Finite Group Databasebeta

← C59×#19244 #28431353

Subgroups — C59×#19244 #28431353

Order 15104.

594 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3246C211yesmaximal, characteristic
2C59×#3230C211yesmaximal, characteristic, complemented
3C59×#3141C211yesmaximal, characteristic
4C59×#2962C211yesmaximal, characteristic, complemented
5C59×#1704C212yesmaximal, complemented
6C59×#1698C212yesmaximal, complemented
7C59×#1684C212yesmaximal, complemented
8C59×#1678C212yesmaximal, complemented
9C59×#1565C211yesmaximal, characteristic, complemented
10C2×C59×#333C211yesmaximal, characteristic, complemented
11C59×#1540C211yesmaximal, characteristic
12C59×#533C2211yescharacteristic
13C59×#532C2211yescharacteristic
14C2×C4⋊Q8×C59C2211yescharacteristic
15C59×#500—21no—
16C59×#489—22no—
17C59×#487—21no—
18C59×#487C2212yes—
19C59×#486C2212yes—
20C59×#484—22no—
21C59×#477C2212yes—
22C59×#477C2212yes—
23C59×#476—21no—
24C59×#475C2212yes—
25C59×#465—22no—
26C59×#461—21no—
27C59×#460C2212yes—
28C59×#446—22no—
29C59×#446C2212yes—
30C8×Q8×C59C2212yes—
31C59×#431C2211yescharacteristic
32C59×#424—21no—
33C2×C4⋊C8×C59C2211yescharacteristic
34C2×C4⋊C8×C59C2211yescharacteristic
35C59×#417—21no—
36C59×#417—21no—
37C59×#405—21no—
38C4×M16×C59C2211yescharacteristic
39C59×#335C2212yes—
40C59×#334C2212yes—
41C59×#333C2212yes—
42C59×#333C2212yes—
43C59×#332C2211yescharacteristic
44C59×#332C2211yescharacteristic
45C59×#331C2211yescharacteristic
46C59×#331C2211yescharacteristic
47C2×#41×C59—21no—
48C22×Q8×C59—21no—
49C2×SD16×C59—22no—
50C2×M16×C59D411yescharacteristic
51C2×M16×C59D411yescharacteristic
52C22×C8×C59—21no—
53C22×C8×C59—21no—
54C4⋊Q8×C59—21no—
55C4⋊Q8×C59—21no—
56C4⋊Q8×C59—21no—
57C4⋊Q8×C59D411yescharacteristic
58C4⋊Q8×C59D411yescharacteristic
59C4⋊Q8×C59C2311yescharacteristic
60C4⋊Q8×C59C2312yes—
61#127×C59C2311yescharacteristic
62#125×C59—21no—
63#124×C59—21no—
64C22⋊Q8×C59—21no—
65C22⋊Q8×C59D412yes—
66#121×C59—21no—
67#121×C59—21no—
68C4×Q8×C59—21no—
69C4×Q8×C59C2312yes—
70C4×D4×C59—21no—
71C4×D4×C59—21no—
72#117×C59—21no—
73C2×C4⋊C4×C59—21no—
74C2×C4⋊C4×C59—21no—
75C2×C42×C59C2311yescharacteristic
76#107×C59—22no—
77#107×C59—22no—
78#106×C59—22no—
79C4⋊C8×C59—22no—
80C4⋊C8×C59—22no—
81C4⋊C8×C59—21no—
82C4⋊C8×C59—21no—
83C4⋊C8×C59C2311yescharacteristic
84C4⋊C8×C59C2311yescharacteristic
85C4⋊C8×C59C2311yescharacteristic
86C4⋊C8×C59C2311yescharacteristic
87C4⋊C8×C59C2312yes—
88#103×C59—22no—
89#103×C59—22no—
90#103×C59—22no—
91#103×C59—22no—
92#103×C59—22no—
93#102×C59—22no—
94#102×C59—22no—
95#102×C59—22no—
96C22⋊C8×C59—21no—
97#97×C59—22no—
98#97×C59D412yes—
99C4×C8×C59—22no—
100C4×C8×C59—21no—
101C4×C8×C59C2312yes—
102#41×C59—42no—
103#41×C59—42no—
104C2×Q8×C59—21no—
105C2×Q8×C59—21no—
106C2×Q8×C59—22no—
107C2×Q8×C59—41no—
108C2×Q8×C59—82no—
109C2×Q8×C59C2×D412yes—
110C2×D4×C59—21no—
111C2×D4×C59—21no—
112C2×D4×C59—21no—
113C2×D4×C59—41no—
114C22×C4×C59—41no—
115C22×C4×C59—41no—
116C22×C4×C59C2×D411yescharacteristic
117C22×C4×C59C2×D411yescharacteristic
118C22×C4×C59#4111yescharacteristic
119SD16×C59—82no—
120M16×C59—22no—
121M16×C59—22no—
122C2×C8×C59—21no—
123C2×C8×C59—21no—
124C2×C8×C59—21no—
125C2×C8×C59—21no—
126C2×C8×C59—22no—
127C2×C8×C59—42no—
128C2×C8×C59—81no—
129C2×C8×C59C2×D412yes—
130C2×C8×C59C2×D412yes—
131C4⋊C4×C59—21no—
132C4⋊C4×C59—21no—
133C4⋊C4×C59—21no—
134C4⋊C4×C59—22no—
135C4⋊C4×C59—22no—
