Finite Group Databasebeta

← C127×#17400 #44581073

Subgroups — C127×#17400 #44581073

Order 32512.

1406 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C127C211yesmaximal, characteristic
2C2×#407×C127C211yesmaximal, characteristic, complemented
3C2×#407×C127C211yesmaximal, characteristic, complemented
4C127×#1472C212yesmaximal, complemented
5C127×#1471C212yesmaximal, complemented
6C127×#1468C214yesmaximal, complemented
7C127×#1465C214yesmaximal, complemented
8C22×#41×C127C411yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C22×M16×C127—21no—
11C22×M16×C127—21no—
12#525×C127—21no—
13#525×C127—21no—
14#525×C127—21no—
15#525×C127—21no—
16#525×C127—21no—
17#525×C127—21no—
18#525×C127—21no—
19#525×C127—21no—
20C2×#123×C127C2212yes—
21C2×C22⋊Q8×C127C411yescharacteristic
22C2×C22⋊Q8×C127C2211yescharacteristic
23C2×#121×C127C411yescharacteristic
24C2×#121×C127C2211yescharacteristic
25C2×#120×C127C412yes—
26C2×C4×D4×C127C412yes—
27C2×C4×D4×C127C2212yes—
28C2×#117×C127C411yescharacteristic
29#407×C127—21no—
30#407×C127—21no—
31#407×C127—21no—
32#407×C127—21no—
33#407×C127C2212yes—
34#407×C127C2212yes—
35#407×C127C2212yes—
36#407×C127C2212yes—
37C2×C22⋊C8×C127—21no—
38C2×C22⋊C8×C127—21no—
39C2×C22⋊C8×C127C2212yes—
40C2×C22⋊C8×C127C2212yes—
41#324×C127C2218yescomplemented
42#323×C127C2218yescomplemented
43C25×C127C2×C411yescharacteristic
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127—21no—
48C2×#41×C127—44no—
49C22×Q8×C127C2×C411yescharacteristic
50C22×D4×C127C2×C412yes—
51C22×D4×C127C2×C412yes—
52C22×D4×C127C2×C412yes—
53C22×D4×C127C2×C411yescharacteristic
54C23×C4×C127—44no—
55C23×C4×C127C2×C411yescharacteristic
56C23×C4×C127C2×C412yes—
57C23×C4×C127C2×C411yescharacteristic
58C23×C4×C127C2×C411yescharacteristic
59C23×C4×C127D411yescharacteristic
60C23×C4×C127D411yescharacteristic
61C23×C4×C127D411yescharacteristic
62C23×C4×C127D411yescharacteristic
63C23×C4×C127D411yescharacteristic
64C23×C4×C127D411yescharacteristic
65C23×C4×C127D411yescharacteristic
66C23×C4×C127D411yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C2×M16×C127—22no—
71C2×M16×C127—22no—
72C2×M16×C127—22no—
73C2×M16×C127—22no—
74C2×M16×C127—44no—
75C2×M16×C127—44no—
76C22×C8×C127—22no—
77C22×C8×C127—22no—
78#123×C127—22no—
79#123×C127—22no—
80#123×C127—22no—
81#123×C127—22no—
82C22⋊Q8×C127—21no—
83C22⋊Q8×C127—21no—
84C22⋊Q8×C127—21no—
85C22⋊Q8×C127—21no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90#121×C127—21no—
91#121×C127—21no—
92#121×C127—21no—
93#121×C127—21no—
94#121×C127—21no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—21no—
98#120×C127—22no—
99#120×C127—22no—
100#120×C127—22no—
101#120×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127—22no—
105C4×D4×C127—22no—
106C4×D4×C127—22no—
107C4×D4×C127—22no—
108C4×D4×C127—22no—
109C4×D4×C127—22no—
110#117×C127—21no—
111#117×C127—21no—
112#117×C127—21no—
113#117×C127—21no—
114C2×C4⋊C4×C127C2×C411yescharacteristic
115C2×C4⋊C4×C127C2×C411yescharacteristic
116C2×C4⋊C4×C127C2×C412yes—
117C2×C4⋊C4×C127C2312yes—
