Finite Group Databasebeta

← #29599355

Subgroups — #29599355

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840137C211yesmaximal, characteristic
2C2×#16839564C211yesmaximal, characteristic, complemented
3C2×#16839563C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic, complemented
5#21446550C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C2×C61×#357C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9C22×#11758199—21no—
10C2×#14519773—21no—
11C22×#11758185C2211yescharacteristic
12#16840137—22no—
13#16840137—22no—
14C2×#14519711C2211yescharacteristic
15C2×C8×Dic61C2211yescharacteristic
16#16839658—21no—
17#16839564—22no—
18#16839563—22no—
19#16839562—22no—
20#16839524—21no—
21C22×D8×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#357—22no—
25C22×D244—21no—
26C22×C22⋊D61—41no—
27C22×C22⋊D61—41no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488D412yes—
34C2×#11758199—24no—
35C2×#11758199—42no—
36C2×#11758199—42no—
37C22×#92418D411yescharacteristic
38#14519773—24no—
39#14519773—42no—
40C2×C4⋊Dic61—21no—
41C2×#11758196—41no—
42C2×C4×Dic61D411yescharacteristic
43C2×#11758185—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46#14519711—21no—
47#14519711D412yescomplemented
48C8×Dic61—21no—
49C8×Dic61—21no—
50#14519684—41no—
51C22×D4×C61—21no—
52C2×D8×C61—21no—
53C2×D8×C61—21no—
54C2×D8×C61—21no—
55C2×D8×C61—21no—
56C2×D8×C61—21no—
57C2×D8×C61D412yes—
58C22×C8×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63#107×C61—21no—
64#107×C61—21no—
65C24×C61—41no—
66C23×D61—41no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C2×C22⋊D61—44no—
76C2×C22⋊D61—44no—
77C2×C22⋊D61—82no—
78C2×C22⋊D61—82no—
79C2×C22⋊D61—82no—
80C2×C22⋊D61—82no—
81C22×Dic61—41no—
82C22×Dic61D811yescharacteristic
83C22×Dic61D811yescharacteristic
84C2×D244—22no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90D8×C61—22no—
91D8×C61—22no—
92D8×C61—41no—
93D8×C61—41no—
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102#11758199—48no—
103C4⋊Dic61—22no—
104C4⋊Dic61—41no—
105#11758196—82no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418SD1612yes—
111D488—22no—
112D488—22no—
113D488—41no—
114D488—41no—
115C16×C61—41no—
116#11758185—41no—
117C23×C61—42no—
118C23×C61—81no—
119C23×C61—81no—
120C23×C61—81no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61—81no—
124C23×C61C2×D811yescharacteristic
125C22×D61—42no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—81no—
135D4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12411yescharacteristic
142C2×C4×C61C2×SD1611yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C22⋊D61—88no—
146C22⋊D61—88no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61D1612yes—
155C2×Dic61SD3212yes—
156D244—42no—
157D244—42no—
158D244—81no—
159D244—81no—
160C8×C61#12111yescharacteristic
161C8×C61#12111yescharacteristic
162C8×C61#12311yescharacteristic
163C8×C61#12311yescharacteristic
164#92418—22no—
165#13407—611nomaximal, Sylow
166C22×C61—82no—
167C22×C61—82no—
168C22×C61—82no—
169C22×C61—161no—
170C22×C61—161no—
171C22×C61—161no—
172C22×C61—161no—
173C22×C61#44711yescharacteristic
174C22×C61#45911yescharacteristic
175C22×C61#48611yescharacteristic
176C22×C61C2×D1611yescharacteristic
177C22×C61C2×SD3211yescharacteristic
178C22×C61#50911yescharacteristic
179C22×C61#50911yescharacteristic
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—82no—
183C2×D61—161no—
184C2×D61—161no—
185C2×D61—161no—
186C2×D61—161no—
187C4×C61—161no—
188C4×C61#39411yescharacteristic
189C4×C61#45011yescharacteristic
190C4×C61#46011yescharacteristic
191C4×C61#49011yescharacteristic
192Dic61—22no—
193Dic61—22no—
194Dic61—82no—
195C2×#493—611no—
196C2×#357—611no—
197C2×#357—611no—
198C2×#357—611no—
199C2×#357D6111yescharacteristic, complemented
200#1942—611no—
201#1374—611no—
202C2×C61—162no—
203C2×C61#204111yescharacteristic
204C2×C61#218411yescharacteristic
205C2×C61#218711yescharacteristic
206C2×C61#220611yescharacteristic
207C2×C61#220711yescharacteristic
208C2×C61#224011yescharacteristic
209C2×C61#224411yescharacteristic
210D61—162no—
211C22×D8—611no—
