Finite Group Databasebeta

← #29597407

Subgroups — #29597407

Order 15616.

484 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic
2C2×#16840000C211yesmaximal, characteristic
3C2×#16839578C211yesmaximal, characteristic, complemented
4#21445854C211yesmaximal, characteristic
5#21443929C211yesmaximal, characteristic, complemented
6#21443928C211yesmaximal, characteristic, complemented
7C2×C61×#362C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9C2×#14519753—21no—
10C2×#14519717C2211yescharacteristic
11C2×#14519716—21no—
12M32×D61—22no—
13M32×D61—22no—
14C2×C16×D61—21no—
15#16840000—21no—
16#16840000—21no—
17#16840000C412yes—
18#16840000C412yes—
19C2×#14519713C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519701—21no—
22#16839725—21no—
23#16839578—22no—
24#16839526—21no—
25C22×Q16×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#362—22no—
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C22×#92418D411yescharacteristic
32C2×C8×D61—21no—
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35C2×C8×D61—21no—
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61D411yescharacteristic
39C2×C8×D61D411yescharacteristic
40#14519753—22no—
41#14519753—22no—
42#14519753—41no—
43#14519753—41no—
44C2×C4⋊Dic61—21no—
45C2×#11758196—41no—
46C2×#11758198—41no—
47#14519717—21no—
48#14519717D412yes—
49#14519716—24no—
50C2×#11758185—21no—
51C16×D61—24no—
52#14519713—21no—
53#14519713—21no—
54#14519711—21no—
55#14519711C2×C412yes—
56#14519701—22no—
57#14519701—22no—
58#14519689—41no—
59#14519689—41no—
60C22×Q8×C61—21no—
61C2×Q16×C61—21no—
62C2×Q16×C61—21no—
63C2×Q16×C61—21no—
64C2×Q16×C61—21no—
65C2×Q16×C61—21no—
66C2×Q16×C61C2×C412yes—
67C2×M16×C61—21no—
68C22×C8×C61C2311yescharacteristic
69M32×C61—21no—
70M32×C61D412yes—
71C2×C16×C61—21no—
72#108×C61—21no—
73#108×C61—21no—
74C23×D61SD1611yescharacteristic
75C2×Q8×C61—22no—
76C2×Q8×C61—41no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—41no—
84C22×Dic61SD1611yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61C22⋊C411yescharacteristic
90C2×C4×D61C22⋊C411yescharacteristic
91C2×C4×D61D811yescharacteristic
92C2×C4×D61D811yescharacteristic
93Q16×C61—22no—
94Q16×C61—22no—
95Q16×C61—41no—
96Q16×C61—41no—
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61#4111yescharacteristic
106#11758198—42no—
107#11758198—42no—
108C4⋊Dic61—22no—
109C4⋊Dic61—41no—
110#11758196—42no—
111#11758196—42no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—41no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119C8×D61—21no—
120C8×D61—21no—
121C8×D61—21no—
122C8×D61—21no—
123C8×D61—21no—
124C8×D61—21no—
125C8×D61—21no—
126C8×D61—21no—
127C16×C61—22no—
128#11758185—22no—
129C23×C61C2×SD1611yescharacteristic
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—22no—
133C22×D61—41no—
134C22×D61#10211yescharacteristic
135C22×D61#10211yescharacteristic
136Q8×C61—42no—
137Q8×C61—42no—
138Q8×C61—81no—
139Q8×C61—81no—
140C2×C4×C61—42no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—82no—
153C2×Dic61#10211yescharacteristic
154C2×Dic61#10211yescharacteristic
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—21no—
163C8×C61—81no—
164C8×C61C4×D411yescharacteristic
165C8×C61C4×D411yescharacteristic
166C8×C61#12011yescharacteristic
167C8×C61#12311yescharacteristic
168#92418—21no—
169#92418—21no—
170#92418—81no—
171#13066—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61C2×#10211yescharacteristic
175C22×C61#46511yescharacteristic
176C22×C61#46511yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61#36212yescomplemented
185C4×C61—82no—
186C4×C61#38611yescharacteristic
187C4×C61#41611yescharacteristic
188C4×C61#46611yescharacteristic
189C4×C61#46611yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—82no—
193C22×M32—611no—
194C2×#467—611no—
195C2×#362—611no—
196C2×#362D6111yescharacteristic, complemented
197#1810—611no—
