Finite Group Databasebeta

← #29595657

Subgroups — #29595657

Order 15616.

934 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D61C211yesmaximal, characteristic
2C2×#16839567C211yesmaximal, characteristic, complemented
3C2×#16839566C211yesmaximal, characteristic, complemented
4C2×#16839565C211yesmaximal, characteristic, complemented
5C2×#16839541C211yesmaximal, characteristic
6#21445845C211yesmaximal, characteristic
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×Q8×D61—21no—
9C22×Dic244C2211yescharacteristic
10C22×#11758202—21no—
11C2×Q16×D61—22no—
12C2×Q16×D61—22no—
13C2×Q16×D61—22no—
14C2×Q16×D61—22no—
15C2×Q16×D61—22no—
16C2×Q16×D61C414yescomplemented
17C22×C8×D61C2211yescharacteristic
18C22×#11758185C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20#16839619—21no—
21#16839567—22no—
22#16839566—22no—
23#16839565—22no—
24#16839541—22no—
25#16839524—21no—
26C22×Q16×C61C2211yescharacteristic
27C22×C16×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C61×#358—22no—
30C22×Dic122—21no—
31C22×Dic122—41no—
32C2×Q8×D61—24no—
33C2×Q8×D61—24no—
34C2×Q8×D61—24no—
35C2×Q8×D61—42no—
36C2×Q8×D61—42no—
37C2×Q8×D61—42no—
38C22×C4×D61—41no—
39C22×C4×D61D411yescharacteristic
40C2×Dic244—21no—
41C2×Dic244—21no—
42C2×Dic244—21no—
43C2×Dic244C2×C412yes—
44C2×Dic244D412yes—
45C2×Dic244D412yes—
46C2×#11758202—24no—
47C2×#11758202—24no—
48C2×#11758202—24no—
49Q16×D61—28no—
50Q16×D61—28no—
51Q16×D61—28no—
52Q16×D61—28no—
53C22×#92418D411yescharacteristic
54C2×C8×D61—21no—
55C2×C8×D61—21no—
56C2×C8×D61—21no—
57C2×C8×D61—21no—
58C2×C8×D61C2×C412yes—
59C2×C8×D61D412yes—
60C2×C4⋊Dic61—21no—
61C2×#11758198—41no—
62C2×#11758185—21no—
63C2×#11758185—21no—
64C2×#11758185—21no—
65#14519711—21no—
66#14519711—21no—
67#14519684—41no—
68C22×Q8×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×Q16×C61—21no—
72C2×Q16×C61C2×C412yes—
73C2×Q16×C61D412yes—
74C2×Q16×C61D412yes—
75C22×C8×C61C2311yescharacteristic
76C2×C4⋊C4×C61—21no—
77C2×C16×C61—21no—
78C2×C16×C61—21no—
79C2×C16×C61—21no—
80#107×C61—21no—
81#107×C61—21no—
82C23×D61D811yescharacteristic
83C2×Q8×C61—22no—
84C2×Q8×C61—22no—
85C2×Q8×C61—22no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61D811yescharacteristic
95Q8×D61—216no—
96Q8×D61—48no—
97Q8×D61—48no—
98Q8×D61—48no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—44no—
104C2×C4×D61—44no—
105C2×C4×D61—44no—
106C2×C4×D61C22⋊C412yes—
107C2×C4×D61SD1612yes—
108C2×Dic122—22no—
109C2×Dic122—22no—
110C2×Dic122—22no—
111C2×Dic122—44no—
112C2×Dic122—44no—
113C2×Dic122—41no—
114C2×Dic122—41no—
115C2×Dic122—41no—
116C2×Dic122—44no—
117Q16×C61—22no—
118Q16×C61—22no—
119Q16×C61—22no—
120Q16×C61C22⋊C414yescomplemented
121C2×C8×C61C22×C411yescharacteristic
122C2×C8×C61C2×D411yescharacteristic
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129#11758202—216no—
130#11758198—82no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418C22⋊C412yes—
136Dic244—22no—
137Dic244—22no—
138Dic244—22no—
139Dic244C22⋊C414yescomplemented
140C8×D61—22no—
141C8×D61—22no—
142C8×D61—22no—
143C8×D61—22no—
144C16×C61—41no—
145#11758185—41no—
146C23×C61C2×D811yescharacteristic
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61#10212yes—
152C22×D61SD3212yes—
153C22×D61Q3212yes—
