Finite Group Databasebeta

← C2×C127×#1636 #44582164

Subgroups — C2×C127×#1636 #44582164

Order 32512.

914 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C127C211yesmaximal, characteristic
2C2×#487×C127C211yesmaximal, characteristic
3C2×#477×C127C211yesmaximal, characteristic
4C2×#477×C127C211yesmaximal, characteristic
5C127×#1636C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic
7C2×Q8⋊C8×C127C211yesmaximal, characteristic
8C2×Q8⋊C8×C127C211yesmaximal, characteristic
9#557×C127—22no—
10#557×C127—22no—
11#557×C127—22no—
12#557×C127C2214yes—
13C2×C4⋊Q8×C127—21no—
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#125×C127—22no—
17C2×#125×C127—21no—
18C2×C4×Q8×C127—21no—
19C2×C4×Q8×C127—21no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×Q8×C127C2211yescharacteristic
22#487×C127—22no—
23#487×C127C2214yes—
24#477×C127—22no—
25#477×C127—22no—
26#477×C127C2214yes—
27#477×C127C2214yes—
28C2×#107×C127—21no—
29C2×#107×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—21no—
33C2×#103×C127—21no—
34C2×#103×C127—22no—
35C2×C4×C8×C127C2211yescharacteristic
36#332×C127C2214yes—
37Q8⋊C8×C127C2214yes—
38Q8⋊C8×C127C2214yes—
39C22×Q8×C127—21no—
40C22×Q8×C127—21no—
41C22×Q8×C127D411yescharacteristic
42C22×Q8×C127D411yescharacteristic
43C22×C8×C127—21no—
44C22×C8×C127—21no—
45C22×C8×C127—21no—
46C4⋊Q8×C127—24no—
47C4⋊Q8×C127—24no—
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127D412yes—
54C4⋊Q8×C127C2312yes—
55C4⋊Q8×C127C2312yes—
56#125×C127—28no—
57#125×C127—24no—
58#125×C127—28no—
59#125×C127—24no—
60C4×Q8×C127—24no—
61C4×Q8×C127—24no—
62C4×Q8×C127—24no—
63C4×Q8×C127—24no—
64C4×Q8×C127—21no—
65C4×Q8×C127—21no—
66C4×Q8×C127—21no—
67C4×Q8×C127—21no—
68C4×Q8×C127D412yes—
69C4×Q8×C127D412yes—
70C4×Q8×C127C2312yes—
71C4×Q8×C127C2312yes—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—21no—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127D411yescharacteristic
81C2×C4⋊C4×C127D411yescharacteristic
82C2×C4⋊C4×C127D412yes—
83C2×C42×C127—22no—
84C2×C42×C127—21no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87#107×C127—24no—
88#107×C127—24no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127C2312yes—
92C4⋊C8×C127C2312yes—
93#103×C127—24no—
94#103×C127—24no—
95#103×C127—28no—
96C4×C8×C127—21no—
97C4×C8×C127C2312yes—
98C2×Q8×C127—21no—
99C2×Q8×C127—21no—
100C2×Q8×C127—22no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—44no—
107C2×Q8×C127—41no—
108C2×Q8×C127—42no—
109C2×Q8×C127—42no—
110C2×Q8×C127Q1614yes—
111C2×Q8×C127C2×D412yes—
112C2×Q8×C127C2×D412yes—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—22no—
118C22×C4×C127—41no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127C2×D411yescharacteristic
122C2×C8×C127—22no—
123C2×C8×C127—22no—
124C2×C8×C127—22no—
125C2×C8×C127—42no—
126C2×C8×C127—42no—
127C2×C8×C127—42no—
128C4⋊C4×C127—28no—
129C4⋊C4×C127—28no—
130C4⋊C4×C127—28no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—41no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127C2×D414yes—
