Finite Group Databasebeta

← #26112363

Subgroups — #26112363

Order 12032.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C47⋊C8C211yesmaximal, characteristic
2#20243408C211yesmaximal, characteristic
3#20241887C211yesmaximal, characteristic, complemented
4#20241843C211yesmaximal, characteristic, complemented
5#20241285C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C47×#3076C211yesmaximal, characteristic
8Q8×C47⋊C8—21no—
9D4×C47⋊C8—22no—
10D4×C47⋊C8—21no—
11#15689176—21no—
12#15689176C2211yescharacteristic
13#15689147C2211yescharacteristic
14C2×#13093951—21no—
15C2×C4×C47⋊C8—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17C4×C4⋊Dic47C2211yescharacteristic
18#15688882—21no—
19#15688860—22no—
20Q8⋊(C47⋊C8)—21no—
21Q8⋊(C47⋊C8)—21no—
22C47×#533C2211yescharacteristic
23C4×#41×C47C2211yescharacteristic
24C47×#479—21no—
25C47×#478—21no—
26C47×#477C411yescharacteristic, complemented
27C47×#476C411yescharacteristic, complemented
28C47×#475C411yescharacteristic, complemented
29C47×#474C411yescharacteristic, complemented
30C47×#427—21no—
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#416—21no—
33C2×#10625329—21no—
34C22×C47⋊C8—22no—
35C22×C47⋊C8—21no—
36C2×C4⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—22no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42#13093951—42no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)D412yes—
45C4×C47⋊C8—22no—
46C4×C47⋊C8—21no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8D411yescharacteristic
49C4×C47⋊C8D411yescharacteristic
50C47⋊#95—21no—
51C2×#41×C47D411yescharacteristic
52C22×C8×C47—21no—
53C4⋊Q8×C47C2×C411yescharacteristic
54C4⋊Q8×C47C2×C411yescharacteristic
55#125×C47—21no—
56C22⋊Q8×C47—21no—
57C22⋊Q8×C47—21no—
58C4×Q8×C47—21no—
59C4×Q8×C47—21no—
60C4×Q8×C47C2×C411yescharacteristic
61C4×Q8×C47D411yescharacteristic
62C4×D4×C47—21no—
63C4×D4×C47—21no—
64C4×D4×C47C2×C411yescharacteristic
65C4×D4×C47D411yescharacteristic
66#117×C47—21no—
67#117×C47—21no—
68#117×C47D411yescharacteristic
69C2×C42×C47—21no—
70C2×C42×C47C2311yescharacteristic
71#107×C47—21no—
72#107×C47—21no—
73#106×C47—21no—
74#106×C47—21no—
75C4⋊C8×C47—21no—
76C4⋊C8×C47C2×C411yescharacteristic
77C4⋊C8×C47C2×C411yescharacteristic
78#103×C47—21no—
79#103×C47—21no—
80#102×C47—21no—
81#102×C47—21no—
82#41×C47—21no—
83#41×C47—21no—
84#41×C47SD1612yes—
85#41×C47Q1612yes—
86C2×Q8×C47—21no—
87C2×Q8×C47—21no—
88C2×Q8×C47C22⋊C411yescharacteristic
89C2×D4×C47—21no—
90C2×D4×C47C22⋊C411yescharacteristic
91C22×C4×C47—21no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47C2×D411yescharacteristic
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47#4111yescharacteristic
97C22×Dic47—41no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—21no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47C22⋊C411yescharacteristic
111C4⋊C4×C47C22⋊C411yescharacteristic
112C22⋊C4×C47—21no—
113C22⋊C4×C47—21no—
114C22⋊C4×C47—21no—
115C22⋊C4×C47—41no—
116C42×C47—21no—
117C42×C47—21no—
118C42×C47—21no—
119C42×C47—41no—
120C42×C47C22×C411yescharacteristic
121C42×C47C2×D411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47#4111yescharacteristic
124C4⋊Dic47—22no—
125C4⋊Dic47—41no—
126C4×Dic47—41no—
127C4×Dic47—41no—
128#10625329—41no—
129#10625329—41no—
