Finite Group Databasebeta

← #28480342

Subgroups — #28480342

Order 15104.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273644C211yesmaximal, characteristic, complemented
2#21422698C212yesmaximal, complemented
3#21422539C212yesmaximal, complemented
4#21422437C211yesmaximal, characteristic, complemented
5C2×C59×#553C211yesmaximal, characteristic
6#16837459C2212yes—
7C2×#14273644—21no—
8C4×#11745664C2212yes—
9#16837171—21no—
10#16837144—24no—
11D4⋊(C59⋊C8)—24no—
12#16837126—21no—
13#16837126—21no—
14C59×#553—24no—
15C59×#553—24no—
16C2×#126×C59—21no—
17C2×#125×C59C2211yescharacteristic
18C2×#123×C59—21no—
19C2×#121×C59—21no—
20C2×#121×C59C411yescharacteristic
21C2×#121×C59C411yescharacteristic
22C2×C4×D4×C59—21no—
23C2×C4×D4×C59C2211yescharacteristic
24C2×C4×D4×C59C2211yescharacteristic
25C2×#117×C59C411yescharacteristic
26C22×C4⋊C4×C59C411yescharacteristic
27C2×#11745664—22no—
28C4⋊(C59⋊C8)—22no—
29#14273644—24no—
30C22⋊(C59⋊C8)—22no—
31#14273638—22no—
32#14273638—22no—
33C4×C59⋊C8—22no—
34C22×D4×C59—21no—
35C22×D4×C59—21no—
36C22×D4×C59C2×C411yescharacteristic
37C22×D4×C59D411yescharacteristic
38C23×C4×C59—21no—
39C23×C4×C59—21no—
40C23×C4×C59C2×C411yescharacteristic
41C23×C4×C59C2×C411yescharacteristic
42#126×C59—28no—
43#125×C59—22no—
44#125×C59D414yes—
45#123×C59—28no—
46#121×C59—28no—
47#121×C59—22no—
48#121×C59—22no—
49#121×C59—22no—
50#121×C59—22no—
51C4×D4×C59—28no—
52C4×D4×C59—22no—
53C4×D4×C59—22no—
54C4×D4×C59—22no—
55C4×D4×C59D414yes—
56#117×C59—22no—
57#117×C59—22no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—22no—
62C2×C4⋊C4×C59—22no—
63C2×C4⋊C4×C59C2×C411yescharacteristic
64C2×C4⋊C4×C59C2×C411yescharacteristic
65C2×C4⋊C4×C59C2×C411yescharacteristic
66C2×C4⋊C4×C59D411yescharacteristic
67C2×C22⋊C4×C59—21no—
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59D411yescharacteristic
72C2×C22⋊C4×C59D411yescharacteristic
73C2×C42×C59—21no—
74C2×C42×C59C2311yescharacteristic
75C24×C59—21no—
76C24×C59C22⋊C411yescharacteristic
77C24×C59C22⋊C411yescharacteristic
78C2×D4×C59—24no—
79C2×D4×C59—22no—
80C2×D4×C59—24no—
81C2×D4×C59—21no—
82C2×D4×C59—22no—
83C2×D4×C59—42no—
84C2×D4×C59—41no—
85C2×D4×C59—42no—
86C2×D4×C59—42no—
87C2×D4×C59—82no—
88C2×D4×C59C22⋊C412yes—
89C22×C4×C59—21no—
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59—24no—
93C22×C4×C59—21no—
94C22×C4×C59—21no—
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—24no—
98C22×C4×C59—42no—
99C22×C4×C59—42no—
100C22×C4×C59—82no—
101C22×C4×C59—82no—
102C22×C4×C59C22⋊C411yescharacteristic
103C22×C4×C59C22⋊C411yescharacteristic
104C22×C4×C59C22×C411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59C2×D411yescharacteristic
107C4⋊C4×C59—24no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—24no—
112C4⋊C4×C59—24no—
113C4⋊C4×C59—22no—
114C4⋊C4×C59C22⋊C412yes—
115C4⋊C4×C59C22⋊C412yes—
116C4⋊C4×C59C22⋊C412yes—
117C22⋊C4×C59—24no—
118C22⋊C4×C59—24no—
119C22⋊C4×C59—24no—
120C22⋊C4×C59—24no—
121C22⋊C4×C59—22no—
122C22⋊C4×C59—22no—
123C42×C59—24no—
124C42×C59C2×D412yes—
125C42×C59C2×D412yes—
126#11745664—24no—
127#11745664—42no—
128C2×C59⋊C8—42no—
129C2×C59⋊C8—42no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—22no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—42no—
139C23×C59—42no—
140C23×C59—41no—
141C23×C59—41no—
142C23×C59—41no—
143C23×C59—41no—
144C23×C59#10412yes—
145C23×C59C2×C22⋊C411yescharacteristic
146D4×C59—24no—
147D4×C59—44no—
148D4×C59—42no—
149D4×C59—48no—
150D4×C59—84no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—22no—
154C2×C4×C59—21no—
155C2×C4×C59—22no—
156C2×C4×C59—22no—
157C2×C4×C59—21no—
158C2×C4×C59—22no—
159C2×C4×C59—41no—
160C2×C4×C59—42no—
161C2×C4×C59—42no—
162C2×C4×C59—42no—
163C2×C4×C59—42no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—42no—
167C2×C4×C59—42no—
168C2×C4×C59—41no—
169C2×C4×C59—41no—
170C2×C4×C59—84no—
171C2×C4×C59—84no—
172C2×C4×C59C2×C22⋊C411yescharacteristic
173C2×C4×C59C2×C22⋊C411yescharacteristic
174C2×C4×C59#12012yes—
175C2×C4×C59#12012yes—
176C59⋊C8—44no—
177C59⋊C8—82no—
178#8373—591nomaximal, Sylow
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—22no—
182C22×C59—42no—
183C22×C59—42no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—42no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—42no—
190C22×C59—41no—
191C22×C59—42no—
