Finite Group Databasebeta

← C47×#19270 #26058968

Subgroups — C47×#19270 #26058968

Order 12032.

670 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
1C2×C47×#498C211yesmaximal, characteristic, complemented
2C47×#3079C211yesmaximal, characteristic
3C47×#3039C211yesmaximal, characteristic
4C8×#41×C47C211yesmaximal, characteristic
5C47×#1672C214yesmaximal, complemented
6C47×#1671C214yesmaximal, complemented
7C47×#1566C211yesmaximal, characteristic, complemented
8C47×#1548C211yesmaximal, characteristic, complemented
9C47×#1546C211yesmaximal, characteristic, complemented
10C2×#137×C47—21no—
11C2×C4⋊Q8×C47C2211yescharacteristic
12C2×C4⋊Q8×C47C2211yescharacteristic
13C4×#41×C47C2211yescharacteristic
14C47×#498—21no—
15C47×#498—21no—
16C47×#498C2214yes—
17C47×#477C2212yes—
18C47×#476C2212yes—
19C47×#475—21no—
20C47×#474—21no—
21C47×#462—21no—
22C47×#462C2212yes—
23C47×#461—21no—
24C47×#461C2212yes—
25C8×Q8×C47C2212yes—
26C8×D4×C47—22no—
27C8×D4×C47C2212yes—
28C47×#431—21no—
29C47×#431C2211yescharacteristic
30C47×#428—21no—
31C2×#106×C47—22no—
32C47×#423C2211yescharacteristic
33C47×#423C2211yescharacteristic
34C47×#419—21no—
35C47×#417—21no—
36C2×C4×C8×C47—21no—
37C2×C4×C8×C47C2211yescharacteristic
38C47×#334C2214yes—
39C47×#333C2214yes—
40C47×#332C2214yes—
41C2×#41×C47D411yescharacteristic
42C22×Q8×C47—21no—
43C22×Q8×C47—21no—
44#137×C47—44no—
45C2×Q16×C47—22no—
46C2×SD16×C47—22no—
47C2×M16×C47—21no—
48C2×M16×C47—21no—
49C22×C8×C47—22no—
50C22×C8×C47D412yes—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—21no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47C2312yes—
58C4⋊Q8×C47C2312yes—
59C4×Q8×C47D411yescharacteristic
60C4×Q8×C47C2311yescharacteristic
61C4×D4×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47D411yescharacteristic
64C4×D4×C47C2311yescharacteristic
65#117×C47—21no—
66#117×C47D411yescharacteristic
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47—21no—
69C2×C4⋊C4×C47—21no—
70C2×C4⋊C4×C47—21no—
71C2×C42×C47—21no—
72C2×C42×C47C2311yescharacteristic
73#107×C47—22no—
74#106×C47—24no—
75#106×C47—24no—
76#106×C47—22no—
77C4⋊C8×C47—22no—
78C4⋊C8×C47—21no—
79C4⋊C8×C47—21no—
80C4⋊C8×C47C2312yes—
81C4⋊C8×C47C2312yes—
82C4⋊C8×C47C2312yes—
83#103×C47—22no—
84#103×C47—22no—
85#103×C47—22no—
86#102×C47—22no—
87C22⋊C8×C47—21no—
88C22⋊C8×C47—22no—
89C4×C8×C47—22no—
90C4×C8×C47—21no—
91C4×C8×C47D411yescharacteristic
92C4×C8×C47D411yescharacteristic
93C4×C8×C47C2312yes—
94#41×C47—22no—
95#41×C47SD1614yes—
96C2×Q8×C47—22no—
97C2×Q8×C47—22no—
98C2×Q8×C47—41no—
99C2×Q8×C47—41no—
100C2×Q8×C47—42no—
101C2×Q8×C47—42no—
102C2×Q8×C47—82no—
103C2×Q8×C47C2×D411yescharacteristic
104C2×D4×C47—21no—
105C2×D4×C47C2×D411yescharacteristic
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—41no—
110C22×C4×C47—41no—
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47#4111yescharacteristic
114Q16×C47—44no—
115SD16×C47—44no—
116M16×C47—42no—
117M16×C47—42no—
118C2×C8×C47—24no—
119C2×C8×C47—22no—
120C2×C8×C47—22no—
121C2×C8×C47—22no—
122C2×C8×C47—44no—
123C2×C8×C47C2×D412yes—
124C2×C8×C47C2×D412yes—
125C4⋊C4×C47—21no—
126C4⋊C4×C47—21no—
127C4⋊C4×C47—22no—
128C4⋊C4×C47—22no—
129C4⋊C4×C47—22no—
130C4⋊C4×C47—22no—
