Finite Group Databasebeta

← #29597409

Subgroups — #29597409

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×#16840004C211yesmaximal, characteristic
3C2×#16839579C211yesmaximal, characteristic, complemented
4C2×#16839577C211yesmaximal, characteristic, complemented
5#21445854C211yesmaximal, characteristic
6#21443927C211yesmaximal, characteristic, complemented
7C61×#1387C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519757—21no—
11C2×#14519717C2211yescharacteristic
12C2×#14519716—21no—
13M32×D61—22no—
14M32×D61—22no—
15C2×C16×D61—21no—
16#16840004—21no—
17#16840004—21no—
18#16840004C412yes—
19#16840004C412yes—
20C2×#14519713C2211yescharacteristic
21C2×#14519700—21no—
22#16839725—21no—
23#16839579—22no—
24#16839577—22no—
25#16839526—21no—
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C22×Dic122—21no—
30C22×C4×D61D411yescharacteristic
31C2×Dic244—21no—
32C2×Dic244—21no—
33C2×Dic244—21no—
34C2×Dic244—21no—
35C2×Dic244—21no—
36C2×Dic244C2×C412yes—
37C2×#11758194—21no—
38C22×#92418D411yescharacteristic
39C2×C8×D61—21no—
40C2×C8×D61—21no—
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C2×C8×D61C2×C411yescharacteristic
44C2×C8×D61C2×C411yescharacteristic
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47#14519757—22no—
48#14519757—22no—
49#14519757—41no—
50#14519757—41no—
51C2×C4⋊Dic61—41no—
52C2×#11758198—41no—
53#14519717—21no—
54#14519717D412yes—
55#14519716—24no—
56C2×#11758185—21no—
57C16×D61—24no—
58#14519713—21no—
59#14519713—21no—
60#14519700—22no—
61#14519700—22no—
62#14519689—41no—
63#14519689—41no—
64C2×M16×C61—21no—
65C22×C8×C61C2311yescharacteristic
66C2×C4⋊C4×C61—21no—
67M32×C61—21no—
68M32×C61D412yes—
69C2×C16×C61—21no—
70#108×C61—21no—
71#108×C61—21no—
72#107×C61—21no—
73#107×C61C2×C412yes—
74C23×D61SD1611yescharacteristic
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—41no—
78C22×Dic61SD1611yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61D811yescharacteristic
86C2×C4×D61D811yescharacteristic
87C2×Dic122—22no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93M16×C61—41no—
94M16×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61C22×C411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104#11758198—42no—
105#11758198—42no—
106C4⋊Dic61—42no—
107C4⋊Dic61—42no—
108#11758194—41no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—41no—
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115Dic244—22no—
116Dic244—22no—
117Dic244—41no—
118Dic244—41no—
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
136C2×C4×C61—42no—
137C2×C4×C61—82no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61C2×D811yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61#10211yescharacteristic
150C2×Dic61#10211yescharacteristic
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159Dic122—42no—
160Dic122—42no—
161Dic122—81no—
162Dic122—81no—
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×#362—611no—
197#1810—611no—
198#1387—611no—
199#1387D6111yescharacteristic, complemented
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#189311yescharacteristic
203C2×C61C2×#36211yescharacteristic
204C2×C61#214811yescharacteristic
205D61—22no—
206D61—41no—
207C22×Q16—611no—
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×#107C2×D6111yescharacteristic
223C2×#103—1221no—
224#407—1221no—
225#362—1222no—
226#362—1222no—
227#341—1221no—
228C61#1306611yescharacteristic, complemented, Sylow
229C22×Q8—1221no—
230C23×C4—611no—
231C2×Q16—612no—
232C2×Q16—1221no—
233C2×Q16—1221no—
234C2×Q16—1221no—
235C2×Q16—1221no—
236C2×Q16—1221no—
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—21no—
254C2×C4⋊C4—2441no—
255C2×C22⋊C4—2441no—
256M32—21no—
257M32—612no—
258M32—1224no—
259M32—1221no—
260M32D24412yes—
261C2×C16—21no—
262C2×C16—1224no—
263C2×C16—1221no—
264#108—21no—
265#108—21no—
266#108—1221no—
267#108—1221no—
268#107—21no—
269#107C4×D6112yes—
270#103—1222no—
271#103—1222no—
272C22⋊C8—2441no—
273C22⋊C8—2441no—
274C24—611no—
275C2×Q8—1222no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
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—1222no—
294Q16—1222no—
295Q16—2441no—
296Q16—2441no—
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×C8C2×D24411yescharacteristic
317C2×C8#1175822211yescharacteristic
318C2×C8D4×D6111yescharacteristic
319C2×C8D4×D6111yescharacteristic
320C2×C8#1175822611yescharacteristic
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—2442no—
324C4⋊C4—2442no—
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—4881no—
337Q8—4881no—
338Q8—2442no—
339Q8—2442no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
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—4881no—
355C2×C4—4881no—
356C2×C4—2442no—
357C2×C4C22⋊C4×D6111yescharacteristic
358C2×C4#1451975011yescharacteristic
359C2×C4#1451975211yescharacteristic
360C2×C4D8×D6111yescharacteristic
361C2×C4#1451979811yescharacteristic
362C2×C4#1451980011yescharacteristic
363C8—81no—
364C8—1221no—
365C8—1221no—
366C8—4881no—
367C8#1451973911yescharacteristic
368C8C4×D24411yescharacteristic
369C8#1451974711yescharacteristic
370C8#1451976211yescharacteristic
371C22—21no—
372C22—21no—
373C22—612no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—2442no—
380C22—2442no—
381C22#102×D6111yescharacteristic
382C22#1683999211yescharacteristic
383C22#1683999411yescharacteristic
384C4—82no—
385C4—1221no—
386C4—1221no—
387C4—4882no—
388C4#1683964011yescharacteristic
389C4#1683975711yescharacteristic
390C4#1683999711yescharacteristic
391C4#1683999911yescharacteristic
392C2—21no—
393C2—21no—
394C2—1222no—
395C2—2441no—
396C2#2144624611yescharacteristic
397C2#362×D6111yescharacteristic
398C2#2144756511yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1387C2
socleC22×C61C2×#102
prime radicalC23×D61SD16
cosocleC22×C8×C61C23
hypercenter#1387D61
hypocenterC61#13066
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
3. C2×#16839579C2semidirect
4. C2×#16839577C2semidirect
6. #21443927C2semidirect
7. C61×#1387C2semidirect
184. C2×D61#362semidirect
199. #1387D61semidirect
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×#168400042
C2×#168395792
C2×#168395772
#214458542
#214439272
C61×#13872
#1306661