Finite Group Databasebeta

← C127×#14468 #44578141

Subgroups — C127×#14468 #44578141

Order 32512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C211yesmaximal, characteristic
3C2×#387×C127C211yesmaximal, characteristic
4C127×#1444C211yesmaximal, characteristic
5C127×#1444C211yesmaximal, characteristic
6C127×#1444C211yesmaximal, characteristic
7C127×#1442C211yesmaximal, characteristic
8C127×#1442C211yesmaximal, characteristic
9C127×#1441C211yesmaximal, characteristic
10C127×#1436C211yesmaximal, characteristic
11C127×#1436C211yesmaximal, characteristic
12C127×#1436C211yesmaximal, characteristic
13C127×C4⋊#95C211yesmaximal, characteristic
14C127×C4⋊#95C211yesmaximal, characteristic
15C127×C4⋊#95C211yesmaximal, characteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28C22×C42×C127C2211yescharacteristic
29#389×C127—24no—
30#387×C127—24no—
31#387×C127C418yescomplemented
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—41no—
79C2×C4⋊C4×C127—41no—
80C2×C4⋊C4×C127—41no—
81C2×C4⋊C4×C127—41no—
82C2×C4⋊C4×C127—41no—
83C2×C4⋊C4×C127—41no—
84C2×C4⋊C4×C127—41no—
85C2×C4⋊C4×C127—41no—
86C2×C4⋊C4×C127—41no—
87C2×C4⋊C4×C127—41no—
88C2×C4⋊C4×C127—41no—
89C2×C4⋊C4×C127—41no—
90C2×C4⋊C4×C127—41no—
91C2×C4⋊C4×C127—41no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127—41no—
94C2×C4⋊C4×C127C2×C414yes—
95C2×C4⋊C4×C127C2×C414yes—
96C2×C4⋊C4×C127D414yes—
97C2×C4⋊C4×C127Q814yes—
98C2×C4⋊C4×C127Q814yes—
99C2×C42×C127—22no—
100C2×C42×C127—22no—
101C2×C42×C127—22no—
102C2×C42×C127—41no—
103C2×C42×C127—41no—
104C2×C42×C127—41no—
105C2×C42×C127—41no—
106C2×C42×C127—41no—
107C2×C42×C127C2×C414yes—
108#95×C127—22no—
109#95×C127—22no—
110#95×C127—22no—
111#95×C127—22no—
112#95×C127—22no—
113#95×C127—22no—
114#95×C127—22no—
115#95×C127—22no—
116#95×C127—22no—
117#95×C127—41no—
118#95×C127—41no—
119#95×C127—41no—
120#95×C127—41no—
121#95×C127—41no—
122#95×C127—41no—
123#95×C127—41no—
124#95×C127—41no—
125#95×C127—41no—
126#95×C127C2×C414yes—
127#95×C127C2×C414yes—
128#95×C127C2×C414yes—
129#95×C127C2×C414yes—
130C24×C127C2411yescharacteristic
131C22×C4×C127—21no—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
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×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
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×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127C22×C412yes—
218C22×C4×C127C22×C412yes—
219C22×C4×C127C22×C412yes—
220C22×C4×C127C22×C412yes—
221C22×C4×C127C22×C412yes—
222C22×C4×C127C22×C412yes—
223C22×C4×C127C22×C412yes—
224C22×C4×C127C2×D412yes—
225C22×C4×C127C2×D412yes—
226C22×C4×C127C2×D412yes—
227C22×C4×C127C2×Q812yes—
228C22×C4×C127C2×Q812yes—
229C22×C4×C127C2×Q812yes—
230C22×C4×C127C2×Q812yes—
231C22×C4×C127C2×Q812yes—
232C22×C4×C127C2×Q812yes—
233C22×C4×C127#4112yes—
234C22×C4×C127#4112yes—
235C22×C4×C127#4112yes—
236C4⋊C4×C127—44no—
237C4⋊C4×C127—44no—
238C4⋊C4×C127—44no—
239C4⋊C4×C127—44no—
240C4⋊C4×C127—44no—
241C4⋊C4×C127—44no—
242C4⋊C4×C127—44no—
243C4⋊C4×C127—44no—
244C4⋊C4×C127—44no—
245C4⋊C4×C127C4⋊C4116yescomplemented
246C42×C127—44no—
247C42×C127—44no—
248C42×C127—44no—
249C23×C127C23×C411yescharacteristic
250C23×C127C22×D411yescharacteristic
251C23×C127C22×Q811yescharacteristic
252C23×C127C22×Q811yescharacteristic
253C23×C127C2×#4111yescharacteristic
254C23×C127C2×#4111yescharacteristic
255C23×C127C2×#4111yescharacteristic
