Finite Group Databasebeta

← #29599168

Subgroups — #29599168

Order 15616.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839998C211yesmaximal, characteristic
2C2×#16839587C211yesmaximal, characteristic, complemented
3C2×#16839562C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5C2×C22⋊#11758185C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C61×#1808C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C2×#14519751—21no—
10C22×#11758185C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839998—22no—
13#16839998—22no—
14C2×#14519711C2211yescharacteristic
15C2×#14519699—21no—
16#16839587—22no—
17#16839562—22no—
18#16839562—22no—
19C22⋊#11758185—22no—
20C23×C8×C61C2211yescharacteristic
21C2×#107×C61C2211yescharacteristic
22C2×#107×C61C2211yescharacteristic
23C61×#380—21no—
24C61×#340—21no—
25C22×D244—21no—
26C22×C22⋊D61—41no—
27C2×D488—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488D412yes—
33#14519751—24no—
34#14519751—42no—
35C2×C4⋊Dic61—21no—
36C2×#11758198—41no—
37C2×#11758185—21no—
38C2×#11758185—21no—
39C2×#11758185—21no—
40C2×#11758185—21no—
41C2×#11758185—21no—
42C2×#11758185D412yescomplemented
43#14519711—21no—
44#14519711D412yes—
45#14519699—24no—
46C23×C4×C61D411yescharacteristic
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C22×C8×C61—21no—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C22⋊C4×C61—41no—
58#107×C61—21no—
59#107×C61—21no—
60#107×C61—21no—
61#107×C61—21no—
62#95×C61—41no—
63C24×C61D811yescharacteristic
64C23×D61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61D811yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—44no—
76C2×C22⋊D61—82no—
77C2×C22⋊D61—82no—
78C22×Dic61—41no—
79C2×D244—22no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61C2×D411yescharacteristic
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—82no—
103#11758198—44no—
104C4⋊Dic61—22no—
105C4⋊Dic61—41no—
106D488—22no—
107D488—22no—
108D488—41no—
109D488—41no—
110#11758185—22no—
111#11758185—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61D1612yes—
119C23×C61C2×D811yescharacteristic
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C22⋊D61—88no—
147C2×Dic61—42no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150D244—42no—
151D244—42no—
152D244—81no—
153D244—81no—
154C8×C61—41no—
155C8×C61#12111yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12311yescharacteristic
158C8×C61#12411yescharacteristic
159#13380—611nomaximal, Sylow
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61#44711yescharacteristic
168C22×C61#46611yescharacteristic
169C22×C61#48011yescharacteristic
170C22×C61C2×D1611yescharacteristic
171C22×C61#50811yescharacteristic
172C22×C61#50911yescharacteristic
173C22×C61#51011yescharacteristic
174C2×D61—82no—
175C2×D61—82no—
176C2×D61—82no—
177C2×D61—161no—
178C2×D61—161no—
179C2×D61—161no—
180C2×D61—161no—
181C4×C61—41no—
182C4×C61—161no—
183C4×C61—161no—
184C4×C61#39411yescharacteristic
185C4×C61#45211yescharacteristic
186C4×C61#46811yescharacteristic
187C4×C61#48211yescharacteristic
188Dic61—82no—
189C2×#466—611no—
190C2×#366—611no—
191C2×#357—611no—
192C2×#357—611no—
193C2×C22⋊C16—611no—
194#1808D6111yescharacteristic, complemented
195#1380—611no—
196C2×C61—42no—
197C2×C61#203311yescharacteristic
198C2×C61#218411yescharacteristic
199C2×C61#218911yescharacteristic
200C2×C61#221511yescharacteristic
201C2×C61#222011yescharacteristic
202C2×C61#223211yescharacteristic
203C2×C61#223411yescharacteristic
204D61—162no—
205C22×D8—611no—
206C23×C8C2×D6111yescharacteristic
207C2×#121—1221no—
208C22×C16—611no—
209C22×C16—611no—
210#466—1222no—
211#466—1222no—
212C2×#107—611no—
