Finite Group Databasebeta

← #28481409

Subgroups — #28481409

Order 15104.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273701C211yesmaximal, characteristic
2#21424076C211yesmaximal, characteristic, complemented
3C2×#16837135C212yesmaximal
4#21421975C212yesmaximal, complemented
5C59×C4⋊#95C211yesmaximal, characteristic, complemented
6C2×#14273701C2211yescharacteristic
7C2×C4×D236C411yescharacteristic, complemented
8C2×C4×C22⋊D59—21no—
9C2×C4⋊(C59⋊C8)—21no—
10C2×C22⋊(C59⋊C8)C2212yes—
11#16837304C411yescharacteristic, complemented
12#16837300C411yescharacteristic, complemented
13#16837293—21no—
14#16837281—21no—
15#16837262C2211yescharacteristic
16C4×C4⋊Dic59C411yescharacteristic, complemented
17C4×(C2×D59)⋊C4—21no—
18#16837157—21no—
19#16837135—24no—
20C22×C4⋊C4×C59—21no—
21C22×C42×C59C2211yescharacteristic
22C2×#95×C59—21no—
23C2×#95×C59C2212yes—
24C22×D236C2×C411yescharacteristic
25C22×C22⋊D59—21no—
26C22×C4×D59—21no—
27C22×C59⋊C8—22no—
28#14273701—21no—
29#14273701—21no—
30#14273701D412yes—
31#14273701Q812yes—
32C4×D236—42no—
33C4×C22⋊D59—42no—
34C4×C22⋊D59—42no—
35C2×C4⋊Dic59C2×C411yescharacteristic
36C2×C4⋊Dic59C2×C411yescharacteristic
37C2×C4⋊Dic59C2×C411yescharacteristic
38C2×Dic59⋊C4—21no—
39C2×C22⋊Dic59—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×C4×Dic59—21no—
45C4⋊(C59⋊C8)—42no—
46C22⋊(C59⋊C8)—22no—
47C22⋊(C59⋊C8)—22no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C23×C4×C59—22no—
52C23×C4×C59D411yescharacteristic
53C23×C4×C59D411yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C2×C4⋊C4×C59—24no—
56C2×C4⋊C4×C59—42no—
57C2×C4⋊C4×C59—42no—
58C2×C42×C59—42no—
59C2×C42×C59C2×C411yescharacteristic
60C2×C42×C59C2×C411yescharacteristic
61C2×C42×C59D411yescharacteristic
62C2×C42×C59D411yescharacteristic
63#95×C59—22no—
64#95×C59—22no—
65#95×C59—42no—
66C24×C59C2×D411yescharacteristic
67C23×D59—21no—
68C22×C4×C59—22no—
69C22×C4×C59—22no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—24no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—42no—
78C22×C4×C59—42no—
79C22×C4×C59—42no—
80C22×C4×C59—42no—
81C22×C4×C59—42no—
82C22×C4×C59—42no—
83C22×C4×C59C22⋊C411yescharacteristic
84C22×C4×C59C22⋊C411yescharacteristic
85C22×C4×C59C22⋊C411yescharacteristic
86C22×C4×C59C22⋊C411yescharacteristic
87C22×C4×C59D812yes—
88C22×C4×C59SD1612yes—
89C22×C4×C59C22×C411yescharacteristic
90C22×C4×C59C2×D411yescharacteristic
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59C2×Q811yescharacteristic
93C22×C4×C59#4111yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C2×C22⋊D59—22no—
96C2×C22⋊D59—22no—
97C2×C22⋊D59—41no—
98C2×C22⋊D59—41no—
99C2×C22⋊D59—41no—
100C2×C22⋊D59—41no—
101C22×Dic59—21no—
102C22×Dic59—21no—
103C22×Dic59—21no—
104C2×D236—21no—
105C2×D236—41no—
106C2×D236—41no—
