Finite Group Databasebeta

← C127×#11013 #44574686

Subgroups — C127×#11013 #44574686

Order 32512.

1262 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C127C211yesmaximal, characteristic
2C2×#421×C127C211yesmaximal, characteristic
3C2×#419×C127C211yesmaximal, characteristic, complemented
4C2×#410×C127C211yesmaximal, characteristic
5C127×#2310C211yesmaximal, characteristic, complemented
6C2×#344×C127C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C127C211yesmaximal, characteristic, complemented
8C22×#41×C127C2211yescharacteristic
9C23×Q8×C127C2211yescharacteristic
10C2×#137×C127—22no—
11C2×#137×C127—22no—
12C2×#137×C127—22no—
13C2×#137×C127—22no—
14C2×#137×C127—22no—
15C2×#137×C127—22no—
16C22×Q16×C127C412yescomplemented
17C22×SD16×C127C412yescomplemented
18C22×M16×C127C2211yescharacteristic
19C22×M16×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21C2×#117×C127C2211yescharacteristic
22C2×#117×C127C2211yescharacteristic
23#421×C127—22no—
24#421×C127—22no—
25C2×#104×C127—22no—
26#419×C127—22no—
27#419×C127—22no—
28C2×#103×C127—22no—
29#410×C127—22no—
30#410×C127—22no—
31C2×#99×C127—22no—
32#391×C127—22no—
33#391×C127—22no—
34#381×C127—22no—
35#344×C127—22no—
36H(3,ℤ/4)×C127—22no—
37C2×#41×C127—21no—
38C2×#41×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127D412yes—
48C2×#41×C127D412yes—
49C22×Q8×C127—21no—
50C22×Q8×C127—21no—
51C22×Q8×C127—21no—
52C22×Q8×C127—21no—
53C22×Q8×C127—21no—
54C22×Q8×C127—21no—
55C22×Q8×C127—21no—
56C22×Q8×C127—21no—
57C22×Q8×C127—21no—
58C22×Q8×C127—21no—
59C22×Q8×C127—21no—
60C22×Q8×C127C2×C412yes—
61C22×Q8×C127C2×C411yescharacteristic
62C22×Q8×C127D412yes—
63C22×Q8×C127D412yes—
64C22×D4×C127—21no—
65C22×D4×C127C2×C411yescharacteristic
66C23×C4×C127—21no—
67C23×C4×C127—21no—
68C23×C4×C127C2311yescharacteristic
69#137×C127—28no—
70#137×C127—28no—
71#137×C127—28no—
72#137×C127—28no—
73C2×Q16×C127—24no—
74C2×Q16×C127—24no—
75C2×Q16×C127—24no—
76C2×SD16×C127—24no—
77C2×SD16×C127—24no—
78C2×SD16×C127—24no—
79C2×M16×C127—21no—
80C2×M16×C127—21no—
81C2×M16×C127—21no—
82C2×M16×C127—21no—
83C2×M16×C127—21no—
84C2×M16×C127—21no—
85C2×M16×C127—21no—
86C2×M16×C127—21no—
87C2×M16×C127—21no—
88C2×M16×C127D412yes—
89C2×M16×C127D412yes—
90C2×M16×C127D412yes—
91C22×C8×C127—21no—
92C22×C8×C127C2×C412yes—
93#117×C127—21no—
94#117×C127—21no—
95#117×C127—21no—
96#117×C127—21no—
97#117×C127—21no—
98#117×C127—21no—
99#117×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102#117×C127—21no—
103#117×C127—21no—
104#117×C127D412yes—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127—21no—
107C2×C4⋊C4×C127—21no—
108C2×C22⋊C4×C127—21no—
109C2×C22⋊C4×C127—21no—
110C2×C22⋊C4×C127D412yes—
111C2×C42×C127—21no—
112C2×C42×C127—21no—
113C2×C42×C127D412yes—
114#104×C127—28no—
115#103×C127—28no—
116#99×C127—28no—
117#95×C127—28no—
118C24×C127—21no—
119C24×C127C2×D411yescharacteristic
120#41×C127—22no—
121#41×C127—22no—
122#41×C127—22no—
123#41×C127—22no—
124#41×C127—22no—
125#41×C127—22no—
