Finite Group Databasebeta

← C2×#11728029 #13381266

Subgroups — C2×#11728029 #13381266

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×#6509C211yesmaximal, characteristic
2C22×C7×#103C211yesmaximal, characteristic, complemented
3C22×#6409C211yesmaximal, characteristic, complemented
4C22×(C2×D7)⋊C8C211yesmaximal, characteristic
5C2×#89759C211yesmaximal, characteristic
6C22×#6381C211yesmaximal, characteristic, complemented
7C2×#89346C211yesmaximal, characteristic, complemented
8#11728029C218yesmaximal, direct product factor
9C23×C7×Q8C2211yescharacteristic
10C23×C4×D7C2211yescharacteristic
11C23×C7×C8C2211yescharacteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C2×#6509—24no—
14C2×#6509—22no—
15C2×#6509—24no—
16C2×#6509C2214yes—
17C22×(C2×D7)⋊C4—21no—
18C22×(C2×D7)⋊C4—21no—
19C22×C4⋊Dic7C2211yescharacteristic
20C22×C4⋊Dic7C2211yescharacteristic
21C22×Dic7⋊C4—21no—
22C23×C7⋊C8C2211yescharacteristic
23C2×C7×#103—24no—
24C2×C7×#103C2214yescomplemented
25C2×#6409—24no—
26C2×#6409C2214yescomplemented
27C2×C7⋊#95—21no—
28C2×(C2×D7)⋊C8—24no—
29C2×(C2×D7)⋊C8C2214yes—
30#89759—22no—
31#89759C2214yes—
32C2×#6381—24no—
33C2×#6381C2214yescomplemented
34#89346C2214yescomplemented
35C2×#2036—71nomaximal, Sylow
36C24×D7D411yescharacteristic
37C22×C7×Q8—22no—
38C22×C7×Q8—21no—
39C22×C7×Q8—22no—
40C22×C7×Q8—22no—
41C22×C7×Q8—22no—
42C22×C7×Q8—22no—
43C22×C7×Q8D414yes—
44C22×C7×Q8C2312yes—
45C23×C4×C7—21no—
46C23×C4×C7—21no—
47C23×C4×C7C2311yescharacteristic
48C23×Dic7—21no—
49C23×Dic7—21no—
50C23×Dic7D411yescharacteristic
51C22×C4×D7—22no—
52C22×C4×D7—22no—
53C22×C4×D7—22no—
54C22×C4×D7—22no—
55C22×C4×D7—22no—
56C22×C4×D7—22no—
57C22×C4×D7D412yes—
58C22×C4×D7C2312yes—
59C22×C7×C8—22no—
60C22×C7×C8—22no—
61C22×C7×C8—22no—
62C22×C7×C8C2312yes—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—21no—
66C2×C7×C4⋊C4C2312yes—
67#6509—216no—
68#6509—28no—
69#6509—28no—
70C2×(C2×D7)⋊C4—28no—
71C2×(C2×D7)⋊C4—24no—
72C2×(C2×D7)⋊C4—24no—
73C2×(C2×D7)⋊C4—44no—
74C2×C4⋊Dic7—21no—
75C2×C4⋊Dic7—22no—
76C2×C4⋊Dic7—22no—
77C2×C4⋊Dic7—22no—
78C2×C4⋊Dic7—21no—
79C2×C4⋊Dic7D414yes—
80C2×C4⋊Dic7C2312yes—
81C2×C4⋊Dic7C2312yes—
82C2×Dic7⋊C4—28no—
83C2×Dic7⋊C4—24no—
84C22×C7⋊C8—22no—
85C22×C7⋊C8—22no—
86C22×C7⋊C8D414yes—
87C22×C7⋊C8C2312yes—
88C7×#103—28no—
89#6409—28no—
90C7⋊#95—24no—
91(C2×D7)⋊C8—28no—
92#6381—28no—
93C22×C22⋊Q8—71no—
94C22×#107—71no—
95C22×#103—71no—
96C22×#103D711yescharacteristic, complemented
97C22×C22⋊C8—71no—
98C2×#380—71no—
99#2036—78no—
100C2×#340—71no—
101C24×C7C2×D411yescharacteristic
102C23×D7—22no—
103C23×D7—22no—
104C23×D7—22no—
105C23×D7—22no—
106C23×D7—22no—
107C23×D7—22no—
108C23×D7Q1614yes—
109C23×D7C2×D412yes—
110C2×C7×Q8—24no—
111C2×C7×Q8—22no—
112C2×C7×Q8—28no—
113C2×C7×Q8—28no—
114C2×C7×Q8—22no—
115C2×C7×Q8—22no—
116C2×C7×Q8—22no—
117C2×C7×Q8—22no—
118C2×C7×Q8—42no—
119C2×C7×Q8—44no—
120C2×C7×Q8—42no—
121C2×C7×Q8—44no—
122C2×C7×Q8C2×D414yes—
123C22×C4×C7—24no—
124C22×C4×C7—22no—
125C22×C4×C7—22no—
126C22×C4×C7—42no—
127C22×C4×C7—42no—
128C22×C4×C7—42no—
129C22×C4×C7—42no—
