Finite Group Databasebeta

← C127×#19573 #44583246

Subgroups — C127×#19573 #44583246

Order 32512.

572 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3254C211yesmaximal, characteristic
2C127×#3230C211yesmaximal, characteristic, complemented
3C127×#3226C211yesmaximal, characteristic
4C127×#2986C211yesmaximal, characteristic, complemented
5C127×#1698C212yesmaximal, complemented
6C127×#1696C212yesmaximal, complemented
7C127×#1678C212yesmaximal, complemented
8C127×#1676C212yesmaximal, complemented
9C127×#1574C211yesmaximal, characteristic, complemented
10C127×#1548C211yesmaximal, characteristic, complemented
11C127×#1543C211yesmaximal, characteristic
12#533×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4⋊Q8×C127C2211yescharacteristic
15#500×C127—21no—
16#500×C127C2212yes—
17#487×C127—21no—
18#486×C127C2212yes—
19#484×C127—22no—
20#480×C127—22no—
21#477×C127C2212yes—
22#477×C127C2212yes—
23#477×C127C2212yes—
24#474×C127—21no—
25#474×C127—21no—
26#474×C127—21no—
27#468×C127—22no—
28#461×C127—21no—
29#460×C127C2212yes—
30#446×C127—21no—
31#446×C127C2212yes—
32C8×Q8×C127—21no—
33C8×Q8×C127C2212yes—
34#433×C127—22no—
35#431×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#423×C127C2211yescharacteristic
39#335×C127C2212yes—
40#334×C127C2212yes—
41#333×C127C2212yes—
42#333×C127C2212yes—
43#333×C127C2211yescharacteristic
44#333×C127C2211yescharacteristic
45#331×C127C2211yescharacteristic
46#331×C127C2211yescharacteristic
47C2×#41×C127—21no—
48C22×Q8×C127—21no—
49C2×SD16×C127—22no—
50C2×M16×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127D411yescharacteristic
55C4⋊Q8×C127D411yescharacteristic
56C4⋊Q8×C127C2311yescharacteristic
57C4⋊Q8×C127C2312yes—
58#127×C127C2311yescharacteristic
59#125×C127—21no—
60#124×C127—21no—
61C22⋊Q8×C127—21no—
62C22⋊Q8×C127D412yes—
63#121×C127—21no—
64#121×C127—21no—
65C4×Q8×C127—21no—
66C4×Q8×C127C2312yes—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69#117×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C4⋊C4×C127—21no—
72C2×C42×C127C2311yescharacteristic
73#107×C127—22no—
74#107×C127—22no—
75#107×C127—22no—
76#107×C127—22no—
77#107×C127—22no—
78C4⋊C8×C127—22no—
79C4⋊C8×C127—22no—
80C4⋊C8×C127—21no—
81C4⋊C8×C127D411yescharacteristic
82C4⋊C8×C127D411yescharacteristic
83C4⋊C8×C127C2311yescharacteristic
84C4⋊C8×C127C2311yescharacteristic
85C4⋊C8×C127C2311yescharacteristic
86C4⋊C8×C127C2311yescharacteristic
87C4⋊C8×C127C2312yes—
88#103×C127—22no—
89#103×C127—22no—
90#103×C127—22no—
91#102×C127—22no—
92#102×C127—22no—
93#102×C127—22no—
94C22⋊C8×C127—21no—
95C22⋊C8×C127—21no—
96C22⋊C8×C127D412yes—
97#97×C127—22no—
98C4×C8×C127—22no—
99C4×C8×C127—21no—
100C4×C8×C127—21no—
101C4×C8×C127C2312yes—
102#41×C127—82no—
103C2×Q8×C127—21no—
104C2×Q8×C127—21no—
105C2×Q8×C127—22no—
106C2×Q8×C127—41no—
107C2×Q8×C127—82no—
108C2×Q8×C127C2×D412yes—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—21no—
112C2×D4×C127—41no—
113C22×C4×C127—41no—
114C22×C4×C127—41no—
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127C2×D411yescharacteristic
117C22×C4×C127#4111yescharacteristic
118SD16×C127—82no—
119M16×C127—81no—
120C2×C8×C127—21no—
121C2×C8×C127—21no—
122C2×C8×C127—21no—
123C2×C8×C127—21no—
