Finite Group Databasebeta

← #28481401

Subgroups — #28481401

Order 15104.

548 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426557C211yesmaximal, characteristic
2#21424212C211yesmaximal, characteristic, complemented
3C4×Dic59⋊C8C211yesmaximal, characteristic, complemented
4C2×#16837131C211yesmaximal, characteristic
5C2×#16837129C211yesmaximal, characteristic
6#21421937C211yesmaximal, characteristic, complemented
7C59×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9C2×#14273684—21no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×Dic59⋊C8—21no—
12C2×C4×C59⋊C8C2211yescharacteristic
13#16837303C411yescharacteristic
14#16837303C411yescharacteristic
15#16837298C411yescharacteristic
16#16837298C411yescharacteristic
17#16837291—21no—
18#16837291—21no—
19C4×(C2×D59)⋊C4—21no—
20C42×Dic59C2211yescharacteristic
21#16837156—21no—
22#16837156—21no—
23#16837156—21no—
24#16837131—22no—
25#16837129—22no—
26C2×C4⋊C8×C59C2211yescharacteristic
27C2×C4×C8×C59C2211yescharacteristic
28C4×C4⋊C4×C59C2211yescharacteristic
29C22×D236C2×C411yescharacteristic
30C22×C4×D59—21no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C4×D236—21no—
34C4×D236—21no—
35C4×D236D412yes—
36C4×D236Q812yes—
37#14273684—42no—
38#14273684—42no—
39C2×C4⋊Dic59C2×C411yescharacteristic
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×(C2×D59)⋊C4—21no—
45C2×(C2×D59)⋊C4—21no—
46C2×(C2×D59)⋊C4—21no—
47C2×C4×Dic59C2×C411yescharacteristic
48C2×C4×Dic59C2×C411yescharacteristic
49C2×C4×Dic59D411yescharacteristic
50C2×C4×Dic59D411yescharacteristic
51C2×C4×Dic59D411yescharacteristic
52C2×C4×Dic59D411yescharacteristic
53C4⋊(C59⋊C8)—21no—
54C4⋊(C59⋊C8)—21no—
55Dic59⋊C8—24no—
56C4×C59⋊C8—21no—
57C4×C59⋊C8—21no—
58C59⋊#95—21no—
59C59⋊#95—21no—
60C22×C8×C59—21no—
61C22×C8×C59—21no—
62C2×C4⋊C4×C59C2×C411yescharacteristic
63C2×C4⋊C4×C59C2×C411yescharacteristic
64C2×C42×C59—21no—
65C2×C42×C59C2311yescharacteristic
66C4⋊C8×C59—21no—
67C4⋊C8×C59—21no—
68C4×C8×C59—21no—
69C4×C8×C59—21no—
70#95×C59—21no—
71C23×D59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×Dic59—21no—
78C22×Dic59C22⋊C411yescharacteristic
79C22×Dic59C22⋊C411yescharacteristic
80C22×Dic59C22⋊C411yescharacteristic
81C22×Dic59C22⋊C411yescharacteristic
82C2×D236—21no—
83C2×D236—21no—
84C2×D236—21no—
85C2×D236—21no—
86C2×D236—21no—
87C2×D236C4⋊C412yes—
88C2×C4×D59—22no—
89C2×C4×D59—22no—
90C2×C4×D59—41no—
91C2×C4×D59—41no—
92C2×C4×D59—41no—
93C2×C4×D59—41no—
94C2×C8×C59—22no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C4⋊C4×C59—21no—
101C4⋊C4×C59—21no—
102C4⋊C4×C59—21no—
103C4⋊C4×C59—21no—
104C42×C59—41no—
105C42×C59—41no—
106C42×C59C2×D411yescharacteristic
107C42×C59C2×Q811yescharacteristic
108C42×C59#4111yescharacteristic
109C42×C59#4111yescharacteristic
110(C2×D59)⋊C4—22no—
111(C2×D59)⋊C4—22no—
112(C2×D59)⋊C4—42no—
113(C2×D59)⋊C4—42no—
114(C2×D59)⋊C4—42no—
115(C2×D59)⋊C4—42no—
116C4⋊Dic59—21no—
117C4⋊Dic59C4⋊C412yes—
118Dic59⋊C4—42no—
119Dic59⋊C4—42no—
120C4×Dic59—21no—
121C4×Dic59—21no—
122C4×Dic59—21no—
123C4×Dic59—21no—
124C4×Dic59—21no—
125C4×Dic59—21no—
126C4×Dic59—21no—
127C4×Dic59—21no—
128C4×Dic59—22no—
129C4×Dic59—41no—
130C2×C59⋊C8—22no—
131C2×C59⋊C8—41no—
132C2×C59⋊C8—41no—
133C2×C59⋊C8—41no—
134C2×C59⋊C8—41no—
135C2×C59⋊C8—41no—
136C23×C59C2×C22⋊C411yescharacteristic
137C22×D59—22no—
138C22×D59—41no—
139C22×D59—41no—
140C22×D59—41no—
141C22×D59—41no—
142C22×D59—41no—
143C22×D59—41no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59C2×C4⋊C411yescharacteristic
153C2×C4×C59#11711yescharacteristic
