Finite Group Databasebeta

← C59×#11843 #28423952

Subgroups — C59×#11843 #28423952

Order 15104.

620 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2539C211yesmaximal, characteristic
2C59×#1819C211yesmaximal, characteristic, complemented
3C2×C59×#323C211yesmaximal, characteristic, complemented
4C59×#1352C212yesmaximal, complemented
5C59×#1343C212yesmaximal, complemented
6C2×#123×C59—21no—
7C2×#121×C59C411yescharacteristic, complemented
8C2×#120×C59—21no—
9C22×C22⋊C4×C59C2211yescharacteristic
10C2×C22⋊C8×C59—21no—
11C59×#399C411yescharacteristic, complemented
12C59×#399C2211yescharacteristic
13C59×#392C411yescharacteristic, complemented
14C59×#392C2211yescharacteristic
15C59×#390—21no—
16C59×#390—21no—
17C59×#379—21no—
18C4×C22⋊C4×C59C411yescharacteristic, complemented
19C59×#342—21no—
20C59×#342C2212yes—
21C59×#323—21no—
22C59×#323C2212yes—
23C25×C59D411yescharacteristic
24C22×D4×C59—21no—
25C22×D4×C59—21no—
26C22×D4×C59—21no—
27C22×D4×C59C2×C411yescharacteristic
28C23×C4×C59C2×C411yescharacteristic
29C23×C4×C59D411yescharacteristic
30C22×C8×C59—41no—
31#123×C59—44no—
32#121×C59—41no—
33#121×C59—41no—
34#120×C59—44no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59C2×C411yescharacteristic
38C2×C22⋊C4×C59—21no—
39C2×C22⋊C4×C59—21no—
40C2×C22⋊C4×C59—21no—
41C2×C22⋊C4×C59—21no—
42C2×C22⋊C4×C59—21no—
43C2×C22⋊C4×C59—21no—
44C2×C22⋊C4×C59—22no—
45C2×C22⋊C4×C59—41no—
46C2×C22⋊C4×C59—41no—
47C2×C22⋊C4×C59—41no—
48C2×C22⋊C4×C59—41no—
49C2×C22⋊C4×C59C2×C411yescharacteristic
50C2×C22⋊C4×C59D411yescharacteristic
51C2×C22⋊C4×C59D411yescharacteristic
52C2×C22⋊C4×C59C2311yescharacteristic
53C2×C42×C59—21no—
54C22⋊C8×C59—22no—
55C22⋊C8×C59—41no—
56#95×C59C2×C411yescharacteristic
57#95×C59C2×C411yescharacteristic
58C24×C59—21no—
59C24×C59—21no—
60C24×C59—22no—
61C24×C59—21no—
62C24×C59—41no—
63C24×C59—42no—
64C24×C59—81no—
65C24×C59C22⋊C411yescharacteristic
66C24×C59C22⋊C411yescharacteristic
67C24×C59C2×D411yescharacteristic
68C2×D4×C59—42no—
69C2×D4×C59—42no—
70C2×D4×C59—41no—
71C2×D4×C59—42no—
72C2×D4×C59—42no—
73C2×D4×C59—42no—
74C2×D4×C59—41no—
75C2×D4×C59—41no—
76C2×D4×C59—42no—
77C2×D4×C59—81no—
78C2×D4×C59—81no—
79C2×D4×C59—81no—
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59—21no—
85C22×C4×C59—21no—
86C22×C4×C59—21no—
87C22×C4×C59—42no—
88C22×C4×C59—42no—
89C22×C4×C59—81no—
90C22×C4×C59C22⋊C411yescharacteristic
91C22×C4×C59C22⋊C411yescharacteristic
92C22×C4×C59C22×C411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C2×C8×C59—42no—
95C2×C8×C59—82no—
96C4⋊C4×C59—42no—
97C4⋊C4×C59—42no—
98C4⋊C4×C59—41no—
99C22⋊C4×C59—24no—
100C22⋊C4×C59—41no—
101C22⋊C4×C59—41no—
102C22⋊C4×C59—41no—
103C22⋊C4×C59—41no—
104C22⋊C4×C59—42no—
105C22⋊C4×C59—42no—
106C22⋊C4×C59—42no—
107C22⋊C4×C59—42no—
108C22⋊C4×C59—42no—
109C22⋊C4×C59—42no—
110C22⋊C4×C59—42no—
111C22⋊C4×C59—82no—
112C22⋊C4×C59—82no—
113C42×C59—81no—
114C23×C59—22no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—21no—
118C23×C59—21no—
119C23×C59—21no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—41no—
123C23×C59—42no—
124C23×C59—42no—
125C23×C59—41no—
126C23×C59—41no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59—42no—
130C23×C59—41no—
131C23×C59—41no—
132C23×C59—41no—
133C23×C59—41no—
134C23×C59—42no—
135C23×C59—41no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—81no—
139C23×C59—81no—
140C23×C59—84no—
141C23×C59—84no—
142C23×C59#9911yescharacteristic
143C23×C59#9911yescharacteristic
144C23×C59C2×C22⋊C411yescharacteristic
145C23×C59#13512yes—
146D4×C59—84no—
147D4×C59—84no—
148D4×C59—82no—
149D4×C59—82no—
150D4×C59—82no—
151C2×C4×C59—22no—
152C2×C4×C59—22no—
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—42no—
160C2×C4×C59—41no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—41no—
169C2×C4×C59—81no—
170C2×C4×C59—81no—
171C2×C4×C59—81no—
172C2×C4×C59—82no—
173C2×C4×C59—82no—
174C2×C4×C59—82no—
175C8×C59—82no—
176#11843C5911yesmaximal, characteristic, direct product factor, Sylow
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—22no—
184C22×C59—21no—
185C22×C59—42no—
186C22×C59—42no—
187C22×C59—42no—
188C22×C59—42no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59—41no—
193C22×C59—41no—
194C22×C59—81no—
195C22×C59—84no—
196C22×C59—81no—
197C22×C59—81no—
198C22×C59—81no—