130C2×C47⋊C8—21no—
131C2×C47⋊C8—22no—
132C2×C47⋊C8—21no—
133C2×C47⋊C8—42no—
134C2×C47⋊C8—44no—
135C2×C47⋊C8—41no—
136C23×C47—21no—
137C23×C47#12111yescharacteristic
138Q8×C47—21no—
139Q8×C47—41no—
140Q8×C47—41no—
141Q8×C47—81no—
142Q8×C47#10312yes—
143D4×C47—22no—
144D4×C47—22no—
145D4×C47—21no—
146D4×C47#10312yes—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—21no—
150C2×C4×C47—22no—
151C2×C4×C47—22no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—41no—
155C2×C4×C47—42no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—41no—
160C2×C4×C47C2×C22⋊C411yescharacteristic
161C2×C4×C47C4×D411yescharacteristic
162C2×C4×C47C4×D411yescharacteristic
163C2×C4×C47#12011yescharacteristic
164C2×C4×C47#12111yescharacteristic
165C2×C4×C47#12311yescharacteristic
166C2×C4×C47C2×SD1611yescharacteristic
167C2×C4×C47C2×Q1611yescharacteristic
168C2×C4×C47#13511yescharacteristic
169C2×C4×C47#13511yescharacteristic
170C2×Dic47—42no—
171C2×Dic47—81no—
172C2×Dic47—81no—
173C8×C47—41no—
174C8×C47—41no—
175C47⋊C8—22no—
176C47⋊C8—42no—
177C47⋊C8—41no—
178C47⋊C8—81no—
179#9207—471nomaximal, Sylow
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—22no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47#38611yescharacteristic
186C22×C47#46511yescharacteristic
187C22×C47#46711yescharacteristic
188C4×C47—21no—
189C4×C47—22no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47—81no—
195C4×C47—81no—
196C4×C47C2×#10311yescharacteristic
197C4×C47#41611yescharacteristic
198C4×C47#44311yescharacteristic
199C4×C47#44411yescharacteristic
200C4×C47#46511yescharacteristic
201C4×C47#46711yescharacteristic
202Dic47—82no—
203#3076D4711yescharacteristic
204C8×#41—471no—
205#1806—471no—
206#1503—471no—
207#1493—471no—
208#1301—471no—
209#1279—471no—
210C2×C47—21no—
211C2×C47—21no—
212C2×C47—42no—
213C2×C47#187611yescharacteristic
214C2×C47#189211yescharacteristic
215C2×C47#190611yescharacteristic
216#533C2×D4711yescharacteristic
217C4×#41C2×D4711yescharacteristic
218#479—21no—
219#478—21no—
220#477Dic4711yescharacteristic, complemented
221#476Dic4711yescharacteristic, complemented
222#475Dic4711yescharacteristic, complemented
223#474Dic4711yescharacteristic, complemented
224C8×Q8—941no—
225C8×D4—942no—
226C8×D4—941no—
227#431—471no—
228#431—941no—
229#427—21no—
230#423—471no—
231C2×C4⋊C8C2×D4711yescharacteristic
232C2×#104—941no—
233#416—21no—
234C2×C4×C8—471no—
235C2×C4×C8—941no—
236C4×C4⋊C4—471no—
237#339—941no—
238#328—942no—
239Q8⋊C8—941no—
240Q8⋊C8—941no—
241C47#920711yescharacteristic, complemented, Sylow
242C2×#41C22⋊D4711yescharacteristic
243C2×M16—941no—
244C22×C8—21no—
245C22×C8—942no—
246C22×C8—941no—
247C4⋊Q8C2×Dic4711yescharacteristic
248C4⋊Q8C2×Dic4711yescharacteristic
249#125—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8C2×Dic4711yescharacteristic
255C4×Q8C22⋊D4711yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C2×Dic4711yescharacteristic
259C4×D4C22⋊D4711yescharacteristic
260#117—21no—
261#117—21no—
262#117C22⋊D4711yescharacteristic
263C2×C4⋊C4—941no—
264C2×C42—21no—
265C2×C42—941no—
266C2×C42C22×D4711yescharacteristic
267#107—21no—
268#107—21no—
269#106—21no—
270#106—21no—
271C4⋊C8—21no—
272C4⋊C8—942no—
273C4⋊C8—941no—
274C4⋊C8—941no—
275C4⋊C8—941no—