154C2×C4×C59#12111yescharacteristic
155C2×C4×C59#12111yescharacteristic
156C2×C4×C59C22⋊Q811yescharacteristic
157C2×C4×C59C22⋊Q811yescharacteristic
158C2×C4×C59#13111yescharacteristic
159C2×C4×C59#13111yescharacteristic
160C2×C4×C59#13111yescharacteristic
161C2×C4×C59#13111yescharacteristic
162C2×C4×C59#13511yescharacteristic
163C2×C4×C59#13511yescharacteristic
164C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—22no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C2×Dic59—21no—
174C2×Dic59—21no—
175C2×Dic59—21no—
176C2×Dic59—21no—
177C2×Dic59—21no—
178C2×Dic59—41no—
179C2×Dic59—41no—
180C2×Dic59#10412yes—
181D236—22no—
182D236—22no—
183D236—41no—
184D236—41no—
185C4×D59—42no—
186C4×D59—42no—
187C4×D59—42no—
188C4×D59—42no—
189C8×C59—42no—
190C8×C59—81no—
191C59⋊C8—42no—
192C59⋊C8—81no—
193#8569—591nomaximal, Sylow
194C22×C59#38011yescharacteristic
195C22×C59#40811yescharacteristic
196C22×C59#40811yescharacteristic
197C22×C59#41611yescharacteristic
198C22×C59#41811yescharacteristic
199C22×C59C2×#10411yescharacteristic
200C22×C59#42111yescharacteristic
201C2×D59—42no—
202C2×D59—42no—
203C2×D59—42no—
204C2×D59—81no—
205C2×D59—81no—
206C2×D59—81no—
207C2×D59—81no—
208C4×C59—21no—
209C4×C59—21no—
210C4×C59—81no—
211C4×C59—81no—
212C4×C59#42411yescharacteristic
213C4×C59#42411yescharacteristic
214C4×C59#43311yescharacteristic
215C4×C59#43311yescharacteristic
216C4×C59#46311yescharacteristic
217C4×C59#46311yescharacteristic
218C4×C59#47811yescharacteristic
219C4×C59#47811yescharacteristic
220Dic59—22no—
221Dic59—42no—
222Dic59—41no—
223Dic59—41no—
224Dic59—41no—
225#2293—591no—
226#1831—591no—
227C4×C4⋊C8—591no—
228C2×D4⋊C8—591no—
229C2×D4⋊C8—591no—
230#1279—591no—
231#1279D5911yescharacteristic, complemented
232C2×C59#148211yescharacteristic
233C2×C59#148411yescharacteristic
234C2×C59#149411yescharacteristic
235C2×C59#149611yescharacteristic
236C2×C59#179811yescharacteristic
237C2×C59#180411yescharacteristic
238C2×C59#180611yescharacteristic
239D59—82no—
240C2×C4×D4—591no—
241C2×#117—1181no—
242C2×C4⋊C8—591no—
243C2×C4⋊C8—1181no—
244C2×C4⋊C8C2×D5911yescharacteristic
245C2×C4×C8—591no—
246C2×C4×C8C2×D5911yescharacteristic
247#390—591no—
248#390—591no—
249#389—591no—
250#389—591no—
251#388—1181no—
252#388—1181no—
253C4×C4⋊C4C2×D5911yescharacteristic
254C4×C22⋊C4—1181no—
255C43—591no—
256#336—1181no—
257#336—1181no—
258#336—1181no—
259D4⋊C8—1182no—
260D4⋊C8—1182no—
261C59#856911yescharacteristic, complemented, Sylow
262C22×D4—591no—
263C23×C4—1181no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—1181no—
267C22×C8—1181no—
268C4×D4—592no—
269C4×D4—592no—
270C4×D4—1181no—
271C4×D4—1181no—
272#117—2362no—
273#117—2362no—
274C2×C4⋊C4—591no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4C4×D5911yescharacteristic
278C2×C4⋊C4C4×D5911yescharacteristic
279C2×C22⋊C4—1181no—
280C2×C22⋊C4—1181no—
281C2×C22⋊C4—1181no—
282C2×C22⋊C4—1181no—
283C2×C22⋊C4—1181no—
284C2×C42—21no—
285C2×C42—591no—
286C2×C42—591no—
287C2×C42—591no—
288C2×C42—591no—
289C2×C42—591no—
290C2×C42—591no—
291C2×C42C22×D5911yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1184no—
295C4⋊C8—1181no—
296C4⋊C8—1181no—
297C4×C8—21no—
298C4×C8—21no—
299C4×C8—1181no—
300C4×C8—1181no—
301#95—21no—
302#95—1181no—
303#95—1181no—
304C24—1181no—
305C2×D4—592no—
306C2×D4—1181no—
307C2×D4—1181no—
308C2×D4—1181no—
309C2×D4—1181no—
310C2×D4—1181no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—591no—
314C22×C4—591no—
315C22×C4—591no—
316C22×C4—591no—
317C22×C4—1181no—
318C22×C4—1182no—
