Finite Group Databasebeta

← C2×C7×#2044 #13200729

Subgroups — C2×C7×#2044 #13200729

Order 1792.

2046 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#534C211yesmaximal, characteristic
2C22×C7×#99C212yesmaximal, complemented
3C2×C7×#386C212yesmaximal, complemented
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C7×#2044C218yesmaximal, direct product factor
6C2×C7×#342C211yesmaximal, characteristic, complemented
7C23×C7×D4C2212yes—
8C24×C4×C7C2211yescharacteristic
9C7×#534—24no—
10C7×#534—22no—
11C7×#534C2214yes—
12C2×C7×#123—22no—
13C2×C7×#121—21no—
14C2×C7×#121—21no—
15C2×C7×#120—22no—
16C22×C7×C4⋊C4—21no—
17C22×C7×C22⋊C4—22no—
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C2×C7×#99—28no—
22C2×C7×#99C2218yescomplemented
23C7×#386—24no—
24C7×#386C2218yescomplemented
25C7×#385—22no—
26C7×#385C2214yescomplemented
27C2×C7×#95—21no—
28C2×C7×#95—22no—
29C7×#342C2214yescomplemented
30C2×#2044C711yesmaximal, characteristic, direct product factor, Sylow
31C25×C7D412yes—
32C25×C7C2311yescharacteristic
33C22×C7×D4—22no—
34C22×C7×D4—22no—
35C22×C7×D4—22no—
36C22×C7×D4—22no—
37C22×C7×D4—24no—
38C22×C7×D4—24no—
39C22×C7×D4—24no—
40C22×C7×D4—24no—
41C22×C7×D4—21no—
42C22×C7×D4—21no—
43C22×C7×D4D414yes—
44C22×C7×D4C2314yes—
45C23×C4×C7—22no—
46C23×C4×C7—21no—
47C23×C4×C7—21no—
48C23×C4×C7—22no—
49C23×C4×C7—21no—
50C23×C4×C7—22no—
51C23×C4×C7—44no—
52C23×C4×C7D412yes—
53C23×C4×C7D411yescharacteristic
54C23×C4×C7D411yescharacteristic
55C23×C4×C7C2312yes—
56C7×#123—28no—
57C7×#123—28no—
58C7×#121—24no—
59C7×#121—24no—
60C7×#121—24no—
61C7×#121—24no—
62C7×#120—28no—
63C7×#120—28no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4—24no—
67C2×C7×C4⋊C4—44no—
68C2×C7×C22⋊C4—22no—
69C2×C7×C22⋊C4—22no—
70C2×C7×C22⋊C4—22no—
71C2×C7×C22⋊C4—21no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—28no—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—48no—
79C2×C7×C22⋊C4D412yes—
80C2×C7×C22⋊C4D414yescomplemented
81C2×C7×C22⋊C4C2314yes—
82C2×C7×C22⋊C4C2312yes—
83C2×C7×C22⋊C4C2312yes—
84C7×#99—216no—
85C7×#95—24no—
86C7×#95—28no—
87C2×#534C2×C711yescharacteristic
88C22×#99C2×C712yescomplemented
89C2×#386C2×C712yescomplemented
90C2×#385C2×C711yescharacteristic, complemented
91#2044C2×C718yesdirect product factor
92C2×#342C2×C711yescharacteristic, complemented
93C24×C7—22no—
94C24×C7—24no—
95C24×C7—22no—
96C24×C7—24no—
97C24×C7—42no—
98C24×C7—42no—
99C24×C7—44no—
100C24×C7—44no—
101C24×C7C2×D412yes—
102C24×C7C2×D411yescharacteristic
103C24×C7C2×D414yes—
104C24×C7C2×D412yes—
105C24×C7C2×D411yescharacteristic
106C24×C7C2×D412yes—
107C24×C7#4112yes—
108C24×C7#4114yes—
109C24×C7C2411yescharacteristic
110C2×C7×D4—24no—
111C2×C7×D4—24no—
112C2×C7×D4—28no—
113C2×C7×D4—28no—
114C2×C7×D4—24no—
115C2×C7×D4—24no—
116C2×C7×D4—24no—
117C2×C7×D4—24no—
118C2×C7×D4—24no—
119C2×C7×D4—24no—
