Finite Group Databasebeta

← C127×#13432 #44577105

Subgroups — C127×#13432 #44577105

Order 32512.

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

normal subgroups only

This group has 440 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×#3199C211yesmaximal, characteristic
2C127×#2128C211yesmaximal, characteristic, complemented
3C127×#2122C211yesmaximal, characteristic, complemented
4C127×#1914C211yesmaximal, characteristic, complemented
5C127×#1910C211yesmaximal, characteristic, complemented
6C127×#1868C211yesmaximal, characteristic, complemented
7C127×#1395C211yesmaximal, characteristic, complemented
8#568×C127C2211yescharacteristic
9#535×C127C2211yescharacteristic
10#535×C127C2211yescharacteristic
11#482×C127—21no—
12#482×C127—21no—
13#469×C127—21no—
14#466×C127—21no—
15#447×C127—21no—
16#447×C127—21no—
17#424×C127—21no—
18#418×C127—21no—
19#413×C127C2211yescharacteristic
20C2×#100×C127—21no—
21#410×C127C2211yescharacteristic
22#410×C127C2211yescharacteristic
23#408×C127C2211yescharacteristic
24#353×C127—22no—
25AΣL(1,𝔽16)×C127—22no—
26#344×C127—21no—
27#344×C127—21no—
28H(3,ℤ/4)×C127—21no—
29C2×#41×C127C2311yescharacteristic
30C22×D4×C127D411yescharacteristic
31C22×D4×C127D411yescharacteristic
32C2×D8×C127—21no—
33C2×D8×C127—21no—
34#131×C127—42no—
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127D411yescharacteristic
40C22×C8×C127D411yescharacteristic
41#127×C127—21no—
42#127×C127—21no—
43#124×C127—21no—
44#124×C127—21no—
45#121×C127—21no—
46#121×C127—21no—
47#121×C127—21no—
48#121×C127—21no—
49#120×C127—21no—
50#120×C127—21no—
51#120×C127—21no—
52#120×C127—21no—
53#117×C127—21no—
54#117×C127—21no—
55#117×C127D411yescharacteristic
56#117×C127D411yescharacteristic
57#107×C127—21no—
58#106×C127—21no—
59C4⋊C8×C127—42no—
60#102×C127—21no—
61#102×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64#102×C127—42no—
65#101×C127—21no—
66#100×C127—21no—
67#100×C127—42no—
68#99×C127—21no—
69#99×C127—21no—
70#99×C127—21no—
71#99×C127D412yes—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C24×C127—21no—
75C24×C127—21no—
76#41×C127—41no—
77#41×C127—41no—
78C2×Q8×C127#4111yescharacteristic
79C2×D4×C127—21no—
80C2×D4×C127—21no—
81C2×D4×C127—21no—
82C2×D4×C127—21no—
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—41no—
90C2×D4×C127—41no—
91C2×D4×C127C2×D411yescharacteristic
92C2×D4×C127#4111yescharacteristic
93C2×D4×C127#4111yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97D8×C127—81no—
98D8×C127—81no—
99M16×C127—22no—
100M16×C127—41no—
101M16×C127—41no—
102M16×C127—41no—
103M16×C127—41no—
104M16×C127—41no—
105M16×C127—41no—
106C2×C8×C127—22no—
107C2×C8×C127—22no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—41no—
117C22⋊C4×C127—22no—
118C22⋊C4×C127—21no—
119C22⋊C4×C127—21no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C42×C127—21no—
126C42×C127—21no—
127C42×C127—41no—
128C42×C127—41no—
129C23×C127—42no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—81no—
133C23×C127—161no—
134C23×C127—161no—
135C23×C127#12111yescharacteristic
136C23×C127#12111yescharacteristic
137C23×C127#12311yescharacteristic
138Q8×C127—41no—
139D4×C127—41no—
140D4×C127—41no—
141D4×C127—41no—
142D4×C127—42no—
143D4×C127—41no—
144D4×C127—41no—
145D4×C127—41no—
146D4×C127—41no—
147D4×C127—81no—
148D4×C127—161no—
149D4×C127—161no—
150D4×C127—161no—
151D4×C127—161no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—42no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—81no—
162C2×C4×C127#12011yescharacteristic
163C2×C4×C127#12111yescharacteristic
164C2×C4×C127#12311yescharacteristic
165C2×C4×C127#12411yescharacteristic
166C8×C127—42no—
167C8×C127—41no—
168C8×C127—41no—
169C8×C127—81no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127—81no—
181C22×C127—81no—
182C22×C127—162no—
183C22×C127—162no—
184C22×C127#39411yescharacteristic
185C4×C127—21no—
186C4×C127—21no—
187C4×C127—21no—
188C4×C127—81no—
189C4×C127—81no—
190C4×C127—82no—
191C4×C127—161no—
192C4×C127B(4,𝔽2)11yescharacteristic
193C4×C127#45811yescharacteristic
