Finite Group Databasebeta

← C2×#11737138 #14232548

Subgroups — C2×#11737138 #14232548

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90270C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic
3C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
4C2×#89946C212yesmaximal, complemented
5C2×#89793C211yesmaximal, characteristic, complemented
6C2×#89780C211yesmaximal, characteristic, complemented
7#11737138C2116yesmaximal, direct product factor
8C2×#89633C212yesmaximal, complemented
9C2×#89586C212yesmaximal, complemented
10C2×#89546C212yesmaximal, complemented
11C2×#89460C211yesmaximal, characteristic, complemented
12C2×#89454C211yesmaximal, characteristic, complemented
13C22×C7×SD16C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×#6509C2212yes—
17C2×#6501C2212yes—
18C2×#6493—21no—
19C2×#6489—21no—
20C22×#1131C2212yes—
21#90270—24no—
22#90270C2218yescomplemented
23#90254—24no—
24#90254C2218yes—
25C2×#6459—22no—
26C2×#6455C2212yes—
27C2×D7×C4⋊C4C2212yes—
28C2×#6448—22no—
29C2×C4×D28—21no—
30C2×C4×D28C2211yescharacteristic
31C2×#6433—21no—
32C2×#6432C2211yescharacteristic
33C2×#6432C2211yescharacteristic
34C4×C7×SD16C2218yescomplemented
35C2×C7×#106C2211yescharacteristic
36C2×C7×#103C2211yescharacteristic
37C2×C7×#102C2211yescharacteristic
38C2×C4×C7×C8C2211yescharacteristic
39C2×#6409C2212yes—
40C2×#6406C2212yes—
41#89946C22116yescomplemented
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×#6392C2212yes—
45#89793C2218yescomplemented
46#89780C2218yescomplemented
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50#89633C22116yescomplemented
51#89586C22116yescomplemented
52#89546C22116yescomplemented
53#89460C2218yescomplemented
54#89454C2218yescomplemented
55C2×#3357—71nomaximal, Sylow
56C22×C7×Q8C2311yescharacteristic
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C22×C22⋊D7—22no—
60C22×D28D411yescharacteristic
61C22×C4×D7—22no—
62C22×C4×D7C2312yes—
63C22×Dic14—21no—
64C22×Dic14—21no—
65C2×C7×SD16—24no—
66C2×C7×SD16C2314yes—
67C22×C7×C8C2311yescharacteristic
68C22×C7×C8C2311yescharacteristic
69C4×C7×Q8—22no—
70C4×C7×Q8C2314yes—
71C4×C7×D4—22no—
72C4×C7×D4C2314yes—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C22⋊C4—21no—
77C2×C42×C7—21no—
78C2×C42×C7C2311yescharacteristic
79C2×C22⋊Dic7—22no—
80#6509—24no—
81#6509C2318yes—
82#6501—24no—
83#6501C2318yes—
84#6493—28no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4D412yes—
88#6489—28no—
89C2×C4⋊Dic7—21no—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7D411yescharacteristic
92C2×C4⋊Dic7C2312yes—
93C2×C4⋊Dic7C2312yes—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×C4×Dic7—22no—
97C22×C7⋊C8C2312yes—
98C2×#1131—28no—
99C2×#1131C2318yes—
100#6459—216no—
101#6455—24no—
102#6455C2318yes—
103D7×C4⋊C4—24no—
104D7×C4⋊C4C2318yes—
105#6448—216no—
106C4×D28—28no—
107C4×D28D414yes—
108C4×D28C2314yes—
109#6433—28no—
110#6432—22no—
111#6432—22no—
112#6432C2314yes—
113#6432C2314yes—
114C7×#106C2314yes—
115C7×#103C2314yes—
116C7×#102C2314yes—
117C4×C7×C8C2314yes—
118#6409C2318yes—
119#6406C2318yes—
120(C2×D7)⋊C8C2318yes—
121#6392C2318yes—
122#6392C2318yes—
123#6382C2318yes—
124#6381C2318yes—
125C4⋊(C7⋊C8)C2314yes—
126C2×#555—71no—
127C2×#554—71no—
128#3357—716no—
129C2×#500—71no—
130C2×#485—72no—
131C2×#480—72no—
132C2×#477—71no—
133C2×#476—71no—
134C2×#468—72no—
135C2×C4×SD16D711yescharacteristic, complemented
136C2×#436—71no—
137C2×#428—72no—
138C24×C7—21no—
139C23×D7C2×D412yes—
140C2×C7×Q8—21no—
141C2×C7×Q8—22no—
142C2×C7×Q8—22no—
143C2×C7×Q8C2412yes—
144C2×C7×D4—21no—
145C2×C7×D4—22no—
146C2×C7×D4—22no—
147C2×C7×D4C2412yes—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—24no—
152C22×C4×C7—44no—
