Finite Group Databasebeta

← C127×#21495 #44585168

Subgroups — C127×#21495 #44585168

Order 32512.

1052 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C127C211yesmaximal, characteristic, complemented
2C2×#435×C127C211yesmaximal, characteristic, complemented
3C2×C8×D4×C127C211yesmaximal, characteristic, complemented
4C2×#405×C127C211yesmaximal, characteristic, complemented
5C127×#2392C211yesmaximal, characteristic
6C127×#1954C211yesmaximal, characteristic, complemented
7C127×#1939C211yesmaximal, characteristic, complemented
8C127×#1923C211yesmaximal, characteristic, complemented
9C127×#1923C211yesmaximal, characteristic, complemented
10C127×#1870C211yesmaximal, characteristic, complemented
11C127×#1870C211yesmaximal, characteristic, complemented
12C127×#1798C211yesmaximal, characteristic, complemented
13C127×#1771C211yesmaximal, characteristic, complemented
14C127×#1753C211yesmaximal, characteristic, complemented
15C127×#1752C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C23×C8×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24#435×C127—24no—
25#435×C127—24no—
26C8×D4×C127—24no—
27C2×C4⋊C8×C127C2211yescharacteristic
28C2×C4⋊C8×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C22⋊C8×C127C2211yescharacteristic
32C2×C22⋊C8×C127C2211yescharacteristic
33C2×C22⋊C8×C127C2211yescharacteristic
34C2×C22⋊C8×C127C2211yescharacteristic
35C2×C22⋊C8×C127C2211yescharacteristic
36C2×C22⋊C8×C127C2211yescharacteristic
37C2×C22⋊C8×C127C2211yescharacteristic
38C2×C22⋊C8×C127C2211yescharacteristic
39#405×C127—24no—
40C2×#97×C127C2211yescharacteristic
41C2×#97×C127C2211yescharacteristic
42C2×#97×C127C2211yescharacteristic
43C2×C4×C8×C127C2211yescharacteristic
44C2×C4×C8×C127C2211yescharacteristic
45C2×C4×C8×C127C2211yescharacteristic
46#398×C127C411yescharacteristic
47#397×C127C411yescharacteristic
48#396×C127C411yescharacteristic
49#396×C127C411yescharacteristic
50#394×C127C411yescharacteristic
51#394×C127C411yescharacteristic
52#394×C127C411yescharacteristic
53#392×C127C411yescharacteristic
54C4×C4⋊C4×C127C2211yescharacteristic
55C4×C22⋊C4×C127C2211yescharacteristic
56C4×C22⋊C4×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62#336×C127C2211yescharacteristic
63C22×D4×C127C2×C411yescharacteristic
64C22×D4×C127C2×C411yescharacteristic
65C22×D4×C127C2×C411yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C2×M16×C127—22no—
70C2×M16×C127—22no—
71C2×M16×C127—22no—
72C2×M16×C127—22no—
73C2×M16×C127—22no—
74C2×M16×C127—22no—
75C22×C8×C127—22no—
76C22×C8×C127—22no—
77C22×C8×C127—22no—
78C22×C8×C127—22no—
79C22×C8×C127—22no—
80C22×C8×C127D414yescomplemented
81C22×C8×C127C2311yescharacteristic
82C22×C8×C127C2311yescharacteristic
83C22×C8×C127C2311yescharacteristic
84C22×C8×C127C2311yescharacteristic
85C22×C8×C127C2311yescharacteristic
86C22×C8×C127C2311yescharacteristic
87C22×C8×C127C2311yescharacteristic
88C22×C8×C127C2311yescharacteristic
89C4×D4×C127—22no—
90C4×D4×C127—22no—
