Finite Group Databasebeta

← #28507357

Subgroups — #28507357

Order 15104.

556 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429047C211yesmaximal, characteristic
2#21424082C211yesmaximal, characteristic
3#99×Dic59C211yesmaximal, characteristic
4#21422221C211yesmaximal, characteristic
5#21422220C211yesmaximal, characteristic
6#21422220C211yesmaximal, characteristic
7C59×#1393C211yesmaximal, characteristic
8C2×#14273726C411yescharacteristic, complemented
9C2×#14273704—21no—
10C2×#14273704—21no—
11C2×D4×Dic59C2211yescharacteristic
12C2×#14273642C2211yescharacteristic
13C2×#14273642C2211yescharacteristic
14#16837338—21no—
15#16837338—21no—
16#16837305C2211yescharacteristic
17#16837272C411yescharacteristic, complemented
18#16837271C411yescharacteristic, complemented
19#16837260—21no—
20C4×Dic59⋊C4C411yescharacteristic, complemented
21C22⋊C4×Dic59—21no—
22#16837168—21no—
23#16837168—21no—
24C2×#99×C59C2211yescharacteristic
25C2×#99×C59C2211yescharacteristic
26C59×#390C2211yescharacteristic
27C22×Dic118—21no—
28C23×Dic59D411yescharacteristic
29C23×Dic59D411yescharacteristic
30#14273726—41no—
31#14273726—41no—
32#14273704—44no—
33#14273704—44no—
34D4×Dic59—41no—
35D4×Dic59—41no—
36C2×C4⋊Dic59—21no—
37C2×C4⋊Dic59—21no—
38C2×C4⋊Dic59C2×C411yescharacteristic
39C2×C4⋊Dic59C2×C411yescharacteristic
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—21no—
42C2×Dic59⋊C4—21no—
43C2×Dic59⋊C4—21no—
44C2×Dic59⋊C4—41no—
45C2×C22⋊Dic59—21no—
46C2×C22⋊Dic59—21no—
47C2×C22⋊Dic59—21no—
48C2×C22⋊Dic59—21no—
49C2×C22⋊Dic59D411yescharacteristic
50C2×C22⋊Dic59D411yescharacteristic
51C2×C4×Dic59—41no—
52C2×C4×Dic59C2×C411yescharacteristic
53C2×C4×Dic59C2×C411yescharacteristic
54#14273642—21no—
55#14273642—21no—
56#14273642—21no—
57#14273642Q812yescomplemented
58C59⋊#95—21no—
59C59⋊#95—41no—
60C59⋊#95—41no—
61C22×D4×C59C2311yescharacteristic
62C2×C4⋊C4×C59C2×C411yescharacteristic
63C2×C22⋊C4×C59—21no—
64C2×C22⋊C4×C59—21no—
65C2×C22⋊C4×C59—21no—
66C2×C22⋊C4×C59—21no—
67C2×C42×C59C2×C411yescharacteristic
68#99×C59—21no—
69#99×C59—21no—
70#99×C59—21no—
71#99×C59Q812yescomplemented
72C24×C59C2×D411yescharacteristic
73C24×C59C2×D411yescharacteristic
74C2×D4×C59—41no—
75C2×D4×C59—41no—
76C2×D4×C59C2×Q811yescharacteristic
77C2×D4×C59C2×Q811yescharacteristic
78C2×D4×C59#4111yescharacteristic
79C2×D4×C59#4111yescharacteristic
80C22×C4×C59—21no—
81C22×C4×C59—21no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59C22×C411yescharacteristic
85C22×Dic59—21no—
86C22×Dic59—21no—
87C22×Dic59—21no—
88C22×Dic59—21no—
89C22×Dic59—21no—
90C22×Dic59—21no—
91C22×Dic59—42no—
92C22×Dic59—42no—
93C22×Dic59—41no—
94C22×Dic59—41no—
95C22×Dic59C22⋊C411yescharacteristic
96C22×Dic59C22⋊C411yescharacteristic
97C22×Dic59C22⋊C411yescharacteristic
98C22×Dic59C22⋊C411yescharacteristic
99C2×Dic118—42no—
100C2×Dic118—42no—
101C2×Dic118—41no—
102C2×Dic118—41no—
103C4⋊C4×C59—41no—
104C22⋊C4×C59—22no—
105C22⋊C4×C59—42no—
106C22⋊C4×C59—42no—
107C22⋊C4×C59—41no—
108C22⋊C4×C59—41no—
109C22⋊C4×C59—41no—
110C42×C59—41no—
111C22⋊Dic59—22no—
112C22⋊Dic59—41no—
113C22⋊Dic59—41no—
114C22⋊Dic59—42no—
115C22⋊Dic59—42no—
116C22⋊Dic59—41no—
117C22⋊Dic59—41no—
118C22⋊Dic59—41no—
119C4⋊Dic59—41no—
120C4⋊Dic59—42no—
121C4⋊Dic59—42no—
122C4⋊Dic59—41no—
123Dic59⋊C4—24no—
124Dic59⋊C4—42no—
125Dic59⋊C4—42no—