118C2×C22⋊C4×C127C2×C412yes—
119C2×C22⋊C4×C127C2×C412yes—
120C2×C22⋊C4×C127C2×C412yes—
121C2×C22⋊C4×C127C2×C412yes—
122C2×C22⋊C4×C127C2312yes—
123C2×C42×C127C2×C412yes—
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×C127C2314yes—
131C22⋊C8×C127C2314yes—
132C24×C127—42no—
133C24×C127—42no—
134C24×C127—42no—
135C24×C127C22⋊C411yescharacteristic
136C24×C127C22⋊C411yescharacteristic
137C24×C127C22⋊C411yescharacteristic
138C24×C127C22⋊C411yescharacteristic
139C24×C127C22×C411yescharacteristic
140C24×C127C22×C411yescharacteristic
141C24×C127C22×C412yes—
142C24×C127C22×C411yescharacteristic
143#41×C127—44no—
144#41×C127—44no—
145#41×C127—44no—
146#41×C127—44no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—42no—
150C2×D4×C127—22no—
151C2×D4×C127—22no—
152C2×D4×C127—22no—
153C2×D4×C127—22no—
154C2×D4×C127—22no—
155C2×D4×C127—22no—
156C2×D4×C127—21no—
157C2×D4×C127—21no—
158C2×D4×C127—44no—
159C2×D4×C127—42no—
160C2×D4×C127—44no—
161C2×D4×C127—44no—
162C22×C4×C127—24no—
163C22×C4×C127—24no—
164C22×C4×C127—24no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—42no—
168C22×C4×C127—42no—
169C22×C4×C127—42no—
170C22×C4×C127—42no—
171C22×C4×C127—42no—
172C22×C4×C127—42no—
173C22×C4×C127—42no—
174C22×C4×C127—42no—
175C22×C4×C127—42no—
176C22×C4×C127—42no—
177C22×C4×C127—42no—
178C22×C4×C127—44no—
179C22×C4×C127C22⋊C411yescharacteristic
180C22×C4×C127C22⋊C411yescharacteristic
181C22×C4×C127C22⋊C411yescharacteristic
182C22×C4×C127C22⋊C411yescharacteristic
183C22×C4×C127C22⋊C411yescharacteristic
184C22×C4×C127C22⋊C411yescharacteristic
185C22×C4×C127C22⋊C411yescharacteristic
186C22×C4×C127C22⋊C411yescharacteristic
187C22×C4×C127C22⋊C411yescharacteristic
188C22×C4×C127C22⋊C411yescharacteristic
189C22×C4×C127C22⋊C411yescharacteristic
190C22×C4×C127C22⋊C411yescharacteristic
191C22×C4×C127C22×C412yes—
192C22×C4×C127C22×C411yescharacteristic
193C22×C4×C127C22×C411yescharacteristic
194C22×C4×C127C22×C412yes—
195C22×C4×C127C22×C412yes—
196C22×C4×C127C22×C411yescharacteristic
197C22×C4×C127C2×D411yescharacteristic
198C22×C4×C127C2×D411yescharacteristic
199C22×C4×C127C2×D411yescharacteristic
200C22×C4×C127C2×D411yescharacteristic
201C22×C4×C127C2×D411yescharacteristic
202C22×C4×C127C2×D411yescharacteristic
203C22×C4×C127C2×D411yescharacteristic
204C22×C4×C127C2×D411yescharacteristic
205C22×C4×C127C2×D411yescharacteristic
206C22×C4×C127C2×D411yescharacteristic
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2411yescharacteristic
210M16×C127—44no—
211M16×C127—44no—
212M16×C127—44no—
213M16×C127—44no—
214C2×C8×C127—24no—
215C2×C8×C127—24no—
216C2×C8×C127—44no—
217C2×C8×C127—44no—
218C4⋊C4×C127—21no—
219C4⋊C4×C127—21no—
220C4⋊C4×C127—21no—
221C4⋊C4×C127—21no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—22no—
224C4⋊C4×C127—22no—
225C4⋊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—22no—
232C22⋊C4×C127—22no—
233C22⋊C4×C127—22no—
234C22⋊C4×C127—22no—
235C22⋊C4×C127—22no—
236C42×C127—22no—
237C42×C127—22no—
238C23×C127—22no—
239C23×C127—22no—
