Finite Group Databasebeta

← #29575867

Subgroups — #29575867

Order 15616.

478 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic
2#21454384C211yesmaximal, characteristic
3#21444500C211yesmaximal, characteristic, complemented
4#21444204C211yesmaximal, characteristic
5#21443716C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C2×C61×#332C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9C4×#11758222C2211yescharacteristic
10#16840054C412yes—
11#16840049C412yes—
12#16840044—21no—
13#16840039—21no—
14#16839815C2211yescharacteristic
15#16839802—21no—
16#16839788—21no—
17#16839787—22no—
18#16839786C2211yescharacteristic
19#16839786C2211yescharacteristic
20#16839784—21no—
21C4⋊C8×D61—21no—
22#16839761—21no—
23#16839511—22no—
24#16839492—21no—
25#16839489—21no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#332—21no—
30C61×#332—21no—
31C2×#11758222D411yescharacteristic
32#14519783—42no—
33#14519783—42no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758189—22no—
37C2×C8×D61—22no—
38C4×Dic122C2×C411yescharacteristic
39C4×Dic122D411yescharacteristic
40C4×D244C2×C411yescharacteristic
41C4×D244D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44#14519736D411yescharacteristic
45#14519734—21no—
46C42×D61—21no—
47#14519710—22no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C412yes—
53C4⋊#92418D412yes—
54#14519706—22no—
55#14519706—22no—
56#14519700—22no—
57#14519697—22no—
58C22⋊#92418—21no—
59C4×#92418—21no—
60C22×Q8×C61—21no—
61C22×C8×C61—21no—
62C22×C8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61C2×C412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61D411yescharacteristic
74C4⋊C8×C61D411yescharacteristic
75C2×Q8×C61—22no—
76C2×Q8×C61—41no—
77C2×Q8×C61—81no—
78C2×Q8×C61—81no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—21no—
84#11758222—21no—
85#11758222—21no—
86#11758222SD1612yes—
87#11758222Q1612yes—
88C2×D244C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×Dic122C22⋊C411yescharacteristic
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—81no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C22⋊Dic61—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61C22⋊C411yescharacteristic
111C4⋊Dic61C22⋊C411yescharacteristic
112#11758196—21no—
113#11758196—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117#11758194—41no—
118#11758194—41no—
119#11758194—41no—
120#11758194—41no—
121C2×#92418—22no—
122C2×#92418—22no—
123C2×#92418—41no—
124#11758189—44no—
125C8×D61—44no—
126C23×C61#12311yescharacteristic
127C22×D61—21no—
128Q8×C61—82no—
129Q8×C61—81no—
130Q8×C61—81no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—82no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61C2×SD1611yescharacteristic
143C2×C4×C61C2×Q1611yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C22⋊D61—22no—
147C22⋊D61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151D244—21no—
152D244#10312yes—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—81no—
158Dic122—21no—
159Dic122#10312yes—
160C8×C61—41no—
161C8×C61—41no—
162C8×C61—81no—
163#92418—42no—
164#92418—42no—
165#92418—81no—
166#9167—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#38611yescharacteristic
170C22×C61#48311yescharacteristic
171C22×C61#48411yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—82no—
179C4×C61C2×#10311yescharacteristic
180C4×C61#41711yescharacteristic
181C4×C61#45011yescharacteristic
182C4×C61#45111yescharacteristic
183C4×C61#47111yescharacteristic
184C4×C61#47211yescharacteristic
185Dic61—22no—
186Dic61—41no—
187Dic61—41no—
188#3079—611no—
189#2906—611no—
190#1548—611no—
191C2×#332D6111yescharacteristic, complemented
192#1477—611no—
193#1301—611no—
194#1292—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#187211yescharacteristic
198C2×C61#190211yescharacteristic
199C2×C61#190711yescharacteristic