136C4⋊C4×C59—22no—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—22no—
139C4⋊C4×C59—21no—
140C4⋊C4×C59—41no—
141C4⋊C4×C59—41no—
142C4⋊C4×C59C2×D412yes—
143C22⋊C4×C59—22no—
144C22⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C42×C59—22no—
147C42×C59C2×D411yescharacteristic
148C42×C59C2×D411yescharacteristic
149C42×C59#4111yescharacteristic
150C42×C59C2411yescharacteristic
151C23×C59—41no—
152C23×C59#12111yescharacteristic
153Q8×C59—22no—
154Q8×C59—22no—
155Q8×C59—41no—
156Q8×C59—41no—
157Q8×C59—81no—
158Q8×C59—82no—
159Q8×C59—82no—
160D4×C59—41no—
161D4×C59—41no—
162D4×C59—41no—
163D4×C59—41no—
164D4×C59—81no—
165D4×C59—82no—
166C2×C4×C59—21no—
167C2×C4×C59—21no—
168C2×C4×C59—22no—
169C2×C4×C59—22no—
170C2×C4×C59—41no—
171C2×C4×C59—41no—
172C2×C4×C59—42no—
173C2×C4×C59—82no—
174C2×C4×C59—82no—
175C2×C4×C59#12111yescharacteristic
176C2×C4×C59#12111yescharacteristic
177C2×C4×C59#12111yescharacteristic
178C2×C4×C59#13512yes—
179C2×C4×C59#13712yes—
180C2×C4×C59C22×D411yescharacteristic
181C2×C4×C59C22×D411yescharacteristic
182C2×C4×C59C2×#4111yescharacteristic
183C8×C59—22no—
184C8×C59—22no—
185C8×C59—41no—
186C8×C59—41no—
187C8×C59—41no—
188C8×C59—42no—
189C8×C59—41no—
190#19244C5911yesmaximal, characteristic, direct product factor, Sylow
191C22×C59—21no—
192C22×C59—21no—
193C22×C59—81no—
194C22×C59—81no—
195C22×C59—81no—
196C22×C59#46412yes—
197C22×C59C2×#12111yescharacteristic
198C4×C59—21no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—42no—
202C4×C59—42no—
203C4×C59—81no—
204C4×C59—82no—
205C4×C59#46412yes—
206C4×C59C2×#13511yescharacteristic
207C4×C59C2×#13711yescharacteristic
208C4×C59#57711yescharacteristic
209C4×C59#57811yescharacteristic
210#3246C2×C5911yescharacteristic
211#3230C2×C5911yescharacteristic, complemented
212#3141C2×C5911yescharacteristic
213#2962C2×C5911yescharacteristic, complemented
214#1704C2×C5912yescomplemented
215#1698C2×C5912yescomplemented
216#1684C2×C5912yescomplemented
217#1678C2×C5912yescomplemented
218#1565C2×C5911yescharacteristic, complemented
219C2×#333C2×C5911yescharacteristic, complemented
220#1540C2×C5911yescharacteristic
221C2×C59—22no—
222C2×C59—161no—
223C2×C59C2×#46411yescharacteristic
224C2×C59#306311yescharacteristic
225C2×C59#306811yescharacteristic
226#533C22×C5911yescharacteristic
227#532C22×C5911yescharacteristic
228C2×C4⋊Q8C22×C5911yescharacteristic
229#500—21no—
230#489—22no—
231#487—21no—
232#487C22×C5912yes—
233#486C22×C5912yes—
234#484—22no—
235#477C22×C5912yes—
236#477C22×C5912yes—
237#476—21no—
238#475C22×C5912yes—
239#465—22no—
240#461—21no—
241#460C22×C5912yes—
242#446—22no—
243#446C22×C5912yes—
244C8×Q8C22×C5912yes—
245#431C22×C5911yescharacteristic
246#424—21no—
247C2×C4⋊C8C22×C5911yescharacteristic
248C2×C4⋊C8C22×C5911yescharacteristic
249#417—21no—
250#417—21no—
251#405—21no—
252C4×M16C22×C5911yescharacteristic
253#335C22×C5912yes—
254#334C22×C5912yes—
255#333C22×C5912yes—
256#333C22×C5912yes—
257#332C22×C5911yescharacteristic
258#332C22×C5911yescharacteristic
259#331C22×C5911yescharacteristic
260#331C22×C5911yescharacteristic
261C59#1924411yescharacteristic, direct product factor, Sylow
262C2×#41—21no—
263C22×Q8—21no—
264C2×SD16—22no—
265C2×M16D4×C5911yescharacteristic
266C2×M16D4×C5911yescharacteristic
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8D4×C5911yescharacteristic
273C4⋊Q8D4×C5911yescharacteristic
274C4⋊Q8C23×C5912yes—