240C23×C127—22no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—24no—
249C23×C127—41no—
250C23×C127—41no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127—41no—
255C23×C127—41no—
256C23×C127—41no—
257C23×C127—41no—
258C23×C127—41no—
259C23×C127—41no—
260C23×C127—41no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—416no—
264C23×C127C2×C22⋊C411yescharacteristic
265C23×C127C2×C22⋊C411yescharacteristic
266C23×C127C2×C22⋊C411yescharacteristic
267C23×C127C2×C22⋊C411yescharacteristic
268C23×C127C2×C22⋊C411yescharacteristic
269C23×C127C2×C22⋊C411yescharacteristic
270C23×C127C23×C411yescharacteristic
271Q8×C127—42no—
272Q8×C127—42no—
273D4×C127—42no—
274D4×C127—44no—
275D4×C127—44no—
276D4×C127—44no—
277D4×C127—44no—
278D4×C127—44no—
279D4×C127—44no—
280D4×C127—42no—
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—24no—
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×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—44no—
313C2×C4×C127—44no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127#9914yes—
317C2×C4×C127C2×C22⋊C411yescharacteristic
318C2×C4×C127C2×C22⋊C411yescharacteristic
319C2×C4×C127C2×C22⋊C411yescharacteristic
320C2×C4×C127C2×C22⋊C411yescharacteristic
321C2×C4×C127C2×C22⋊C411yescharacteristic
322C2×C4×C127C2×C22⋊C411yescharacteristic
323C2×C4×C127C22×D411yescharacteristic
324C2×C4×C127C22×D411yescharacteristic
325C8×C127—44no—
326C8×C127—44no—
327C22×C127—21no—
328C22×C127—21no—
329C22×C127—21no—
330C22×C127—21no—
331C22×C127—21no—
332C22×C127—21no—
333C22×C127—21no—
334C22×C127—21no—
335C22×C127—21no—
336C22×C127—21no—
337C22×C127—21no—
338C22×C127—21no—
339C22×C127—21no—
340C22×C127—21no—
341C22×C127—21no—
342C22×C127—21no—
343C22×C127—21no—
344C22×C127—21no—
345C22×C127—44no—
346C22×C127—44no—
347C22×C127—44no—
348C22×C127—44no—
349C22×C127—44no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127—42no—
353C22×C127—42no—
354C22×C127—42no—
355C22×C127—84no—
356C22×C127C2×#9912yes—
357C22×C127#41312yes—
358C22×C127C22×C22⋊C411yescharacteristic
359C22×C127#56812yes—
360C4×C127—21no—
361C4×C127—21no—
362C4×C127—21no—
363C4×C127—21no—
364C4×C127—21no—
365C4×C127—21no—
366C4×C127—42no—
367C4×C127—42no—
368C4×C127—42no—
369C4×C127C2×#9912yes—
370C4×C127C2×#9912yes—
371#17400C12711yesmaximal, characteristic, direct product factor, Sylow
372C2×C127—22no—
373C2×C127—22no—
374C2×C127—22no—
375C2×C127—41no—
376C2×C127—41no—
377C2×C127—41no—
378C2×C127—41no—
379C2×C127—82no—
380C2×C127#287911yescharacteristic
381C2×C127C22×#9911yescharacteristic
382C2×C127C2×#41311yescharacteristic
383C2×#525C2×C12711yescharacteristic
384C2×#407C2×C12711yescharacteristic, complemented
385C2×#407C2×C12711yescharacteristic, complemented
386#1472C2×C12712yescomplemented
387#1471C2×C12712yescomplemented
388#1468C2×C12714yescomplemented
389#1465C2×C12714yescomplemented
390C127#1740011yescharacteristic, direct product factor, Sylow
391C22×#41C4×C12711yescharacteristic
392C24×C4C22×C12711yescharacteristic
393C22×M16—21no—
394C22×M16—21no—
395#525—21no—
396#525—21no—
397#525—21no—
