Finite Group Databasebeta

← #28485148

Subgroups — #28485148

Order 15104.

566 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837720C211yesmaximal, characteristic
2#21426973C211yesmaximal, characteristic, complemented
3#21424931C211yesmaximal, characteristic
4#21422665C211yesmaximal, characteristic
5#21421963C211yesmaximal, characteristic, complemented
6#21421942C211yesmaximal, characteristic, complemented
7C59×#1824C211yesmaximal, characteristic, complemented
8C2×#14273701C2211yescharacteristic
9#16837720—21no—
10#16837720—21no—
11#16837720—22no—
12C2×#14273658C412yescomplemented
13C2×#14273647C412yescomplemented
14C2×#14273641—21no—
15C2×#14273641—21no—
16C2×C22⋊(C59⋊C8)C2211yescharacteristic
17#16837301—21no—
18#16837288—22no—
19#16837262—21no—
20#16837262C2211yescharacteristic
21C4⋊C4×Dic59—21no—
22C4×C22⋊Dic59—21no—
23C4×C22⋊Dic59C2211yescharacteristic
24#16837137—22no—
25C22×C4⋊C4×C59C2211yescharacteristic
26C2×C22⋊C8×C59C2211yescharacteristic
27C59×#380C2211yescharacteristic
28C59×#340—22no—
29C22×D236C2×C411yescharacteristic
30C22×C22⋊D59—21no—
31C22×C59⋊C8C2×C412yes—
32#14273701—21no—
33#14273701—21no—
34#14273701—21no—
35#14273701—21no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—22no—
38C2×C4⋊Dic59C2×C411yescharacteristic
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59D411yescharacteristic
41C2×C22⋊Dic59D411yescharacteristic
42C2×(C2×D59)⋊C4—21no—
43C2×C4×Dic59—21no—
44C2×C4×Dic59—22no—
45#14273658—22no—
46#14273658—22no—
47#14273647—22no—
48#14273647—22no—
49#14273641—42no—
50#14273641—42no—
51C22⋊(C59⋊C8)—21no—
52C22⋊(C59⋊C8)—21no—
53C59⋊#95—22no—
54C59⋊#95—22no—
55C59⋊#95—21no—
56C59⋊#95D412yes—
57C23×C4×C59—21no—
58C23×C4×C59C2311yescharacteristic
59C22×C8×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59C2×C412yes—
65C2×C4⋊C4×C59D411yescharacteristic
66C2×C4⋊C4×C59D411yescharacteristic
67C2×C4⋊C4×C59D412yes—
68C2×C22⋊C4×C59—21no—
69C22⋊C8×C59—21no—
70C22⋊C8×C59—21no—
71#95×C59—21no—
72C24×C59C2×D411yescharacteristic
73C23×D59—21no—
74C22×C4×C59—21no—
75C22×C4×C59—21no—
76C22×C4×C59—22no—
77C22×C4×C59—22no—
78C22×C4×C59—42no—
79C22×C4×C59—41no—
80C22×C4×C59—82no—
81C22×C4×C59C22×C411yescharacteristic
82C22×C4×C59C2×D411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59#4111yescharacteristic
86C22×C4×C59#4111yescharacteristic
87C2×C22⋊D59—41no—
88C2×C22⋊D59—41no—
89C2×C22⋊D59—41no—
90C2×C22⋊D59—41no—
91C2×C22⋊D59—41no—
92C2×C22⋊D59—41no—
93C22×Dic59—21no—
94C22×Dic59—21no—
95C22×Dic59—21no—
96C22×Dic59—22no—
97C2×D236—21no—
98C2×D236—21no—
99C2×D236—42no—
100C2×C8×C59—42no—
101C2×C8×C59—41no—
102C4⋊C4×C59—22no—
103C4⋊C4×C59—22no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—42no—
107C4⋊C4×C59C22⋊C412yes—
108C4⋊C4×C59C22⋊C412yes—
109C22⋊C4×C59—41no—
110C22⋊C4×C59—41no—
111C22⋊Dic59—21no—
112C22⋊Dic59—21no—
113C22⋊Dic59—21no—
114C22⋊Dic59—41no—
115C22⋊Dic59—41no—
116C22⋊Dic59SD1612yes—
117(C2×D59)⋊C4—41no—
118(C2×D59)⋊C4—41no—
119C4⋊Dic59—21no—
120C4⋊Dic59—21no—
121C4⋊Dic59—42no—
122C4⋊Dic59—82no—
123C4×Dic59—42no—
124C4×Dic59—82no—
125C2×C59⋊C8—22no—
126C2×C59⋊C8—42no—
127C23×C59—41no—
128C23×C59—41no—
129C23×C59C4×D411yescharacteristic
130C23×C59#12011yescharacteristic
131C23×C59#12111yescharacteristic
