Finite Group Databasebeta

← #28477487

Subgroups — #28477487

Order 15104.

574 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#21425424C211yesmaximal, characteristic, complemented
2#21425232C211yesmaximal, characteristic, complemented
3#21425178C211yesmaximal, characteristic, complemented
4#21421919C211yesmaximal, characteristic, complemented
5#21421917C211yesmaximal, characteristic, complemented
6#21421917C211yesmaximal, characteristic, complemented
7C59×#2682C211yesmaximal, characteristic
8C22×#11745670—21no—
9C2×#14273727C2211yescharacteristic
10C2×#14273660—21no—
11C2×#14273650—21no—
12C2×#14273648—21no—
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C2×#123×C59—21no—
19C2×#121×C59—21no—
20C59×#396—21no—
21C59×#394—21no—
22C59×#392—21no—
23C59×#390C2211yescharacteristic
24C59×#390C2211yescharacteristic
25C59×#389C2211yescharacteristic
26C59×#385—21no—
27C22×Dic118—21no—
28C2×#11745670—42no—
29C2×#11745670—42no—
30C2×#11745670—42no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34#14273727—42no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59—21no—
37#14273660—42no—
38#14273650—42no—
39#14273648—42no—
40C22×D4×C59—21no—
41C22×D4×C59—21no—
42C22×D4×C59D411yescharacteristic
43C22×D4×C59D411yescharacteristic
44C23×C4×C59—21no—
45#123×C59—42no—
46#123×C59—42no—
47#121×C59—42no—
48#121×C59—42no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C4⋊C4×C59D411yescharacteristic
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C22⋊C4×C59—21no—
56C2×C22⋊C4×C59—21no—
57C2×C22⋊C4×C59—21no—
58C2×C22⋊C4×C59—21no—
59C2×C22⋊C4×C59—21no—
60C2×C22⋊C4×C59—21no—
61C2×C22⋊C4×C59—21no—
62C2×C42×C59C2311yescharacteristic
63#95×C59—21no—
64#95×C59—21no—
65C24×C59—21no—
66C24×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59—41no—
71C2×D4×C59—41no—
72C2×D4×C59—41no—
73C2×D4×C59—41no—
74C2×D4×C59—42no—
75C2×D4×C59—42no—
76C2×D4×C59—42no—
77C2×D4×C59—81no—
78C2×D4×C59—81no—
79C2×D4×C59—81no—
80C2×D4×C59D812yes—
81C22×C4×C59—21no—
82C22×C4×C59—21no—
83C22×C4×C59—21no—
84C22×C4×C59—21no—
85C22×C4×C59—42no—
86C22×C4×C59—42no—
87C22×C4×C59—81no—
88C22×C4×C59C2×D411yescharacteristic
89C22×C4×C59C2×D411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×Dic59—41no—
92C2×Dic118—22no—
93C2×Dic118—41no—
94C2×Dic118—41no—
95C2×Dic118—41no—
96C2×Dic118—41no—
97C2×Dic118—41no—
98C4⋊C4×C59—21no—
99C4⋊C4×C59—42no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59SD1612yescomplemented
106C22⋊C4×C59—42no—
107C22⋊C4×C59—42no—
108C22⋊C4×C59—41no—
109C22⋊C4×C59—41no—
110C22⋊C4×C59—41no—
111C22⋊C4×C59—41no—
112C22⋊C4×C59—41no—
113C22⋊C4×C59—41no—
114C22⋊C4×C59—41no—
115C22⋊C4×C59—41no—
116C22⋊C4×C59—81no—
117C42×C59—41no—
118#11745670—48no—
119C4⋊Dic59—22no—
120C4⋊Dic59—22no—
121C4⋊Dic59—41no—
122C4⋊Dic59—41no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—22no—
125C2×C59⋊C8—41no—
126C2×C59⋊C8—41no—
127C2×C59⋊C8—41no—
128C2×C59⋊C8—41no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132C23×C59—22no—
133C23×C59—41no—
134C23×C59—41no—
135C23×C59—41no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—41no—
139C23×C59—41no—
140C23×C59—41no—
141C23×C59—41no—
142C23×C59—41no—
143C23×C59—41no—
144C23×C59—41no—
145C23×C59—41no—
146C23×C59#12011yescharacteristic
147D4×C59—42no—
148D4×C59—42no—
149D4×C59—81no—
150D4×C59—81no—
151D4×C59—84no—
152D4×C59—84no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C2×C4×C59—22no—
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—41no—
170C2×C4×C59—41no—
171C2×C4×C59—84no—
172C2×C4×C59C2×D811yescharacteristic
173C2×C4×C59C2×SD1611yescharacteristic
174C2×C4×C59#13511yescharacteristic
175C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C59#13711yescharacteristic
178C2×Dic59—42no—
179C2×Dic59—81no—
180C2×Dic59—81no—
181Dic118—42no—
182Dic118—42no—
183Dic118—81no—
184Dic118—81no—
185C59⋊C8—42no—
186C59⋊C8—42no—
187C59⋊C8—81no—
188#7752—591nomaximal, Sylow
189C22×C59—42no—
190C22×C59—42no—
191C22×C59—42no—
192C22×C59—81no—
193C22×C59—81no—
194C22×C59—81no—
195C22×C59—81no—
196C22×C59—81no—
197C22×C59—81no—
198C22×C59—81no—
199C22×C59—81no—
200C22×C59—81no—
201C22×C59—81no—
202C22×C59—81no—
203C22×C59#44711yescharacteristic
204C22×C59#45011yescharacteristic
205C22×C59#45211yescharacteristic
206C22×C59#45311yescharacteristic
207C22×C59#45511yescharacteristic
208C22×C59#45611yescharacteristic
209C22×C59B(4,𝔽2)11yescharacteristic
