Finite Group Databasebeta

← C127×#10079 #44573752

Subgroups — C127×#10079 #44573752

Order 32512.

658 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×#496×C127C211yesmaximal, characteristic
2C2×#490×C127C211yesmaximal, characteristic, complemented
3C127×#2820C211yesmaximal, characteristic, complemented
4C127×#1961C211yesmaximal, characteristic, complemented
5C2×#330×C127C211yesmaximal, characteristic, complemented
6C2×#329×C127C211yesmaximal, characteristic, complemented
7C127×#1295C211yesmaximal, characteristic, complemented
8C22×SD16×C127—21no—
9C22×D8×C127—21no—
10C2×#127×C127C2211yescharacteristic
11C2×#125×C127C2211yescharacteristic
12C2×#124×C127C2211yescharacteristic
13#496×C127—22no—
14#496×C127—22no—
15#490×C127—22no—
16#490×C127—22no—
17C2×#102×C127—21no—
18C2×#102×C127—21no—
19C2×#102×C127—22no—
20C2×#97×C127C2211yescharacteristic
21C2×#97×C127C2211yescharacteristic
22C2×#97×C127C2211yescharacteristic
23#399×C127—21no—
24#397×C127—21no—
25#396×C127—22no—
26#395×C127—21no—
27#394×C127—21no—
28#382×C127C2211yescharacteristic
29#330×C127—22no—
30#329×C127—22no—
31C22×Q8×C127D411yescharacteristic
32C22×D4×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—21no—
35C22×D4×C127D411yescharacteristic
36C2×SD16×C127—24no—
37C2×SD16×C127—44no—
38C2×D8×C127—24no—
39C2×D8×C127—44no—
40C22×C8×C127—21no—
41C22×C8×C127—21no—
42C22×C8×C127—21no—
43#127×C127—21no—
44#127×C127—21no—
45#127×C127—21no—
46#127×C127D412yes—
47#125×C127—21no—
48#125×C127—21no—
49#125×C127—21no—
50#125×C127—21no—
51#124×C127—21no—
52#124×C127—21no—
53#124×C127—21no—
54#124×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127D411yescharacteristic
59C2×C4⋊C4×C127D411yescharacteristic
60C2×C4⋊C4×C127D412yes—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—22no—
65C2×C42×C127C2311yescharacteristic
66#102×C127—24no—
67#102×C127—24no—
68#102×C127—44no—
69#97×C127—21no—
70#97×C127—21no—
71#97×C127—21no—
72#97×C127—21no—
73#97×C127D412yes—
74#97×C127D412yes—
75#95×C127—22no—
76#95×C127—21no—
77#95×C127—21no—
78C24×C127—21no—
79C24×C127—41no—
80C2×Q8×C127—21no—
81C2×Q8×C127—21no—
82C2×Q8×C127—42no—
83C2×D4×C127—22no—
84C2×D4×C127—21no—
85C2×D4×C127—22no—
86C2×D4×C127—22no—
87C2×D4×C127—21no—
88C2×D4×C127—42no—
89C2×D4×C127—42no—
90C2×D4×C127—42no—
91C2×D4×C127—42no—
92C2×D4×C127—44no—
93C2×D4×C127—42no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127C2×D411yescharacteristic
103C22×C4×C127C2×D411yescharacteristic
104SD16×C127—48no—
105D8×C127—48no—
106C2×C8×C127—24no—
107C2×C8×C127—22no—
108C2×C8×C127—22no—
109C2×C8×C127—22no—
110C2×C8×C127—42no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—42no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C4⋊C4×C127—41no—
122C4⋊C4×C127—82no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C22⋊C4×C127—82no—
128C22⋊C4×C127—82no—
129C42×C127C2×D411yescharacteristic
130C42×C127C2×D411yescharacteristic
131C42×C127C2×D411yescharacteristic
132C42×C127#4111yescharacteristic
133C23×C127—41no—
134C23×C127—42no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—42no—
138C23×C127—41no—
139C23×C127—82no—
140C23×C127—81no—
141C23×C127—82no—
142C23×C127—81no—
143C23×C127#12011yescharacteristic
144Q8×C127—42no—
145Q8×C127—81no—
146D4×C127—42no—
147D4×C127—42no—
148D4×C127—42no—
149D4×C127—44no—
150D4×C127—44no—
151D4×C127—81no—
152D4×C127—82no—
153D4×C127—82no—
154D4×C127—82no—
155C2×C4×C127—21no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—21no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—41no—
169C2×C4×C127#12011yescharacteristic
170C2×C4×C127#12011yescharacteristic
171C2×C4×C127#12111yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127#12111yescharacteristic
174C2×C4×C127#12711yescharacteristic
175C8×C127—24no—
176C8×C127—42no—
177C8×C127—42no—
178C22×C127—82no—
179C22×C127—82no—
180C22×C127—82no—
181C22×C127—81no—
182C22×C127—82no—
183C22×C127—81no—
184C22×C127—82no—
185C22×C127—81no—
186C22×C127—162no—
187C22×C127—162no—
188C22×C127#39211yescharacteristic
189C22×C127#45311yescharacteristic
190C22×C127#45312yes—
191C22×C127#45412yes—
192C22×C127#45411yescharacteristic
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—21no—
196C4×C127—21no—
197C4×C127—21no—
198C4×C127—21no—
199C4×C127—82no—
200C4×C127—81no—
201C4×C127—81no—
202C4×C127—81no—
