Finite Group Databasebeta

← #28492070

Subgroups — #28492070

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429098C211yesmaximal, characteristic
2#21424901C211yesmaximal, characteristic
3#21424098C211yesmaximal, characteristic, complemented
4C2×#16837145C211yesmaximal, characteristic
5C2×#16837132C211yesmaximal, characteristic, complemented
6#21421937C211yesmaximal, characteristic, complemented
7C59×#1947C211yesmaximal, characteristic, complemented
8C2×#14273724C2211yescharacteristic
9C2×#14273715—21no—
10C2×C4×Dic118C2211yescharacteristic
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×#14273650—21no—
13C2×#14273647—22no—
14C2×C4×C59⋊C8C2211yescharacteristic
15#16837320—22no—
16#16837304—21no—
17#16837303—21no—
18#16837303—21no—
19#16837164—21no—
20#16837145—22no—
21#16837132—22no—
22C2×#107×C59—21no—
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C4×C4⋊C4×C59C2211yescharacteristic
26C59×#340—21no—
27C22×Dic118D411yescharacteristic
28C22×D236—21no—
29C22×D236—21no—
30C22×D236D412yes—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33#14273724—21no—
34#14273724—21no—
35#14273724—21no—
36#14273724—21no—
37#14273715—42no—
38#14273715—42no—
39C4×Dic118—21no—
40C4×Dic118—21no—
41C4×Dic118—21no—
42C4×Dic118—21no—
43C2×C4⋊Dic59D411yescharacteristic
44C2×Dic59⋊C4—21no—
45C2×(C2×D59)⋊C4—22no—
46C2×(C2×D59)⋊C4—22no—
47C2×(C2×D59)⋊C4—22no—
48C2×(C2×D59)⋊C4—22no—
49C2×C4×Dic59—21no—
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)—21no—
52#14273650—42no—
53#14273647—44no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8—21no—
56C22×C8×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59D411yescharacteristic
61C2×C4⋊C4×C59D411yescharacteristic
62C2×C42×C59—21no—
63C2×C42×C59C2311yescharacteristic
64#107×C59—42no—
65C4⋊C8×C59—21no—
66C4⋊C8×C59D412yes—
67#95×C59—21no—
68C23×D59—22no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—41no—
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×D236—22no—
78C2×D236—22no—
79C2×D236—42no—
80C2×D236—42no—
81C2×D236—41no—
82C2×D236—41no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×Dic118—21no—
94C2×Dic118—21no—
95C2×Dic118—21no—
96C2×Dic118—21no—
97C2×Dic118—21no—
98C2×Dic118D812yes—
99C2×C8×C59—22no—
100C2×C8×C59—41no—
101C2×C8×C59—41no—
102C4⋊C4×C59—21no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—42no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59—41no—
110C4⋊C4×C59—41no—
111C42×C59—41no—
112C42×C59—41no—
113C42×C59C2×D411yescharacteristic
114C42×C59#4111yescharacteristic
115C42×C59#4111yescharacteristic
116C42×C59#4111yescharacteristic
117(C2×D59)⋊C4—44no—
118(C2×D59)⋊C4—44no—
119(C2×D59)⋊C4—82no—
120(C2×D59)⋊C4—82no—
121C4⋊Dic59—21no—
122C4⋊Dic59—21no—
123Dic59⋊C4—41no—
124Dic59⋊C4—41no—
125C4×Dic59—41no—
126C4×Dic59—41no—
127C2×C59⋊C8—22no—
128C2×C59⋊C8—41no—
129C2×C59⋊C8—41no—
130C2×C59⋊C8—41no—
131C2×C59⋊C8—41no—
132C2×C59⋊C8—41no—
133C23×C59#12011yescharacteristic
134C22×D59—42no—
135C22×D59—42no—
136C22×D59—42no—
137C22×D59—42no—
138C22×D59—42no—
139C22×D59—42no—
140C22×D59—42no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—81no—
150C2×C4×C59—81no—
151C2×C4×C59—81no—
152C2×C4×C59#12111yescharacteristic
153C2×C4×C59#12111yescharacteristic
154C2×C4×C59#12111yescharacteristic
155C2×C4×C59#12311yescharacteristic
156C2×C4×C59#12311yescharacteristic
