Finite Group Databasebeta

← #28483882

Subgroups — #28483882

Order 15104.

544 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434092C211yesmaximal, characteristic
2#21424894C211yesmaximal, characteristic, complemented
3#21422745C211yesmaximal, characteristic, complemented
4#21422520C211yesmaximal, characteristic, complemented
5#21421991C211yesmaximal, characteristic, complemented
6#21421941C211yesmaximal, characteristic, complemented
7C59×#2932C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9#16837713C412yes—
10#16837679—21no—
11#16837594—21no—
12#16837535C412yes—
13C4×#11745669—22no—
14#16837455C2211yescharacteristic
15#16837455C2211yescharacteristic
16C2×C4⋊(C59⋊C8)C2211yescharacteristic
17C2×(C2×D59)⋊C8—21no—
18C2×(C2×D59)⋊C8—21no—
19#16837148—21no—
20#16837146—21no—
21#16837129—22no—
22C2×#131×C59—21no—
23C59×#532C2211yescharacteristic
24C59×#435—22no—
25C59×#435—22no—
26C59×#423C2211yescharacteristic
27C59×#408—21no—
28C2×#97×C59C2211yescharacteristic
29C22×D236C2×C411yescharacteristic
30C22×C4×D59—21no—
31C2×#11745669—22no—
32C22×C59⋊C8—21no—
33C4×D236—21no—
34C4×D236—21no—
35C4×D236—21no—
36C4×D236—21no—
37C2×C4⋊Dic59C2×C411yescharacteristic
38C2×(C2×D59)⋊C4—21no—
39#14273660—22no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44#14273648—22no—
45#14273647—22no—
46C22⋊(C59⋊C8)—21no—
47C22⋊(C59⋊C8)C2×C412yes—
48(C2×D59)⋊C8—42no—
49(C2×D59)⋊C8—42no—
50C4×C59⋊C8—21no—
51C4×C59⋊C8—21no—
52C2×#41×C59—21no—
53#131×C59—42no—
54#131×C59—42no—
55C2×M16×C59—22no—
56C2×M16×C59—21no—
57C22×C8×C59—22no—
58C22×C8×C59D411yescharacteristic
59C22×C8×C59D411yescharacteristic
60C4⋊Q8×C59D411yescharacteristic
61#127×C59D411yescharacteristic
62#124×C59—21no—
63#121×C59—21no—
64#121×C59C2×C412yes—
65C4×D4×C59—21no—
66C4×D4×C59D412yes—
67C2×C42×C59C2311yescharacteristic
68C4⋊C8×C59—21no—
69C4⋊C8×C59D412yes—
70C22⋊C8×C59—24no—
71#97×C59—21no—
72#97×C59—21no—
73C23×D59—21no—
74#41×C59—41no—
75#41×C59—41no—
76#41×C59—41no—
77#41×C59—41no—
78C2×Q8×C59—21no—
79C2×D4×C59—22no—
80C2×D4×C59—21no—
81C2×D4×C59—21no—
82C2×D4×C59C22⋊C412yes—
83C22×C4×C59—22no—
84C22×C4×C59C22×C411yescharacteristic
85C22×C4×C59C2×D411yescharacteristic
86C22×C4×C59#4111yescharacteristic
87C22×Dic59—21no—
88C2×D236—21no—
89C2×D236—21no—
90C2×D236—42no—
91C2×C4×D59—41no—
92C2×C4×D59—41no—
93C2×C4×D59—41no—
94C2×C4×D59—41no—
95C2×C4×D59—41no—
96C2×C4×D59—41no—
97M16×C59—44no—
98M16×C59—41no—
99M16×C59—41no—
100C2×C8×C59—21no—
101C2×C8×C59—21no—
102C2×C8×C59—21no—
103C2×C8×C59—22no—
104C2×C8×C59—21no—
105C2×C8×C59—21no—
106C2×C8×C59—44no—
107C2×C8×C59D812yescomplemented
108C4⋊C4×C59—21no—
109C4⋊C4×C59C22⋊C412yes—
110C22⋊C4×C59—22no—
111C22⋊C4×C59—22no—
112C42×C59C2×D411yescharacteristic
113C42×C59C2×D411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59#4111yescharacteristic
116#11745669—44no—
117(C2×D59)⋊C4—41no—
118(C2×D59)⋊C4—41no—
119C4⋊Dic59—21no—
120C4⋊Dic59—21no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8—41no—
123C2×C59⋊C8—41no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8—41no—
126C23×C59—22no—
127C23×C59C4×D411yescharacteristic
128C22×D59—22no—
