Finite Group Databasebeta

← C47×#19277 #26058975

Subgroups — C47×#19277 #26058975

Order 12032.

638 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×C47×#487C211yesmaximal, characteristic, complemented
2C47×#3079C211yesmaximal, characteristic
3C47×#3079C211yesmaximal, characteristic
4C8×#41×C47C211yesmaximal, characteristic
5C47×#1684C214yesmaximal, complemented
6C47×#1683C214yesmaximal, complemented
7C47×#1567C211yesmaximal, characteristic, complemented
8C47×#1549C211yesmaximal, characteristic, complemented
9C47×#1548C211yesmaximal, characteristic, complemented
10C2×C4⋊Q8×C47C2211yescharacteristic
11C2×C4⋊Q8×C47C2211yescharacteristic
12C4×#41×C47C2211yescharacteristic
13C47×#487—21no—
14C47×#487—21no—
15C47×#487C2214yes—
16C47×#477—21no—
17C47×#477C2212yes—
18C47×#476—21no—
19C47×#476C2212yes—
20C47×#475—21no—
21C47×#475C2212yes—
22C47×#474—21no—
23C47×#474C2212yes—
24C8×Q8×C47C2212yes—
25C8×D4×C47—22no—
26C8×D4×C47C2212yes—
27C47×#431—21no—
28C47×#431C2211yescharacteristic
29C47×#428—21no—
30C47×#428—21no—
31C47×#423C2211yescharacteristic
32C47×#423C2211yescharacteristic
33C47×#417—21no—
34C47×#417—21no—
35C2×#103×C47—22no—
36C2×C4×C8×C47—21no—
37C2×C4×C8×C47C2211yescharacteristic
38C47×#335C2214yes—
39C47×#333C2214yes—
40C47×#332C2214yes—
41C2×#41×C47D411yescharacteristic
42C22×Q8×C47—21no—
43C22×Q8×C47—21no—
44C2×M16×C47—21no—
45C2×M16×C47—21no—
46C22×C8×C47—22no—
47C22×C8×C47D412yes—
48C4⋊Q8×C47—21no—
49C4⋊Q8×C47—21no—
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—21no—
54C4⋊Q8×C47C2312yes—
55C4⋊Q8×C47C2312yes—
56C4×Q8×C47D411yescharacteristic
57C4×Q8×C47C2311yescharacteristic
58C4×D4×C47—21no—
59C4×D4×C47—21no—
60C4×D4×C47D411yescharacteristic
61C4×D4×C47C2311yescharacteristic
62#117×C47—21no—
63#117×C47D411yescharacteristic
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47—21no—
68C2×C42×C47—21no—
69C2×C42×C47C2311yescharacteristic
70#107×C47—22no—
71#107×C47—22no—
72#106×C47—22no—
73#106×C47—22no—
74C4⋊C8×C47—22no—
75C4⋊C8×C47—21no—
76C4⋊C8×C47—21no—
77C4⋊C8×C47C2312yes—
78C4⋊C8×C47C2312yes—
79C4⋊C8×C47C2312yes—
80#103×C47—22no—
81#103×C47—22no—
82#103×C47—24no—
83#103×C47—24no—
84#102×C47—22no—
85#102×C47—22no—
86C22⋊C8×C47—21no—
87C22⋊C8×C47—22no—
88C4×C8×C47—22no—
89C4×C8×C47—21no—
90C4×C8×C47D411yescharacteristic
91C4×C8×C47D411yescharacteristic
92C4×C8×C47C2312yes—
93#41×C47—22no—
94#41×C47Q1614yes—
95C2×Q8×C47—22no—
96C2×Q8×C47—22no—
97C2×Q8×C47—44no—
98C2×Q8×C47—41no—
99C2×Q8×C47—41no—
100C2×Q8×C47—82no—
101C2×Q8×C47C2×D411yescharacteristic
102C2×D4×C47—21no—
103C2×D4×C47C2×D411yescharacteristic
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—41no—
108C22×C4×C47—41no—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47#4111yescharacteristic
112M16×C47—42no—
113M16×C47—42no—
114C2×C8×C47—22no—
115C2×C8×C47—22no—
116C2×C8×C47—22no—
117C2×C8×C47—42no—
118C2×C8×C47—44no—
119C2×C8×C47C2×D412yes—
120C2×C8×C47C2×D412yes—
121C4⋊C4×C47—21no—
122C4⋊C4×C47—21no—
123C4⋊C4×C47—22no—
124C4⋊C4×C47—22no—
125C4⋊C4×C47—22no—
126C4⋊C4×C47—22no—
127C4⋊C4×C47—41no—
