Finite Group Databasebeta

← #26115236

Subgroups — #26115236

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094013C211yesmaximal, characteristic
2C4⋊C8×Dic47C211yesmaximal, characteristic, complemented
3C4×Dic47⋊C8C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5C2×#15688852C211yesmaximal, characteristic
6C2×#15688850C211yesmaximal, characteristic
7C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#13094013C411yescharacteristic
9C2×C4×D188C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—21no—
12C2×C4×C47⋊C8C2211yescharacteristic
13C2×C8×Dic47—21no—
14#15689030C411yescharacteristic
15#15689024C411yescharacteristic
16#15689013—21no—
17#15689013—21no—
18#15688988C411yescharacteristic
19C4×(C2×D47)⋊C4—21no—
20C4×(C2×D47)⋊C4—21no—
21C42×Dic47C2211yescharacteristic
22#15688877—21no—
23#15688877—21no—
24Q8⋊(C47⋊C8)—22no—
25#15688852—22no—
26#15688850—22no—
27C2×C4×Q8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×Q8⋊C8—22no—
31C22×D188C2×C411yescharacteristic
32C22×C4×D47—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35#13094013—22no—
36#13094013C814yescomplemented
37C4×D188—21no—
38C4×D188—21no—
39C4×D188—21no—
40C4×D188—21no—
41C2×C4⋊Dic47C2×C411yescharacteristic
42C2×(C2×D47)⋊C4—21no—
43C2×(C2×D47)⋊C4—21no—
44C2×(C2×D47)⋊C4—21no—
45C2×(C2×D47)⋊C4—21no—
46C2×(C2×D47)⋊C4—21no—
47C2×C4×Dic47C2×C411yescharacteristic
48C2×C4×Dic47C2×C411yescharacteristic
49C2×C4×Dic47D411yescharacteristic
50C2×C4×Dic47D411yescharacteristic
51C2×C4×Dic47D411yescharacteristic
52C2×C4×Dic47D411yescharacteristic
53C4⋊(C47⋊C8)—21no—
54C4⋊(C47⋊C8)D412yes—
55Dic47⋊C8—24no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8—21no—
58C8×Dic47—42no—
59C47⋊#95—21no—
60C47⋊#95—21no—
61C47⋊#95—21no—
62C47⋊#95—21no—
63C22×Q8×C47C2×C411yescharacteristic
64C22×C8×C47—21no—
65C22×C8×C47—21no—
66C4×Q8×C47—21no—
67C4×Q8×C47—21no—
68C4×Q8×C47—21no—
69C4×Q8×C47—21no—
70C2×C4⋊C4×C47—21no—
71C2×C4⋊C4×C47C2×C411yescharacteristic
72C2×C42×C47—21no—
73C2×C42×C47C2311yescharacteristic
74C4⋊C8×C47—21no—
75C4⋊C8×C47D412yes—
76C4×C8×C47—21no—
77C4×C8×C47—21no—
78C23×D47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47—21no—
81C2×Q8×C47—21no—
82C2×Q8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47C2×C812yes—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47C22×C411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×Dic47—21no—
91C22×Dic47C22⋊C411yescharacteristic
92C22×Dic47C22⋊C411yescharacteristic
93C22×Dic47C22⋊C411yescharacteristic
94C22×Dic47C22⋊C411yescharacteristic
95C2×D188—21no—
96C2×D188—21no—
97C2×D188—21no—
98C2×D188—21no—
99C2×D188—21no—
100C2×D188C2×C812yes—
101C2×C4×D47—41no—
102C2×C4×D47—41no—
103C2×C4×D47—41no—
104C2×C4×D47—41no—
105C2×C4×D47—41no—
106C2×C4×D47—41no—
107C2×C8×C47—22no—
108C2×C8×C47—22no—
109C2×C8×C47—41no—
110C2×C8×C47—41no—
111C2×C8×C47—41no—
112C2×C8×C47—41no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—41no—
116C4⋊C4×C47—41no—
117C42×C47—41no—
118C42×C47—41no—
119C42×C47C2×D411yescharacteristic
120C42×C47C2×D411yescharacteristic
121C42×C47#4111yescharacteristic
122C42×C47#4111yescharacteristic
123(C2×D47)⋊C4—24no—
124(C2×D47)⋊C4—24no—
125(C2×D47)⋊C4—42no—
126(C2×D47)⋊C4—41no—
127(C2×D47)⋊C4—41no—
128(C2×D47)⋊C4—42no—
129C4⋊Dic47—21no—
130C4⋊Dic47—21no—
131C4×Dic47—21no—
132C4×Dic47—21no—
133C4×Dic47—21no—
134C4×Dic47—21no—
135C4×Dic47—21no—
136C4×Dic47—21no—
137C4×Dic47—22no—
138C4×Dic47—41no—
139C4×Dic47C2×C812yes—
140C4×Dic47M1612yes—
141C2×C47⋊C8—22no—
142C2×C47⋊C8—22no—
143C2×C47⋊C8—41no—
144C2×C47⋊C8—41no—
145C2×C47⋊C8—41no—
146C2×C47⋊C8—41no—
147C23×C47C2×C22⋊C411yescharacteristic
148C22×D47—22no—
149C22×D47—41no—
150C22×D47—41no—
151C22×D47—41no—
