Finite Group Databasebeta

← #28479618

Subgroups — #28479618

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426635C211yesmaximal, characteristic
2#21423844C211yesmaximal, characteristic, complemented
3#97×Dic59C211yesmaximal, characteristic, complemented
4C2×#16837141C211yesmaximal, characteristic
5C2×#16837141C211yesmaximal, characteristic
6#21421977C211yesmaximal, characteristic, complemented
7C59×#1295C211yesmaximal, characteristic, complemented
8C2×#14273715C2211yescharacteristic
9C2×#14273692C411yescharacteristic
10C2×#14273689C411yescharacteristic
11C2×#14273638C2211yescharacteristic
12C2×#14273638C2211yescharacteristic
13C2×#14273637—21no—
14C2×C8×Dic59—21no—
15#16837307C411yescharacteristic
16#16837303C411yescharacteristic
17#16837291—21no—
18#16837291—21no—
19#16837249—21no—
20#16837249—21no—
21C42×Dic59C2211yescharacteristic
22#16837156—21no—
23#16837156—21no—
24#16837141C414yescomplemented
25#16837141C414yescomplemented
26C2×#97×C59C2211yescharacteristic
27C2×#97×C59C2211yescharacteristic
28C59×#382C2211yescharacteristic
29C22×Dic118C2×C411yescharacteristic
30C22×D236C2×C411yescharacteristic
31C22×C4×D59—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34#14273715—21no—
35#14273715—21no—
36#14273715C2×C412yes—
37#14273715C2×C412yes—
38#14273692—42no—
39#14273689—42no—
40C2×Dic59⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×(C2×D59)⋊C4—21no—
45C2×(C2×D59)⋊C4—21no—
46C2×C4×Dic59—21no—
47C2×C4×Dic59C2×C411yescharacteristic
48C2×C4×Dic59C2×C411yescharacteristic
49C2×C4×Dic59D411yescharacteristic
50C2×C4×Dic59D411yescharacteristic
51C2×C4×Dic59D411yescharacteristic
52C2×C4×Dic59D411yescharacteristic
53#14273638—21no—
54#14273638—21no—
55#14273638C2×C412yescomplemented
56#14273638C2×C412yescomplemented
57#14273637—24no—
58C8×Dic59—24no—
59C59⋊#95—21no—
60C59⋊#95—21no—
61C22×C8×C59—21no—
62C22×C8×C59—21no—
63C2×C4⋊C4×C59C2×C411yescharacteristic
64C2×C4⋊C4×C59C2×C411yescharacteristic
65C2×C42×C59C2311yescharacteristic
66#97×C59—21no—
67#97×C59—21no—
68#97×C59C2×C412yescomplemented
69#97×C59C2×C412yescomplemented
70#95×C59—21no—
71#95×C59—21no—
72C23×D59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C22×C411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×Dic59—21no—
79C22×Dic59C22⋊C411yescharacteristic
80C22×Dic59C22⋊C411yescharacteristic
81C22×Dic59C22⋊C411yescharacteristic
82C22×Dic59C22⋊C411yescharacteristic
83C2×D236—21no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236C4212yes—
87C2×C4×D59—42no—
88C2×C4×D59—42no—
89C2×C4×D59—42no—
90C2×Dic118—21no—
91C2×Dic118—41no—
92C2×Dic118—41no—
93C2×Dic118C4212yes—
94C2×C8×C59—22no—
95C2×C8×C59—22no—
96C2×C8×C59—22no—
97C2×C8×C59—22no—
98C2×C8×C59—41no—
99C2×C8×C59—41no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C42×C59C22×C411yescharacteristic
103C42×C59C22×C411yescharacteristic
104C42×C59#4111yescharacteristic
105C42×C59#4111yescharacteristic
106(C2×D59)⋊C4—22no—
107(C2×D59)⋊C4—22no—
108(C2×D59)⋊C4—22no—
109(C2×D59)⋊C4—22no—
110(C2×D59)⋊C4—42no—
111(C2×D59)⋊C4—42no—
112(C2×D59)⋊C4—42no—
113Dic59⋊C4—42no—
114C4×Dic59—22no—
115C4×Dic59—22no—
116C4×Dic59—22no—
117C4×Dic59—41no—
118C4×Dic59—41no—
119C4×Dic59—41no—