91C4×D4×C127—22no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95#117×C127—22no—
96#117×C127—22no—
97C2×C4⋊C4×C127C2×C411yescharacteristic
98C2×C4⋊C4×C127C2×C411yescharacteristic
99C2×C4⋊C4×C127C2×C411yescharacteristic
100C2×C4⋊C4×C127C2×C411yescharacteristic
101C2×C4⋊C4×C127C2×C411yescharacteristic
102C2×C4⋊C4×C127C2×C411yescharacteristic
103C2×C4⋊C4×C127C2×C411yescharacteristic
104C2×C22⋊C4×C127C2×C411yescharacteristic
105C2×C22⋊C4×C127C2×C411yescharacteristic
106C2×C22⋊C4×C127C2×C411yescharacteristic
107C2×C22⋊C4×C127C2×C411yescharacteristic
108C2×C22⋊C4×C127C2×C411yescharacteristic
109C2×C22⋊C4×C127C2×C411yescharacteristic
110C2×C22⋊C4×C127C2×C411yescharacteristic
111C2×C22⋊C4×C127C2×C411yescharacteristic
112C2×C22⋊C4×C127C2×C411yescharacteristic
113C2×C22⋊C4×C127C2×C411yescharacteristic
114C2×C22⋊C4×C127C2×C411yescharacteristic
115C2×C22⋊C4×C127C2×C411yescharacteristic
116C2×C42×C127C2311yescharacteristic
117C2×C42×C127C2311yescharacteristic
118C2×C42×C127C2311yescharacteristic
119C2×C42×C127C2311yescharacteristic
120C4⋊C8×C127—22no—
121C4⋊C8×C127—22no—
122C4⋊C8×C127—22no—
123C4⋊C8×C127—22no—
124C22⋊C8×C127—22no—
125C22⋊C8×C127—22no—
126C22⋊C8×C127—22no—
127C22⋊C8×C127—22no—
128C22⋊C8×C127—22no—
129C22⋊C8×C127—22no—
130C22⋊C8×C127—22no—
131C22⋊C8×C127—22no—
132#97×C127—22no—
133#97×C127—22no—
134#97×C127D414yescomplemented
135C4×C8×C127—22no—
136C4×C8×C127—22no—
137C4×C8×C127—22no—
138#95×C127C2×C411yescharacteristic
139#95×C127C2×C411yescharacteristic
140#95×C127C2×C411yescharacteristic
141#95×C127C2×C411yescharacteristic
142#95×C127C2×C411yescharacteristic
143#95×C127C2×C411yescharacteristic
144C24×C127C22×C411yescharacteristic
145C24×C127C22×C411yescharacteristic
146C24×C127C22×C411yescharacteristic
147C2×D4×C127—22no—
148C2×D4×C127—22no—
149C2×D4×C127—22no—
150C2×D4×C127—22no—
151C2×D4×C127—22no—
152C2×D4×C127—22no—
153C2×D4×C127—41no—
154C2×D4×C127—41no—
155C2×D4×C127—41no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127C22×C411yescharacteristic
173C22×C4×C127C22×C411yescharacteristic
174C22×C4×C127C22×C411yescharacteristic
175C22×C4×C127C22×C411yescharacteristic
176C22×C4×C127C22×C411yescharacteristic
177C22×C4×C127C22×C411yescharacteristic
178C22×C4×C127C22×C411yescharacteristic
179C22×C4×C127C22×C411yescharacteristic
180C22×C4×C127C22×C411yescharacteristic
181C22×C4×C127C22×C411yescharacteristic
182C22×C4×C127C22×C411yescharacteristic
183C22×C4×C127C2×D412yes—
184C22×C4×C127#4112yes—
185C22×C4×C127C2411yescharacteristic
186M16×C127—28no—
187M16×C127—44no—
188C2×C8×C127—21no—
189C2×C8×C127—21no—
190C2×C8×C127—21no—
191C2×C8×C127—21no—
192C2×C8×C127—21no—
193C2×C8×C127—21no—
194C2×C8×C127—28no—
195C2×C8×C127—21no—
196C2×C8×C127—21no—
197C2×C8×C127—21no—
198C2×C8×C127—21no—
199C2×C8×C127—21no—
200C2×C8×C127—21no—
201C2×C8×C127—21no—
202C2×C8×C127—21no—
203C2×C8×C127—21no—
204C2×C8×C127—21no—
205C2×C8×C127—21no—
206C2×C8×C127—21no—
207C2×C8×C127—44no—
208C2×C8×C127C2×D412yes—