107C2×D236C4⋊C412yescomplemented
108C2×C4×D59—42no—
109C2×C4×D59—42no—
110C2×C4×D59—42no—
111C4⋊C4×C59—48no—
112C42×C59—22no—
113C42×C59—22no—
114C42×C59—41no—
115C42×C59—41no—
116C22⋊Dic59—41no—
117C22⋊Dic59—41no—
118(C2×D59)⋊C4—22no—
119(C2×D59)⋊C4—22no—
120(C2×D59)⋊C4—42no—
121(C2×D59)⋊C4—42no—
122(C2×D59)⋊C4—42no—
123C4⋊Dic59—21no—
124C4⋊Dic59—41no—
125C4⋊Dic59—41no—
126C4⋊Dic59C4⋊C412yescomplemented
127Dic59⋊C4—42no—
128C4×Dic59—42no—
129C2×C59⋊C8—42no—
130C2×C59⋊C8—42no—
131C2×C59⋊C8—42no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59C2×C22⋊C411yescharacteristic
137C23×C59#12111yescharacteristic
138C23×C59C22⋊Q811yescharacteristic
139C23×C59C2×D811yescharacteristic
140C23×C59C2×SD1611yescharacteristic
141C23×C59AGL(1,ℤ/8)11yescharacteristic
142C23×C59#13711yescharacteristic
143C22×D59—22no—
144C22×D59—41no—
145C22×D59—41no—
146C22×D59—41no—
147C22×D59—41no—
148C22×D59—41no—
149C22×D59—41no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—24no—
157C2×C4×C59—24no—
158C2×C4×C59—21no—
159C2×C4×C59—21no—
160C2×C4×C59—21no—
161C2×C4×C59—21no—
162C2×C4×C59—21no—
163C2×C4×C59—21no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—42no—
169C2×C4×C59—42no—
170C2×C4×C59—44no—
171C2×C4×C59—44no—
172C2×C4×C59—44no—
173C2×C4×C59—82no—
174C2×C4×C59—82no—
175C2×C4×C59—82no—
176C2×C4×C59—82no—
177C2×C4×C59#9912yes—
178C2×C4×C59#10212yes—
179C2×C4×C59#10212yes—
180C2×C4×C59#10412yes—
181C2×C4×C59C2×C4⋊C411yescharacteristic
182C2×C4×C59#11711yescharacteristic
183C2×C4×C59#12111yescharacteristic
184C2×C4×C59C22⋊Q811yescharacteristic
185C22⋊D59—42no—
186C22⋊D59—42no—
187C22⋊D59—42no—
188C22⋊D59—42no—
189C2×Dic59—22no—
190C2×Dic59—41no—
191C2×Dic59—41no—
192C2×Dic59—41no—
193C2×Dic59—41no—
194C2×Dic59—41no—
195C2×Dic59—41no—
196C2×Dic59—41no—
197C2×Dic59—41no—
198D236—42no—
199D236—42no—
200C4×D59—84no—
201C59⋊C8—82no—
202#8571—591nomaximal, Sylow
203C22×C59—21no—
204C22×C59—21no—
205C22×C59—21no—
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59—21no—
210C22×C59—21no—
211C22×C59—21no—
212C22×C59—21no—
213C22×C59—21no—
214C22×C59—21no—
215C22×C59#38011yescharacteristic
216C22×C59C2×#9911yescharacteristic
217C22×C59#41011yescharacteristic
218C22×C59C2×#10211yescharacteristic
219C22×C59#41711yescharacteristic
220C22×C59C2×#10411yescharacteristic
221C22×C59#42111yescharacteristic
222C22×C59#45911yescharacteristic
223C22×C59#46111yescharacteristic
224C22×C59#47411yescharacteristic
225C22×C59#47611yescharacteristic
226C2×D59—42no—
227C2×D59—42no—
228C2×D59—42no—
229C2×D59—81no—
230C2×D59—81no—
231C2×D59—81no—
232C2×D59—81no—
233C4×C59—21no—
234C4×C59—21no—
235C4×C59—21no—
236C4×C59—21no—
237C4×C59—22no—
238C4×C59—41no—
239C4×C59—41no—
240C4×C59—84no—
241C4×C59#32714yescomplemented
242Dic59—42no—
243Dic59—81no—