256C23×C127H(5,𝔽2)11yescharacteristic
257C23×C127H(5,𝔽2)11yescharacteristic
258C23×C127H(5,𝔽2)11yescharacteristic
259C23×C127H(5,𝔽2)11yescharacteristic
260C23×C127H(5,𝔽2)11yescharacteristic
261C23×C1272−1+411yescharacteristic
262C23×C1272−1+411yescharacteristic
263C23×C1272−1+411yescharacteristic
264C2×C4×C127—22no—
265C2×C4×C127—22no—
266C2×C4×C127—22no—
267C2×C4×C127—22no—
268C2×C4×C127—22no—
269C2×C4×C127—22no—
270C2×C4×C127—22no—
271C2×C4×C127—22no—
272C2×C4×C127—22no—
273C2×C4×C127—22no—
274C2×C4×C127—22no—
275C2×C4×C127—22no—
276C2×C4×C127—22no—
277C2×C4×C127—22no—
278C2×C4×C127—22no—
279C2×C4×C127—22no—
280C2×C4×C127—22no—
281C2×C4×C127—22no—
282C2×C4×C127—22no—
283C2×C4×C127—22no—
284C2×C4×C127—22no—
285C2×C4×C127—22no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—22no—
303C2×C4×C127—22no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—41no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
343C2×C4×C127—41no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—41no—
347C2×C4×C127—41no—
348C2×C4×C127—41no—
349C2×C4×C127—41no—
350C2×C4×C127—41no—
351C2×C4×C127—41no—
352C2×C4×C127—41no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—41no—
356C2×C4×C127—41no—
357C2×C4×C127—41no—
358C2×C4×C127—41no—
359C2×C4×C127—41no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127C2×C4⋊C414yes—
366C2×C4×C127C2×C4⋊C414yes—
367C2×C4×C127C2×C4⋊C414yes—
368C2×C4×C127C4×Q814yes—
369C22×C127C22×C4⋊C411yescharacteristic
370C22×C127C2×C4×Q811yescharacteristic
371C22×C127C4×#4111yescharacteristic
372C22×C127#51811yescharacteristic
373C22×C127#52011yescharacteristic
374C22×C127#52011yescharacteristic
375C22×C127#52011yescharacteristic
376C22×C127#53511yescharacteristic
377C22×C127#53611yescharacteristic
378C22×C127#53811yescharacteristic
379C22×C127#53811yescharacteristic
380C22×C127#53911yescharacteristic
381C22×C127#53911yescharacteristic
382C22×C127#54111yescharacteristic
383C22×C127#54211yescharacteristic
384C22×C127#54311yescharacteristic
385C22×C127#54411yescharacteristic
386C22×C127#54411yescharacteristic
387C22×C127#54411yescharacteristic
388C22×C127#54611yescharacteristic
389C22×C127#54611yescharacteristic
390C22×C127D4×Q811yescharacteristic
391C22×C127#55011yescharacteristic
392C22×C127#55211yescharacteristic
393C22×C127#55311yescharacteristic
394C22×C127#55411yescharacteristic
395C22×C127#55411yescharacteristic
396C22×C127#55411yescharacteristic
397C22×C127#55711yescharacteristic
398C22×C127#55711yescharacteristic
399C22×C127Q8211yescharacteristic
400C22×C127#56011yescharacteristic
401C22×C127#56211yescharacteristic
402C22×C127#56211yescharacteristic
403C22×C127#56311yescharacteristic
404C4×C127—24no—
405C4×C127—24no—
406C4×C127—24no—
407C4×C127—24no—
408C4×C127—42no—
409C4×C127—42no—
410C4×C127—42no—
411C4×C127—42no—
412C4×C127—42no—
413C4×C127—42no—
414C4×C127—42no—
415C4×C127—81no—
416C4×C127—81no—
417C4×C127—81no—
418C4×C127—81no—
419#14468C12711yesmaximal, characteristic, direct product factor, Sylow
420C2×C127#231711yescharacteristic
421C2×C127#232911yescharacteristic
422C2×C127#233411yescharacteristic
423C2×C127#234911yescharacteristic
424C2×C127Q8×C4⋊C411yescharacteristic
425C2×C127#237011yescharacteristic
426C2×C127#237611yescharacteristic
427C2×C127#269211yescharacteristic
428C2×C127#269411yescharacteristic
429C2×C127#271311yescharacteristic
430C2×C127#271411yescharacteristic
431C2×C127#277411yescharacteristic