192C22×C59—81no—
193C22×C59—81no—
194C22×C59—82no—
195C22×C59—82no—
196C22×C59#37911yescharacteristic
197C22×C59C2×#10411yescharacteristic
198C22×C59#42111yescharacteristic
199C4×C59—22no—
200C4×C59—21no—
201C4×C59—22no—
202C4×C59—42no—
203C4×C59—42no—
204C4×C59—41no—
205C4×C59—41no—
206C4×C59—42no—
207C4×C59#41312yes—
208C2×#553D5911yescharacteristic
209C4×#100—591no—
210#1528—592no—
211#1490—592no—
212#1466—591no—
213C2×C59—21no—
214C2×C59—21no—
215C2×C59—42no—
216C2×C59—81no—
217C2×C59—82no—
218C2×C59#178511yescharacteristic
219C2×C59#178911yescharacteristic
220C2×C59#179511yescharacteristic
221#553—24no—
222#553—24no—
223C2×#126—21no—
224C2×#125C2×D5911yescharacteristic
225C2×#123—21no—
226C2×#121—21no—
227C2×#121Dic5911yescharacteristic
228C2×#121Dic5911yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2×D5911yescharacteristic
231C2×C4×D4C2×D5911yescharacteristic
232C2×#117Dic5911yescharacteristic
233C22×C4⋊C4Dic5911yescharacteristic
234#432—592no—
235C2×#100—1181no—
236C4×M16—592no—
237#343—1181no—
238#330—1184no—
239D4⋊C8—1184no—
240#323—1181no—
241#323—1181no—
242C59#837311yescharacteristic, complemented, Sylow
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C2×Dic5911yescharacteristic
246C22×D4C22⋊D5911yescharacteristic
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C2×Dic5911yescharacteristic
250C23×C4C2×Dic5911yescharacteristic
251C2×M16—1182no—
252#126—28no—
253#125—22no—
254#125C22⋊D5914yes—
255#123—28no—
256#121—28no—
257#121—22no—
258#121—22no—
259#121—22no—
260#121—22no—
261C4×D4—28no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4C22⋊D5914yes—
266#117—22no—
267#117—22no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4C2×Dic5911yescharacteristic
274C2×C4⋊C4C2×Dic5911yescharacteristic
275C2×C4⋊C4C2×Dic5911yescharacteristic
276C2×C4⋊C4C22⋊D5911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4C22⋊D5911yescharacteristic
282C2×C22⋊C4C22⋊D5911yescharacteristic
283C2×C42—21no—
284C2×C42C22×D5911yescharacteristic
285C4⋊C8—1182no—
286#100—1184no—
287C22⋊C8—1182no—
288#97—1182no—
289#97—1182no—
290C4×C8—1182no—
291C24—21no—
292C24C22⋊Dic5911yescharacteristic
293C24C22⋊Dic5911yescharacteristic
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—24no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—42no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—82no—
304C2×D4C22⋊Dic5912yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4C22⋊Dic5911yescharacteristic
319C22×C4C22⋊Dic5911yescharacteristic
320C22×C4C22×Dic5911yescharacteristic
321C22×C4C2×C22⋊D5911yescharacteristic
322C22×C4C2×C22⋊D5911yescharacteristic
323M16—1184no—
324M16—2362no—
325C2×C8—2362no—
326C2×C8—2362no—
327C4⋊C4—24no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4C22⋊Dic5912yes—
335C4⋊C4C22⋊Dic5912yes—
336C4⋊C4C22⋊Dic5912yes—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C42—24no—
344C42C2×C22⋊D5912yes—
345C42C2×C22⋊D5912yes—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23#1427365412yes—
361C23C2×C22⋊Dic5911yescharacteristic
362D4—24no—
363D4—44no—
364D4—42no—
365D4—48no—
366D4—84no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—84no—
387C2×C4—84no—
388C2×C4C2×C22⋊Dic5911yescharacteristic
389C2×C4C2×C22⋊Dic5911yescharacteristic
390C2×C4#1427369612yes—
391C2×C4#1427369612yes—
392C8—4722no—
393C8—2364no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—41no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22#1683725811yescharacteristic
412C22C2×#1427365411yescharacteristic
413C22#1683741911yescharacteristic
414C4—21no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4#1683738612yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—82no—
427C2—81no—
428C2#2142402411yescharacteristic
429C2#2142404011yescharacteristic
430C2#2142406611yescharacteristic
subgroupG/H
centerC22#16837258
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
Fitting, prime radicalC2×C59×#553C2
socleC22×C59#379
cosocleC2×C42×C59C23
hypercenterC2×#553D59
hypocenterC59#8373
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C4×#14273644C2semidirect
2. #21422698C2semidirect
3. #21422539C2semidirect
4. #21422437C2semidirect
242. C59#8373semidirect

Maximal subgroups

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

subgroupindex
C4×#142736442
#214226982
#214225392
#214224372
C2×C59×#5532
#837359