132C23×C59C2×SD1611yescharacteristic
133C23×C59#13511yescharacteristic
134C23×C59AGL(1,ℤ/8)11yescharacteristic
135C23×C59#13711yescharacteristic
136C22×D59—41no—
137C22×D59—41no—
138C22×D59—41no—
139C22×D59—81no—
140C22×D59—81no—
141C2×C4×C59—22no—
142C2×C4×C59—22no—
143C2×C4×C59—22no—
144C2×C4×C59—22no—
145C2×C4×C59—22no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—82no—
152C2×C4×C59—82no—
153C2×C4×C59—81no—
154C2×C4×C59—81no—
155C2×C4×C59—81no—
156C2×C4×C59C2×C22⋊C411yescharacteristic
157C2×C4×C59C4×D411yescharacteristic
158C2×C4×C59#12111yescharacteristic
159C2×C4×C59#12311yescharacteristic
160C22⋊D59—81no—
161C22⋊D59—81no—
162C22⋊D59—81no—
163C22⋊D59—81no—
164C2×Dic59—22no—
165C2×Dic59—41no—
166C2×Dic59—41no—
167C2×Dic59—41no—
168C2×Dic59—42no—
169C2×Dic59—42no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172C2×Dic59—41no—
173C2×Dic59—41no—
174C2×Dic59—41no—
175C2×Dic59—42no—
176D236—42no—
177D236—81no—
178C8×C59—81no—
179C59⋊C8—42no—
180#9261—591nomaximal, Sylow
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—41no—
188C22×C59—41no—
189C22×C59—41no—
190C22×C59—41no—
191C22×C59#38611yescharacteristic
192C22×C59C4×SD1611yescharacteristic
193C22×C59#44011yescharacteristic
194C22×C59#44811yescharacteristic
195C22×C59#44911yescharacteristic
196C22×C59#46011yescharacteristic
197C22×C59#46411yescharacteristic
198C2×D59—81no—
199C2×D59—81no—
200C2×D59—81no—
201C2×D59—161no—
202C2×D59—161no—
203C4×C59—21no—
204C4×C59—21no—
205C4×C59—21no—
206C4×C59—42no—
207C4×C59—42no—
208C4×C59—161no—
209C4×C59#41012yes—
210Dic59—42no—
211Dic59—81no—
212Dic59—82no—
213Dic59—81no—
214C2×#481—591no—
215#2345—591no—
216#1964—591no—
217#1824D5911yescharacteristic, complemented
218#1519—591no—
219#1289—591no—
220#1282—591no—
221C2×C59—21no—
222C2×C59—21no—
223C2×C59—21no—
224C2×C59—21no—
225C2×C59—21no—
226C2×C59—21no—
227C2×C59#188011yescharacteristic
228C2×C59#189911yescharacteristic
229C2×C59#190411yescharacteristic
230D59—161no—
231C2×#121—591no—
232C22×C4⋊C4C2×D5911yescharacteristic
233#481—1181no—
234#481—1181no—
235#481—1182no—
236C2×#106—592no—
237C2×#102—592no—
238C2×#99—1181no—
239C2×#99—1181no—
240C2×C22⋊C8—591no—
241C2×C22⋊C8C2×D5911yescharacteristic
242#389—1181no—
243#387—1182no—
244#380—591no—
245#380—1181no—
246#380C2×D5911yescharacteristic
247C4×C4⋊C4—1181no—
248C4×C22⋊C4—591no—
249C4×C22⋊C4—1181no—
250#340—22no—
251#327—1182no—
252C59#926111yescharacteristic, complemented, Sylow
253C22×D4—591no—
254C22×D4—1181no—
255C23×C4—21no—
256C23×C4C22×D5911yescharacteristic
257C22×C8—21no—
258C22×C8—592no—
259#121—1181no—
260#121—1181no—
261#121—1181no—
262#121—1181no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—591no—
268C2×C4⋊C4—1182no—
269C2×C4⋊C4—1181no—
270C2×C4⋊C4C4×D5912yes—
271C2×C4⋊C4D23611yescharacteristic
272C2×C4⋊C4D23611yescharacteristic
273C2×C4⋊C4C22⋊D5912yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—591no—
276C2×C22⋊C4—591no—
277C2×C22⋊C4—1181no—
278C2×C22⋊C4—1181no—
279C2×C42—1182no—
280C2×C42—1181no—
281#106—1182no—
282#106—1182no—
283#102—1182no—
284#102—1182no—
285#99—2362no—
286#99—2362no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—1181no—
290C22⋊C8—1181no—
291#95—21no—
292#95—592no—
