Finite Group Databasebeta

← #28488983

Subgroups — #28488983

Order 15104.

778 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837737C211yesmaximal, characteristic, complemented
2#21429901C211yesmaximal, characteristic
3#21424186C211yesmaximal, characteristic, complemented
4C2×#16837138C211yesmaximal, characteristic, complemented
5C2×#16837126C211yesmaximal, characteristic
6#21421975C211yesmaximal, characteristic, complemented
7C2×C59×#399C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9#16837737—22no—
10#16837737—22no—
11C2×#14273660—21no—
12C2×#14273650—21no—
13C2×C22⋊(C59⋊C8)C2211yescharacteristic
14C2×C22⋊(C59⋊C8)C2211yescharacteristic
15#16837338—21no—
16#16837325—22no—
17#16837314—21no—
18#16837275—21no—
19#16837262C2211yescharacteristic
20#16837258—21no—
21#16837164—22no—
22#16837138—22no—
23#16837126—22no—
24C22×C4⋊C4×C59—21no—
25C22×C4⋊C4×C59C2211yescharacteristic
26C22×C22⋊C4×C59—21no—
27C22×C22⋊C4×C59C2211yescharacteristic
28C59×#399—22no—
29C59×#399—22no—
30C2×#95×C59C2211yescharacteristic
31C22×Dic118D411yescharacteristic
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34#14273706—21no—
35#14273706—21no—
36#14273706—21no—
37#14273706—21no—
38C2×C4⋊Dic59D411yescharacteristic
39C2×C4⋊Dic59D412yes—
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—22no—
42C2×C22⋊Dic59—21no—
43C2×C22⋊Dic59—21no—
44C2×C22⋊Dic59—22no—
45C2×C22⋊Dic59—22no—
46#14273660—24no—
47#14273650—24no—
48C22⋊(C59⋊C8)—21no—
49C22⋊(C59⋊C8)—21no—
50C22⋊(C59⋊C8)—21no—
51C22⋊(C59⋊C8)D412yes—
52C59⋊#95—22no—
53C59⋊#95—21no—
54C25×C59D411yescharacteristic
55C23×C4×C59—21no—
56C23×C4×C59—21no—
57C23×C4×C59D411yescharacteristic
58C23×C4×C59C2311yescharacteristic
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C4⋊C4×C59—21no—
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—24no—
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59—44no—
66C2×C4⋊C4×C59D412yes—
67C2×C22⋊C4×C59—24no—
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59—21no—
72C2×C22⋊C4×C59—21no—
73C2×C22⋊C4×C59—21no—
74C2×C22⋊C4×C59—44no—
75#95×C59—21no—
76#95×C59D412yes—
77C24×C59—21no—
78C24×C59—21no—
79C24×C59—21no—
80C24×C59—21no—
81C24×C59—21no—
82C24×C59—21no—
83C24×C59—42no—
84C24×C59—42no—
85C24×C59Q1612yes—
86C24×C59C2×D411yescharacteristic
87C22×C4×C59—24no—
88C22×C4×C59—22no—
89C22×C4×C59—21no—
90C22×C4×C59—22no—
91C22×C4×C59—21no—
92C22×C4×C59—21no—
93C22×C4×C59—42no—
94C22×C4×C59—42no—
95C22×C4×C59—41no—
96C22×C4×C59—41no—
97C22×C4×C59—42no—
98C22×C4×C59—42no—
99C22×C4×C59—42no—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59C2×D411yescharacteristic
107C22×C4×C59#4111yescharacteristic
108C22×Dic59—22no—
109C22×Dic59—21no—
110C22×Dic59—21no—
111C2×Dic118—21no—
112C2×Dic118—21no—
113C2×Dic118—42no—
114C4⋊C4×C59—22no—
115C4⋊C4×C59—22no—
116C4⋊C4×C59—48no—
117C4⋊C4×C59—41no—
118C4⋊C4×C59—41no—
119C22⋊C4×C59—48no—
120C22⋊C4×C59—41no—
121C22⋊C4×C59—41no—
122C22⋊C4×C59—41no—
123C22⋊C4×C59—41no—
124C22⋊Dic59—41no—
125C22⋊Dic59—41no—
126C22⋊Dic59—41no—
127C22⋊Dic59—41no—
128C22⋊Dic59—82no—
129C22⋊Dic59—82no—
130C4⋊Dic59—21no—
131C4⋊Dic59—21no—
132C4⋊Dic59—42no—
133Dic59⋊C4—41no—
134Dic59⋊C4—41no—
135Dic59⋊C4—82no—
136C2×C59⋊C8—22no—
137C2×C59⋊C8—42no—
138C2×C59⋊C8—42no—
139C2×C59⋊C8—41no—
140C23×C59—22no—