244Dic59—81no—
245C4×#121—591no—
246#1797—591no—
247C2×#327—592no—
248C4⋊#95D5911yescharacteristic, complemented
249#1294—592no—
250C2×C59—21no—
251C2×C59—21no—
252C2×C59—21no—
253C2×C59—21no—
254C2×C59C2×#32711yescharacteristic
255C2×C59#150911yescharacteristic
256C2×C59#151311yescharacteristic
257C2×C59#151711yescharacteristic
258C2×C59#179911yescharacteristic
259C2×C59#180211yescharacteristic
260C2×C59#180611yescharacteristic
261D59—82no—
262C2×#121—591no—
263C2×C4×D4—591no—
264C2×C4×D4—1181no—
265C22×C4⋊C4—21no—
266C22×C42C2×D5911yescharacteristic
267C2×C4⋊C8—1181no—
268C2×C22⋊C8—592no—
269#390—591no—
270#389—591no—
271#388—1181no—
272#386—1181no—
273#380—591no—
274C4×C4⋊C4—591no—
275C4×C22⋊C4—1181no—
276C2×#95—21no—
277C2×#95C2×D5912yes—
278#336—1181no—
279#327—1184no—
280C59#857111yescharacteristic, complemented, Sylow
281C22×D4—591no—
282C22×D4—1181no—
283C23×C4—22no—
284C23×C4—1181no—
285C23×C4C22⋊D5911yescharacteristic
286C23×C4C22⋊D5911yescharacteristic
287C23×C4C22×D5911yescharacteristic
288C22×C8—1182no—
289#121—592no—
290#121—592no—
291#121—1181no—
292#121—1181no—
293C4×D4—2362no—
294C4×D4—2362no—
295C4×D4—2362no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—591no—
300C2×C4⋊C4—591no—
301C2×C4⋊C4—591no—
302C2×C4⋊C4—1181no—
303C2×C22⋊C4—1181no—
304C2×C22⋊C4—1181no—
305C2×C22⋊C4—1181no—
306C2×C22⋊C4—1181no—
307C2×C22⋊C4—1181no—
308C2×C42—42no—
309C2×C42—1181no—
310C2×C42C4×D5911yescharacteristic
311C2×C42C4×D5911yescharacteristic
312C2×C42D23611yescharacteristic
313C2×C42D23611yescharacteristic
314C4⋊C8—2362no—
315C22⋊C8—1182no—
316C22⋊C8—1182no—
317#95—22no—
318#95—22no—
319#95—42no—
320#95—1181no—
321#95—1181no—
322#95—1181no—
323C24—1181no—
324C24C2×C22⋊D5911yescharacteristic
325C2×D4—592no—
326C2×D4—1182no—
327C2×D4—1182no—
328C2×D4—1181no—
329C2×D4—2361no—
330C2×D4—2361no—
331C2×D4—2361no—
332C2×D4—2361no—
333C2×D4—2361no—
334C2×D4—2361no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—24no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—1181no—
351C22×C4—1181no—
352C22×C4—1181no—
353C22×C4—2362no—
354C22×C4—2362no—
355C22×C4—2362no—
356C22×C4(C2×D59)⋊C411yescharacteristic
357C22×C4(C2×D59)⋊C411yescharacteristic
358C22×C4(C2×D59)⋊C411yescharacteristic
359C22×C4(C2×D59)⋊C411yescharacteristic
360C22×C4#1174566912yes—
361C22×C4#1174567112yes—
362C22×C4C2×C4×D5911yescharacteristic
363C22×C4C2×D23611yescharacteristic
364C22×C4D4×D5911yescharacteristic
365C22×C4#1174568711yescharacteristic
366C22×C4Q8×D5911yescharacteristic
367C22×C4#1174568911yescharacteristic
368C2×C8—2362no—
369C2×C8—2362no—
370C2×C8—2362no—
371C4⋊C4—48no—
372C4⋊C4—592no—
373C4⋊C4—1181no—
374C4⋊C4—2361no—
375C4⋊C4—2361no—
376C4⋊C4—2362no—
377C22⋊C4—1182no—
378C22⋊C4—1182no—
379C22⋊C4—2362no—
380C22⋊C4—2362no—
