
150C2×C4×C59C4×D411yescharacteristic
151C2×C4×C59#12011yescharacteristic
152C2×C4×C59#12111yescharacteristic
153C2×C4×C59#12311yescharacteristic
154C2×C4×C59C2×SD1611yescharacteristic
155C2×C4×C59#13511yescharacteristic
156C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C59#13711yescharacteristic
161C2×C4×C59#13711yescharacteristic
162C2×Dic59—22no—
163C2×Dic59—41no—
164C2×Dic59—41no—
165D236—22no—
166D236—22no—
167D236—41no—
168D236—41no—
169C4×D59—42no—
170C4×D59—42no—
171C4×D59—42no—
172C4×D59—42no—
173C8×C59—22no—
174C8×C59—41no—
175C59⋊C8—42no—
176C59⋊C8—42no—
177C59⋊C8—81no—
178#9225—591nomaximal, Sylow
179C22×C59#38611yescharacteristic
180C22×C59#46111yescharacteristic
181C22×C59#46311yescharacteristic
182C22×C59#46811yescharacteristic
183C22×C59#46911yescharacteristic
184C22×C59#47111yescharacteristic
185C22×C59#47311yescharacteristic
186C2×D59—42no—
187C2×D59—42no—
188C2×D59—42no—
189C2×D59—81no—
190C2×D59—81no—
191C2×D59—81no—
192C2×D59—81no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—82no—
196C4×C59—161no—
197C4×C59#41711yescharacteristic
198C4×C59#41811yescharacteristic
199C4×C59C4×SD1611yescharacteristic
200C4×C59#44011yescharacteristic
201C4×C59#45011yescharacteristic
202C4×C59#45211yescharacteristic
203C4×C59#46811yescharacteristic
204C4×C59#46911yescharacteristic
205Dic59—42no—
206C2×#461—591no—
207C2×#436—591no—
208#1990D5911yescharacteristic, complemented
209#1802—591no—
210C2×#332—591no—
211#1296—591no—
212#1277—591no—
213C2×C59#169111yescharacteristic
214C2×C59#169311yescharacteristic
215C2×C59#169911yescharacteristic
216C2×C59#170111yescharacteristic
217C2×C59#187711yescharacteristic
218C2×C59#189511yescharacteristic
219C2×C59#190811yescharacteristic
220D59—82no—
221C22×SD16—1181no—
222C22×M16—1181no—
223C2×C4⋊Q8C2×D5911yescharacteristic
224C2×C4×D4—591no—
225#461—594no—
226#461—1182no—
227#436—1182no—
228#436—1182no—
229C2×C4⋊C8—591no—
230C2×C4⋊C8—591no—
231C2×C4⋊C8—591no—
232C2×#103—1181no—
233C2×#102—1181no—
234C2×C22⋊C8—1181no—
235C2×C4×C8C2×D5911yescharacteristic
236#384C2×D5911yescharacteristic
237#340—21no—
238#340—21no—
239#340—1181no—
240#332—1182no—
241C59#922511yescharacteristic, complemented, Sylow
242C22×Q8—21no—
243C22×D4—591no—
244C23×C4—1181no—
245C2×SD16—1184no—
246C2×SD16—2362no—
247C2×SD16—2362no—
248C2×M16—1184no—
249C2×M16—2362no—
250C2×M16—2362no—
251C22×C8—1181no—
252C22×C8—1181no—
253C22×C8—1181no—
254C22×C8C22⋊D5911yescharacteristic
255C22×C8C22⋊D5911yescharacteristic
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C4×D5912yes—
260C4×D4—592no—
261C4×D4—592no—
262C4×D4—1181no—
263C4×D4—1181no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—591no—
270C2×C22⋊C4—1181no—
271C2×C42C22×D5911yescharacteristic
272C4⋊C8—592no—
273C4⋊C8—592no—
274C4⋊C8—1181no—
275C4⋊C8—1181no—
276C4⋊C8—1181no—
277C4⋊C8—1181no—
278#103—1184no—
279#102—2362no—
280C22⋊C8—1184no—
281C4×C8—21no—
282C4×C8—21no—
283C24—1181no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—592no—
291C2×D4—1181no—
292C2×D4—1181no—
293C2×D4—1181no—
294C2×D4—1181no—
295C2×D4—1181no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—1181no—
299C22×C4—1182no—
300C22×C4—1182no—
301C22×C4—2361no—
302C22×C4—2361no—
303C22×C4—2361no—