398#525—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525—21no—
403C2×#123C22×C12712yes—
404C2×C22⋊Q8C4×C12711yescharacteristic
405C2×C22⋊Q8C22×C12711yescharacteristic
406C2×#121C4×C12711yescharacteristic
407C2×#121C22×C12711yescharacteristic
408C2×#120C4×C12712yes—
409C2×C4×D4C4×C12712yes—
410C2×C4×D4C22×C12712yes—
411C2×#117C4×C12711yescharacteristic
412#407—21no—
413#407—21no—
414#407—21no—
415#407—21no—
416#407C22×C12712yes—
417#407C22×C12712yes—
418#407C22×C12712yes—
419#407C22×C12712yes—
420C2×C22⋊C8—21no—
421C2×C22⋊C8—21no—
422C2×C22⋊C8C22×C12712yes—
423C2×C22⋊C8C22×C12712yes—
424#324C22×C12718yescomplemented
425#323C22×C12718yescomplemented
426C25C2×C4×C12711yescharacteristic
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—44no—
432C22×Q8C2×C4×C12711yescharacteristic
433C22×D4C2×C4×C12712yes—
434C22×D4C2×C4×C12712yes—
435C22×D4C2×C4×C12712yes—
436C22×D4C2×C4×C12711yescharacteristic
437C23×C4—44no—
438C23×C4C2×C4×C12711yescharacteristic
439C23×C4C2×C4×C12712yes—
440C23×C4C2×C4×C12711yescharacteristic
441C23×C4C2×C4×C12711yescharacteristic
442C23×C4D4×C12711yescharacteristic
443C23×C4D4×C12711yescharacteristic
444C23×C4D4×C12711yescharacteristic
445C23×C4D4×C12711yescharacteristic
446C23×C4D4×C12711yescharacteristic
447C23×C4D4×C12711yescharacteristic
448C23×C4D4×C12711yescharacteristic
449C23×C4D4×C12711yescharacteristic
450C23×C4C23×C12711yescharacteristic
451C23×C4C23×C12711yescharacteristic
452C23×C4C23×C12711yescharacteristic
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C2×M16—44no—
458C2×M16—44no—
459C22×C8—22no—
460C22×C8—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#120—22no—
482#120—22no—
483#120—22no—
484#120—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493#117—21no—
494#117—21no—
495#117—21no—
496#117—21no—
497C2×C4⋊C4C2×C4×C12711yescharacteristic
498C2×C4⋊C4C2×C4×C12711yescharacteristic
499C2×C4⋊C4C2×C4×C12712yes—
500C2×C4⋊C4C23×C12712yes—
501C2×C22⋊C4C2×C4×C12712yes—
502C2×C22⋊C4C2×C4×C12712yes—
503C2×C22⋊C4C2×C4×C12712yes—
504C2×C22⋊C4C2×C4×C12712yes—
505C2×C22⋊C4C23×C12712yes—
506C2×C42C2×C4×C12712yes—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8C23×C12714yes—
514C22⋊C8C23×C12714yes—
515C24—42no—
516C24—42no—
517C24—42no—
518C24C22⋊C4×C12711yescharacteristic
519C24C22⋊C4×C12711yescharacteristic
520C24C22⋊C4×C12711yescharacteristic
521C24C22⋊C4×C12711yescharacteristic
522C24C22×C4×C12711yescharacteristic
523C24C22×C4×C12711yescharacteristic
524C24C22×C4×C12712yes—
525C24C22×C4×C12711yescharacteristic
526#41—44no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—44no—
544C2×D4—44no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4C22⋊C4×C12711yescharacteristic
563C22×C4C22⋊C4×C12711yescharacteristic
564C22×C4C22⋊C4×C12711yescharacteristic
565C22×C4C22⋊C4×C12711yescharacteristic
566C22×C4C22⋊C4×C12711yescharacteristic
567C22×C4C22⋊C4×C12711yescharacteristic
568C22×C4C22⋊C4×C12711yescharacteristic
569C22×C4C22⋊C4×C12711yescharacteristic
570C22×C4C22⋊C4×C12711yescharacteristic
