Finite Group Databasebeta

← #29663090

Subgroups — #29663090

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456942C211yesmaximal, characteristic
2#21456940C211yesmaximal, characteristic
3C2×#16840141C211yesmaximal, characteristic, complemented
4#21454530C211yesmaximal, characteristic
5#21445307C214yesmaximal, complemented
6#21445183C214yesmaximal, complemented
7#21444565C211yesmaximal, characteristic, complemented
8#21444492C211yesmaximal, characteristic, complemented
9C61×#1546C211yesmaximal, characteristic, complemented
10C22×#11758202—21no—
11C22×#11758202—21no—
12C2×#14519785—21no—
13#16840312C2211yescharacteristic
14C2×#14519777C2211yescharacteristic
15#16840167—21no—
16#16840165—21no—
17#16840141—21no—
18#16840141—21no—
19#16840141C2212yes—
20#16840141C2212yes—
21#16840110—21no—
22#16840109—21no—
23#16840076—22no—
24#16840075—22no—
25#16840043C2214yes—
26#16840039C2214yes—
27#16839839—21no—
28#16839839C2212yes—
29#16839827—21no—
30#16839827C2212yes—
31#16839815C2211yescharacteristic
32#16839730—21no—
33C2×C4×#92418C2211yescharacteristic
34#16839514C2212yes—
35#16839512C2212yes—
36#16839509C2214yes—
37C2×C4⋊Q8×C61C2211yescharacteristic
38C61×#431C2211yescharacteristic
39C61×#423C2211yescharacteristic
40C61×#332C2214yes—
41C2×#11758222—21no—
42C22×Dic122—21no—
43C2×#11758202—22no—
44C2×#11758202—22no—
45C2×#11758202—22no—
46C2×#11758202—22no—
47C2×#11758202—44no—
48C2×#11758202—44no—
49#14519785—44no—
50C2×#11758189—22no—
51C22×#92418D411yescharacteristic
52C22×#92418D411yescharacteristic
53C2×C8×D61—22no—
54#14519777—21no—
55#14519777—21no—
56#14519777—21no—
57#14519777D411yescharacteristic
58#14519777C2312yes—
59#14519774D411yescharacteristic
60#14519765—21no—
61#14519751—21no—
62#14519751D412yes—
63C4×D244—21no—
64C4×D244C2312yes—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67#14519711—24no—
68#14519710—24no—
69C4⋊#92418C2312yes—
70#14519699—24no—
71#14519697—24no—
72C22⋊#92418—21no—
73#14519689—22no—
74#14519689—22no—
75C4×#92418—21no—
76C4×#92418D411yescharacteristic
77C4×#92418D411yescharacteristic
78C4×#92418C2311yescharacteristic
79C4×#92418C2311yescharacteristic
80C22×Q8×C61—21no—
81C2×M16×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C42×C61C2311yescharacteristic
89C4⋊C8×C61—21no—
90C4⋊C8×C61C2312yes—
91C4⋊C8×C61C2312yes—
92C22⋊C8×C61—21no—
93C4×C8×C61—21no—
94C2×Q8×C61—22no—
95C2×Q8×C61—41no—
96C2×Q8×C61—42no—
97C2×Q8×C61—42no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C2×C22⋊D61—22no—
103C22×Dic61—41no—
104#11758222—42no—
105#11758222—42no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244C2×D412yes—
109C2×C4×D61—22no—
110C2×Dic122—21no—
111C2×Dic122—22no—
112C2×Dic122—42no—
113C2×Dic122—42no—
114C2×Dic122—41no—
115M16×C61—42no—
116C2×C8×C61—22no—
117C2×C8×C61—22no—
118C4⋊C4×C61—22no—
119C4⋊C4×C61—22no—
120C4⋊C4×C61—41no—
121C4⋊C4×C61—41no—
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61#4111yescharacteristic
125C42×C61C2411yescharacteristic
126#11758202—44no—
127#11758202—44no—
128#11758202—44no—
129#11758202—44no—
130#11758198—22no—