145C4⋊C4×C127C2×D412yes—
146C4⋊C4×C127C2×D412yes—
147C42×C127—28no—
148C42×C127—22no—
149C42×C127—22no—
150C42×C127—22no—
151C42×C127—22no—
152C42×C127C2×D411yescharacteristic
153C42×C127C2×D411yescharacteristic
154C42×C127C2×D411yescharacteristic
155C42×C127C2411yescharacteristic
156C23×C127#12011yescharacteristic
157Q8×C127—22no—
158Q8×C127—24no—
159Q8×C127—22no—
160Q8×C127—22no—
161Q8×C127—44no—
162Q8×C127—42no—
163Q8×C127—42no—
164Q8×C127—42no—
165Q8×C127—44no—
166Q8×C127—82no—
167Q8×C127C2×Q1614yes—
168C2×C4×C127—22no—
169C2×C4×C127—24no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—24no—
175C2×C4×C127—42no—
176C2×C4×C127—44no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—82no—
181C2×C4×C127#12011yescharacteristic
182C2×C4×C127#12011yescharacteristic
183C2×C4×C127#12011yescharacteristic
184C2×C4×C127C2×Q1612yes—
185C2×C4×C127#13512yes—
186C2×C4×C127#13712yes—
187C2×C4×C127#13712yes—
188C2×C4×C127C22×D411yescharacteristic
189C2×C4×C127C22×D411yescharacteristic
190C2×C4×C127C22×D411yescharacteristic
191C8×C127—42no—
192C8×C127—42no—
193C8×C127—42no—
194C22×C127#45112yes—
195C22×C127#45212yes—
196C22×C127#45412yes—
197C22×C127C2×#12011yescharacteristic
198C4×C127—24no—
199C4×C127—21no—
200C4×C127—21no—
201C4×C127—42no—
202C4×C127—44no—
203C4×C127—42no—
204C4×C127—42no—
205C4×C127—82no—
206C4×C127#45112yes—
207C4×C127#45212yes—
208C4×C127C22×Q1611yescharacteristic
209C4×C127C2×#13511yescharacteristic
210C4×C127C2×#13711yescharacteristic
211C4×C127C2×#13711yescharacteristic
212C2×#1636C12711yesmaximal, characteristic, direct product factor, Sylow
213C2×C127#163614yesdirect product factor
214C2×C127C2×#45111yescharacteristic
215C2×C127C2×#45211yescharacteristic
216C2×C127C2×#45411yescharacteristic
217C2×#557C2×C12711yescharacteristic
218C2×#487C2×C12711yescharacteristic
219C2×#477C2×C12711yescharacteristic
220C2×#477C2×C12711yescharacteristic
221#1636C2×C12718yesdirect product factor
222C2×#332C2×C12711yescharacteristic
223C2×Q8⋊C8C2×C12711yescharacteristic
224C2×Q8⋊C8C2×C12711yescharacteristic
225C127C2×#163611yescharacteristic, direct product factor, Sylow
226#557—22no—
227#557—22no—
228#557—22no—
229#557C22×C12714yes—
230C2×C4⋊Q8—21no—
231C2×C4⋊Q8C22×C12711yescharacteristic
232C2×C4⋊Q8C22×C12711yescharacteristic
233C2×#125—22no—
234C2×#125—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8—21no—
237C2×C4×Q8C22×C12711yescharacteristic
238C2×C4×Q8C22×C12711yescharacteristic
239#487—22no—
240#487C22×C12714yes—
241#477—22no—
242#477—22no—
243#477C22×C12714yes—
244#477C22×C12714yes—
245C2×#107—21no—
246C2×#107—21no—
247C2×C4⋊C8C22×C12711yescharacteristic
248C2×C4⋊C8C22×C12711yescharacteristic
249C2×#103—21no—
250C2×#103—21no—
251C2×#103—22no—
252C2×C4×C8C22×C12711yescharacteristic
253#332C22×C12714yes—
254Q8⋊C8C22×C12714yes—
255Q8⋊C8C22×C12714yes—
256C22×Q8—21no—
257C22×Q8—21no—
258C22×Q8D4×C12711yescharacteristic
259C22×Q8D4×C12711yescharacteristic