126#41×C127—22no—
127#41×C127—22no—
128#41×C127—41no—
129#41×C127—41no—
130#41×C127—41no—
131#41×C127—41no—
132#41×C127—41no—
133#41×C127—41no—
134#41×C127—41no—
135#41×C127—41no—
136C2×Q8×C127—22no—
137C2×Q8×C127—21no—
138C2×Q8×C127—22no—
139C2×Q8×C127—22no—
140C2×Q8×C127—22no—
141C2×Q8×C127—22no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—22no—
145C2×Q8×C127—22no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—22no—
149C2×Q8×C127—22no—
150C2×Q8×C127—22no—
151C2×Q8×C127—22no—
152C2×Q8×C127—22no—
153C2×Q8×C127—22no—
154C2×Q8×C127—22no—
155C2×Q8×C127—22no—
156C2×Q8×C127—41no—
157C2×Q8×C127—41no—
158C2×Q8×C127—41no—
159C2×Q8×C127—41no—
160C2×Q8×C127—41no—
161C2×Q8×C127—41no—
162C2×Q8×C127—41no—
163C2×Q8×C127—41no—
164C2×Q8×C127—41no—
165C2×Q8×C127—41no—
166C2×Q8×C127—41no—
167C2×Q8×C127—41no—
168C2×Q8×C127C22⋊C414yes—
169C2×Q8×C127C22⋊C412yes—
170C2×D4×C127—22no—
171C2×D4×C127—22no—
172C2×D4×C127—21no—
173C2×D4×C127—21no—
174C2×D4×C127—21no—
175C2×D4×C127—21no—
176C2×D4×C127—21no—
177C2×D4×C127—41no—
178C2×D4×C127—41no—
179C2×D4×C127—41no—
180C2×D4×C127—41no—
181C2×D4×C127C22⋊C412yes—
182C22×C4×C127—21no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—41no—
191C22×C4×C127—41no—
192C22×C4×C127—41no—
193C22×C4×C127—41no—
194C22×C4×C127—41no—
195C22×C4×C127—41no—
196C22×C4×C127—41no—
197C22×C4×C127—41no—
198C22×C4×C127—41no—
199C22×C4×C127C22×C411yescharacteristic
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×C127#4111yescharacteristic
210C22×C4×C127#4111yescharacteristic
211C22×C4×C127#4111yescharacteristic
212C22×C4×C127#4111yescharacteristic
213Q16×C127—216no—
214SD16×C127—216no—
215M16×C127—22no—
216M16×C127—22no—
217M16×C127—22no—
218M16×C127—22no—
219M16×C127—22no—
220M16×C127—22no—
221M16×C127—41no—
222M16×C127—41no—
223C2×C8×C127—22no—
224C2×C8×C127—22no—
225C2×C8×C127—22no—
226C2×C8×C127—41no—
227C2×C8×C127—41no—
228C2×C8×C127C22⋊C414yes—
229C4⋊C4×C127—22no—
230C4⋊C4×C127—41no—
231C4⋊C4×C127—41no—
232C4⋊C4×C127—41no—
233C4⋊C4×C127—41no—
234C4⋊C4×C127—41no—
235C22⋊C4×C127—22no—
236C22⋊C4×C127—22no—
237C22⋊C4×C127—22no—
238C22⋊C4×C127—41no—
239C22⋊C4×C127—41no—
240C22⋊C4×C127—41no—
241C42×C127—22no—
242C42×C127—22no—
243C42×C127—22no—
244C42×C127—41no—
245C42×C127—41no—
246C42×C127—41no—
247C23×C127—22no—
248C23×C127—42no—
249C23×C127—41no—
250C23×C127—41no—
251C23×C127—82no—
252C23×C127C4×D411yescharacteristic
253C23×C127#12011yescharacteristic
254C23×C127#12011yescharacteristic
255C23×C127#12111yescharacteristic
256C23×C127#12111yescharacteristic
257C23×C127#12111yescharacteristic
258C23×C127#12711yescharacteristic
259Q8×C127—24no—
260Q8×C127—22no—
261Q8×C127—24no—
262Q8×C127—22no—
263Q8×C127—42no—
264Q8×C127—41no—
265Q8×C127—42no—
266Q8×C127—41no—
267Q8×C127—42no—
268Q8×C127—42no—
269Q8×C127—42no—
270Q8×C127—42no—
271D4×C127—22no—
272D4×C127—22no—
273D4×C127—42no—
274D4×C127—42no—
275D4×C127—42no—
276D4×C127—42no—
277D4×C127—41no—
278D4×C127—41no—
279C2×C4×C127—22no—