293#95—1182no—
294#95—1182no—
295#95—1181no—
296C24—1181no—
297C24D4×D5911yescharacteristic
298C2×D4—1181no—
299C2×D4—1181no—
300C2×D4—2362no—
301C2×D4—2361no—
302C2×D4—2361no—
303C2×D4—2361no—
304C2×D4—2361no—
305C2×D4—2361no—
306C2×D4—2361no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—82no—
314C22×C4—1181no—
315C22×C4—1181no—
316C22×C4—1182no—
317C22×C4—1181no—
318C22×C4C2×C4×D5911yescharacteristic
319C22×C4C2×D23611yescharacteristic
320C22×C4D4×D5911yescharacteristic
321C22×C4#1174568711yescharacteristic
322C22×C4#1174568711yescharacteristic
323C22×C4C2×C22⋊D5911yescharacteristic
324C2×C8—42no—
325C2×C8—41no—
326C2×C8—1182no—
327C2×C8—2362no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—42no—
333C4⋊C4—1181no—
334C4⋊C4—1181no—
335C4⋊C4—4722no—
336C4⋊C4—2362no—
337C4⋊C4(C2×D59)⋊C412yes—
338C4⋊C4(C2×D59)⋊C412yes—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—592no—
342C22⋊C4—1181no—
343C22⋊C4—1181no—
344C22⋊C4—1181no—
345C22⋊C4—2361no—
346C22⋊C4—2361no—
347C22⋊C4—2361no—
348C22⋊C4—2361no—
349C42—4722no—
350C42—2362no—
351C23—41no—
352C23—41no—
353C23—4721no—
354C23—4721no—
355C23—2361no—
356C23—2361no—
357C23—2361no—
358C23(C22⋊D59)⋊C411yescharacteristic
359C23#1427369711yescharacteristic
360C23#1427369911yescharacteristic
361C23SD16×D5911yescharacteristic
362C23#1427375011yescharacteristic
363C23#1427375411yescharacteristic
364C23#1427375911yescharacteristic
365D4—4721no—
366D4—4721no—
367D4—4721no—
368D4—4721no—
369D4—4721no—
370D4—2362no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—1182no—
387C2×C4—2362no—
388C2×C4—2361no—
389C2×C4—2361no—
390C2×C4—2362no—
391C2×C4—2361no—
392C2×C4—2361no—
393C2×C4—2361no—
394C2×C4—2361no—
395C2×C4—2362no—
396C2×C4—2361no—
397C2×C4—2361no—
398C2×C4C2×(C2×D59)⋊C411yescharacteristic
399C2×C4(C22⋊D59)⋊C411yescharacteristic
400C2×C4#1427369911yescharacteristic
401C2×C4#1427371111yescharacteristic
402C8—81no—
403C8—2362no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—9441no—
415C22—9441no—
416C22—4721no—
417C22—4721no—
418C22—4721no—
419C22#1683727911yescharacteristic
420C22#1683748711yescharacteristic
421C22#1683750511yescharacteristic
422C22#1683754211yescharacteristic
423C22#1683755011yescharacteristic
424C22#1683760011yescharacteristic
425C22#1683762611yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—161no—
432C4—4722no—
433C4—4721no—
434C4—4721no—
435C4—2362no—
436C4#1683737512yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—9441no—
444C2#2142444911yescharacteristic
445C2#2142455211yescharacteristic
446C2#2142458111yescharacteristic
subgroupG/H
centerC22#16837279
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1824C2
socleC22×C59#386
prime radicalC2×#14273701C22
cosocleC23×C4×C59C23
hypercenter#1824D59
hypocenterC59#9261
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. #21426973C2semidirect
5. #21421963C2semidirect
6. #21421942C2semidirect
7. C59×#1824C2semidirect
12. C2×#14273658C4semidirect
13. C2×#14273647C4semidirect
217. #1824D59semidirect
252. C59#9261semidirect

Maximal subgroups

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

subgroupindex
C2×#168377202
#214269732
#214249312
#214226652
#214219632
#214219422
C59×#18242
#926159