Finite Group Databasebeta

← #28488209

Subgroups — #28488209

Order 15104.

606 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837636C211yesmaximal, characteristic
2#21424932C211yesmaximal, characteristic, complemented
3#21424123C211yesmaximal, characteristic, complemented
4C22⋊C4×C59⋊C8C211yesmaximal, characteristic, complemented
5#21422664C211yesmaximal, characteristic, complemented
6#21422663C211yesmaximal, characteristic, complemented
7C59×#1964C211yesmaximal, characteristic, complemented
8C22×#11745669C411yescharacteristic, complemented
9C23×C59⋊C8C2211yescharacteristic
10C2×#14273701C2211yescharacteristic
11#16837636—21no—
12#16837636—21no—
13#16837636—21no—
14#16837636—21no—
15C2×#14273660—21no—
16C2×#14273660C411yescharacteristic, complemented
17C2×#14273648C411yescharacteristic, complemented
18C2×#14273647C411yescharacteristic, complemented
19C2×#14273641—22no—
20C2×C22⋊(C59⋊C8)C2211yescharacteristic
21C2×C4×C59⋊C8—21no—
22#16837262C2211yescharacteristic
23#16837164—21no—
24#16837157—21no—
25#16837136—22no—
26#16837135—22no—
27C2×#121×C59C2211yescharacteristic
28C2×#99×C59—22no—
29C59×#380C2211yescharacteristic
30C4×C22⋊C4×C59C2211yescharacteristic
31C22×D236C2×C411yescharacteristic
32C22×C22⋊D59—21no—
33C2×#11745669—21no—
34C2×#11745669—21no—
35C2×#11745669—42no—
36C22×C59⋊C8—21no—
37C22×C59⋊C8—42no—
38C22×C59⋊C8C2×C411yescharacteristic
39C22×C59⋊C8C2×C411yescharacteristic
40C22×C59⋊C8D411yescharacteristic
41C22×C59⋊C8D411yescharacteristic
42C22×C59⋊C8D411yescharacteristic
43C22×C59⋊C8D411yescharacteristic
44#14273701—21no—
45#14273701—21no—
46#14273701—21no—
47#14273701—21no—
48C2×C4⋊Dic59—21no—
49C2×C4⋊Dic59C2×C411yescharacteristic
50C2×C22⋊Dic59—21no—
51C2×(C2×D59)⋊C4—21no—
52#14273660—21no—
53#14273660—21no—
54#14273660—42no—
55#14273648—21no—
56#14273648—21no—
57#14273647—21no—
58#14273647—21no—
59#14273641—44no—
60C22⋊(C59⋊C8)—21no—
61C22⋊(C59⋊C8)D412yes—
62C4×C59⋊C8—42no—
63C59⋊#95—21no—
64C22×D4×C59—21no—
65C22×D4×C59C2×C411yescharacteristic
66C23×C4×C59C2311yescharacteristic
67#121×C59—21no—
68#121×C59—21no—
69#121×C59—21no—
70#121×C59—21no—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59C2×C411yescharacteristic
73C2×C22⋊C4×C59—21no—
74C2×C22⋊C4×C59—21no—
75C2×C22⋊C4×C59D412yes—
76C2×C42×C59—21no—
77#99×C59—44no—
78#95×C59—21no—
79#95×C59—21no—
80C24×C59—21no—
81C24×C59C2×D411yescharacteristic
82C23×D59—21no—
83C2×D4×C59—21no—
84C2×D4×C59—21no—
85C2×D4×C59—41no—
86C2×D4×C59—41no—
87C2×D4×C59—41no—
88C2×D4×C59—41no—
89C2×D4×C59—42no—
90C2×D4×C59—42no—
91C22×C4×C59—22no—
92C22×C4×C59—21no—
93C22×C4×C59—41no—
94C22×C4×C59—41no—
95C22×C4×C59—41no—
96C22×C4×C59C22×C411yescharacteristic
97C22×C4×C59C2×D411yescharacteristic
98C22×C4×C59C2×D411yescharacteristic
99C22×C4×C59C2×D411yescharacteristic
100C22×C4×C59#4111yescharacteristic
101C22×C4×C59#4111yescharacteristic
102C2×C22⋊D59—41no—
103C2×C22⋊D59—41no—
104C2×C22⋊D59—42no—
105C2×C22⋊D59—42no—
106C22×Dic59—21no—
107C22×Dic59—41no—
108C2×D236—21no—
109C2×D236—21no—
110C2×D236—41no—
111C2×D236—41no—
112C4⋊C4×C59—21no—
113C4⋊C4×C59—21no—
114C4⋊C4×C59—41no—
115C4⋊C4×C59—41no—
116C22⋊C4×C59—22no—
117C22⋊C4×C59—41no—
118C22⋊C4×C59—41no—
119C22⋊C4×C59—42no—
120C22⋊C4×C59D814yescomplemented
121C42×C59—41no—
122C42×C59—41no—
123C22⋊Dic59—42no—
124#11745669—42no—
125#11745669—42no—
126(C2×D59)⋊C4—41no—
127(C2×D59)⋊C4—41no—
128C4⋊Dic59—21no—
129C4⋊Dic59—21no—
130C4⋊Dic59—41no—
131C4⋊Dic59—41no—
132C2×C59⋊C8—22no—
133C2×C59⋊C8—22no—
134C2×C59⋊C8—22no—
135C2×C59⋊C8—22no—
136C2×C59⋊C8—41no—