154Q8×C61—24no—
155Q8×C61—42no—
156Q8×C61—42no—
157Q8×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61C2×C22⋊C411yescharacteristic
165C2×C4×C61#12011yescharacteristic
166C2×C4×C61#12011yescharacteristic
167C2×C4×C61C2×SD1611yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—81no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C2×Dic61#10212yes—
179C4×D61—22no—
180C4×D61—22no—
181C4×D61—22no—
182C4×D61—22no—
183C4×D61—416no—
184Dic122—24no—
185Dic122—416no—
186Dic122—42no—
187Dic122—42no—
188Dic122—42no—
189C8×C61C2×C22⋊C411yescharacteristic
190C8×C61C2×C22⋊C411yescharacteristic
191C8×C61#12011yescharacteristic
192C8×C61#12011yescharacteristic
193#92418—22no—
194#12732—611nomaximal, Sylow
195C22×C61C2×#10211yescharacteristic
196C22×C61#44711yescharacteristic
197C22×C61#44711yescharacteristic
198C22×C61C2×SD3211yescharacteristic
199C22×C61C2×Q3211yescharacteristic
200C22×C61#51011yescharacteristic
201C22×C61#51011yescharacteristic
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61#35814yescomplemented
209C4×C61—44no—
210C4×C61—161no—
211C4×C61#37911yescharacteristic
212C4×C61#41811yescharacteristic
213C4×C61#45011yescharacteristic
214C4×C61#45011yescharacteristic
215Dic61—22no—
216Dic61—44no—
217Dic61—161no—
218C23×Q16—611no—
219C2×#358—611no—
220C2×#358—611no—
221C2×#358—611no—
222C2×#358D6111yescharacteristic, complemented
223C2×C22⋊C16—611no—
224#1808—611no—
225C2×C61#178611yescharacteristic
226C2×C61C2×#35811yescharacteristic
227C2×C61#214111yescharacteristic
228C2×C61#218511yescharacteristic
229C2×C61#218511yescharacteristic
230C2×C61#218811yescharacteristic
231C2×C61#218811yescharacteristic
232D61—24no—
233C23×Q8—1221no—
234C22×Q16—614no—
235C22×Q16—611no—
236C22×Q16—1222no—
237C22×Q16—1221no—
238C22×Q16—1222no—
239C22×Q16—1222no—
240C22×Q16—1222no—
241C22×Q16—1222no—
242C22×Q16C2×D6111yescharacteristic
243C23×C8—611no—
244C22×C16—611no—
245C22×C16C2×D6111yescharacteristic
246C2×#107—611no—
247C2×#107C2×D6111yescharacteristic
248#380—1221no—
249#358—22no—
250#358—1222no—
251#358—1222no—
252#358—1222no—
253C22⋊C16—1222no—
254#340—1221no—
255C61#1273211yescharacteristic, complemented, Sylow
256C22×Q8—21no—
257C22×Q8—1224no—
258C22×Q8—1224no—
259C22×Q8—1224no—
260C22×Q8—1221no—
261C22×Q8—2441no—
262C22×Q8—2442no—
263C22×Q8—2442no—
264C22×Q8—2442no—
265C23×C4—611no—
266C23×C4—2441no—
267C2×Q16—21no—
268C2×Q16—21no—
269C2×Q16—21no—
270C2×Q16—612no—
271C2×Q16—612no—
272C2×Q16—612no—
273C2×Q16—1224no—
274C2×Q16—1228no—
275C2×Q16—1228no—
276C2×Q16—1228no—
277C2×Q16—1224no—
278C2×Q16—1224no—
279C2×Q16—1228no—
280C2×Q16—1221no—
281C2×Q16—1221no—
282C2×Q16—1221no—
283C2×Q16C4×D6112yes—
284C2×Q16D24412yes—
285C2×Q16C22⋊D6112yes—
286C22×C8—611no—
287C22×C8—612no—
288C22×C8—612no—
289C22×C8—1221no—
290C22×C8—1221no—
291C22×C8—1221no—
292C22×C8—1221no—
293C22×C8C22×D6111yescharacteristic
294C2×C4⋊C4—21no—
295C2×C4⋊C4—1221no—
296C2×C22⋊C4—2441no—
297C2×C16—21no—
298C2×C16—21no—
299C2×C16—21no—
300C2×C16—1221no—
301C2×C16—1221no—
302C2×C16—1221no—
303#107—21no—
304#107—21no—
305#107—1221no—
306#107—1221no—
307#95—2441no—
308C24—611no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—12216no—
316C2×Q8—1222no—
317C2×Q8—1222no—
318C2×Q8—1222no—
319C2×Q8—2444no—