126Dic59⋊C4—42no—
127Dic59⋊C4—82no—
128C4×Dic59—21no—
129C4×Dic59—21no—
130C4×Dic59—41no—
131C4×Dic59—82no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59—21no—
136C23×C59—41no—
137C23×C59—41no—
138C23×C59—41no—
139C23×C59—41no—
140C23×C59C2×C22⋊C411yescharacteristic
141C23×C59C22⋊Q811yescharacteristic
142C23×C59C22⋊Q811yescharacteristic
143C23×C59#12411yescharacteristic
144C23×C59C4⋊Q811yescharacteristic
145D4×C59—41no—
146D4×C59—41no—
147D4×C59—41no—
148D4×C59—41no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—22no—
152C2×C4×C59—41no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59—41no—
156C2×C4×C59—42no—
157C2×C4×C59—41no—
158C2×C4×C59—81no—
159C2×C4×C59—81no—
160C2×C4×C59—81no—
161C2×C4×C59—81no—
162C2×C4×C59—81no—
163C2×C4×C59C4×Q811yescharacteristic
164C2×C4×C59C4×Q811yescharacteristic
165C2×Dic59—22no—
166C2×Dic59—22no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—41no—
171C2×Dic59—41no—
172C2×Dic59—42no—
173C2×Dic59—42no—
174C2×Dic59—41no—
175C2×Dic59—41no—
176C2×Dic59—41no—
177C2×Dic59—41no—
178C2×Dic59—41no—
179C2×Dic59—42no—
180C2×Dic59—41no—
181C2×Dic59—81no—
182C2×Dic59—81no—
183C2×Dic59—81no—
184C2×Dic59—81no—
185C2×Dic59—81no—
186C2×Dic59—81no—
187C2×Dic59—81no—
188C2×Dic59#9911yescharacteristic
189C2×Dic59#9911yescharacteristic
190Dic118—82no—
191Dic118—82no—
192#13298—591nomaximal, Sylow
193C22×C59—21no—
194C22×C59—21no—
195C22×C59—21no—
196C22×C59—21no—
197C22×C59—21no—
198C22×C59—21no—
199C22×C59—41no—
200C22×C59—41no—
201C22×C59—41no—
202C22×C59—41no—
203C22×C59—41no—
204C22×C59—41no—
205C22×C59—41no—
206C22×C59—41no—
207C22×C59—81no—
208C22×C59—81no—
209C22×C59#39111yescharacteristic
210C22×C59C2×#9911yescharacteristic
211C22×C59#41011yescharacteristic
212C4×C59—21no—
213C4×C59—21no—
214C4×C59—42no—
215C4×C59—82no—
216C4×C59—81no—
217C4×C59—161no—
218Dic59—21no—
219Dic59—42no—
220Dic59—41no—
221Dic59—41no—
222Dic59—41no—
223Dic59—82no—
224Dic59—81no—
225Dic59—161no—
226Dic59#35312yes—
227#2542—591no—
228#1799—591no—
229C4×#99—591no—
230#1393—591no—
231#1393—591no—
232#1393—591no—
233#1393D5911yescharacteristic
234C2×C59—21no—
235C2×C59—21no—
236C2×C59—41no—
237C2×C59—41no—
238C2×C59—41no—
239C2×C59—41no—
240C2×C59#199611yescharacteristic
241C2×C59C2×#35311yescharacteristic
242C2×C59#212911yescharacteristic
243C2×C4⋊Q8—591no—
244C2×C22⋊Q8—1181no—
245C2×C22⋊Q8—1181no—
246C2×C4×D4—591no—
247C2×#99—591no—
248C2×#99—591no—
249C2×#99C2×D5911yescharacteristic
250C2×#99C2×D5911yescharacteristic
251#399—1181no—
252#399—1181no—
253#390—591no—
254#390C2×D5911yescharacteristic
255#384—591no—
256#384—591no—
257#380—1181no—
258C4×C4⋊C4—591no—
259C4×C22⋊C4—1181no—
260#342—1181no—
261#342—1181no—
262C59#1329811yescharacteristic, complemented, Sylow
263C22×Q8—1181no—
264C22×D4C22×D5911yescharacteristic
265C23×C4—591no—
266C23×C4—591no—
267C4⋊Q8—2361no—
268C4⋊Q8—2361no—
269C22⋊Q8—2364no—
270C22⋊Q8—2364no—
271C4×D4—2361no—
272C4×D4—2361no—
273C2×C4⋊C4—591no—
274C2×C4⋊C4—591no—
275C2×C4⋊C4—1181no—
276C2×C4⋊C4—1181no—
277C2×C4⋊C4—1181no—
278C2×C4⋊C4—1181no—
279C2×C4⋊C4—1181no—
280C2×C4⋊C4—1181no—
281C2×C4⋊C4—2361no—
282C2×C4⋊C4C4×D5911yescharacteristic
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—591no—
288C2×C22⋊C4—591no—
289C2×C22⋊C4—1181no—
290C2×C22⋊C4—1181no—
291C2×C22⋊C4—1181no—
