Finite Group Databasebeta

← C127×#13435 #44577108

Subgroups — C127×#13435 #44577108

Order 32512.

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

normal subgroups only

This group has 408 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×#3202C211yesmaximal, characteristic
2C127×#2129C211yesmaximal, characteristic
3C127×#2123C211yesmaximal, characteristic
4C127×#1915C211yesmaximal, characteristic
5C127×#1909C211yesmaximal, characteristic
6C127×#1868C211yesmaximal, characteristic
7C127×#1395C211yesmaximal, characteristic
8#568×C127C2211yescharacteristic
9#536×C127C2211yescharacteristic
10#536×C127C2211yescharacteristic
11#485×C127—21no—
12#485×C127—21no—
13#470×C127—21no—
14#467×C127—21no—
15#451×C127—21no—
16#451×C127—21no—
17#424×C127—21no—
18#419×C127—21no—
19#413×C127C2211yescharacteristic
20C2×#101×C127—21no—
21#410×C127C2211yescharacteristic
22#410×C127C2211yescharacteristic
23#408×C127C2211yescharacteristic
24#354×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×Q8×C127D411yescharacteristic
32C2×Q16×C127—21no—
33C2×Q16×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—
42C4⋊Q8×C127—21no—
43#124×C127—21no—
44#124×C127—21no—
45#123×C127—21no—
46#123×C127—21no—
47#123×C127—21no—
48#123×C127—21no—
49C22⋊Q8×C127—21no—
50C22⋊Q8×C127—21no—
51C22⋊Q8×C127—21no—
52C22⋊Q8×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—21no—
63#103×C127—21no—
64#103×C127—42no—
65#101×C127—21no—
66#101×C127—42no—
67#100×C127—21no—
68#99×C127—21no—
69#99×C127—21no—
70#99×C127—21no—
71#99×C127D412yes—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74#41×C127—41no—
75#41×C127—41no—
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×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127#4111yescharacteristic
85C2×D4×C127C2×D411yescharacteristic
86C2×D4×C127#4111yescharacteristic
87C2×D4×C127#4111yescharacteristic
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93Q16×C127—81no—
94Q16×C127—81no—
95M16×C127—22no—
96M16×C127—41no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102C2×C8×C127—22no—
103C2×C8×C127—22no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—41no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
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#12111yescharacteristic
130C23×C127#12111yescharacteristic
131C23×C127#12311yescharacteristic
132Q8×C127—41no—
133Q8×C127—42no—
134Q8×C127—41no—
135Q8×C127—41no—
136Q8×C127—41no—
137Q8×C127—41no—
138Q8×C127—81no—
139D4×C127—41no—
140D4×C127—41no—
141D4×C127—41no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127#12011yescharacteristic
157C2×C4×C127#12111yescharacteristic
158C2×C4×C127#12311yescharacteristic
159C2×C4×C127#12411yescharacteristic
160C8×C127—42no—
161C8×C127—41no—
162C8×C127—41no—
163C8×C127—81no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127#39411yescharacteristic
171C4×C127—21no—
172C4×C127—21no—
173C4×C127—21no—
174C4×C127—81no—
175C4×C127—81no—
176C4×C127—82no—
177C4×C127—81no—
178C4×C127—81no—
179C4×C127—161no—
180C4×C127B(4,𝔽2)11yescharacteristic
181C4×C127#45811yescharacteristic
182#13435C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—21no—
184C2×C127—41no—
185C2×C127—41no—
186C2×C127—41no—
187C2×C127#204411yescharacteristic
188#3202C2×C12711yescharacteristic
189#2129C2×C12711yescharacteristic
190#2123C2×C12711yescharacteristic
191#1915C2×C12711yescharacteristic
192#1909C2×C12711yescharacteristic
193#1868C2×C12711yescharacteristic
194#1395C2×C12711yescharacteristic
195C127#1343511yescharacteristic, direct product factor, Sylow
196#568C22×C12711yescharacteristic
197#536C22×C12711yescharacteristic
198#536C22×C12711yescharacteristic
199#485—21no—
200#485—21no—
201#470—21no—
202#467—21no—
203#451—21no—
204#451—21no—
205#424—21no—
206#419—21no—
207#413C22×C12711yescharacteristic
208C2×#101—21no—
209#410C22×C12711yescharacteristic
210#410C22×C12711yescharacteristic
211#408C22×C12711yescharacteristic
212#354—22no—
213#352—22no—
214#344—21no—
215#344—21no—
216H(3,ℤ/4)—21no—
217C2×#41C23×C12711yescharacteristic
218C22×Q8D4×C12711yescharacteristic
219C22×Q8D4×C12711yescharacteristic
220C2×Q16—21no—
221C2×Q16—21no—
222#131—42no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16D4×C12711yescharacteristic
228C22×C8D4×C12711yescharacteristic
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231#124—21no—
232#124—21no—
233#123—21no—
234#123—21no—
235#123—21no—
236#123—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241#117—21no—
242#117—21no—
243#117D4×C12711yescharacteristic
244#117D4×C12711yescharacteristic
245#107—21no—
246#106—21no—
247C4⋊C8—42no—
248#103—21no—
249#103—21no—
250#103—21no—
251#103—21no—
252#103—42no—
253#101—21no—
254#101—42no—
255#100—21no—
256#99—21no—
257#99—21no—
258#99—21no—
259#99D4×C12712yes—
260C22⋊C8—21no—
261C22⋊C8—21no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8#41×C12711yescharacteristic
273C2×D4C2×D4×C12711yescharacteristic
274C2×D4#41×C12711yescharacteristic
275C2×D4#41×C12711yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4C2×D4×C12711yescharacteristic
279C22×C4C2×D4×C12711yescharacteristic
280C22×C4C2×D4×C12711yescharacteristic
281Q16—81no—
282Q16—81no—
283M16—22no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289M16—41no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C22⋊C4—22no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—21no—
314C42—21no—
315C42—41no—
316C42—41no—
317C23#121×C12711yescharacteristic
318C23#121×C12711yescharacteristic
319C23#123×C12711yescharacteristic
320Q8—41no—
321Q8—42no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327D4—41no—
328D4—41no—
329D4—41no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4#120×C12711yescharacteristic
345C2×C4#121×C12711yescharacteristic
346C2×C4#123×C12711yescharacteristic
347C2×C4#124×C12711yescharacteristic
348C8—42no—
349C8—41no—
350C8—41no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22#394×C12711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—81no—
367C4—161no—
368C4B(4,𝔽2)×C12711yescharacteristic
369C4#458×C12711yescharacteristic
370C2—21no—
371C2—41no—
372C2—41no—
373C2—41no—
374C2C127×#204411yescharacteristic
subgroupG/H
center, socleC2×C127#2044
commutator, Frattini, cosocleC2×#41C23×C127
prime radicalC2×#41×C127C23
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
182. #13435C127direct (N × H)
195. C127#13435direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32022
C127×#21292
C127×#21232
C127×#19152
C127×#19092
C127×#18682
C127×#13952
#13435127