Finite Group Databasebeta

← #28482793

Subgroups — #28482793

Order 15104.

464 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424399C211yesmaximal, characteristic
2#21424300C211yesmaximal, characteristic, complemented
3#21424278C211yesmaximal, characteristic, complemented
4#21422587C211yesmaximal, characteristic
5#21421981C211yesmaximal, characteristic, complemented
6#21421943C211yesmaximal, characteristic, complemented
7C59×#2976C211yesmaximal, characteristic
8C22×#11745664C2211yescharacteristic
9C2×#14273662—21no—
10C2×Dic59⋊C8—21no—
11C2×#14273654—21no—
12C2×C22⋊(C59⋊C8)C2211yescharacteristic
13C4×C22⋊Dic59C2211yescharacteristic
14C4×C22⋊Dic59C2211yescharacteristic
15#16837166—21no—
16#16837161—21no—
17#16837156—21no—
18#16837139C411yescharacteristic, complemented
19#16837139C411yescharacteristic, complemented
20#16837136C411yescharacteristic, complemented
21#16837136C411yescharacteristic, complemented
22C59×#525C2211yescharacteristic
23C59×#436—21no—
24C59×#435—21no—
25C59×#435—21no—
26C8×D4×C59—21no—
27C59×#433—21no—
28C59×#408—21no—
29C59×#407C2211yescharacteristic
30C2×C22⋊C8×C59C2211yescharacteristic
31C2×#11745664—21no—
32C2×#11745664—21no—
33C2×#11745664—42no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36C2×C22⋊Dic59—21no—
37C2×C22⋊Dic59—21no—
38C2×C4×Dic59—21no—
39C2×C4×Dic59—21no—
40#14273662—42no—
41Dic59⋊C8—42no—
42#14273654—42no—
43C22⋊(C59⋊C8)—21no—
44C22⋊(C59⋊C8)C2×C411yescharacteristic
45C22⋊(C59⋊C8)C2×C411yescharacteristic
46C59⋊#95—21no—
47C59⋊#95C2×C411yescharacteristic
48C59⋊#95C2×C411yescharacteristic
49C2×#41×C59D411yescharacteristic
50C23×C4×C59C2311yescharacteristic
51C2×M16×C59—21no—
52C2×M16×C59D411yescharacteristic
53C2×M16×C59D411yescharacteristic
54C22×C8×C59—21no—
55C22×C8×C59D411yescharacteristic
56C22×C8×C59D411yescharacteristic
57#123×C59—21no—
58C22⋊Q8×C59C2×C411yescharacteristic
59C22⋊Q8×C59Q811yescharacteristic
60#121×C59C2×C411yescharacteristic
61#121×C59Q811yescharacteristic
62#120×C59—21no—
63C4×D4×C59—21no—
64C4×D4×C59—21no—
65#117×C59D411yescharacteristic
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C22⋊C8×C59—21no—
69C22⋊C8×C59—21no—
70C22⋊C8×C59—21no—
71C22⋊C8×C59—21no—
72C22⋊C8×C59—21no—
73C22⋊C8×C59—21no—
74#97×C59—21no—
75C4×C8×C59—21no—
76C24×C59#4111yescharacteristic
77#41×C59—41no—
78#41×C59—41no—
79C2×Q8×C59C4⋊C411yescharacteristic
80C2×D4×C59—21no—
81C2×D4×C59—21no—
82C2×D4×C59—21no—
83C2×D4×C59C4⋊C411yescharacteristic
84C22×C4×C59—21no—
85C22×C4×C59—41no—
86C22×C4×C59—41no—
87C22×C4×C59C22×C411yescharacteristic
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×Q811yescharacteristic
92C22×C4×C59#4111yescharacteristic
93C22×Dic59—21no—
94C22×Dic59—21no—
95C22×Dic59—41no—
96M16×C59—41no—
97M16×C59—41no—
98M16×C59—81no—
99C2×C8×C59—21no—
100C2×C8×C59—21no—
101C2×C8×C59—21no—
102C2×C8×C59—21no—
103C2×C8×C59—41no—
104C2×C8×C59—41no—
105C2×C8×C59—81no—
106C4⋊C4×C59—21no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59C4⋊C411yescharacteristic
109C4⋊C4×C59C4⋊C411yescharacteristic
110C22⋊C4×C59—21no—
111C22⋊C4×C59—21no—
112C22⋊C4×C59—21no—
113C22⋊C4×C59—21no—
114C22⋊C4×C59—21no—
115C42×C59—21no—