152C22×D47—41no—
153C22×D47—41no—
154C22×D47—41no—
155Q8×C47—22no—
156Q8×C47—22no—
157Q8×C47—41no—
158Q8×C47—41no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—22no—
162C2×C4×C47—41no—
163C2×C4×C47—41no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47C4×D411yescharacteristic
168C2×C4×C47C4×D411yescharacteristic
169C2×C4×C47#12111yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47#12411yescharacteristic
172C2×C4×C47#12711yescharacteristic
173C2×C4×C47C22×C811yescharacteristic
174C2×C4×C47C2×M1611yescharacteristic
175C2×C4×C47#13111yescharacteristic
176C2×C4×C47#13111yescharacteristic
177C2×C4×C47#13511yescharacteristic
178C2×C4×C47#13511yescharacteristic
179C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C47#13711yescharacteristic
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47—21no—
190C2×Dic47—41no—
191C2×Dic47—41no—
192C2×Dic47—41no—
193C2×Dic47C22⋊C812yes—
194C2×Dic47C22⋊C812yes—
195C2×Dic47#10412yes—
196D188—22no—
197D188—22no—
198D188—41no—
199D188—41no—
200C4×D47—81no—
201C4×D47—81no—
202C4×D47—81no—
203C4×D47—81no—
204C8×C47—42no—
205C8×C47—42no—
206C47⋊C8—42no—
207C47⋊C8—42no—
208#9675—471nomaximal, Sylow
209C22×C47#39011yescharacteristic
210C22×C47C2×C22⋊C811yescharacteristic
211C22×C47#40811yescharacteristic
212C22×C47#41611yescharacteristic
213C22×C47#41711yescharacteristic
214C22×C47C2×#10411yescharacteristic
215C22×C47#42111yescharacteristic
216C2×D47—42no—
217C2×D47—42no—
218C2×D47—42no—
219C2×D47—81no—
220C2×D47—81no—
221C2×D47—81no—
222C2×D47—81no—
223C4×C47—21no—
224C4×C47—21no—
225C4×C47—42no—
226C4×C47—81no—
227C4×C47C8×D411yescharacteristic
228C4×C47C8×D411yescharacteristic
229C4×C47#43611yescharacteristic
230C4×C47#43611yescharacteristic
231C4×C47#46311yescharacteristic
232C4×C47#46311yescharacteristic
233C4×C47#46411yescharacteristic
234C4×C47#46411yescharacteristic
235Dic47—22no—
236Dic47—22no—
237Dic47—22no—
238Dic47—41no—
239Dic47—81no—
240C4×#124—471no—
241C4×C4⋊C8—471no—
242C4×C4⋊C8—471no—
243C2×Q8⋊C8—471no—
244C2×Q8⋊C8D4711yescharacteristic, complemented
245C2×D4⋊C8—471no—
246C2×D4⋊C8—471no—
247C2×C47#147611yescharacteristic
248C2×C47#147711yescharacteristic
249C2×C47#148211yescharacteristic
250C2×C47#148311yescharacteristic
251C2×C47#195411yescharacteristic
252C2×C47#198011yescharacteristic
253C2×C47#198311yescharacteristic
254D47—82no—
255C2×#124—471no—
256C2×C4×Q8C2×D4711yescharacteristic
257C2×C4×D4—471no—
258C2×C4⋊C8—471no—
259C2×C4⋊C8—941no—
260C2×C4⋊C8C2×D4711yescharacteristic
261C2×C4×C8—471no—
262C2×C4×C8—941no—
263C2×C4×C8C2×D4711yescharacteristic
264#391—471no—
265#390—471no—
266#388—941no—
267#388—941no—
268#382—471no—
269C4×C22⋊C4—941no—
270C4×C22⋊C4—941no—
271C43—471no—
272#336—941no—
273#336—941no—
274Q8⋊C8—22no—
275Q8⋊C8—942no—
276D4⋊C8—942no—
277D4⋊C8—942no—
278C47#967511yescharacteristic, complemented, Sylow
279C22×Q8C4×D4711yescharacteristic
280C22×D4—471no—
281C23×C4—941no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—941no—
285C22×C8—941no—
286#124—474no—
287#124—942no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×D4—941no—
293C4×D4—941no—
294C4×D4—941no—
295C4×D4—941no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—471no—
298C2×C4⋊C4C4×D4711yescharacteristic
299C2×C22⋊C4—941no—
300C2×C22⋊C4—941no—
301C2×C22⋊C4—941no—
302C2×C22⋊C4—941no—
303C2×C22⋊C4—941no—
304C2×C42—21no—
305C2×C42—471no—
306C2×C42—471no—
307C2×C42—471no—
308C2×C42—471no—
309C2×C42—471no—
310C2×C42—471no—
311C2×C42C22×D4711yescharacteristic
312C4⋊C8—21no—
313C4⋊C8—472no—
314C4⋊C8—944no—
315C4⋊C8—941no—
316C4⋊C8C22⋊D4712yes—
317C4×C8—21no—
318C4×C8—21no—
319C4×C8—941no—
320C4×C8—941no—
321C4×C8—1882no—
322#95—941no—
323#95—941no—
324#95—941no—
