Finite Group Databasebeta

← #29599170

Subgroups — #29599170

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×#16839999C211yesmaximal, characteristic
2C2×#16839564C211yesmaximal, characteristic, complemented
3C2×#16839562C211yesmaximal, characteristic, complemented
4C2×#16839541C211yesmaximal, characteristic, complemented
5#21445845C211yesmaximal, characteristic, complemented
6#21443910C211yesmaximal, characteristic, complemented
7C2×C61×#366C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×C8×D61C2211yescharacteristic
10C2×#14519752—21no—
11C22×#11758185C2211yescharacteristic
12#16839999—22no—
13#16839999—22no—
14C2×#14519711C2211yescharacteristic
15C2×#14519697—21no—
16#16839619—21no—
17#16839564—22no—
18#16839562—22no—
19#16839541—22no—
20#16839524—21no—
21C22×C16×C61C2211yescharacteristic
22C2×#107×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#366—22no—
25C22×D244—21no—
26C22×D244—41no—
27C22×C4×D61D411yescharacteristic
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488D412yes—
34C22×#92418D411yescharacteristic
35C2×C8×D61—21no—
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C2×C8×D61—21no—
39C2×C8×D61—21no—
40C2×C8×D61—21no—
41#14519752—24no—
42#14519752—42no—
43C2×C4⋊Dic61—21no—
44C2×#11758198—41no—
45C2×#11758198—41no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49#14519711—21no—
50#14519711—21no—
51#14519697—24no—
52#14519684—41no—
53C22×C8×C61C2311yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C2×C16×C61D412yescomplemented
59#107×C61—21no—
60#107×C61—21no—
61#107×C61—21no—
62#107×C61D412yes—
63C23×D61—41no—
64C23×D61D811yescharacteristic
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—41no—
69C22×Dic61D811yescharacteristic
70C2×D244—22no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—44no—
76C2×D244—41no—
77C2×D244—82no—
78C2×D244—82no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C8×C61C2×D411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61#4111yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C4⋊C4×C61—22no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95#11758198—44no—
96#11758198—82no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418—21no—
102D488—22no—
103D488—22no—
104D488—41no—
105D488—41no—
106C8×D61—41no—
107C8×D61—41no—
108C8×D61—41no—
109C8×D61—41no—
110C16×C61—22no—
111#11758185—41no—
112C23×C61C2×D811yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61D1612yes—
127C2×C4×C61—42no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145D244—42no—
146D244—42no—
147D244—88no—
148D244—81no—
149D244—81no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—41no—
154C8×C61#12111yescharacteristic
155C8×C61#12111yescharacteristic
156C8×C61#12311yescharacteristic
157C8×C61#12411yescharacteristic
158#92418—41no—
159#13380—611nomaximal, Sylow
160C22×C61#44711yescharacteristic
161C22×C61#46611yescharacteristic
162C22×C61#48011yescharacteristic
163C22×C61C2×D1611yescharacteristic
164C22×C61#50811yescharacteristic
165C22×C61#50911yescharacteristic
166C22×C61#51011yescharacteristic
167C2×D61—22no—
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—82no—
175C2×D61—82no—
176C2×D61—82no—
177C2×D61—161no—
178C2×D61—161no—
179C2×D61—161no—
180C2×D61—161no—
181C4×C61—82no—
182C4×C61—161no—
183C4×C61#39411yescharacteristic
184C4×C61#45211yescharacteristic
185C4×C61#46811yescharacteristic
186C4×C61#48211yescharacteristic
187Dic61—41no—
188Dic61—161no—
189C2×#466—611no—
190C2×#366D6111yescharacteristic, complemented
191C2×#357—611no—
192C2×#357—611no—
193C2×C22⋊C16—611no—
194#1808—611no—
195#1380—611no—
196C2×C61#203311yescharacteristic
197C2×C61#218411yescharacteristic
198C2×C61#218911yescharacteristic
199C2×C61#221511yescharacteristic
200C2×C61#222011yescharacteristic
201C2×C61#223211yescharacteristic
202C2×C61#223411yescharacteristic
203D61—42no—
204D61—162no—