141C23×C59—22no—
142C23×C59—22no—
143C23×C59—22no—
144C23×C59—22no—
145C23×C59—44no—
146C23×C59—42no—
147C23×C59—44no—
148C23×C59—42no—
149C23×C59—41no—
150C23×C59—41no—
151C23×C59—41no—
152C23×C59—42no—
153C23×C59—42no—
154C23×C59—41no—
155C23×C59—82no—
156C23×C59—82no—
157C23×C59—81no—
158C23×C59—81no—
159C23×C59#12011yescharacteristic
160C23×C59#12011yescharacteristic
161C23×C59#12111yescharacteristic
162C23×C59C2×Q1611yescharacteristic
163C23×C59#13511yescharacteristic
164C23×C59#13711yescharacteristic
165C23×C59#13711yescharacteristic
166C2×C4×C59—22no—
167C2×C4×C59—22no—
168C2×C4×C59—24no—
169C2×C4×C59—41no—
170C2×C4×C59—41no—
171C2×C4×C59—41no—
172C2×C4×C59—41no—
173C2×C4×C59—44no—
174C2×C4×C59—44no—
175C2×C4×C59—42no—
176C2×C4×C59—42no—
177C2×C4×C59—42no—
178C2×C4×C59—42no—
179C2×C4×C59—42no—
180C2×C4×C59—41no—
181C2×C4×C59—42no—
182C2×C4×C59—42no—
183C2×C4×C59—82no—
184C2×C4×C59—82no—
185C2×C4×C59—81no—
186C2×C4×C59#12011yescharacteristic
187C2×C4×C59#12111yescharacteristic
188C2×C4×C59#12111yescharacteristic
189C2×C4×C59#12711yescharacteristic
190C2×Dic59—41no—
191C2×Dic59—41no—
192C2×Dic59—42no—
193C2×Dic59—42no—
194C2×Dic59—42no—
195C2×Dic59—42no—
196C2×Dic59—42no—
197Dic118—42no—
198Dic118—81no—
199C59⋊C8—42no—
200C59⋊C8—81no—
201#9928—591nomaximal, Sylow
202C22×C59—22no—
203C22×C59—22no—
204C22×C59—22no—
205C22×C59—22no—
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59—21no—
210C22×C59—44no—
211C22×C59—44no—
212C22×C59—42no—
213C22×C59—82no—
214C22×C59—82no—
215C22×C59—82no—
216C22×C59—82no—
217C22×C59—81no—
218C22×C59—81no—
219C22×C59#39211yescharacteristic
220C22×C59#45111yescharacteristic
221C22×C59#45111yescharacteristic
222C22×C59#45211yescharacteristic
223C22×C59#45211yescharacteristic
224C22×C59#45312yes—
225C22×C59#45812yes—
226C22×C59#46711yescharacteristic
227C22×C59#47011yescharacteristic
228C4×C59—21no—
229C4×C59—21no—
230C4×C59—21no—
231C4×C59—21no—
232C4×C59—44no—
233C4×C59—81no—
234C4×C59—82no—
235Dic59—82no—
236Dic59—81no—
237Dic59—81no—
238C2×#484—591no—
239#2626—591no—
240C2×#399D5911yescharacteristic
241#1824—591no—
242C2×#328—591no—
243C2×#323—591no—
244#1294—591no—
245C2×C59—21no—
246C2×C59—21no—
247C2×C59—21no—
248C2×C59—21no—
249C2×C59—82no—
250C2×C59#161412yes—
251C2×C59#161812yes—
252C2×C59#200111yescharacteristic
253C2×C59#200211yescharacteristic
254C2×C59#202211yescharacteristic
255C2×C22⋊Q8—591no—
256C22×C4⋊C4—21no—
257C22×C4⋊C4C2×D5911yescharacteristic
258C22×C22⋊C4—21no—
259C22×C22⋊C4C2×D5911yescharacteristic
260#484—1182no—
261#484—1182no—
262C2×#107—1181no—
263C2×#103—1181no—
264C2×C22⋊C8—591no—
265C2×C22⋊C8—591no—
266#399—22no—
267#399—22no—
268#399—1181no—
269#396—1182no—
270#393—1181no—
271#385—1181no—
272#380—591no—
273#379—1181no—
274C2×#95C2×D5911yescharacteristic
275#340—1182no—
276#328—1182no—
277#323—1182no—
278C59#992811yescharacteristic, complemented, Sylow
279C25C22⋊D5911yescharacteristic
280C22×Q8—591no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4C22⋊D5911yescharacteristic
284C23×C4C22×D5911yescharacteristic
285C22×C8—1181no—
286C22×C8—1181no—
287C22⋊Q8—1181no—
288C22⋊Q8—1181no—
289C22⋊Q8—1181no—
290C22⋊Q8—1181no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—591no—
299C2×C4⋊C4—592no—
300C2×C4⋊C4—1182no—
301C2×C4⋊C4—1181no—