130C22×C4×C7—42no—
131C22×C4×C7C2×D411yescharacteristic
132C22×C4×C7C2×D412yes—
133C22×C4×C7C2×D412yes—
134C22×C4×C7C2×D412yes—
135C22×C4×C7#4112yes—
136C22×C4×C7#4112yes—
137C22×C4×C7#4112yes—
138C22×C4×C7C2411yescharacteristic
139C22×Dic7—22no—
140C22×Dic7—24no—
141C22×Dic7—22no—
142C22×Dic7—22no—
143C22×Dic7—22no—
144C22×Dic7—22no—
145C22×Dic7—42no—
146C22×Dic7—42no—
147C22×Dic7—42no—
148C22×Dic7—42no—
149C22×Dic7—42no—
150C22×Dic7C2×D412yes—
151C2×C4×D7—24no—
152C2×C4×D7—24no—
153C2×C4×D7—24no—
154C2×C4×D7—22no—
155C2×C4×D7—22no—
156C2×C4×D7—22no—
157C2×C4×D7—22no—
158C2×C4×D7—22no—
159C2×C4×D7—22no—
160C2×C4×D7—44no—
161C2×C4×D7—44no—
162C2×C4×D7—44no—
163C2×C4×D7—44no—
164C2×C7×C8—22no—
165C2×C7×C8—22no—
166C2×C7×C8—22no—
167C2×C7×C8—44no—
168C7×C4⋊C4—22no—
169C7×C4⋊C4—22no—
170C7×C4⋊C4—42no—
171(C2×D7)⋊C4—216no—
172(C2×D7)⋊C4—48no—
173C4⋊Dic7—24no—
174C4⋊Dic7—22no—
175C4⋊Dic7—22no—
176C4⋊Dic7—22no—
177C4⋊Dic7—42no—
178C4⋊Dic7C2×D414yes—
179Dic7⋊C4—216no—
180C2×C7⋊C8—28no—
181C2×C7⋊C8—22no—
182C2×C7⋊C8—22no—
183C2×C7⋊C8C2×D414yes—
184C23×Q8C2×D711yescharacteristic
185C24×C4—71no—
186C23×C8—71no—
187C23×C8C2×D711yescharacteristic
188C2×C22⋊Q8—74no—
189C2×C22⋊Q8—144no—
190C2×C22⋊Q8—142no—
191C2×C22⋊Q8—144no—
192C22×C4⋊C4—71no—
193C22×C4⋊C4—71no—
194C22×C4⋊C4—141no—
195C22×C4⋊C4C2×D711yescharacteristic
196C22×C22⋊C4—141no—
197C22×C22⋊C4—141no—
198C2×#107—74no—
199C2×#107—144no—
200C2×#103—24no—
201C2×#103—74no—
202C2×#103—144no—
203C2×#103C2×D714yescomplemented
204C2×C22⋊C8—74no—
205C2×C22⋊C8—144no—
206#380—74no—
207#380—142no—
208C2×#95—141no—
209#340—74no—
210C23×C7#12012yes—
211C23×C7#12112yes—
212C23×C7#12312yes—
213C23×C7C2×Q1612yes—
214C23×C7#13512yes—
215C23×C7AGL(1,ℤ/8)12yes—
216C23×C7#13712yes—
217C23×C7C22×D411yescharacteristic
218C22×D7—22no—
219C22×D7—22no—
220C22×D7—22no—
221C22×D7—22no—
222C22×D7—22no—
223C22×D7—22no—
224C22×D7—28no—
225C22×D7—28no—
226C22×D7—28no—
227C22×D7—44no—
228C22×D7—44no—
229C22×D7—44no—
230C22×D7—44no—
231C22×D7C2×Q1614yes—
232C7×Q8—24no—
233C7×Q8—24no—
234C7×Q8—42no—
235C7×Q8—42no—
236C7×Q8—48no—
237C2×C4×C7—24no—
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—84no—
245C2×C4×C7#12012yes—
246C2×C4×C7#12114yes—
247C2×C4×C7#12112yes—
248C2×C4×C7#12114yes—
249C2×C4×C7#12312yes—
250C2×C4×C7#12314yes—
251C2×C4×C7#12414yes—
252C2×C4×C7C22×D411yescharacteristic
253C2×C4×C7C22×D411yescharacteristic
254C2×C4×C7C22×D411yescharacteristic
255C2×C4×C7C2×#4111yescharacteristic
256C2×C4×C7C2×#4111yescharacteristic
257C2×C4×C7C2×#4111yescharacteristic
258C2×Dic7—22no—
259C2×Dic7—24no—
260C2×Dic7—22no—
261C2×Dic7—22no—
262C2×Dic7—42no—
263C2×Dic7—42no—
264C2×Dic7—44no—
265C2×Dic7—48no—
266C2×Dic7—42no—
267C2×Dic7—42no—
268C2×Dic7—42no—
269C2×Dic7—84no—
270C4×D7—42no—
271C4×D7—42no—
272C4×D7—42no—
273C4×D7—42no—
274C4×D7—48no—
275C7×C8—42no—
276C7⋊C8—24no—
277C25—71no—
278C22×Q8—22no—
279C22×Q8—21no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8C22⋊D714yes—
285C22×Q8C22×D712yes—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—71no—