116C22⋊Dic59—22no—
117C22⋊Dic59—42no—
118C22⋊Dic59—41no—
119C4×Dic59—41no—
120C4×Dic59—41no—
121C4×Dic59—41no—
122C4×Dic59—41no—
123#11745664—22no—
124#11745664—22no—
125#11745664—41no—
126#11745664—41no—
127C2×C59⋊C8—22no—
128C2×C59⋊C8—21no—
129C2×C59⋊C8—21no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132C2×C59⋊C8—41no—
133C2×C59⋊C8—41no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—21no—
137C23×C59—41no—
138C23×C59—41no—
139C23×C59C4×D411yescharacteristic
140C23×C59C22⋊Q811yescharacteristic
141C23×C59#12311yescharacteristic
142Q8×C59—41no—
143D4×C59—41no—
144D4×C59—41no—
145D4×C59—41no—
146D4×C59—81no—
147D4×C59—81no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—41no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—41no—
162C2×C4×C59C2×C4⋊C411yescharacteristic
163C2×C4×C59C4×D411yescharacteristic
164C2×C4×C59#12011yescharacteristic
165C2×C4×C59C22⋊Q811yescharacteristic
166C2×Dic59—22no—
167C2×Dic59—41no—
168C2×Dic59—41no—
169C2×Dic59—41no—
170C2×Dic59—42no—
171C2×Dic59—41no—
172C2×Dic59—41no—
173C2×Dic59—81no—
174C2×Dic59—81no—
175C8×C59—41no—
176C8×C59—41no—
177C8×C59—41no—
178C8×C59—41no—
179C59⋊C8—41no—
180C59⋊C8—41no—
181C59⋊C8—42no—
182#8874—591nomaximal, Sylow
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—21no—
191C22×C59—41no—
192C22×C59—41no—
193C22×C59—41no—
194C22×C59—81no—
195C22×C59—81no—
196C22×C59#38511yescharacteristic
197C22×C59#44311yescharacteristic
198C22×C59#44411yescharacteristic
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—21no—
202C4×C59—41no—
203C4×C59—41no—
204C4×C59—41no—
205C4×C59B(4,𝔽2)11yescharacteristic
206C4×C59#45811yescharacteristic
207Dic59—42no—
208Dic59—81no—
209Dic59—82no—
210#2976D5911yescharacteristic
211#1871—591no—
212#1855—591no—
213#1851—591no—
214#1501—591no—
215#1297—591no—
216#1282—591no—
217C2×C59—21no—
218C2×C59—21no—
219C2×C59—41no—
220C2×C59—41no—
221C2×C59—81no—
222C2×C59#186111yescharacteristic
223C2×C59#186611yescharacteristic
224C2×C59#186711yescharacteristic
225C22×M16—591no—
226#525C2×D5911yescharacteristic
227#436—21no—
228#435—21no—
229#435—21no—
230C8×D4—21no—
231#433—21no—
232C2×#108—1181no—
233C2×C4⋊C8—1181no—
234C2×#104—1181no—
235#408—21no—
236#407C2×D5911yescharacteristic
237C2×C22⋊C8—591no—
238C2×C22⋊C8C2×D5911yescharacteristic
239C4×C22⋊C4—591no—
240C4×C22⋊C4—591no—
241#341—1181no—
242#339—1181no—
243#336—1181no—
244#328—591no—
245#328—591no—
246#327—591no—
247#327—591no—
248C59#887411yescharacteristic, complemented, Sylow
249C2×#41C22⋊D5911yescharacteristic
250C23×C4C22×D5911yescharacteristic
251C2×M16—21no—
252C2×M16—1181no—
253C2×M16—1181no—
254C2×M16—2362no—
255C2×M16C22⋊D5911yescharacteristic
256C2×M16C22⋊D5911yescharacteristic
257C22×C8—21no—
258C22×C8—1181no—
259C22×C8—1181no—
260C22×C8C22⋊D5911yescharacteristic
261C22×C8C22⋊D5911yescharacteristic
262#123—21no—
263C22⋊Q8Dic11811yescharacteristic
264C22⋊Q8C4×D5911yescharacteristic
265#121Dic11811yescharacteristic
266#121C4×D5911yescharacteristic
267#120—21no—
268C4×D4—21no—
269C4×D4—21no—
270#117C22⋊D5911yescharacteristic
271C2×C22⋊C4—1181no—
272C2×C22⋊C4—1181no—
273C2×C42—1181no—
274C2×C42—1181no—
