Finite Group Databasebeta

← C127×#20603 #44584276

Subgroups — C127×#20603 #44584276

Order 32512.

3666 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×2−1+4×C127C211yesmaximal, characteristic
2C2×#417×C127C211yesmaximal, characteristic, complemented
3C2×#419×C127C211yesmaximal, characteristic, complemented
4C2×#416×C127C211yesmaximal, characteristic, complemented
5C22×#103×C127C211yesmaximal, characteristic, complemented
6C2×#408×C127C211yesmaximal, characteristic, complemented
7C127×#2311C211yesmaximal, characteristic, complemented
8C127×#1788C214yesmaximal, complemented
9C127×#1787C214yesmaximal, complemented
10C2×2−1+4×C127—24no—
11C2×2−1+4×C127—24no—
12C2×2−1+4×C127—24no—
13C2×2−1+4×C127—24no—
14C2×2−1+4×C127—24no—
15C2×2−1+4×C127C418yescomplemented
16C22×#41×C127—22no—
17C22×#41×C127—21no—
18C22×#41×C127C2212yes—
19C22×#41×C127C2211yescharacteristic
20C22×#41×C127C2211yescharacteristic
21C23×Q8×C127—21no—
22C23×Q8×C127C2212yes—
23C23×Q8×C127C2211yescharacteristic
24C22×M16×C127C2211yescharacteristic
25C23×C8×C127C2211yescharacteristic
26C2×#117×C127C2211yescharacteristic
27C22×C4⋊C4×C127C2211yescharacteristic
28#419×C127—24no—
29#417×C127—24no—
30#416×C127—24no—
31C2×#103×C127—24no—
32C2×#103×C127C2214yes—
33C2×#103×C127C2212yes—
34C2×#103×C127C2214yes—
35C2×#103×C127C2212yes—
36C2×#102×C127C2212yes—
37C2×#102×C127C2212yes—
38#408×C127—24no—
39C2×C22⋊C8×C127C2214yes—
40#391×C127—21no—
41#390×C127—21no—
42#386×C127—22no—
43#380×C127C2214yes—
442−1+4×C127—232no—
452−1+4×C127—232no—
462−1+4×C127—232no—
472−1+4×C127—232no—
48C2×#41×C127—216no—
49C2×#41×C127—216no—
50C2×#41×C127—28no—
51C2×#41×C127—28no—
52C2×#41×C127—24no—
53C2×#41×C127—24no—
54C2×#41×C127—216no—
55C2×#41×C127—28no—
56C2×#41×C127—24no—
57C2×#41×C127—24no—
58C2×#41×C127—22no—
59C2×#41×C127—24no—
60C2×#41×C127—22no—
61C2×#41×C127—22no—
62C2×#41×C127—22no—
63C2×#41×C127—22no—
64C2×#41×C127—22no—
65C2×#41×C127—22no—
66C2×#41×C127C2×C414yes—
67C2×#41×C127C2×C414yes—
68C2×#41×C127C2×C418yescomplemented
69C2×#41×C127D414yes—
70C2×#41×C127D414yes—
71C2×#41×C127D414yes—
72C22×Q8×C127—28no—
73C22×Q8×C127—28no—
74C22×Q8×C127—28no—
75C22×Q8×C127—24no—
76C22×Q8×C127—24no—
77C22×Q8×C127—24no—
78C22×Q8×C127—24no—
79C22×Q8×C127—22no—
80C22×Q8×C127—21no—
81C22×Q8×C127—22no—
82C22×Q8×C127—24no—
83C22×Q8×C127—22no—
84C22×Q8×C127—22no—
85C22×Q8×C127C2×C414yes—
86C22×Q8×C127C2×C418yescomplemented
87C22×Q8×C127D414yes—
88C22×Q8×C127D414yes—
89C22×Q8×C127D411yescharacteristic
90C22×Q8×C127C2312yes—
91C22×Q8×C127C2311yescharacteristic
92C22×D4×C127—22no—
93C22×D4×C127—21no—
94C22×D4×C127D412yes—
95C22×D4×C127D411yescharacteristic
96C22×D4×C127C2311yescharacteristic