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C4⋊Q8—24no—
264C4⋊Q8—24no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8D4×C12712yes—
271C4⋊Q8C23×C12712yes—
272C4⋊Q8C23×C12712yes—
273#125—28no—
274#125—24no—
275#125—28no—
276#125—24no—
277C4×Q8—24no—
278C4×Q8—24no—
279C4×Q8—24no—
280C4×Q8—24no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8D4×C12712yes—
286C4×Q8D4×C12712yes—
287C4×Q8C23×C12712yes—
288C4×Q8C23×C12712yes—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4D4×C12711yescharacteristic
298C2×C4⋊C4D4×C12711yescharacteristic
299C2×C4⋊C4D4×C12712yes—
300C2×C42—22no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42C23×C12711yescharacteristic
304#107—24no—
305#107—24no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8C23×C12712yes—
309C4⋊C8C23×C12712yes—
310#103—24no—
311#103—24no—
312#103—28no—
313C4×C8—21no—
314C4×C8C23×C12712yes—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—44no—
324C2×Q8—41no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8Q16×C12714yes—
328C2×Q8C2×D4×C12712yes—
329C2×Q8C2×D4×C12712yes—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C22×C4C2×D4×C12711yescharacteristic
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4C2×D4×C12714yes—
362C4⋊C4C2×D4×C12712yes—
363C4⋊C4C2×D4×C12712yes—
364C42—28no—
365C42—22no—
366C42—22no—
367C42—22no—
368C42—22no—
369C42C2×D4×C12711yescharacteristic
370C42C2×D4×C12711yescharacteristic
371C42C2×D4×C12711yescharacteristic
372C42C24×C12711yescharacteristic
373C23#120×C12711yescharacteristic
374Q8—22no—
375Q8—24no—
376Q8—22no—
377Q8—22no—
378Q8—44no—
379Q8—42no—
380Q8—42no—
381Q8—42no—
382Q8—44no—
383Q8—82no—
384Q8C2×Q16×C12714yes—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—82no—
398C2×C4#120×C12711yescharacteristic
399C2×C4#120×C12711yescharacteristic
400C2×C4#120×C12711yescharacteristic
401C2×C4C2×Q16×C12712yes—
402C2×C4#135×C12712yes—
403C2×C4#137×C12712yes—
404C2×C4#137×C12712yes—
405C2×C4C22×D4×C12711yescharacteristic
406C2×C4C22×D4×C12711yescharacteristic
407C2×C4C22×D4×C12711yescharacteristic
408C8—42no—
409C8—42no—
410C8—42no—
411C22#451×C12712yes—
412C22#452×C12712yes—
413C22#454×C12712yes—
414C22C2×#120×C12711yescharacteristic
415C4—24no—
416C4—21no—
417C4—21no—
418C4—42no—
419C4—44no—
420C4—42no—
421C4—42no—
422C4—82no—
423C4#451×C12712yes—
424C4#452×C12712yes—
425C4C22×Q16×C12711yescharacteristic
426C4C2×#135×C12711yescharacteristic
427C4C2×#137×C12711yescharacteristic
428C4C2×#137×C12711yescharacteristic
429C2C127×#163614yesdirect product factor
430C2C2×#451×C12711yescharacteristic
431C2C2×#452×C12711yescharacteristic
432C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C127×#1636C2direct (N × H)
212. C2×#1636C127direct (N × H)
213. C2×C127#1636direct (N × H)
221. #1636C2×C127direct (N × H)
225. C127C2×#1636direct (N × H)
429. C2C127×#1636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#557×C1272
C2×#487×C1272
C2×#477×C1272
C127×#16362
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×#1636127