Finite Group Databasebeta

← C127×#10498 #44574171

Subgroups — C127×#10498 #44574171

Order 32512.

380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3215C211yesmaximal, characteristic
2C127×#1967C211yesmaximal, characteristic
3C127×#1569C211yesmaximal, characteristic, complemented
4C127×#1559C211yesmaximal, characteristic, complemented
5C127×#1527C211yesmaximal, characteristic
6C127×#1526C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9C2×#124×C127C2211yescharacteristic
10#497×C127—21no—
11#489×C127—21no—
12#464×C127—21no—
13#464×C127—21no—
14#451×C127—21no—
15#450×C127—21no—
16#432×C127C2211yescharacteristic
17#432×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19C2×#101×C127—21no—
20C2×#100×C127—21no—
21C4×M16×C127C2211yescharacteristic
22C4×M16×C127C2211yescharacteristic
23#335×C127—21no—
24#334×C127—21no—
25#333×C127—21no—
26#332×C127—21no—
27#330×C127—21no—
28#330×C127—21no—
29#329×C127—21no—
30#329×C127—21no—
31C22×Q8×C127D411yescharacteristic
32C22×D4×C127D411yescharacteristic
33C2×Q16×C127—21no—
34C2×Q16×C127—21no—
35C2×SD16×C127—21no—
36C2×SD16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42#125×C127—21no—
43#124×C127—21no—
44#124×C127—21no—
45#124×C127—21no—
46#124×C127—21no—
47C22⋊Q8×C127—21no—
48C22⋊Q8×C127—21no—
49C4×Q8×C127—21no—
50C4×Q8×C127—21no—
51#117×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C42×C127C2311yescharacteristic
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127D411yescharacteristic
59C4⋊C8×C127D411yescharacteristic
60#103×C127—21no—
61#103×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64#101×C127—42no—
65#100×C127—42no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127—21no—
68#97×C127—21no—
69#97×C127—21no—
70#97×C127—21no—
71#97×C127D411yescharacteristic
72#97×C127D411yescharacteristic
73C4×C8×C127—21no—
74C4×C8×C127—21no—
75C24×C127—21no—
76C2×Q8×C127—21no—
77C2×Q8×C127—21no—
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127—41no—
81C2×Q8×C127—41no—
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C22×C4×C127—21no—
87C22×C4×C127C2×D411yescharacteristic
88C22×C4×C127#4111yescharacteristic
89C22×C4×C127#4111yescharacteristic
90Q16×C127—81no—
91Q16×C127—81no—
92SD16×C127—81no—
93SD16×C127—81no—
94M16×C127—22no—
95M16×C127—42no—
96M16×C127—41no—
97M16×C127—41no—
98M16×C127—41no—
99C2×C8×C127—21no—
100C2×C8×C127—21no—
101C2×C8×C127—21no—
102C2×C8×C127—21no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127—41no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127—41no—
117C42×C127—41no—
118C42×C127C2×D411yescharacteristic
119C42×C127C2×D411yescharacteristic
120C42×C127C2×D411yescharacteristic
121C42×C127#4111yescharacteristic
122C23×C127—42no—
123C23×C127—41no—
124C23×C127—81no—
125C23×C127—81no—
126C23×C127#12311yescharacteristic
127Q8×C127—41no—
128Q8×C127—41no—
129Q8×C127—41no—
130Q8×C127—41no—
131Q8×C127—81no—
132Q8×C127—81no—
133D4×C127—41no—
134D4×C127—41no—
135D4×C127—81no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—42no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127#12011yescharacteristic
145C2×C4×C127#12111yescharacteristic
146C2×C4×C127#12111yescharacteristic
147C2×C4×C127#12111yescharacteristic
148C2×C4×C127#12311yescharacteristic
149C2×C4×C127#12411yescharacteristic
150C8×C127—22no—
151C8×C127—41no—
152C8×C127—42no—
153C8×C127—41no—
154C8×C127—41no—
155C8×C127—81no—
156C8×C127—81no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—81no—
161C22×C127—81no—
162C22×C127—81no—
163C22×C127—162no—
164C22×C127#39411yescharacteristic
165C4×C127—21no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—81no—
171C4×C127—81no—
172C4×C127—81no—
173C4×C127#45311yescharacteristic