97C23×C4×C127—22no—
98C23×C4×C127—21no—
99C23×C4×C127—22no—
100C23×C4×C127—21no—
101C23×C4×C127—21no—
102C23×C4×C127C2312yes—
103C23×C4×C127C2311yescharacteristic
104C2×M16×C127—22no—
105C2×M16×C127—22no—
106C2×M16×C127—22no—
107C22×C8×C127—22no—
108C22×C8×C127—22no—
109C22×C8×C127—22no—
110C22×C8×C127C2312yes—
111C22×C8×C127C2312yes—
112#117×C127—22no—
113#117×C127—22no—
114C2×C4⋊C4×C127—22no—
115C2×C4⋊C4×C127—22no—
116C2×C4⋊C4×C127—21no—
117C2×C4⋊C4×C127C2312yes—
118C2×C4⋊C4×C127C2312yes—
119C2×C22⋊C4×C127—21no—
120C2×C22⋊C4×C127—24no—
121C2×C42×C127—21no—
122#103×C127—28no—
123#103×C127—24no—
124#103×C127—24no—
125#103×C127—28no—
126#102×C127—24no—
127#102×C127—24no—
128C22⋊C8×C127—28no—
129#95×C127—24no—
130C24×C127—21no—
131C24×C127C2×D412yes—
132C24×C127C2×D411yescharacteristic
133#41×C127—2128no—
134#41×C127—216no—
135#41×C127—216no—
136#41×C127—264no—
137#41×C127—216no—
138#41×C127—216no—
139#41×C127—28no—
140#41×C127—28no—
141#41×C127—28no—
142#41×C127—28no—
143#41×C127—28no—
144#41×C127—28no—
145#41×C127—28no—
146#41×C127C22⋊C4116yescomplemented
147C2×Q8×C127—28no—
148C2×Q8×C127—28no—
149C2×Q8×C127—216no—
150C2×Q8×C127—216no—
151C2×Q8×C127—264no—
152C2×Q8×C127—216no—
153C2×Q8×C127—216no—
154C2×Q8×C127—24no—
155C2×Q8×C127—28no—
156C2×Q8×C127—28no—
157C2×Q8×C127—24no—
158C2×Q8×C127—24no—
159C2×Q8×C127—22no—
160C2×Q8×C127—22no—
161C2×Q8×C127—28no—
162C2×Q8×C127—28no—
163C2×Q8×C127—22no—
164C2×Q8×C127—21no—
165C2×Q8×C127—21no—
166C2×Q8×C127—21no—
167C2×Q8×C127—22no—
168C2×Q8×C127—22no—
169C2×Q8×C127C22⋊C414yes—
170C2×Q8×C127C22⋊C4116yescomplemented
171C2×Q8×C127C22×C414yes—
172C2×Q8×C127C22×C412yes—
173C2×Q8×C127C2×D412yes—
174C2×Q8×C127C2×D412yes—
175C2×Q8×C127C2×D414yes—
176C2×Q8×C127C2×D414yes—
177C2×D4×C127—28no—
178C2×D4×C127—28no—
179C2×D4×C127—24no—
180C2×D4×C127—28no—
181C2×D4×C127—24no—
182C2×D4×C127—24no—
183C2×D4×C127—24no—
184C2×D4×C127—24no—
185C2×D4×C127—22no—
186C2×D4×C127—22no—
187C2×D4×C127—21no—
188C2×D4×C127—21no—
189C2×D4×C127—21no—
190C2×D4×C127C22⋊C418yes—
191C2×D4×C127C22⋊C414yes—
192C2×D4×C127C22×C412yes—
193C2×D4×C127C2×D412yes—
194C2×D4×C127C2×D412yes—
195C22×C4×C127—28no—
196C22×C4×C127—28no—
197C22×C4×C127—28no—
198C22×C4×C127—28no—
199C22×C4×C127—24no—
200C22×C4×C127—28no—
201C22×C4×C127—24no—
202C22×C4×C127—24no—
203C22×C4×C127—22no—
204C22×C4×C127—21no—
205C22×C4×C127—24no—
206C22×C4×C127—28no—
207C22×C4×C127—24no—
208C22×C4×C127—24no—
209C22×C4×C127—22no—
210C22×C4×C127—22no—
211C22×C4×C127—22no—
212C22×C4×C127—22no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—42no—
216C22×C4×C127—82no—
217C22×C4×C127C22×C414yes—
218C22×C4×C127C22×C412yes—