129C22×D59—41no—
130C22×D59—41no—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135Q8×C59—41no—
136Q8×C59—41no—
137D4×C59—42no—
138D4×C59—42no—
139D4×C59—42no—
140D4×C59—41no—
141D4×C59—41no—
142D4×C59—81no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—42no—
147C2×C4×C59—42no—
148C2×C4×C59C2×C22⋊C411yescharacteristic
149C2×C4×C59C4×D411yescharacteristic
150C2×C4×C59#12011yescharacteristic
151C2×C4×C59#12111yescharacteristic
152C2×C4×C59#12111yescharacteristic
153C2×C4×C59#12311yescharacteristic
154C2×C4×C59C2×D811yescharacteristic
155C2×C4×C59#13511yescharacteristic
156C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
158C2×Dic59—41no—
159C2×Dic59—41no—
160C2×Dic59—41no—
161D236—22no—
162D236—22no—
163D236—41no—
164D236—41no—
165C4×D59—81no—
166C4×D59—81no—
167C4×D59—81no—
168C4×D59—81no—
169C8×C59—22no—
170C8×C59—42no—
171C8×C59—41no—
172C59⋊C8—42no—
173C59⋊C8—81no—
174C59⋊C8—81no—
175#9049—591nomaximal, Sylow
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—42no—
179C22×C59—42no—
180C22×C59—42no—
181C22×C59#38611yescharacteristic
182C22×C59C4×D811yescharacteristic
183C22×C59#44211yescharacteristic
184C2×D59—42no—
185C2×D59—42no—
186C2×D59—42no—
187C2×D59—81no—
188C2×D59—81no—
189C2×D59—81no—
190C2×D59—81no—
191C4×C59—21no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—42no—
196C4×C59#44711yescharacteristic
197C4×C59#44911yescharacteristic
198C4×C59#45911yescharacteristic
199C4×C59#46311yescharacteristic
200Dic59—81no—
201#3100—591no—
202#2932D5911yescharacteristic, complemented
203#1955—591no—
204#1540—591no—
205#1486—591no—
206#1301—591no—
207#1281—591no—
208C2×C59—21no—
209C2×C59—21no—
210C2×C59—82no—
211C2×C59#187911yescharacteristic
212C2×C59#188111yescharacteristic
213C2×C59#189111yescharacteristic
214D59—82no—
215C2×#131—21no—
216#532C2×D5911yescharacteristic
217C2×C4×D4—591no—
218#480—592no—
219#474—1181no—
220#459—1181no—
221#447—592no—
222C4×D8—1182no—
223#435—22no—
224#435—22no—
225#431—591no—
226#431—591no—
227#423C2×D5911yescharacteristic
228C2×C4⋊C8—591no—
229#408—21no—
230C2×C22⋊C8—1181no—
231C2×C22⋊C8—1181no—
232C2×#97C2×D5911yescharacteristic
233#332—1181no—
234#331—1181no—
235D4⋊C8—1182no—
236C59#904911yescharacteristic, complemented, Sylow
237C2×#41—21no—
238C22×D4—591no—
239C23×C4—1181no—
240C2×D8—1182no—
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C22×C8—22no—
246C22×C8—1181no—
247C22×C8C22⋊D5911yescharacteristic
248C22×C8C22⋊D5911yescharacteristic
249C4⋊Q8D23611yescharacteristic
250#127D23611yescharacteristic
251#124—21no—
252#121—21no—
253#121C4×D5912yes—
254C4×D4—21no—
255C4×D4—1181no—
256C4×D4—1181no—
257C4×D4—1181no—
258C4×D4—1181no—
259C4×D4C22⋊D5912yes—
260C2×C4⋊C4—591no—
261C2×C22⋊C4—1181no—
262C2×C42C22×D5911yescharacteristic
263#107—1182no—
264C4⋊C8—21no—
265C4⋊C8—1181no—
266C4⋊C8—1181no—
267C4⋊C8—1181no—
268C4⋊C8—1181no—
269C4⋊C8C22⋊D5912yes—
270#102—1182no—
271#102—1182no—
272C22⋊C8—24no—
273C22⋊C8—592no—
274C22⋊C8—1181no—
275C22⋊C8—2362no—
276C22⋊C8—2362no—
277#97—21no—
278#97—21no—
279C4×C8—1181no—
280C4×C8—1181no—
281C24—1181no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—21no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—1181no—
