Finite Group Databasebeta

← #29662455

Subgroups — #29662455

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455601C212yesmaximal
2C8×#11758222C211yesmaximal, characteristic
3#21445274C212yesmaximal, complemented
4#21445267C212yesmaximal, complemented
5#21445220C211yesmaximal, characteristic, complemented
6#21445215C211yesmaximal, characteristic, complemented
7#21445186C211yesmaximal, characteristic, complemented
8#21445181C211yesmaximal, characteristic, complemented
9C2×#16839515C211yesmaximal, characteristic, complemented
10#21444476C212yesmaximal, complemented
11C61×#3170C211yesmaximal, characteristic, complemented
12C4×#11758222C2211yescharacteristic
13#16840066—22no—
14#16840059—22no—
15#16840054C2212yes—
16#16840049C2212yes—
17#16840044C2212yes—
18#16840039C2212yes—
19C8×Dic122C2211yescharacteristic
20C8×Dic122C2211yescharacteristic
21C8×D244C2211yescharacteristic
22C8×D244C2211yescharacteristic
23C8×C22⋊D61—21no—
24C8×C22⋊D61—21no—
25#16839815C2211yescharacteristic
26#16839813—21no—
27#16839798—22no—
28C2×C4⋊#92418C2212yes—
29#16839756—22no—
30C4×C8×D61—21no—
31#16839515C2211yescharacteristic
32#16839515C2211yescharacteristic
33#16839515C2212yes—
34#16839511C2212yes—
35#16839511C2212yes—
36#16839508C2212yes—
37#16839508C2212yes—
38C61×#533C2212yes—
39C61×#500C2211yescharacteristic
40C61×#494C2211yescharacteristic
41C61×#487C2212yes—
42C61×#467—21no—
43C61×#467—21no—
44C4×Q16×C61—21no—
45C4×Q16×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222D411yescharacteristic
48C22×#92418—22no—
49C2×C8×D61—21no—
50C2×C8×D61—21no—
51C4×Dic122D411yescharacteristic
52C4×Dic122C2311yescharacteristic
53C4×D244D411yescharacteristic
54C4×D244C2311yescharacteristic
55C4×C22⋊D61—21no—
56C4×C22⋊D61—21no—
57#14519736D411yescharacteristic
58#14519734—21no—
59C42×D61—21no—
60#14519710—22no—
61#14519710—22no—
62#14519708—22no—
63#14519708—22no—
64C4⋊#92418—22no—
65C4⋊#92418C2311yescharacteristic
66C4⋊#92418C2311yescharacteristic
67C4⋊#92418C2312yes—
68C4⋊#92418C2312yes—
69#14519706—21no—
70#14519706—21no—
71#14519700—22no—
72#14519700—22no—
73#14519697—22no—
74#14519697—22no—
75C22⋊#92418—21no—
76#14519689—21no—
77#14519689—21no—
78C4×#92418—21no—
79C8×Dic61—21no—
80C8×Dic61—21no—
81C2×Q16×C61—21no—
82C2×Q16×C61—21no—
83C22×C8×C61D411yescharacteristic
84C22×C8×C61D411yescharacteristic
85C4⋊Q8×C61C2312yes—
86C4⋊Q8×C61C2312yes—
87#125×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C4×Q8×C61—22no—
91C4×Q8×C61—22no—
92#117×C61—22no—
93C2×C42×C61C2311yescharacteristic
94#107×C61—21no—
95#107×C61—21no—
96#103×C61—22no—
97#103×C61—22no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C2×C22⋊D61—21no—
108#11758222—22no—
109#11758222Q1614yescomplemented
110C2×D244C2×D411yescharacteristic
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×Dic122C2×D411yescharacteristic
115Q16×C61—42no—
116Q16×C61—42no—
117C2×C8×C61—22no—
118C2×C8×C61—41no—
119C2×C8×C61C2×D411yescharacteristic
120C2×C8×C61C2×D411yescharacteristic
121C2×C8×C61C2×D411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C4⋊C4×C61—22no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—42no—
128C4⋊C4×C61—42no—
129C22⋊C4×C61—42no—
130C42×C61—42no—
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134C42×C61C2411yescharacteristic
