Finite Group Databasebeta

← C127×#10560 #44574233

Subgroups — C127×#10560 #44574233

Order 32512.

490 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3192C211yesmaximal, characteristic
2C127×#1900C211yesmaximal, characteristic, complemented
3C127×#1895C211yesmaximal, characteristic, complemented
4C127×#1855C211yesmaximal, characteristic, complemented
5C127×#1519C211yesmaximal, characteristic, complemented
6C127×#1471C211yesmaximal, characteristic, complemented
7C127×#1305C211yesmaximal, characteristic, complemented
8C22×M16×C127C2211yescharacteristic
9C2×#121×C127C2211yescharacteristic
10C2×#121×C127C2211yescharacteristic
11#481×C127—21no—
12#481×C127—21no—
13#469×C127—21no—
14#469×C127—21no—
15#447×C127—21no—
16#447×C127—21no—
17C2×#108×C127—21no—
18C2×#102×C127—21no—
19C2×#100×C127—21no—
20#407×C127C2211yescharacteristic
21#407×C127C2211yescharacteristic
22C2×C22⋊C8×C127C2211yescharacteristic
23#380×C127C2211yescharacteristic
24#343×C127—21no—
25#341×C127—21no—
26#340×C127—21no—
27#327×C127—22no—
28#323×C127—22no—
29C22×D4×C127—21no—
30C22×D4×C127—21no—
31C22×D4×C127D411yescharacteristic
32C22×D4×C127D411yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C2×D8×C127—21no—
35C2×D8×C127—21no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—42no—
40C2×M16×C127D411yescharacteristic
41C2×M16×C127D411yescharacteristic
42C22×C8×C127—21no—
43C22×C8×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46#121×C127—21no—
47#121×C127—21no—
48#121×C127—21no—
49#121×C127—21no—
50#121×C127—21no—
51#121×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127D411yescharacteristic
54C2×C4⋊C4×C127D411yescharacteristic
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58#108×C127—42no—
59#106×C127—21no—
60#106×C127—21no—
61#102×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64#102×C127—21no—
65#102×C127—42no—
66#100×C127—42no—
67C22⋊C8×C127—21no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127—21no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127D412yes—
73#95×C127—21no—
74C24×C127—21no—
75C24×C127—21no—
76C24×C127#4111yescharacteristic
77C2×D4×C127—21no—
78C2×D4×C127—21no—
79C2×D4×C127—21no—
80C2×D4×C127—21no—
81C2×D4×C127—41no—
82C2×D4×C127—41no—
83C2×D4×C127—41no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—41no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—81no—
90C2×D4×C127—81no—
91C2×D4×C127—82no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×D411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127#4111yescharacteristic
102C22×C4×C127#4111yescharacteristic
103D8×C127—81no—
104D8×C127—81no—
105M16×C127—22no—
106M16×C127—22no—
107M16×C127—41no—
108M16×C127—41no—
109M16×C127—41no—
110M16×C127—41no—
111M16×C127—41no—
112M16×C127—41no—
113C2×C8×C127—22no—
114C2×C8×C127—21no—
115C2×C8×C127—21no—
116C2×C8×C127—22no—
117C2×C8×C127—41no—
118C2×C8×C127—41no—
119C2×C8×C127—41no—
120C2×C8×C127—41no—
121C2×C8×C127—41no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—21no—
124C4⋊C4×C127—21no—
125C4⋊C4×C127—21no—
126C4⋊C4×C127—41no—
127C4⋊C4×C127—41no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C22⋊C4×C127—41no—
132C22⋊C4×C127—81no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—42no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—81no—
143C23×C127—81no—
144C23×C127—81no—
145C23×C127—81no—
146C23×C127#12111yescharacteristic
147C23×C127#12311yescharacteristic
148C23×C127#12411yescharacteristic
149D4×C127—42no—
150D4×C127—41no—
151D4×C127—41no—
152D4×C127—41no—
153D4×C127—41no—
154D4×C127—81no—
155D4×C127—82no—
156D4×C127—82no—
157D4×C127—82no—
158D4×C127—81no—
159D4×C127—81no—
160C2×C4×C127—21no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—21no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127—81no—
174C2×C4×C127—81no—
175C2×C4×C127—81no—
176C2×C4×C127#12011yescharacteristic
177C2×C4×C127#12111yescharacteristic
178C2×C4×C127#12111yescharacteristic
179C2×C4×C127#12311yescharacteristic
180C8×C127—42no—
181C8×C127—42no—
182C8×C127—41no—
183C8×C127—41no—
184C8×C127—81no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127—161no—
202C22×C127—161no—
203C22×C127—162no—
204C22×C127#39411yescharacteristic
205C22×C127#47111yescharacteristic
206C22×C127#47211yescharacteristic
207C4×C127—21no—
208C4×C127—21no—
