Finite Group Databasebeta

← C127×#13430 #44577103

Subgroups — C127×#13430 #44577103

Order 32512.

418 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3200C211yesmaximal, characteristic
2C127×#2135C211yesmaximal, characteristic, complemented
3C127×#2134C211yesmaximal, characteristic
4C127×#1915C211yesmaximal, characteristic, complemented
5C127×#1914C211yesmaximal, characteristic
6C127×#1858C211yesmaximal, characteristic, complemented
7C127×#1392C211yesmaximal, characteristic, complemented
8#568×C127C2211yescharacteristic
9#536×C127C2211yescharacteristic
10#535×C127C2211yescharacteristic
11#485×C127—21no—
12#482×C127—21no—
13#468×C127—21no—
14#465×C127—21no—
15#450×C127—21no—
16#448×C127—21no—
17#430×C127—21no—
18#413×C127C2211yescharacteristic
19#413×C127C2211yescharacteristic
20#413×C127C2211yescharacteristic
21C2×#101×C127—21no—
22C2×#100×C127—21no—
23#408×C127C2211yescharacteristic
24#356×C127—22no—
25#355×C127—22no—
26#344×C127—21no—
27#344×C127—21no—
28#341×C127—21no—
29C2×#41×C127C2311yescharacteristic
30C22×Q8×C127D411yescharacteristic
31C22×D4×C127D411yescharacteristic
32C2×SD16×C127—21no—
33C2×SD16×C127—21no—
34#131×C127—42no—
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C2×M16×C127D411yescharacteristic
42C22×C8×C127D411yescharacteristic
43C4⋊Q8×C127—21no—
44#127×C127—21no—
45#124×C127—21no—
46#124×C127—21no—
47#123×C127—21no—
48#123×C127—21no—
49C22⋊Q8×C127—21no—
50C22⋊Q8×C127—21no—
51#121×C127—21no—
52#121×C127—21no—
53#120×C127—21no—
54#120×C127—21no—
55#117×C127D411yescharacteristic
56#117×C127D411yescharacteristic
57#108×C127—42no—
58#107×C127—21no—
59#106×C127—21no—
60#103×C127—21no—
61#103×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64#101×C127—21no—
65#101×C127—21no—
66#101×C127—42no—
67#101×C127D412yes—
68#100×C127—21no—
69#100×C127—21no—
70#100×C127—21no—
71#100×C127—42no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C24×C127—21no—
75#41×C127—41no—
76#41×C127—41no—
77C2×Q8×C127—21no—
78C2×Q8×C127—21no—
79C2×Q8×C127—41no—
80C2×Q8×C127—41no—
81C2×Q8×C127C2×D411yescharacteristic
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—41no—
87C2×D4×C127—41no—
88C2×D4×C127#4111yescharacteristic
89C2×D4×C127#4111yescharacteristic
90C2×D4×C127#4111yescharacteristic
91C22×C4×C127—21no—
92C22×C4×C127C2×D411yescharacteristic
93C22×C4×C127C2×D411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95SD16×C127—81no—
96SD16×C127—81no—
97M16×C127—22no—
98M16×C127—22no—
99M16×C127—22no—
100M16×C127—22no—
101M16×C127—41no—
102M16×C127—41no—
103M16×C127—41no—
104M16×C127—41no—
105M16×C127—41no—
106M16×C127—41no—
107M16×C127—41no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C22⋊C4×C127—21no—
122C22⋊C4×C127—21no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C42×C127—21no—
128C42×C127—21no—
129C23×C127—42no—
130C23×C127—41no—
131C23×C127—161no—
132C23×C127#12311yescharacteristic
133C23×C127#12311yescharacteristic
134C23×C127#12411yescharacteristic
135Q8×C127—41no—
136Q8×C127—41no—
137Q8×C127—41no—
138Q8×C127—81no—
139D4×C127—41no—
140D4×C127—41no—
141D4×C127—41no—
142D4×C127—41no—
143D4×C127—41no—
144D4×C127—81no—
145D4×C127—161no—
146D4×C127—161no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—42no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127#12011yescharacteristic
158C2×C4×C127#12111yescharacteristic
159C2×C4×C127#12111yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C8×C127—42no—
162C8×C127—41no—
163C8×C127—42no—
164C8×C127—41no—
165C8×C127—81no—
166C8×C127—81no—
167C22×C127—21no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—162no—
177C22×C127#39411yescharacteristic
178C4×C127—21no—
179C4×C127—21no—
180C4×C127—21no—
181C4×C127—81no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127B(4,𝔽2)11yescharacteristic
185C4×C127#45811yescharacteristic
