Finite Group Databasebeta

← C2×#11727280 #13381252

Subgroups — C2×#11727280 #13381252

Order 1792.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6487C211yesmaximal, characteristic
2C2×C7×#380C211yesmaximal, characteristic
3C22×C22⋊(C7⋊C8)C211yesmaximal, characteristic
4C22×#6384C211yesmaximal, characteristic, complemented
5C22×#6384C211yesmaximal, characteristic, complemented
6C22×#6382C211yesmaximal, characteristic, complemented
7C2×#89324C211yesmaximal, characteristic, complemented
8#11727280C218yesmaximal, direct product factor
9C24×C4×C7C2211yescharacteristic
10C23×Dic14C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C22⋊C4—21no—
14C22×C22⋊Dic7—21no—
15C22×C4⋊Dic7C2211yescharacteristic
16C2×#6487—22no—
17C2×#6487—24no—
18C2×#6487—24no—
19C2×#6487C2214yes—
20C22×Dic7⋊C4—21no—
21C23×C7⋊C8C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C7×#380—22no—
24C7×#380C2214yes—
25C2×C7×#95—21no—
26C2×C22⋊(C7⋊C8)—24no—
27C2×C22⋊(C7⋊C8)C2214yes—
28C2×#6384—24no—
29C2×#6384—24no—
30C2×#6384C2214yescomplemented
31C2×#6384C2214yescomplemented
32C2×#6382—24no—
33C2×#6382C2214yescomplemented
34#89324C2214yescomplemented
35C2×#2035—71nomaximal, Sylow
36C25×C7D411yescharacteristic
37C23×C4×C7—22no—
38C23×C4×C7—22no—
39C23×C4×C7—22no—
40C23×C4×C7—22no—
41C23×C4×C7—22no—
42C23×C4×C7—22no—
43C23×C4×C7—21no—
44C23×C4×C7—21no—
45C23×C4×C7D411yescharacteristic
46C23×C4×C7D412yes—
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×Dic7—21no—
50C23×Dic7—21no—
51C22×Dic14—22no—
52C22×Dic14—22no—
53C22×Dic14—22no—
54C22×Dic14—22no—
55C22×Dic14—21no—
56C22×Dic14—22no—
57C22×Dic14D414yes—
58C22×Dic14C2312yes—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—21no—
64C2×C7×C4⋊C4—21no—
65C2×C7×C4⋊C4C2312yes—
66C2×C7×C4⋊C4C2312yes—
67C2×C7×C22⋊C4—24no—
68C2×C7×C22⋊C4—44no—
69C2×C22⋊Dic7—28no—
70C2×C22⋊Dic7—24no—
71C2×C4⋊Dic7—21no—
72C2×C4⋊Dic7—22no—
73C2×C4⋊Dic7D414yes—
74C2×C4⋊Dic7C2312yes—
75#6487—216no—
76#6487—28no—
77#6487—28no—
78C2×Dic7⋊C4—28no—
79C2×Dic7⋊C4—24no—
80C22×C7⋊C8—22no—
81C22×C7⋊C8—22no—
82C22×C7⋊C8—22no—
83C22×C7⋊C8—22no—
84C22×C7⋊C8—22no—
85C22×C7⋊C8D414yes—
86C22×C7⋊C8C2312yes—
87C22×C7⋊C8C2312yes—
88C7×#95—24no—
89C22⋊(C7⋊C8)—28no—
90#6384—28no—
91#6384—28no—
92#6382—28no—
93C22×C22⋊Q8—71no—
94C22×#106—71no—
95C22×#103—71no—
96C22×#103—71no—
97C22×C22⋊C8—71no—
98C2×#380D711yescharacteristic
99#2035—78no—
100C2×#340—71no—
101C24×C7—22no—
102C24×C7—22no—
103C24×C7—22no—
104C24×C7—22no—
105C24×C7—22no—
106C24×C7—22no—
107C24×C7SD1614yes—
108C24×C7C2×D412yes—
109C24×C7C2×D411yescharacteristic
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7—24no—
114C22×C4×C7—24no—
115C22×C4×C7—24no—
116C22×C4×C7—22no—
117C22×C4×C7—22no—
118C22×C4×C7—22no—
119C22×C4×C7—22no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—44no—
125C22×C4×C7—44no—
126C22×C4×C7—44no—
127C22×C4×C7—44no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7—42no—
