Finite Group Databasebeta

← C127×#21571 #44585244

Subgroups — C127×#21571 #44585244

Order 32512.

872 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C127C211yesmaximal, characteristic
2C2×#405×C127C211yesmaximal, characteristic, complemented
3C127×#2395C211yesmaximal, characteristic
4C127×#1924C211yesmaximal, characteristic, complemented
5C127×#1923C211yesmaximal, characteristic, complemented
6C127×#1917C211yesmaximal, characteristic, complemented
7C127×#1916C211yesmaximal, characteristic, complemented
8C127×#1869C211yesmaximal, characteristic
9C127×#1850C211yesmaximal, characteristic, complemented
10C127×#1818C211yesmaximal, characteristic, complemented
11C127×#1771C211yesmaximal, characteristic, complemented
12C8×C4⋊C4×C127C211yesmaximal, characteristic, complemented
13C127×#1753C211yesmaximal, characteristic, complemented
14C127×#1753C211yesmaximal, characteristic, complemented
15C127×#1753C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C2×C4×D4×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21#436×C127—24no—
22C2×C4⋊C8×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×C22⋊C8×C127C2211yescharacteristic
26C2×C22⋊C8×C127C2211yescharacteristic
27C2×C22⋊C8×C127C2211yescharacteristic
28C2×C22⋊C8×C127C2211yescharacteristic
29C2×C22⋊C8×C127C2211yescharacteristic
30#405×C127—24no—
31C2×#97×C127C2211yescharacteristic
32C2×#97×C127C2211yescharacteristic
33C2×#97×C127C2211yescharacteristic
34C2×C4×C8×C127C2211yescharacteristic
35C2×C4×C8×C127C2211yescharacteristic
36C2×C4×C8×C127C2211yescharacteristic
37C2×C4×C8×C127C2211yescharacteristic
38#400×C127C411yescharacteristic
39#399×C127C411yescharacteristic
40#398×C127C411yescharacteristic
41#397×C127C411yescharacteristic
42#397×C127C411yescharacteristic
43#397×C127C411yescharacteristic
44#394×C127C411yescharacteristic
45#394×C127C411yescharacteristic
46C4×C4⋊C4×C127C2211yescharacteristic
47C4×C4⋊C4×C127C2211yescharacteristic
48C4×C22⋊C4×C127C2211yescharacteristic
49C4×C22⋊C4×C127C2211yescharacteristic
50C4×C22⋊C4×C127C2211yescharacteristic
51#336×C127C2211yescharacteristic
52#336×C127C2211yescharacteristic
53#336×C127C2211yescharacteristic
54#336×C127C2211yescharacteristic
55#336×C127C2211yescharacteristic
56#336×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61C22×D4×C127C2×C411yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C2×M16×C127—22no—
65C2×M16×C127—22no—
66C2×M16×C127—22no—
67C2×M16×C127—22no—
68C2×M16×C127—22no—
69C2×M16×C127D414yes—
70C22×C8×C127—22no—
71C22×C8×C127—22no—
72C22×C8×C127—22no—
73C22×C8×C127C2311yescharacteristic
74C22×C8×C127C2311yescharacteristic
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22×C8×C127C2311yescharacteristic
81C4×D4×C127—22no—
82C4×D4×C127—22no—
83#117×C127—22no—
84#117×C127—22no—
85C2×C4⋊C4×C127C2×C411yescharacteristic
86C2×C4⋊C4×C127C2×C411yescharacteristic
87C2×C4⋊C4×C127C2×C411yescharacteristic
88C2×C4⋊C4×C127C2×C411yescharacteristic
89C2×C4⋊C4×C127C2×C411yescharacteristic
90C2×C4⋊C4×C127C2×C411yescharacteristic
91C2×C4⋊C4×C127C2×C411yescharacteristic
92C2×C22⋊C4×C127C2×C411yescharacteristic