289C23×C4—72no—
290C23×C4—72no—
291C23×C4—141no—
292C23×C4—142no—
293C23×C4—142no—
294C23×C4—142no—
295C23×C4—142no—
296C23×C4—142no—
297C23×C4—142no—
298C23×C4—141no—
299C23×C4C22×D711yescharacteristic
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—74no—
304C22×C8—72no—
305C22×C8—142no—
306C22×C8—142no—
307C22×C8C22×D712yes—
308C22⋊Q8—148no—
309C22⋊Q8—1416no—
310C22⋊Q8—148no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—74no—
315C2×C4⋊C4—72no—
316C2×C4⋊C4—72no—
317C2×C4⋊C4—144no—
318C2×C4⋊C4—148no—
319C2×C4⋊C4—141no—
320C2×C4⋊C4—142no—
321C2×C4⋊C4—142no—
322C2×C4⋊C4—142no—
323C2×C4⋊C4—141no—
324C2×C4⋊C4C22×D712yes—
325C2×C22⋊C4—144no—
326C2×C22⋊C4—148no—
327C2×C22⋊C4—144no—
328C2×C22⋊C4—284no—
329#107—148no—
330#103—28no—
331#103—148no—
332C22⋊C8—148no—
333#95—144no—
334C22×C7#39414yes—
335C22×C7#44914yes—
336C22×C7#45114yes—
337C22×C7#46714yes—
338C22×C7#46814yes—
339C22×C7#48414yes—
340C22×C7#48514yes—
341C22×C7C2×#12011yescharacteristic
342C22×C7C2×#12111yescharacteristic
343C22×C7C2×#12311yescharacteristic
344C22×C7C22×Q1611yescharacteristic
345C22×C7C2×#13511yescharacteristic
346C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C7C2×#13711yescharacteristic
348C2×D7—24no—
349C2×D7—24no—
350C2×D7—24no—
351C2×D7—42no—
352C2×D7—42no—
353C2×D7—42no—
354C2×D7—42no—
355C2×D7—416no—
356C4×C7—44no—
357C4×C7—82no—
358C4×C7#39414yes—
359C4×C7C2×#12111yescharacteristic
360C4×C7C2×#12111yescharacteristic
361C4×C7C2×#12311yescharacteristic
362C4×C7C2×#12411yescharacteristic
363Dic7—42no—
364Dic7—44no—
365Dic7—82no—
366C24—74no—
367C24—72no—
368C24—142no—
369C24—142no—
370C24—142no—
371C24—142no—
372C24—142no—
373C24—142no—
374C24D4×D711yescharacteristic
375C2×Q8—24no—
376C2×Q8—22no—
377C2×Q8—28no—
378C2×Q8—28no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8C2×C22⋊D714yes—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—72no—
397C22×C4—142no—
398C22×C4—142no—
399C22×C4—144no—
400C22×C4—142no—
401C22×C4—142no—
402C22×C4—144no—
403C22×C4—144no—
404C22×C4—144no—
405C22×C4—142no—
406C22×C4—142no—
407C22×C4—142no—
408C22×C4—142no—
409C22×C4—142no—
410C22×C4—142no—
411C22×C4—142no—
412C22×C4—282no—
413C22×C4—282no—
414C22×C4—284no—
415C22×C4—284no—
416C22×C4—284no—
417C22×C4—284no—
418C22×C4—282no—
419C22×C4—282no—
420C22×C4—282no—
421C22×C4#115712yes—
422C22×C4#115712yes—
423C22×C4D4×D711yescharacteristic
424C22×C4D4×D712yes—
425C22×C4D4×D712yes—
426C22×C4#115912yes—
427C22×C4C2×C22⋊D712yes—
428C22×C4C23×D711yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—44no—
433C2×C8—74no—
434C2×C8—148no—
435C2×C8—142no—
436C2×C8—142no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—74no—
441C4⋊C4—1416no—
442C4⋊C4—144no—
443C4⋊C4—142no—
444C4⋊C4—142no—
445C4⋊C4—142no—
446C4⋊C4—282no—
447C22⋊C4—1416no—
448C22⋊C4—288no—
449C2×C7#203618yescomplemented
450C2×C7C2×#39411yescharacteristic
451C2×C7C2×#45111yescharacteristic
452C2×C7C2×#44911yescharacteristic
453C2×C7C2×#46711yescharacteristic
454C2×C7C2×#46811yescharacteristic
455C2×C7C2×#48511yescharacteristic