319C22×C4—1182no—
320C22×C4—2361no—
321C22×C4—2361no—
322C22×C4—2361no—
323C22×C4—2361no—
324C22×C4C2×C4×D5911yescharacteristic
325C22×C4D4×D5911yescharacteristic
326C22×C4D4×D5911yescharacteristic
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—1182no—
334C2×C8—2361no—
335C2×C8—2361no—
336C2×C8—2361no—
337C2×C8—2361no—
338C2×C8—2361no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—592no—
344C4⋊C4—1181no—
345C4⋊C4—2362no—
346C4⋊C4—2362no—
347C22⋊C4—1182no—
348C22⋊C4—1182no—
349C22⋊C4—2362no—
350C22⋊C4—2362no—
351C22⋊C4—2362no—
352C22⋊C4—2362no—
353C42—41no—
354C42—41no—
355C42—1182no—
356C42—1181no—
357C42—1181no—
358C42—1181no—
359C42—1181no—
360C42—1181no—
361C42—1181no—
362C42—1181no—
363C42—1181no—
364C42—2361no—
365C42#1174568511yescharacteristic
366C42#1174568511yescharacteristic
367C42D4×D5911yescharacteristic
368C42Q8×D5911yescharacteristic
369C23—1182no—
370C23—2361no—
371C23—2361no—
372C23—2361no—
373C23—2361no—
374C23—2361no—
375C23—2361no—
376C23C22⋊C4×D5911yescharacteristic
377D4—1182no—
378D4—1182no—
379D4—2361no—
380D4—2361no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—592no—
390C2×C4—1181no—
391C2×C4—1181no—
392C2×C4—1181no—
393C2×C4—1181no—
394C2×C4—1181no—
395C2×C4—1181no—
396C2×C4—1181no—
397C2×C4—1181no—
398C2×C4—1182no—
399C2×C4—1181no—
400C2×C4—1181no—
401C2×C4—1181no—
402C2×C4—2361no—
403C2×C4—2361no—
404C2×C4—2362no—
405C2×C4—2362no—
406C2×C4—2362no—
407C2×C4—2362no—
408C2×C4C4⋊C4×D5911yescharacteristic
409C2×C4#1427368411yescharacteristic
410C2×C4#1427370011yescharacteristic
411C2×C4#1427370011yescharacteristic
412C2×C4#1427370511yescharacteristic
413C2×C4#1427370511yescharacteristic
414C2×C4#1427373311yescharacteristic
415C2×C4#1427373311yescharacteristic
416C2×C4#1427373511yescharacteristic
417C2×C4#1427373511yescharacteristic
418C2×C4#1427374811yescharacteristic
419C2×C4#1427375011yescharacteristic
420C2×C4#1427375111yescharacteristic
421C2×C4#1427375411yescharacteristic
422C8—42no—
423C8—81no—
424C8—4721no—
425C8—2362no—
426C22—4721no—
427C22—4721no—
428C22—4721no—
429C22—4721no—
430C22—2362no—
431C22—2362no—
432C22—2362no—
433C22#1683726111yescharacteristic
434C22#1683736711yescharacteristic
435C22#1683736711yescharacteristic
436C22#1683739711yescharacteristic
437C22#1683740511yescharacteristic
438C22#104×D5911yescharacteristic
439C22#1683741711yescharacteristic
440C4—21no—
441C4—21no—
442C4—81no—
443C4—81no—
444C4—1182no—
445C4—2361no—
446C4—2361no—
447C4—2361no—
448C4—2362no—
449C4#1683742711yescharacteristic
450C4#1683742711yescharacteristic
451C4#1683746111yescharacteristic
452C4#1683746411yescharacteristic
453C4#1683761611yescharacteristic
454C4#1683762011yescharacteristic
455C4#1683770111yescharacteristic
456C4#1683770511yescharacteristic
457C2—4722no—
458C2#2142250311yescharacteristic
459C2#2142251111yescharacteristic
460C2#2142255511yescharacteristic
461C2#2142256311yescharacteristic
462C2#2142407911yescharacteristic
463C2#2142410511yescharacteristic
464C2#2142411511yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1279C2
socleC23×C59C2×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenter#1279D59
hypocenterC59#8569
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21424212C2semidirect
3. C4×Dic59⋊C8C2semidirect
6. #21421937C2semidirect
7. C59×#1279C2semidirect
231. #1279D59semidirect
261. C59#8569semidirect

Maximal subgroups

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

subgroupindex
#214265572
#214242122
C4×Dic59⋊C82
C2×#168371312
C2×#168371292
#214219372
C59×#12792
#856959