Finite Group Databasebeta

← C2×C7×#1877 #13198136

Subgroups — C2×C7×#1877 #13198136

Order 1792.

2254 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C7×SD16C211yesmaximal, characteristic
2C22×C4×C7×D4C211yesmaximal, characteristic
3C22×C7×#103C211yesmaximal, characteristic, complemented
4C22×C7×#102C211yesmaximal, characteristic
5C2×C7×#391C211yesmaximal, characteristic, complemented
6C7×#1877C218yesmaximal, direct product factor
7C2×C7×#340C211yesmaximal, characteristic, complemented
8C2×C7×#336C211yesmaximal, characteristic, complemented
9C23×C7×Q8C2211yescharacteristic
10C23×C7×D4C2211yescharacteristic
11C24×C4×C7—21no—
12C22×C7×SD16—24no—
13C22×C7×SD16—24no—
14C22×C7×SD16C418yescomplemented
15C22×C7×SD16C2214yes—
16C23×C7×C8C2211yescharacteristic
17C23×C7×C8C2211yescharacteristic
18C2×C4×C7×D4—24no—
19C2×C4×C7×D4—24no—
20C2×C4×C7×D4—22no—
21C2×C4×C7×D4C2214yes—
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4—21no—
25C22×C42×C7C2211yescharacteristic
26C2×C7×#103—24no—
27C2×C7×#103C2214yescomplemented
28C2×C7×#102—24no—
29C2×C7×#102C2214yes—
30C7×#391—22no—
31C7×#391C2214yescomplemented
32C2×C7×#95—21no—
33C2×C7×#95—21no—
34C7×#340C2214yescomplemented
35C7×#336C2214yescomplemented
36C2×#1877C711yesmaximal, characteristic, direct product factor, Sylow
37C25×C7—21no—
38C22×C7×Q8—21no—
39C22×C7×Q8—22no—
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8—22no—
44C22×C7×Q8C2×C414yescomplemented
45C22×C7×Q8C2312yes—
46C22×C7×D4—21no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4—22no—
50C22×C7×D4C2×C414yes—
51C22×C7×D4D414yes—
52C22×C7×D4D414yes—
53C22×C7×D4C2312yes—
54C23×C4×C7—28no—
55C23×C4×C7—21no—
56C23×C4×C7—21no—
57C23×C4×C7—24no—
58C23×C4×C7—21no—
59C23×C4×C7—44no—
60C23×C4×C7—44no—
61C23×C4×C7D411yescharacteristic
62C23×C4×C7D411yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C2×C7×SD16—232no—
65C2×C7×SD16—28no—
66C2×C7×SD16—28no—
67C2×C7×SD16C2×C4116yescomplemented
68C22×C7×C8—22no—
69C22×C7×C8—22no—
70C22×C7×C8—22no—
71C22×C7×C8—22no—
72C22×C7×C8—22no—
73C22×C7×C8C2×C414yescomplemented
74C22×C7×C8C2312yes—
75C22×C7×C8C2312yes—
76C4×C7×D4—216no—
77C4×C7×D4—28no—
78C4×C7×D4—28no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4D414yes—
85C2×C7×C4⋊C4C2312yes—
86C2×C7×C4⋊C4C2312yes—
87C2×C7×C22⋊C4—28no—
88C2×C7×C22⋊C4—24no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7D412yes—
92C2×C42×C7C2312yes—
93C7×#103—28no—
94C7×#102—28no—
95C7×#95—24no—
96C7×#95—24no—
97C23×SD16C2×C711yescharacteristic
98C22×C4×D4C2×C711yescharacteristic
99C22×#103C2×C711yescharacteristic, complemented
100C22×#102C2×C711yescharacteristic
101C2×#391C2×C711yescharacteristic, complemented
102#1877C2×C718yesdirect product factor
103C2×#340C2×C711yescharacteristic, complemented
104C2×#336C2×C711yescharacteristic, complemented
105C24×C7—24no—
106C24×C7—24no—
107C24×C7—24no—
108C24×C7—22no—
109C24×C7—42no—
110C24×C7—42no—
111C24×C7—42no—
112C24×C7—42no—
113C24×C7C2×D411yescharacteristic
114C2×C7×Q8—24no—
115C2×C7×Q8—22no—
116C2×C7×Q8—28no—
117C2×C7×Q8—28no—
118C2×C7×Q8—22no—
119C2×C7×Q8—22no—
120C2×C7×Q8—22no—
121C2×C7×Q8—22no—
122C2×C7×Q8—42no—
123C2×C7×Q8—42no—
124C2×C7×Q8—44no—
125C2×C7×Q8—44no—
126C2×C7×Q8C22×C414yescomplemented
127C2×C7×D4—28no—
128C2×C7×D4—24no—
129C2×C7×D4—24no—
130C2×C7×D4—28no—
131C2×C7×D4—24no—
132C2×C7×D4—28no—
133C2×C7×D4—22no—
134C2×C7×D4—22no—
135C2×C7×D4—22no—
136C2×C7×D4C22⋊C4116yes—
