Finite Group Databasebeta

← C47×#19720 #26059418

Subgroups — C47×#19720 #26059418

Order 12032.

656 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3231C211yesmaximal, characteristic
2C47×#3231C211yesmaximal, characteristic
3C47×#3229C211yesmaximal, characteristic
4C47×#3209C211yesmaximal, characteristic
5C47×#3185C211yesmaximal, characteristic
6C47×#3165C211yesmaximal, characteristic
7C47×#1723C211yesmaximal, characteristic, complemented
8C47×#1723C211yesmaximal, characteristic, complemented
9C47×#1718C211yesmaximal, characteristic, complemented
10C47×#1718C211yesmaximal, characteristic, complemented
11C47×#1716C211yesmaximal, characteristic, complemented
12C47×#1716C211yesmaximal, characteristic, complemented
13C47×#1707C211yesmaximal, characteristic, complemented
14C47×#1707C211yesmaximal, characteristic, complemented
15C47×#1453C211yesmaximal, characteristic
16C47×#533C2211yescharacteristic
17C47×#533C2211yescharacteristic
18C47×#533C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C47×#501—22no—
21C47×#500C2211yescharacteristic
22C47×#500C2211yescharacteristic
23C47×#500C2211yescharacteristic
24C47×#500C2211yescharacteristic
25C47×#498C2211yescharacteristic
26C47×#498C2211yescharacteristic
27C47×#498C2211yescharacteristic
28C47×#498C2211yescharacteristic
29C47×#498C2211yescharacteristic
30C47×#498C2211yescharacteristic
31C47×#498C2211yescharacteristic
32C47×#494C2211yescharacteristic
33C47×#494C2211yescharacteristic
34C47×#494C2211yescharacteristic
35C47×#487C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#487C2211yescharacteristic
38C47×#487C2211yescharacteristic
39C47×#487C2211yescharacteristic
40C47×#487C2211yescharacteristic
41C47×#487C2211yescharacteristic
42C47×#487C2211yescharacteristic
43C47×#487C2211yescharacteristic
44C47×#487C2211yescharacteristic
45C47×#485—22no—
46C47×#485—22no—
47C47×#483—22no—
48C47×#479—22no—
49C47×#479—22no—
50C47×#475—22no—
51C47×#470—22no—
52C47×#462—22no—
53C47×#451—22no—
54C47×#441—22no—
55C47×#431C2211yescharacteristic
56C47×#431C2211yescharacteristic
57C47×#428—22no—
58C4×M16×C47C2211yescharacteristic
59C47×#322C2211yescharacteristic
60C47×#322C2211yescharacteristic
61C47×#322C2211yescharacteristic
62C82×C47C2211yescharacteristic
63C22×Q8×C47—21no—
64C2×Q16×C47—22no—
65C2×Q16×C47—22no—
66C2×Q16×C47—22no—
67C2×M16×C47D412yes—
68C4⋊Q8×C47—21no—
69C4⋊Q8×C47—21no—
70C4⋊Q8×C47—21no—
71C4⋊Q8×C47C2311yescharacteristic
72C4⋊Q8×C47C2311yescharacteristic
73C4⋊Q8×C47C2311yescharacteristic
74C4⋊Q8×C47C2311yescharacteristic
75C4⋊Q8×C47C2311yescharacteristic
76C4⋊Q8×C47C2311yescharacteristic
77C4⋊Q8×C47C2311yescharacteristic
78C4⋊Q8×C47C2311yescharacteristic
79#125×C47—21no—
80#125×C47—21no—
81#125×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47—21no—
88C4×Q8×C47—21no—
89C4×Q8×C47—21no—
90C4×Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94#117×C47—21no—
95#117×C47—21no—
96#117×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C42×C47C2311yescharacteristic
100#107×C47—22no—
101#107×C47—22no—
102#107×C47—22no—
103#107×C47—22no—
104#106×C47—22no—
105#106×C47—22no—
106#106×C47—22no—
107#106×C47—22no—
108#106×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47D412yes—
112C4⋊C8×C47D412yes—
113#103×C47—22no—
114#103×C47—22no—
115#103×C47—22no—
116#103×C47—22no—
117#103×C47—22no—
118#103×C47—22no—
119#103×C47—22no—
120#103×C47—22no—
121#103×C47—22no—
122#103×C47—22no—
123C22⋊C8×C47D412yes—
124C22⋊C8×C47D412yes—
125#97×C47D412yes—
126C4×C8×C47C2311yescharacteristic
127C4×C8×C47C2311yescharacteristic
128C4×C8×C47C2311yescharacteristic
129C4×C8×C47C2311yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C4×C8×C47C2311yescharacteristic
