Finite Group Databasebeta

← #29834661

Subgroups — #29834661

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456333C211yesmaximal, characteristic, complemented
2C4×#14519799C211yesmaximal, characteristic
3#21447984C212yesmaximal, complemented
4#21447977C212yesmaximal, complemented
5#21447972C211yesmaximal, characteristic, complemented
6#21447967C211yesmaximal, characteristic, complemented
7#21447962C211yesmaximal, characteristic, complemented
8#21447957C211yesmaximal, characteristic, complemented
9#21447603C212yesmaximal, complemented
10#21447527C212yesmaximal
11C2×C61×C4⋊C16C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13#16840319—21no—
14C4×#11758222—21no—
15#16840167C2211yescharacteristic
16#16840167C2211yescharacteristic
17#16840164—21no—
18#16840164C2212yes—
19#16840160—21no—
20C4×Dic244C2211yescharacteristic
21C4×Dic244C2211yescharacteristic
22C4×#11758190—21no—
23C4×#11758190—21no—
24C4×D488C2211yescharacteristic
25C4×D488C2211yescharacteristic
26#16839800—21no—
27#16839800C2211yescharacteristic
28#16839800C2212yes—
29#16839759—21no—
30#16839590C2212yes—
31#16839590C2212yes—
32#16839588C2212yes—
33#16839588C2212yes—
34#16839567C2212yes—
35#16839567C2212yes—
36#16839564C2212yes—
37#16839564C2212yes—
38C22×C16×C61C2212yes—
39C2×C4×C8×C61C2211yescharacteristic
40C61×C4⋊C16C2211yescharacteristic
41C61×C4⋊C16C2211yescharacteristic
42C61×C4⋊C16C2212yes—
43C2×#11758222—21no—
44#14519799—22no—
45#14519799Q814yescomplemented
46C2×Dic244C2311yescharacteristic
47C2×#11758190—21no—
48C2×D488C2311yescharacteristic
49#14519777—21no—
50#14519777—21no—
51#14519769—22no—
52#14519756—41no—
53#14519756—41no—
54C4×Dic122—21no—
55C4×Dic122—21no—
56C4×Dic122—41no—
57C4×Dic122—41no—
58C4×D244—21no—
59C4×D244—21no—
60C4×C22⋊D61—41no—
61C4×C22⋊D61—41no—
62#14519736—21no—
63#14519736—22no—
64#14519734—41no—
65C42×D61—41no—
66#14519711—21no—
67#14519711—21no—
68#14519711C2312yes—
69#14519711C2312yes—
70#14519711C2311yescharacteristic
71#14519711C2311yescharacteristic
72#14519709—22no—
73#14519709—21no—
74#14519709—22no—
75#14519702—21no—
76#14519702—21no—
77#14519699—21no—
78#14519699—21no—
79C22×C8×C61D411yescharacteristic
80C22×C8×C61C2311yescharacteristic
81C2×C42×C61D411yescharacteristic
82C2×C16×C61—24no—
83C2×C16×C61C2312yes—
84C2×C16×C61C2312yes—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C22×C4×C61D811yescharacteristic
90C22×C4×C61D811yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—41no—
93#11758222—24no—
94#11758222—42no—
95C2×D244—21no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×Dic122—21no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×C8×C61—22no—
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×Q812yes—
107C2×C8×C61#4112yes—
108C2×C8×C61C2411yescharacteristic
109C42×C61D811yescharacteristic
110C42×C61D811yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C22⋊Dic61—41no—
114C22⋊Dic61—42no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123#11758196—41no—
124#11758196—41no—
125#11758196—42no—
126#11758196—42no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130C4×Dic61—42no—
131Dic244—21no—
132Dic244C2×Q812yes—
133D488—21no—
134D488C2×Q812yes—
135#11758190—24no—
136C16×C61—22no—
137C16×C61—22no—
138C23×C61C2×D811yescharacteristic
139C22×D61—41no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61C22⋊Q812yes—
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×D811yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61#13712yes—
149C2×C4×C61C22×D411yescharacteristic
150C22⋊D61—44no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156D244—22no—
157D244—41no—
158C4×D61—44no—
159C4×D61—82no—
160C4×D61—82no—
161Dic122—22no—
162Dic122—41no—
163Dic122—82no—
164Dic122—82no—
165C8×C61—21no—
166C8×C61—21no—
167C8×C61C22⋊Q812yes—
168C8×C61C22×Q811yescharacteristic
169C8×C61C2×#4111yescharacteristic
170#33626—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61#47412yes—
174C22×C61C22×D811yescharacteristic
175C2×D61—42no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61#47412yes—
182C4×C61#50812yes—
183C4×C61C2×C22⋊Q811yescharacteristic
184C4×C61C2×#13711yescharacteristic
185Dic61—42no—
186Dic61—82no—
187Dic61—81no—
188Dic61—82no—
189Dic61—81no—
190#3160—611no—
191C4×#135—611no—
192#2229—612no—
193#2228—612no—
194#2227—611no—
195#2226—611no—
196#2225—611no—
197#2224—611no—
198#2158—612no—
199C2×C4⋊C16D6111yescharacteristic, complemented
200#2138—612no—
201C2×C61—22no—