157C2×C4×C59#12411yescharacteristic
158C2×C4×C59C2×D811yescharacteristic
159C2×C4×C59#13511yescharacteristic
160C2×C4×C59#13511yescharacteristic
161C2×C4×C59#13511yescharacteristic
162C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C59#13711yescharacteristic
165C2×C4×C59#13711yescharacteristic
166C2×Dic59—22no—
167C2×Dic59—41no—
168C2×Dic59—41no—
169C2×Dic59—41no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172D236—44no—
173D236—82no—
174D236—81no—
175D236—81no—
176D236—81no—
177D236—81no—
178D236—81no—
179D236—81no—
180D236—81no—
181D236—81no—
182Dic118—22no—
183Dic118—22no—
184Dic118—41no—
185Dic118—41no—
186C8×C59—42no—
187C59⋊C8—42no—
188C59⋊C8—81no—
189#10411—591nomaximal, Sylow
190C22×C59#39411yescharacteristic
191C22×C59#44711yescharacteristic
192C22×C59#44911yescharacteristic
193C22×C59#45211yescharacteristic
194C22×C59#45211yescharacteristic
195C22×C59#45311yescharacteristic
196C22×C59#45511yescharacteristic
197C2×D59—82no—
198C2×D59—82no—
199C2×D59—82no—
200C2×D59—82no—
201C2×D59—82no—
202C2×D59—82no—
203C2×D59—82no—
204C4×C59—21no—
205C4×C59—21no—
206C4×C59—81no—
207C4×C59—81no—
208C4×C59—161no—
209C4×C59#46311yescharacteristic
210C4×C59#46411yescharacteristic
211C4×C59#46611yescharacteristic
212C4×C59#46811yescharacteristic
213C4×C59#48011yescharacteristic
214C4×C59#48211yescharacteristic
215C4×C59#48811yescharacteristic
216C4×C59#48911yescharacteristic
217Dic59—42no—
218Dic59—81no—
219#2548—591no—
220#1957—591no—
221#1947D5911yescharacteristic, complemented
222#1803—591no—
223C2×#331—591no—
224C2×Q8⋊C8—591no—
225#1279—591no—
226C2×C59#162111yescharacteristic
227C2×C59#163011yescharacteristic
228C2×C59#164011yescharacteristic
229C2×C59#164111yescharacteristic
230C2×C59#203311yescharacteristic
231C2×C59#203711yescharacteristic
232C2×C59#204211yescharacteristic
233D59—162no—
234C2×#127—591no—
235C2×#124—1181no—
236C2×C4×Q8—591no—
237C2×#107—21no—
238C2×C4⋊C8—591no—
239C2×C4⋊C8C2×D5911yescharacteristic
240C2×#103—1181no—
241C2×#102—1182no—
242C2×C4×C8—591no—
243#394—1182no—
244#390—1181no—
245#390—1181no—
246#390—1181no—
247#384C2×D5911yescharacteristic
248C4×C4⋊C4C2×D5911yescharacteristic
249#340—21no—
250#340—1181no—
251#331—1182no—
252Q8⋊C8—1182no—
253C59#1041111yescharacteristic, complemented, Sylow
254C22×Q8—591no—
255C22×D4—592no—
256C22×D4—1181no—
257C22×D4—1181no—
258C22×C8—21no—
259C22×C8—1181no—
260C22×C8—1181no—
261#127—1181no—
262#127—1181no—
263#127—1181no—
264#127—1181no—
265#124—2362no—
266#124—2362no—
267C4×Q8—1181no—
268C4×Q8—1181no—
269C4×Q8—1181no—
270C4×Q8—1181no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—591no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4C22⋊D5911yescharacteristic
277C2×C4⋊C4C22⋊D5911yescharacteristic
278C2×C22⋊C4—1182no—
279C2×C22⋊C4—1182no—
280C2×C22⋊C4—1182no—
281C2×C22⋊C4—1182no—
282C2×C42—21no—
283C2×C42—1181no—
284C2×C42C22×D5911yescharacteristic
285#107—42no—
286C4⋊C8—21no—
287C4⋊C8—1181no—
288C4⋊C8—1181no—
289C4⋊C8D23612yes—
290#103—2362no—
291#102—2364no—
292C4×C8—1181no—
293C4×C8—1181no—
294#95—21no—
295C24—1182no—
296C2×Q8—592no—
297C2×Q8—1181no—
298C2×Q8—1181no—
299C2×Q8—1181no—
300C2×Q8—1181no—
301C2×Q8—1181no—
302C2×D4—1182no—
303C2×D4—1182no—
304C2×D4—2362no—
305C2×D4—2362no—
306C2×D4—2361no—
307C2×D4—2361no—
308C2×D4—2361no—
309C2×D4—2361no—
310C2×D4—2361no—
311C2×D4—2361no—