280C2×C4×C127—24no—
281C2×C4×C127—42no—
282C2×C4×C127—41no—
283C2×C4×C127—41no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—42no—
287C2×C4×C127—42no—
288C2×C4×C127—42no—
289C2×C4×C127—42no—
290C2×C4×C127—42no—
291C2×C4×C127—42no—
292C2×C4×C127—42no—
293C2×C4×C127—44no—
294C2×C4×C127—44no—
295C2×C4×C127—42no—
296C2×C4×C127—42no—
297C2×C4×C127—42no—
298C2×C4×C127—82no—
299C2×C4×C127C2×C22⋊C411yescharacteristic
300C2×C4×C127C2×C22⋊C411yescharacteristic
301C2×C4×C127C2×C22⋊C411yescharacteristic
302C2×C4×C127C4×D411yescharacteristic
303C2×C4×C127C4×D411yescharacteristic
304C2×C4×C127C4×D411yescharacteristic
305C2×C4×C127#12011yescharacteristic
306C2×C4×C127#12011yescharacteristic
307C2×C4×C127#12011yescharacteristic
308C2×C4×C127#12011yescharacteristic
309C2×C4×C127#12011yescharacteristic
310C2×C4×C127#12011yescharacteristic
311C2×C4×C127#12111yescharacteristic
312C2×C4×C127#12111yescharacteristic
313C2×C4×C127#12111yescharacteristic
314C2×C4×C127#12111yescharacteristic
315C2×C4×C127#12111yescharacteristic
316C2×C4×C127#12111yescharacteristic
317C2×C4×C127#12111yescharacteristic
318C2×C4×C127#12111yescharacteristic
319C2×C4×C127#12111yescharacteristic
320C2×C4×C127#12311yescharacteristic
321C2×C4×C127#12311yescharacteristic
322C2×C4×C127#12311yescharacteristic
323C2×C4×C127#12311yescharacteristic
324C2×C4×C127#12411yescharacteristic
325C2×C4×C127#12411yescharacteristic
326C2×C4×C127#12711yescharacteristic
327C8×C127—24no—
328C8×C127—42no—
329C22×C127—22no—
330C22×C127—22no—
331C22×C127—22no—
332C22×C127—41no—
333C22×C127—41no—
334C22×C127—41no—
335C22×C127—41no—
336C22×C127—42no—
337C22×C127—82no—
338C22×C127—82no—
339C22×C127—82no—
340C22×C127#38611yescharacteristic
341C22×C127#38611yescharacteristic
342C22×C127#39011yescharacteristic
343C22×C127#39211yescharacteristic
344C22×C127#39211yescharacteristic
345C22×C127#39211yescharacteristic
346C22×C127#39411yescharacteristic
347C4×C127—42no—
348C4×C127—44no—
349C4×C127—82no—
350C4×C127—82no—
351C4×C127—82no—
352C4×C127#37911yescharacteristic
353C4×C127#38611yescharacteristic
354C4×C127#38611yescharacteristic
355C4×C127#39011yescharacteristic
356C4×C127#39211yescharacteristic
357C4×C127#39411yescharacteristic
358C4×C127#39411yescharacteristic
359C4×C127#39411yescharacteristic
360#11013C12711yesmaximal, characteristic, direct product factor, Sylow
361C2×C127—21no—
362C2×C127—21no—
363C2×C127—21no—
364C2×C127—21no—
365C2×C127—21no—
366C2×C127—21no—
367C2×C127—82no—
368C2×C127#143811yescharacteristic
369C2×C127#190512yes—
370C22×#137C2×C12711yescharacteristic
371C2×#421C2×C12711yescharacteristic
372C2×#419C2×C12711yescharacteristic, complemented
373C2×#410C2×C12711yescharacteristic
374#2310C2×C12711yescharacteristic, complemented
375C2×#344C2×C12711yescharacteristic, complemented
376C2×H(3,ℤ/4)C2×C12711yescharacteristic, complemented
377C127#1101311yescharacteristic, direct product factor, Sylow
378C22×#41C22×C12711yescharacteristic
379C23×Q8C22×C12711yescharacteristic