571C22×C4C22⋊C4×C12711yescharacteristic
572C22×C4C22⋊C4×C12711yescharacteristic
573C22×C4C22⋊C4×C12711yescharacteristic
574C22×C4C22×C4×C12712yes—
575C22×C4C22×C4×C12711yescharacteristic
576C22×C4C22×C4×C12711yescharacteristic
577C22×C4C22×C4×C12712yes—
578C22×C4C22×C4×C12712yes—
579C22×C4C22×C4×C12711yescharacteristic
580C22×C4C2×D4×C12711yescharacteristic
581C22×C4C2×D4×C12711yescharacteristic
582C22×C4C2×D4×C12711yescharacteristic
583C22×C4C2×D4×C12711yescharacteristic
584C22×C4C2×D4×C12711yescharacteristic
585C22×C4C2×D4×C12711yescharacteristic
586C22×C4C2×D4×C12711yescharacteristic
587C22×C4C2×D4×C12711yescharacteristic
588C22×C4C2×D4×C12711yescharacteristic
589C22×C4C2×D4×C12711yescharacteristic
590C22×C4C2×D4×C12711yescharacteristic
591C22×C4C2×D4×C12711yescharacteristic
592C22×C4C24×C12711yescharacteristic
593M16—44no—
594M16—44no—
595M16—44no—
596M16—44no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—44no—
600C2×C8—44no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C42—22no—
620C42—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—416no—
647C23C2×C22⋊C4×C12711yescharacteristic
648C23C2×C22⋊C4×C12711yescharacteristic
649C23C2×C22⋊C4×C12711yescharacteristic
650C23C2×C22⋊C4×C12711yescharacteristic
651C23C2×C22⋊C4×C12711yescharacteristic
652C23C2×C22⋊C4×C12711yescharacteristic
653C23C23×C4×C12711yescharacteristic
654Q8—42no—
655Q8—42no—
656D4—42no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—42no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4#99×C12714yes—
700C2×C4C2×C22⋊C4×C12711yescharacteristic
701C2×C4C2×C22⋊C4×C12711yescharacteristic
702C2×C4C2×C22⋊C4×C12711yescharacteristic
703C2×C4C2×C22⋊C4×C12711yescharacteristic
704C2×C4C2×C22⋊C4×C12711yescharacteristic
705C2×C4C2×C22⋊C4×C12711yescharacteristic
706C2×C4C22×D4×C12711yescharacteristic
707C2×C4C22×D4×C12711yescharacteristic
708C8—44no—
709C8—44no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—84no—
739C22C2×#99×C12712yes—
740C22#413×C12712yes—
741C22C22×C22⋊C4×C12711yescharacteristic
742C22#568×C12712yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4C2×#99×C12712yes—
753C4C2×#99×C12712yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—41no—
758C2—41no—
759C2—41no—
760C2—41no—
761C2—82no—
762C2C127×#287911yescharacteristic
763C2C22×#99×C12711yescharacteristic
764C2C2×#413×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#525×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#407×C127C2semidirect
3. C2×#407×C127C2semidirect
4. C127×#1472C2semidirect
5. C127×#1471C2semidirect
6. C127×#1468C2semidirect
7. C127×#1465C2semidirect
41. #324×C127C22semidirect
42. #323×C127C22semidirect
371. #17400C127direct (N × H)
384. C2×#407C2×C127semidirect
385. C2×#407C2×C127semidirect
386. #1472C2×C127semidirect
387. #1471C2×C127semidirect
388. #1468C2×C127semidirect
389. #1465C2×C127semidirect
390. C127#17400direct (N × H)
424. #324C22×C127semidirect
425. #323C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1272
C2×#407×C1272
C127×#14722
C127×#14712
C127×#14682
C127×#14652
#17400127