131C22×C4×C7—42no—
132C22×C4×C7—42no—
133C22×C4×C7—42no—
134C22×C4×C7C2×D412yes—
135C22×C4×C7C2×D411yescharacteristic
136C22×C4×C7C2×D412yes—
137C22×C4×C7C2×D412yes—
138C22×C4×C7C2×D412yes—
139C22×C4×C7#4112yes—
140C22×C4×C7#4112yes—
141C22×C4×C7#4112yes—
142C22×C4×C7C2411yescharacteristic
143C22×Dic7—24no—
144C22×Dic7—24no—
145C22×Dic7—22no—
146C22×Dic7—22no—
147C22×Dic7—42no—
148C22×Dic7—42no—
149C22×Dic7—42no—
150C22×Dic7—42no—
151C2×Dic14—28no—
152C2×Dic14—28no—
153C2×Dic14—22no—
154C2×Dic14—22no—
155C2×Dic14—22no—
156C2×Dic14—22no—
157C2×Dic14—24no—
158C2×Dic14—22no—
159C2×Dic14—44no—
160C2×Dic14—42no—
161C2×Dic14—42no—
162C2×Dic14—44no—
163C2×Dic14C2×D414yes—
164C7×C4⋊C4—22no—
165C7×C4⋊C4—22no—
166C7×C4⋊C4—22no—
167C7×C4⋊C4—22no—
168C7×C4⋊C4—42no—
169C7×C4⋊C4—42no—
170C7×C22⋊C4—48no—
171C22⋊Dic7—216no—
172C4⋊Dic7—24no—
173C4⋊Dic7—22no—
174C4⋊Dic7C2×D414yes—
175Dic7⋊C4—216no—
176C2×C7⋊C8—28no—
177C2×C7⋊C8—22no—
178C2×C7⋊C8—22no—
179C2×C7⋊C8—22no—
180C2×C7⋊C8—22no—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—44no—
183C2×C7⋊C8C2×D414yes—
184C23×Q8—71no—
185C24×C4C2×D711yescharacteristic
186C23×C8—71no—
187C23×C8—71no—
188C2×C22⋊Q8—74no—
189C2×C22⋊Q8—144no—
190C2×C22⋊Q8—144no—
191C2×C22⋊Q8—142no—
192C22×C4⋊C4—71no—
193C22×C4⋊C4—141no—
194C22×C4⋊C4C2×D711yescharacteristic
195C22×C4⋊C4C2×D711yescharacteristic
196C22×C22⋊C4—21no—
197C22×C22⋊C4—141no—
198C2×#106—74no—
199C2×#106—144no—
200C2×#103—74no—
201C2×#103—74no—
202C2×#103—144no—
203C2×#103—144no—
204C2×C22⋊C8—74no—
205C2×C22⋊C8—144no—
206#380—22no—
207#380C2×D714yes—
208C2×#95—21no—
209#340—74no—
210C23×C7—22no—
211C23×C7—22no—
212C23×C7—22no—
213C23×C7—22no—
214C23×C7—22no—
215C23×C7—22no—
216C23×C7—28no—
217C23×C7—28no—
218C23×C7—28no—
219C23×C7—44no—
220C23×C7—44no—
221C23×C7—44no—
222C23×C7—44no—
223C23×C7#12012yes—
224C23×C7#12112yes—
225C23×C7#12312yes—
226C23×C7C2×SD1614yes—
227C23×C7C2×SD1612yes—
228C23×C7#13512yes—
229C23×C7#13712yes—
230C23×C7#13712yes—
231C23×C7C22×D411yescharacteristic
232C2×C4×C7—22no—
233C2×C4×C7—22no—
234C2×C4×C7—22no—
235C2×C4×C7—44no—
236C2×C4×C7—42no—
237C2×C4×C7—42no—
238C2×C4×C7—42no—
239C2×C4×C7—42no—
240C2×C4×C7—48no—
241C2×C4×C7—42no—
242C2×C4×C7—42no—
243C2×C4×C7—42no—
244C2×C4×C7—42no—
245C2×C4×C7—42no—
246C2×C4×C7—42no—
247C2×C4×C7—84no—
248C2×C4×C7—84no—
249C2×C4×C7#12012yes—
250C2×C4×C7#12114yes—
251C2×C4×C7#12114yes—
252C2×C4×C7#12112yes—
253C2×C4×C7#12314yes—
254C2×C4×C7#12312yes—
255C2×C4×C7#12414yes—
256C2×C4×C7C22×D411yescharacteristic
257C2×C4×C7C22×D411yescharacteristic
258C2×C4×C7C22×D411yescharacteristic
259C2×C4×C7C2×#4111yescharacteristic
260C2×C4×C7C2×#4111yescharacteristic
261C2×C4×C7C2×#4111yescharacteristic
262C2×Dic7—24no—
263C2×Dic7—24no—
264C2×Dic7—42no—
265C2×Dic7—42no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—48no—
269C2×Dic7—48no—
270Dic14—24no—