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—41no—
141C2×Q8×C47—82no—
142C22×C4×C47—41no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146Q16×C47—44no—
147Q16×C47—82no—
148Q16×C47—82no—
149M16×C47—24no—
150C2×C8×C47C2×D412yes—
151C2×C8×C47C2×D412yes—
152C2×C8×C47C2×D412yes—
153C2×C8×C47C2×D412yes—
154C2×C8×C47C2×D412yes—
155C2×C8×C47C2×D412yes—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—41no—
173C4⋊C4×C47—41no—
174C4⋊C4×C47—41no—
175C4⋊C4×C47—41no—
176C4⋊C4×C47—41no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—41no—
182C22⋊C4×C47—41no—
183C42×C47—41no—
184C42×C47—41no—
185C42×C47—41no—
186C42×C47C2×D411yescharacteristic
187C42×C47C2×D411yescharacteristic
188C42×C47C2×D411yescharacteristic
189C42×C47C2411yescharacteristic
190C23×C47#12711yescharacteristic
191Q8×C47—42no—
192Q8×C47—42no—
193Q8×C47—42no—
194Q8×C47—42no—
195Q8×C47—42no—
196Q8×C47—42no—
197Q8×C47—42no—
198Q8×C47—42no—
199Q8×C47—82no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—82no—
212C2×C4×C47#12711yescharacteristic
213C2×C4×C47#12711yescharacteristic
214C2×C4×C47#12711yescharacteristic
215C2×C4×C47C22×D411yescharacteristic
216C2×C4×C47C22×D411yescharacteristic
217C2×C4×C47C22×D411yescharacteristic
218C8×C47—22no—
219C8×C47—22no—
220C8×C47—22no—
221C8×C47—22no—
222C8×C47—22no—
223C8×C47#13714yes—
224#19720C4711yesmaximal, characteristic, direct product factor, Sylow
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—21no—
228C22×C47C2×#12711yescharacteristic
229C4×C47—21no—
230C4×C47—21no—
231C4×C47—21no—
232C4×C47—81no—
233C4×C47—81no—
234C4×C47—81no—
235C4×C47—81no—
236C4×C47—81no—
237C4×C47—81no—
238C4×C47—81no—
239C4×C47—81no—
240C4×C47C2×#13712yes—
241C4×C47#57712yes—
242C4×C47#57812yes—
243#3231C2×C4711yescharacteristic
244#3231C2×C4711yescharacteristic
245#3229C2×C4711yescharacteristic
246#3209C2×C4711yescharacteristic
247#3185C2×C4711yescharacteristic
248#3165C2×C4711yescharacteristic
249#1723C2×C4711yescharacteristic, complemented
250#1723C2×C4711yescharacteristic, complemented
251#1718C2×C4711yescharacteristic, complemented
252#1718C2×C4711yescharacteristic, complemented
253#1716C2×C4711yescharacteristic, complemented
254#1716C2×C4711yescharacteristic, complemented
255#1707C2×C4711yescharacteristic, complemented
256#1707C2×C4711yescharacteristic, complemented
257#1453C2×C4711yescharacteristic
258C2×C47—41no—
259C2×C47#315211yescharacteristic
260C2×C47#315411yescharacteristic
261C2×C47#315611yescharacteristic
262#533C22×C4711yescharacteristic
263#533C22×C4711yescharacteristic
264#533C22×C4711yescharacteristic
265C2×C4⋊Q8C22×C4711yescharacteristic
266#501—22no—
267#500C22×C4711yescharacteristic
268#500C22×C4711yescharacteristic
269#500C22×C4711yescharacteristic
270#500C22×C4711yescharacteristic
271#498C22×C4711yescharacteristic
272#498C22×C4711yescharacteristic
273#498C22×C4711yescharacteristic
274#498C22×C4711yescharacteristic
275#498C22×C4711yescharacteristic
276#498C22×C4711yescharacteristic
277#498C22×C4711yescharacteristic
278#494C22×C4711yescharacteristic
279#494C22×C4711yescharacteristic
280#494C22×C4711yescharacteristic
281#487C22×C4711yescharacteristic
282#487C22×C4711yescharacteristic
283#487C22×C4711yescharacteristic
284#487C22×C4711yescharacteristic
285#487C22×C4711yescharacteristic
286#487C22×C4711yescharacteristic
287#487C22×C4711yescharacteristic
288#487C22×C4711yescharacteristic
289#487C22×C4711yescharacteristic
290#487C22×C4711yescharacteristic
291#485—22no—
292#485—22no—
293#483—22no—
294#479—22no—
295#479—22no—
296#475—22no—
297#470—22no—
298#462—22no—
299#451—22no—
300#441—22no—
301#431C22×C4711yescharacteristic
302#431C22×C4711yescharacteristic