219C22×C4×C127C2×D412yes—
220C22×C4×C127C2×D414yes—
221C22×C4×C127C2×D411yescharacteristic
222C22×C4×C127C2×D412yes—
223C22×C4×C127C2×D412yes—
224C22×C4×C127C2×D412yes—
225C22×C4×C127C2×D412yes—
226C22×C4×C127C2×D412yes—
227C22×C4×C127C2411yescharacteristic
228M16×C127—44no—
229C2×C8×C127—22no—
230C2×C8×C127—22no—
231C2×C8×C127—22no—
232C2×C8×C127—22no—
233C2×C8×C127—22no—
234C2×C8×C127—22no—
235C2×C8×C127—44no—
236C4⋊C4×C127—22no—
237C4⋊C4×C127—22no—
238C4⋊C4×C127—22no—
239C4⋊C4×C127—22no—
240C4⋊C4×C127—42no—
241C22⋊C4×C127—42no—
242C22⋊C4×C127—84no—
243C42×C127—42no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—22no—
249C23×C127—22no—
250C23×C127—22no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127C2×C22⋊C414yes—
256C23×C127C2×C22⋊C412yes—
257C23×C127#12012yes—
258C23×C127#12012yes—
259C23×C127C22×D411yescharacteristic
260Q8×C127—232no—
261Q8×C127—22no—
262Q8×C127—24no—
263Q8×C127—22no—
264Q8×C127—22no—
265Q8×C127—24no—
266Q8×C127—24no—
267Q8×C127—28no—
268Q8×C127—216no—
269Q8×C127C2×C22⋊C414yes—
270Q8×C127C2×C22⋊C418yes—
271D4×C127—232no—
272D4×C127—216no—
273D4×C127—216no—
274D4×C127—22no—
275D4×C127—22no—
276D4×C127—22no—
277D4×C127—28no—
278D4×C127C2×C22⋊C414yes—
279C2×C4×C127—232no—
280C2×C4×C127—232no—
281C2×C4×C127—24no—
282C2×C4×C127—22no—
283C2×C4×C127—24no—
284C2×C4×C127—22no—
285C2×C4×C127—24no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—216no—
290C2×C4×C127—24no—
291C2×C4×C127—24no—
292C2×C4×C127—24no—
293C2×C4×C127—24no—
294C2×C4×C127—216no—
295C2×C4×C127—42no—
296C2×C4×C127—42no—
297C2×C4×C127—42no—
298C2×C4×C127—44no—
299C2×C4×C127—42no—
300C2×C4×C127—84no—
301C2×C4×C127C2×C22⋊C414yes—
302C2×C4×C127C2×C22⋊C414yes—
303C2×C4×C127C2×C22⋊C414yes—
304C2×C4×C127C2×C22⋊C412yes—
305C2×C4×C127#12014yes—
306C2×C4×C127#12014yes—
307C2×C4×C127#12012yes—
308C2×C4×C127#12012yes—
309C2×C4×C127C23×C411yescharacteristic
310C2×C4×C127C22×D411yescharacteristic
311C2×C4×C127C22×D411yescharacteristic
312C2×C4×C127C22×D411yescharacteristic
313C2×C4×C127C22×D411yescharacteristic
314C2×C4×C127C22×D411yescharacteristic
315C8×C127—42no—
316C8×C127—42no—
317C22×C127—24no—
318C22×C127—22no—
319C22×C127—22no—
320C22×C127—24no—
321C22×C127—28no—
322C22×C127—24no—
323C22×C127—24no—
324C22×C127—44no—
325C22×C127—42no—
326C22×C127—42no—
327C22×C127—42no—
328C22×C127—42no—
329C22×C127—44no—
330C22×C127—44no—
331C22×C127#37914yes—
332C22×C127C22×C22⋊C411yescharacteristic
333C22×C127C2×#12011yescharacteristic
334C22×C127C2×#12011yescharacteristic
335C22×C127#57712yes—
336C22×C127#57812yes—
337C4×C127—28no—
338C4×C127—24no—
339C4×C127—24no—
340C4×C127—82no—
341C4×C127—82no—
342C4×C127#37914yes—