120C4×Dic59—42no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8—22no—
123C2×C59⋊C8—22no—
124C2×C59⋊C8—22no—
125C2×C59⋊C8—41no—
126C2×C59⋊C8—41no—
127C23×C59C2×C22⋊C411yescharacteristic
128C22×D59—22no—
129C22×D59—41no—
130C22×D59—41no—
131C22×D59—41no—
132C22×D59—41no—
133C22×D59—41no—
134C22×D59—41no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—41no—
147C2×C4×C59C2×C4211yescharacteristic
148C2×C4×C59#11711yescharacteristic
149C2×C4×C59C4×D411yescharacteristic
150C2×C4×C59C4×D411yescharacteristic
151C2×C4×C59C4×D411yescharacteristic
152C2×C4×C59C4×D411yescharacteristic
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—22no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—21no—
163C2×Dic59—41no—
164C2×Dic59—41no—
165C2×Dic59#10012yes—
166C2×Dic59#10412yes—
167C2×Dic59#10412yes—
168D236—42no—
169D236—42no—
170C4×D59—84no—
171Dic118—42no—
172Dic118—42no—
173C8×C59—24no—
174C8×C59—42no—
175C59⋊C8—24no—
176C59⋊C8—42no—
177#8226—591nomaximal, Sylow
178C22×C59C4×C22⋊C411yescharacteristic
179C22×C59C2×#10011yescharacteristic
180C22×C59#41311yescharacteristic
181C22×C59C2×#10411yescharacteristic
182C22×C59C2×#10411yescharacteristic
183C22×C59#42111yescharacteristic
184C22×C59#42111yescharacteristic
185C2×D59—42no—
186C2×D59—42no—
187C2×D59—42no—
188C2×D59—81no—
189C2×D59—81no—
190C2×D59—81no—
191C2×D59—81no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—81no—
199C4×C59—81no—
200Dic59—22no—
201Dic59—22no—
202Dic59—22no—
203Dic59—42no—
204Dic59—41no—
205C4×#124—591no—
206#1745—591no—
207C4×#97—591no—
208C2×#329—591no—
209C2×#329—591no—
210#1295—591no—
211#1295D5911yescharacteristic, complemented
212C2×C59#152711yescharacteristic
213C2×C59#152911yescharacteristic
214C2×C59#153011yescharacteristic
215C2×C59#153211yescharacteristic
216C2×C59C4×#10011yescharacteristic
217C2×C59C4×#10411yescharacteristic
218C2×C59#175911yescharacteristic
219D59—82no—
220C2×#124—591no—
221C2×C4×Q8—591no—
222C2×C4×D4—591no—
223C2×#97—591no—
224C2×#97—591no—
225C2×#97—1181no—
226C2×#97C2×D5911yescharacteristic
227C2×#97C2×D5911yescharacteristic
228C2×C4×C8—1181no—
229#391—591no—
230#390—591no—
231#388—1181no—
232#388—1181no—
233#382C2×D5911yescharacteristic
234C4×C22⋊C4—1181no—
235C4×C22⋊C4—1181no—
236C43—591no—
237#336—1181no—
238#336—1181no—
239#329—594no—
240#329—594no—
241C59#822611yescharacteristic, complemented, Sylow
242C22×Q8—591no—
243C22×D4—591no—
244C23×C4—1181no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—1181no—
248C22×C8—1181no—
249#124—592no—
250#124—592no—
251#124—1181no—
252#124—1181no—
253C4×Q8—2362no—
254C4×D4—2362no—
255C2×C4⋊C4—1181no—
256C2×C4⋊C4C4×D5911yescharacteristic
257C2×C4⋊C4C4×D5911yescharacteristic
258C2×C22⋊C4—1181no—
259C2×C22⋊C4—1181no—
260C2×C22⋊C4—1181no—
261C2×C22⋊C4—1181no—
262C2×C22⋊C4—1181no—
263C2×C42—591no—
264C2×C42—591no—
265C2×C42—591no—
266C2×C42—591no—
267C2×C42—591no—
268C2×C42—591no—
269C2×C42—1181no—
270C2×C42C22×D5911yescharacteristic
271#97—21no—
272#97—21no—
273#97—592no—
274#97—592no—
275#97—1184no—
276#97—1181no—
277#97—1181no—
278#97C4×D5912yescomplemented
279#97C4×D5912yescomplemented
280C4×C8—1184no—
281#95—21no—
282#95—21no—
283#95—1181no—
284#95—1181no—
285C24—1181no—
286C2×Q8—592no—
287C2×Q8—1181no—
288C2×Q8—2361no—