380C2×#137—22no—
381C2×#137—22no—
382C2×#137—22no—
383C2×#137—22no—
384C2×#137—22no—
385C2×#137—22no—
386C22×Q16C4×C12712yescomplemented
387C22×SD16C4×C12712yescomplemented
388C22×M16C22×C12711yescharacteristic
389C22×M16C22×C12711yescharacteristic
390C2×#117C22×C12711yescharacteristic
391C2×#117C22×C12711yescharacteristic
392C2×#117C22×C12711yescharacteristic
393#421—22no—
394#421—22no—
395C2×#104—22no—
396#419—22no—
397#419—22no—
398C2×#103—22no—
399#410—22no—
400#410—22no—
401C2×#99—22no—
402#391—22no—
403#391—22no—
404#381—22no—
405#344—22no—
406H(3,ℤ/4)—22no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41D4×C12712yes—
418C2×#41D4×C12712yes—
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8C2×C4×C12712yes—
431C22×Q8C2×C4×C12711yescharacteristic
432C22×Q8D4×C12712yes—
433C22×Q8D4×C12712yes—
434C22×D4—21no—
435C22×D4C2×C4×C12711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C12711yescharacteristic
439#137—28no—
440#137—28no—
441#137—28no—
442#137—28no—
443C2×Q16—24no—
444C2×Q16—24no—
445C2×Q16—24no—
446C2×SD16—24no—
447C2×SD16—24no—
448C2×SD16—24no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16—21no—
454C2×M16—21no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16D4×C12712yes—
459C2×M16D4×C12712yes—
460C2×M16D4×C12712yes—
461C22×C8—21no—
462C22×C8C2×C4×C12712yes—
463#117—21no—
464#117—21no—
465#117—21no—
466#117—21no—
467#117—21no—
468#117—21no—
469#117—21no—
470#117—21no—
471#117—21no—
472#117—21no—
473#117—21no—
474#117D4×C12712yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C12712yes—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42D4×C12712yes—
484#104—28no—
485#103—28no—
486#99—28no—
487#95—28no—
488C24—21no—
489C24C2×D4×C12711yescharacteristic
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506C2×Q8—22no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8C22⋊C4×C12714yes—
539C2×Q8C22⋊C4×C12712yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4C22⋊C4×C12712yes—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4C22×C4×C12711yescharacteristic
570C22×C4C2×D4×C12711yescharacteristic
571C22×C4C2×D4×C12711yescharacteristic
572C22×C4C2×D4×C12711yescharacteristic
573C22×C4C2×D4×C12711yescharacteristic
574C22×C4C2×D4×C12711yescharacteristic
575C22×C4C2×D4×C12711yescharacteristic
576C22×C4C2×D4×C12711yescharacteristic
577C22×C4C2×D4×C12711yescharacteristic
578C22×C4C2×D4×C12711yescharacteristic
579C22×C4#41×C12711yescharacteristic
580C22×C4#41×C12711yescharacteristic
581C22×C4#41×C12711yescharacteristic
582C22×C4#41×C12711yescharacteristic
583Q16—216no—
584SD16—216no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—22no—
590M16—22no—
591M16—41no—
592M16—41no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8C22⋊C4×C12714yes—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—41no—
615C42—41no—
616C42—41no—
617C23—22no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—82no—
622C23C4×D4×C12711yescharacteristic
623C23#120×C12711yescharacteristic