199C22×C59—81no—
200C22×C59—81no—
201C22×C59—84no—
202C22×C59—81no—
203C22×C59—81no—
204C22×C59—81no—
205C22×C59#35312yes—
206C22×C59C2×#9911yescharacteristic
207C22×C59#41611yescharacteristic
208C22×C59#42111yescharacteristic
209C4×C59—42no—
210C4×C59—42no—
211C4×C59—41no—
212C4×C59—41no—
213C4×C59—41no—
214C4×C59—41no—
215C4×C59—81no—
216C4×C59—162no—
217#2539C2×C5911yescharacteristic
218#1819C2×C5911yescharacteristic, complemented
219C2×#323C2×C5911yescharacteristic, complemented
220#1352C2×C5912yescomplemented
221#1343C2×C5912yescomplemented
222C2×C59—21no—
223C2×C59—21no—
224C2×C59—22no—
225C2×C59—42no—
226C2×C59—41no—
227C2×C59—81no—
228C2×C59—161no—
229C2×C59#151611yescharacteristic
230C2×C59#212111yescharacteristic
231C2×C59C2×#35311yescharacteristic
232C2×#123—21no—
233C2×#121C4×C5911yescharacteristic, complemented
234C2×#120—21no—
235C22×C22⋊C4C22×C5911yescharacteristic
236C2×C22⋊C8—21no—
237#399C4×C5911yescharacteristic, complemented
238#399C22×C5911yescharacteristic
239#392C4×C5911yescharacteristic, complemented
240#392C22×C5911yescharacteristic
241#390—21no—
242#390—21no—
243#379—21no—
244C4×C22⋊C4C4×C5911yescharacteristic, complemented
245#342—21no—
246#342C22×C5912yes—
247#323—21no—
248#323C22×C5912yes—
249C59#1184311yescharacteristic, direct product factor, Sylow
250C25D4×C5911yescharacteristic
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4C2×C4×C5911yescharacteristic
255C23×C4C2×C4×C5911yescharacteristic
256C23×C4D4×C5911yescharacteristic
257C22×C8—41no—
258#123—44no—
259#121—41no—
260#121—41no—
261#120—44no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C5911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—41no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—41no—
275C2×C22⋊C4—41no—
276C2×C22⋊C4C2×C4×C5911yescharacteristic
277C2×C22⋊C4D4×C5911yescharacteristic
278C2×C22⋊C4D4×C5911yescharacteristic
279C2×C22⋊C4C23×C5911yescharacteristic
280C2×C42—21no—
281C22⋊C8—22no—
282C22⋊C8—41no—
283#95C2×C4×C5911yescharacteristic
284#95C2×C4×C5911yescharacteristic
285C24—21no—
286C24—21no—
287C24—22no—
288C24—21no—
289C24—41no—
290C24—42no—
291C24—81no—
292C24C22⋊C4×C5911yescharacteristic
293C24C22⋊C4×C5911yescharacteristic
294C24C2×D4×C5911yescharacteristic
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—81no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4C22⋊C4×C5911yescharacteristic
318C22×C4C22⋊C4×C5911yescharacteristic
319C22×C4C22×C4×C5911yescharacteristic
320C22×C4C2×D4×C5911yescharacteristic
321C2×C8—42no—
322C2×C8—82no—
323C4⋊C4—41no—
324C4⋊C4—42no—
325C4⋊C4—42no—
326C22⋊C4—24no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—82no—
339C22⋊C4—82no—
340C42—81no—
341C23—22no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—81no—
367C23—84no—
368C23—84no—
369C23#99×C5911yescharacteristic
370C23#99×C5911yescharacteristic
371C23C2×C22⋊C4×C5911yescharacteristic
372C23#135×C5912yes—
373D4—84no—
374D4—84no—
375D4—82no—
376D4—82no—
377D4—82no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C8—82no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22C59×#35312yes—
432C22C2×#99×C5911yescharacteristic
433C22C59×#41611yescharacteristic
434C22C59×#42111yescharacteristic
435C4—42no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—162no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—161no—
450C2C59×#151611yescharacteristic
451C2C59×#212111yescharacteristic
452C2C2×C59×#35311yescharacteristic
subgroupG/H
center, socleC22×C59C2×#99
commutatorC22×C4C22×C4×C59
Frattini, cosocleC2×C22⋊C4C23×C59
prime radicalC59×#2539C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C24×C59 ◁ C22×C22⋊C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C59×#1819C2semidirect
3. C2×C59×#323C2semidirect
4. C59×#1352C2semidirect
5. C59×#1343C2semidirect
7. C2×#121×C59C4semidirect
11. C59×#399C4semidirect
13. C59×#392C4semidirect
18. C4×C22⋊C4×C59C4semidirect
176. #11843C59direct (N × H)
218. #1819C2×C59semidirect
219. C2×#323C2×C59semidirect
220. #1352C2×C59semidirect
221. #1343C2×C59semidirect
233. C2×#121C4×C59semidirect
237. #399C4×C59semidirect
239. #392C4×C59semidirect
244. C4×C22⋊C4C4×C59semidirect
249. C59#11843direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#25392
C59×#18192
C2×C59×#3232
C59×#13522
C59×#13432
#1184359