432C2×C127#279211yescharacteristic
433C2×C127#280211yescharacteristic
434C2×C127#280611yescharacteristic
435C2×#389C2×C12711yescharacteristic
436C2×#387C2×C12711yescharacteristic
437C2×#387C2×C12711yescharacteristic
438#1444C2×C12711yescharacteristic
439#1444C2×C12711yescharacteristic
440#1444C2×C12711yescharacteristic
441#1442C2×C12711yescharacteristic
442#1442C2×C12711yescharacteristic
443#1441C2×C12711yescharacteristic
444#1436C2×C12711yescharacteristic
445#1436C2×C12711yescharacteristic
446#1436C2×C12711yescharacteristic
447C4⋊#95C2×C12711yescharacteristic
448C4⋊#95C2×C12711yescharacteristic
449C4⋊#95C2×C12711yescharacteristic
450C127#1446811yescharacteristic, direct product factor, Sylow
451C22×C4⋊C4C22×C12711yescharacteristic
452C22×C4⋊C4C22×C12711yescharacteristic
453C22×C4⋊C4C22×C12711yescharacteristic
454C22×C4⋊C4C22×C12711yescharacteristic
455C22×C4⋊C4C22×C12711yescharacteristic
456C22×C4⋊C4C22×C12711yescharacteristic
457C22×C4⋊C4C22×C12711yescharacteristic
458C22×C4⋊C4C22×C12711yescharacteristic
459C22×C4⋊C4C22×C12711yescharacteristic
460C22×C4⋊C4C22×C12711yescharacteristic
461C22×C42C22×C12711yescharacteristic
462C22×C42C22×C12711yescharacteristic
463C22×C42C22×C12711yescharacteristic
464#389—24no—
465#387—24no—
466#387C4×C12718yescomplemented
467C2×#95C22×C12711yescharacteristic
468C2×#95C22×C12711yescharacteristic
469C2×#95C22×C12711yescharacteristic
470C2×#95C22×C12711yescharacteristic
471C2×#95C22×C12711yescharacteristic
472C2×#95C22×C12711yescharacteristic
473C2×#95C22×C12711yescharacteristic
474C2×#95C22×C12711yescharacteristic
475C2×#95C22×C12711yescharacteristic
476C2×#95C22×C12711yescharacteristic
477C2×#95C22×C12711yescharacteristic
478C2×#95C22×C12711yescharacteristic
479C2×#95C22×C12711yescharacteristic
480C2×#95C22×C12711yescharacteristic
481C2×#95C22×C12711yescharacteristic
482C2×#95C22×C12711yescharacteristic
483C2×#95C22×C12711yescharacteristic
484C2×#95C22×C12711yescharacteristic
485C2×#95C22×C12711yescharacteristic
486C2×#95C22×C12711yescharacteristic
487C2×#95C22×C12711yescharacteristic
488C2×#95C22×C12711yescharacteristic
489C23×C4C23×C12711yescharacteristic
490C23×C4C23×C12711yescharacteristic
491C23×C4C23×C12711yescharacteristic
492C23×C4C23×C12711yescharacteristic
493C23×C4C23×C12711yescharacteristic
494C23×C4C23×C12711yescharacteristic
495C23×C4C23×C12711yescharacteristic
496C23×C4C23×C12711yescharacteristic
497C23×C4C23×C12711yescharacteristic
498C23×C4C23×C12711yescharacteristic
499C23×C4C23×C12711yescharacteristic
500C23×C4C23×C12711yescharacteristic
501C23×C4C23×C12711yescharacteristic
502C23×C4C23×C12711yescharacteristic
503C23×C4C23×C12711yescharacteristic
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4C2×C4×C12714yes—
530C2×C4⋊C4C2×C4×C12714yes—
531C2×C4⋊C4D4×C12714yes—
532C2×C4⋊C4Q8×C12714yes—
533C2×C4⋊C4Q8×C12714yes—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—41no—
538C2×C42—41no—
539C2×C42—41no—
540C2×C42—41no—
541C2×C42—41no—
542C2×C42C2×C4×C12714yes—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—41no—
553#95—41no—
554#95—41no—
555#95—41no—
556#95—41no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95C2×C4×C12714yes—
562#95C2×C4×C12714yes—
563#95C2×C4×C12714yes—
564#95C2×C4×C12714yes—
565C24C24×C12711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4C22×C4×C12712yes—
653C22×C4C22×C4×C12712yes—
654C22×C4C22×C4×C12712yes—