275#108—2362no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—2362no—
279#104—2362no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—591no—
287C22⋊C8—591no—
288C22⋊C8—1181no—
289#97—21no—
290C4×C8—21no—
291#95—591no—
292#95—591no—
293#95—1181no—
294C24#1174568511yescharacteristic
295#41—41no—
296#41—41no—
297C2×Q8Dic59⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4Dic59⋊C411yescharacteristic
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—1181no—
306C22×C4—1181no—
307C22×C4—2361no—
308C22×C4C2×Dic11811yescharacteristic
309C22×C4C2×C4×D5911yescharacteristic
310C22×C4#1174568511yescharacteristic
311C22×C4C2×C22⋊D5911yescharacteristic
312C22×C4C2×C22⋊D5911yescharacteristic
313C22×C4C2×C22⋊D5911yescharacteristic
314M16—41no—
315M16—41no—
316M16—81no—
317M16—1182no—
318M16—1182no—
319M16—2361no—
320M16—2361no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—81no—
328C2×C8—1182no—
329C2×C8—1181no—
330C2×C8—1181no—
331C2×C8—2361no—
332C2×C8—2361no—
333C2×C8—2361no—
334C2×C8—2361no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4Dic59⋊C411yescharacteristic
338C4⋊C4Dic59⋊C411yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—1182no—
345C22⋊C4—2362no—
346C22⋊C4—2361no—
347C42—21no—
348C42—2361no—
349C42—2361no—
350C42—2361no—
351C42—2361no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23C4×C22⋊D5911yescharacteristic
358C23#1427370611yescharacteristic
359C23#1427371011yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
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—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—1182no—
381C2×C4—4721no—
382C2×C4—4721no—
383C2×C4—2361no—
384C2×C4—2362no—
385C2×C4—2361no—
386C2×C4—2361no—
387C2×C4—2361no—
388C2×C4—2361no—
389C2×C4C2×Dic59⋊C411yescharacteristic
390C2×C4C4×C22⋊D5911yescharacteristic
391C2×C4#1427369611yescharacteristic
392C2×C4#1427370611yescharacteristic
393C8—41no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—2361no—
398C8—2361no—
399C8—2362no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1683727511yescharacteristic
414C22#1683751711yescharacteristic
415C22#1683752211yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—4721no—
423C4—4722no—
424C4—2362no—
425C4#1683758911yescharacteristic
426C4#1683759211yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—81no—
432C2#2142433611yescharacteristic
433C2#2142437111yescharacteristic
434C2#2142437711yescharacteristic
subgroupG/H
centerC2×C4#14273696
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2976C2
socleC22×C59#385
prime radicalC59×#525C22
cosocleC23×C4×C59C23
hypercenter#2976D59
hypocenterC59#8874
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2976

Complements

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

NH ≅ G/Ntype
2. #21424300C2semidirect
3. #21424278C2semidirect
5. #21421981C2semidirect
6. #21421943C2semidirect
18. #16837139C4semidirect
19. #16837139C4semidirect
20. #16837136C4semidirect
21. #16837136C4semidirect
248. C59#8874semidirect

Maximal subgroups

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

subgroupindex
#214243992
#214243002
#214242782
#214225872
#214219812
#214219432
C59×#29762
#887459