Finite Group Databasebeta

← #29596890

Subgroups — #29596890

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839877C211yesmaximal, characteristic
2C2×#16839547C211yesmaximal, characteristic, complemented
3C2×#16839546C211yesmaximal, characteristic, complemented
4#21447432C211yesmaximal, characteristic, complemented
5#21443900C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C2×C61×#504C211yesmaximal, characteristic, complemented
8C2×#14519797C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839877—22no—
13#16839877—22no—
14C2×#14519712C411yescharacteristic
15C2×#14519704C411yescharacteristic
16C2×#14519703C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18#16839547—22no—
19#16839546—22no—
20#16839541—21no—
21#16839541—21no—
22C2×#131×C61C2211yescharacteristic
23C61×#504—22no—
24C61×#504—22no—
25C2×M32×C61—21no—
26C2×M32×C61C2211yescharacteristic
27C22×C16×C61—21no—
28C22×C16×C61C2211yescharacteristic
29C2×#11758222C2×C411yescharacteristic
30#14519797—22no—
31#14519797—22no—
32C2×#11758202C811yescharacteristic
33C2×#11758200C811yescharacteristic
34C2×#11758201C811yescharacteristic
35C2×#11758199C811yescharacteristic
36#14519783—21no—
37#14519783—21no—
38#14519783—21no—
39#14519783—21no—
40C2×#11758194C2×C411yescharacteristic
41C2×#11758189—21no—
42C22×#92418C2×C411yescharacteristic
43C2×C8×D61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45#14519717—21no—
46#14519717—21no—
47C2×#11758185—21no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50C2×#11758185—21no—
51#14519712—22no—
52#14519704—22no—
53#14519703—22no—
54C8×Dic61—21no—
55C8×Dic61—21no—
56C2×#41×C61C2×C411yescharacteristic
57#131×C61—21no—
58#131×C61—21no—
59#131×C61D412yes—
60#131×C61D412yes—
61C2×M16×C61—21no—
62C2×M16×C61C2×C411yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61C2311yescharacteristic
65M32×C61—24no—
66M32×C61—21no—
67M32×C61D412yes—
68C2×C16×C61—24no—
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61—21no—
72C2×C16×C61D411yescharacteristic
73C2×C16×C61D411yescharacteristic
74#41×C61—21no—
75#41×C61—21no—
76#41×C61C22⋊C412yes—
77#41×C61M1612yes—
78C2×Q8×C61C2×C811yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61C2×C811yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C2×C22⋊D61—21no—
84C22×Dic61—21no—
85#11758222—21no—
86#11758222—21no—
87#11758222—21no—
88#11758222—21no—
89C2×D244C2×C811yescharacteristic
90C2×C4×D61—21no—
91C2×Dic122C2×C811yescharacteristic
92M16×C61—21no—
93M16×C61—22no—
94M16×C61—22no—
95M16×C61C22⋊C412yes—
96C2×C8×C61—21no—
97C2×C8×C61—22no—
98C2×C8×C61—22no—
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105#11758202—22no—
106#11758201—22no—
107#11758200—22no—
108#11758199—22no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111#11758194—21no—
112#11758194—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418C2×C811yescharacteristic
117C2×#92418C2×C811yescharacteristic
118#11758189—41no—
119#11758189—41no—
120C8×D61—41no—
121C8×D61—41no—
122C16×C61—21no—
123C16×C61—22no—
124C16×C61—21no—
125#11758185—41no—
126#11758185—41no—
127C23×C61—21no—
128C23×C61#13111yescharacteristic
129C22×D61—21no—
130Q8×C61—21no—
131Q8×C61C22⋊C812yes—
132D4×C61—22no—
133D4×C61—22no—
134D4×C61—21no—
135D4×C61C22⋊C812yes—
136C2×C4×C61—21no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C22×C811yescharacteristic
143C2×C4×C61C2×M1611yescharacteristic
144C2×C4×C61#13111yescharacteristic
145C22⋊D61—41no—
146C22⋊D61—41no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151D244—21no—
152D244—21no—
153C4×D61—41no—
154C4×D61—41no—
155Dic122—21no—
156Dic122—21no—
157C8×C61—22no—
158C8×C61#12011yescharacteristic
159C8×C61#12111yescharacteristic
160C8×C61#12111yescharacteristic
161C8×C61#12311yescharacteristic
162#92418—21no—
163#92418—21no—
164#92418—41no—
165#12980—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—22no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61#40811yescharacteristic
172C22×C61C8×D411yescharacteristic
173C22×C61#43511yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—22no—
178C4×C61#38611yescharacteristic
179C4×C61C2×C22⋊C811yescharacteristic
180C4×C61C8×D411yescharacteristic
181C4×C61#43511yescharacteristic
182Dic61—42no—
183Dic61—41no—
184C2×#504D6111yescharacteristic, complemented
185C2×#443—611no—
186C2×#350—611no—