203#10079C12711yesmaximal, characteristic, direct product factor, Sylow
204C2×C127—161no—
205C2×C127—162no—
206C2×C127#165612yes—
207C2×C127#165712yes—
208C2×C127#200211yescharacteristic
209C2×C127#200311yescharacteristic
210C2×C127#200611yescharacteristic
211C2×#496C2×C12711yescharacteristic
212C2×#490C2×C12711yescharacteristic, complemented
213#2820C2×C12711yescharacteristic, complemented
214#1961C2×C12711yescharacteristic, complemented
215C2×#330C2×C12711yescharacteristic, complemented
216C2×#329C2×C12711yescharacteristic, complemented
217#1295C2×C12711yescharacteristic, complemented
218C127#1007911yescharacteristic, direct product factor, Sylow
219C22×SD16—21no—
220C22×D8—21no—
221C2×#127C22×C12711yescharacteristic
222C2×#125C22×C12711yescharacteristic
223C2×#124C22×C12711yescharacteristic
224#496—22no—
225#496—22no—
226#490—22no—
227#490—22no—
228C2×#102—21no—
229C2×#102—21no—
230C2×#102—22no—
231C2×#97C22×C12711yescharacteristic
232C2×#97C22×C12711yescharacteristic
233C2×#97C22×C12711yescharacteristic
234#399—21no—
235#397—21no—
236#396—22no—
237#395—21no—
238#394—21no—
239#382C22×C12711yescharacteristic
240#330—22no—
241#329—22no—
242C22×Q8D4×C12711yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4D4×C12711yescharacteristic
247C2×SD16—24no—
248C2×SD16—44no—
249C2×D8—24no—
250C2×D8—44no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254#127—21no—
255#127—21no—
256#127—21no—
257#127D4×C12712yes—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262#124—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4D4×C12711yescharacteristic
270C2×C4⋊C4D4×C12711yescharacteristic
271C2×C4⋊C4D4×C12712yes—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C42C23×C12711yescharacteristic
277#102—24no—
278#102—24no—
279#102—44no—
280#97—21no—
281#97—21no—
282#97—21no—
283#97—21no—
284#97D4×C12712yes—
285#97D4×C12712yes—
286#95—22no—
287#95—21no—
288#95—21no—
289C24—21no—
290C24—41no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—42no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—44no—
304C2×D4—42no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4C2×D4×C12711yescharacteristic
313C22×C4C2×D4×C12711yescharacteristic
314C22×C4C2×D4×C12711yescharacteristic
315SD16—48no—
316D8—48no—
317C2×C8—24no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—41no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—82no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—82no—
339C22⋊C4—82no—
340C42C2×D4×C12711yescharacteristic
341C42C2×D4×C12711yescharacteristic
342C42C2×D4×C12711yescharacteristic
343C42#41×C12711yescharacteristic
344C23—41no—
345C23—42no—
346C23—41no—
347C23—42no—
348C23—42no—
349C23—41no—
350C23—82no—
351C23—81no—
352C23—82no—
353C23—81no—
354C23#120×C12711yescharacteristic
355Q8—42no—
356Q8—81no—
357D4—42no—
358D4—42no—
359D4—42no—
360D4—44no—
361D4—44no—
362D4—81no—
363D4—82no—
364D4—82no—
365D4—82no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4#120×C12711yescharacteristic
381C2×C4#120×C12711yescharacteristic
382C2×C4#121×C12711yescharacteristic
383C2×C4#121×C12711yescharacteristic
384C2×C4#121×C12711yescharacteristic
385C2×C4#127×C12711yescharacteristic
386C8—24no—
387C8—42no—
388C8—42no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—82no—
394C22—81no—
395C22—82no—
396C22—81no—
397C22—162no—
398C22—162no—
399C22#392×C12711yescharacteristic
400C22#453×C12711yescharacteristic
401C22#453×C12712yes—
402C22#454×C12712yes—
403C22#454×C12711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—82no—
411C4—81no—
412C4—81no—
413C4—81no—
414C2—161no—
415C2—162no—
416C2C127×#165612yes—
417C2C127×#165712yes—
418C2C127×#200211yescharacteristic
419C2C127×#200311yescharacteristic
420C2C127×#200611yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#496×C127C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#490×C127C2semidirect
3. C127×#2820C2semidirect
4. C127×#1961C2semidirect
5. C2×#330×C127C2semidirect
6. C2×#329×C127C2semidirect
7. C127×#1295C2semidirect
203. #10079C127direct (N × H)
212. C2×#490C2×C127semidirect
213. #2820C2×C127semidirect
214. #1961C2×C127semidirect
215. C2×#330C2×C127semidirect
216. C2×#329C2×C127semidirect
217. #1295C2×C127semidirect
218. C127#10079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#496×C1272
C2×#490×C1272
C127×#28202
C127×#19612
C2×#330×C1272
C2×#329×C1272
C127×#12952
#10079127