137C2×C7×D4C22×C414yes—
138C2×C7×D4C2×D414yes—
139C2×C7×D4C2×D414yes—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—216no—
143C22×C4×C7—24no—
144C22×C4×C7—22no—
145C22×C4×C7—24no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—48no—
152C22×C4×C7—432no—
153C22×C4×C7—42no—
154C22×C4×C7—42no—
155C22×C4×C7—42no—
156C22×C4×C7—42no—
157C22×C4×C7—48no—
158C22×C4×C7—42no—
159C22×C4×C7—42no—
160C22×C4×C7—42no—
161C22×C4×C7SD1614yescomplemented
162C22×C4×C7C22×C412yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C22×C4×C7C2×D412yes—
166C22×C4×C7C2×D412yes—
167C22×C4×C7C2×D411yescharacteristic
168C22×C4×C7C2×D412yes—
169C22×C4×C7#4112yes—
170C22×C4×C7#4112yes—
171C22×C4×C7C2411yescharacteristic
172C7×SD16—232no—
173C2×C7×C8—28no—
174C2×C7×C8—22no—
175C2×C7×C8—22no—
176C2×C7×C8—22no—
177C2×C7×C8—22no—
178C2×C7×C8—22no—
179C2×C7×C8—44no—
180C2×C7×C8C22×C414yescomplemented
181C7×C4⋊C4—24no—
182C7×C4⋊C4—22no—
183C7×C4⋊C4—22no—
184C7×C4⋊C4—22no—
185C7×C4⋊C4—42no—
186C7×C4⋊C4C2×D414yes—
187C7×C22⋊C4—216no—
188C42×C7—24no—
189C42×C7—22no—
190C42×C7—22no—
191C23×Q8C22×C711yescharacteristic
192C23×D4C22×C711yescharacteristic
193C24×C4—21no—
194C22×SD16—24no—
195C22×SD16—24no—
196C22×SD16C4×C718yescomplemented
197C22×SD16C22×C714yes—
198C23×C8C22×C711yescharacteristic
199C23×C8C22×C711yescharacteristic
200C2×C4×D4—24no—
201C2×C4×D4—24no—
202C2×C4×D4—22no—
203C2×C4×D4C22×C714yes—
204C22×C4⋊C4C22×C711yescharacteristic
205C22×C4⋊C4C22×C711yescharacteristic
206C22×C22⋊C4—21no—
207C22×C42C22×C711yescharacteristic
208C2×#103—24no—
209C2×#103C22×C714yescomplemented
210C2×#102—24no—
211C2×#102C22×C714yes—
212#391—22no—
213#391C22×C714yescomplemented
214C2×#95—21no—
215C2×#95—21no—
216#340C22×C714yescomplemented
217#336C22×C714yescomplemented
218C23×C7—24no—
219C23×C7—24no—
220C23×C7—24no—
221C23×C7—216no—
222C23×C7—42no—
223C23×C7—42no—
224C23×C7—42no—
225C23×C7—42no—
226C23×C7—48no—
227C23×C7—48no—
228C23×C7—48no—
229C23×C7—48no—
230C23×C7—48no—
231C23×C7—48no—
232C23×C7C4×D412yes—
233C23×C7#12012yes—
234C23×C7#12112yes—
235C23×C7C2×SD1612yes—
236C23×C7#13512yes—
237C23×C7AGL(1,ℤ/8)12yes—
238C23×C7#13712yes—
239C23×C7C22×D411yescharacteristic
240C7×Q8—24no—
241C7×Q8—24no—
242C7×Q8—42no—
243C7×Q8—42no—
244C7×Q8—48no—
245C7×D4—24no—
246C7×D4—24no—
247C7×D4—24no—
248C7×D4—216no—
249C7×D4C2×C22⋊C418yes—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—28no—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—432no—
259C2×C4×C7—42no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—42no—
263C2×C4×C7—48no—
264C2×C4×C7—48no—
265C2×C4×C7—44no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—42no—
269C2×C4×C7—84no—
270C2×C4×C7C2×C22⋊C414yes—
271C2×C4×C7C4×D414yes—
272C2×C4×C7C4×D412yes—
273C2×C4×C7#12012yes—
274C2×C4×C7#12114yes—
275C2×C4×C7#12112yes—
276C2×C4×C7#12314yes—
277C2×C4×C7C2×SD1614yescomplemented
278C2×C4×C7C23×C411yescharacteristic
279C2×C4×C7C22×D411yescharacteristic
280C2×C4×C7C22×D411yescharacteristic
281C2×C4×C7C22×D411yescharacteristic
282C2×C4×C7C2×#4111yescharacteristic
283C2×C4×C7C2×#4111yescharacteristic
284C7×C8—24no—
285C7×C8—42no—
286C25—21no—
287C22×Q8—21no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8C2×C4×C714yescomplemented
294C22×Q8C23×C712yes—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4C2×C4×C714yes—
300C22×D4C7×D414yes—
301C22×D4C7×D414yes—
302C22×D4C23×C712yes—