304C22×C4—2361no—
305C22×C4D4×D5911yescharacteristic
306C22×C4#1174568711yescharacteristic
307C22×C4C2×C22⋊D5911yescharacteristic
308SD16—2368no—
309M16—2368no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—1182no—
316C2×C8—1182no—
317C2×C8—2361no—
318C2×C8—2361no—
319C2×C8—2361no—
320C2×C8—2361no—
321C2×C8—2361no—
322C2×C8—2361no—
323C2×C8—2361no—
324C2×C8#1174567112yescomplemented
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C4⋊C4—592no—
335C4⋊C4—1181no—
336C22⋊C4—1182no—
337C22⋊C4—1182no—
338C42C2×C4×D5911yescharacteristic
339C42#1174568511yescharacteristic
340C42D4×D5911yescharacteristic
341C42D4×D5911yescharacteristic
342C23—1182no—
343C23—2361no—
344C23—2361no—
345C23—2361no—
346C23—2361no—
347C23—2361no—
348C23—2361no—
349C23#1427369811yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354D4—1182no—
355D4—1182no—
356D4—2361no—
357D4—2361no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—1182no—
367C2×C4—2361no—
368C2×C4—2361no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4—2362no—
372C2×C4—2362no—
373C2×C4C22⋊C4×D5911yescharacteristic
374C2×C4(C22⋊D59)⋊C411yescharacteristic
375C2×C4C4×C22⋊D5911yescharacteristic
376C2×C4#1427369511yescharacteristic
377C2×C4#1427370011yescharacteristic
378C2×C4#1427370911yescharacteristic
379C2×C4C2×#1174567111yescharacteristic
380C2×C4#1427374711yescharacteristic
381C2×C4#1427375111yescharacteristic
382C2×C4#1427375111yescharacteristic
383C2×C4#1427375211yescharacteristic
384C2×C4#1427375411yescharacteristic
385C2×C4#1427375611yescharacteristic
386C2×C4#1427375811yescharacteristic
387C8—22no—
388C8—41no—
389C8—4721no—
390C8—2362no—
391C8—2362no—
392C22—4721no—
393C22—4721no—
394C22—4721no—
395C22—4721no—
396C22—2362no—
397C22—2362no—
398C22—2362no—
399C22#1683727811yescharacteristic
400C22#1683760411yescharacteristic
401C22#1683761411yescharacteristic
402C22#1683764511yescharacteristic
403C22#1683765211yescharacteristic
404C22#1683766211yescharacteristic
405C22#1683767411yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—2362no—
411C4#1683740011yescharacteristic
412C4#1683740511yescharacteristic
413C4C4×#1174567111yescharacteristic
414C4#1683750011yescharacteristic
415C4#1683755211yescharacteristic
416C4#1683756211yescharacteristic
417C4#1683764711yescharacteristic
418C4#1683765411yescharacteristic
419C2—4722no—
420C2#2142359211yescharacteristic
421C2#2142360611yescharacteristic
422C2#2142364011yescharacteristic
423C2#2142365411yescharacteristic
424C2#2142443311yescharacteristic
425C2#2142453111yescharacteristic
426C2#2142461411yescharacteristic
subgroupG/H
centerC23#14273698
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1990C2
socleC23×C59#121
prime radicalC22×D236D4
cosocleC2×C42×C59C23
hypercenter#1990D59
hypocenterC59#9225
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#16837148C2semidirect
5. #21421979C2semidirect
6. #21421931C2semidirect
7. C59×#1990C2semidirect
12. #16837604C4semidirect
99. C2×C8×C59SD16semidirect
208. #1990D59semidirect
241. C59#9225semidirect
324. C2×C8#11745671semidirect

Maximal subgroups

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

subgroupindex
C2×#168376042
C2×#168374812
#214240932
C2×#168371482
#214219792
#214219312
C59×#19902
#922559