93C2×C22⋊C4×C127C2×C411yescharacteristic
94C2×C22⋊C4×C127C2×C411yescharacteristic
95C2×C22⋊C4×C127C2×C411yescharacteristic
96C2×C22⋊C4×C127C2×C411yescharacteristic
97C2×C22⋊C4×C127C2×C411yescharacteristic
98C2×C22⋊C4×C127C2×C411yescharacteristic
99C2×C22⋊C4×C127C2×C411yescharacteristic
100C2×C22⋊C4×C127C2×C411yescharacteristic
101C2×C22⋊C4×C127C2×C411yescharacteristic
102C2×C42×C127C2311yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C2×C42×C127C2311yescharacteristic
105C2×C42×C127C2311yescharacteristic
106C2×C42×C127C2311yescharacteristic
107C4⋊C8×C127—22no—
108C4⋊C8×C127—22no—
109C4⋊C8×C127—22no—
110C22⋊C8×C127—22no—
111C22⋊C8×C127—22no—
112C22⋊C8×C127—22no—
113C22⋊C8×C127—22no—
114C22⋊C8×C127—22no—
115#97×C127—22no—
116#97×C127—22no—
117#97×C127—22no—
118C4×C8×C127—22no—
119C4×C8×C127—22no—
120C4×C8×C127—22no—
121C4×C8×C127—22no—
122#95×C127C2×C411yescharacteristic
123#95×C127C2×C411yescharacteristic
124#95×C127C2×C411yescharacteristic
125#95×C127C2×C411yescharacteristic
126#95×C127C2×C411yescharacteristic
127#95×C127C2×C411yescharacteristic
128#95×C127C2×C411yescharacteristic
129#95×C127C2×C411yescharacteristic
130#95×C127C2×C411yescharacteristic
131#95×C127C2×C411yescharacteristic
132C24×C127C22×C411yescharacteristic
133C24×C127C22×C411yescharacteristic
134C2×D4×C127—22no—
135C2×D4×C127—22no—
136C2×D4×C127—41no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127C22×C411yescharacteristic
148C22×C4×C127C22×C411yescharacteristic
149C22×C4×C127C22×C411yescharacteristic
150C22×C4×C127C22×C411yescharacteristic
151C22×C4×C127C22×C411yescharacteristic
152C22×C4×C127C22×C411yescharacteristic
153C22×C4×C127C22×C411yescharacteristic
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C22×C411yescharacteristic
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C2×D412yes—
160C22×C4×C127#4112yes—
161C22×C4×C127C2411yescharacteristic
162M16×C127—28no—
163M16×C127—44no—
164C2×C8×C127—28no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127C2×D412yes—
184C2×C8×C127C2×D412yes—
185C2×C8×C127#4112yes—
186C2×C8×C127#4112yes—
187C2×C8×C127#4112yes—
188C2×C8×C127#4112yes—
189C4⋊C4×C127—22no—
190C4⋊C4×C127—22no—
191C4⋊C4×C127—22no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—22no—
195C4⋊C4×C127—41no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—22no—
200C22⋊C4×C127—22no—
201C22⋊C4×C127—22no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C42×C127—21no—
207C42×C127—21no—
208C42×C127—21no—
209C42×C127—21no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—21no—
214C42×C127—21no—
215C42×C127—21no—
216C23×C127—21no—
217C23×C127—21no—
218C23×C127—21no—
219C23×C127—21no—
220C23×C127—21no—
221C23×C127—21no—
222C23×C127—21no—
223C23×C127—21no—
224C23×C127—21no—
225C23×C127—21no—
226C23×C127—21no—
227C23×C127—21no—
228C23×C127—21no—
229C23×C127C4×D412yes—
230C23×C127C23×C411yescharacteristic
231D4×C127—44no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—22no—
239C2×C4×C127—22no—
240C2×C4×C127—22no—
241C2×C4×C127—22no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
262C2×C4×C127—21no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
