Finite Group Databasebeta

← #30607579

Subgroups — #30607579

Order 15616.

496 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462578C211yesmaximal, characteristic
2D61⋊#361C211yesmaximal, characteristic
3#21462129C211yesmaximal, characteristic, complemented
4#21461981C211yesmaximal, characteristic, complemented
5#21460881C211yesmaximal, characteristic, complemented
6#21460872C211yesmaximal, characteristic, complemented
7C2×SD32×D61C211yesmaximal, characteristic
8#16840829—21no—
9D61⋊M32C2211yescharacteristic
10#16840803—22no—
11D8×#6923—22no—
12D61⋊#108C2211yescharacteristic
13#16840772C2211yescharacteristic
14#16840755—21no—
15#16840754—21no—
16D61⋊#101—21no—
17#16840725C2211yescharacteristic
18#16840680—22no—
19#16840675—22no—
20C2×Q16×D61C2211yescharacteristic
21C2×D8×D61C2211yescharacteristic
22C2×#14519722C411yescharacteristic, complemented
23C2×#14519721C411yescharacteristic, complemented
24C2×#14519720C411yescharacteristic, complemented
25SD32×D61—22no—
26SD32×D61—22no—
27C2×C16×D61C2211yescharacteristic
28C2×SD32×C61C411yescharacteristic, complemented
29D61⋊M16—21no—
30D61⋊M16D411yescharacteristic
31D4×#6923—24no—
32D4×#6923—42no—
33#14519856—21no—
34#14519856D411yescharacteristic
35C2×C22⋊#6923—42no—
36#14519852—21no—
37#14519851—21no—
38D61⋊C16—21no—
39#14519848—21no—
40#14519847—21no—
41#14519846D412yes—
42#14519845—21no—
43#14519840—42no—
44#14519839—24no—
45#14519838—42no—
46#14519831—21no—
47C8×#6923—21no—
48C2×Q8×D61—21no—
49C2×D4×D61—21no—
50C2×Dic244C2×C411yescharacteristic, complemented
51C2×#11758202—21no—
52Q16×D61—21no—
53Q16×D61—21no—
54Q16×D61—21no—
55Q16×D61—21no—
56C2×D488C2×C411yescharacteristic
57C2×#11758199—21no—
58D8×D61—21no—
59D8×D61—21no—
60D8×D61D412yes—
61D8×D61D412yes—
62C2×C8×D61C2311yescharacteristic
63#14519722—22no—
64#14519721—22no—
65#14519720—22no—
66C2×#11758185C2×C411yescharacteristic, complemented
67C16×D61—21no—
68C16×D61—21no—
69C2×Q16×C61C2×C411yescharacteristic, complemented
70C2×D8×C61C2×C411yescharacteristic
71SD32×C61—22no—
72C2×C16×C61C2×C411yescharacteristic, complemented
73C23×D61—41no—
74C22×#6923—44no—
75C2×Q8×C61—21no—
76C2×D4×C61—21no—
77C2×C22⋊D61—41no—
78Q8×D61—41no—
79Q8×D61—41no—
80Q8×D61—41no—
81Q8×D61—41no—
82D4×D61—22no—
83D4×D61—22no—
84D4×D61—41no—
85D4×D61—41no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×C4×D61C2×D411yescharacteristic
89C2×Dic122—21no—
90C2×Dic122—41no—
91C22⋊#6923—21no—
92C22⋊#6923—44no—
93C22⋊#6923—41no—
94#11758217—21no—
95#11758217—41no—
96C4⋊#6923—22no—
97C4⋊#6923D812yes—
98C4×#6923—21no—
99C4×#6923—41no—
100#11758213—21no—
101#11758213—41no—
102D61⋊C8—21no—
103D61⋊C8—41no—
104Q16×C61—21no—
105Q16×C61—21no—
106D8×C61—21no—
107D8×C61C22⋊C412yes—
108C2×C8×C61C22×C411yescharacteristic
109#11758202—41no—
110#11758202—41no—
111#11758199—22no—
112#11758199—22no—