131C4⋊C4×C47—41no—
132C4⋊C4×C47—41no—
133C4⋊C4×C47—41no—
134C4⋊C4×C47—41no—
135C4⋊C4×C47C2×D411yescharacteristic
136C4⋊C4×C47C2×D411yescharacteristic
137C22⋊C4×C47—21no—
138C22⋊C4×C47—21no—
139C22⋊C4×C47—21no—
140C42×C47—21no—
141C42×C47—21no—
142C42×C47—21no—
143C42×C47C2×D411yescharacteristic
144C42×C47C2×D411yescharacteristic
145C42×C47#4111yescharacteristic
146C42×C47C2411yescharacteristic
147C23×C47—21no—
148C23×C47#12111yescharacteristic
149Q8×C47—21no—
150Q8×C47—42no—
151Q8×C47—42no—
152Q8×C47—82no—
153Q8×C47—82no—
154Q8×C47—82no—
155Q8×C47C2×SD1612yes—
156D4×C47—24no—
157D4×C47—21no—
158D4×C47C2×SD1612yes—
159C2×C4×C47—21no—
160C2×C4×C47—22no—
161C2×C4×C47—24no—
162C2×C4×C47—22no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—42no—
166C2×C4×C47—42no—
167C2×C4×C47—42no—
168C2×C4×C47—42no—
169C2×C4×C47—82no—
170C2×C4×C47—82no—
171C2×C4×C47#12111yescharacteristic
172C2×C4×C47#12111yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C2×C4×C47C2×SD1612yes—
175C2×C4×C47#13512yes—
176C2×C4×C47C22×D411yescharacteristic
177C2×C4×C47C22×D411yescharacteristic
178C2×C4×C47C2×#4111yescharacteristic
179C8×C47—22no—
180C8×C47—42no—
181C8×C47—42no—
182C8×C47—42no—
183C8×C47#13714yescomplemented
184#19270C4711yesmaximal, characteristic, direct product factor, Sylow
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—22no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47#46512yes—
191C22×C47C2×#12111yescharacteristic
192C4×C47—21no—
193C4×C47—22no—
194C4×C47—21no—
195C4×C47—41no—
196C4×C47—41no—
197C4×C47—82no—
198C4×C47—82no—
199C4×C47#46512yes—
200C4×C47#47112yes—
201C4×C47C22×SD1611yescharacteristic
202C4×C47C2×#13511yescharacteristic
203C4×C47C2×#13712yes—
204C2×#498C2×C4711yescharacteristic, complemented
205#3079C2×C4711yescharacteristic
206#3039C2×C4711yescharacteristic
207C8×#41C2×C4711yescharacteristic
208#1672C2×C4714yescomplemented
209#1671C2×C4714yescomplemented
210#1566C2×C4711yescharacteristic, complemented
211#1548C2×C4711yescharacteristic, complemented
212#1546C2×C4711yescharacteristic, complemented
213C2×C47—22no—
214C2×C47—42no—
215C2×C47#303911yescharacteristic
216C2×C47C2×#46511yescharacteristic
217C2×C47C2×#47111yescharacteristic
218C2×#137—21no—
219C2×C4⋊Q8C22×C4711yescharacteristic
220C2×C4⋊Q8C22×C4711yescharacteristic
221C4×#41C22×C4711yescharacteristic
222#498—21no—
223#498—21no—
224#498C22×C4714yes—
225#477C22×C4712yes—
226#476C22×C4712yes—
227#475—21no—
228#474—21no—
229#462—21no—
230#462C22×C4712yes—
231#461—21no—
232#461C22×C4712yes—
233C8×Q8C22×C4712yes—
234C8×D4—22no—
235C8×D4C22×C4712yes—
236#431—21no—
237#431C22×C4711yescharacteristic
238#428—21no—
239C2×#106—22no—
240#423C22×C4711yescharacteristic
241#423C22×C4711yescharacteristic
242#419—21no—
243#417—21no—
244C2×C4×C8—21no—
245C2×C4×C8C22×C4711yescharacteristic
246#334C22×C4714yes—
247#333C22×C4714yes—
248#332C22×C4714yes—
249C47#1927011yescharacteristic, direct product factor, Sylow
250C2×#41D4×C4711yescharacteristic
251C22×Q8—21no—
252C22×Q8—21no—
253#137—44no—
254C2×Q16—22no—
255C2×SD16—22no—
256C2×M16—21no—
257C2×M16—21no—
258C22×C8—22no—
259C22×C8D4×C4712yes—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8C23×C4712yes—