343C4×C127C22×C22⋊C411yescharacteristic
344C4×C127C22×C22⋊C411yescharacteristic
345C4×C127C2×#12011yescharacteristic
346C4×C127C2×#12011yescharacteristic
347#20603C12711yesmaximal, characteristic, direct product factor, Sylow
348C2×C127—24no—
349C2×C127—44no—
350C2×C127—44no—
351C2×C127C2×#37911yescharacteristic
352C2×C127#289812yes—
353C2×C127#301011yescharacteristic
354C2×C127#301111yescharacteristic
355C2×C127#301312yes—
356C22×2−1+4C2×C12711yescharacteristic
357C2×#417C2×C12711yescharacteristic, complemented
358C2×#419C2×C12711yescharacteristic, complemented
359C2×#416C2×C12711yescharacteristic, complemented
360C22×#103C2×C12711yescharacteristic, complemented
361C2×#408C2×C12711yescharacteristic, complemented
362#2311C2×C12711yescharacteristic, complemented
363#1788C2×C12714yescomplemented
364#1787C2×C12714yescomplemented
365C127#2060311yescharacteristic, direct product factor, Sylow
366C2×2−1+4—24no—
367C2×2−1+4—24no—
368C2×2−1+4—24no—
369C2×2−1+4—24no—
370C2×2−1+4—24no—
371C2×2−1+4C4×C12718yescomplemented
372C22×#41—22no—
373C22×#41—21no—
374C22×#41C22×C12712yes—
375C22×#41C22×C12711yescharacteristic
376C22×#41C22×C12711yescharacteristic
377C23×Q8—21no—
378C23×Q8C22×C12712yes—
379C23×Q8C22×C12711yescharacteristic
380C22×M16C22×C12711yescharacteristic
381C23×C8C22×C12711yescharacteristic
382C2×#117C22×C12711yescharacteristic
383C22×C4⋊C4C22×C12711yescharacteristic
384#419—24no—
385#417—24no—
386#416—24no—
387C2×#103—24no—
388C2×#103C22×C12714yes—
389C2×#103C22×C12712yes—
390C2×#103C22×C12714yes—
391C2×#103C22×C12712yes—
392C2×#102C22×C12712yes—
393C2×#102C22×C12712yes—
394#408—24no—
395C2×C22⋊C8C22×C12714yes—
396#391—21no—
397#390—21no—
398#386—22no—
399#380C22×C12714yes—
4002−1+4—232no—
4012−1+4—232no—
4022−1+4—232no—
4032−1+4—232no—
404C2×#41—216no—
405C2×#41—216no—
406C2×#41—28no—
407C2×#41—28no—
408C2×#41—24no—
409C2×#41—24no—
410C2×#41—216no—
411C2×#41—28no—
412C2×#41—24no—
413C2×#41—24no—
414C2×#41—22no—
415C2×#41—24no—
416C2×#41—22no—
417C2×#41—22no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41C2×C4×C12714yes—
423C2×#41C2×C4×C12714yes—
424C2×#41C2×C4×C12718yescomplemented
425C2×#41D4×C12714yes—
426C2×#41D4×C12714yes—
427C2×#41D4×C12714yes—
428C22×Q8—28no—
429C22×Q8—28no—
430C22×Q8—28no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8—22no—
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—24no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8C2×C4×C12714yes—
442C22×Q8C2×C4×C12718yescomplemented
443C22×Q8D4×C12714yes—
444C22×Q8D4×C12714yes—
445C22×Q8D4×C12711yescharacteristic
446C22×Q8C23×C12712yes—
447C22×Q8C23×C12711yescharacteristic
448C22×D4—22no—
449C22×D4—21no—