200D61—42no—
201C2×#131—1221no—
202C2×C4⋊Q8C2×D6111yescharacteristic
203C4×#41—611no—
204#477—612no—
205#476—612no—
206#475—1221no—
207#474—1221no—
208#431—611no—
209#428—1221no—
210#424—1222no—
211#424—1221no—
212#423—611no—
213#423—611no—
214#423—1221no—
215C2×C4⋊C8—1221no—
216C2×C4⋊C8C2×D6111yescharacteristic
217C2×C4⋊C8C2×D6111yescharacteristic
218#417—1221no—
219#333—1222no—
220#332—21no—
221#332—21no—
222Q8⋊C8—1221no—
223D4⋊C8—1221no—
224C61#916711yescharacteristic, complemented, Sylow
225C2×#41—611no—
226C22×Q8—21no—
227#131—2442no—
228#131—2442no—
229C2×M16—1222no—
230C2×M16—1221no—
231C2×M16—1221no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—1222no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8C4×D6112yes—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—611no—
243C4×D4—1221no—
244C4×D4—1221no—
245#117—611no—
246#117—1221no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C42—1221no—
250C2×C42C22×D6111yescharacteristic
251#107—1222no—
252#106—1222no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—612no—
257C4⋊C8—612no—
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8C22⋊D6111yescharacteristic
264C4⋊C8C22⋊D6111yescharacteristic
265#103—1222no—
266#102—1222no—
267C22⋊C8—1221no—
268C4×C8—1221no—
269#41—612no—
270#41—612no—
271#41—1221no—
272#41—1221no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—81no—
276C2×Q8—81no—
277C2×Q8—611no—
278C2×D4—611no—
279C2×D4—1221no—
280C22×C4—41no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4#1175822211yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4#1175822411yescharacteristic
287M16—2444no—
288M16—2441no—
289M16—2441no—
290M16—2441no—
291M16—2441no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—1222no—
299C2×C8—1222no—
300C2×C8—2444no—
301C2×C8—2441no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42C2×C4×D6111yescharacteristic
317C42D4×D6111yescharacteristic
318C42D4×D6111yescharacteristic
319C42C2×C22⋊D6111yescharacteristic
320C23—1221no—
321C23#1451975911yescharacteristic
322Q8—82no—
323Q8—81no—
324Q8—81no—
325Q8—612no—
326Q8—1221no—
327D4—612no—
328D4—1222no—
329D4—1222no—
330D4—1221no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—82no—
336C2×C4—1221no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—4881no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4C22⋊C4×D6111yescharacteristic
345C2×C4#1451973711yescharacteristic
346C2×C4C4×C22⋊D6111yescharacteristic
347C2×C4#1451974511yescharacteristic
348C2×C4#1451974811yescharacteristic
349C2×C4#1451975011yescharacteristic
350C2×C4SD16×D6111yescharacteristic
351C2×C4Q16×D6111yescharacteristic
352C2×C4#1451980411yescharacteristic
353C2×C4#1451980911yescharacteristic
354C8—41no—
355C8—41no—
356C8—81no—
357C8—4881no—
358C8—2442no—
359C8—2442no—
360C22—21no—
361C22—21no—
362C22—1222no—
363C22—2441no—
364C22—2441no—
365C22#1683963811yescharacteristic
366C22#1684009111yescharacteristic
367C22#1684009611yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—82no—
372C4—1222no—
373C4—2441no—
374C4—2441no—
375C4#103×D6111yescharacteristic
376C4#1683976211yescharacteristic
377C4#1683991111yescharacteristic
378C4#1683991611yescharacteristic
379C4#1684002211yescharacteristic
380C4#1684002911yescharacteristic
381C2—21no—
382C2—21no—
383C2—2442no—
384C2#2144612311yescharacteristic
385C2#2144629511yescharacteristic
386C2#2144633011yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#332C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenterC2×#332D61
hypocenterC61#9167
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #21444500C2semidirect
5. #21443716C2semidirect
6. #21443694C2semidirect
7. C2×C61×#332C2semidirect
191. C2×#332D61semidirect
224. C61#9167semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214543842
#214445002
#214442042
#214437162
#214436942
C2×C61×#3322
#916761