205C22×D8—611no—
206C23×C8—611no—
207C2×#121—1221no—
208C22×C16—611no—
209C22×C16C2×D6111yescharacteristic
210#466—1222no—
211#466—1222no—
212C2×#107—611no—
213C2×#107C2×D6111yescharacteristic
214C2×#107C2×D6111yescharacteristic
215C2×#102—1221no—
216#380—1221no—
217#366—22no—
218#357—1222no—
219#357—1222no—
220C22⋊C16—1222no—
221#340—1221no—
222C61#1338011yescharacteristic, complemented, Sylow
223C22×D4—1221no—
224C22×D4—2441no—
225C23×C4—611no—
226C2×D8—612no—
227C2×D8—1221no—
228C2×D8—1221no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8—1221no—
232C22×C8—611no—
233C22×C8—1221no—
234C22×C8—1221no—
235C22×C8—1221no—
236C22×C8—1221no—
237C22×C8—1221no—
238C22×C8—1221no—
239C22×C8C22×D6111yescharacteristic
240#121—1224no—
241#121—2442no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—2441no—
246C2×C22⋊C4—2441no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—1221no—
250C2×C16—1221no—
251C2×C16—1221no—
252C2×C16D24412yescomplemented
253#107—21no—
254#107—21no—
255#107—21no—
256#107—1221no—
257#107—1221no—
258#107C22⋊D6112yes—
259#102—1224no—
260#95—2441no—
261C24—611no—
262C24—2441no—
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—41no—
273C22×C4—41no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—2441no—
282C22×C4D4×D6111yescharacteristic
283D8—1222no—
284D8—1222no—
285D8—2441no—
286D8—2441no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C2×C8C2×D24411yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8D4×D6111yescharacteristic
297C2×C8#1175822611yescharacteristic
298C2×C8#1175822611yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—4882no—
307C22⋊C4—2444no—
308C16—22no—
309C16—2441no—
310C23—612no—
311C23—1221no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—4881no—
318C23—4881no—
319C23—4881no—
320C23—4881no—
321C23—4881no—
322C23—4881no—
323C23—2442no—
324C23D8×D6111yescharacteristic
325D4—4888no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2442no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4#1451974511yescharacteristic
347C2×C4#1451975211yescharacteristic
348C2×C4#1451976211yescharacteristic
349C2×C4#1451980011yescharacteristic
350C2×C4#1451980111yescharacteristic
351C2×C4#1451980911yescharacteristic
352C8—2441no—
353C8#1451975111yescharacteristic
354C8#1451975211yescharacteristic
355C8#1451976211yescharacteristic
356C8#1451976611yescharacteristic
357C22—1222no—
358C22—1222no—
359C22—1222no—
360C22—9761no—
361C22—9761no—
362C22—9761no—
363C22—9761no—
364C22—4882no—
365C22—4882no—
366C22—4882no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22#1683989411yescharacteristic
372C22#1683999911yescharacteristic
373C22#1684007711yescharacteristic
374C22D16×D6111yescharacteristic
375C22#1684019511yescharacteristic
376C22#1684019611yescharacteristic
377C22#1684020411yescharacteristic
378C4—82no—
379C4—161no—
380C4—9761no—
381C4—2441no—
382C4#1683967911yescharacteristic
383C4#1683992311yescharacteristic
384C4#1684000911yescharacteristic
385C4#1684008911yescharacteristic
386C2—9762no—
387C2—2442no—
388C2#2144700311yescharacteristic
389C2#2144772911yescharacteristic
390C2#2144775811yescharacteristic
391C2#2144790611yescharacteristic
392C2#2144793311yescharacteristic
393C2#2144800111yescharacteristic
394C2#2144801311yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#366C2
socleC23×C61C2×D8
prime radicalC2×#16839999C2
hypercenterC2×#366D61
hypocenterC61#13380
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
2. C2×#16839564C2semidirect
3. C2×#16839562C2semidirect
4. C2×#16839541C2semidirect
5. #21445845C2semidirect
6. #21443910C2semidirect
7. C2×C61×#366C2semidirect
58. C2×C16×C61D4semidirect
190. C2×#366D61semidirect
222. C61#13380semidirect
252. C2×C16D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399992
C2×#168395642
C2×#168395622
C2×#168395412
#214458452
#214439102
C2×C61×#3662
#1338061