131#11758198—22no—
132C4⋊Dic61—21no—
133C4⋊Dic61—22no—
134C4⋊Dic61—22no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61C2×D412yes—
138C2×#92418—22no—
139C2×#92418—22no—
140C2×#92418D814yes—
141C2×#92418C2×D411yescharacteristic
142C2×#92418C2×D411yescharacteristic
143C2×#92418C2×D411yescharacteristic
144C2×#92418C2×D411yescharacteristic
145#11758189—44no—
146C8×D61—44no—
147C23×C61#12111yescharacteristic
148C22×D61—22no—
149Q8×C61—42no—
150Q8×C61—42no—
151Q8×C61—82no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—42no—
155C2×C4×C61—82no—
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61C2×D812yes—
160C2×C4×C61AGL(1,ℤ/8)12yes—
161C2×C4×C61C22×D411yescharacteristic
162C2×C4×C61C22×D411yescharacteristic
163C2×C4×C61C2×#4111yescharacteristic
164C22⋊D61—44no—
165C2×Dic61—22no—
166C2×Dic61—42no—
167C2×Dic61—82no—
168D244—24no—
169D244—42no—
170D244—42no—
171C4×D61—42no—
172C4×D61—42no—
173Dic122—42no—
174Dic122—42no—
175Dic122—42no—
176Dic122—82no—
177C8×C61—42no—
178C8×C61—42no—
179#92418—21no—
180#92418—21no—
181#92418—42no—
182#92418C2×D812yes—
183#92418C2×D812yes—
184#19188—611nomaximal, Sylow
185C22×C61—21no—
186C22×C61—21no—
187C22×C61#45912yes—
188C22×C61C2×#12111yescharacteristic
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—42no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—82no—
195C4×C61#45912yes—
196C4×C61#47312yes—
197C4×C61C22×D811yescharacteristic
198C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C61#57812yes—
200Dic61—42no—
201Dic61—82no—
202#3226—611no—
203#3226—611no—
204C2×#494—611no—
205#2931—611no—
206#1689—614no—
207#1669—614no—
208#1564—611no—
209#1546—611no—
210#1546D6111yescharacteristic, complemented
211C2×C61—22no—
212C2×C61C2×#45911yescharacteristic
213C2×C61#305911yescharacteristic
214C2×C61C2×#47311yescharacteristic
215D61—82no—
216C22×Q16—1221no—
217C22×Q16—1221no—
218C2×#131—1221no—
219#532—611no—
220C2×C4⋊Q8—611no—
221C2×C4⋊Q8C2×D6111yescharacteristic
222#500—1221no—
223#500—1221no—
224#494—612no—
225#494—612no—
226#494—1221no—
227#494—1221no—
228#486—1221no—
229#486—1221no—
230#480—1222no—
231#480—1222no—
232#474—614no—
233#474—614no—
234#436—612no—
235#436—1221no—
236C8×D4—612no—
237C8×D4—1221no—
238#431—611no—
239#431C2×D6111yescharacteristic
240#423C2×D6111yescharacteristic
241#408—1221no—
242C2×C4×C8—611no—
243#335—612no—
244#334—612no—
245#332—614no—
246#332C2×D6114yes—
247C61#1918811yescharacteristic, complemented, Sylow
248C2×#41—1221no—
249C22×Q8—21no—
250C22×Q8—1221no—
251C2×Q16—1222no—
252C2×Q16—1222no—
253C2×Q16—1222no—
254C2×Q16—1222no—
255C2×Q16—2444no—
256C2×Q16—2444no—
257#131—2444no—
258C2×M16—21no—
259C2×M16—1222no—
260C22×C8—611no—
261C22×C8—611no—
262C22×C8—1222no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—611no—
267C4⋊Q8—612no—
268C4⋊Q8—1221no—
269C4⋊Q8—1221no—
270C4⋊Q8—1221no—
271C4⋊Q8C22×D6112yes—
272#127—611no—
273#124—1221no—
274#121—612no—
275#121—1221no—
276C4×D4—612no—
277C4×D4—1221no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1221no—
282C2×C42C22×D6111yescharacteristic