302C2×C4⋊C4C22⋊D5912yes—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—1182no—
312C2×C22⋊C4—1182no—
313C2×C22⋊C4—1181no—
314C2×C22⋊C4—1181no—
315#107—1184no—
316#103—1184no—
317C22⋊C8—592no—
318C22⋊C8—1181no—
319C22⋊C8—1181no—
320C22⋊C8—1181no—
321#95—21no—
322#95—1182no—
323#95—1181no—
324#95C22⋊D5912yes—
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—42no—
332C24—42no—
333C24#1174567212yes—
334C24C2×C22⋊D5911yescharacteristic
335C2×Q8—1181no—
336C2×Q8—1181no—
337C2×Q8—2362no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—1182no—
354C22×C4—1181no—
355C22×C4—1181no—
356C22×C4D4×D5911yescharacteristic
357C22×C4D4×D5911yescharacteristic
358C22×C4D4×D5911yescharacteristic
359C22×C4#1174568711yescharacteristic
360C22×C4C2×C22⋊D5911yescharacteristic
361C22×C4C2×C22⋊D5911yescharacteristic
362C2×C8—1182no—
363C2×C8—2362no—
364C2×C8—2361no—
365C2×C8—2362no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—48no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—1181no—
372C4⋊C4—1181no—
373C4⋊C4—4722no—
374C4⋊C4—2362no—
375C4⋊C4—2361no—
376C4⋊C4—2361no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—4722no—
383C22⋊C4—4722no—
384C22⋊C4—2361no—
385C22⋊C4—2361no—
386C22⋊C4—2361no—
387C22⋊C4—2361no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—44no—
394C23—42no—
395C23—44no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—42no—
402C23—42no—
403C23—82no—
404C23—82no—
405C23—81no—
406C23—81no—
407C23#1427369511yescharacteristic
408C23#1427369611yescharacteristic
409C23#1427369911yescharacteristic
410C23C2×#1174567211yescharacteristic
411C23#1427374711yescharacteristic
412C23#1427375711yescharacteristic
413C23#1427375811yescharacteristic
414Q8—4721no—
415Q8—2362no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—2362no—
437C2×C4—2361no—
438C2×C4—2361no—
439C2×C4—2362no—
440C2×C4—2362no—
441C2×C4—2362no—
442C2×C4—2362no—
443C2×C4#1427369511yescharacteristic
444C2×C4#1427369811yescharacteristic
445C2×C4#1427369911yescharacteristic
446C2×C4#1427372311yescharacteristic
447C8—4721no—
448C8—2362no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—44no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22#1683731011yescharacteristic
467C22#1683755711yescharacteristic
468C22#1683755811yescharacteristic
469C22#1683756211yescharacteristic
470C22#1683756411yescharacteristic
471C22#1683756912yes—
472C22#1683759112yes—
473C22#1683764111yescharacteristic
474C22#1683765811yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—44no—
480C4—81no—
481C4—82no—
482C4—4722no—
483C4—4721no—
484C4—4721no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—82no—
490C2#2142312012yes—
491C2#2142314212yes—
492C2#2142510411yescharacteristic
493C2#2142511111yescharacteristic
494C2#2142522411yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC2×C59×#399C2
socleC23×C59#120
prime radicalC25×C59D4
hypercenterC2×#399D59
hypocenterC59#9928
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#16837737C2semidirect
3. #21424186C2semidirect
4. C2×#16837138C2semidirect
6. #21421975C2semidirect
278. C59#9928semidirect

Maximal subgroups

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

subgroupindex
C2×#168377372
#214299012
#214241862
C2×#168371382
C2×#168371262
#214219752
C2×C59×#3992
#992859