113C2×#92418#4111yescharacteristic
114Dic244—21no—
115Dic244—21no—
116D488—21no—
117D488C22⋊C412yes—
118C8×D61C2×D411yescharacteristic
119C8×D61C2×D411yescharacteristic
120C8×D61C2×D411yescharacteristic
121C8×D61#4111yescharacteristic
122#11758187—41no—
123C16×C61—21no—
124#11758185—21no—
125C23×C61—41no—
126C22×D61—41no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—162no—
130C22×D61AGL(1,ℤ/8)11yescharacteristic
131C2×#6923—22no—
132C2×#6923—42no—
133C2×#6923—164no—
134Q8×C61—41no—
135Q8×C61—41no—
136D4×C61—22no—
137D4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C4×D411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C2×Dic61—41no—
143C2×Dic61AGL(1,ℤ/8)11yescharacteristic
144D244—22no—
145D244—41no—
146C4×D61—81no—
147C4×D61—81no—
148C4×D61#12011yescharacteristic
149C4×D61#12111yescharacteristic
150C4×D61C2×D811yescharacteristic
151C4×D61#13511yescharacteristic
152Dic122—41no—
153Dic122—41no—
154Dic122—81no—
155Dic122—81no—
156#92420—41no—
157#92420—81no—
158C8×C61C2×C22⋊C411yescharacteristic
159C8×C61C4×D411yescharacteristic
160#92418#12111yescharacteristic
161#92418#12311yescharacteristic
162#13019—611nomaximal, Sylow
163C22×C61—42no—
164C22×C61—161no—
165C22×C61#44211yescharacteristic
166C2×D61—22no—
167C2×D61—42no—
168C2×D61—84no—
169C2×D61—162no—
170C2×D61—161no—
171C2×D61#44711yescharacteristic
172C2×D61#46311yescharacteristic
173#6923—42no—
174#6923—82no—
175C4×C61—81no—
176C4×C61#38611yescharacteristic
177C4×C61C4×D811yescharacteristic
178Dic61—81no—
179Dic61#44911yescharacteristic
180Dic61#45911yescharacteristic
181C22×SD32—611no—
182#2948—611no—
183C2×#361—611no—
184#2141—611no—
185#1979—611no—
186#1382—611no—
187#1379—611no—
188C2×C61—21no—
189C2×C61—82no—
190C2×C61#187911yescharacteristic
191D61—21no—
192D61—82no—
193D61#219412yes—
194C22×Q16—611no—
195C22×D8—611no—
196#518—1221no—
197C2×SD32—611no—
198C2×SD32—611no—
199C2×SD32—611no—
200C2×SD32—1222no—
201C2×SD32—1222no—
202C2×SD32#692311yescharacteristic, complemented
203C2×M32—611no—
204C22×C16—611no—
205#442—1222no—
206C4×D8—1222no—
207C2×#108—611no—
208#427—611no—
209#419—1221no—
210#418—1221no—
211C2×#101—1221no—
212#405—611no—
213#361—1222no—
214#358—1222no—
215C61#1301911yescharacteristic, complemented, Sylow
216C22×Q8—1221no—
217C22×D4—1221no—
218C2×Q16—611no—
219C2×Q16—1221no—
220C2×Q16—1221no—
221C2×Q16—1221no—
222C2×Q16—1221no—
223C2×Q16—1221no—
224C2×Q16C2×#692311yescharacteristic, complemented
225C2×D8—612no—
226C2×D8—612no—
227C2×D8—611no—
228C2×D8—1221no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8C2×#692311yescharacteristic
232C2×M16—611no—
233C2×M16—1221no—
234C22×C8—611no—
235C4×D4—1224no—
236C4×D4—2442no—
237#117—611no—
238#117—1221no—
239C2×C22⋊C4—2442no—
240SD32—22no—
241SD32—1222no—
242SD32—1222no—
243SD32—1222no—
244M32—1221no—
245M32—1221no—
246C2×C16—611no—
247C2×C16—1221no—