187C2×#350—611no—
188#2113—611no—
189#1376—611no—
190#1374—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—42no—
194C2×C61#186911yescharacteristic
195C2×C61#217011yescharacteristic
196C2×C61#217111yescharacteristic
197D61—81no—
198C2×#135—611no—
199C2×#131—611no—
200C2×#131C2×D6111yescharacteristic
201#504—22no—
202#504—22no—
203C2×M32—21no—
204C2×M32—611no—
205C2×M32C2×D6111yescharacteristic
206C22×C16—21no—
207C22×C16—611no—
208C22×C16C2×D6111yescharacteristic
209#443—1222no—
210#443—1222no—
211C2×#108—611no—
212C2×#104—611no—
213C2×#104—611no—
214C2×C4×C8—611no—
215#350—1222no—
216#350—1222no—
217C22⋊C16—1221no—
218C22⋊C16—1221no—
219C61#1298011yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41C4×D6111yescharacteristic
222#135—1222no—
223#135—1222no—
224C2×Q16—611no—
225C2×SD16—611no—
226C2×SD16—611no—
227C2×D8—611no—
228#131—21no—
229#131—21no—
230#131—1221no—
231#131—1221no—
232#131—1221no—
233#131—1221no—
234#131D24412yes—
235#131C22⋊D6112yes—
236C2×M16—21no—
237C2×M16—611no—
238C2×M16—1221no—
239C2×M16C4×D6111yescharacteristic
240C22×C8—21no—
241C22×C8—611no—
242C22×C8—1221no—
243C22×C8C22×D6111yescharacteristic
244C2×C42—611no—
245M32—24no—
246M32—21no—
247M32—1221no—
248M32—1221no—
249M32C22⋊D6112yes—
250C2×C16—24no—
251C2×C16—21no—
252C2×C16—21no—
253C2×C16—21no—
254C2×C16—1221no—
255C2×C16—1221no—
256C2×C16—1221no—
257C2×C16—1221no—
258C2×C16C22⋊D6111yescharacteristic
259C2×C16C22⋊D6111yescharacteristic
260#108—1222no—
261#104—1222no—
262#104—1222no—
263C4×C8—1221no—
264C4×C8—1221no—
265#41—21no—
266#41—21no—
267#41—1221no—
268#41—1221no—
269#41—1221no—
270#41—1221no—
271#41#1175818912yes—
272#41#1175819812yes—
273C2×Q8—611no—
274C2×Q8C8×D6111yescharacteristic
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4C8×D6111yescharacteristic
279C22×C4—21no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4C2×C4×D6111yescharacteristic
283Q16—1222no—
284SD16—1222no—
285SD16—1222no—
286D8—1222no—
287M16—21no—
288M16—22no—
289M16—22no—
290M16—1221no—
291M16—1221no—
292M16—2441no—
293M16—2441no—
294M16#1175819812yes—
295C2×C8—21no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—2441no—
304C2×C8—2441no—
305C2×C8C2×D24411yescharacteristic
306C2×C8#1175822211yescharacteristic
307C2×C8#1175822211yescharacteristic
308C2×C8C2×C22⋊D6111yescharacteristic
309C2×C8C2×C22⋊D6111yescharacteristic
310C2×C8C2×C22⋊D6111yescharacteristic
311C42—1221no—
312C42—1221no—
313C16—21no—
314C16—22no—
315C16—21no—
316C16—2441no—
317C16—2441no—
318C23—21no—
319C23—1221no—
320C23#1451978311yescharacteristic
321Q8—21no—
322Q8—1221no—
323Q8—1221no—
324Q8#1451968912yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—1221no—
329D4—1221no—
330D4—2441no—
331D4—2441no—
332D4#1451968912yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—1222no—
337C2×C4—1221no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4C2×#1175819811yescharacteristic
343C2×C4C4×C22⋊D6111yescharacteristic
344C2×C4C4×C22⋊D6111yescharacteristic
345C2×C4C2×C8×D6111yescharacteristic
346C2×C4C2×#1175818911yescharacteristic
347C2×C4#1451978311yescharacteristic
348C8—22no—
349C8—1221no—
350C8—1221no—
351C8—2441no—
352C8#1451974611yescharacteristic
353C8#1451975111yescharacteristic
354C8#1451975111yescharacteristic
355C8#1451976011yescharacteristic
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22#1683972811yescharacteristic
365C22C8×C22⋊D6111yescharacteristic
366C22#1683983311yescharacteristic
367C4—22no—
368C4—2442no—
369C4—2441no—
370C4#1683964111yescharacteristic
371C4C2×#1451968911yescharacteristic
372C4C8×C22⋊D6111yescharacteristic
373C4#1683983311yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—4881no—
378C2#2144611111yescharacteristic
379C2#2144765411yescharacteristic
380C2#2144765911yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#504C2
socleC22×C61C8×D4
prime radicalC2×#14519797C4
cosocleC22×C8×C61C23
hypercenterC2×#504D61
hypocenterC61#12980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#16839547C2semidirect
3. C2×#16839546C2semidirect
4. #21447432C2semidirect
5. #21443900C2semidirect
6. #21443896C2semidirect
7. C2×C61×#504C2semidirect
184. C2×#504D61semidirect
219. C61#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#168398772
C2×#168395472
C2×#168395462
#214474322
#214439002
#214438962
C2×C61×#5042
#1298061