Finite Group Databasebeta

← C59×#8994 #28421103

Subgroups — C59×#8994 #28421103

Order 15104.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3076C211yesmaximal, characteristic
2C59×#2925C211yesmaximal, characteristic
3C59×#1493C211yesmaximal, characteristic, complemented
4C59×#1481C211yesmaximal, characteristic, complemented
5C59×#1476C211yesmaximal, characteristic
6C59×#1301C211yesmaximal, characteristic, complemented
7C59×#1277C211yesmaximal, characteristic, complemented
8C59×#533C2211yescharacteristic
9C4×#41×C59C2211yescharacteristic
10C59×#479—21no—
11C59×#478—21no—
12C59×#477C411yescharacteristic
13C59×#476C411yescharacteristic
14C59×#475C411yescharacteristic
15C59×#474C411yescharacteristic
16C59×#433—22no—
17C59×#432—21no—
18C59×#431—21no—
19C59×#431C2211yescharacteristic
20C59×#427—21no—
21C59×#423C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#416—21no—
25C59×#408—21no—
26C59×#405—21no—
27C2×C4×C8×C59C2211yescharacteristic
28C59×Q8⋊C8—21no—
29C59×Q8⋊C8—21no—
30C59×Q8⋊C8—21no—
31C59×Q8⋊C8—22no—
32C59×D4⋊C8—21no—
33C2×#41×C59D411yescharacteristic
34C2×M16×C59—21no—
35C22×C8×C59—21no—
36C22×C8×C59—21no—
37C22×C8×C59—21no—
38C4⋊Q8×C59C2×C411yescharacteristic
39C4⋊Q8×C59C2×C411yescharacteristic
40#125×C59—21no—
41C22⋊Q8×C59—21no—
42C22⋊Q8×C59—21no—
43C4×Q8×C59—21no—
44C4×Q8×C59—21no—
45C4×Q8×C59C2×C411yescharacteristic
46C4×Q8×C59D411yescharacteristic
47C4×D4×C59—21no—
48C4×D4×C59—21no—
49C4×D4×C59C2×C411yescharacteristic
50C4×D4×C59D411yescharacteristic
51#117×C59—21no—
52#117×C59—21no—
53#117×C59D411yescharacteristic
54C2×C42×C59—21no—
55C2×C42×C59C2311yescharacteristic
56#107×C59—21no—
57#107×C59—21no—
58#106×C59—21no—
59#106×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59C2×C411yescharacteristic
65C4⋊C8×C59C2×C411yescharacteristic
66C4⋊C8×C59D411yescharacteristic
67C4⋊C8×C59D411yescharacteristic
68C4⋊C8×C59D412yes—
69#103×C59—21no—
70#103×C59—21no—
71#102×C59—21no—
72#102×C59—21no—
73C22⋊C8×C59—22no—
74C22⋊C8×C59—22no—
75C22⋊C8×C59—21no—
76#97×C59—22no—
77C4×C8×C59—22no—
78C4×C8×C59—21no—
79C4×C8×C59—21no—
80C4×C8×C59—21no—
81#41×C59—21no—
82#41×C59—21no—
83#41×C59—21no—
84#41×C59—21no—
85C2×Q8×C59—21no—
86C2×Q8×C59—21no—
87C2×Q8×C59C22⋊C411yescharacteristic
88C2×D4×C59—21no—
89C2×D4×C59C22⋊C411yescharacteristic
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59—21no—
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C22×C4×C59#4111yescharacteristic
96M16×C59—41no—
97M16×C59—41no—
98C2×C8×C59—22no—
99C2×C8×C59—21no—
100C2×C8×C59—21no—
101C2×C8×C59—21no—
102C2×C8×C59—22no—
103C2×C8×C59—21no—
104C2×C8×C59—41no—
105C2×C8×C59—41no—
106C2×C8×C59—41no—
107C2×C8×C59—41no—
108C2×C8×C59—41no—
109C2×C8×C59—41no—
110C2×C8×C59—41no—
111C4⋊C4×C59—21no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—21no—
115C4⋊C4×C59—21no—
116C4⋊C4×C59—21no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C4⋊C4×C59C22⋊C411yescharacteristic
120C4⋊C4×C59C22⋊C411yescharacteristic
121C22⋊C4×C59—21no—
122C22⋊C4×C59—21no—
123C22⋊C4×C59—21no—
124C22⋊C4×C59—41no—
125C42×C59—21no—
126C42×C59—21no—
127C42×C59—21no—
128C42×C59—41no—
129C42×C59C22×C411yescharacteristic
130C42×C59C2×D411yescharacteristic
131C42×C59C2×D411yescharacteristic
132C42×C59C2×D411yescharacteristic
133C23×C59—21no—
134C23×C59#12311yescharacteristic
135Q8×C59—21no—
136Q8×C59—21no—
137Q8×C59—42no—
138Q8×C59—41no—
139Q8×C59—41no—
140D4×C59—21no—
141D4×C59—21no—
142D4×C59—41no—
143D4×C59—41no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—81no—
157C2×C4×C59C2×C22⋊C411yescharacteristic
158C2×C4×C59C4×D411yescharacteristic
159C2×C4×C59C4×D411yescharacteristic
160C2×C4×C59#12011yescharacteristic
161C2×C4×C59#12111yescharacteristic
162C2×C4×C59#12111yescharacteristic
163C2×C4×C59#13511yescharacteristic
164C2×C4×C59#13511yescharacteristic
165C2×C4×C59#13711yescharacteristic
166C2×C4×C59#13711yescharacteristic
167C8×C59—42no—
168C8×C59—41no—
169C8×C59—41no—
170C8×C59—41no—
171C8×C59—41no—
172C8×C59—42no—
173C8×C59—81no—
174#8994C5911yesmaximal, characteristic, direct product factor, Sylow
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59—41no—
180C22×C59#38611yescharacteristic
181C22×C59#48511yescharacteristic
182C22×C59#48511yescharacteristic
183C4×C59—21no—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—41no—
187C4×C59—41no—
188C4×C59—41no—
189C4×C59—81no—
190C4×C59—81no—
191C4×C59#41611yescharacteristic
