Finite Group Databasebeta

← #30607495

Subgroups — #30607495

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×#16840820C211yesmaximal, characteristic, complemented
2C2×#16840661C211yesmaximal, characteristic, complemented
3C2×#16840660C211yesmaximal, characteristic, complemented
4#21462051C211yesmaximal, characteristic, complemented
5#21460863C211yesmaximal, characteristic, complemented
6#21460857C211yesmaximal, characteristic, complemented
7C2×#16839876C211yesmaximal, characteristic
8#16840820—22no—
9#16840820—22no—
10C2×#14519851—21no—
11C2×#14519851C2211yescharacteristic
12C2×#14519851C2211yescharacteristic
13C22×#11758187—21no—
14C22×#11758187C2211yescharacteristic
15C22×#11758187C2211yescharacteristic
16#16840661—22no—
17#16840660—22no—
18#16840657—21no—
19#16840657—21no—
20C2×#14519797C411yescharacteristic
21C2×#14519785C2211yescharacteristic
22C2×#14519784C2211yescharacteristic
23#16839876—22no—
24#16839876—22no—
25C2×#14519712C411yescharacteristic
26C2×#14519705C411yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28C2×#104×C61C411yescharacteristic
29#14519851—24no—
30#14519851—21no—
31#14519851—21no—
32#14519851—21no—
33#14519851D412yes—
34C2×#11758187—24no—
35C2×#11758187—21no—
36C2×#11758187—21no—
37C2×#11758187—21no—
38C2×#11758187—21no—
39C2×#11758187—21no—
40C2×#11758187—21no—
41C2×#11758187—21no—
42C2×#11758187D411yescharacteristic
43C2×#11758187D411yescharacteristic
44C2×#11758222C2×C411yescharacteristic
45#14519797—22no—
46#14519797—22no—
47C2×#11758202C811yescharacteristic
48C2×#11758200C811yescharacteristic
49C2×#11758201C811yescharacteristic
50C2×#11758199C811yescharacteristic
51#14519785—21no—
52#14519785—21no—
53#14519785—21no—
54#14519785—21no—
55#14519784—21no—
56#14519784—21no—
57#14519784D412yes—
58#14519784D412yes—
59C2×#11758194—21no—
60C2×#11758194C2×C411yescharacteristic
61C2×#11758189—21no—
62C22×#92418—21no—
63C22×#92418C2×C411yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—21no—
66#14519712—22no—
67#14519705—22no—
68C4×#92418—21no—
69C4×#92418—21no—
70C2×#41×C61C2×C411yescharacteristic
71C2×M16×C61C2×C411yescharacteristic
72C2×C42×C61C2×C411yescharacteristic
73#104×C61—22no—
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×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C2×C22⋊D61—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—21no—
94C2×C8×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97#11758202—22no—
98#11758201—22no—
99#11758200—22no—
100#11758199—22no—
101#11758194—21no—
102#11758194—22no—
103#11758194—22no—
104#11758194C22⋊C412yes—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—22no—
109C2×#92418—22no—
110C2×#92418C2×C811yescharacteristic
111C2×#92418C2×C811yescharacteristic
112C2×#92418C2×D411yescharacteristic
113C2×#92418C2×D411yescharacteristic
114C2×#92418C2×D411yescharacteristic
115C2×#92418C2×D411yescharacteristic
116C2×#92418#4111yescharacteristic
117C2×#92418#4111yescharacteristic
118#11758189—41no—
119#11758189—41no—
120C8×D61—41no—
121C8×D61—41no—
122#11758187—21no—
123#11758187—22no—
124#11758187—21no—
125#11758187—41no—
126#11758187—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×C61—22no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61C22×C811yescharacteristic
146C2×C4×C61C2×M1611yescharacteristic
147C2×C4×C61#13111yescharacteristic
148C22⋊D61—41no—
149C22⋊D61—41no—
150C2×Dic61—21no—
151D244—21no—
152D244—21no—
153C4×D61—41no—
154C4×D61—41no—
155Dic122—21no—
156Dic122—21no—
157C8×C61—41no—
158#92418—22no—
159#92418—21no—
160#92418—21no—
161#92418#12011yescharacteristic
162#92418#12111yescharacteristic
163#92418#12111yescharacteristic
164#92418#12311yescharacteristic
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—42no—
179C4×C61#38611yescharacteristic
180C4×C61C2×C22⋊C811yescharacteristic
181C4×C61C8×D411yescharacteristic