312C2×D4—2361no—
313C2×D4—2361no—
314C2×D4—2361no—
315C2×D4—2361no—
316C2×D4—2361no—
317C2×D4—2361no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—1181no—
322C22×C4—1181no—
323C22×C4D4×D5911yescharacteristic
324C22×C4D4×D5911yescharacteristic
325C22×C4C2×C22⋊D5911yescharacteristic
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—1182no—
330C2×C8—2361no—
331C2×C8—2361no—
332C2×C8—2361no—
333C2×C8—2361no—
334C2×C8—2361no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—1181no—
345C4⋊C4—1181no—
346C4⋊C4—2361no—
347C4⋊C4—2361no—
348C22⋊C4—4722no—
349C22⋊C4—4722no—
350C22⋊C4—2364no—
351C22⋊C4—2364no—
352C42—41no—
353C42—41no—
354C42—2361no—
355C42—2361no—
356C42C2×D23611yescharacteristic
357C42#1174568511yescharacteristic
358C42#1174568911yescharacteristic
359C42#1174568911yescharacteristic
360C23—2362no—
361C23—2362no—
362C23—2362no—
363C23—2362no—
364C23—2362no—
365C23—2362no—
366C23—2362no—
367C23#1427369511yescharacteristic
368Q8—1182no—
369Q8—1182no—
370Q8—2361no—
371Q8—2361no—
372D4—4722no—
373D4—4721no—
374D4—4721no—
375D4—4721no—
376D4—4721no—
377D4—4721no—
378D4—4721no—
379D4—4721no—
380D4—4721no—
381D4—2364no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1182no—
394C2×C4—2361no—
395C2×C4—2361no—
396C2×C4—2361no—
397C2×C4—2361no—
398C2×C4—2361no—
399C2×C4#1427370111yescharacteristic
400C2×C4#1427370211yescharacteristic
401C2×C4#1427370211yescharacteristic
402C2×C4#1427371211yescharacteristic
403C2×C4#1427371211yescharacteristic
404C2×C4#1427371611yescharacteristic
405C2×C4D8×D5911yescharacteristic
406C2×C4#1427374711yescharacteristic
407C2×C4#1427374711yescharacteristic
408C2×C4#1427375011yescharacteristic
409C2×C4#1427375111yescharacteristic
410C2×C4#1427375311yescharacteristic
411C2×C4#1427375811yescharacteristic
412C2×C4#1427375911yescharacteristic
413C8—42no—
414C8—4721no—
415C8—2362no—
416C22—4722no—
417C22—4722no—
418C22—4722no—
419C22—4722no—
420C22—4722no—
421C22—4722no—
422C22—4722no—
423C22#1683731911yescharacteristic
424C22#1683753411yescharacteristic
425C22#1683754511yescharacteristic
426C22#1683756211yescharacteristic
427C22#1683756311yescharacteristic
428C22#1683756811yescharacteristic
429C22#1683757811yescharacteristic
430C4—21no—
431C4—21no—
432C4—81no—
433C4—81no—
434C4—161no—
435C4—4721no—
436C4—2362no—
437C4#1683761711yescharacteristic
438C4#1683762411yescharacteristic
439C4#1683763911yescharacteristic
440C4#1683764911yescharacteristic
441C4#1683771711yescharacteristic
442C4#1683772911yescharacteristic
443C4#1683775911yescharacteristic
444C4#1683776411yescharacteristic
445C2—9442no—
446C2#2142316011yescharacteristic
447C2#2142321611yescharacteristic
448C2#2142328011yescharacteristic
449C2#2142328811yescharacteristic
450C2#2142528011yescharacteristic
451C2#2142530811yescharacteristic
452C2#2142533711yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1947C2
socleC23×C59#120
prime radicalC2×#14273724C22
hypercenter#1947D59
hypocenterC59#10411
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #21424098C2semidirect
5. C2×#16837132C2semidirect
6. #21421937C2semidirect
7. C59×#1947C2semidirect
221. #1947D59semidirect
253. C59#10411semidirect

Maximal subgroups

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

subgroupindex
#214290982
#214249012
#214240982
C2×#168371452
C2×#168371322
#214219372
C59×#19472
#1041159