135C22⋊Dic61—21no—
136#11758198—21no—
137#11758198—21no—
138C4⋊Dic61C2×D411yescharacteristic
139C4⋊Dic61C2×D411yescharacteristic
140#11758196—21no—
141#11758196—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C4×Dic61—21no—
145C2×#92418—21no—
146C2×#92418—21no—
147C2×#92418—22no—
148C2×#92418—22no—
149C2×#92418—44no—
150C8×D61—42no—
151C8×D61—42no—
152C23×C61#12111yescharacteristic
153C22×D61—21no—
154Q8×C61—42no—
155Q8×C61—42no—
156Q8×C61—82no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—41no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12111yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61C2×Q1612yes—
166C2×C4×C61#13512yes—
167C2×C4×C61C22×D411yescharacteristic
168C2×C4×C61C22×D411yescharacteristic
169C2×C4×C61C2×#4111yescharacteristic
170C22⋊D61—24no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174D244—21no—
175D244C2×Q1612yes—
176C4×D61—24no—
177C4×D61—42no—
178C4×D61—41no—
179C4×D61—41no—
180Dic122—21no—
181Dic122C2×Q1612yes—
182C8×C61—21no—
183C8×C61—21no—
184C8×C61—21no—
185C8×C61#13512yes—
186#92418—41no—
187#92418—42no—
188#92418—42no—
189#92418—41no—
190#19126—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#46712yes—
194C22×C61C2×#12111yescharacteristic
195C2×D61—22no—
196C2×D61—41no—
197C2×D61—41no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—82no—
202C4×C61—82no—
203C4×C61#46712yes—
204C4×C61C22×Q1611yescharacteristic
205C4×C61C2×#13511yescharacteristic
206C4×C61C2×#13511yescharacteristic
207C4×C61#57511yescharacteristic
208Dic61—22no—
209Dic61—41no—
210Dic61—41no—
211#3170D6111yescharacteristic, complemented
212#3076—612no—
213C8×#41—611no—
214#1684—612no—
215#1683—612no—
216#1676—611no—
217#1675—611no—
218#1670—611no—
219#1669—611no—
220C2×#335—611no—
221#1542—612no—
222C2×C61—22no—
223C2×C61#303511yescharacteristic
224C2×C61C2×#46711yescharacteristic
225C2×C61#306711yescharacteristic
226D61—42no—
227#533C2×D6112yes—
228C4×#41—611no—
229#500C2×D6111yescharacteristic
230#494C2×D6111yescharacteristic
231#487C2×D6112yes—
232#479—1222no—
233#478—1222no—
234#477—612no—
235#476—612no—
236#475—612no—
237#474—612no—
238#467—21no—
239#467—21no—
240C8×Q8—611no—
241C8×Q8—611no—
242C4×Q16—21no—
243C4×Q16—21no—
244C8×D4—611no—
245C8×D4—611no—
246C8×D4—1221no—
247C8×D4—1221no—
248#431—611no—
249#431—1221no—
250#427—1222no—
251C2×C4⋊C8—612no—
252#416—1222no—
253C2×C4×C8—1221no—
254C2×C4×C8C2×D6111yescharacteristic
255#335—611no—
256#335—611no—
257#335—612no—
258#333—612no—
259#333—612no—
260#332—612no—
261#332—612no—
262C61#1912611yescharacteristic, complemented, Sylow
263C2×#41—611no—
264C2×Q16—21no—
265C2×Q16—21no—
266C22×C8—1222no—
267C22×C8—1221no—
268C22×C8—1221no—
269C22×C8C22⋊D6111yescharacteristic
270C22×C8C22⋊D6111yescharacteristic
271C4⋊Q8C22×D6112yes—
272C4⋊Q8C22×D6112yes—
273#125—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×Q8—611no—
279C4×Q8—611no—
280C4×D4—611no—
281C4×D4—611no—
282C4×D4—1221no—
283C4×D4—1221no—
284#117—22no—
285#117—611no—
286#117—1221no—
287C2×C42—1221no—
288C2×C42C22×D6111yescharacteristic
289#107—21no—
290#107—21no—
291#107—1222no—
292#107—1222no—
293#106—1222no—
294#106—1222no—
295C4⋊C8—611no—
296C4⋊C8—611no—
297C4⋊C8—612no—
298C4⋊C8—612no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1222no—