275C4⋊Q8C23×C5911yescharacteristic
276#127C23×C5911yescharacteristic
277#125—21no—
278#124—21no—
279C22⋊Q8—21no—
280C22⋊Q8D4×C5912yes—
281#121—21no—
282#121—21no—
283C4×Q8—21no—
284C4×Q8C23×C5912yes—
285C4×D4—21no—
286C4×D4—21no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C42C23×C5911yescharacteristic
291#107—22no—
292#107—22no—
293#106—22no—
294C4⋊C8—22no—
295C4⋊C8—22no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8C23×C5911yescharacteristic
299C4⋊C8C23×C5911yescharacteristic
300C4⋊C8C23×C5911yescharacteristic
301C4⋊C8C23×C5911yescharacteristic
302C4⋊C8C23×C5912yes—
303#103—22no—
304#103—22no—
305#103—22no—
306#103—22no—
307#103—22no—
308#102—22no—
309#102—22no—
310#102—22no—
311C22⋊C8—21no—
312#97—22no—
313#97D4×C5912yes—
314C4×C8—22no—
315C4×C8—21no—
316C4×C8C23×C5912yes—
317#41—42no—
318#41—42no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—22no—
322C2×Q8—41no—
323C2×Q8—82no—
324C2×Q8C2×D4×C5912yes—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×D4×C5911yescharacteristic
332C22×C4C2×D4×C5911yescharacteristic
333C22×C4#41×C5911yescharacteristic
334SD16—82no—
335M16—22no—
336M16—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—81no—
344C2×C8C2×D4×C5912yes—
345C2×C8C2×D4×C5912yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4C2×D4×C5912yes—
358C22⋊C4—22no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—22no—
362C42C2×D4×C5911yescharacteristic
363C42C2×D4×C5911yescharacteristic
364C42#41×C5911yescharacteristic
365C42C24×C5911yescharacteristic
366C23—41no—
367C23#121×C5911yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372Q8—81no—
373Q8—82no—
374Q8—82no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—82no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4#121×C5911yescharacteristic
391C2×C4#121×C5911yescharacteristic
392C2×C4#121×C5911yescharacteristic
393C2×C4#135×C5912yes—
394C2×C4#137×C5912yes—
395C2×C4C22×D4×C5911yescharacteristic
396C2×C4C22×D4×C5911yescharacteristic
397C2×C4C2×#41×C5911yescharacteristic
398C8—22no—
399C8—22no—
400C8—41no—
401C8—41no—
402C8—41no—
403C8—42no—
404C8—41no—
405C22—21no—
406C22—21no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22C59×#46412yes—
411C22C2×#121×C5911yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—42no—
417C4—81no—
418C4—82no—
419C4C59×#46412yes—
420C4C2×#135×C5911yescharacteristic
421C4C2×#137×C5911yescharacteristic
422C4C59×#57711yescharacteristic
423C4C59×#57811yescharacteristic
424C2—22no—
425C2—161no—
426C2C2×C59×#46411yescharacteristic
427C2C59×#306311yescharacteristic
428C2C59×#306811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#121
commutator, Frattini, cosocleC42C24×C59
prime radicalC59×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#3230C2semidirect
4. C59×#2962C2semidirect
5. C59×#1704C2semidirect
6. C59×#1698C2semidirect
7. C59×#1684C2semidirect
8. C59×#1678C2semidirect
9. C59×#1565C2semidirect
10. C2×C59×#333C2semidirect
190. #19244C59direct (N × H)
211. #3230C2×C59semidirect
213. #2962C2×C59semidirect
214. #1704C2×C59semidirect
215. #1698C2×C59semidirect
216. #1684C2×C59semidirect
217. #1678C2×C59semidirect
218. #1565C2×C59semidirect
219. C2×#333C2×C59semidirect
261. C59#19244direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#32462
C59×#32302
C59×#31412
C59×#29622
C59×#17042
C59×#16982
C59×#16842
C59×#16782
C59×#15652
C2×C59×#3332
C59×#15402
#1924459