209C2×C8×C127C2×D412yes—
210C2×C8×C127C2×D412yes—
211C2×C8×C127C2×D412yes—
212C2×C8×C127#4112yes—
213C2×C8×C127#4112yes—
214C4⋊C4×C127—22no—
215C4⋊C4×C127—22no—
216C4⋊C4×C127—22no—
217C4⋊C4×C127—22no—
218C4⋊C4×C127—22no—
219C4⋊C4×C127—22no—
220C4⋊C4×C127—41no—
221C22⋊C4×C127—22no—
222C22⋊C4×C127—22no—
223C22⋊C4×C127—22no—
224C22⋊C4×C127—22no—
225C22⋊C4×C127—22no—
226C22⋊C4×C127—22no—
227C22⋊C4×C127—22no—
228C22⋊C4×C127—22no—
229C22⋊C4×C127—22no—
230C22⋊C4×C127—22no—
231C22⋊C4×C127—41no—
232C22⋊C4×C127—41no—
233C42×C127—21no—
234C42×C127—21no—
235C42×C127—21no—
236C42×C127—21no—
237C42×C127—21no—
238C42×C127—21no—
239C42×C127C2×D412yes—
240C42×C127#4112yes—
241C23×C127—21no—
242C23×C127—21no—
243C23×C127—21no—
244C23×C127—21no—
245C23×C127—21no—
246C23×C127—21no—
247C23×C127—21no—
248C23×C127—21no—
249C23×C127—21no—
250C23×C127—21no—
251C23×C127—21no—
252C23×C127—21no—
253C23×C127—21no—
254C23×C127—21no—
255C23×C127—21no—
256C23×C127—21no—
257C23×C127—21no—
258C23×C127—21no—
259C23×C127—21no—
260C23×C127C4×D412yes—
261C23×C127#13112yes—
262C23×C127C23×C411yescharacteristic
263D4×C127—28no—
264D4×C127—44no—
265D4×C127—44no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
268C2×C4×C127—21no—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—21no—
274C2×C4×C127—22no—
275C2×C4×C127—22no—
276C2×C4×C127—22no—
277C2×C4×C127—22no—
278C2×C4×C127—21no—
279C2×C4×C127—21no—
280C2×C4×C127—21no—
281C2×C4×C127—21no—
282C2×C4×C127—21no—
283C2×C4×C127—21no—
284C2×C4×C127—21no—
285C2×C4×C127—21no—
286C2×C4×C127—21no—
287C2×C4×C127—21no—
288C2×C4×C127—21no—
289C2×C4×C127—21no—
290C2×C4×C127—21no—
291C2×C4×C127—21no—
292C2×C4×C127—21no—
293C2×C4×C127—21no—
294C2×C4×C127—21no—
295C2×C4×C127—21no—
296C2×C4×C127—21no—
297C2×C4×C127—21no—
298C2×C4×C127—21no—
299C2×C4×C127—41no—
300C2×C4×C127—41no—
301C2×C4×C127—41no—
302C2×C4×C127—41no—
303C2×C4×C127—41no—
304C2×C4×C127—41no—
305C2×C4×C127—41no—
306C2×C4×C127—41no—
307C2×C4×C127C4×D412yes—
308C2×C4×C127C4×D412yes—
309C2×C4×C127C4×D412yes—
310C2×C4×C127#13112yes—
311C2×C4×C127C22×D411yescharacteristic
312C2×C4×C127C22×D411yescharacteristic
313C2×C4×C127C2×#4111yescharacteristic
314C2×C4×C127C2×#4111yescharacteristic
315C2×C4×C127C2×#4111yescharacteristic
316C2×C4×C127C2×#4111yescharacteristic
317C8×C127—22no—
318C8×C127—22no—
319C8×C127—22no—
320C8×C127—41no—
321C8×C127—41no—
322C8×C127—41no—
323C8×C127—41no—
324C8×C127#12114yes—
325C22×C127—22no—
326C22×C127—22no—
327C22×C127—22no—
328C22×C127—22no—
329C22×C127—22no—
330C22×C127—22no—
331C22×C127—41no—
332C22×C127—41no—
333C22×C127—41no—
334C22×C127—41no—
335C22×C127—41no—
336C22×C127—41no—
337C22×C127—41no—
338C22×C127—41no—
339C22×C127—41no—
340C22×C127—41no—
341C22×C127—41no—
342C22×C127—41no—
343C22×C127—41no—
344C22×C127—41no—
345C22×C127—41no—
346C22×C127C2×C4×D411yescharacteristic
347C22×C127C2×C4×D411yescharacteristic
348C22×C127C4×#4111yescharacteristic
349C22×C127C2×#13111yescharacteristic