194#13432C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—21no—
196C2×C127—41no—
197C2×C127—41no—
198C2×C127—41no—
199C2×C127—161no—
200C2×C127—161no—
201C2×C127#204411yescharacteristic
202#3199C2×C12711yescharacteristic
203#2128C2×C12711yescharacteristic, complemented
204#2122C2×C12711yescharacteristic, complemented
205#1914C2×C12711yescharacteristic, complemented
206#1910C2×C12711yescharacteristic, complemented
207#1868C2×C12711yescharacteristic, complemented
208#1395C2×C12711yescharacteristic, complemented
209C127#1343211yescharacteristic, direct product factor, Sylow
210#568C22×C12711yescharacteristic
211#535C22×C12711yescharacteristic
212#535C22×C12711yescharacteristic
213#482—21no—
214#482—21no—
215#469—21no—
216#466—21no—
217#447—21no—
218#447—21no—
219#424—21no—
220#418—21no—
221#413C22×C12711yescharacteristic
222C2×#100—21no—
223#410C22×C12711yescharacteristic
224#410C22×C12711yescharacteristic
225#408C22×C12711yescharacteristic
226#353—22no—
227AΣL(1,𝔽16)—22no—
228#344—21no—
229#344—21no—
230H(3,ℤ/4)—21no—
231C2×#41C23×C12711yescharacteristic
232C22×D4D4×C12711yescharacteristic
233C22×D4D4×C12711yescharacteristic
234C2×D8—21no—
235C2×D8—21no—
236#131—42no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16D4×C12711yescharacteristic
242C22×C8D4×C12711yescharacteristic
243#127—21no—
244#127—21no—
245#124—21no—
246#124—21no—
247#121—21no—
248#121—21no—
249#121—21no—
250#121—21no—
251#120—21no—
252#120—21no—
253#120—21no—
254#120—21no—
255#117—21no—
256#117—21no—
257#117D4×C12711yescharacteristic
258#117D4×C12711yescharacteristic
259#107—21no—
260#106—21no—
261C4⋊C8—42no—
262#102—21no—
263#102—21no—
264#102—21no—
265#102—21no—
266#102—42no—
267#101—21no—
268#100—21no—
269#100—42no—
270#99—21no—
271#99—21no—
272#99—21no—
273#99D4×C12712yes—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C24—21no—
277C24—21no—
278#41—41no—
279#41—41no—
280C2×Q8#41×C12711yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4C2×D4×C12711yescharacteristic
294C2×D4#41×C12711yescharacteristic
295C2×D4#41×C12711yescharacteristic
296C22×C4C2×D4×C12711yescharacteristic
297C22×C4C2×D4×C12711yescharacteristic
298C22×C4C2×D4×C12711yescharacteristic
299D8—81no—
300D8—81no—
301M16—22no—
302M16—41no—
303M16—41no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—22no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—21no—
328C42—21no—
329C42—41no—
330C42—41no—
331C23—42no—
332C23—41no—
333C23—41no—
334C23—81no—
335C23—161no—
336C23—161no—
337C23#121×C12711yescharacteristic
338C23#121×C12711yescharacteristic
339C23#123×C12711yescharacteristic
340Q8—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—42no—
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—81no—
350D4—161no—
351D4—161no—
352D4—161no—
353D4—161no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4#120×C12711yescharacteristic
365C2×C4#121×C12711yescharacteristic
366C2×C4#123×C12711yescharacteristic
367C2×C4#124×C12711yescharacteristic
368C8—42no—
369C8—41no—
370C8—41no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—162no—
385C22—162no—
386C22#394×C12711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—81no—
391C4—81no—
392C4—82no—
393C4—161no—
394C4B(4,𝔽2)×C12711yescharacteristic
395C4#458×C12711yescharacteristic
396C2—21no—
397C2—41no—
398C2—41no—
399C2—41no—
400C2—161no—
401C2—161no—
402C2C127×#204411yescharacteristic
subgroupG/H
center, socleC2×C127#2044
commutator, Frattini, cosocleC2×#41C23×C127
prime radicalC127×#3199C2
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×#2128C2semidirect
3. C127×#2122C2semidirect
4. C127×#1914C2semidirect
5. C127×#1910C2semidirect
6. C127×#1868C2semidirect
7. C127×#1395C2semidirect
194. #13432C127direct (N × H)
203. #2128C2×C127semidirect
204. #2122C2×C127semidirect
205. #1914C2×C127semidirect
206. #1910C2×C127semidirect
207. #1868C2×C127semidirect
208. #1395C2×C127semidirect
209. C127#13432direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31992
C127×#21282
C127×#21222
C127×#19142
C127×#19102
C127×#18682
C127×#13952
#13432127