174C4×C127#45511yescharacteristic
175#10498C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—41no—
177C2×C127—161no—
178C2×C127#203711yescharacteristic
179C2×C127#204911yescharacteristic
180C2×C127#205011yescharacteristic
181#3215C2×C12711yescharacteristic
182#1967C2×C12711yescharacteristic
183#1569C2×C12711yescharacteristic, complemented
184#1559C2×C12711yescharacteristic, complemented
185#1527C2×C12711yescharacteristic
186#1526C2×C12711yescharacteristic, complemented
187#1291C2×C12711yescharacteristic, complemented
188C127#1049811yescharacteristic, direct product factor, Sylow
189#533C22×C12711yescharacteristic
190C2×#124C22×C12711yescharacteristic
191#497—21no—
192#489—21no—
193#464—21no—
194#464—21no—
195#451—21no—
196#450—21no—
197#432C22×C12711yescharacteristic
198#432C22×C12711yescharacteristic
199#423C22×C12711yescharacteristic
200C2×#101—21no—
201C2×#100—21no—
202C4×M16C22×C12711yescharacteristic
203C4×M16C22×C12711yescharacteristic
204#335—21no—
205#334—21no—
206#333—21no—
207#332—21no—
208#330—21no—
209#330—21no—
210#329—21no—
211#329—21no—
212C22×Q8D4×C12711yescharacteristic
213C22×D4D4×C12711yescharacteristic
214C2×Q16—21no—
215C2×Q16—21no—
216C2×SD16—21no—
217C2×SD16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C4⋊Q8D4×C12711yescharacteristic
222C4⋊Q8D4×C12711yescharacteristic
223#125—21no—
224#124—21no—
225#124—21no—
226#124—21no—
227#124—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232#117—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C42C23×C12711yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8D4×C12711yescharacteristic
240C4⋊C8D4×C12711yescharacteristic
241#103—21no—
242#103—21no—
243#102—21no—
244#102—21no—
245#101—42no—
246#100—42no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249#97—21no—
250#97—21no—
251#97—21no—
252#97D4×C12711yescharacteristic
253#97D4×C12711yescharacteristic
254C4×C8—21no—
255C4×C8—21no—
256C24—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4C2×D4×C12711yescharacteristic
269C22×C4#41×C12711yescharacteristic
270C22×C4#41×C12711yescharacteristic
271Q16—81no—
272Q16—81no—
273SD16—81no—
274SD16—81no—
275M16—22no—
276M16—42no—
277M16—41no—
278M16—41no—
279M16—41no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—41no—
299C42C2×D4×C12711yescharacteristic
300C42C2×D4×C12711yescharacteristic
301C42C2×D4×C12711yescharacteristic
302C42#41×C12711yescharacteristic
303C23—42no—
304C23—41no—
305C23—81no—
306C23—81no—
307C23#123×C12711yescharacteristic
308Q8—41no—
309Q8—41no—
310Q8—41no—
311Q8—41no—
312Q8—81no—
313Q8—81no—
314D4—41no—
315D4—41no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4#120×C12711yescharacteristic
326C2×C4#121×C12711yescharacteristic
327C2×C4#121×C12711yescharacteristic
328C2×C4#121×C12711yescharacteristic
329C2×C4#123×C12711yescharacteristic
330C2×C4#124×C12711yescharacteristic
331C8—22no—
332C8—41no—
333C8—42no—
334C8—41no—
335C8—41no—
336C8—81no—
337C8—81no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—162no—
345C22#394×C12711yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4#453×C12711yescharacteristic
355C4#455×C12711yescharacteristic
356C2—41no—
357C2—161no—
358C2C127×#203711yescharacteristic
359C2C127×#204911yescharacteristic
360C2C127×#205011yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1569C2semidirect
4. C127×#1559C2semidirect
6. C127×#1526C2semidirect
7. C127×#1291C2semidirect
175. #10498C127direct (N × H)
183. #1569C2×C127semidirect
184. #1559C2×C127semidirect
186. #1526C2×C127semidirect
187. #1291C2×C127semidirect
188. C127#10498direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32152
C127×#19672
C127×#15692
C127×#15592
C127×#15272
C127×#15262
C127×#12912
#10498127