Finite Group Databasebeta

← #26216639

Subgroups — #26216639

Order 12032.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251810C211yesmaximal, characteristic
2#20243536C212yesmaximal, complemented
3#20243512C211yesmaximal, characteristic, complemented
4#20243490C212yesmaximal
5#20243435C211yesmaximal, characteristic
6#20243431C211yesmaximal, characteristic
7#20243270C211yesmaximal, characteristic, complemented
8#20243269C211yesmaximal, characteristic, complemented
9#20243187C212yesmaximal
10#20243142C212yesmaximal, complemented
11C47×#1833C211yesmaximal, characteristic, complemented
12C2×#13094032C2211yescharacteristic
13C2×#13094030C2211yescharacteristic
14#15689591C2211yescharacteristic
15C2×#13093960C2211yescharacteristic
16#15689161C2211yescharacteristic
17#15689105C2212yes—
18#15689096C2212yes—
19#15689081C2212yes—
20#15689080C412yescomplemented
21#15689079C2212yes—
22#15689079C2211yescharacteristic
23#15689077C412yescomplemented
24#15689075C412yescomplemented
25M16×Dic47C2211yescharacteristic
26C2×C8×Dic47C2211yescharacteristic
27C4×C8×D47C412yescomplemented
28#15688894C2212yes—
29#15688884C2212yes—
30#15688882C2212yes—
31C47⋊#338C2212yes—
32#15688879C2212yes—
33#15688879C2212yes—
34C2×#108×C47C2211yescharacteristic
35C47×#427C2211yescharacteristic
36C47×#405C2211yescharacteristic
37C47×#344C2212yes—
38C47×H(3,ℤ/4)C2212yes—
39C2×#10625350C2311yescharacteristic
40#13094032—21no—
41#13094032—21no—
42#13094032—21no—
43#13094032—21no—
44#13094030—21no—
45#13094030—21no—
46#13094030—21no—
47#13094030—21no—
48C2×#10625329C2312yes—
49C2×#10625329C2311yescharacteristic
50C2×#10625324C2×C412yes—
51C2×#10625324C2×C412yes—
52C22×C47⋊C8C2311yescharacteristic
53C2×C8×D47C2×C412yes—
54C2×C8×D47C2×C412yes—
55#13093989—21no—
56#13093986—21no—
57(C22⋊D47)⋊C4—22no—
58#13093983C2312yes—
59#13093981C2×C412yes—
60C2×C4×Dic47C2311yescharacteristic
61C42×D47C2×C412yes—
62#13093960—21no—
63#13093960—21no—
64#13093958—21no—
65#13093956—21no—
66#13093942—22no—
67#13093940—22no—
68#13093938—24no—
69#13093935—22no—
70#13093935C2×C412yes—
71#13093934—22no—
72#13093934C2×C412yes—
73C4×C47⋊C8—22no—
74C4×C47⋊C8C2×C412yes—
75C8×Dic47—22no—
76C8×Dic47C2×C411yescharacteristic
77C8×Dic47C2×C412yes—
78C8×Dic47C2×C411yescharacteristic
79C8×Dic47C2×C411yescharacteristic
80C8×Dic47C2×C411yescharacteristic
81C2×M16×C47C2312yes—
82C2×M16×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84#117×C47C2312yes—
85#117×C47C2311yescharacteristic
86#108×C47—21no—
87#108×C47—21no—
88#107×C47—21no—
89#106×C47—21no—
90#97×C47C2×C412yes—
91C4×C8×C47C2×C412yes—
92C22×C4×C47C2411yescharacteristic
93C2×C22⋊D47#4112yes—
94C22×Dic47—21no—
95#10625350—21no—
96#10625350—21no—
97#10625350—21no—
98#10625350—21no—
99C2×D188#4111yescharacteristic
100C2×C4×D47—22no—
101C2×C4×D47C22×C412yes—
102C2×Dic94#4111yescharacteristic
103M16×C47—21no—
104M16×C47—21no—
105M16×C47—22no—
106M16×C47—22no—
107C2×C8×C47—22no—
108C2×C8×C47C22×C412yes—
109C2×C8×C47C22×C411yescharacteristic
110C2×C8×C47C22×C411yescharacteristic
111C2×C8×C47#4111yescharacteristic
112C2×C8×C47#4111yescharacteristic
113C2×C8×C47#4111yescharacteristic
114C2×C8×C47#4111yescharacteristic
115C4⋊C4×C47—21no—
116C4⋊C4×C47—22no—
117C22⋊C4×C47—21no—
118C22⋊C4×C47—22no—
119C42×C47—22no—
120C42×C47C22×C412yes—
121C22⋊Dic47—22no—
122(C2×D47)⋊C4—22no—
123C4⋊Dic47—22no—
124Dic47⋊C4—22no—
125C4×Dic47—21no—
126C4×Dic47—22no—