271Dic14—24no—
272Dic14—42no—
273Dic14—42no—
274Dic14—48no—
275C7⋊C8—24no—
276C7⋊C8—42no—
277C25C22⋊D711yescharacteristic
278C22×Q8—74no—
279C22×Q8—72no—
280C22×Q8—142no—
281C22×Q8—141no—
282C22×Q8—142no—
283C22×Q8—142no—
284C22×Q8—142no—
285C22×Q8—142no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—141no—
295C23×C4—141no—
296C23×C4C22⋊D712yes—
297C23×C4C22⋊D711yescharacteristic
298C23×C4C22×D712yes—
299C23×C4C22×D711yescharacteristic
300C22×C8—74no—
301C22×C8—72no—
302C22×C8—72no—
303C22×C8—142no—
304C22×C8—142no—
305C22×C8—142no—
306C22×C8—142no—
307C22×C8—142no—
308C22⋊Q8—148no—
309C22⋊Q8—148no—
310C22⋊Q8—1416no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—74no—
318C2×C4⋊C4—72no—
319C2×C4⋊C4—148no—
320C2×C4⋊C4—142no—
321C2×C4⋊C4—141no—
322C2×C4⋊C4—144no—
323C2×C4⋊C4C22×D712yes—
324C2×C4⋊C4C22×D712yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—148no—
328C2×C22⋊C4—144no—
329#106—148no—
330#103—148no—
331#103—148no—
332C22⋊C8—148no—
333#95—24no—
334C22×C7—24no—
335C22×C7—24no—
336C22×C7—24no—
337C22×C7—42no—
338C22×C7—42no—
339C22×C7—42no—
340C22×C7—42no—
341C22×C7—416no—
342C22×C7#39414yes—
343C22×C7#44814yes—
344C22×C7#45214yes—
345C22×C7#46514yes—
346C22×C7#47014yes—
347C22×C7#48314yes—
348C22×C7#48514yes—
349C22×C7C2×#12011yescharacteristic
350C22×C7C2×#12111yescharacteristic
351C22×C7C2×#12311yescharacteristic
352C22×C7C22×SD1611yescharacteristic
353C22×C7C2×#13511yescharacteristic
354C22×C7C2×#13711yescharacteristic
355C22×C7C2×#13711yescharacteristic
356C4×C7—42no—
357C4×C7—82no—
358C4×C7—82no—
359C4×C7#39414yes—
360C4×C7C2×#12111yescharacteristic
361C4×C7C2×#12111yescharacteristic
362C4×C7C2×#12311yescharacteristic
363C4×C7C2×#12411yescharacteristic
364Dic7—44no—
365Dic7—44no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24#114214yes—
373C24C2×C22⋊D712yes—
374C24C2×C22⋊D711yescharacteristic
375C2×Q8—74no—
376C2×Q8—144no—
377C2×Q8—142no—
378C2×Q8—148no—
379C2×Q8—148no—
380C2×Q8—142no—
381C2×Q8—142no—
382C2×Q8—142no—
383C2×Q8—142no—
384C2×Q8—284no—
385C2×Q8—284no—
386C2×Q8—282no—
387C2×Q8—282no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—144no—
413C22×C4—144no—
414C22×C4—142no—
415C22×C4—142no—
416C22×C4—282no—
417C22×C4—282no—
418C22×C4—282no—
419C22×C4—282no—
420C22×C4#115712yes—
421C22×C4#115712yes—
422C22×C4D4×D712yes—
423C22×C4D4×D712yes—
424C22×C4D4×D712yes—
425C22×C4#115912yes—
426C22×C4C2×C22⋊D712yes—
427C22×C4C2×C22⋊D711yescharacteristic
428C22×C4C23×D711yescharacteristic
429C2×C8—74no—
430C2×C8—148no—
431C2×C8—142no—
432C2×C8—142no—
433C2×C8—142no—
434C2×C8—142no—
435C2×C8—142no—
436C2×C8—284no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—42no—
442C4⋊C4—42no—
443C4⋊C4—74no—
444C4⋊C4—1416no—
445C4⋊C4—144no—
446C4⋊C4—142no—
447C22⋊C4—48no—
448C22⋊C4—1416no—
449C2×C7—44no—
450C2×C7#203518yescomplemented
451C2×C7C2×#39411yescharacteristic