320C2×Q8—2444no—
321C2×Q8—2444no—
322C2×Q8—2448no—
323C2×Q8—2448no—
324C2×Q8—2448no—
325C2×Q8—2441no—
326C2×Q8—2441no—
327C2×Q8—2441no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—611no—
331C22×C4—612no—
332C22×C4—612no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—2444no—
338C22×C4—2444no—
339C22×C4—2444no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4D4×D6111yescharacteristic
343Q16—22no—
344Q16—22no—
345Q16—22no—
346Q16—614no—
347Q16—12216no—
348Q16—1222no—
349Q16—1222no—
350Q16—1222no—
351Q16#1175819814yescomplemented
352C2×C8—612no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1222no—
356C2×C8—1222no—
357C2×C8—1222no—
358C2×C8—1222no—
359C2×C8C2×C4×D6111yescharacteristic
360C2×C8C2×D24411yescharacteristic
361C2×C8D4×D6111yescharacteristic
362C2×C8D4×D6111yescharacteristic
363C2×C8D4×D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C22⋊C4—4882no—
370C16—41no—
371C16—2441no—
372C23—612no—
373C23—612no—
374C23—612no—
375C23—1221no—
376C23—1221no—
377C23—1221no—
378C23—1221no—
379C23D8×D6111yescharacteristic
380Q8—24no—
381Q8—42no—
382Q8—42no—
383Q8—42no—
384Q8—1224no—
385Q8—24416no—
386Q8—2442no—
387Q8—2442no—
388Q8—2442no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—612no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1222no—
399C2×C4—1222no—
400C2×C4—1222no—
401C2×C4—1222no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—24416no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4C22⋊C4×D6111yescharacteristic
410C2×C4#1451974511yescharacteristic
411C2×C4#1451974711yescharacteristic
412C2×C4SD16×D6111yescharacteristic
413C2×C4#1451980111yescharacteristic
414C2×C4#1451980411yescharacteristic
415C8—1222no—
416C8C22⋊C4×D6111yescharacteristic
417C8C2×#1175819811yescharacteristic
418C8#1451974511yescharacteristic
419C8#1451974711yescharacteristic
420C22—614no—
421C22—1222no—
422C22—1222no—
423C22—1222no—
424C22—1222no—
425C22—1222no—
426C22—1222no—
427C22#102×D6111yescharacteristic
428C22#1683989411yescharacteristic
429C22#1683989711yescharacteristic
430C22SD32×D6111yescharacteristic
431C22Q32×D6111yescharacteristic
432C22#1684020111yescharacteristic
433C22#1684020411yescharacteristic
434C4—44no—
435C4—161no—
436C4—1222no—
437C4—9761no—
438C4—2444no—
439C4#1683961711yescharacteristic
440C4#1683976511yescharacteristic
441C4#1683991111yescharacteristic
442C4#1683991411yescharacteristic
443C2—1224no—
444C2#2144574811yescharacteristic
445C2#358×D6111yescharacteristic
446C2#2144753711yescharacteristic
447C2#2144773411yescharacteristic
448C2#2144773711yescharacteristic
449C2#2144775111yescharacteristic
450C2#2144775411yescharacteristic
subgroupG/H
centerC23D8×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenterC2×#358D61
hypocenterC61#12732
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16839567C2semidirect
3. C2×#16839566C2semidirect
4. C2×#16839565C2semidirect
7. C2×C61×#358C2semidirect
16. C2×Q16×D61C4semidirect
120. Q16×C61C22⋊C4semidirect
139. Dic244C22⋊C4semidirect
208. C2×D61#358semidirect
222. C2×#358D61semidirect
255. C61#12732semidirect
351. Q16#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D612
C2×#168395672
C2×#168395662
C2×#168395652
C2×#168395412
#214458452
C2×C61×#3582
#1273261