120C2×C7×D4—24no—
121C2×C7×D4—24no—
122C2×C7×D4—44no—
123C2×C7×D4—44no—
124C2×C7×D4—44no—
125C2×C7×D4—44no—
126C2×C7×D4—44no—
127C2×C7×D4—44no—
128C2×C7×D4—44no—
129C2×C7×D4—44no—
130C2×C7×D4—82no—
131C2×C7×D4—82no—
132C22×C4×C7—28no—
133C22×C4×C7—24no—
134C22×C4×C7—22no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—22no—
138C22×C4×C7—24no—
139C22×C4×C7—24no—
140C22×C4×C7—24no—
141C22×C4×C7—24no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—24no—
147C22×C4×C7—44no—
148C22×C4×C7—48no—
149C22×C4×C7—44no—
150C22×C4×C7—42no—
151C22×C4×C7—42no—
152C22×C4×C7—42no—
153C22×C4×C7—44no—
154C22×C4×C7—42no—
155C22×C4×C7—41no—
156C22×C4×C7—41no—
157C22×C4×C7—42no—
158C22×C4×C7—42no—
159C22×C4×C7—44no—
160C22×C4×C7—44no—
161C22×C4×C7—44no—
162C22×C4×C7C2×D414yes—
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2×D412yes—
165C7×C4⋊C4—24no—
166C7×C4⋊C4—24no—
167C7×C4⋊C4—48no—
168C7×C22⋊C4—28no—
169C7×C22⋊C4—28no—
170C7×C22⋊C4—24no—
171C7×C22⋊C4—24no—
172C7×C22⋊C4—24no—
173C7×C22⋊C4—22no—
174C7×C22⋊C4—24no—
175C7×C22⋊C4—24no—
176C7×C22⋊C4—416no—
177C7×C22⋊C4—44no—
178C7×C22⋊C4C2×D414yescomplemented
179C23×D4C22×C712yes—
180C24×C4C22×C711yescharacteristic
181#534—24no—
182#534—22no—
183#534C22×C714yes—
184C2×#123—22no—
185C2×#121—21no—
186C2×#121—21no—
187C2×#120—22no—
188C22×C4⋊C4—21no—
189C22×C22⋊C4—22no—
190C22×C22⋊C4C22×C712yes—
191C22×C22⋊C4C22×C711yescharacteristic
192C22×C22⋊C4C22×C711yescharacteristic
193C2×#99—28no—
194C2×#99C22×C718yescomplemented
195#386—24no—
196#386C22×C718yescomplemented
197#385—22no—
198#385C22×C714yescomplemented
199C2×#95—21no—
200C2×#95—22no—
201#342C22×C714yescomplemented
202C23×C7—22no—
203C23×C7—24no—
204C23×C7—22no—
205C23×C7—24no—
206C23×C7—24no—
207C23×C7—24no—
208C23×C7—24no—
209C23×C7—41no—
210C23×C7—42no—
211C23×C7—41no—
212C23×C7—41no—
213C23×C7—42no—
214C23×C7—44no—
215C23×C7—44no—
216C23×C7—48no—
217C23×C7—41no—
218C23×C7—44no—
219C23×C7—44no—
220C23×C7—416no—
221C23×C7—44no—
222C23×C7—44no—
223C23×C7—44no—
224C23×C7—44no—
225C23×C7—82no—
226C23×C7—82no—
227C23×C7—88no—
228C23×C7#12012yes—
229C23×C7#12011yescharacteristic
230C23×C7#12011yescharacteristic
231C23×C7#12112yes—
232C23×C7#12114yes—
233C23×C7#12112yes—
234C23×C7#12114yes—
235C23×C7#12314yes—
236C23×C7#12314yes—
237C23×C7#12412yes—
238C23×C7#12412yes—
239C23×C7C22×D412yes—
240C23×C7C22×D411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C2×#4111yescharacteristic
243C23×C7C2×#4112yes—
244C7×D4—44no—
245C7×D4—44no—
246C7×D4—44no—
247C7×D4—44no—
248C7×D4—48no—
249C7×D4—48no—
250C7×D4—84no—
251C7×D4—84no—
252C2×C4×C7—28no—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—24no—
259C2×C4×C7—24no—
260C2×C4×C7—42no—
261C2×C4×C7—42no—
262C2×C4×C7—48no—
263C2×C4×C7—42no—
264C2×C4×C7—44no—
265C2×C4×C7—44no—
266C2×C4×C7—48no—
267C2×C4×C7—42no—
268C2×C4×C7—44no—