268C2×C4×C127—21no—
269C2×C4×C127—41no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127C4×D412yes—
274C2×C4×C127#13112yes—
275C2×C4×C127#13112yes—
276C2×C4×C127C22×D411yescharacteristic
277C2×C4×C127C2×#4111yescharacteristic
278C2×C4×C127C2×#4111yescharacteristic
279C2×C4×C127C2×#4111yescharacteristic
280C2×C4×C127C2×#4111yescharacteristic
281C2×C4×C127C2×#4111yescharacteristic
282C8×C127—22no—
283C8×C127—22no—
284C8×C127—22no—
285C8×C127—41no—
286C8×C127—41no—
287C8×C127—41no—
288C8×C127—41no—
289C8×C127#12314yes—
290C22×C127—22no—
291C22×C127—22no—
292C22×C127—22no—
293C22×C127—41no—
294C22×C127—41no—
295C22×C127—41no—
296C22×C127—41no—
297C22×C127—41no—
298C22×C127—41no—
299C22×C127—41no—
300C22×C127—41no—
301C22×C127—41no—
302C22×C127—41no—
303C22×C127—41no—
304C22×C127C2×C4×D411yescharacteristic
305C22×C127C4×#4111yescharacteristic
306C22×C127C4×#4111yescharacteristic
307C22×C127C2×#13111yescharacteristic
308C22×C127C2×#13111yescharacteristic
309C22×C127#56811yescharacteristic
310C22×C127#56811yescharacteristic
311C4×C127—22no—
312C4×C127—22no—
313C4×C127—22no—
314C4×C127—41no—
315C4×C127—41no—
316C4×C127—41no—
317C4×C127—41no—
318C4×C127—41no—
319C4×C127—41no—
320C4×C127—41no—
321C4×C127—41no—
322C4×C127—41no—
323C4×C127C2×#12311yescharacteristic
324C4×C127#52511yescharacteristic
325C4×C127#52911yescharacteristic
326C4×C127#52911yescharacteristic
327#21571C12711yesmaximal, characteristic, direct product factor, Sylow
328C2×C127—42no—
329C2×C127—81no—
330C2×C127C4×#12311yescharacteristic
331C2×C127#293311yescharacteristic
332C2×C127#293511yescharacteristic
333C2×C127#296611yescharacteristic
334C2×C127#296711yescharacteristic
335C2×C127#296911yescharacteristic
336C2×C127#296911yescharacteristic
337C2×#436C2×C12711yescharacteristic
338C2×#405C2×C12711yescharacteristic, complemented
339#2395C2×C12711yescharacteristic
340#1924C2×C12711yescharacteristic, complemented
341#1923C2×C12711yescharacteristic, complemented
342#1917C2×C12711yescharacteristic, complemented
343#1916C2×C12711yescharacteristic, complemented
344#1869C2×C12711yescharacteristic
345#1850C2×C12711yescharacteristic, complemented
346#1818C2×C12711yescharacteristic, complemented
347#1771C2×C12711yescharacteristic, complemented
348C8×C4⋊C4C2×C12711yescharacteristic, complemented
349#1753C2×C12711yescharacteristic, complemented
350#1753C2×C12711yescharacteristic, complemented
351#1753C2×C12711yescharacteristic, complemented
352C127#2157111yescharacteristic, direct product factor, Sylow
353C22×M16C22×C12711yescharacteristic
354C22×M16C22×C12711yescharacteristic
355C23×C8C22×C12711yescharacteristic
356C2×C4×D4C22×C12711yescharacteristic
357C2×#117C22×C12711yescharacteristic
358#436—24no—
359C2×C4⋊C8C22×C12711yescharacteristic
360C2×C4⋊C8C22×C12711yescharacteristic
361C2×C4⋊C8C22×C12711yescharacteristic
362C2×C22⋊C8C22×C12711yescharacteristic
363C2×C22⋊C8C22×C12711yescharacteristic
364C2×C22⋊C8C22×C12711yescharacteristic
365C2×C22⋊C8C22×C12711yescharacteristic
366C2×C22⋊C8C22×C12711yescharacteristic
367#405—24no—
368C2×#97C22×C12711yescharacteristic
369C2×#97C22×C12711yescharacteristic