292C2×C22⋊C4—1181no—
293C2×C42—591no—
294C2×C42—591no—
295C2×C42—2361no—
296C2×C42C4×D5911yescharacteristic
297#99—21no—
298#99—21no—
299#99—21no—
300#99—592no—
301#99—1181no—
302#99—1181no—
303#99—1181no—
304#99Dic11812yescomplemented
305#95—1181no—
306#95—2361no—
307#95—2361no—
308C24D4×D5911yescharacteristic
309C24D4×D5911yescharacteristic
310C2×Q8—2361no—
311C2×Q8—2361no—
312C2×Q8—2362no—
313C2×Q8—2362no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4C2×Dic11811yescharacteristic
317C2×D4#1174568511yescharacteristic
318C2×D4#1174568711yescharacteristic
319C2×D4Q8×D5911yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—591no—
325C22×C4—591no—
326C22×C4—591no—
327C22×C4—591no—
328C22×C4—1181no—
329C22×C4—1181no—
330C22×C4—1181no—
331C22×C4—1181no—
332C22×C4—1181no—
333C22×C4—1181no—
334C22×C4—2362no—
335C22×C4—2362no—
336C22×C4—2361no—
337C22×C4—2361no—
338C22×C4C2×C4×D5911yescharacteristic
339C4⋊C4—41no—
340C4⋊C4—1184no—
341C4⋊C4—4722no—
342C4⋊C4—2361no—
343C4⋊C4—2361no—
344C4⋊C4—2362no—
345C4⋊C4—2362no—
346C4⋊C4—2362no—
347C4⋊C4—2362no—
348C4⋊C4—2362no—
349C22⋊C4—22no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—1182no—
356C22⋊C4—2361no—
357C22⋊C4—2361no—
358C22⋊C4—2362no—
359C22⋊C4—2362no—
360C22⋊C4—2361no—
361C22⋊C4—2361no—
362C22⋊C4—2361no—
363C42—41no—
364C42—1181no—
365C42—1181no—
366C42—4722no—
367C42—2361no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23C22⋊C4×D5911yescharacteristic
377C23#1427370411yescharacteristic
378C23#1427370511yescharacteristic
379C23#1427371311yescharacteristic
380C23#1427372611yescharacteristic
381Q8—4722no—
382Q8—4722no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—591no—
402C2×C4—591no—
403C2×C4—1182no—
404C2×C4—1182no—
405C2×C4—1181no—
406C2×C4—1181no—
407C2×C4—1181no—
408C2×C4—4721no—
409C2×C4—4721no—
410C2×C4—4721no—
411C2×C4—4721no—
412C2×C4—4721no—
413C2×C4—4721no—
414C2×C4—4721no—
415C2×C4—2362no—
416C2×C4—2362no—
417C2×C4—2362no—
418C2×C4—2361no—
419C2×C4—2361no—
420C2×C4—2361no—
421C2×C4—2361no—
422C2×C4—2361no—
423C2×C4—2361no—
424C2×C4—2361no—
425C2×C4—2361no—
426C2×C4#1427369211yescharacteristic
427C2×C4C4×Dic11811yescharacteristic
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—81no—
443C22—81no—
444C22#1683730611yescharacteristic
445C22#99×D5911yescharacteristic
446C22#1683737411yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—161no—
453C4—592no—
454C4—1181no—
455C4—9441no—
456C4—4722no—
457C4—4721no—
458C4—2362no—
459C4—2361no—
460C4—2361no—
461C4—2361no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—41no—
467C2—41no—
468C2#2142507911yescharacteristic
469C2#353×D5911yescharacteristic
470C2#2142576911yescharacteristic
subgroupG/H
centerC22#99×D59
commutatorC22×C4×C59C22×C4
FrattiniC22×D4C22×D59
FittingC59×#1393C2
socleC22×C59C2×#99
prime radical, cosocleC22×D4×C59C23
hypercenter#1393D59
hypocenterC59#13298
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
8. C2×#14273726C4semidirect
17. #16837272C4semidirect
18. #16837271C4semidirect
20. C4×Dic59⋊C4C4semidirect
57. #14273642Q8semidirect
71. #99×C59Q8semidirect
262. C59#13298semidirect
304. #99Dic118semidirect

Maximal subgroups

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

subgroupindex
#214290472
#214240822
#99×Dic592
#214222212
#214222202
C59×#13932
#1329859