267C4⋊Q8C23×C4712yes—
268C4×Q8D4×C4711yescharacteristic
269C4×Q8C23×C4711yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4D4×C4711yescharacteristic
273C4×D4C23×C4711yescharacteristic
274#117—21no—
275#117D4×C4711yescharacteristic
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42—21no—
281C2×C42C23×C4711yescharacteristic
282#107—22no—
283#106—24no—
284#106—24no—
285#106—22no—
286C4⋊C8—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8C23×C4712yes—
290C4⋊C8C23×C4712yes—
291C4⋊C8C23×C4712yes—
292#103—22no—
293#103—22no—
294#103—22no—
295#102—22no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298C4×C8—22no—
299C4×C8—21no—
300C4×C8D4×C4711yescharacteristic
301C4×C8D4×C4711yescharacteristic
302C4×C8C23×C4712yes—
303#41—22no—
304#41SD16×C4714yes—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—82no—
312C2×Q8C2×D4×C4711yescharacteristic
313C2×D4—21no—
314C2×D4C2×D4×C4711yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C4711yescharacteristic
321C22×C4C2×D4×C4711yescharacteristic
322C22×C4#41×C4711yescharacteristic
323Q16—44no—
324SD16—44no—
325M16—42no—
326M16—42no—
327C2×C8—24no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—44no—
332C2×C8C2×D4×C4712yes—
333C2×C8C2×D4×C4712yes—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C2×D4×C4711yescharacteristic
345C4⋊C4C2×D4×C4711yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42C2×D4×C4711yescharacteristic
353C42C2×D4×C4711yescharacteristic
354C42#41×C4711yescharacteristic
355C42C24×C4711yescharacteristic
356C23—21no—
357C23#121×C4711yescharacteristic
358Q8—21no—
359Q8—42no—
360Q8—42no—
361Q8—82no—
362Q8—82no—
363Q8—82no—
364Q8C2×SD16×C4712yes—
365D4—24no—
366D4—21no—
367D4C2×SD16×C4712yes—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4#121×C4711yescharacteristic
381C2×C4#121×C4711yescharacteristic
382C2×C4#121×C4711yescharacteristic
383C2×C4C2×SD16×C4712yes—
384C2×C4#135×C4712yes—
385C2×C4C22×D4×C4711yescharacteristic
386C2×C4C22×D4×C4711yescharacteristic
387C2×C4C2×#41×C4711yescharacteristic
388C8—22no—
389C8—42no—
390C8—42no—
391C8—42no—
392C8#137×C4714yescomplemented
393C22—21no—
394C22—21no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22C47×#46512yes—
399C22C2×#121×C4711yescharacteristic
400C4—21no—
401C4—22no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—82no—
406C4—82no—
407C4C47×#46512yes—
408C4C47×#47112yes—
409C4C22×SD16×C4711yescharacteristic
410C4C2×#135×C4711yescharacteristic
411C4C2×#137×C4712yes—
412C2—22no—
413C2—42no—
414C2C47×#303911yescharacteristic
415C2C2×C47×#46511yescharacteristic
416C2C2×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×#498C2semidirect
5. C47×#1672C2semidirect
6. C47×#1671C2semidirect
7. C47×#1566C2semidirect
8. C47×#1548C2semidirect
9. C47×#1546C2semidirect
183. C8×C47#137semidirect
184. #19270C47direct (N × H)
204. C2×#498C2×C47semidirect
208. #1672C2×C47semidirect
209. #1671C2×C47semidirect
210. #1566C2×C47semidirect
211. #1548C2×C47semidirect
212. #1546C2×C47semidirect
249. C47#19270direct (N × H)
392. C8#137×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4982
C47×#30792
C47×#30392
C8×#41×C472
C47×#16722
C47×#16712
C47×#15662
C47×#15482
C47×#15462
#1927047