283#107—1224no—
284#107—1224no—
285C4⋊C8—21no—
286C4⋊C8—612no—
287C4⋊C8C22×D6112yes—
288C4⋊C8C22×D6112yes—
289#102—1224no—
290#102—1224no—
291C22⋊C8—21no—
292C22⋊C8—1222no—
293C22⋊C8—1222no—
294C22⋊C8—1221no—
295C4×C8—21no—
296C4×C8—611no—
297C4×C8—611no—
298C4×C8—611no—
299C4×C8—611no—
300C4×C8—1221no—
301#41—2442no—
302#41—2442no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—42no—
306C2×Q8—42no—
307C2×Q8—1221no—
308C2×Q8—1222no—
309C2×Q8—2442no—
310C2×Q8—2442no—
311C2×Q8—2441no—
312C2×D4—612no—
313C2×D4—1222no—
314C2×D4—1221no—
315C2×D4—1221no—
316C22×C4—41no—
317C22×C4—1222no—
318C22×C4—2441no—
319C22×C4#1175822211yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4D4×D6111yescharacteristic
322Q16—2444no—
323Q16—2444no—
324Q16—2444no—
325Q16—2444no—
326M16—42no—
327M16—2444no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—611no—
331C2×C8—611no—
332C2×C8—614no—
333C2×C8—611no—
334C2×C8—611no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—2444no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—612no—
343C4⋊C4—1221no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—2441no—
347C4⋊C4—2441no—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C42#1175822211yescharacteristic
351C42D4×D6111yescharacteristic
352C42D4×D6111yescharacteristic
353C42C23×D6111yescharacteristic
354C23—1222no—
355C23#1451975011yescharacteristic
356Q8—42no—
357Q8—42no—
358Q8—82no—
359Q8—4882no—
360Q8—2442no—
361Q8—2442no—
362Q8—2442no—
363D4—1224no—
364D4—2444no—
365D4—2442no—
366D4—2442no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—82no—
371C2×C4—1222no—
372C2×C4—4882no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4#1451975011yescharacteristic
377C2×C4#1451975011yescharacteristic
378C2×C4#1451975011yescharacteristic
379C2×C4D8×D6112yes—
380C2×C4#1451980412yes—
381C2×C4C2×D4×D6111yescharacteristic
382C2×C4C2×D4×D6111yescharacteristic
383C2×C4C2×#1175822211yescharacteristic
384C8—42no—
385C8—42no—
386C8—612no—
387C8—612no—
388C8—1221no—
389C8—1221no—
390C8—2442no—
391C22—21no—
392C22—21no—
393C22—2442no—
394C22—2442no—
395C22—2442no—
396C22#1683995612yes—
397C22C2×#1451975011yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—4882no—
402C4—2442no—
403C4#1683995612yes—
404C4#1684003612yes—
405C4C2×D8×D6111yescharacteristic
406C4C2×#1451980411yescharacteristic
407C4#1684057812yes—
408C2—22no—
409C2—4882no—
410C2C2×#1683995611yescharacteristic
411C2#2145547311yescharacteristic
412C2C2×#1684003611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1546C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1546D61
hypocenterC61#19188
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#16840141C2semidirect
5. #21445307C2semidirect
6. #21445183C2semidirect
7. #21444565C2semidirect
8. #21444492C2semidirect
9. C61×#1546C2semidirect
210. #1546D61semidirect
247. C61#19188semidirect

Maximal subgroups

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

subgroupindex
#214569422
#214569402
C2×#168401412
#214545302
#214453072
#214451832
#214445652
#214444922
C61×#15462
#1918861