370C2×#97C22×C12711yescharacteristic
371C2×C4×C8C22×C12711yescharacteristic
372C2×C4×C8C22×C12711yescharacteristic
373C2×C4×C8C22×C12711yescharacteristic
374C2×C4×C8C22×C12711yescharacteristic
375#400C4×C12711yescharacteristic
376#399C4×C12711yescharacteristic
377#398C4×C12711yescharacteristic
378#397C4×C12711yescharacteristic
379#397C4×C12711yescharacteristic
380#397C4×C12711yescharacteristic
381#394C4×C12711yescharacteristic
382#394C4×C12711yescharacteristic
383C4×C4⋊C4C22×C12711yescharacteristic
384C4×C4⋊C4C22×C12711yescharacteristic
385C4×C22⋊C4C22×C12711yescharacteristic
386C4×C22⋊C4C22×C12711yescharacteristic
387C4×C22⋊C4C22×C12711yescharacteristic
388#336C22×C12711yescharacteristic
389#336C22×C12711yescharacteristic
390#336C22×C12711yescharacteristic
391#336C22×C12711yescharacteristic
392#336C22×C12711yescharacteristic
393#336C22×C12711yescharacteristic
394#336C22×C12711yescharacteristic
395#336C22×C12711yescharacteristic
396#336C22×C12711yescharacteristic
397#336C22×C12711yescharacteristic
398C22×D4C2×C4×C12711yescharacteristic
399C23×C4C23×C12711yescharacteristic
400C23×C4C23×C12711yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16D4×C12714yes—
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—22no—
410C22×C8C23×C12711yescharacteristic
411C22×C8C23×C12711yescharacteristic
412C22×C8C23×C12711yescharacteristic
413C22×C8C23×C12711yescharacteristic
414C22×C8C23×C12711yescharacteristic
415C22×C8C23×C12711yescharacteristic
416C22×C8C23×C12711yescharacteristic
417C22×C8C23×C12711yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4C2×C4×C12711yescharacteristic
423C2×C4⋊C4C2×C4×C12711yescharacteristic
424C2×C4⋊C4C2×C4×C12711yescharacteristic
425C2×C4⋊C4C2×C4×C12711yescharacteristic
426C2×C4⋊C4C2×C4×C12711yescharacteristic
427C2×C4⋊C4C2×C4×C12711yescharacteristic
428C2×C4⋊C4C2×C4×C12711yescharacteristic
429C2×C22⋊C4C2×C4×C12711yescharacteristic
430C2×C22⋊C4C2×C4×C12711yescharacteristic
431C2×C22⋊C4C2×C4×C12711yescharacteristic
432C2×C22⋊C4C2×C4×C12711yescharacteristic
433C2×C22⋊C4C2×C4×C12711yescharacteristic
434C2×C22⋊C4C2×C4×C12711yescharacteristic
435C2×C22⋊C4C2×C4×C12711yescharacteristic
436C2×C22⋊C4C2×C4×C12711yescharacteristic
437C2×C22⋊C4C2×C4×C12711yescharacteristic
438C2×C22⋊C4C2×C4×C12711yescharacteristic
439C2×C42C23×C12711yescharacteristic
440C2×C42C23×C12711yescharacteristic
441C2×C42C23×C12711yescharacteristic
442C2×C42C23×C12711yescharacteristic
443C2×C42C23×C12711yescharacteristic
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452#97—22no—
453#97—22no—
454#97—22no—
455C4×C8—22no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459#95C2×C4×C12711yescharacteristic
460#95C2×C4×C12711yescharacteristic
461#95C2×C4×C12711yescharacteristic
462#95C2×C4×C12711yescharacteristic
463#95C2×C4×C12711yescharacteristic
464#95C2×C4×C12711yescharacteristic
465#95C2×C4×C12711yescharacteristic
466#95C2×C4×C12711yescharacteristic
467#95C2×C4×C12711yescharacteristic
468#95C2×C4×C12711yescharacteristic
469C24C22×C4×C12711yescharacteristic
