Finite Group Databasebeta

← C2×#11732227 #13520411

Subgroups — C2×#11732227 #13520411

Order 1792.

3002 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6498C211yesmaximal, characteristic
2C23×Dic7⋊C4C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×#89992C211yesmaximal, characteristic
5C2×#89982C211yesmaximal, characteristic, complemented
6C2×#89721C212yesmaximal, complemented
7C2×#89724C212yesmaximal, complemented
8C2×#89722C211yesmaximal, characteristic, complemented
9C2×#89715C211yesmaximal, characteristic, complemented
10#11732227C2116yesmaximal, direct product factor
11C2×#89430C212yesmaximal, complemented
12C2×#89429C212yesmaximal, complemented
13C23×C7×D4C2211yescharacteristic
14C24×C4×C7C2211yescharacteristic
15C24×Dic7C2211yescharacteristic
16C24×Dic7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C22⋊Dic7C2211yescharacteristic
20C22×C22⋊Dic7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2212yes—
24C2×#6498—28no—
25C2×#6498C2218yes—
26C22×C4⋊Dic7C2212yes—
27C22×Dic7⋊C4—28no—
28C22×Dic7⋊C4C2212yes—
29C22×Dic7⋊C4C2212yes—
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2212yes—
33C22×Dic7⋊C4C2218yescomplemented
34C7×#386C2218yes—
35C2×C7×#95C2212yes—
36#89992C2218yes—
37#89982C2218yescomplemented
38C2×C7⋊#95C2212yes—
39C2×C7⋊#95C2212yes—
40C2×C7⋊#95C2212yes—
41C2×C7⋊#95C2212yes—
42C2×C7⋊#95C2212yes—
43#89724C22116yescomplemented
44#89722C2218yescomplemented
45#89721C22116yescomplemented
46#89715C2218yescomplemented
47#89430C22116yescomplemented
48#89429C22116yescomplemented
49C2×#2623—71nomaximal, Sylow
50C25×C7C2311yescharacteristic
51C25×C7C2311yescharacteristic
52C22×C7×D4—24no—
53C22×C7×D4—24no—
54C22×C7×D4—24no—
55C22×C7×D4C2314yes—
56C23×C4×C7—24no—
57C23×C4×C7—44no—
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2312yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2314yes—
62C23×Dic7—24no—
63C23×Dic7—24no—
64C23×Dic7—24no—
65C23×Dic7—44no—
66C23×Dic7D418yes—
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2312yes—
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2312yes—
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2314yes—
74C23×Dic7C2314yes—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—44no—
77C2×C7×C22⋊C4C2314yes—
78C2×C7×C22⋊C4C2318yes—
79C2×C22⋊Dic7—24no—
80C2×C22⋊Dic7—24no—
81C2×C22⋊Dic7—24no—
82C2×C22⋊Dic7—24no—
83C2×C22⋊Dic7—44no—
84C2×C22⋊Dic7C2314yes—
85C2×C22⋊Dic7C2314yes—
86C2×C22⋊Dic7C2314yes—
87C2×C22⋊Dic7C2314yes—
88C2×C22⋊Dic7C2318yes—
89#6498—232no—
90C2×C4⋊Dic7—44no—
91C2×C4⋊Dic7C2318yes—
92C2×Dic7⋊C4—28no—
93C2×Dic7⋊C4—28no—
94C2×Dic7⋊C4—232no—
95C2×Dic7⋊C4—24no—
96C2×Dic7⋊C4—24no—
97C2×Dic7⋊C4—44no—
98C2×Dic7⋊C4C2314yes—
99C2×Dic7⋊C4C2318yes—
100C2×Dic7⋊C4C2314yes—
101C2×Dic7⋊C4C2318yes—
102C2×Dic7⋊C4C2318yes—
103C7×#95C2318yes—
104C7⋊#95C2318yes—
105C7⋊#95C2318yes—
106C7⋊#95C2318yes—
107C7⋊#95C2318yes—
108C7⋊#95C2318yes—
109C22×#123—71no—
110C23×C4⋊C4—71no—
111#2623—716no—
112C2×#400—72no—
113C2×#399—72no—
114C2×#398—72no—