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—21no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59—42no—
217C4×C59—81no—
218C4×C59—81no—
219C4×C59—81no—
220Dic59—82no—
221#2682D5911yescharacteristic
222#2057—591no—
223#2023—591no—
224#2013—591no—
225#1271—591no—
226#1270—591no—
227#1270—591no—
228C2×C59—82no—
229C2×C59—161no—
230C2×C59#159511yescharacteristic
231C2×C59#160411yescharacteristic
232C2×C59#160611yescharacteristic
233C2×C59#163111yescharacteristic
234C2×C59#163911yescharacteristic
235C2×C59#164711yescharacteristic
236C2×C59#166111yescharacteristic
237C22×SD16—1181no—
238C2×C4⋊Q8—591no—
239C2×#123—21no—
240C2×#121—21no—
241C2×#107—1181no—
242C2×#103—1181no—
243C2×#102—1181no—
244#396—21no—
245#394—21no—
246#392—21no—
247#390C2×D5911yescharacteristic
248#390C2×D5911yescharacteristic
249#389C2×D5911yescharacteristic
250#385—21no—
251#340—1181no—
252#340—1181no—
253#336—591no—
254#336—591no—
255#336—591no—
256C59#775211yescharacteristic, complemented, Sylow
257C22×Q8—1181no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4C22⋊D5911yescharacteristic
261C22×D4C22⋊D5911yescharacteristic
262C23×C4—21no—
263C2×SD16—2362no—
264C2×SD16—2362no—
265C2×SD16—2362no—
266C22×C8—1181no—
267C22×C8—1181no—
268C22×C8—1181no—
269C4⋊Q8—2362no—
270#123—42no—
271#123—42no—
272#121—42no—
273#121—42no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4—1181no—
278C2×C4⋊C4C22⋊D5911yescharacteristic
279C2×C4⋊C4C22⋊D5911yescharacteristic
280C2×C4⋊C4C22⋊D5911yescharacteristic
281C2×C4⋊C4C22⋊D5911yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C42C22×D5911yescharacteristic
290#107—2362no—
291#103—2362no—
292#102—2362no—
293#95—21no—
294#95—21no—
295C24—21no—
296C24—21no—
297C2×Q8—1182no—
298C2×Q8—2361no—
299C2×Q8—2361no—
300C2×Q8—2361no—
301C2×Q8—2361no—
302C2×Q8—2361no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—42no—
312C2×D4—42no—
313C2×D4—81no—
314C2×D4—81no—
315C2×D4—81no—
316C2×D4#1174566912yes—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—81no—
324C22×C4—2361no—
325C22×C4C2×C22⋊D5911yescharacteristic
326C22×C4C2×C22⋊D5911yescharacteristic
327C22×C4C2×C22⋊D5911yescharacteristic
328SD16—2368no—
329C2×C8—1182no—
330C2×C8—1182no—
331C2×C8—2361no—
332C2×C8—2361no—
333C2×C8—2361no—
334C2×C8—2361no—
335C2×C8—2361no—
336C2×C8—2361no—
337C2×C8—2361no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—1182no—
346C4⋊C4—1182no—
347C4⋊C4—2361no—
348C4⋊C4—2361no—
349C4⋊C4#1174567012yescomplemented
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—81no—
361C42—41no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23#1427369611yescharacteristic
377Q8—4721no—
378Q8—4721no—
379Q8—2362no—
380Q8—2362no—
381D4—42no—
382D4—42no—
383D4—81no—
384D4—81no—
385D4—84no—
386D4—84no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—84no—
406C2×C4—4721no—
407C2×C4—4721no—
408C2×C4—2362no—
409C2×C4C2×#1174566911yescharacteristic
410C2×C4C2×#1174567011yescharacteristic
411C2×C4#1427374711yescharacteristic
412C2×C4#1427375311yescharacteristic
413C2×C4#1427375311yescharacteristic
414C2×C4#1427375711yescharacteristic
415C8—4721no—
416C8—2362no—
417C8—2362no—
418C22—42no—
419C22—42no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22#1683753611yescharacteristic
433C22#1683755311yescharacteristic
434C22#1683756411yescharacteristic
435C22#1683757011yescharacteristic
436C22#1683758011yescharacteristic
437C22#1683758511yescharacteristic
438C22#1683758911yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—4722no—
450C2—82no—
451C2—161no—
452C2#2142301411yescharacteristic
453C2#2142306511yescharacteristic
454C2#2142307611yescharacteristic
455C2#2142322311yescharacteristic
456C2#2142327511yescharacteristic
457C2#2142333111yescharacteristic
458C2#2142341311yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
Fitting, prime radicalC59×#2682C2
socleC23×C59#120
hypercenter#2682D59
hypocenterC59#7752
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #21425424C2semidirect
2. #21425232C2semidirect
3. #21425178C2semidirect
4. #21421919C2semidirect
5. #21421917C2semidirect
6. #21421917C2semidirect
105. C4⋊C4×C59SD16semidirect
256. C59#7752semidirect
349. C4⋊C4#11745670semidirect

Maximal subgroups

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

subgroupindex
#214254242
#214252322
#214251782
#214219192
#214219172
C59×#26822
#775259