303#428—22no—
304C4×M16C22×C4711yescharacteristic
305#322C22×C4711yescharacteristic
306#322C22×C4711yescharacteristic
307#322C22×C4711yescharacteristic
308C82C22×C4711yescharacteristic
309C47#1972011yescharacteristic, direct product factor, Sylow
310C22×Q8—21no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—22no—
314C2×M16D4×C4712yes—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8C23×C4711yescharacteristic
319C4⋊Q8C23×C4711yescharacteristic
320C4⋊Q8C23×C4711yescharacteristic
321C4⋊Q8C23×C4711yescharacteristic
322C4⋊Q8C23×C4711yescharacteristic
323C4⋊Q8C23×C4711yescharacteristic
324C4⋊Q8C23×C4711yescharacteristic
325C4⋊Q8C23×C4711yescharacteristic
326#125—21no—
327#125—21no—
328#125—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341#117—21no—
342#117—21no—
343#117—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C42C23×C4711yescharacteristic
347#107—22no—
348#107—22no—
349#107—22no—
350#107—22no—
351#106—22no—
352#106—22no—
353#106—22no—
354#106—22no—
355#106—22no—
356#106—22no—
357#106—22no—
358C4⋊C8D4×C4712yes—
359C4⋊C8D4×C4712yes—
360#103—22no—
361#103—22no—
362#103—22no—
363#103—22no—
364#103—22no—
365#103—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370C22⋊C8D4×C4712yes—
371C22⋊C8D4×C4712yes—
372#97D4×C4712yes—
373C4×C8C23×C4711yescharacteristic
374C4×C8C23×C4711yescharacteristic
375C4×C8C23×C4711yescharacteristic
376C4×C8C23×C4711yescharacteristic
377C4×C8C23×C4711yescharacteristic
378C4×C8C23×C4711yescharacteristic
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—41no—
388C2×Q8—82no—
389C22×C4—41no—
390C22×C4C2×D4×C4711yescharacteristic
391C22×C4C2×D4×C4711yescharacteristic
392C22×C4C2×D4×C4711yescharacteristic
393Q16—44no—
394Q16—82no—
395Q16—82no—
396M16—24no—
397C2×C8C2×D4×C4712yes—
398C2×C8C2×D4×C4712yes—
399C2×C8C2×D4×C4712yes—
400C2×C8C2×D4×C4712yes—
401C2×C8C2×D4×C4712yes—
402C2×C8C2×D4×C4712yes—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C42—41no—
431C42—41no—
432C42—41no—
433C42C2×D4×C4711yescharacteristic
434C42C2×D4×C4711yescharacteristic
435C42C2×D4×C4711yescharacteristic
436C42C24×C4711yescharacteristic
437C23#127×C4711yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—42no—
446Q8—82no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—82no—
459C2×C4#127×C4711yescharacteristic
460C2×C4#127×C4711yescharacteristic
461C2×C4#127×C4711yescharacteristic
462C2×C4C22×D4×C4711yescharacteristic
463C2×C4C22×D4×C4711yescharacteristic
464C2×C4C22×D4×C4711yescharacteristic
465C8—22no—
466C8—22no—
467C8—22no—
468C8—22no—
469C8—22no—
470C8#137×C4714yes—
471C22—21no—
472C22—21no—
473C22—21no—
474C22C2×#127×C4711yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4C2×#137×C4712yes—
487C4C47×#57712yes—
488C4C47×#57812yes—
489C2—41no—
490C2C47×#315211yescharacteristic
491C2C47×#315411yescharacteristic
492C2C47×#315611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#127
commutator, Frattini, cosocleC42C24×C47
prime radicalC23×C47#127
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
7. C47×#1723C2semidirect
8. C47×#1723C2semidirect
9. C47×#1718C2semidirect
10. C47×#1718C2semidirect
11. C47×#1716C2semidirect
12. C47×#1716C2semidirect
13. C47×#1707C2semidirect
14. C47×#1707C2semidirect
224. #19720C47direct (N × H)
249. #1723C2×C47semidirect
250. #1723C2×C47semidirect
251. #1718C2×C47semidirect
252. #1718C2×C47semidirect
253. #1716C2×C47semidirect
254. #1716C2×C47semidirect
255. #1707C2×C47semidirect
256. #1707C2×C47semidirect
309. C47#19720direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32312
C47×#32292
C47×#32092
C47×#31852
C47×#31652
C47×#17232
C47×#17182
C47×#17162
C47×#17072
C47×#14532
#1972047