624C23#120×C12711yescharacteristic
625C23#121×C12711yescharacteristic
626C23#121×C12711yescharacteristic
627C23#121×C12711yescharacteristic
628C23#127×C12711yescharacteristic
629Q8—24no—
630Q8—22no—
631Q8—24no—
632Q8—22no—
633Q8—42no—
634Q8—41no—
635Q8—42no—
636Q8—41no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641D4—22no—
642D4—22no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—41no—
648D4—41no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—82no—
669C2×C4C2×C22⋊C4×C12711yescharacteristic
670C2×C4C2×C22⋊C4×C12711yescharacteristic
671C2×C4C2×C22⋊C4×C12711yescharacteristic
672C2×C4C4×D4×C12711yescharacteristic
673C2×C4C4×D4×C12711yescharacteristic
674C2×C4C4×D4×C12711yescharacteristic
675C2×C4#120×C12711yescharacteristic
676C2×C4#120×C12711yescharacteristic
677C2×C4#120×C12711yescharacteristic
678C2×C4#120×C12711yescharacteristic
679C2×C4#120×C12711yescharacteristic
680C2×C4#120×C12711yescharacteristic
681C2×C4#121×C12711yescharacteristic
682C2×C4#121×C12711yescharacteristic
683C2×C4#121×C12711yescharacteristic
684C2×C4#121×C12711yescharacteristic
685C2×C4#121×C12711yescharacteristic
686C2×C4#121×C12711yescharacteristic
687C2×C4#121×C12711yescharacteristic
688C2×C4#121×C12711yescharacteristic
689C2×C4#121×C12711yescharacteristic
690C2×C4#123×C12711yescharacteristic
691C2×C4#123×C12711yescharacteristic
692C2×C4#123×C12711yescharacteristic
693C2×C4#123×C12711yescharacteristic
694C2×C4#124×C12711yescharacteristic
695C2×C4#124×C12711yescharacteristic
696C2×C4#127×C12711yescharacteristic
697C8—24no—
698C8—42no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22#386×C12711yescharacteristic
711C22#386×C12711yescharacteristic
712C22#390×C12711yescharacteristic
713C22#392×C12711yescharacteristic
714C22#392×C12711yescharacteristic
715C22#392×C12711yescharacteristic
716C22#394×C12711yescharacteristic
717C4—42no—
718C4—44no—
719C4—82no—
720C4—82no—
721C4—82no—
722C4#379×C12711yescharacteristic
723C4#386×C12711yescharacteristic
724C4#386×C12711yescharacteristic
725C4#390×C12711yescharacteristic
726C4#392×C12711yescharacteristic
727C4#394×C12711yescharacteristic
728C4#394×C12711yescharacteristic
729C4#394×C12711yescharacteristic
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—82no—
737C2C127×#143811yescharacteristic
738C2C127×#190512yes—
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×#41×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#419×C127C2semidirect
5. C127×#2310C2semidirect
6. C2×#344×C127C2semidirect
7. C2×H(3,ℤ/4)×C127C2semidirect
16. C22×Q16×C127C4semidirect
17. C22×SD16×C127C4semidirect
360. #11013C127direct (N × H)
372. C2×#419C2×C127semidirect
374. #2310C2×C127semidirect
375. C2×#344C2×C127semidirect
376. C2×H(3,ℤ/4)C2×C127semidirect
377. C127#11013direct (N × H)
386. C22×Q16C4×C127semidirect
387. C22×SD16C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1272
C2×#421×C1272
C2×#419×C1272
C2×#410×C1272
C127×#23102
C2×#344×C1272
C2×H(3,ℤ/4)×C1272
#11013127