186#13430C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127—21no—
188C2×C127—41no—
189C2×C127—41no—
190C2×C127—41no—
191C2×C127—161no—
192C2×C127#204411yescharacteristic
193#3200C2×C12711yescharacteristic
194#2135C2×C12711yescharacteristic, complemented
195#2134C2×C12711yescharacteristic
196#1915C2×C12711yescharacteristic, complemented
197#1914C2×C12711yescharacteristic
198#1858C2×C12711yescharacteristic, complemented
199#1392C2×C12711yescharacteristic, complemented
200C127#1343011yescharacteristic, direct product factor, Sylow
201#568C22×C12711yescharacteristic
202#536C22×C12711yescharacteristic
203#535C22×C12711yescharacteristic
204#485—21no—
205#482—21no—
206#468—21no—
207#465—21no—
208#450—21no—
209#448—21no—
210#430—21no—
211#413C22×C12711yescharacteristic
212#413C22×C12711yescharacteristic
213#413C22×C12711yescharacteristic
214C2×#101—21no—
215C2×#100—21no—
216#408C22×C12711yescharacteristic
217#356—22no—
218#355—22no—
219#344—21no—
220#344—21no—
221#341—21no—
222C2×#41C23×C12711yescharacteristic
223C22×Q8D4×C12711yescharacteristic
224C22×D4D4×C12711yescharacteristic
225C2×SD16—21no—
226C2×SD16—21no—
227#131—42no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16D4×C12711yescharacteristic
235C22×C8D4×C12711yescharacteristic
236C4⋊Q8—21no—
237#127—21no—
238#124—21no—
239#124—21no—
240#123—21no—
241#123—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244#121—21no—
245#121—21no—
246#120—21no—
247#120—21no—
248#117D4×C12711yescharacteristic
249#117D4×C12711yescharacteristic
250#108—42no—
251#107—21no—
252#106—21no—
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257#101—21no—
258#101—21no—
259#101—42no—
260#101D4×C12712yes—
261#100—21no—
262#100—21no—
263#100—21no—
264#100—42no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C24—21no—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8C2×D4×C12711yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4#41×C12711yescharacteristic
282C2×D4#41×C12711yescharacteristic
283C2×D4#41×C12711yescharacteristic
284C22×C4—21no—
285C22×C4C2×D4×C12711yescharacteristic
286C22×C4C2×D4×C12711yescharacteristic
287C22×C4C2×D4×C12711yescharacteristic
288SD16—81no—
289SD16—81no—
290M16—22no—
291M16—22no—
292M16—22no—
293M16—22no—
294M16—41no—
295M16—41no—
296M16—41no—
297M16—41no—
298M16—41no—
299M16—41no—
300M16—41no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—21no—
321C42—21no—
322C23—42no—
323C23—41no—
324C23—161no—
325C23#123×C12711yescharacteristic
326C23#123×C12711yescharacteristic
327C23#124×C12711yescharacteristic
328Q8—41no—
329Q8—41no—
330Q8—41no—
331Q8—81no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—81no—
338D4—161no—
339D4—161no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4#120×C12711yescharacteristic
351C2×C4#121×C12711yescharacteristic
352C2×C4#121×C12711yescharacteristic
353C2×C4#121×C12711yescharacteristic
354C8—42no—
355C8—41no—
356C8—42no—
357C8—41no—
358C8—81no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—162no—
370C22#394×C12711yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4B(4,𝔽2)×C12711yescharacteristic
378C4#458×C12711yescharacteristic
379C2—21no—
380C2—41no—
381C2—41no—
382C2—41no—
383C2—161no—
384C2C127×#204411yescharacteristic
subgroupG/H
center, socleC2×C127#2044
commutator, Frattini, cosocleC2×#41C23×C127
prime radical#535×C127C22
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2135C2semidirect
4. C127×#1915C2semidirect
6. C127×#1858C2semidirect
7. C127×#1392C2semidirect
186. #13430C127direct (N × H)
194. #2135C2×C127semidirect
196. #1915C2×C127semidirect
198. #1858C2×C127semidirect
199. #1392C2×C127semidirect
200. C127#13430direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32002
C127×#21352
C127×#21342
C127×#19152
C127×#19142
C127×#18582
C127×#13922
#13430127