Finite Group Databasebeta

← #28483403

Subgroups — #28483403

Order 15104.

514 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433228C211yesmaximal, characteristic, complemented
2#21424925C211yesmaximal, characteristic, complemented
3C4×#14273654C211yesmaximal, characteristic, complemented
4#21422513C211yesmaximal, characteristic, complemented
5#21421987C211yesmaximal, characteristic, complemented
6#21421928C211yesmaximal, characteristic, complemented
7C59×#3106C211yesmaximal, characteristic
8Q8×C59⋊C8—21no—
9#16837480—22no—
10#16837480—21no—
11#16837455—21no—
12#16837455C2211yescharacteristic
13#16837426—21no—
14#16837426C2211yescharacteristic
15C2×#14273654—22no—
16C2×#14273654—21no—
17C4×#11745664C2211yescharacteristic
18C42×Dic59C2211yescharacteristic
19#16837161—21no—
20D4⋊(C59⋊C8)—21no—
21D4⋊(C59⋊C8)—21no—
22C59×#532C2211yescharacteristic
23C4×#41×C59C2211yescharacteristic
24C59×#482—21no—
25C59×#477C411yescharacteristic, complemented
26C59×#476C411yescharacteristic, complemented
27C59×#460C411yescharacteristic, complemented
28C59×#459C411yescharacteristic, complemented
29C59×#449—21no—
30C4×SD16×C59—21no—
31C4×D8×C59—21no—
32C59×#431C2211yescharacteristic
33C2×#11745664—22no—
34C2×#11745664—21no—
35C2×#11745664D412yes—
36C2×C4×Dic59—21no—
37C2×C4×Dic59—21no—
38C2×C4×Dic59—21no—
39C4⋊(C59⋊C8)—22no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)D411yescharacteristic
43C4⋊(C59⋊C8)D411yescharacteristic
44#14273654—24no—
45#14273654—44no—
46C22⋊(C59⋊C8)—22no—
47C22⋊(C59⋊C8)—21no—
48#14273638—21no—
49C4×C59⋊C8—22no—
50C4×C59⋊C8—21no—
51C4×C59⋊C8—21no—
52C2×#41×C59—21no—
53C2×#41×C59D411yescharacteristic
54C2×SD16×C59—21no—
55C2×D8×C59—21no—
56C4⋊Q8×C59C2×C411yescharacteristic
57#127×C59C2×C411yescharacteristic
58#124×C59—21no—
59#121×C59—21no—
60#121×C59—21no—
61C4×Q8×C59C2×C411yescharacteristic
62C4×Q8×C59D411yescharacteristic
63C4×D4×C59—21no—
64C4×D4×C59—21no—
65C4×D4×C59—21no—
66C4×D4×C59—21no—
67C4×D4×C59C2×C411yescharacteristic
68C4×D4×C59D411yescharacteristic
69#117×C59—21no—
70#117×C59D411yescharacteristic
71C2×C42×C59—21no—
72C2×C42×C59C2311yescharacteristic
73#107×C59—21no—
74#106×C59—21no—
75C4⋊C8×C59C2×C411yescharacteristic
76C4⋊C8×C59C2×C411yescharacteristic
77#103×C59—21no—
78#102×C59—21no—
79#102×C59—21no—
80#102×C59—21no—
81C22⋊C8×C59—21no—
82C4×C8×C59—21no—
83#41×C59—22no—
84#41×C59—41no—
85#41×C59—42no—
86#41×C59—42no—
87C2×Q8×C59—21no—
88C2×Q8×C59C22⋊C411yescharacteristic
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59—21no—
92C2×D4×C59—21no—
93C2×D4×C59—41no—
94C2×D4×C59C22⋊C411yescharacteristic
95C22×C4×C59—21no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—41no—
99C22×C4×C59C2×D411yescharacteristic
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59#4111yescharacteristic
102C22×Dic59—41no—
103SD16×C59—42no—
104D8×C59—42no—
105C2×C8×C59—21no—
106C2×C8×C59—21no—
107C4⋊C4×C59—21no—
108C4⋊C4×C59—21no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59C22⋊C411yescharacteristic
112C4⋊C4×C59C22⋊C411yescharacteristic
113C22⋊C4×C59—21no—
114C22⋊C4×C59—21no—
115C22⋊C4×C59—21no—
116C22⋊C4×C59—41no—
117C22⋊C4×C59—41no—
118C42×C59—21no—
119C42×C59—21no—
120C42×C59—21no—