452C2×C7C2×#44811yescharacteristic
453C2×C7C2×#45211yescharacteristic
454C2×C7C2×#46511yescharacteristic
455C2×C7C2×#47011yescharacteristic
456C2×C7C2×#48311yescharacteristic
457C2×C7C2×#48511yescharacteristic
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—28no—
463C23—22no—
464C23—22no—
465C23—28no—
466C23—28no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23#649212yes—
472C23C2×#114214yes—
473C23C2×#114212yes—
474C23#650012yes—
475C23#650212yes—
476C23#650512yes—
477C23#651312yes—
478C23#651412yes—
479C23C22×C22⋊D711yescharacteristic
480Q8—144no—
481Q8—144no—
482Q8—282no—
483Q8—282no—
484Q8—288no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—44no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—84no—
501C2×C4—84no—
502C2×C4—144no—
503C2×C4—144no—
504C2×C4—282no—
505C2×C4—282no—
506C2×C4—288no—
507C2×C4—282no—
508C2×C4—282no—
509C2×C4—288no—
510C2×C4#644614yes—
511C2×C4#644714yes—
512C2×C4#644714yes—
513C2×C4#644814yes—
514C2×C4#649212yes—
515C2×C4#650012yes—
516C2×C4#650212yes—
517C2×C4C2×#115711yescharacteristic
518C2×C4C2×#115711yescharacteristic
519C2×C4C2×D4×D711yescharacteristic
520C2×C4C2×D4×D711yescharacteristic
521C2×C4C2×D4×D711yescharacteristic
522C2×C4C2×#115911yescharacteristic
523C8—144no—
524C8—282no—
525C7C2×#203511yescharacteristic, complemented, Sylow
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—416no—
533C22—42no—
534C22#8973114yes—
535C22#8974314yes—
536C22#8976814yes—
537C22#8981214yes—
538C22#8981314yes—
539C22#8981914yes—
540C22#8982414yes—
541C22C2×#649211yescharacteristic
542C22C22×#114211yescharacteristic
543C22C2×#650011yescharacteristic
544C22C2×#650211yescharacteristic
545C22C2×#650511yescharacteristic
546C22C2×#651311yescharacteristic
547C22C2×#651411yescharacteristic
548C4—42no—
549C4—82no—
550C4—82no—
551C4—284no—
552C4—284no—
553C4#8973114yes—
554C4C2×#644611yescharacteristic
555C4C2×#644711yescharacteristic
556C4C2×#644711yescharacteristic
557C4C2×#644811yescharacteristic
558C2—44no—
559C2#1172728018yesdirect product factor
560C2C2×#8973111yescharacteristic
561C2C2×#8974311yescharacteristic
562C2C2×#8976811yescharacteristic
563C2C2×#8981311yescharacteristic
564C2C2×#8981211yescharacteristic
565C2C2×#8982411yescharacteristic
566C2C2×#8981911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#380C2
socleC24×C7C2×D4
prime radicalC25×C7D4
hypercenterC2×#380D7
hypocenterC7C2×#2035
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C22×#6384C2semidirect
5. C22×#6384C2semidirect
6. C22×#6382C2semidirect
7. C2×#89324C2semidirect
8. #11727280C2direct (N × H)
30. C2×#6384C22semidirect
31. C2×#6384C22semidirect
33. C2×#6382C22semidirect
34. #89324C22semidirect
450. C2×C7#2035semidirect
525. C7C2×#2035semidirect
559. C2#11727280direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64872
C2×C7×#3802
C22×C22⋊(C7⋊C8)2
C22×#63842
C22×#63822
C2×#893242
#117272802
C2×#20357