269C2×C4×C7—44no—
270C2×C4×C7—44no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—42no—
275C2×C4×C7—44no—
276C2×C4×C7—44no—
277C2×C4×C7—44no—
278C2×C4×C7—81no—
279C2×C4×C7—81no—
280C2×C4×C7—88no—
281C25C7×D412yes—
282C25C23×C711yescharacteristic
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—24no—
288C22×D4—24no—
289C22×D4—24no—
290C22×D4—24no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C7×D414yes—
294C22×D4C23×C714yes—
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—44no—
302C23×C4C7×D412yes—
303C23×C4C7×D411yescharacteristic
304C23×C4C7×D411yescharacteristic
305C23×C4C23×C712yes—
306#123—28no—
307#123—28no—
308#121—24no—
309#121—24no—
310#121—24no—
311#121—24no—
312#120—28no—
313#120—28no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—44no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—48no—
329C2×C22⋊C4C7×D412yes—
330C2×C22⋊C4C7×D414yescomplemented
331C2×C22⋊C4C23×C714yes—
332C2×C22⋊C4C23×C712yes—
333C2×C22⋊C4C23×C712yes—
334#99—216no—
335#95—24no—
336#95—28no—
337C22×C7—21no—
338C22×C7—22no—
339C22×C7—21no—
340C22×C7—22no—
341C22×C7—21no—
342C22×C7—22no—
343C22×C7—21no—
344C22×C7—22no—
345C22×C7—24no—
346C22×C7—28no—
347C22×C7—28no—
348C22×C7—24no—
349C22×C7—42no—
350C22×C7—44no—
351C22×C7—44no—
352C22×C7—42no—
353C22×C7—41no—
354C22×C7—41no—
355C22×C7—42no—
356C22×C7—48no—
357C22×C7—44no—
358C22×C7—44no—
359C22×C7—44no—
360C22×C7—84no—
361C22×C7—88no—
362C22×C7—88no—
363C22×C7#39414yes—
364C22×C7#39412yes—
365C22×C7#39412yes—
366C22×C7B(4,𝔽2)12yes—
367C22×C7#45812yes—
368C22×C7C2×#12011yescharacteristic
369C22×C7C2×#12111yescharacteristic
370C22×C7C2×#12112yes—
371C22×C7C2×#12312yes—
372C22×C7C2×#12411yescharacteristic
373C4×C7—44no—
374C4×C7—44no—
375C4×C7—44no—
376C4×C7—42no—
377C4×C7—42no—
378C4×C7—84no—
379C24—22no—
380C24—24no—
381C24—22no—
382C24—24no—
383C24—42no—
384C24—42no—
385C24—44no—
386C24—44no—
387C24C2×C7×D412yes—
388C24C2×C7×D411yescharacteristic
389C24C2×C7×D414yes—
390C24C2×C7×D412yes—
391C24C2×C7×D411yescharacteristic
392C24C2×C7×D412yes—
393C24C7×#4112yes—
394C24C7×#4114yes—
395C24C24×C711yescharacteristic
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—82no—
417C2×D4—82no—
418C22×C4—28no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—44no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4C2×C7×D414yes—
449C22×C4C2×C7×D412yes—
450C22×C4C2×C7×D412yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—48no—
454C22⋊C4—28no—
455C22⋊C4—28no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—416no—
463C22⋊C4—44no—
464C22⋊C4C2×C7×D414yescomplemented
465C2×C7—21no—
466C2×C7—22no—
467C2×C7—22no—
468C2×C7—24no—
469C2×C7—21no—
470C2×C7—22no—
471C2×C7—84no—
472C2×C7#204414yesdirect product factor
473C2×C7C2×#39411yescharacteristic
474C2×C7C2×B(4,𝔽2)11yescharacteristic
475C2×C7C2×#45811yescharacteristic
