Finite Group Databasebeta

← #29713303

Subgroups — #29713303

Order 15616.

1144 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840090C212yesmaximal
2C2×#16839660C211yesmaximal, characteristic
3#21447149C212yesmaximal, complemented
4#21447062C212yesmaximal, complemented
5#21446127C212yesmaximal
6#21446087C214yesmaximal, complemented
7#21445887C211yesmaximal, characteristic
8C2×C61×#533C211yesmaximal, characteristic
9C22×C4⋊Dic61C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×#11758196—21no—
12#16840090—28no—
13C2×#14519708C2214yes—
14C2×#14519701C2214yes—
15C2×#14519701C2214yes—
16C2×C22⋊#92418C2212yes—
17#16839660—21no—
18#16839660—21no—
19#16839660C2212yes—
20#16839660C2212yes—
21C2×#14519684—21no—
22#16839524C2214yes—
23#16839517C2212yes—
24#16839517C2212yes—
25C61×#533—28no—
26C2×C4⋊Q8×C61C2211yescharacteristic
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#125×C61—21no—
29C2×C22⋊Q8×C61—21no—
30C2×C22⋊Q8×C61C2212yes—
31C2×C4×Q8×C61—21no—
32C2×C4×Q8×C61C2212yes—
33C2×#117×C61—21no—
34C22×C42×C61C2211yescharacteristic
35C23×Dic61—21no—
36C23×Dic61—21no—
37C22×#92418C2314yes—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—24no—
40C2×C4⋊Dic61—24no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2312yes—
43C2×C4⋊Dic61C2312yes—
44C2×#11758196—22no—
45C2×#11758196—22no—
46C2×#11758196—44no—
47#14519708—28no—
48#14519701—28no—
49#14519701—28no—
50C22⋊#92418—24no—
51#14519684—22no—
52#14519684—22no—
53C22×Q8×C61—21no—
54C22×Q8×C61C2312yes—
55C23×C4×C61D411yescharacteristic
56C23×C4×C61D411yescharacteristic
57C23×C4×C61C2311yescharacteristic
58C4⋊Q8×C61—24no—
59C4⋊Q8×C61—24no—
60#125×C61—28no—
61C22⋊Q8×C61—28no—
62C22⋊Q8×C61—24no—
63C22⋊Q8×C61D418yes—
64C4×Q8×C61—28no—
65C4×Q8×C61—24no—
66C4×Q8×C61—24no—
67#117×C61—28no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61C2312yes—
74C2×C22⋊C4×C61—22no—
75C2×C42×C61—24no—
76C2×C42×C61—22no—
77C2×C42×C61D411yescharacteristic
78C2×C42×C61D411yescharacteristic
79C2×C42×C61C2311yescharacteristic
80C2×C42×C61C2311yescharacteristic
81C24×C61C2×D411yescharacteristic
82C2×Q8×C61—24no—
83C2×Q8×C61—22no—
84C2×Q8×C61—24no—
85C2×Q8×C61—24no—
86C2×Q8×C61—42no—
87C2×Q8×C61—42no—
88C2×Q8×C61C2×D414yes—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—41no—
98C22×C4×C61SD1614yes—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D414yes—
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2411yescharacteristic
106C22×Dic61—24no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—42no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C22×Dic61—42no—
114C4⋊C4×C61—24no—
115C4⋊C4×C61—24no—
116C4⋊C4×C61—28no—
117C4⋊C4×C61—24no—
118C4⋊C4×C61—28no—
119C4⋊C4×C61—22no—
120C4⋊C4×C61C2×D414yes—
121C22⋊C4×C61—28no—
122C42×C61—28no—
123C42×C61—22no—
124C42×C61—22no—
125C42×C61—22no—
126C42×C61—22no—
127C4⋊Dic61—24no—
128C4⋊Dic61—22no—
129C4⋊Dic61—24no—
130C4⋊Dic61—42no—
131C4⋊Dic61#4114yes—
132#11758196—44no—
133#11758196—44no—
134C2×#92418—24no—
135C2×#92418—24no—
136C2×#92418—24no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61#12012yes—
142C23×C61C2×SD1612yes—
143C23×C61#13712yes—
144C23×C61C22×D411yescharacteristic
145Q8×C61—28no—
146Q8×C61—48no—
147Q8×C61—44no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—28no—
157C2×C4×C61—28no—
158C2×C4×C61—21no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—44no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61#12012yes—
169C2×C4×C61C2×SD1612yes—
170C2×C4×C61C2×SD1612yes—
171C2×C4×C61#13712yes—
172C2×C4×C61C22×D412yes—
173C2×C4×C61C2×#4112yes—
174C2×C4×C612−1+412yes—
175C2×Dic61—24no—
176C2×Dic61—48no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—84no—
183#92418—44no—
184#24063—611nomaximal, Sylow
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61#44814yes—
192C22×C61C2×#12011yescharacteristic
193C22×C61#52511yescharacteristic
194C22×C61#53611yescharacteristic
195C22×C61C22×SD1611yescharacteristic
196C22×C61C2×#13711yescharacteristic
197C22×C61C2×#13711yescharacteristic
198C22×C61#57511yescharacteristic
199C4×C61—22no—
200C4×C61—22no—
201C4×C61—22no—
202C4×C61—22no—
203C4×C61—44no—
204C4×C61—41no—
205C4×C61—44no—
206C4×C61#54714yes—
207Dic61—44no—
208Dic61—82no—
209C2×#533D6111yescharacteristic
210C2×#483—612no—
211C2×#389—611no—
212#2058—612no—
213#2043—612no—
214#1872—612no—
215#1865—614no—
216#1817—611no—
217C2×C61—24no—
218C2×C61#240611yescharacteristic
219C2×C61C2×#44811yescharacteristic