121C42×C59C22×C411yescharacteristic
122C42×C59C2×D411yescharacteristic
123C42×C59C2×D411yescharacteristic
124C42×C59#4111yescharacteristic
125C4×Dic59—22no—
126C4×Dic59—22no—
127C4×Dic59—22no—
128C4×Dic59—41no—
129C4×Dic59—41no—
130C4×Dic59—41no—
131#11745664—22no—
132#11745664—41no—
133#11745664—42no—
134#11745664—82no—
135C2×C59⋊C8—21no—
136C2×C59⋊C8—22no—
137C2×C59⋊C8—21no—
138C2×C59⋊C8—41no—
139C23×C59—21no—
140C23×C59—41no—
141C23×C59#12111yescharacteristic
142Q8×C59—21no—
143Q8×C59—42no—
144Q8×C59#10412yescomplemented
145D4×C59—21no—
146D4×C59—21no—
147D4×C59—42no—
148D4×C59—42no—
149D4×C59—41no—
150D4×C59—41no—
151D4×C59—41no—
152D4×C59—41no—
153D4×C59—82no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C2×C4×C59—21no—
160C2×C4×C59—21no—
161C2×C4×C59—21no—
162C2×C4×C59—21no—
163C2×C4×C59—42no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—41no—
167C2×C4×C59—41no—
168C2×C4×C59—41no—
169C2×C4×C59—81no—
170C2×C4×C59—81no—
171C2×C4×C59C2×C22⋊C411yescharacteristic
172C2×C4×C59C4×D411yescharacteristic
173C2×C4×C59C4×D411yescharacteristic
174C2×C4×C59#12011yescharacteristic
175C2×C4×C59#12111yescharacteristic
176C2×C4×C59#12311yescharacteristic
177C2×Dic59—42no—
178C2×Dic59—42no—
179C2×Dic59—42no—
180C8×C59—41no—
181C8×C59—41no—
182C59⋊C8—42no—
183C59⋊C8—42no—
184C59⋊C8—41no—
185C59⋊C8—41no—
186#8970—591nomaximal, Sylow
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—41no—
191C22×C59—41no—
192C22×C59—41no—
193C22×C59—81no—
194C22×C59—81no—
195C22×C59—81no—
196C22×C59#38611yescharacteristic
197C4×C59—21no—
198C4×C59—22no—
199C4×C59—21no—
200C4×C59—21no—
201C4×C59—41no—
202C4×C59—41no—
203C4×C59—81no—
204C4×C59C2×#10411yescharacteristic
205C4×C59#42111yescharacteristic
206C4×C59#44311yescharacteristic
207C4×C59#44411yescharacteristic
208C4×C59#45311yescharacteristic
209C4×C59#45411yescharacteristic
210Dic59—44no—
211#3106D5911yescharacteristic
212#2991—591no—
213#1962—591no—
214C4×#104—591no—
215#1484—591no—
216#1299—591no—
217#1276—591no—
218C2×C59—41no—
219C2×C59—81no—
220C2×C59—161no—
221C2×C59#187111yescharacteristic
222C2×C59#187611yescharacteristic
223C2×C59#188311yescharacteristic
224#532C2×D5911yescharacteristic
225C4×#41C2×D5911yescharacteristic
226#482—21no—
227#477Dic5911yescharacteristic, complemented
228#476Dic5911yescharacteristic, complemented
229#460Dic5911yescharacteristic, complemented
230#459Dic5911yescharacteristic, complemented
231#449—21no—
232C8×Q8—1181no—
233C4×SD16—21no—
234C4×D8—21no—
235#436—1182no—
236#436—1181no—
237#431—591no—
238#431—1181no—
239#431C2×D5911yescharacteristic
240#423—591no—
241#423—1181no—
242C2×#104—1181no—
243C2×#104—1182no—
244C4×M16—591no—
245C43—591no—
246#339—1181no—
247D4⋊C8—1181no—
248D4⋊C8—1181no—
249C59#897011yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41C22⋊D5911yescharacteristic
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—592no—
255C2×M16—1182no—
256C2×M16—1181no—
257C4⋊Q8C2×Dic5911yescharacteristic
258#127C2×Dic5911yescharacteristic
259#124—21no—
260#121—21no—
261#121—21no—
262C4×Q8C2×Dic5911yescharacteristic
263C4×Q8C22⋊D5911yescharacteristic
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4C2×Dic5911yescharacteristic
269C4×D4C22⋊D5911yescharacteristic