655C22×C4C22×C4×C12712yes—
656C22×C4C22×C4×C12712yes—
657C22×C4C22×C4×C12712yes—
658C22×C4C22×C4×C12712yes—
659C22×C4C2×D4×C12712yes—
660C22×C4C2×D4×C12712yes—
661C22×C4C2×D4×C12712yes—
662C22×C4C2×Q8×C12712yes—
663C22×C4C2×Q8×C12712yes—
664C22×C4C2×Q8×C12712yes—
665C22×C4C2×Q8×C12712yes—
666C22×C4C2×Q8×C12712yes—
667C22×C4C2×Q8×C12712yes—
668C22×C4#41×C12712yes—
669C22×C4#41×C12712yes—
670C22×C4#41×C12712yes—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4C4⋊C4×C127116yescomplemented
681C42—44no—
682C42—44no—
683C42—44no—
684C23C23×C4×C12711yescharacteristic
685C23C22×D4×C12711yescharacteristic
686C23C22×Q8×C12711yescharacteristic
687C23C22×Q8×C12711yescharacteristic
688C23C2×#41×C12711yescharacteristic
689C23C2×#41×C12711yescharacteristic
690C23C2×#41×C12711yescharacteristic
691C23H(5,𝔽2)×C12711yescharacteristic
692C23H(5,𝔽2)×C12711yescharacteristic
693C23H(5,𝔽2)×C12711yescharacteristic
694C23H(5,𝔽2)×C12711yescharacteristic
695C23H(5,𝔽2)×C12711yescharacteristic
696C232−1+4×C12711yescharacteristic
697C232−1+4×C12711yescharacteristic
698C232−1+4×C12711yescharacteristic
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4C2×C4⋊C4×C12714yes—
801C2×C4C2×C4⋊C4×C12714yes—
802C2×C4C2×C4⋊C4×C12714yes—
803C2×C4C4×Q8×C12714yes—
804C22C22×C4⋊C4×C12711yescharacteristic
805C22C2×C4×Q8×C12711yescharacteristic
806C22C4×#41×C12711yescharacteristic
807C22#518×C12711yescharacteristic
808C22#520×C12711yescharacteristic
809C22#520×C12711yescharacteristic
810C22#520×C12711yescharacteristic
811C22#535×C12711yescharacteristic
812C22#536×C12711yescharacteristic
813C22#538×C12711yescharacteristic
814C22#538×C12711yescharacteristic
815C22#539×C12711yescharacteristic
816C22#539×C12711yescharacteristic
817C22#541×C12711yescharacteristic
818C22#542×C12711yescharacteristic
819C22#543×C12711yescharacteristic
820C22#544×C12711yescharacteristic
821C22#544×C12711yescharacteristic
822C22#544×C12711yescharacteristic
823C22#546×C12711yescharacteristic
824C22#546×C12711yescharacteristic
825C22D4×Q8×C12711yescharacteristic
826C22#550×C12711yescharacteristic
827C22#552×C12711yescharacteristic
828C22#553×C12711yescharacteristic
829C22#554×C12711yescharacteristic
830C22#554×C12711yescharacteristic
831C22#554×C12711yescharacteristic
832C22#557×C12711yescharacteristic
833C22#557×C12711yescharacteristic
834C22Q82×C12711yescharacteristic
835C22#560×C12711yescharacteristic
836C22#562×C12711yescharacteristic
837C22#562×C12711yescharacteristic
838C22#563×C12711yescharacteristic
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C2C127×#231711yescharacteristic
855C2C127×#232911yescharacteristic
856C2C127×#233411yescharacteristic
857C2C127×#234911yescharacteristic
858C2Q8×C4⋊C4×C12711yescharacteristic
859C2C127×#237011yescharacteristic
860C2C127×#237611yescharacteristic
861C2C127×#269211yescharacteristic
862C2C127×#269411yescharacteristic
863C2C127×#271311yescharacteristic
864C2C127×#271411yescharacteristic
865C2C127×#277411yescharacteristic
866C2C127×#279211yescharacteristic
867C2C127×#280211yescharacteristic
868C2C127×#280611yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
31. #387×C127C4semidirect
245. C4⋊C4×C127C4⋊C4semidirect
419. #14468C127direct (N × H)
450. C127#14468direct (N × H)
466. #387C4×C127semidirect
680. C4⋊C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C127×#14442
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
#14468127