220C2×C61#300711yescharacteristic
221C2×C61#310111yescharacteristic
222C2×C61#311311yescharacteristic
223C2×C61#322911yescharacteristic
224C2×C61#323611yescharacteristic
225#533—28no—
226C2×C4⋊Q8C2×D6111yescharacteristic
227C2×C4⋊Q8C2×D6111yescharacteristic
228C2×#125—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2×D6112yes—
231C2×C4×Q8—21no—
232C2×C4×Q8C2×D6112yes—
233C2×#117—21no—
234C22×C4⋊C4—611no—
235C22×C4⋊C4—611no—
236C22×C4⋊C4—1221no—
237C22×C42C2×D6111yescharacteristic
238#483—1228no—
239C2×#106—614no—
240C2×#103—614no—
241C2×#103—614no—
242C2×C22⋊C8—612no—
243#389—612no—
244#389—612no—
245#389—1221no—
246#389—1221no—
247C2×#95—1221no—
248#340—614no—
249#336—612no—
250#336—612no—
251C61#2406311yescharacteristic, complemented, Sylow
252C22×Q8—21no—
253C22×Q8C22×D6112yes—
254C23×C4—1221no—
255C23×C4—1221no—
256C23×C4C22⋊D6111yescharacteristic
257C23×C4C22⋊D6111yescharacteristic
258C23×C4C22×D6111yescharacteristic
259C22×C8—614no—
260C4⋊Q8—24no—
261C4⋊Q8—24no—
262#125—28no—
263C22⋊Q8—28no—
264C22⋊Q8—24no—
265C22⋊Q8C22⋊D6118yes—
266C4×Q8—28no—
267C4×Q8—24no—
268C4×Q8—24no—
269#117—28no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—612no—
276C2×C4⋊C4—612no—
277C2×C4⋊C4—1224no—
278C2×C4⋊C4—1221no—
279C2×C4⋊C4—1224no—
280C2×C4⋊C4—1221no—
281C2×C4⋊C4—1222no—
282C2×C4⋊C4—1222no—
283C2×C4⋊C4—2444no—
284C2×C4⋊C4C22×D6112yes—
285C2×C22⋊C4—22no—
286C2×C42—22no—
287C2×C42—24no—
288C2×C42C22⋊D6111yescharacteristic
289C2×C42C22⋊D6111yescharacteristic
290C2×C42C22×D6111yescharacteristic
291C2×C42C22×D6111yescharacteristic
292#106—1228no—
293#103—1228no—
294#103—1228no—
295C22⋊C8—1224no—
296#95—1222no—
297#95—1222no—
298C24C2×C22⋊D6111yescharacteristic
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—42no—
304C2×Q8—42no—
305C2×Q8C2×C22⋊D6114yes—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—1224no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—2442no—
319C22×C4—2442no—
320C22×C4—2442no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4#1175820114yes—
324C22×C4C2×C22⋊D6111yescharacteristic
325C22×C4C2×C22⋊D6114yes—
326C22×C4C2×C22⋊D6111yescharacteristic
327C22×C4C2×C22⋊D6111yescharacteristic
328C22×C4C2×C22⋊D6111yescharacteristic
329C22×C4C2×C22⋊D6111yescharacteristic
330C22×C4C23×D6111yescharacteristic
331C2×C8—1224no—
332C2×C8—1224no—
333C2×C8—1224no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—28no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—28no—
340C4⋊C4—614no—
341C4⋊C4—1224no—
342C4⋊C4—1222no—
343C4⋊C4—1224no—
344C4⋊C4—2442no—
345C4⋊C4—2444no—
346C4⋊C4—2444no—
347C4⋊C4C2×C22⋊D6114yes—
348C22⋊C4—28no—
349C42—28no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42—22no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23#1451974612yes—
359C23C2×#1175820112yes—
360C23#1451980812yes—
361C23C22×C22⋊D6111yescharacteristic
362Q8—28no—
363Q8—48no—
364Q8—44no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—28no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—1224no—
386C2×C4—4884no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2448no—
391C2×C4—2442no—
392C2×C4—2442no—
393C2×C4#1451974612yes—
394C2×C4C2×#1175820112yes—
395C2×C4C2×#1175820112yes—
396C2×C4#1451980712yes—
397C2×C4C22×C22⋊D6112yes—
398C2×C4#41×D6112yes—
399C2×C4#1451982412yes—
400C8—2444no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22#1683990114yes—
408C22C2×#1451974611yescharacteristic
409C22#1684026911yescharacteristic
410C22#1684033311yescharacteristic
411C22C22×#1175820111yescharacteristic
412C22C2×#1451980711yescharacteristic
413C22C2×#1451980811yescharacteristic
414C22#1684056011yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—44no—
420C4—41no—
421C4—44no—
422C4—4882no—
423C4—2444no—
424C4#1684041114yes—
425C2—24no—
426C2#2144915011yescharacteristic
427C2C2×#1683990111yescharacteristic
428C2#2145507911yescharacteristic
429C2#2145582311yescharacteristic
430C2#2145594511yescharacteristic
431C2#2145696011yescharacteristic
432C2#2145702111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#533C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenterC2×#533D61
hypocenterC61#24063
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #21447149C2semidirect
4. #21447062C2semidirect
6. #21446087C2semidirect
251. C61#24063semidirect

Maximal subgroups

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

subgroupindex
C2×#168400902
C2×#168396602
#214471492
#214470622
#214461272
#214460872
#214458872
C2×C61×#5332
#2406361