325#95—941no—
326C24—941no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8C8×D4712yes—
333C2×D4—472no—
334C2×D4—941no—
335C2×D4—941no—
336C2×D4—941no—
337C2×D4—941no—
338C2×D4—941no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—471no—
342C22×C4—471no—
343C22×C4—471no—
344C22×C4—471no—
345C22×C4—941no—
346C22×C4—1881no—
347C22×C4—1881no—
348C22×C4—1881no—
349C22×C4—1881no—
350C22×C4—1881no—
351C22×C4—1881no—
352C22×C4C2×C4×D4711yescharacteristic
353C22×C4D4×D4711yescharacteristic
354C22×C4D4×D4711yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—942no—
362C2×C8—942no—
363C2×C8—1881no—
364C2×C8—1881no—
365C2×C8—1881no—
366C2×C8—1881no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—941no—
372C4⋊C4—941no—
373C22⋊C4—944no—
374C22⋊C4—944no—
375C22⋊C4—1882no—
376C22⋊C4—1882no—
377C22⋊C4—1881no—
378C22⋊C4—1881no—
379C42—41no—
380C42—41no—
381C42—472no—
382C42—472no—
383C42—942no—
384C42—941no—
385C42—941no—
386C42—941no—
387C42—941no—
388C42—941no—
389C42—941no—
390C42—1881no—
391C42#1062535011yescharacteristic
392C42D4×D4711yescharacteristic
393C42#1062535211yescharacteristic
394C42C2×C22⋊D4711yescharacteristic
395C23—942no—
396C23—1881no—
397C23—1881no—
398C23—1881no—
399C23—1881no—
400C23—1881no—
401C23—1881no—
402C23C22⋊C4×D4711yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407D4—942no—
408D4—942no—
409D4—1881no—
410D4—1881no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—472no—
420C2×C4—472no—
421C2×C4—472no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—941no—
431C2×C4—3761no—
432C2×C4—3761no—
433C2×C4—3761no—
434C2×C4—3761no—
435C2×C4—1881no—
436C2×C4—1881no—
437C2×C4—1881no—
438C2×C4(C22⋊D47)⋊C411yescharacteristic
439C2×C4C4×C22⋊D4711yescharacteristic
440C2×C4#1309399611yescharacteristic
441C2×C4#1309399711yescharacteristic
442C2×C4#1309401011yescharacteristic
443C2×C4#1309402011yescharacteristic
444C2×C4C2×C8×D4711yescharacteristic
445C2×C4M16×D4711yescharacteristic
446C2×C4#1309403011yescharacteristic
447C2×C4#1309403211yescharacteristic
448C2×C4#1309404511yescharacteristic
449C2×C4#1309404711yescharacteristic
450C2×C4#1309405111yescharacteristic
451C2×C4#1309405611yescharacteristic
452C8—42no—
453C8—42no—
454C8—1882no—
455C8—1882no—
456C22—3761no—
457C22—3761no—
458C22—3761no—
459C22—3761no—
460C22—1882no—
461C22—1882no—
462C22—1882no—
463C22#1568902311yescharacteristic
464C22C22⋊C8×D4711yescharacteristic
465C22#1568908811yescharacteristic
466C22#1568911811yescharacteristic
467C22#1568912311yescharacteristic
468C22#104×D4711yescharacteristic
469C22#1568913811yescharacteristic
470C4—21no—
471C4—21no—
472C4—42no—
473C4—81no—
474C4—942no—
475C4—942no—
476C4—942no—
477C4—3761no—
478C4—1881no—
479C4(C22⋊D47)⋊C811yescharacteristic
480C4C8×C22⋊D4711yescharacteristic
481C4#1568919811yescharacteristic
482C4#1568919911yescharacteristic
483C4#1568934011yescharacteristic
484C4#1568934111yescharacteristic
485C4#1568934711yescharacteristic
486C4#1568934811yescharacteristic
487C2—3762no—
488C2#2024176911yescharacteristic
489C2#2024177411yescharacteristic
490C2#2024179511yescharacteristic
491C2#2024180011yescharacteristic
492C2#2024418011yescharacteristic
493C2#2024430511yescharacteristic
494C2#2024431711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#9675
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×Dic47C2semidirect
3. C4×Dic47⋊C8C2semidirect
4. C2×Q8⋊(C47⋊C8)C2semidirect
7. C2×C47×Q8⋊C8C2semidirect
36. #13094013C8semidirect
244. C2×Q8⋊C8D47semidirect
278. C47#9675semidirect

Maximal subgroups

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

subgroupindex
C4×#130940132
C4⋊C8×Dic472
C4×Dic47⋊C82
C2×Q8⋊(C47⋊C8)2
C2×#156888522
C2×#156888502
C2×C47×Q8⋊C82
#967547