212C22×D8—1221no—
213C22×D8C2×D6111yescharacteristic
214C2×#127—1221no—
215C22×C16—611no—
216C22×C16C2×D6111yescharacteristic
217#493—1222no—
218#493—1222no—
219C2×#107—611no—
220C2×#107C2×D6111yescharacteristic
221C2×C4×C8—611no—
222#389—1221no—
223#357—22no—
224#357—1222no—
225#357—1222no—
226#357—1222no—
227#340—1221no—
228C61#1340711yescharacteristic, complemented, Sylow
229C22×D4—21no—
230C22×D4—1221no—
231C22×D4—2441no—
232C22×D4—2441no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—612no—
239C2×D8—1224no—
240C2×D8—1221no—
241C2×D8—1221no—
242C2×D8—1221no—
243C2×D8—1221no—
244C2×D8—1221no—
245C2×D8—2442no—
246C2×D8—2442no—
247C2×D8C22⋊D6112yes—
248C22×C8—611no—
249C22×C8C22×D6111yescharacteristic
250#127—1224no—
251#127—2442no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C42—611no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16—1221no—
260C2×C16—1221no—
261C2×C16—1221no—
262#107—21no—
263#107—21no—
264#107—612no—
265#107—1221no—
266C4×C8—1221no—
267C4×C8—1221no—
268#95—2441no—
269C24—41no—
270C24—2441no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—1222no—
278C2×D4—4882no—
279C2×D4—4882no—
280C2×D4—4882no—
281C2×D4—4882no—
282C2×D4—2444no—
283C2×D4—2444no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—2441no—
293C22×C4D4×D6111yescharacteristic
294D8—22no—
295D8—22no—
296D8—41no—
297D8—41no—
298D8—1222no—
299D8—1222no—
300D8—2448no—
301D8—2441no—
302D8—2441no—
303C2×C8—612no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8#1175822211yescharacteristic
307C2×C8#1175822211yescharacteristic
308C2×C8D4×D6111yescharacteristic
309C2×C8D4×D6111yescharacteristic
310C2×C8#1175822411yescharacteristic
311C2×C8C2×C22⋊D6111yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—1222no—
315C4⋊C4—4882no—
316C4⋊C4—2441no—
317C42—1221no—
318C42—1221no—
319C16—41no—
320C16—2441no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—4881no—
333C23—4881no—
334C23—2442no—
335C23D8×D6111yescharacteristic
336D4—42no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—4888no—
341D4—4888no—
342D4—4881no—
343D4—4881no—
344D4—2442no—
345D4—2442no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—612no—
350C2×C4—612no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—2442no—
358C2×C4#1451974511yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4#1451976311yescharacteristic
361C2×C4SD16×D6111yescharacteristic
362C2×C4#1451980111yescharacteristic
363C2×C4#1451980411yescharacteristic
364C8—1222no—
365C8#1451974911yescharacteristic
366C8#1451975011yescharacteristic
367C8#1451975911yescharacteristic
368C8#1451976011yescharacteristic
369C22—82no—
370C22—82no—
371C22—82no—
372C22—161no—
373C22—161no—
374C22—161no—
375C22—161no—
376C22—9761no—
377C22—9761no—
378C22—9761no—
379C22—9761no—
380C22—4882no—
381C22—4882no—
382C22—4882no—
383C22#1683989411yescharacteristic
384C22#1683995611yescharacteristic
385C22#1684010711yescharacteristic
386C22D16×D6111yescharacteristic
387C22SD32×D6111yescharacteristic
388C22#1684019611yescharacteristic
389C22#1684019911yescharacteristic
390C4—161no—
391C4—1222no—
392C4—1222no—
393C4—4882no—
394C4#1683967711yescharacteristic
395C4#1683991111yescharacteristic
396C4#1683996111yescharacteristic
397C4#1684012511yescharacteristic
398C2—162no—
399C2—9762no—
400C2#2144705111yescharacteristic
401C2#2144772911yescharacteristic
402C2#2144774611yescharacteristic
403C2#2144785311yescharacteristic
404C2#2144785811yescharacteristic
405C2#2144804111yescharacteristic
406C2#2144805911yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC2×#16840137C2
hypercenterC2×#357D61
hypocenterC61#13407
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#16839564C2semidirect
3. C2×#16839563C2semidirect
4. C2×#16839562C2semidirect
5. #21446550C2semidirect
6. #21443896C2semidirect
7. C2×C61×#357C2semidirect
47. #14519711D4semidirect
199. C2×#357D61semidirect
228. C61#13407semidirect

Maximal subgroups

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

subgroupindex
C2×#168401372
C2×#168395642
C2×#168395632
C2×#168395622
#214465502
#214438962
C2×C61×#3572
#1340761