303C23×C4—28no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—24no—
307C23×C4—21no—
308C23×C4—44no—
309C23×C4—44no—
310C23×C4C7×D411yescharacteristic
311C23×C4C7×D411yescharacteristic
312C23×C4C23×C711yescharacteristic
313C2×SD16—232no—
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16C2×C4×C7116yescomplemented
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8C2×C4×C714yescomplemented
323C22×C8C23×C712yes—
324C22×C8C23×C712yes—
325C4×D4—216no—
326C4×D4—28no—
327C4×D4—28no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C7×D414yes—
334C2×C4⋊C4C23×C712yes—
335C2×C4⋊C4C23×C712yes—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42C7×D412yes—
341C2×C42C23×C712yes—
342#103—28no—
343#102—28no—
344#95—24no—
345#95—24no—
346C22×C7—28no—
347C22×C7—432no—
348C22×C7—44no—
349C22×C7—44no—
350C22×C7—44no—
351C22×C7—44no—
352C22×C7—44no—
353C22×C7—44no—
354C22×C7#38614yes—
355C22×C7C4×SD1614yes—
356C22×C7#44014yes—
357C22×C7#45014yes—
358C22×C7#45214yes—
359C22×C7#46114yes—
360C22×C7#46314yes—
361C22×C7C2×C4×D411yescharacteristic
362C22×C7C2×#12011yescharacteristic
363C22×C7C2×#12111yescharacteristic
364C22×C7C22×SD1611yescharacteristic
365C22×C7C2×#13511yescharacteristic
366C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C7C2×#13711yescharacteristic
368C4×C7—24no—
369C4×C7—44no—
370C4×C7—42no—
371C4×C7—44no—
372C4×C7—82no—
373C4×C7#38614yes—
374C4×C7C22×C22⋊C411yescharacteristic
375C4×C7C2×C4×D411yescharacteristic
376C4×C7C2×#12111yescharacteristic
377C4×C7C2×#12311yescharacteristic
378C24—24no—
379C24—24no—
380C24—24no—
381C24—22no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C2×C7×D411yescharacteristic
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—28no—
390C2×Q8—28no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8—44no—
398C2×Q8—44no—
399C2×Q8C22×C4×C714yescomplemented
400C2×D4—28no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—28no—
404C2×D4—24no—
405C2×D4—28no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4C7×C22⋊C4116yes—
410C2×D4C22×C4×C714yes—
411C2×D4C2×C7×D414yes—
412C2×D4C2×C7×D414yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—216no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—48no—
425C22×C4—432no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—48no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C7×SD1614yescomplemented
435C22×C4C22×C4×C712yes—
436C22×C4C2×C7×D412yes—
437C22×C4C2×C7×D412yes—
438C22×C4C2×C7×D412yes—
439C22×C4C2×C7×D412yes—
440C22×C4C2×C7×D411yescharacteristic
441C22×C4C2×C7×D412yes—
442C22×C4C7×#4112yes—
443C22×C4C7×#4112yes—
444C22×C4C24×C711yescharacteristic
445SD16—232no—
446C2×C8—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—44no—
453C2×C8C22×C4×C714yescomplemented
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4C2×C7×D414yes—
460C22⋊C4—216no—
461C42—24no—
462C42—22no—
463C42—22no—
464C2×C7—48no—
465C2×C7#187718yesdirect product factor
466C2×C7C2×#38611yescharacteristic
467C2×C7C2×C4×SD1611yescharacteristic
468C2×C7C2×#44011yescharacteristic
469C2×C7C2×#45011yescharacteristic
470C2×C7C2×#45211yescharacteristic
471C2×C7C2×#46111yescharacteristic
472C2×C7C2×#46311yescharacteristic
473C23—24no—
474C23—24no—
475C23—24no—
476C23—216no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—48no—
482C23—48no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23C4×C7×D412yes—
488C23C7×#12012yes—
489C23C7×#12112yes—
490C23C2×C7×SD1612yes—
491C23C7×#13512yes—