124C2×C8×C127—22no—
125C2×C8×C127C2×D412yes—
126C2×C8×C127C2×D412yes—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—41no—
137C4⋊C4×C127—41no—
138C4⋊C4×C127C2×D412yes—
139C22⋊C4×C127—22no—
140C22⋊C4×C127—41no—
141C22⋊C4×C127—41no—
142C42×C127—22no—
143C42×C127C2×D411yescharacteristic
144C42×C127C2×D411yescharacteristic
145C42×C127#4111yescharacteristic
146C42×C127C2411yescharacteristic
147C23×C127—41no—
148C23×C127#12111yescharacteristic
149Q8×C127—22no—
150Q8×C127—22no—
151Q8×C127—42no—
152Q8×C127—82no—
153Q8×C127—81no—
154Q8×C127—82no—
155D4×C127—41no—
156D4×C127—41no—
157D4×C127—41no—
158D4×C127—41no—
159D4×C127—81no—
160D4×C127—82no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—41no—
169C2×C4×C127—42no—
170C2×C4×C127—82no—
171C2×C4×C127—82no—
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127#12111yescharacteristic
174C2×C4×C127#12111yescharacteristic
175C2×C4×C127C22×D411yescharacteristic
176C2×C4×C127C22×D411yescharacteristic
177C2×C4×C127C2×#4111yescharacteristic
178C8×C127—22no—
179C8×C127—22no—
180C8×C127—41no—
181C8×C127—42no—
182C8×C127—41no—
183C8×C127—41no—
184C8×C127—41no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—81no—
189C22×C127—81no—
190C22×C127—81no—
191C22×C127C2×#12111yescharacteristic
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—42no—
196C4×C127—42no—
197C4×C127—81no—
198C4×C127—82no—
199C4×C127#47212yes—
200C4×C127#57711yescharacteristic
201C4×C127#57811yescharacteristic
202C4×C127#57811yescharacteristic
203C4×C127#57811yescharacteristic
204#19573C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—41no—
206C2×C127—161no—
207C2×C127#304411yescharacteristic
208C2×C127#306311yescharacteristic
209C2×C127C2×#47211yescharacteristic
210#3254C2×C12711yescharacteristic
211#3230C2×C12711yescharacteristic, complemented
212#3226C2×C12711yescharacteristic
213#2986C2×C12711yescharacteristic, complemented
214#1698C2×C12712yescomplemented
215#1696C2×C12712yescomplemented
216#1678C2×C12712yescomplemented
217#1676C2×C12712yescomplemented
218#1574C2×C12711yescharacteristic, complemented
219#1548C2×C12711yescharacteristic, complemented
220#1543C2×C12711yescharacteristic
221C127#1957311yescharacteristic, direct product factor, Sylow
222#533C22×C12711yescharacteristic
223#532C22×C12711yescharacteristic
224C2×C4⋊Q8C22×C12711yescharacteristic
225#500—21no—
226#500C22×C12712yes—
227#487—21no—
228#486C22×C12712yes—
229#484—22no—
230#480—22no—
231#477C22×C12712yes—
232#477C22×C12712yes—
233#477C22×C12712yes—
234#474—21no—
235#474—21no—
236#474—21no—
237#468—22no—
238#461—21no—
239#460C22×C12712yes—
240#446—21no—
241#446C22×C12712yes—
242C8×Q8—21no—
243C8×Q8C22×C12712yes—
244#433—22no—
245#431C22×C12711yescharacteristic
246#431C22×C12711yescharacteristic
247#431C22×C12711yescharacteristic
248#423C22×C12711yescharacteristic
249#335C22×C12712yes—
250#334C22×C12712yes—
251#333C22×C12711yescharacteristic
252#333C22×C12711yescharacteristic
253#333C22×C12712yes—
254#333C22×C12712yes—
255#331C22×C12711yescharacteristic
256#331C22×C12711yescharacteristic
257C2×#41—21no—
258C22×Q8—21no—
259C2×SD16—22no—
260C2×M16—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8D4×C12711yescharacteristic
265C4⋊Q8D4×C12711yescharacteristic