128C4⋊C4×C47—41no—
129C4⋊C4×C47—41no—
130C4⋊C4×C47—41no—
131C4⋊C4×C47C2×D411yescharacteristic
132C4⋊C4×C47C2×D411yescharacteristic
133C22⋊C4×C47—21no—
134C22⋊C4×C47—21no—
135C22⋊C4×C47—21no—
136C42×C47—21no—
137C42×C47—21no—
138C42×C47—21no—
139C42×C47C2×D411yescharacteristic
140C42×C47C2×D411yescharacteristic
141C42×C47#4111yescharacteristic
142C42×C47C2411yescharacteristic
143C23×C47—21no—
144C23×C47#12111yescharacteristic
145Q8×C47—21no—
146Q8×C47—44no—
147Q8×C47—82no—
148Q8×C47—82no—
149Q8×C47—82no—
150Q8×C47C2×Q1612yes—
151D4×C47—24no—
152D4×C47—21no—
153D4×C47C2×Q1612yes—
154C2×C4×C47—21no—
155C2×C4×C47—22no—
156C2×C4×C47—24no—
157C2×C4×C47—22no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—42no—
163C2×C4×C47—42no—
164C2×C4×C47—82no—
165C2×C4×C47—82no—
166C2×C4×C47#12111yescharacteristic
167C2×C4×C47#12111yescharacteristic
168C2×C4×C47#12111yescharacteristic
169C2×C4×C47C2×Q1612yes—
170C2×C4×C47#13512yes—
171C2×C4×C47C22×D411yescharacteristic
172C2×C4×C47C22×D411yescharacteristic
173C2×C4×C47C2×#4111yescharacteristic
174C8×C47—22no—
175C8×C47—22no—
176C8×C47—42no—
177C8×C47—42no—
178C8×C47—42no—
179#19277C4711yesmaximal, characteristic, direct product factor, Sylow
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—22no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47#46712yes—
186C22×C47C2×#12111yescharacteristic
187C4×C47—21no—
188C4×C47—22no—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—82no—
193C4×C47—82no—
194C4×C47#46712yes—
195C4×C47#47112yes—
196C4×C47C22×Q1611yescharacteristic
197C4×C47C2×#13511yescharacteristic
198C4×C47#57512yes—
199C2×#487C2×C4711yescharacteristic, complemented
200#3079C2×C4711yescharacteristic
201#3079C2×C4711yescharacteristic
202C8×#41C2×C4711yescharacteristic
203#1684C2×C4714yescomplemented
204#1683C2×C4714yescomplemented
205#1567C2×C4711yescharacteristic, complemented
206#1549C2×C4711yescharacteristic, complemented
207#1548C2×C4711yescharacteristic, complemented
208C2×C47—22no—
209C2×C47—42no—
210C2×C47#304011yescharacteristic
211C2×C47C2×#46711yescharacteristic
212C2×C47C2×#47111yescharacteristic
213C2×C4⋊Q8C22×C4711yescharacteristic
214C2×C4⋊Q8C22×C4711yescharacteristic
215C4×#41C22×C4711yescharacteristic
216#487—21no—
217#487—21no—
218#487C22×C4714yes—
219#477—21no—
220#477C22×C4712yes—
221#476—21no—
222#476C22×C4712yes—
223#475—21no—
224#475C22×C4712yes—
225#474—21no—
226#474C22×C4712yes—
227C8×Q8C22×C4712yes—
228C8×D4—22no—
229C8×D4C22×C4712yes—
230#431—21no—
231#431C22×C4711yescharacteristic
232#428—21no—
233#428—21no—
234#423C22×C4711yescharacteristic
235#423C22×C4711yescharacteristic
236#417—21no—
237#417—21no—
238C2×#103—22no—
239C2×C4×C8—21no—
240C2×C4×C8C22×C4711yescharacteristic
241#335C22×C4714yes—
242#333C22×C4714yes—
243#332C22×C4714yes—
244C47#1927711yescharacteristic, direct product factor, Sylow
245C2×#41D4×C4711yescharacteristic
246C22×Q8—21no—
247C22×Q8—21no—
248C2×M16—21no—
249C2×M16—21no—
250C22×C8—22no—
251C22×C8D4×C4712yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C23×C4712yes—
259C4⋊Q8C23×C4712yes—