381C22⋊C4—2361no—
382C22⋊C4—2361no—
383C22⋊C4—2362no—
384C42—22no—
385C42—22no—
386C42—41no—
387C42—41no—
388C42—2362no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—1182no—
394C23—2361no—
395C23—2361no—
396C23—2361no—
397C23—2361no—
398C23—2361no—
399C23—2361no—
400C23C2×(C2×D59)⋊C411yescharacteristic
401C23#1427369811yescharacteristic
402C23#1427370311yescharacteristic
403C23C2×#1174566911yescharacteristic
404C23C2×#1174567111yescharacteristic
405C23#1427375311yescharacteristic
406C23#1427375811yescharacteristic
407D4—2362no—
408D4—2362no—
409D4—2362no—
410D4—2362no—
411D4—2362no—
412D4—2362no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—1182no—
441C2×C4—4724no—
442C2×C4—2361no—
443C2×C4—2361no—
444C2×C4—2361no—
445C2×C4—2361no—
446C2×C4—2361no—
447C2×C4—2361no—
448C2×C4—2361no—
449C2×C4—2361no—
450C2×C4#1427364112yes—
451C2×C4#1427364712yes—
452C2×C4#1427364712yes—
453C2×C4#1427365512yes—
454C2×C4C4⋊C4×D5911yescharacteristic
455C2×C4#1427368511yescharacteristic
456C2×C4#1427370211yescharacteristic
457C2×C4#1427370711yescharacteristic
458C8—4722no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—4721no—
472C22—4721no—
473C22—4721no—
474C22—4721no—
475C22—2362no—
476C22—2362no—
477C22—2362no—
478C22#1683725911yescharacteristic
479C22C2×#1427364111yescharacteristic
480C22#1683737511yescharacteristic
481C22C2×#1427364711yescharacteristic
482C22#1683740111yescharacteristic
483C22C2×#1427365511yescharacteristic
484C22#1683742011yescharacteristic
485C22#1683759411yescharacteristic
486C22#1683760411yescharacteristic
487C22#1683767911yescharacteristic
488C22#1683768911yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—84no—
497C4—4721no—
498C4—4721no—
499C4—2362no—
500C4#1683713514yescomplemented
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—4722no—
506C2C2×#1683713511yescharacteristic
507C2#2142261911yescharacteristic
508C2#2142263711yescharacteristic
509C2#2142265511yescharacteristic
510C2#2142408111yescharacteristic
511C2#2142409311yescharacteristic
512C2#2142411711yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×C4⋊#95C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#14273701C22
cosocleC23×C4×C59C23
hypercenterC4⋊#95D59
hypocenterC59#8571
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. #21424076C2semidirect
4. #21421975C2semidirect
5. C59×C4⋊#95C2semidirect
7. C2×C4×D236C4semidirect
11. #16837304C4semidirect
12. #16837300C4semidirect
16. C4×C4⋊Dic59C4semidirect
107. C2×D236C4⋊C4semidirect
126. C4⋊Dic59C4⋊C4semidirect
241. C4×C59#327semidirect
248. C4⋊#95D59semidirect
280. C59#8571semidirect
500. C4#16837135semidirect

Maximal subgroups

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

subgroupindex
C4×#142737012
#214240762
C2×#168371352
#214219752
C59×C4⋊#952
#857159