350C22×C127C2×#13111yescharacteristic
351C22×C127#56811yescharacteristic
352C22×C127#56811yescharacteristic
353C4×C127—22no—
354C4×C127—22no—
355C4×C127—22no—
356C4×C127—22no—
357C4×C127—41no—
358C4×C127—41no—
359C4×C127—41no—
360C4×C127—41no—
361C4×C127—41no—
362C4×C127—41no—
363C4×C127—41no—
364C4×C127C2×#12111yescharacteristic
365C4×C127#52511yescharacteristic
366C4×C127#52911yescharacteristic
367C4×C127#53211yescharacteristic
368#21495C12711yesmaximal, characteristic, direct product factor, Sylow
369C2×C127—42no—
370C2×C127—42no—
371C2×C127—81no—
372C2×C127C4×#12111yescharacteristic
373C2×C127#292911yescharacteristic
374C2×C127#293011yescharacteristic
375C2×C127#293311yescharacteristic
376C2×C127#293511yescharacteristic
377C2×C127#296811yescharacteristic
378C2×C127#296911yescharacteristic
379C2×#435C2×C12711yescharacteristic, complemented
380C2×#435C2×C12711yescharacteristic, complemented
381C2×C8×D4C2×C12711yescharacteristic, complemented
382C2×#405C2×C12711yescharacteristic, complemented
383#2392C2×C12711yescharacteristic
384#1954C2×C12711yescharacteristic, complemented
385#1939C2×C12711yescharacteristic, complemented
386#1923C2×C12711yescharacteristic, complemented
387#1923C2×C12711yescharacteristic, complemented
388#1870C2×C12711yescharacteristic, complemented
389#1870C2×C12711yescharacteristic, complemented
390#1798C2×C12711yescharacteristic, complemented
391#1771C2×C12711yescharacteristic, complemented
392#1753C2×C12711yescharacteristic, complemented
393#1752C2×C12711yescharacteristic, complemented
394C127#2149511yescharacteristic, direct product factor, Sylow
395C22×M16C22×C12711yescharacteristic
396C22×M16C22×C12711yescharacteristic
397C23×C8C22×C12711yescharacteristic
398C23×C8C22×C12711yescharacteristic
399C2×C4×D4C22×C12711yescharacteristic
400C2×C4×D4C22×C12711yescharacteristic
401C2×C4×D4C22×C12711yescharacteristic
402C2×#117C22×C12711yescharacteristic
403#435—24no—
404#435—24no—
405C8×D4—24no—
406C2×C4⋊C8C22×C12711yescharacteristic
407C2×C4⋊C8C22×C12711yescharacteristic
408C2×C4⋊C8C22×C12711yescharacteristic
409C2×C4⋊C8C22×C12711yescharacteristic
410C2×C22⋊C8C22×C12711yescharacteristic
411C2×C22⋊C8C22×C12711yescharacteristic
412C2×C22⋊C8C22×C12711yescharacteristic
413C2×C22⋊C8C22×C12711yescharacteristic
414C2×C22⋊C8C22×C12711yescharacteristic
415C2×C22⋊C8C22×C12711yescharacteristic
416C2×C22⋊C8C22×C12711yescharacteristic
417C2×C22⋊C8C22×C12711yescharacteristic
418#405—24no—
419C2×#97C22×C12711yescharacteristic
420C2×#97C22×C12711yescharacteristic
421C2×#97C22×C12711yescharacteristic
422C2×C4×C8C22×C12711yescharacteristic
423C2×C4×C8C22×C12711yescharacteristic
424C2×C4×C8C22×C12711yescharacteristic
425#398C4×C12711yescharacteristic
426#397C4×C12711yescharacteristic
427#396C4×C12711yescharacteristic
428#396C4×C12711yescharacteristic
429#394C4×C12711yescharacteristic
430#394C4×C12711yescharacteristic
431#394C4×C12711yescharacteristic
432#392C4×C12711yescharacteristic