260C4×Q8D4×C4711yescharacteristic
261C4×Q8C23×C4711yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4D4×C4711yescharacteristic
265C4×D4C23×C4711yescharacteristic
266#117—21no—
267#117D4×C4711yescharacteristic
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C23×C4711yescharacteristic
274#107—22no—
275#107—22no—
276#106—22no—
277#106—22no—
278C4⋊C8—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8C23×C4712yes—
282C4⋊C8C23×C4712yes—
283C4⋊C8C23×C4712yes—
284#103—22no—
285#103—22no—
286#103—24no—
287#103—24no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—22no—
292C4×C8—22no—
293C4×C8—21no—
294C4×C8D4×C4711yescharacteristic
295C4×C8D4×C4711yescharacteristic
296C4×C8C23×C4712yes—
297#41—22no—
298#41Q16×C4714yes—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—82no—
305C2×Q8C2×D4×C4711yescharacteristic
306C2×D4—21no—
307C2×D4C2×D4×C4711yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C2×D4×C4711yescharacteristic
314C22×C4C2×D4×C4711yescharacteristic
315C22×C4#41×C4711yescharacteristic
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—42no—
322C2×C8—44no—
323C2×C8C2×D4×C4712yes—
324C2×C8C2×D4×C4712yes—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4C2×D4×C4711yescharacteristic
336C4⋊C4C2×D4×C4711yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D4×C4711yescharacteristic
344C42C2×D4×C4711yescharacteristic
345C42#41×C4711yescharacteristic
346C42C24×C4711yescharacteristic
347C23—21no—
348C23#121×C4711yescharacteristic
349Q8—21no—
350Q8—44no—
351Q8—82no—
352Q8—82no—
353Q8—82no—
354Q8C2×Q16×C4712yes—
355D4—24no—
356D4—21no—
357D4C2×Q16×C4712yes—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4#121×C4711yescharacteristic
371C2×C4#121×C4711yescharacteristic
372C2×C4#121×C4711yescharacteristic
373C2×C4C2×Q16×C4712yes—
374C2×C4#135×C4712yes—
375C2×C4C22×D4×C4711yescharacteristic
376C2×C4C22×D4×C4711yescharacteristic
377C2×C4C2×#41×C4711yescharacteristic
378C8—22no—
379C8—22no—
380C8—42no—
381C8—42no—
382C8—42no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—41no—
387C22—41no—
388C22C47×#46712yes—
389C22C2×#121×C4711yescharacteristic
390C4—21no—
391C4—22no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—82no—
397C4C47×#46712yes—
398C4C47×#47112yes—
399C4C22×Q16×C4711yescharacteristic
400C4C2×#135×C4711yescharacteristic
401C4C47×#57512yes—
402C2—22no—
403C2—42no—
404C2C47×#304011yescharacteristic
405C2C2×C47×#46711yescharacteristic
406C2C2×C47×#47111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×#41×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#487C2semidirect
5. C47×#1684C2semidirect
6. C47×#1683C2semidirect
7. C47×#1567C2semidirect
8. C47×#1549C2semidirect
9. C47×#1548C2semidirect
179. #19277C47direct (N × H)
199. C2×#487C2×C47semidirect
203. #1684C2×C47semidirect
204. #1683C2×C47semidirect
205. #1567C2×C47semidirect
206. #1549C2×C47semidirect
207. #1548C2×C47semidirect
244. C47#19277direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4872
C47×#30792
C8×#41×C472
C47×#16842
C47×#16832
C47×#15672
C47×#15492
C47×#15482
#1927747