492C23C7×AGL(1,ℤ/8)12yes—
493C23C7×#13712yes—
494C23C22×C7×D411yescharacteristic
495Q8—24no—
496Q8—24no—
497Q8—42no—
498Q8—48no—
499Q8—42no—
500D4—24no—
501D4—24no—
502D4—216no—
503D4—24no—
504D4C2×C7×C22⋊C418yes—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—28no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—432no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—48no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—48no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4C2×C7×C22⋊C414yes—
526C2×C4C4×C7×D414yes—
527C2×C4C4×C7×D412yes—
528C2×C4C7×#12012yes—
529C2×C4C7×#12114yes—
530C2×C4C7×#12112yes—
531C2×C4C7×#12314yes—
532C2×C4C2×C7×SD1614yescomplemented
533C2×C4C23×C4×C711yescharacteristic
534C2×C4C22×C7×D411yescharacteristic
535C2×C4C22×C7×D411yescharacteristic
536C2×C4C22×C7×D411yescharacteristic
537C2×C4C2×C7×#4111yescharacteristic
538C2×C4C2×C7×#4111yescharacteristic
539C8—24no—
540C8—42no—
541C7C2×#187711yescharacteristic, direct product factor, Sylow
542C22—28no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—432no—
550C22C7×#38614yes—
551C22C4×C7×SD1614yes—
552C22C7×#44014yes—
553C22C7×#45014yes—
554C22C7×#45214yes—
555C22C7×#46114yes—
556C22C7×#46314yes—
557C22C2×C4×C7×D411yescharacteristic
558C22C2×C7×#12011yescharacteristic
559C22C2×C7×#12111yescharacteristic
560C22C22×C7×SD1611yescharacteristic
561C22C2×C7×#13511yescharacteristic
562C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
563C22C2×C7×#13711yescharacteristic
564C4—24no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—82no—
569C4C7×#38614yes—
570C4C22×C7×C22⋊C411yescharacteristic
571C4C2×C4×C7×D411yescharacteristic
572C4C2×C7×#12111yescharacteristic
573C4C2×C7×#12311yescharacteristic
574C2—48no—
575C2C7×#187718yesdirect product factor
576C2C2×C7×#38611yescharacteristic
577C2C2×C4×C7×SD1611yescharacteristic
578C2C2×C7×#44011yescharacteristic
579C2C2×C7×#45011yescharacteristic
580C2C2×C7×#45211yescharacteristic
581C2C2×C7×#46111yescharacteristic
582C2C2×C7×#46311yescharacteristic
subgroupG/H
center, socleC24×C7C2×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C7 ◁ C22×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C7×#103C2semidirect
5. C2×C7×#391C2semidirect
6. C7×#1877C2direct (N × H)
7. C2×C7×#340C2semidirect
8. C2×C7×#336C2semidirect
14. C22×C7×SD16C4semidirect
27. C2×C7×#103C22semidirect
31. C7×#391C22semidirect
34. C7×#340C22semidirect
35. C7×#336C22semidirect
36. C2×#1877C7direct (N × H)
44. C22×C7×Q8C2×C4semidirect
67. C2×C7×SD16C2×C4semidirect
73. C22×C7×C8C2×C4semidirect
99. C22×#103C2×C7semidirect
101. C2×#391C2×C7semidirect
102. #1877C2×C7direct (N × H)
103. C2×#340C2×C7semidirect
104. C2×#336C2×C7semidirect
126. C2×C7×Q8C22×C4semidirect
161. C22×C4×C7SD16semidirect
180. C2×C7×C8C22×C4semidirect
196. C22×SD16C4×C7semidirect
209. C2×#103C22×C7semidirect
213. #391C22×C7semidirect
216. #340C22×C7semidirect
217. #336C22×C7semidirect
277. C2×C4×C7C2×SD16semidirect
293. C22×Q8C2×C4×C7semidirect
316. C2×SD16C2×C4×C7semidirect
322. C22×C8C2×C4×C7semidirect
399. C2×Q8C22×C4×C7semidirect
434. C22×C4C7×SD16semidirect
453. C2×C8C22×C4×C7semidirect
465. C2×C7#1877direct (N × H)
532. C2×C4C2×C7×SD16semidirect
541. C7C2×#1877direct (N × H)
575. C2C7×#1877direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C7×SD162
C22×C4×C7×D42
C22×C7×#1032
C22×C7×#1022
C2×C7×#3912
C7×#18772
C2×C7×#3402
C2×C7×#3362
C2×#18777