115C2×#397—72no—
116C2×#386—71no—
117C2×#386D711yescharacteristic
118C2×#385—71no—
119C2×#385—71no—
120C2×#381—71no—
121C24×C7—24no—
122C24×C7—24no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—24no—
127C24×C7—24no—
128C24×C7C2×D414yes—
129C24×C7#4114yes—
130C24×C7#4114yes—
131C24×C7C2412yes—
132C24×C7C2412yes—
133C24×C7C2411yescharacteristic
134C2×C7×D4—28no—
135C2×C7×D4—28no—
136C2×C7×D4—28no—
137C2×C7×D4—416no—
138C22×C4×C7—28no—
139C22×C4×C7—24no—
140C22×C4×C7—22no—
141C22×C4×C7—24no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—24no—
145C22×C4×C7—24no—
146C22×C4×C7—24no—
147C22×C4×C7—24no—
148C22×C4×C7—48no—
149C22×C4×C7—416no—
150C22×C4×C7C2414yes—
151C22×C4×C7C2412yes—
152C22×C4×C7C2414yes—
153C22×Dic7—232no—
154C22×Dic7—28no—
155C22×Dic7—22no—
156C22×Dic7—22no—
157C22×Dic7—28no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7—28no—
161C22×Dic7—24no—
162C22×Dic7—22no—
163C22×Dic7—22no—
164C22×Dic7—24no—
165C22×Dic7—24no—
166C22×Dic7—24no—
167C22×Dic7—24no—
168C22×Dic7—24no—
169C22×Dic7—24no—
170C22×Dic7—24no—
171C22×Dic7—48no—
172C22×Dic7—416no—
173C22×Dic7C2×D414yes—
174C22×Dic7C2×D414yes—
175C22×Dic7C2×D4116yes—
176C22×Dic7C2412yes—
177C22×Dic7C2414yes—
178C22×Dic7C2414yes—
179C22×Dic7C2412yes—
180C22×Dic7C2412yes—
181C22×Dic7C2412yes—
182C7×C22⋊C4—28no—
183C7×C22⋊C4—48no—
184C22⋊Dic7—28no—
185C22⋊Dic7—28no—
186C22⋊Dic7—28no—
187C22⋊Dic7—28no—
188C22⋊Dic7—48no—
189C4⋊Dic7—48no—
190Dic7⋊C4—216no—
191Dic7⋊C4—216no—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194Dic7⋊C4—48no—
195C23×D4C2×D711yescharacteristic
196C24×C4—71no—
197C24×C4—71no—
198C24×C4C2×D711yescharacteristic
199C2×#123—78no—
200C2×#123—148no—
201C22×C4⋊C4—78no—
202C22×C4⋊C4—72no—
203C22×C4⋊C4—71no—
204C22×C4⋊C4—72no—
205C22×C4⋊C4—71no—
206C22×C4⋊C4—72no—
207C22×C4⋊C4—72no—
208C22×C4⋊C4—148no—
209C22×C22⋊C4—71no—
210C22×C22⋊C4—71no—
211C22×C22⋊C4—71no—
212C22×C22⋊C4—71no—
213C22×C22⋊C4—72no—
214C22×C22⋊C4C2×D711yescharacteristic
215C22×C22⋊C4C2×D712yes—
216#400—716no—
217#399—716no—
218#398—716no—
219#397—716no—
220#386—78no—
221#386C2×D718yes—
222#385—78no—
223#385—78no—
224#381—78no—
225C2×#95—72no—
226C2×#95—72no—
227C2×#95—72no—
228C2×#95—72no—
229C2×#95—72no—
230C2×#95C2×D712yes—
231C23×C7—28no—
232C23×C7—28no—
233C23×C7—216no—
234C23×C7—216no—
235C23×C7—24no—
236C23×C7—24no—
237C23×C7—22no—
238C23×C7—22no—
239C23×C7—22no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—44no—
243C23×C7—44no—
244C23×C7—44no—
245C23×C7—48no—
246C23×C7—48no—
247C23×C7#123116yes—
248C23×C7C22×D414yes—
249C23×C7C22×D412yes—
250C23×C7C2×#4114yes—
251C23×C7C2×#4112yes—
252C23×C7C2×#4114yes—
253C23×C7C2×#4112yes—
254C23×C7H(5,𝔽2)14yes—
255C23×C72−1+414yes—
256C23×C7C2511yescharacteristic
257C7×D4—416no—
258C2×C4×C7—24no—
259C2×C4×C7—22no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—416no—
268C2×C4×C7—44no—
269C2×C4×C7—48no—
270C2×C4×C7—48no—
271C2×Dic7—232no—
272C2×Dic7—28no—
273C2×Dic7—28no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—22no—