433C4×C4⋊C4C22×C12711yescharacteristic
434C4×C22⋊C4C22×C12711yescharacteristic
435C4×C22⋊C4C22×C12711yescharacteristic
436#336C22×C12711yescharacteristic
437#336C22×C12711yescharacteristic
438#336C22×C12711yescharacteristic
439#336C22×C12711yescharacteristic
440#336C22×C12711yescharacteristic
441#336C22×C12711yescharacteristic
442C22×D4C2×C4×C12711yescharacteristic
443C22×D4C2×C4×C12711yescharacteristic
444C22×D4C2×C4×C12711yescharacteristic
445C23×C4C23×C12711yescharacteristic
446C23×C4C23×C12711yescharacteristic
447C23×C4C23×C12711yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8D4×C12714yescomplemented
460C22×C8C23×C12711yescharacteristic
461C22×C8C23×C12711yescharacteristic
462C22×C8C23×C12711yescharacteristic
463C22×C8C23×C12711yescharacteristic
464C22×C8C23×C12711yescharacteristic
465C22×C8C23×C12711yescharacteristic
466C22×C8C23×C12711yescharacteristic
467C22×C8C23×C12711yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—22no—
476C2×C4⋊C4C2×C4×C12711yescharacteristic
477C2×C4⋊C4C2×C4×C12711yescharacteristic
478C2×C4⋊C4C2×C4×C12711yescharacteristic
479C2×C4⋊C4C2×C4×C12711yescharacteristic
480C2×C4⋊C4C2×C4×C12711yescharacteristic
481C2×C4⋊C4C2×C4×C12711yescharacteristic
482C2×C4⋊C4C2×C4×C12711yescharacteristic
483C2×C22⋊C4C2×C4×C12711yescharacteristic
484C2×C22⋊C4C2×C4×C12711yescharacteristic
485C2×C22⋊C4C2×C4×C12711yescharacteristic
486C2×C22⋊C4C2×C4×C12711yescharacteristic
487C2×C22⋊C4C2×C4×C12711yescharacteristic
488C2×C22⋊C4C2×C4×C12711yescharacteristic
489C2×C22⋊C4C2×C4×C12711yescharacteristic
490C2×C22⋊C4C2×C4×C12711yescharacteristic
491C2×C22⋊C4C2×C4×C12711yescharacteristic
492C2×C22⋊C4C2×C4×C12711yescharacteristic
493C2×C22⋊C4C2×C4×C12711yescharacteristic
494C2×C22⋊C4C2×C4×C12711yescharacteristic
495C2×C42C23×C12711yescharacteristic
496C2×C42C23×C12711yescharacteristic
497C2×C42C23×C12711yescharacteristic
498C2×C42C23×C12711yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—22no—
502C4⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511#97—22no—
512#97—22no—
513#97D4×C12714yescomplemented
514C4×C8—22no—
515C4×C8—22no—
516C4×C8—22no—
517#95C2×C4×C12711yescharacteristic
518#95C2×C4×C12711yescharacteristic
519#95C2×C4×C12711yescharacteristic
520#95C2×C4×C12711yescharacteristic
521#95C2×C4×C12711yescharacteristic
522#95C2×C4×C12711yescharacteristic
523C24C22×C4×C12711yescharacteristic
524C24C22×C4×C12711yescharacteristic
525C24C22×C4×C12711yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4C22×C4×C12711yescharacteristic
552C22×C4C22×C4×C12711yescharacteristic
553C22×C4C22×C4×C12711yescharacteristic
554C22×C4C22×C4×C12711yescharacteristic
555C22×C4C22×C4×C12711yescharacteristic
556C22×C4C22×C4×C12711yescharacteristic
557C22×C4C22×C4×C12711yescharacteristic
558C22×C4C22×C4×C12711yescharacteristic
559C22×C4C22×C4×C12711yescharacteristic
560C22×C4C22×C4×C12711yescharacteristic
561C22×C4C22×C4×C12711yescharacteristic
562C22×C4C2×D4×C12712yes—
563C22×C4#41×C12712yes—