209C4×C127—21no—
210C4×C127—81no—
211C4×C127—81no—
212C4×C127—161no—
213C4×C127B(4,𝔽2)11yescharacteristic
214C4×C127#45811yescharacteristic
215#10560C12711yesmaximal, characteristic, direct product factor, Sylow
216C2×C127—21no—
217C2×C127—21no—
218C2×C127—41no—
219C2×C127—41no—
220C2×C127—161no—
221C2×C127—161no—
222C2×C127#204411yescharacteristic
223C2×C127#204811yescharacteristic
224C2×C127#205111yescharacteristic
225#3192C2×C12711yescharacteristic
226#1900C2×C12711yescharacteristic, complemented
227#1895C2×C12711yescharacteristic, complemented
228#1855C2×C12711yescharacteristic, complemented
229#1519C2×C12711yescharacteristic, complemented
230#1471C2×C12711yescharacteristic, complemented
231#1305C2×C12711yescharacteristic, complemented
232C127#1056011yescharacteristic, direct product factor, Sylow
233C22×M16C22×C12711yescharacteristic
234C2×#121C22×C12711yescharacteristic
235C2×#121C22×C12711yescharacteristic
236#481—21no—
237#481—21no—
238#469—21no—
239#469—21no—
240#447—21no—
241#447—21no—
242C2×#108—21no—
243C2×#102—21no—
244C2×#100—21no—
245#407C22×C12711yescharacteristic
246#407C22×C12711yescharacteristic
247C2×C22⋊C8C22×C12711yescharacteristic
248#380C22×C12711yescharacteristic
249#343—21no—
250#341—21no—
251#340—21no—
252#327—22no—
253#323—22no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C12711yescharacteristic
257C22×D4D4×C12711yescharacteristic
258C23×C4C23×C12711yescharacteristic
259C2×D8—21no—
260C2×D8—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—42no—
265C2×M16D4×C12711yescharacteristic
266C2×M16D4×C12711yescharacteristic
267C22×C8—21no—
268C22×C8—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276#121—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4D4×C12711yescharacteristic
279C2×C4⋊C4D4×C12711yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283#108—42no—
284#106—21no—
285#106—21no—
286#102—21no—
287#102—21no—
288#102—21no—
289#102—21no—
290#102—42no—
291#100—42no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8D4×C12712yes—
298#95—21no—
299C24—21no—
300C24—21no—
301C24#41×C12711yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—81no—
315C2×D4—81no—
316C2×D4—82no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4C2×D4×C12711yescharacteristic
323C22×C4C2×D4×C12711yescharacteristic
324C22×C4C2×D4×C12711yescharacteristic
325C22×C4C2×D4×C12711yescharacteristic
326C22×C4#41×C12711yescharacteristic
327C22×C4#41×C12711yescharacteristic
328D8—81no—
329D8—81no—
330M16—22no—
331M16—22no—
332M16—41no—
333M16—41no—
334M16—41no—
335M16—41no—
336M16—41no—
337M16—41no—
338C2×C8—22no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—81no—
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23#121×C12711yescharacteristic
372C23#123×C12711yescharacteristic
373C23#124×C12711yescharacteristic
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—82no—
381D4—82no—
382D4—82no—
383D4—81no—
384D4—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4#120×C12711yescharacteristic
402C2×C4#121×C12711yescharacteristic
403C2×C4#121×C12711yescharacteristic
404C2×C4#123×C12711yescharacteristic
405C8—42no—
406C8—42no—
407C8—41no—
408C8—41no—
409C8—81no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—161no—
427C22—161no—
428C22—162no—
429C22#394×C12711yescharacteristic
430C22#471×C12711yescharacteristic
431C22#472×C12711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—81no—
436C4—81no—
437C4—161no—
438C4B(4,𝔽2)×C12711yescharacteristic
439C4#458×C12711yescharacteristic
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—161no—
445C2—161no—
446C2C127×#204411yescharacteristic
447C2C127×#204811yescharacteristic
448C2C127×#205111yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC127×#3192C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1900C2semidirect
3. C127×#1895C2semidirect
4. C127×#1855C2semidirect
5. C127×#1519C2semidirect
6. C127×#1471C2semidirect
7. C127×#1305C2semidirect
215. #10560C127direct (N × H)
226. #1900C2×C127semidirect
227. #1895C2×C127semidirect
228. #1855C2×C127semidirect
229. #1519C2×C127semidirect
230. #1471C2×C127semidirect
231. #1305C2×C127semidirect
232. C127#10560direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31922
C127×#19002
C127×#18952
C127×#18552
C127×#15192
C127×#14712
C127×#13052
#10560127