276C4⋊C8C2×Dic4711yescharacteristic
277C4⋊C8C2×Dic4711yescharacteristic
278#104—1882no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283C22⋊C8—472no—
284C22⋊C8—942no—
285C4×C8—471no—
286C4×C8—471no—
287C4×C8—942no—
288C4×C8—941no—
289C4×C8—941no—
290#95—941no—
291#41—21no—
292#41—21no—
293#41#1062533612yes—
294#41#1062533712yes—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8C22⋊Dic4711yescharacteristic
298C2×D4—21no—
299C2×D4C22⋊Dic4711yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—1881no—
304C22×C4D4×D4711yescharacteristic
305C22×C4#1062535211yescharacteristic
306C22×C4C2×C22⋊D4711yescharacteristic
307M16—1881no—
308M16—1881no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—941no—
314C2×C8—941no—
315C2×C8—942no—
316C2×C8—1882no—
317C2×C8—1884no—
318C2×C8—1881no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—942no—
328C4⋊C4—1881no—
329C4⋊C4C22⋊Dic4711yescharacteristic
330C4⋊C4C22⋊Dic4711yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—41no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—41no—
339C42—1881no—
340C42—1881no—
341C42D4×D4711yescharacteristic
342C42#1062535211yescharacteristic
343C42C22×Dic4711yescharacteristic
344C42C2×C22⋊D4711yescharacteristic
345C23—21no—
346C23#1309399611yescharacteristic
347Q8—21no—
348Q8—41no—
349Q8—41no—
350Q8—81no—
351Q8#1309394812yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#1309394812yes—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—3761no—
370C2×C4—3761no—
371C2×C4—1882no—
372C2×C4C2×C22⋊Dic4711yescharacteristic
373C2×C4D4×Dic4711yescharacteristic
374C2×C4D4×Dic4711yescharacteristic
375C2×C4#1309399211yescharacteristic
376C2×C4#1309399611yescharacteristic
377C2×C4#1309400511yescharacteristic
378C2×C4C2×#1062533611yescharacteristic
379C2×C4C2×#1062533711yescharacteristic
380C2×C4#1309404411yescharacteristic
381C2×C4#1309404411yescharacteristic
382C8—41no—
383C8—41no—
384C8—942no—
385C8—3761no—
386C8—1881no—
387C8—1882no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1568900311yescharacteristic
394C22#1568935411yescharacteristic
395C22#1568936211yescharacteristic
396C4—21no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—81no—
403C4—81no—
404C4—3762no—
405C4C2×#1309394811yescharacteristic
406C4#1568911911yescharacteristic
407C4#1568924011yescharacteristic
408C4#1568924511yescharacteristic
409C4#1568935411yescharacteristic
410C4#1568936211yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#2024371711yescharacteristic
415C2#2024381211yescharacteristic
416C2#2024389111yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#3076C2
socleC22×C47#386
prime radicalC2×#41×C47D4
cosocleC2×C42×C47C23
hypercenter#3076D47
hypocenterC47#9207
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
3. #20241887C2semidirect
4. #20241843C2semidirect
5. #20241285C2semidirect
6. #20241227C2semidirect
26. C47×#477C4semidirect
27. C47×#476C4semidirect
28. C47×#475C4semidirect
29. C47×#474C4semidirect
220. #477Dic47semidirect
221. #476Dic47semidirect
222. #475Dic47semidirect
223. #474Dic47semidirect
241. C47#9207semidirect

Maximal subgroups

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

subgroupindex
#41×C47⋊C82
#202434082
#202418872
#202418432
#202412852
#202412272
C47×#30762
#920747