213C2×#107C2×D6111yescharacteristic
214C2×#107C2×D6111yescharacteristic
215C2×#102—1221no—
216#380—21no—
217#366—1222no—
218#357—1222no—
219#357—1222no—
220C22⋊C16—1222no—
221#340—21no—
222C61#1338011yescharacteristic, complemented, Sylow
223C22×D4—1221no—
224C22×D4—2441no—
225C23×C4C22⋊D6111yescharacteristic
226C2×D8—612no—
227C2×D8—1221no—
228C2×D8—1221no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8—1221no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8C22⋊D6111yescharacteristic
239C22×C8C22×D6111yescharacteristic
240#121—1224no—
241#121—2442no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—2441no—
247C2×C16—612no—
248C2×C16—1221no—
249C2×C16—1221no—
250C2×C16—1221no—
251C2×C16—1221no—
252C2×C16—1221no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—612no—
258#107—1221no—
259#102—1224no—
260#95—41no—
261C24—2441no—
262C24#1175819911yescharacteristic
263C2×D4—1222no—
264C2×D4—4882no—
265C2×D4—4882no—
266C2×D4—2444no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—2441no—
281C22×C4#1175819911yescharacteristic
282C22×C4C2×C22⋊D6111yescharacteristic
283D8—1222no—
284D8—1222no—
285D8—2441no—
286D8—2441no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8#1175822211yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8D4×D6111yescharacteristic
297C2×C8D4×D6111yescharacteristic
298C2×C8D4×D6111yescharacteristic
299C2×C8#1175822411yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—1222no—
305C4⋊C4—2441no—
306C22⋊C4—82no—
307C22⋊C4—2444no—
308C16—1222no—
309C16—2441no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—4881no—
317C23—4881no—
318C23—4881no—
319C23—4881no—
320C23—4881no—
321C23—4881no—
322C23—2442no—
323C23#1451971812yes—
324C23C2×#1175819911yescharacteristic
325D4—4888no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2442no—
346C2×C4#1451974511yescharacteristic
347C2×C4#1451974911yescharacteristic
348C2×C4#1451976011yescharacteristic
349C2×C4#1451979711yescharacteristic
350C2×C4#1451980211yescharacteristic
351C2×C4#1451980811yescharacteristic
352C8—41no—
353C8#1451975011yescharacteristic
354C8#1451975011yescharacteristic
355C8#1451975911yescharacteristic
356C8#1451976311yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—9761no—
365C22—9761no—
366C22—9761no—
367C22—9761no—
368C22—4882no—
369C22—4882no—
370C22—4882no—
371C22#1683989511yescharacteristic
372C22#1683999611yescharacteristic
373C22#1684007511yescharacteristic
374C22C2×#1451971811yescharacteristic
375C22#1684019211yescharacteristic
376C22#1684019711yescharacteristic
377C22#1684020311yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—4882no—
382C4#1683967711yescharacteristic
383C4#1683992211yescharacteristic
384C4#1684001011yescharacteristic
385C4#1684008611yescharacteristic
386C2—42no—
387C2—9762no—
388C2#2144700111yescharacteristic
389C2#2144773011yescharacteristic
390C2#2144775711yescharacteristic
391C2#2144790311yescharacteristic
392C2#2144793411yescharacteristic
393C2#2144799911yescharacteristic
394C2#2144801011yescharacteristic
subgroupG/H
centerC23C2×#11758199
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1808C2
socleC23×C61C2×D8
prime radicalC2×#16839998C2
hypercenter#1808D61
hypocenterC61#13380
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#16839587C2semidirect
3. C2×#16839562C2semidirect
4. C2×#16839562C2semidirect
5. C2×C22⋊#11758185C2semidirect
6. #21443910C2semidirect
7. C61×#1808C2semidirect
42. C2×#11758185D4semidirect
194. #1808D61semidirect
222. C61#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#168399982
C2×#168395872
C2×#168395622
C2×C22⋊#117581852
#214439102
C61×#18082
#1338061