456C2×C7C2×#48411yescharacteristic
457D7—44no—
458C23—74no—
459C23—142no—
460C23—142no—
461C23—142no—
462C23—142no—
463C23—142no—
464C23—148no—
465C23—142no—
466C23—148no—
467C23—148no—
468C23—284no—
469C23—284no—
470C23—284no—
471C23—284no—
472C23#644612yes—
473C23#644712yes—
474C23#647712yes—
475C23#647912yes—
476C23D7×Q1612yes—
477C23#648112yes—
478C23#650012yes—
479C23C2×D4×D711yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—42no—
483Q8—42no—
484Q8—48no—
485C2×C4—24no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—48no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—84no—
493C2×C4—142no—
494C2×C4—142no—
495C2×C4—144no—
496C2×C4—142no—
497C2×C4—282no—
498C2×C4—282no—
499C2×C4—288no—
500C2×C4—284no—
501C2×C4—282no—
502C2×C4—282no—
503C2×C4—282no—
504C2×C4—282no—
505C2×C4—288no—
506C2×C4—282no—
507C2×C4—282no—
508C2×C4—282no—
509C2×C4—564no—
510C2×C4#644612yes—
511C2×C4#644714yes—
512C2×C4#644712yes—
513C2×C4#644814yes—
514C2×C4#649214yes—
515C2×C4#650012yes—
516C2×C4#650214yes—
517C2×C4C2×#115711yescharacteristic
518C2×C4C2×#115711yescharacteristic
519C2×C4C2×D4×D711yescharacteristic
520C2×C4C2×D4×D711yescharacteristic
521C2×C4C2×#115911yescharacteristic
522C2×C4C22×C22⋊D711yescharacteristic
523C8—42no—
524C8—144no—
525C7C2×#203611yescharacteristic, complemented, Sylow
526C22—144no—
527C22—144no—
528C22—144no—
529C22—282no—
530C22—2816no—
531C22—282no—
532C22—282no—
533C22—282no—
534C22#8958114yes—
535C22#8958414yes—
536C22#8958514yes—
537C22#8958714yes—
538C22#8973114yes—
539C22#8994414yes—
540C22#8995814yes—
541C22C2×#644611yescharacteristic
542C22C2×#644711yescharacteristic
543C22C2×#647711yescharacteristic
544C22C2×#647911yescharacteristic
545C22C2×D7×Q1611yescharacteristic
546C22C2×#648111yescharacteristic
547C22C2×#650011yescharacteristic
548C4—44no—
549C4—82no—
550C4—284no—
551C4—282no—
552C4—562no—
553C4#8973114yes—
554C4C2×#644711yescharacteristic
555C4C2×#644811yescharacteristic
556C4C2×#649211yescharacteristic
557C4C2×#650211yescharacteristic
558C2—284no—
559C2#1172802918yesdirect product factor
560C2C2×#8958511yescharacteristic
561C2C2×#8958411yescharacteristic
562C2C2×#8958711yescharacteristic
563C2C2×#8958111yescharacteristic
564C2C2×#8973111yescharacteristic
565C2C2×#8994411yescharacteristic
566C2C2×#8995811yescharacteristic
subgroupG/H
centerC24D4×D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC22×C7×#103C2
socleC24×C7C2×D4
prime radicalC24×D7D4
hypercenterC22×#103D7
hypocenterC7C2×#2036
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×C7×#103C2semidirect
3. C22×#6409C2semidirect
6. C22×#6381C2semidirect
7. C2×#89346C2semidirect
8. #11728029C2direct (N × H)
24. C2×C7×#103C22semidirect
26. C2×#6409C22semidirect
33. C2×#6381C22semidirect
34. #89346C22semidirect
96. C22×#103D7semidirect
203. C2×#103C2×D7semidirect
449. C2×C7#2036semidirect
525. C7C2×#2036semidirect
559. C2#11728029direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65092
C22×C7×#1032
C22×#64092
C22×(C2×D7)⋊C82
C2×#897592
C22×#63812
C2×#893462
#117280292
C2×#20367