137C2×C59⋊C8—41no—
138C2×C59⋊C8—41no—
139C2×C59⋊C8—41no—
140C2×C59⋊C8—41no—
141C2×C59⋊C8C22⋊C411yescharacteristic
142C2×C59⋊C8C22⋊C411yescharacteristic
143C2×C59⋊C8C22⋊C411yescharacteristic
144C2×C59⋊C8C22⋊C411yescharacteristic
145C23×C59—41no—
146C23×C59—41no—
147C23×C59—41no—
148C23×C59—42no—
149C23×C59—81no—
150C23×C59—81no—
151C23×C59C4×D411yescharacteristic
152C23×C59#12111yescharacteristic
153C23×C59#12711yescharacteristic
154C23×C59C2×D812yes—
155C23×C59#13512yes—
156C22×D59—41no—
157C22×D59—42no—
158C22×D59—81no—
159C22×D59—81no—
160D4×C59—41no—
161D4×C59—41no—
162D4×C59—81no—
163D4×C59—82no—
164D4×C59—81no—
165D4×C59—81no—
166C2×C4×C59—21no—
167C2×C4×C59—21no—
168C2×C4×C59—21no—
169C2×C4×C59—21no—
170C2×C4×C59—21no—
171C2×C4×C59—21no—
172C2×C4×C59—24no—
173C2×C4×C59—41no—
174C2×C4×C59—41no—
175C2×C4×C59—41no—
176C2×C4×C59—42no—
177C2×C4×C59—42no—
178C2×C4×C59—41no—
179C2×C4×C59—42no—
180C2×C4×C59—81no—
181C2×C4×C59—81no—
182C2×C4×C59—81no—
183C2×C4×C59C2×C22⋊C411yescharacteristic
184C2×C4×C59C4×D411yescharacteristic
185C2×C4×C59#12111yescharacteristic
186C2×C4×C59#12411yescharacteristic
187C22⋊D59—82no—
188C22⋊D59—81no—
189C22⋊D59—81no—
190C2×Dic59—41no—
191C2×Dic59—42no—
192C2×Dic59—81no—
193C2×Dic59—81no—
194C2×Dic59—81no—
195D236—41no—
196D236—41no—
197D236—81no—
198C59⋊C8—21no—
199C59⋊C8—21no—
200C59⋊C8—21no—
201C59⋊C8—42no—
202C59⋊C8#9912yescomplemented
203#9783—591nomaximal, Sylow
204C22×C59—21no—
205C22×C59—21no—
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59—21no—
210C22×C59—42no—
211C22×C59—42no—
212C22×C59—81no—
213C22×C59—81no—
214C22×C59—81no—
215C22×C59—162no—
216C22×C59#39011yescharacteristic
217C22×C59C4×D812yes—
218C22×C59#46612yes—
219C22×C59#49311yescharacteristic
220C22×C59#49511yescharacteristic
221C2×D59—81no—
222C2×D59—81no—
223C2×D59—81no—
224C2×D59—162no—
225C4×C59—21no—
226C4×C59—21no—
227C4×C59—21no—
228C4×C59—44no—
229C4×C59—81no—
230C4×C59—161no—
231C4×C59C2×#9911yescharacteristic
232C4×C59#41011yescharacteristic
233Dic59—81no—
234Dic59—161no—
235C2×#466—591no—
236#1964—591no—
237#1964D5911yescharacteristic, complemented
238#1808—591no—
239C8×C22⋊C4—591no—
240#1519—591no—
241#1519—591no—
242C2×C59—21no—
243C2×C59—22no—
244C2×C59—22no—
245C2×C59—21no—
246C2×C59—161no—
247C2×C59#196411yescharacteristic
248C2×C59#197011yescharacteristic
249C2×C59#197611yescharacteristic
250D59—161no—
251C22×D8—591no—
252C23×C8—591no—
253C2×#121—591no—
254C2×#121C2×D5911yescharacteristic
255#466—1181no—
256#466—1181no—
257#466—1181no—
258#466—1181no—
259C2×#107—591no—
260C2×#107—1181no—
261C2×#102—591no—
262C2×#102—591no—
263C2×#99—22no—
264C2×#99—1182no—
265C2×C22⋊C8—591no—
266C2×C4×C8—1181no—
267#380—591no—
268#380C2×D5911yescharacteristic
269C4×C22⋊C4C2×D5911yescharacteristic
270#340—1181no—
271#336—1181no—
272#327—1182no—
273#327—1182no—
274C59#978311yescharacteristic, complemented, Sylow
275C22×D4—21no—
276C22×D4—591no—
277C22×D4—1181no—
278C22×D4C4×D5911yescharacteristic
279C23×C4C22×D5911yescharacteristic
280C2×D8—1181no—
281C2×D8—1181no—
282C2×D8—2362no—
283C22×C8—591no—
284C22×C8—591no—
285C22×C8—591no—
286C22×C8—591no—
287C22×C8—591no—
288C22×C8—591no—
289C22×C8—1181no—
290C22×C8—2362no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—1181no—
296#121—1181no—
297#121—1181no—
298#121—1181no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—591no—
301C2×C4⋊C4—1181no—
302C2×C4⋊C4C4×D5911yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—1181no—
306C2×C22⋊C4—1181no—
307C2×C22⋊C4C22⋊D5912yes—
308C2×C42—21no—
