Finite Group Databasebeta

← C127×#13434 #44577107

Subgroups — C127×#13434 #44577107

Order 32512.

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

normal subgroups only

This group has 424 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×#2128C211yesmaximal, characteristic
3C127×#2123C211yesmaximal, characteristic, complemented
4C127×#1914C211yesmaximal, characteristic
5C127×#1909C211yesmaximal, characteristic, complemented
6C127×#1868C211yesmaximal, characteristic, complemented
7C127×#1395C211yesmaximal, 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#424×C127—21no—
18#419×C127—21no—
19#413×C127C2211yescharacteristic
20C2×#100×C127—21no—
21#410×C127C2211yescharacteristic
22#410×C127C2211yescharacteristic
23#408×C127C2211yescharacteristic
24#353×C127—22no—
25#352×C127—22no—
26#344×C127—21no—
27#344×C127—21no—
28H(3,ℤ/4)×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×C127D411yescharacteristic
40C22×C8×C127D411yescharacteristic
41C4⋊Q8×C127—21no—
42#127×C127—21no—
43#124×C127—21no—
44#124×C127—21no—
45#123×C127—21no—
46#123×C127—21no—
47C22⋊Q8×C127—21no—
48C22⋊Q8×C127—21no—
49#121×C127—21no—
50#121×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#103×C127—21no—
61#103×C127—21no—
62#103×C127—42no—
63#102×C127—21no—
64#102×C127—21no—
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—
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×C127#4111yescharacteristic
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×C127C2×D411yescharacteristic
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—41no—
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102M16×C127—41no—
103M16×C127—41no—
104C2×C8×C127—22no—
105C2×C8×C127—22no—
106C2×C8×C127—21no—
107C2×C8×C127—21no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C2×C8×C127—41no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
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—161no—
132C23×C127#12111yescharacteristic
133C23×C127#12111yescharacteristic
134C23×C127#12311yescharacteristic
135Q8×C127—41no—
136Q8×C127—42no—
137Q8×C127—41no—
138Q8×C127—41no—
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—81no—
158C2×C4×C127—81no—
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127#12311yescharacteristic
162C2×C4×C127#12411yescharacteristic
163C8×C127—42no—
164C8×C127—41no—
165C8×C127—41no—
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—82no—
184C4×C127—81no—
185C4×C127—161no—
186C4×C127B(4,𝔽2)11yescharacteristic
187C4×C127#45811yescharacteristic
188#13434C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127—21no—
190C2×C127—41no—
191C2×C127—41no—
192C2×C127—41no—
193C2×C127—161no—
194C2×C127#204411yescharacteristic
195#3200C2×C12711yescharacteristic
196#2128C2×C12711yescharacteristic
197#2123C2×C12711yescharacteristic, complemented
198#1914C2×C12711yescharacteristic
199#1909C2×C12711yescharacteristic, complemented
200#1868C2×C12711yescharacteristic, complemented
201#1395C2×C12711yescharacteristic, complemented
202C127#1343411yescharacteristic, direct product factor, Sylow
203#568C22×C12711yescharacteristic
204#536C22×C12711yescharacteristic
205#535C22×C12711yescharacteristic
206#485—21no—
207#482—21no—
208#468—21no—
209#465—21no—
210#450—21no—
211#448—21no—
212#424—21no—
213#419—21no—
214#413C22×C12711yescharacteristic
215C2×#100—21no—
216#410C22×C12711yescharacteristic
217#410C22×C12711yescharacteristic
218#408C22×C12711yescharacteristic
219#353—22no—
220#352—22no—
221#344—21no—
222#344—21no—
223H(3,ℤ/4)—21no—
224C2×#41C23×C12711yescharacteristic
225C22×Q8D4×C12711yescharacteristic
226C22×D4D4×C12711yescharacteristic
227C2×SD16—21no—
228C2×SD16—21no—
229#131—42no—
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#117—21no—
249#117—21no—
250#117D4×C12711yescharacteristic
251#117D4×C12711yescharacteristic
252#107—21no—
253#106—21no—
254C4⋊C8—42no—
255#103—21no—
256#103—21no—
257#103—42no—
258#102—21no—
259#102—21no—
260#101—21no—
261#100—21no—
262#100—42no—
263#99—21no—
264#99—21no—
265#99—21no—
266#99D4×C12712yes—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C24—21no—
270#41—41no—
271#41—41no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8#41×C12711yescharacteristic
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C2×D4×C12711yescharacteristic
284C2×D4#41×C12711yescharacteristic
285C2×D4#41×C12711yescharacteristic
286C22×C4—21no—
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4C2×D4×C12711yescharacteristic
289C22×C4C2×D4×C12711yescharacteristic
290SD16—81no—
291SD16—81no—
292M16—22no—
293M16—41no—
294M16—41no—
295M16—41no—
296M16—41no—
297M16—41no—
298M16—41no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C22⋊C4—22no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—21no—
321C42—21no—
322C42—41no—
323C42—41no—
324C23—42no—
325C23—41no—
326C23—161no—
327C23#121×C12711yescharacteristic
328C23#121×C12711yescharacteristic
329C23#123×C12711yescharacteristic
330Q8—41no—
331Q8—42no—
332Q8—41no—
333Q8—41no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—41no—
339D4—81no—
340D4—161no—
341D4—161no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4#120×C12711yescharacteristic
355C2×C4#121×C12711yescharacteristic
356C2×C4#123×C12711yescharacteristic
357C2×C4#124×C12711yescharacteristic
358C8—42no—
359C8—41no—
360C8—41no—
361C8—81no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—162no—
372C22#394×C12711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—82no—
379C4—81no—
380C4—161no—
381C4B(4,𝔽2)×C12711yescharacteristic
382C4#458×C12711yescharacteristic
383C2—21no—
384C2—41no—
385C2—41no—
386C2—41no—
387C2—161no—
388C2C127×#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
3. C127×#2123C2semidirect
5. C127×#1909C2semidirect
6. C127×#1868C2semidirect
7. C127×#1395C2semidirect
188. #13434C127direct (N × H)
197. #2123C2×C127semidirect
199. #1909C2×C127semidirect
200. #1868C2×C127semidirect
201. #1395C2×C127semidirect
202. C127#13434direct (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×#21282
C127×#21232
C127×#19142
C127×#19092
C127×#18682
C127×#13952
#13434127