270#117—21no—
271#117C22⋊D5911yescharacteristic
272C2×C42—21no—
273C2×C42—1181no—
274C2×C42—1181no—
275C2×C42—1181no—
276C2×C42C22×D5911yescharacteristic
277#107—21no—
278#106—21no—
279C4⋊C8—591no—
280C4⋊C8—591no—
281C4⋊C8—1182no—
282C4⋊C8—1181no—
283C4⋊C8—1181no—
284C4⋊C8C2×Dic5911yescharacteristic
285C4⋊C8C2×Dic5911yescharacteristic
286#104—1184no—
287#104—2364no—
288#103—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—1182no—
294C22⋊C8—1181no—
295#97—1181no—
296C4×C8—21no—
297C4×C8—1182no—
298C4×C8—1181no—
299C4×C8—1181no—
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊Dic5911yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊Dic5911yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—2361no—
317C22×C4D4×D5911yescharacteristic
318C22×C4#1174568711yescharacteristic
319C22×C4C2×C22⋊D5911yescharacteristic
320SD16—42no—
321D8—42no—
322M16—1182no—
323M16—4722no—
324M16—2361no—
325M16—2362no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—1181no—
329C2×C8—1181no—
330C2×C8—1182no—
331C2×C8—2361no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊Dic5911yescharacteristic
337C4⋊C4C22⋊Dic5911yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—1182no—
347C42—1182no—
348C42—1182no—
349C42—2361no—
350C42—2361no—
351C42—2361no—
352C42D4×D5911yescharacteristic
353C42#1174568711yescharacteristic
354C42C22×Dic5911yescharacteristic
355C42C2×C22⋊D5911yescharacteristic
356C23—21no—
357C23—41no—
358C23#1427369911yescharacteristic
359Q8—21no—
360Q8—42no—
361Q8#1427365412yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—2362no—
389C2×C4—2362no—
390C2×C4—2362no—
391C2×C4C2×C22⋊Dic5911yescharacteristic
392C2×C4D4×Dic5911yescharacteristic
393C2×C4D4×Dic5911yescharacteristic
394C2×C4#1427369511yescharacteristic
395C2×C4#1427369911yescharacteristic
396C2×C4#1427370811yescharacteristic
397C8—41no—
398C8—41no—
399C8—2362no—
400C8—2361no—
401C8—2362no—
402C8—2361no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1683728211yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—2364no—
421C4C2×#1427365411yescharacteristic
422C4#1683741911yescharacteristic
423C4#1683751911yescharacteristic
424C4#1683752411yescharacteristic
425C4#1683756811yescharacteristic
426C4#1683757311yescharacteristic
427C2—41no—
428C2—81no—
429C2—161no—
430C2#2142439911yescharacteristic
431C2#2142442511yescharacteristic
432C2#2142447411yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
Fitting, prime radicalC59×#3106C2
socleC22×C59#386
cosocleC2×C42×C59C23
hypercenter#3106D59
hypocenterC59#8970
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #21433228C2semidirect
2. #21424925C2semidirect
3. C4×#14273654C2semidirect
4. #21422513C2semidirect
5. #21421987C2semidirect
6. #21421928C2semidirect
25. C59×#477C4semidirect
26. C59×#476C4semidirect
27. C59×#460C4semidirect
28. C59×#459C4semidirect
144. Q8×C59#104semidirect
227. #477Dic59semidirect
228. #476Dic59semidirect
229. #460Dic59semidirect
230. #459Dic59semidirect
249. C59#8970semidirect
361. Q8#14273654semidirect

Maximal subgroups

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

subgroupindex
#214332282
#214249252
C4×#142736542
#214225132
#214219872
#214219282
C59×#31062
#897059