182C4×C61#43511yescharacteristic
183Dic61—41no—
184C2×#504—611no—
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×#131—611no—
201#504—1222no—
202#504—1222no—
203C2×M32—611no—
204C2×M32—611no—
205C2×M32—1221no—
206C22×C16—611no—
207C22×C16—611no—
208C22×C16—1221no—
209#443—1222no—
210#443—1222no—
211C2×#108—611no—
212C2×#104—611no—
213C2×#104#692311yescharacteristic
214C2×C4×C8—611no—
215#350—1222no—
216#350—1222no—
217C22⋊C16—1221no—
218C22⋊C16—1221no—
219C61#1298011yescharacteristic, complemented, Sylow
220C2×#41—611no—
221C2×#41C2×#692311yescharacteristic
222#135—1222no—
223#135—1222no—
224C2×Q16—611no—
225C2×SD16—611no—
226C2×SD16—611no—
227C2×D8—611no—
228#131—612no—
229#131—612no—
230#131—1221no—
231#131—1221no—
232#131—1221no—
233#131—1221no—
234#131—1221no—
235#131—1221no—
236C2×M16—611no—
237C2×M16—1221no—
238C2×M16—1221no—
239C2×M16C2×#692311yescharacteristic
240C22×C8—611no—
241C22×C8—611no—
242C22×C8—1221no—
243C22×C8—1221no—
244C2×C42C2×#692311yescharacteristic
245M32—612no—
246M32—1221no—
247M32—1224no—
248M32—1221no—
249M32—1221no—
250C2×C16—611no—
251C2×C16—611no—
252C2×C16—1221no—
253C2×C16—1221no—
254C2×C16—1221no—
255C2×C16—1224no—
256C2×C16—1221no—
257C2×C16—1221no—
258C2×C16—1221no—
259C2×C16—1221no—
260#108—1222no—
261#104—22no—
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#1175821312yes—
272#41C22⋊#692312yes—
273C2×Q8—611no—
274C2×Q8D61⋊C811yescharacteristic
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4D61⋊C811yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1221no—
282C22×C4C22×#692311yescharacteristic
283Q16—1222no—
284SD16—1222no—
285SD16—1222no—
286D8—1222no—
287M16—21no—
288M16—21no—
289M16—612no—
290M16—1222no—
291M16—1222no—
292M16—1221no—
293M16—2441no—
294M16—2441no—
295C2×C8—21no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—611no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—611no—
304C2×C8—1222no—
305C2×C8—1222no—
306C2×C8—1221no—
307C2×C8—1221no—
308C2×C8—1221no—
309C2×C8—2441no—
310C2×C8—2441no—
311C42—21no—
312C42—21no—
313C16—1221no—
314C16—1221no—
315C16—1222no—
316C16—2441no—
317C16—2441no—
318C23—21no—
319C23—1221no—
320C23#1451986411yescharacteristic
321Q8—21no—
322Q8—1221no—
323Q8—1221no—
324Q8#1451983412yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—1221no—
329D4—1221no—
330D4—2441no—
331D4—2441no—
332D4#1451983412yes—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—1221no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4C2×C22⋊#692311yescharacteristic
343C2×C4D4×#692311yescharacteristic
344C2×C4D4×#692311yescharacteristic
345C2×C4C2×D61⋊C811yescharacteristic
346C2×C4C2×#1175821311yescharacteristic
347C2×C4#1451986411yescharacteristic
348C8—41no—
349C8—611no—
350C8—611no—
351C8—611no—
352C8—611no—
353C8—1222no—
354C8—1221no—
355C8—1221no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22#1684073511yescharacteristic
365C22#1684078911yescharacteristic
366C22#1684079111yescharacteristic
367C4—22no—
368C4—42no—
369C4—2441no—
370C4#1684071011yescharacteristic
371C4C2×#1451983411yescharacteristic
372C4#1684078911yescharacteristic
373C4#1684079111yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—4881no—
378C2#2146179411yescharacteristic
379C2#2146220711yescharacteristic
380C2#2146221011yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#104×C61C4
socleC22×C61C8×D4
prime radicalC2×#14519797C4
cosocleC22×#92418C23
hypercenterC2×#104#6923
hypocenterC61#12980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#16840820C2semidirect
2. C2×#16840661C2semidirect
3. C2×#16840660C2semidirect
4. #21462051C2semidirect
5. #21460863C2semidirect
6. #21460857C2semidirect
219. C61#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#168408202
C2×#168406612
C2×#168406602
#214620512
#214608632
#214608572
C2×#168398762
#1298061