248C2×C16—1221no—
249C2×C16—1221no—
250C2×C16C2×#692311yescharacteristic, complemented
251#108—1221no—
252#108—1221no—
253#107—612no—
254#106—1221no—
255#103—2442no—
256#102—1224no—
257#101—2442no—
258#97—1221no—
259C4×C8—1221no—
260C24—2441no—
261C2×Q8—21no—
262C2×Q8—1221no—
263C2×Q8—2441no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×D4—21no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1221no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2441no—
275C22×C4—611no—
276C22×C4—2441no—
277C22×C4—2444no—
278Q16—21no—
279Q16—21no—
280Q16—1221no—
281Q16—1221no—
282Q16—2441no—
283Q16—2441no—
284D8—21no—
285D8—612no—
286D8—1222no—
287D8—1222no—
288D8—1221no—
289D8C22⋊#692312yes—
290M16—1221no—
291M16—1221no—
292M16—2441no—
293M16—2441no—
294C2×C8—611no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—1221no—
300C2×C8—2441no—
301C2×C8C22×#692311yescharacteristic
302C4⋊C4—612no—
303C4⋊C4—1222no—
304C22⋊C4—1221no—
305C22⋊C4—2444no—
306C22⋊C4—2441no—
307C42—1221no—
308C42—2441no—
309C16—21no—
310C16—1221no—
311C16—2441no—
312C23—41no—
313C23—611no—
314C23—9762no—
315C23—2442no—
316C23—2442no—
317C23—2441no—
318Q8—41no—
319Q8—41no—
320Q8—4881no—
321Q8—4881no—
322Q8—2441no—
323Q8—2441no—
324D4—22no—
325D4—41no—
326D4—1222no—
327D4—2442no—
328D4—2442no—
329D4—2441no—
330C2×C4—41no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1222no—
337C2×C4—9764no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4D4×#692311yescharacteristic
343C8—611no—
344C8—611no—
345C8—4881no—
346C8—2441no—
347C8C2×C22⋊#692311yescharacteristic
348C8D4×#692311yescharacteristic
349C22—42no—
350C22—161no—
351C22—611no—
352C22—611no—
353C22—1222no—
354C22—9761no—
355C22—9762no—
356C22—4884no—
357C22—2442no—
358C22#1684080311yescharacteristic
359C4—81no—
360C4—611no—
361C4—611no—
362C4—4882no—
363C4—4881no—
364C4—2442no—
365C4#1684071011yescharacteristic
366C4D8×#692311yescharacteristic
367C2—21no—
368C2—82no—
369C2—612no—
370C2—1221no—
371C2—4882no—
372C2#2146181411yescharacteristic
subgroupG/H
centerC2#21461814
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×SD32×C61C4
socleC2×C61#1879
prime radicalC2×D8×D61C22
cosocleC2×C8×D61C23
hypercenterC2×SD32#6923
hypocenterC61#13019
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
3. #21462129C2semidirect
4. #21461981C2semidirect
5. #21460881C2semidirect
6. #21460872C2semidirect
22. C2×#14519722C4semidirect
23. C2×#14519721C4semidirect
24. C2×#14519720C4semidirect
28. C2×SD32×C61C4semidirect
50. C2×Dic244C2×C4semidirect
66. C2×#11758185C2×C4semidirect
69. C2×Q16×C61C2×C4semidirect
72. C2×C16×C61C2×C4semidirect
202. C2×SD32#6923semidirect
215. C61#13019semidirect
224. C2×Q16C2×#6923semidirect
250. C2×C16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625782
D61⋊#3612
#214621292
#214619812
#214608812
#214608722
C2×SD32×D612
#1301961