266C4⋊Q8C23×C12712yes—
267C4⋊Q8C23×C12711yescharacteristic
268#127C23×C12711yescharacteristic
269#125—21no—
270#124—21no—
271C22⋊Q8—21no—
272C22⋊Q8D4×C12712yes—
273#121—21no—
274#121—21no—
275C4×Q8—21no—
276C4×Q8C23×C12712yes—
277C4×D4—21no—
278C4×D4—21no—
279#117—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C42C23×C12711yescharacteristic
283#107—22no—
284#107—22no—
285#107—22no—
286#107—22no—
287#107—22no—
288C4⋊C8—22no—
289C4⋊C8—22no—
290C4⋊C8—21no—
291C4⋊C8D4×C12711yescharacteristic
292C4⋊C8D4×C12711yescharacteristic
293C4⋊C8C23×C12711yescharacteristic
294C4⋊C8C23×C12711yescharacteristic
295C4⋊C8C23×C12711yescharacteristic
296C4⋊C8C23×C12711yescharacteristic
297C4⋊C8C23×C12712yes—
298#103—22no—
299#103—22no—
300#103—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8D4×C12712yes—
307#97—22no—
308C4×C8—22no—
309C4×C8—21no—
310C4×C8—21no—
311C4×C8C23×C12712yes—
312#41—82no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—22no—
316C2×Q8—41no—
317C2×Q8—82no—
318C2×Q8C2×D4×C12712yes—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4C2×D4×C12711yescharacteristic
326C22×C4C2×D4×C12711yescharacteristic
327C22×C4#41×C12711yescharacteristic
328SD16—82no—
329M16—81no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—22no—
335C2×C8C2×D4×C12712yes—
336C2×C8C2×D4×C12712yes—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4C2×D4×C12712yes—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—22no—
353C42C2×D4×C12711yescharacteristic
354C42C2×D4×C12711yescharacteristic
355C42#41×C12711yescharacteristic
356C42C24×C12711yescharacteristic
357C23—41no—
358C23#121×C12711yescharacteristic
359Q8—22no—
360Q8—22no—
361Q8—42no—
362Q8—82no—
363Q8—81no—
364Q8—82no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4#121×C12711yescharacteristic
383C2×C4#121×C12711yescharacteristic
384C2×C4#121×C12711yescharacteristic
385C2×C4C22×D4×C12711yescharacteristic
386C2×C4C22×D4×C12711yescharacteristic
387C2×C4C2×#41×C12711yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—41no—
392C8—41no—
393C8—41no—
394C8—41no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22C2×#121×C12711yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—42no—
406C4—42no—
407C4—81no—
408C4—82no—
409C4#472×C12712yes—
410C4#577×C12711yescharacteristic
411C4#578×C12711yescharacteristic
412C4#578×C12711yescharacteristic
413C4#578×C12711yescharacteristic
414C2—41no—
415C2—161no—
416C2C127×#304411yescharacteristic
417C2C127×#306311yescharacteristic
418C2C2×#472×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3230C2semidirect
4. C127×#2986C2semidirect
5. C127×#1698C2semidirect
6. C127×#1696C2semidirect
7. C127×#1678C2semidirect
8. C127×#1676C2semidirect
9. C127×#1574C2semidirect
10. C127×#1548C2semidirect
204. #19573C127direct (N × H)
211. #3230C2×C127semidirect
213. #2986C2×C127semidirect
214. #1698C2×C127semidirect
215. #1696C2×C127semidirect
216. #1678C2×C127semidirect
217. #1676C2×C127semidirect
218. #1574C2×C127semidirect
219. #1548C2×C127semidirect
221. C127#19573direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32542
C127×#32302
C127×#32262
C127×#29862
C127×#16982
C127×#16962
C127×#16782
C127×#16762
C127×#15742
C127×#15482
C127×#15432
#19573127