277C2×Dic7—22no—
278C2×Dic7—24no—
279C2×Dic7—22no—
280C2×Dic7—22no—
281C2×Dic7—24no—
282C2×Dic7—24no—
283C2×Dic7—24no—
284C2×Dic7—24no—
285C2×Dic7—24no—
286C2×Dic7—24no—
287C2×Dic7—24no—
288C2×Dic7—416no—
289C2×Dic7—44no—
290C2×Dic7—48no—
291C2×Dic7—44no—
292C2×Dic7—48no—
293C2×Dic7C22×D414yes—
294C2×Dic7C22×D414yes—
295C25C22×D711yescharacteristic
296C25C22×D711yescharacteristic
297C22×D4—24no—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4C22×D714yes—
301C23×C4—24no—
302C23×C4—44no—
303C23×C4—78no—
304C23×C4—74no—
305C23×C4—71no—
306C23×C4—71no—
307C23×C4—71no—
308C23×C4—72no—
309C23×C4—71no—
310C23×C4—72no—
311C23×C4—74no—
312C23×C4—144no—
313C23×C4—144no—
314C23×C4—144no—
315C23×C4—284no—
316C23×C4C22×D712yes—
317C23×C4C22×D712yes—
318C23×C4C22×D711yescharacteristic
319C23×C4C22×D714yes—
320#123—1432no—
321C2×C4⋊C4—78no—
322C2×C4⋊C4—78no—
323C2×C4⋊C4—74no—
324C2×C4⋊C4—74no—
325C2×C4⋊C4—78no—
326C2×C4⋊C4—78no—
327C2×C4⋊C4—148no—
328C2×C4⋊C4—148no—
329C2×C4⋊C4—1432no—
330C2×C4⋊C4—144no—
331C2×C4⋊C4—144no—
332C2×C4⋊C4—284no—
333C2×C4⋊C4—284no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—74no—
337C2×C22⋊C4—74no—
338C2×C22⋊C4—74no—
339C2×C22⋊C4—74no—
340C2×C22⋊C4—78no—
341C2×C22⋊C4—144no—
342C2×C22⋊C4—144no—
343C2×C22⋊C4—144no—
344C2×C22⋊C4—144no—
345C2×C22⋊C4—284no—
346C2×C22⋊C4C22×D714yes—
347C2×C22⋊C4C22×D718yes—
348#95—78no—
349#95—78no—
350#95—78no—
351#95—78no—
352#95—78no—
353#95C22×D718yes—
354C22×C7—232no—
355C22×C7—24no—
356C22×C7—24no—
357C22×C7—28no—
358C22×C7—28no—
359C22×C7—42no—
360C22×C7—42no—
361C22×C7—42no—
362C22×C7—44no—
363C22×C7—44no—
364C22×C7—88no—
365C22×C7C2×#12318yes—
366C22×C7C2×#12314yes—
367C22×C7#53514yes—
368C22×C7#53614yes—
369C22×C7#53918yes—
370C22×C7#53918yes—
371C22×C7C23×D411yescharacteristic
372C22×C7C22×#4111yescharacteristic
373C22×C7C22×#4111yescharacteristic
374C22×C7C2×H(5,𝔽2)12yes—
375C22×C7C2×2−1+412yes—
376C4×C7—42no—
377C4×C7—44no—
378C4×C7—44no—
379Dic7—24no—
380Dic7—24no—
381Dic7—42no—
382Dic7—44no—
383Dic7—42no—
384Dic7—44no—
385C24—24no—
386C24—24no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—24no—
391C24—24no—
392C24#115714yes—
393C24D4×D714yes—
394C24#115914yes—
395C24C23×D712yes—
396C24C23×D712yes—
397C24C23×D711yescharacteristic
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—416no—
402C22×C4—22no—
403C22×C4—28no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—48no—
413C22×C4—416no—
414C22×C4—74no—
415C22×C4—74no—
416C22×C4—716no—
417C22×C4—72no—
418C22×C4—72no—
419C22×C4—74no—
420C22×C4—72no—
421C22×C4—74no—
422C22×C4—72no—
423C22×C4—1432no—
424C22×C4—148no—
425C22×C4—142no—
426C22×C4—142no—
427C22×C4—148no—
428C22×C4—142no—
429C22×C4—142no—
430C22×C4—144no—
431C22×C4—142no—
432C22×C4—142no—
433C22×C4—148no—
434C22×C4—144no—
435C22×C4—144no—
436C22×C4—144no—
437C22×C4—144no—
438C22×C4—144no—
439C22×C4—144no—
440C22×C4—144no—
441C22×C4—288no—
442C22×C4—2816no—
443C22×C4C23×D714yes—
444C22×C4C23×D712yes—
445C22×C4C23×D714yes—