450C22×D4D4×C12712yes—
451C22×D4D4×C12711yescharacteristic
452C22×D4C23×C12711yescharacteristic
453C23×C4—22no—
454C23×C4—21no—
455C23×C4—22no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C23×C12712yes—
459C23×C4C23×C12711yescharacteristic
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—22no—
466C22×C8C23×C12712yes—
467C22×C8C23×C12712yes—
468#117—22no—
469#117—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4C23×C12712yes—
474C2×C4⋊C4C23×C12712yes—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—24no—
477C2×C42—21no—
478#103—28no—
479#103—24no—
480#103—24no—
481#103—28no—
482#102—24no—
483#102—24no—
484C22⋊C8—28no—
485#95—24no—
486C24—21no—
487C24C2×D4×C12712yes—
488C24C2×D4×C12711yescharacteristic
489#41—2128no—
490#41—216no—
491#41—216no—
492#41—264no—
493#41—216no—
494#41—216no—
495#41—28no—
496#41—28no—
497#41—28no—
498#41—28no—
499#41—28no—
500#41—28no—
501#41—28no—
502#41C22⋊C4×C127116yescomplemented
503C2×Q8—28no—
504C2×Q8—28no—
505C2×Q8—216no—
506C2×Q8—216no—
507C2×Q8—264no—
508C2×Q8—216no—
509C2×Q8—216no—
510C2×Q8—24no—
511C2×Q8—28no—
512C2×Q8—28no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8C22⋊C4×C12714yes—
526C2×Q8C22⋊C4×C127116yescomplemented
527C2×Q8C22×C4×C12714yes—
528C2×Q8C22×C4×C12712yes—
529C2×Q8C2×D4×C12712yes—
530C2×Q8C2×D4×C12712yes—
531C2×Q8C2×D4×C12714yes—
532C2×Q8C2×D4×C12714yes—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—24no—
536C2×D4—28no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4C22⋊C4×C12718yes—
547C2×D4C22⋊C4×C12714yes—
548C2×D4C22×C4×C12712yes—
549C2×D4C2×D4×C12712yes—
550C2×D4C2×D4×C12712yes—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—24no—
556C22×C4—28no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—28no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—42no—
572C22×C4—82no—
573C22×C4C22×C4×C12714yes—
574C22×C4C22×C4×C12712yes—
575C22×C4C2×D4×C12712yes—
576C22×C4C2×D4×C12714yes—
577C22×C4C2×D4×C12711yescharacteristic
578C22×C4C2×D4×C12712yes—
579C22×C4C2×D4×C12712yes—
580C22×C4C2×D4×C12712yes—
581C22×C4C2×D4×C12712yes—
582C22×C4C2×D4×C12712yes—
583C22×C4C24×C12711yescharacteristic
584M16—44no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—44no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—84no—
599C42—42no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—42no—
610C23—42no—
611C23C2×C22⋊C4×C12714yes—
612C23C2×C22⋊C4×C12712yes—
613C23#120×C12712yes—
614C23#120×C12712yes—
615C23C22×D4×C12711yescharacteristic
616Q8—232no—
617Q8—22no—
618Q8—24no—
619Q8—22no—
620Q8—22no—
621Q8—24no—
622Q8—24no—
623Q8—28no—
624Q8—216no—
625Q8C2×C22⋊C4×C12714yes—
626Q8C2×C22⋊C4×C12718yes—
627D4—232no—
628D4—216no—