564C22×C4C24×C12711yescharacteristic
565M16—28no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—28no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8C2×D4×C12712yes—
588C2×C8C2×D4×C12712yes—
589C2×C8C2×D4×C12712yes—
590C2×C8C2×D4×C12712yes—
591C2×C8#41×C12712yes—
592C2×C8#41×C12712yes—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C12712yes—
619C42#41×C12712yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C4×D4×C12712yes—
640C23#131×C12712yes—
641C23C23×C4×C12711yescharacteristic
642D4—28no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4C4×D4×C12712yes—
687C2×C4C4×D4×C12712yes—
688C2×C4C4×D4×C12712yes—
689C2×C4#131×C12712yes—
690C2×C4C22×D4×C12711yescharacteristic
691C2×C4C22×D4×C12711yescharacteristic
692C2×C4C2×#41×C12711yescharacteristic
693C2×C4C2×#41×C12711yescharacteristic
694C2×C4C2×#41×C12711yescharacteristic
695C2×C4C2×#41×C12711yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8#121×C12714yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×C4×D4×C12711yescharacteristic
726C22C2×C4×D4×C12711yescharacteristic
727C22C4×#41×C12711yescharacteristic
728C22C2×#131×C12711yescharacteristic
729C22C2×#131×C12711yescharacteristic
730C22#568×C12711yescharacteristic
731C22#568×C12711yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4C2×#121×C12711yescharacteristic
744C4#525×C12711yescharacteristic
745C4#529×C12711yescharacteristic
746C4#532×C12711yescharacteristic
747C2—42no—
748C2—42no—
749C2—81no—
750C2C4×#121×C12711yescharacteristic
751C2C127×#292911yescharacteristic
752C2C127×#293011yescharacteristic
753C2C127×#293311yescharacteristic
754C2C127×#293511yescharacteristic
755C2C127×#296811yescharacteristic
756C2C127×#296911yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radical#392×C127C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C127C2semidirect
2. C2×#435×C127C2semidirect
3. C2×C8×D4×C127C2semidirect
4. C2×#405×C127C2semidirect
6. C127×#1954C2semidirect
7. C127×#1939C2semidirect
8. C127×#1923C2semidirect
9. C127×#1923C2semidirect
10. C127×#1870C2semidirect
11. C127×#1870C2semidirect
12. C127×#1798C2semidirect
13. C127×#1771C2semidirect
14. C127×#1753C2semidirect
15. C127×#1752C2semidirect
80. C22×C8×C127D4semidirect
134. #97×C127D4semidirect
368. #21495C127direct (N × H)
379. C2×#435C2×C127semidirect
380. C2×#435C2×C127semidirect
381. C2×C8×D4C2×C127semidirect
382. C2×#405C2×C127semidirect
384. #1954C2×C127semidirect
385. #1939C2×C127semidirect
386. #1923C2×C127semidirect
387. #1923C2×C127semidirect
388. #1870C2×C127semidirect
389. #1870C2×C127semidirect
390. #1798C2×C127semidirect
391. #1771C2×C127semidirect
392. #1753C2×C127semidirect
393. #1752C2×C127semidirect
394. C127#21495direct (N × H)
459. C22×C8D4×C127semidirect
513. #97D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1272
C2×C8×D4×C1272
C2×#405×C1272
C127×#23922
C127×#19542
C127×#19392
C127×#19232
C127×#18702
C127×#17982
C127×#17712
C127×#17532
C127×#17522
#21495127