476C23—22no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—41no—
484C23—42no—
485C23—41no—
486C23—44no—
487C23—41no—
488C23—42no—
489C23—44no—
490C23—48no—
491C23—41no—
492C23—44no—
493C23—44no—
494C23—416no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—82no—
500C23—82no—
501C23—88no—
502C23C7×#12012yes—
503C23C7×#12011yescharacteristic
504C23C7×#12011yescharacteristic
505C23C7×#12112yes—
506C23C7×#12114yes—
507C23C7×#12112yes—
508C23C7×#12114yes—
509C23C7×#12314yes—
510C23C7×#12314yes—
511C23C7×#12412yes—
512C23C7×#12412yes—
513C23C22×C7×D412yes—
514C23C22×C7×D411yescharacteristic
515C23C22×C7×D411yescharacteristic
516C23C2×C7×#4111yescharacteristic
517C23C2×C7×#4112yes—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—44no—
522D4—48no—
523D4—48no—
524D4—84no—
525D4—84no—
526C2×C4—28no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—88no—
555C7C2×#204411yescharacteristic, direct product factor, Sylow
556C22—24no—
557C22—28no—
558C22—28no—
559C22—24no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—22no—
564C22—21no—
565C22—22no—
566C22—21no—
567C22—22no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—42no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—84no—
580C22—88no—
581C22—88no—
582C22C7×#39414yes—
583C22C7×#39412yes—
584C22C7×#39412yes—
585C22C7×B(4,𝔽2)12yes—
586C22C7×#45812yes—
587C22C2×C7×#12011yescharacteristic
588C22C2×C7×#12111yescharacteristic
589C22C2×C7×#12112yes—
590C22C2×C7×#12312yes—
591C22C2×C7×#12411yescharacteristic
592C4—44no—
593C4—44no—
594C4—42no—
595C4—42no—
596C4—44no—
597C4—84no—
598C2—21no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—21no—
603C2—22no—
604C2—84no—
605C2C7×#204414yesdirect product factor
606C2C2×C7×#39411yescharacteristic
607C2C2×C7×B(4,𝔽2)11yescharacteristic
608C2C2×C7×#45811yescharacteristic
subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC24C24×C7
prime radicalC2×C7×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C25×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C7×#99C2semidirect
3. C2×C7×#386C2semidirect
4. C2×C7×#385C2semidirect
5. C7×#2044C2direct (N × H)
6. C2×C7×#342C2semidirect
22. C2×C7×#99C22semidirect
24. C7×#386C22semidirect
26. C7×#385C22semidirect
29. C7×#342C22semidirect
30. C2×#2044C7direct (N × H)
80. C2×C7×C22⋊C4D4semidirect
88. C22×#99C2×C7semidirect
89. C2×#386C2×C7semidirect
90. C2×#385C2×C7semidirect
91. #2044C2×C7direct (N × H)
92. C2×#342C2×C7semidirect
178. C7×C22⋊C4C2×D4semidirect
194. C2×#99C22×C7semidirect
196. #386C22×C7semidirect
198. #385C22×C7semidirect
201. #342C22×C7semidirect
330. C2×C22⋊C4C7×D4semidirect
464. C22⋊C4C2×C7×D4semidirect
472. C2×C7#2044direct (N × H)
555. C7C2×#2044direct (N × H)
605. C2C7×#2044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5342
C22×C7×#992
C2×C7×#3862
C2×C7×#3852
C7×#20442
C2×C7×#3422
C2×#20447