291C2×D4—1181no—
292C2×D4—2362no—
293C2×D4(C2×D59)⋊C412yes—
294C22×C4—22no—
295C22×C4—1181no—
296C22×C4—2361no—
297C22×C4—2361no—
298C22×C4—2361no—
299C22×C4—2361no—
300C22×C4—2361no—
301C22×C4—2361no—
302C22×C4C2×C4×D5911yescharacteristic
303C22×C4#1174568511yescharacteristic
304C22×C4C2×C22⋊D5911yescharacteristic
305D8—2364no—
306M16—44no—
307M16—41no—
308M16—41no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—44no—
316C2×C8—1182no—
317C2×C8—2361no—
318C2×C8—2361no—
319C2×C8—2361no—
320C2×C8—2361no—
321C2×C8#1174566912yescomplemented
322C4⋊C4—21no—
323C4⋊C4—1181no—
324C4⋊C4—1181no—
325C4⋊C4(C2×D59)⋊C412yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—2361no—
329C22⋊C4—2361no—
330C42C2×D23611yescharacteristic
331C42#1174568511yescharacteristic
332C42C2×C22⋊D5911yescharacteristic
333C42C2×C22⋊D5911yescharacteristic
334C23—22no—
335C23—1182no—
336C23—2361no—
337C23—2361no—
338C23—2361no—
339C23—2361no—
340C23—2361no—
341C23—2361no—
342C23C4×C22⋊D5911yescharacteristic
343Q8—41no—
344Q8—41no—
345D4—42no—
346D4—42no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—1182no—
352D4—1182no—
353D4—2361no—
354D4—2361no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—4721no—
361C2×C4—4721no—
362C2×C4—4721no—
363C2×C4—4721no—
364C2×C4—2361no—
365C2×C4—2361no—
366C2×C4—2361no—
367C2×C4C2×(C2×D59)⋊C411yescharacteristic
368C2×C4C4×C22⋊D5911yescharacteristic
369C2×C4#1427369611yescharacteristic
370C2×C4#1427370111yescharacteristic
371C2×C4#1427370111yescharacteristic
372C2×C4#1427371011yescharacteristic
373C2×C4C2×#1174566911yescharacteristic
374C2×C4#1427374711yescharacteristic
375C2×C4#1427375211yescharacteristic
376C2×C4#1427375311yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—4721no—
381C8—4721no—
382C8—2362no—
383C22—21no—
384C22—21no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—4721no—
389C22—4721no—
390C22—4721no—
391C22—4721no—
392C22—2362no—
393C22—2362no—
394C22—2362no—
395C22#1683728111yescharacteristic
396C22C4×#1174566911yescharacteristic
397C22#1683751211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—4721no—
404C4#1683753611yescharacteristic
405C4#1683754711yescharacteristic
406C4#1683759711yescharacteristic
407C4#1683761711yescharacteristic
408C2—21no—
409C2—21no—
410C2—82no—
411C2—4722no—
412C2#2142444411yescharacteristic
413C2#2142445811yescharacteristic
414C2#2142451411yescharacteristic
subgroupG/H
centerC2×C4#14273696
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2932C2
socleC22×C59#386
prime radical#21434092C2
cosocleC2×C42×C59C23
hypercenter#2932D59
hypocenterC59#9049
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #21424894C2semidirect
3. #21422745C2semidirect
4. #21422520C2semidirect
5. #21421991C2semidirect
6. #21421941C2semidirect
7. C59×#2932C2semidirect
107. C2×C8×C59D8semidirect
202. #2932D59semidirect
236. C59#9049semidirect
321. C2×C8#11745669semidirect

Maximal subgroups

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

subgroupindex
#214340922
#214248942
#214227452
#214225202
#214219912
#214219412
C59×#29322
#904959