127C4×Dic47—22no—
128C4×Dic47C22×C411yescharacteristic
129C4×Dic47C22×C411yescharacteristic
130#10625329—21no—
131#10625329—21no—
132#10625329—22no—
133#10625329—22no—
134C2×C47⋊C8—22no—
135C2×C47⋊C8C22×C412yes—
136C2×C47⋊C8C22×C411yescharacteristic
137C2×C47⋊C8C22×C411yescharacteristic
138C2×C47⋊C8#4111yescharacteristic
139C2×C47⋊C8#4111yescharacteristic
140C2×C47⋊C8#4111yescharacteristic
141C2×C47⋊C8#4111yescharacteristic
142#10625324—22no—
143#10625324—22no—
144#10625324—22no—
145#10625324—22no—
146C8×D47—22no—
147C8×D47—22no—
148C8×D47—22no—
149C8×D47—22no—
150C23×C47C2×#4111yescharacteristic
151C22×D47#11712yes—
152C2×C4×C47—22no—
153C2×C4×C47—42no—
154C2×C4×C47C23×C411yescharacteristic
155C2×C4×C47C2×#4111yescharacteristic
156C2×C4×C47C2×#4111yescharacteristic
157C2×C4×C47C2×#4111yescharacteristic
158C2×C4×C47C2×#4111yescharacteristic
159C2×C4×C47C2×#4111yescharacteristic
160C22⋊D47—22no—
161C22⋊D47—22no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—42no—
165C2×Dic47—42no—
166C2×Dic47#11712yes—
167D188—21no—
168D188—21no—
169C4×D47—22no—
170C4×D47—22no—
171C4×D47—44no—
172Dic94—21no—
173Dic94—21no—
174C8×C47—22no—
175C8×C47—42no—
176C8×C47#11711yescharacteristic
177C8×C47#11711yescharacteristic
178C8×C47#11711yescharacteristic
179C8×C47#11711yescharacteristic
180C47⋊C8—22no—
181C47⋊C8—42no—
182C47⋊C8#11711yescharacteristic
183C47⋊C8#11711yescharacteristic
184C47⋊C8#11711yescharacteristic
185C47⋊C8#11711yescharacteristic
186#20787—471nomaximal, Sylow
187C22×C47—41no—
188C22×C47C2×#11711yescharacteristic
189C22×C47#52911yescharacteristic
190C22×C47#52911yescharacteristic
191C2×D47—22no—
192C2×D47—42no—
193C4×C47—42no—
194C4×C47—82no—
195C4×C47C2×#11711yescharacteristic
196C4×C47C2×#11711yescharacteristic
197C4×C47#52911yescharacteristic
198C4×C47#52911yescharacteristic
199Dic47—22no—
200Dic47—22no—
201Dic47—41no—
202Dic47—82no—
203C4×#131—471no—
204#1841—472no—
205#1833—471no—
206#1833D4711yescharacteristic, complemented
207#1827—472no—
208#1813—471no—
209#1812—471no—
210#1772—471no—
211#1772—471no—
212#1757—472no—
213#1747—472no—
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—21no—
217C2×C47#228311yescharacteristic
218D47—42no—
219C2×#131—471no—
220C2×#131—471no—
221C4×#41—471no—
222C2×#108—471no—
223C2×#108C2×D4711yescharacteristic
224#427—471no—
225#427C2×D4711yescharacteristic
226#413—472no—
227#410—472no—
228#405—471no—
229#405—472no—
230#405—472no—
231#405—472no—
232#405—472no—
233#405C2×D4711yescharacteristic
234C4×M16—471no—
235C4×M16—472no—
236C2×C4×C8—471no—
237C2×C4×C8—472no—
238#344—472no—
239#344C2×D4712yes—
240#339—472no—
241#339—472no—
242#338—472no—
243H(3,ℤ/4)—472no—
244H(3,ℤ/4)—472no—
245H(3,ℤ/4)C2×D4712yes—
246C47#2078711yescharacteristic, complemented, Sylow
247C2×#41—471no—
248#131—941no—
249#131—941no—
250#131—941no—
251#131—941no—
252#131—941no—
253#131—941no—
254#131—941no—
255#131—941no—
256C2×M16—471no—
257C2×M16—472no—
258C2×M16—472no—
259C2×M16—472no—
260C2×M16C22×D4712yes—
261C2×M16C22×D4711yescharacteristic
262C22×C8—471no—
263C22×C8—472no—
264C22×C8—472no—
265C22×C8C22×D4711yescharacteristic
266C4×Q8—941no—
267C4×D4—942no—
268C4×D4—941no—
269#117—472no—
270#117—472no—
271#117C22×D4712yes—
272#117C22×D4711yescharacteristic
273C2×C42—471no—
274C2×C42—472no—
275#108—21no—
276#108—21no—
277#108—941no—
278#108—941no—
279#107—21no—
280#107—941no—
281#106—21no—