446C4⋊C4—1416no—
447C4⋊C4—1416no—
448C4⋊C4—148no—
449C4⋊C4—148no—
450C4⋊C4—288no—
451C4⋊C4—288no—
452C22⋊C4—28no—
453C22⋊C4—48no—
454C22⋊C4—148no—
455C22⋊C4—148no—
456C22⋊C4—148no—
457C22⋊C4—148no—
458C22⋊C4—288no—
459C2×C7—28no—
460C2×C7—82no—
461C2×C7#262318yescomplemented
462C2×C7C22×#12311yescharacteristic
463C2×C7C2×#53511yescharacteristic
464C2×C7C2×#53611yescharacteristic
465C2×C7C2×#53912yes—
466C2×C7C2×#53912yes—
467C23—216no—
468C23—28no—
469C23—216no—
470C23—28no—
471C23—24no—
472C23—24no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—44no—
479C23—48no—
480C23—44no—
481C23—48no—
482C23—44no—
483C23#6446116yes—
484C23C2×#115714yes—
485C23C2×#115712yes—
486C23C2×D4×D714yes—
487C23C2×D4×D712yes—
488C23C2×#115914yes—
489C23C2×#115912yes—
490C23#654814yes—
491C23#655414yes—
492C23C24×D711yescharacteristic
493D4—416no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—416no—
504C2×C4—44no—
505C2×C4—48no—
506C2×C4—48no—
507C2×C4—74no—
508C2×C4—74no—
509C2×C4—1432no—
510C2×C4—148no—
511C2×C4—148no—
512C2×C4—142no—
513C2×C4—142no—
514C2×C4—142no—
515C2×C4—142no—
516C2×C4—144no—
517C2×C4—142no—
518C2×C4—142no—
519C2×C4—144no—
520C2×C4—144no—
521C2×C4—144no—
522C2×C4—144no—
523C2×C4—144no—
524C2×C4—144no—
525C2×C4—144no—
526C2×C4—2816no—
527C2×C4—288no—
528C2×C4—284no—
529C2×C4—288no—
530C2×C4—284no—
531C7C2×#262311yescharacteristic, complemented, Sylow
532C22—24no—
533C22—232no—
534C22—28no—
535C22—24no—
536C22—28no—
537C22—42no—
538C22—44no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—88no—
543C22C2×#644618yes—
544C22C2×#644614yes—
545C22#9025518yes—
546C22#9028314yes—
547C22#9029318yes—
548C22#9033914yes—
549C22C22×#115711yescharacteristic
550C22C22×D4×D711yescharacteristic
551C22C22×#115911yescharacteristic
552C22C2×#654812yes—
553C22C2×#655412yes—
554C4—44no—
555C4—44no—
556C4—42no—
557C4—144no—
558C4—144no—
559C4—284no—
560C4—282no—
561C4—282no—
562C4—284no—
563C2—28no—
564C2—82no—
565C2#1173222718yesdirect product factor
566C2C22×#644611yescharacteristic
567C2C2×#9025512yes—
568C2C2×#9028311yescharacteristic
569C2C2×#9029312yes—
570C2C2×#9033911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#386C2
socleC24×C7C24
prime radicalC23×C7×D4C22
hypercenterC2×#386D7
hypocenterC7C2×#2623
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×Dic7⋊C4C2semidirect
5. C2×#89982C2semidirect
6. C2×#89721C2semidirect
7. C2×#89724C2semidirect
8. C2×#89722C2semidirect
9. C2×#89715C2semidirect
10. #11732227C2direct (N × H)
11. C2×#89430C2semidirect
12. C2×#89429C2semidirect
33. C22×Dic7⋊C4C22semidirect
37. #89982C22semidirect
43. #89724C22semidirect
44. #89722C22semidirect
45. #89721C22semidirect
46. #89715C22semidirect
47. #89430C22semidirect
48. #89429C22semidirect
461. C2×C7#2623semidirect
531. C7C2×#2623semidirect
565. C2#11732227direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64982
C23×Dic7⋊C42
C2×C7×#3862
C2×#899922
C2×#899822
C2×#897212
C2×#897242
C2×#897222
C2×#897152
#117322272
C2×#894302
C2×#894292
C2×#26237