192C4×C59#41911yescharacteristic
193C4×C59#44311yescharacteristic
194C4×C59#44411yescharacteristic
195C4×C59#45211yescharacteristic
196C4×C59#45211yescharacteristic
197#3076C2×C5911yescharacteristic
198#2925C2×C5911yescharacteristic
199#1493C2×C5911yescharacteristic, complemented
200#1481C2×C5911yescharacteristic, complemented
201#1476C2×C5911yescharacteristic
202#1301C2×C5911yescharacteristic, complemented
203#1277C2×C5911yescharacteristic, complemented
204C2×C59—21no—
205C2×C59—21no—
206C2×C59—81no—
207C2×C59#187311yescharacteristic
208C2×C59#187611yescharacteristic
209C2×C59#188111yescharacteristic
210#533C22×C5911yescharacteristic
211C4×#41C22×C5911yescharacteristic
212#479—21no—
213#478—21no—
214#477C4×C5911yescharacteristic
215#476C4×C5911yescharacteristic
216#475C4×C5911yescharacteristic
217#474C4×C5911yescharacteristic
218#433—22no—
219#432—21no—
220#431—21no—
221#431C22×C5911yescharacteristic
222#427—21no—
223#423C22×C5911yescharacteristic
224C2×C4⋊C8C22×C5911yescharacteristic
225C2×C4⋊C8C22×C5911yescharacteristic
226#416—21no—
227#408—21no—
228#405—21no—
229C2×C4×C8C22×C5911yescharacteristic
230Q8⋊C8—21no—
231Q8⋊C8—21no—
232Q8⋊C8—21no—
233Q8⋊C8—22no—
234D4⋊C8—21no—
235C59#899411yescharacteristic, direct product factor, Sylow
236C2×#41D4×C5911yescharacteristic
237C2×M16—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C5911yescharacteristic
242C4⋊Q8C2×C4×C5911yescharacteristic
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C2×C4×C5911yescharacteristic
249C4×Q8D4×C5911yescharacteristic
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C5911yescharacteristic
253C4×D4D4×C5911yescharacteristic
254#117—21no—
255#117—21no—
256#117D4×C5911yescharacteristic
257C2×C42—21no—
258C2×C42C23×C5911yescharacteristic
259#107—21no—
260#107—21no—
261#106—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C5911yescharacteristic
268C4⋊C8C2×C4×C5911yescharacteristic
269C4⋊C8D4×C5911yescharacteristic
270C4⋊C8D4×C5911yescharacteristic
271C4⋊C8D4×C5912yes—
272#103—21no—
273#103—21no—
274#102—21no—
275#102—21no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—21no—
279#97—22no—
280C4×C8—22no—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8C22⋊C4×C5911yescharacteristic
291C2×D4—21no—
292C2×D4C22⋊C4×C5911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D4×C5911yescharacteristic
297C22×C4#41×C5911yescharacteristic
298C22×C4#41×C5911yescharacteristic
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C5911yescharacteristic
323C4⋊C4C22⋊C4×C5911yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42C22×C4×C5911yescharacteristic
333C42C2×D4×C5911yescharacteristic
334C42C2×D4×C5911yescharacteristic
335C42C2×D4×C5911yescharacteristic
336C23—21no—
337C23#123×C5911yescharacteristic
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—41no—
342Q8—41no—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—41no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4C2×C22⋊C4×C5911yescharacteristic
361C2×C4C4×D4×C5911yescharacteristic
362C2×C4C4×D4×C5911yescharacteristic
363C2×C4#120×C5911yescharacteristic
364C2×C4#121×C5911yescharacteristic
365C2×C4#121×C5911yescharacteristic
366C2×C4#135×C5911yescharacteristic
367C2×C4#135×C5911yescharacteristic
368C2×C4#137×C5911yescharacteristic
369C2×C4#137×C5911yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—42no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22C59×#38611yescharacteristic
383C22C59×#48511yescharacteristic
384C22C59×#48511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4C59×#41611yescharacteristic
394C4C59×#41911yescharacteristic
395C4C59×#44311yescharacteristic
396C4C59×#44411yescharacteristic
397C4C59×#45211yescharacteristic
398C4C59×#45211yescharacteristic
399C2—21no—
400C2—21no—
401C2—81no—
402C2C59×#187311yescharacteristic
403C2C59×#187611yescharacteristic
404C2C59×#188111yescharacteristic
subgroupG/H
centerC2×C4×C59#120
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
socleC22×C59#386
prime radicalC2×#41×C59D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#1493C2semidirect
4. C59×#1481C2semidirect
6. C59×#1301C2semidirect
7. C59×#1277C2semidirect
174. #8994C59direct (N × H)
199. #1493C2×C59semidirect
200. #1481C2×C59semidirect
202. #1301C2×C59semidirect
203. #1277C2×C59semidirect
235. C59#8994direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#30762
C59×#29252
C59×#14932
C59×#14812
C59×#14762
C59×#13012
C59×#12772
#899459