282#106—941no—
283#101—942no—
284#100—942no—
285#99—944no—
286#97—472no—
287#97—472no—
288#97—942no—
289#97—942no—
290#97C4×D4712yes—
291C4×C8—471no—
292C4×C8—471no—
293C4×C8—472no—
294C4×C8—471no—
295C4×C8—471no—
296C4×C8—472no—
297C4×C8—942no—
298C4×C8—942no—
299C4×C8C4×D4712yes—
300#41—941no—
301#41—941no—
302#41—941no—
303#41—941no—
304C2×Q8—471no—
305C2×D4—472no—
306C2×D4—471no—
307C22×C4—472no—
308C22×C4—942no—
309C22×C4—941no—
310C22×C4C23×D4711yescharacteristic
311M16—21no—
312M16—21no—
313M16—22no—
314M16—22no—
315M16—942no—
316M16—942no—
317M16—941no—
318M16—941no—
319M16—942no—
320M16—942no—
321M16—942no—
322M16—942no—
323C2×C8—22no—
324C2×C8—471no—
325C2×C8—471no—
326C2×C8—471no—
327C2×C8—471no—
328C2×C8—471no—
329C2×C8—471no—
330C2×C8—472no—
331C2×C8—942no—
332C2×C8—942no—
333C2×C8—942no—
334C2×C8—942no—
335C2×C8—942no—
336C2×C8C2×C4×D4712yes—
337C2×C8C2×C4×D4711yescharacteristic
338C2×C8C2×C4×D4711yescharacteristic
339C2×C8#1062535211yescharacteristic
340C2×C8#1062535211yescharacteristic
341C2×C8#1062535411yescharacteristic
342C2×C8#1062535411yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—942no—
346C4⋊C4—942no—
347C22⋊C4—21no—
348C22⋊C4—22no—
349C22⋊C4—942no—
350C22⋊C4—942no—
351C42—22no—
352C42—471no—
353C42—471no—
354C42—942no—
355C42—941no—
356C42—942no—
357C42C2×C4×D4712yes—
358C23—472no—
359C23#41×D4711yescharacteristic
360Q8—941no—
361Q8—941no—
362D4—942no—
363D4—942no—
364D4—941no—
365D4—941no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—472no—
369C2×C4—941no—
370C2×C4—942no—
371C2×C4—942no—
372C2×C4—941no—
373C2×C4—1884no—
374C2×C4—1882no—
375C2×C4—1882no—
376C2×C4C22×C4×D4711yescharacteristic
377C2×C4#41×D4711yescharacteristic
378C2×C4#41×D4711yescharacteristic
379C2×C4#41×D4711yescharacteristic
380C2×C4C2×#1062535211yescharacteristic
381C2×C4C2×#1062535411yescharacteristic
382C8—22no—
383C8—42no—
384C8—471no—
385C8—471no—
386C8—471no—
387C8—471no—
388C8—942no—
389C8—1882no—
390C8#1309398211yescharacteristic
391C8#1309398211yescharacteristic
392C8#1309398211yescharacteristic
393C8#1309398211yescharacteristic
394C22—41no—
395C22—942no—
396C22—1882no—
397C22#117×D4711yescharacteristic
398C22#1568965211yescharacteristic
399C22#1568965811yescharacteristic
400C4—42no—
401C4—82no—
402C4—942no—
403C4—942no—
404C4—3762no—
405C4—1881no—
406C4#117×D4711yescharacteristic
407C4C2×#1309398211yescharacteristic
408C4#1568965211yescharacteristic
409C4#1568965811yescharacteristic
410C2—21no—
411C2—21no—
412C2—21no—
413C2—1882no—
414C2#2024578111yescharacteristic
subgroupG/H
centerC4#117×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1833C2
socleC2×C47#2283
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#1833D47
hypocenterC47#20787
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ #117 ◁ #1833

Complements

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

NH ≅ G/Ntype
2. #20243536C2semidirect
3. #20243512C2semidirect
7. #20243270C2semidirect
8. #20243269C2semidirect
10. #20243142C2semidirect
11. C47×#1833C2semidirect
20. #15689080C4semidirect
23. #15689077C4semidirect
24. #15689075C4semidirect
27. C4×C8×D47C4semidirect
206. #1833D47semidirect
246. C47#20787semidirect

Maximal subgroups

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

subgroupindex
#202518102
#202435362
#202435122
#202434902
#202434352
#202434312
#202432702
#202432692
#202431872
#202431422
C47×#18332
#2078747