302#103—22no—
303#103—22no—
304#103—1222no—
305#103—1222no—
306#102—1222no—
307#102—1222no—
308C22⋊C8—1221no—
309C22⋊C8—1221no—
310C22⋊C8—1221no—
311C4×C8—1221no—
312C4×C8—1221no—
313C4×C8—1221no—
314C4×C8C22⋊D6111yescharacteristic
315C4×C8C22⋊D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317C4×C8C22×D6111yescharacteristic
318#41—614no—
319#41—1222no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—611no—
323C2×D4—611no—
324C2×D4—1221no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4D4×D6111yescharacteristic
329C22×C4#1175822411yescharacteristic
330C22×C4C2×C22⋊D6111yescharacteristic
331Q16—42no—
332Q16—42no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—1221no—
339C2×C8—2442no—
340C2×C8—2444no—
341C2×C8—2442no—
342C2×C8C2×C22⋊D6111yescharacteristic
343C2×C8C2×C22⋊D6111yescharacteristic
344C2×C8C2×C22⋊D6111yescharacteristic
345C2×C8C2×C22⋊D6111yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—611no—
353C4⋊C4—611no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C22⋊C4—42no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C42—42no—
361C42—1221no—
362C42—1221no—
363C42—1221no—
364C42D4×D6111yescharacteristic
365C42#1175822411yescharacteristic
366C42C2×C22⋊D6111yescharacteristic
367C42C23×D6111yescharacteristic
368C23—1221no—
369C23#1451974811yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—82no—
373Q8—612no—
374Q8—1221no—
375D4—612no—
376D4—1224no—
377D4—1221no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—1221no—
384C2×C4—1224no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2441no—
390C2×C4#1451974811yescharacteristic
391C2×C4#1451974811yescharacteristic
392C2×C4#1451974811yescharacteristic
393C2×C4Q16×D6112yes—
394C2×C4#1451980012yes—
395C2×C4C2×D4×D6111yescharacteristic
396C2×C4C22×C22⋊D6111yescharacteristic
397C2×C4C2×#1175822411yescharacteristic
398C8—21no—
399C8—21no—
400C8—21no—
401C8—2441no—
402C8—2442no—
403C8—2442no—
404C8—2441no—
405C8#1451979712yes—
406C22—21no—
407C22—21no—
408C22—1222no—
409C22—2441no—
410C22—2441no—
411C22#1684000012yes—
412C22C2×#1451974811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—82no—
417C4—82no—
418C4—1222no—
419C4—2441no—
420C4—2441no—
421C4#1684000012yes—
422C4C2×Q16×D6111yescharacteristic
423C4C2×#1451979711yescharacteristic
424C4C2×#1451980011yescharacteristic
425C4#1684056011yescharacteristic
426C2—22no—
427C2—2442no—
428C2#2145526811yescharacteristic
429C2C2×#1684000011yescharacteristic
430C2#2145553511yescharacteristic
subgroupG/H
centerC2×C4#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3170C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3170D61
hypocenterC61#19126
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #21445274C2semidirect
4. #21445267C2semidirect
5. #21445220C2semidirect
6. #21445215C2semidirect
7. #21445186C2semidirect
8. #21445181C2semidirect
9. C2×#16839515C2semidirect
10. #21444476C2semidirect
11. C61×#3170C2semidirect
109. #11758222Q16semidirect
211. #3170D61semidirect
262. C61#19126semidirect

Maximal subgroups

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

subgroupindex
#214556012
C8×#117582222
#214452742
#214452672
#214452202
#214452152
#214451862
#214451812
C2×#168395152
#214444762
C61×#31702
#1912661