470C24C22×C4×C12711yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—41no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4C22×C4×C12711yescharacteristic
485C22×C4C22×C4×C12711yescharacteristic
486C22×C4C22×C4×C12711yescharacteristic
487C22×C4C22×C4×C12711yescharacteristic
488C22×C4C22×C4×C12711yescharacteristic
489C22×C4C22×C4×C12711yescharacteristic
490C22×C4C22×C4×C12711yescharacteristic
491C22×C4C22×C4×C12711yescharacteristic
492C22×C4C22×C4×C12711yescharacteristic
493C22×C4C22×C4×C12711yescharacteristic
494C22×C4C22×C4×C12711yescharacteristic
495C22×C4C22×C4×C12711yescharacteristic
496C22×C4C2×D4×C12712yes—
497C22×C4#41×C12712yes—
498C22×C4C24×C12711yescharacteristic
499M16—28no—
500M16—44no—
501C2×C8—28no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C12712yes—
521C2×C8C2×D4×C12712yes—
522C2×C8#41×C12712yes—
523C2×C8#41×C12712yes—
524C2×C8#41×C12712yes—
525C2×C8#41×C12712yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C4×D4×C12712yes—
567C23C23×C4×C12711yescharacteristic
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4C4×D4×C12712yes—
611C2×C4#131×C12712yes—
612C2×C4#131×C12712yes—
613C2×C4C22×D4×C12711yescharacteristic
614C2×C4C2×#41×C12711yescharacteristic
615C2×C4C2×#41×C12711yescharacteristic
616C2×C4C2×#41×C12711yescharacteristic
617C2×C4C2×#41×C12711yescharacteristic
618C2×C4C2×#41×C12711yescharacteristic
619C8—22no—
620C8—22no—
621C8—22no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#123×C12714yes—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×C4×D4×C12711yescharacteristic
642C22C4×#41×C12711yescharacteristic
643C22C4×#41×C12711yescharacteristic
644C22C2×#131×C12711yescharacteristic
645C22C2×#131×C12711yescharacteristic
646C22#568×C12711yescharacteristic
647C22#568×C12711yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4C2×#123×C12711yescharacteristic
661C4#525×C12711yescharacteristic
662C4#529×C12711yescharacteristic
663C4#529×C12711yescharacteristic
664C2—42no—
665C2—81no—
666C2C4×#123×C12711yescharacteristic
667C2C127×#293311yescharacteristic
668C2C127×#293511yescharacteristic
669C2C127×#296611yescharacteristic
670C2C127×#296711yescharacteristic
671C2C127×#296911yescharacteristic
672C2C127×#296911yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#405×C127C2semidirect
4. C127×#1924C2semidirect
5. C127×#1923C2semidirect
6. C127×#1917C2semidirect
7. C127×#1916C2semidirect
9. C127×#1850C2semidirect
10. C127×#1818C2semidirect
11. C127×#1771C2semidirect
12. C8×C4⋊C4×C127C2semidirect
13. C127×#1753C2semidirect
14. C127×#1753C2semidirect
15. C127×#1753C2semidirect
327. #21571C127direct (N × H)
338. C2×#405C2×C127semidirect
340. #1924C2×C127semidirect
341. #1923C2×C127semidirect
342. #1917C2×C127semidirect
343. #1916C2×C127semidirect
345. #1850C2×C127semidirect
346. #1818C2×C127semidirect
347. #1771C2×C127semidirect
348. C8×C4⋊C4C2×C127semidirect
349. #1753C2×C127semidirect
350. #1753C2×C127semidirect
351. #1753C2×C127semidirect
352. C127#21571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#436×C1272
C2×#405×C1272
C127×#23952
C127×#19242
C127×#19232
C127×#19172
C127×#19162
C127×#18692
C127×#18502
C127×#18182
C127×#17712
C8×C4⋊C4×C1272
C127×#17532
#21571127