198#1387—611no—
199#1387—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#189311yescharacteristic
203C2×C61C2×#36211yescharacteristic
204C2×C61#214811yescharacteristic
205D61—22no—
206D61—41no—
207C22×Q16C2×D6111yescharacteristic
208C23×C8—611no—
209C2×C22⋊Q8—1221no—
210C2×M32—611no—
211C2×M32—1221no—
212C2×M32—1222no—
213C2×M32—1222no—
214C2×M32C2×D6111yescharacteristic
215C22×C16—1221no—
216#467—612no—
217#467—612no—
218#467—1221no—
219#467—1221no—
220C2×#108—611no—
221C2×#108C2×D6111yescharacteristic
222C2×#107—611no—
223C2×#103—1221no—
224#407—1221no—
225#362—22no—
226#362—1222no—
227#341—1221no—
228C61#1306611yescharacteristic, complemented, Sylow
229C22×Q8—21no—
230C23×C4—611no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16C4×D6112yes—
237C2×M16—21no—
238C2×M16—1221no—
239C22×C8—611no—
240C22×C8—611no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—611no—
244C22×C8—1221no—
245C22×C8—1221no—
246C22×C8—1221no—
247C22×C8—1221no—
248C22×C8C22×D6111yescharacteristic
249C22⋊Q8—1222no—
250C22⋊Q8—1222no—
251C22⋊Q8—2441no—
252C22⋊Q8—2441no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C22⋊C4—2441no—
256M32—21no—
257M32—612no—
258M32—1224no—
259M32—1221no—
260M32C22⋊D6112yes—
261C2×C16—21no—
262C2×C16—1224no—
263C2×C16—1221no—
264#108—21no—
265#108—21no—
266#108—1221no—
267#108—1221no—
268#107—612no—
269#107—1221no—
270#103—1222no—
271#103—1222no—
272C22⋊C8—2441no—
273C22⋊C8—2441no—
274C24—611no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C22×C4—41no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—2441no—
292C22×C4D4×D6111yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—41no—
296Q16—41no—
297M16—41no—
298M16—41no—
299M16—2441no—
300M16—2441no—
301C2×C8—41no—
302C2×C8—611no—
303C2×C8—611no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—2441no—
315C2×C8C2×C4×D6111yescharacteristic
316C2×C8#1175822211yescharacteristic
317C2×C8D4×D6111yescharacteristic
318C2×C8D4×D6111yescharacteristic
319C2×C8#1175822411yescharacteristic
320C2×C8C2×C22⋊D6111yescharacteristic
321C4⋊C4—1222no—
322C4⋊C4—2442no—
323C4⋊C4—2442no—
324C4⋊C4—2441no—
325C22⋊C4—2442no—
326C22⋊C4—2442no—
327C16—22no—
328C16—1222no—
329C23—611no—
330C23—611no—
331C23—1222no—
332C23—1221no—
333C23—1221no—
334C23—2441no—
335C23SD16×D6111yescharacteristic
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4882no—
356C2×C4—2442no—
357C2×C4C22⋊C4×D6111yescharacteristic
358C2×C4#1451974811yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4D8×D6111yescharacteristic
361C2×C4#1451979611yescharacteristic
362C2×C4#1451979811yescharacteristic
363C8—81no—
364C8—1221no—
365C8—1221no—
366C8—4881no—
367C8#1451973711yescharacteristic
368C8C4×C22⋊D6111yescharacteristic
369C8#1451974511yescharacteristic
370C8#1451975911yescharacteristic
371C22—21no—
372C22—21no—
373C22—612no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—2442no—
380C22—2442no—
381C22#102×D6111yescharacteristic
382C22#1683998811yescharacteristic
383C22#1683999011yescharacteristic
384C4—82no—
385C4—1221no—
386C4—1221no—
387C4—4882no—
388C4#1683963811yescharacteristic
389C4#1683975511yescharacteristic
390C4#1683999511yescharacteristic
391C4#1683999711yescharacteristic
392C2—21no—
393C2—21no—
394C2—1222no—
395C2—2441no—
396C2#2144624411yescharacteristic
397C2#362×D6111yescharacteristic
398C2#2144756711yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#362C2
socleC22×C61C2×#102
prime radicalC23×D61SD16
cosocleC22×C8×C61C23
hypercenterC2×#362D61
hypocenterC61#13066
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. C2×#16839578C2semidirect
5. #21443929C2semidirect
6. #21443928C2semidirect
7. C2×C61×#362C2semidirect
184. C2×D61#362semidirect
196. C2×#362D61semidirect
228. C61#13066semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
C2×#168400002
C2×#168395782
#214458542
#214439292
#214439282
C2×C61×#3622
#1306661