289C2×Q8—2361no—
290C2×D4—592no—
291C2×D4—1181no—
292C2×D4—2361no—
293C2×D4—2361no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—591no—
297C22×C4—591no—
298C22×C4—591no—
299C22×C4—591no—
300C22×C4—1181no—
301C22×C4—2362no—
302C22×C4—2362no—
303C22×C4—2362no—
304C22×C4C2×C4×D5911yescharacteristic
305C22×C4D4×D5911yescharacteristic
306C22×C4D4×D5911yescharacteristic
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—1182no—
314C2×C8—1182no—
315C2×C8—1182no—
316C2×C8—1182no—
317C2×C8—2361no—
318C2×C8—2361no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—2362no—
322C22⋊C4—1182no—
323C22⋊C4—1182no—
324C22⋊C4—1182no—
325C22⋊C4—1182no—
326C22⋊C4—2362no—
327C22⋊C4—2362no—
328C22⋊C4—2362no—
329C42—1182no—
330C42—1182no—
331C42—1182no—
332C42—2361no—
333C42—2361no—
334C42—2361no—
335C42—2362no—
336C42C2×C4×D5911yescharacteristic
337C42C2×C4×D5911yescharacteristic
338C42#1174568711yescharacteristic
339C42#1174568911yescharacteristic
340C23—1182no—
341C23—2361no—
342C23—2361no—
343C23—2361no—
344C23—2361no—
345C23—2361no—
346C23—2361no—
347C23C22⋊C4×D5911yescharacteristic
348Q8—2362no—
349Q8—2362no—
350D4—2362no—
351D4—2362no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—592no—
365C2×C4—592no—
366C2×C4—592no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—1181no—
370C2×C4—1181no—
371C2×C4—1181no—
372C2×C4—1181no—
373C2×C4—1181no—
374C2×C4—1181no—
375C2×C4—1181no—
376C2×C4—1182no—
377C2×C4—4724no—
378C2×C4—2361no—
379C2×C4—2361no—
380C2×C4C42×D5911yescharacteristic
381C2×C4#1427368511yescharacteristic
382C2×C4(C22⋊D59)⋊C411yescharacteristic
383C2×C4(C22⋊D59)⋊C411yescharacteristic
384C2×C4#1427368911yescharacteristic
385C2×C4#1427368911yescharacteristic
386C8—24no—
387C8—42no—
388C8—1184no—
389C8—2362no—
390C22—4721no—
391C22—4721no—
392C22—4721no—
393C22—4721no—
394C22—2362no—
395C22—2362no—
396C22—2362no—
397C22#1683724911yescharacteristic
398C22#100×D5911yescharacteristic
399C22#1683738511yescharacteristic
400C22#104×D5911yescharacteristic
401C22#104×D5911yescharacteristic
402C22#1683741711yescharacteristic
403C22#1683741711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—81no—
411C4—81no—
412C4—1182no—
413C4—1182no—
414C4—1182no—
415C4—2362no—
416C4—2361no—
417C2—4722no—
418C2#2142269211yescharacteristic
419C2#2142270211yescharacteristic
420C2#2142270511yescharacteristic
421C2#2142271511yescharacteristic
422C2#2142388711yescharacteristic
423C2#2142390011yescharacteristic
424C2#2142390511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socleC23×C59C2×C22⋊C4
prime radicalC22×D236C2×C4
cosocleC2×C42×C59C23
hypercenter#1295D59
hypocenterC59#8226
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21423844C2semidirect
3. #97×Dic59C2semidirect
6. #21421977C2semidirect
7. C59×#1295C2semidirect
24. #16837141C4semidirect
25. #16837141C4semidirect
55. #14273638C2×C4semidirect
56. #14273638C2×C4semidirect
68. #97×C59C2×C4semidirect
69. #97×C59C2×C4semidirect
211. #1295D59semidirect
241. C59#8226semidirect
278. #97C4×D59semidirect
279. #97C4×D59semidirect

Maximal subgroups

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

subgroupindex
#214266352
#214238442
#97×Dic592
C2×#168371412
#214219772
C59×#12952
#822659