309#107—1181no—
310#107—1181no—
311#107—2362no—
312#102—1181no—
313#102—1181no—
314#102—1181no—
315#102—1181no—
316#99—44no—
317#99—2364no—
318C22⋊C8—592no—
319C22⋊C8—1181no—
320C4×C8—2362no—
321#95—21no—
322#95—21no—
323#95—1181no—
324C24—21no—
325C24—1181no—
326C24C2×C22⋊D5911yescharacteristic
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—1181no—
336C2×D4—1181no—
337C2×D4—2361no—
338C2×D4—2361no—
339C2×D4—2361no—
340C2×D4—2361no—
341C2×D4—2362no—
342C2×D4—2362no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—1181no—
349C22×C4—2361no—
350C22×C4C2×C4×D5911yescharacteristic
351C22×C4#1174568511yescharacteristic
352C22×C4D4×D5911yescharacteristic
353C22×C4D4×D5911yescharacteristic
354C22×C4D4×D5911yescharacteristic
355C22×C4#1174568711yescharacteristic
356D8—2362no—
357D8—2362no—
358C2×C8—591no—
359C2×C8—591no—
360C2×C8—591no—
361C2×C8—591no—
362C2×C8—1182no—
363C2×C8—1182no—
364C2×C8—1182no—
365C2×C8—1182no—
366C2×C8—2361no—
367C2×C8—2361no—
368C2×C8—2361no—
369C2×C8—2361no—
370C2×C8—2361no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—1181no—
376C4⋊C4—1181no—
377C4⋊C4—2361no—
378C4⋊C4—2361no—
379C22⋊C4—22no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—2362no—
384C22⋊C4—2361no—
385C22⋊C4—2361no—
386C22⋊C4#1174566914yescomplemented
387C42—41no—
388C42—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—81no—
394C23—81no—
395C23—4721no—
396C23—4721no—
397C23—2362no—
398C23—2361no—
399C23C4×C22⋊D5911yescharacteristic
400C23#1427369911yescharacteristic
401C23#1427372311yescharacteristic
402C23C2×#1174566912yes—
403C23#1427374712yes—
404D4—41no—
405D4—41no—
406D4—81no—
407D4—82no—
408D4—81no—
409D4—81no—
410D4—4721no—
411D4—4722no—
412D4—4721no—
413D4—4721no—
414D4—2361no—
415D4—2361no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—4721no—
434C2×C4—4721no—
435C2×C4—4721no—
436C2×C4—2362no—
437C2×C4—2361no—
438C2×C4C22⋊C4×D5911yescharacteristic
439C2×C4(C22⋊D59)⋊C411yescharacteristic
440C2×C4#1427370011yescharacteristic
441C2×C4#1427371311yescharacteristic
442C8—592no—
443C8—1181no—
444C8—1181no—
445C8—1181no—
446C8—2362no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—162no—
459C22—9442no—
460C22—4721no—
461C22—4721no—
462C22—4721no—
463C22#1683730211yescharacteristic
464C22C4×#1174566912yes—
465C22#1683763612yes—
466C22#1683777811yescharacteristic
467C22#1683778411yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—44no—
472C4—81no—
473C4—161no—
474C4—9441no—
475C4—4721no—
476C4#99×D5911yescharacteristic
477C4#1683737411yescharacteristic
478C2—22no—
479C2—21no—
480C2—22no—
481C2—21no—
482C2—161no—
483C2—9441no—
484C2#2142493011yescharacteristic
485C2#2142496111yescharacteristic
486C2#2142499111yescharacteristic
subgroupG/H
centerC22#16837302
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1964C2
socleC22×C59#390
prime radicalC2×#16837636C2
cosocleC23×C4×C59C23
hypercenter#1964D59
hypocenterC59#9783
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21424932C2semidirect
3. #21424123C2semidirect
4. C22⋊C4×C59⋊C8C2semidirect
5. #21422664C2semidirect
6. #21422663C2semidirect
7. C59×#1964C2semidirect
8. C22×#11745669C4semidirect
16. C2×#14273660C4semidirect
17. C2×#14273648C4semidirect
18. C2×#14273647C4semidirect
120. C22⋊C4×C59D8semidirect
202. C59⋊C8#99semidirect
237. #1964D59semidirect
274. C59#9783semidirect
386. C22⋊C4#11745669semidirect

Maximal subgroups

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

subgroupindex
C2×#168376362
#214249322
#214241232
C22⋊C4×C59⋊C82
#214226642
#214226632
C59×#19642
#978359