629D4—216no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—28no—
634D4C2×C22⋊C4×C12714yes—
635C2×C4—232no—
636C2×C4—232no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—216no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—216no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—84no—
657C2×C4C2×C22⋊C4×C12714yes—
658C2×C4C2×C22⋊C4×C12714yes—
659C2×C4C2×C22⋊C4×C12714yes—
660C2×C4C2×C22⋊C4×C12712yes—
661C2×C4#120×C12714yes—
662C2×C4#120×C12714yes—
663C2×C4#120×C12712yes—
664C2×C4#120×C12712yes—
665C2×C4C23×C4×C12711yescharacteristic
666C2×C4C22×D4×C12711yescharacteristic
667C2×C4C22×D4×C12711yescharacteristic
668C2×C4C22×D4×C12711yescharacteristic
669C2×C4C22×D4×C12711yescharacteristic
670C2×C4C22×D4×C12711yescharacteristic
671C8—42no—
672C8—42no—
673C22—24no—
674C22—22no—
675C22—22no—
676C22—24no—
677C22—28no—
678C22—24no—
679C22—24no—
680C22—44no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—44no—
686C22—44no—
687C22#379×C12714yes—
688C22C22×C22⋊C4×C12711yescharacteristic
689C22C2×#120×C12711yescharacteristic
690C22C2×#120×C12711yescharacteristic
691C22#577×C12712yes—
692C22#578×C12712yes—
693C4—28no—
694C4—24no—
695C4—24no—
696C4—82no—
697C4—82no—
698C4#379×C12714yes—
699C4C22×C22⋊C4×C12711yescharacteristic
700C4C22×C22⋊C4×C12711yescharacteristic
701C4C2×#120×C12711yescharacteristic
702C4C2×#120×C12711yescharacteristic
703C2—24no—
704C2—44no—
705C2—44no—
706C2C2×#379×C12711yescharacteristic
707C2C127×#289812yes—
708C2C127×#301011yescharacteristic
709C2C127×#301111yescharacteristic
710C2C127×#301312yes—
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×2−1+4×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#417×C127C2semidirect
3. C2×#419×C127C2semidirect
4. C2×#416×C127C2semidirect
5. C22×#103×C127C2semidirect
6. C2×#408×C127C2semidirect
7. C127×#2311C2semidirect
8. C127×#1788C2semidirect
9. C127×#1787C2semidirect
15. C2×2−1+4×C127C4semidirect
68. C2×#41×C127C2×C4semidirect
86. C22×Q8×C127C2×C4semidirect
146. #41×C127C22⋊C4semidirect
170. C2×Q8×C127C22⋊C4semidirect
347. #20603C127direct (N × H)
357. C2×#417C2×C127semidirect
358. C2×#419C2×C127semidirect
359. C2×#416C2×C127semidirect
360. C22×#103C2×C127semidirect
361. C2×#408C2×C127semidirect
362. #2311C2×C127semidirect
363. #1788C2×C127semidirect
364. #1787C2×C127semidirect
365. C127#20603direct (N × H)
371. C2×2−1+4C4×C127semidirect
424. C2×#41C2×C4×C127semidirect
442. C22×Q8C2×C4×C127semidirect
502. #41C22⋊C4×C127semidirect
526. C2×Q8C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×2−1+4×C1272
C2×#417×C1272
C2×#419×C1272
C2×#416×C1272
C22×#103×C1272
C2×#408×C1272
C127×#23112
C127×#17882
C127×#17872
#20603127