202C2×C61C2×#47411yescharacteristic
203C2×C61C2×#50811yescharacteristic
204C2×C61#341411yescharacteristic
205D61—82no—
206C2×#135—611no—
207#533—1221no—
208C4×#41—1221no—
209C22×C16C2×D6112yes—
210#500—611no—
211#500—611no—
212#499—612no—
213#499—1221no—
214#498—1221no—
215C4×Q16—611no—
216C4×Q16—611no—
217C4×SD16—1221no—
218C4×SD16—1221no—
219C4×D8—611no—
220C4×D8—611no—
221#427—612no—
222#427—611no—
223#427—1221no—
224#416—1221no—
225C2×C4×C8C2×D6111yescharacteristic
226#367—612no—
227#367—612no—
228#366—612no—
229#366—612no—
230C4⋊C16C2×D6111yescharacteristic
231C4⋊C16C2×D6111yescharacteristic
232C4⋊C16C2×D6112yes—
233#358—612no—
234#358—612no—
235#357—612no—
236#357—612no—
237C61#3362611yescharacteristic, complemented, Sylow
238C2×#41—1221no—
239#135—614no—
240#135—1222no—
241C2×Q16—611no—
242C2×SD16—1221no—
243C2×D8—611no—
244C22×C8D24411yescharacteristic
245C22×C8C22×D6111yescharacteristic
246C4⋊Q8—1221no—
247C4⋊Q8—1221no—
248#125—1222no—
249C22⋊Q8—2441no—
250C22⋊Q8—2441no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C4×Q8—2441no—
254C4×Q8—2441no—
255C4×D4—1221no—
256C4×D4—1221no—
257C4×D4—2441no—
258C4×D4—2441no—
259#117—1221no—
260#117—1222no—
261#117—2441no—
262C2×C42—2441no—
263C2×C42D24411yescharacteristic
264C2×C16—24no—
265C2×C16C22×D6112yes—
266C2×C16C22×D6112yes—
267#107—612no—
268#107—612no—
269#107—611no—
270#107—611no—
271#107—1221no—
272#107—1221no—
273#106—1221no—
274#106—1222no—
275#106—1222no—
276#103—1221no—
277#103—1221no—
278#102—1221no—
279#102—1221no—
280C4×C8D24411yescharacteristic
281C4×C8D24411yescharacteristic
282C4×C8C22×D6111yescharacteristic
283C4×C8C22×D6111yescharacteristic
284#41—1224no—
285#41—2442no—
286C2×Q8—1221no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4D48811yescharacteristic
295C22×C4D48811yescharacteristic
296C22×C4C2×D24411yescharacteristic
297Q16—612no—
298Q16—1221no—
299SD16—1224no—
300D8—612no—
301D8—1221no—
302C2×C8—22no—
303C2×C8C2×D24411yescharacteristic
304C2×C8C2×D24411yescharacteristic
305C2×C8C2×D24411yescharacteristic
306C2×C8#1175822412yes—
307C2×C8Q8×D6112yes—
308C2×C8C23×D6111yescharacteristic
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1222no—
312C4⋊C4—1222no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2442no—
316C4⋊C4—2442no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2442no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C42—2441no—
324C42—2441no—
325C42—2441no—
326C42—2442no—
327C42D48811yescharacteristic
328C42D48811yescharacteristic
329C42C2×D24411yescharacteristic
330C42C2×D24411yescharacteristic
331C16—22no—
332C16—22no—
333C23—2441no—
334C23C2×D48811yescharacteristic
335Q8—1222no—
336Q8—4882no—
337Q8—4882no—
338Q8—2441no—
339D4—1222no—
340D4—2444no—
341D4—2441no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—4882no—
345C2×C4—4882no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2444no—
352C2×C4#1451975712yes—
353C2×C4C2×D48811yescharacteristic
354C2×C4C2×D48811yescharacteristic
355C2×C4C2×D48811yescharacteristic
356C2×C4C2×D48811yescharacteristic
357C2×C4C2×D48811yescharacteristic
358C2×C4#1451981012yes—
359C2×C4C22×D24411yescharacteristic
360C8—21no—
361C8—21no—
362C8#1451975712yes—
363C8C2×Q8×D6111yescharacteristic
364C8C2×#1175822411yescharacteristic
365C22—21no—
366C22—21no—
367C22—4881no—
368C22—4881no—
369C22—2442no—
370C22#1684004312yes—
371C22C22×D48811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—4881no—
376C4—4882no—
377C4—4881no—
378C4—4882no—
379C4—2442no—
380C4#1684004312yes—
381C4#1684019412yes—
382C4C2×#1451975711yescharacteristic
383C4C2×#1451981011yescharacteristic
384C2—22no—
385C2—4882no—
386C2C2×#1684004311yescharacteristic
387C2C2×#1684019411yescharacteristic
388C2#2145895511yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×C4⋊C16C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenterC2×C4⋊C16D61
hypocenterC61#33626
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
1. #21456333C2semidirect
3. #21447984C2semidirect
4. #21447977C2semidirect
5. #21447972C2semidirect
6. #21447967C2semidirect
7. #21447962C2semidirect
8. #21447957C2semidirect
9. #21447603C2semidirect
11. C2×C61×C4⋊C16C2semidirect
45. #14519799Q8semidirect
199. C2×C4⋊C16D61semidirect
237. C61#33626semidirect

Maximal subgroups

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

subgroupindex
#214563332
C4×#145197992
#214479842
#214479772
#214479722
#214479672
#214479622
#214479572
#214476032
#214475272
C2×C61×C4⋊C162
#3362661