153C22×C4×C7C2×D411yescharacteristic
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2411yescharacteristic
156C2×C22⋊D7—28no—
157C2×C22⋊D7—84no—
158C22×Dic7—22no—
159C22×Dic7—22no—
160C22×Dic7C2×D412yes—
161C2×D28—24no—
162C2×D28C2×D414yes—
163C2×C4×D7—24no—
164C2×C4×D7—24no—
165C2×C4×D7—28no—
166C2×C4×D7—84no—
167C2×C4×D7C2×D414yes—
168C2×C4×D7C2414yes—
169C2×Dic14—24no—
170C2×Dic14—24no—
171C2×Dic14—82no—
172C2×Dic14—82no—
173C7×SD16—28no—
174C2×C7×C8—22no—
175C2×C7×C8#4114yes—
176C2×C7×C8C2412yes—
177C2×C7×C8C2412yes—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—24no—
181C7×C4⋊C4C2412yes—
182C7×C4⋊C4C2412yes—
183C7×C22⋊C4—24no—
184C42×C7—24no—
185C42×C7C2×D412yes—
186C42×C7C2412yes—
187C22⋊Dic7—28no—
188(C2×D7)⋊C4—28no—
189(C2×D7)⋊C4—28no—
190(C2×D7)⋊C4C2×D418yes—
191C4⋊Dic7—22no—
192C4⋊Dic7—22no—
193C4⋊Dic7—24no—
194C4⋊Dic7—24no—
195C4⋊Dic7C2×D414yes—
196C4⋊Dic7C2414yes—
197C4⋊Dic7C2414yes—
198Dic7⋊C4—28no—
199Dic7⋊C4—28no—
200C4×Dic7—28no—
201C2×C7⋊C8—24no—
202C2×C7⋊C8C2414yes—
203#1131—216no—
204C22×SD16C2×D711yescharacteristic
205C22×M16—72no—
206#555—78no—
207#555—144no—
208#554—78no—
209#554—144no—
210C2×C4⋊Q8—71no—
211C2×C4⋊Q8—71no—
212C2×#125—141no—
213C2×#124—142no—
214C2×C22⋊Q8—72no—
215C2×C22⋊Q8—142no—
216C2×#121—72no—
217C2×#121—141no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—71no—
220C2×C4×D4—141no—
221C2×C4×D4C2×D711yescharacteristic
222C2×#117—72no—
223C2×#117—141no—
224C22×C4⋊C4—72no—
225#500—78no—
226#485—716no—
227#480—716no—
228#477—78no—
229#476—78no—
230#468—716no—
231C4×SD16C2×D718yescomplemented
232#436—78no—
233#428—716no—
234C2×#107—72no—
235C2×#107—72no—
236C2×#107—72no—
237C2×#106—72no—
238C2×#106C2×D711yescharacteristic
239C2×C4⋊C8—71no—
240C2×#103—72no—
241C2×#103C2×D711yescharacteristic
242C2×#102—72no—
243C2×#102C2×D711yescharacteristic
244C2×C22⋊C8—72no—
245C2×C4×C8C2×D711yescharacteristic
246C23×C7—22no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7C22×D411yescharacteristic
251C22×D7—24no—
252C22×D7—24no—
253C22×D7—24no—
254C22×D7C22×D414yes—
255C7×Q8—22no—
256C7×Q8—22no—
257C7×Q8—42no—
258C7×D4—22no—
259C7×D4—22no—
260C7×D4—42no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—42no—
266C2×C4×C7—42no—
267C2×C4×C7—42no—
268C2×C4×C7—48no—
269C2×C4×C7#13714yes—
270C2×C4×C7C22×D412yes—
271C2×C4×C7C22×D411yescharacteristic
272C2×C4×C7C22×D412yes—
273C2×C4×C7C2×#4112yes—
274C2×C4×C72−1+412yes—
275C2×C4×C7C2511yescharacteristic
276C22⋊D7—88no—
277C2×Dic7—24no—
278C2×Dic7—24no—
279C2×Dic7—24no—
280C2×Dic7—44no—
281C2×Dic7—44no—
282C2×Dic7C22×D414yes—
283D28—28no—
284C4×D7—28no—
285C4×D7—24no—
286C4×D7—24no—
287C4×D7—88no—
288Dic14—84no—
289Dic14—84no—
290C7×C8—22no—
291C7×C8C2×#4114yes—
292C7⋊C8—24no—
293C22×Q8—141no—
294C22×Q8—141no—
295C22×Q8C22×D711yescharacteristic
296C22×D4—71no—
297C22×D4—142no—
298C22×D4C22×D711yescharacteristic
299C23×C4—21no—
300C23×C4—72no—
301C23×C4—142no—
302C2×SD16—24no—
303C2×SD16C22×D714yes—
304C2×M16—78no—
305C2×M16—148no—
306C22×C8—72no—
307C22×C8C22×D711yescharacteristic
308C22×C8C22×D711yescharacteristic
309C4⋊Q8—74no—
310C4⋊Q8—74no—
311C4⋊Q8—142no—
312C4⋊Q8—142no—
313#125—148no—
314#124—1416no—
315C22⋊Q8—78no—
316C22⋊Q8—1416no—
317C22⋊Q8—144no—
318#121—78no—
319#121—148no—
320#121—144no—
321C4×Q8—22no—
322C4×Q8C22×D714yes—
323C4×D4—22no—
324C4×D4—74no—
325C4×D4—74no—
326C4×D4—148no—
327C4×D4C22×D714yes—
328#117—78no—
329#117—144no—
330#117—148no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—71no—
333C2×C4⋊C4—72no—
334C2×C4⋊C4—72no—
335C2×C4⋊C4—78no—
336C2×C4⋊C4—144no—
337C2×C4⋊C4—142no—
338C2×C4⋊C4—142no—
339C2×C4⋊C4—141no—
340C2×C4⋊C4—141no—
341C2×C4⋊C4C22×D711yescharacteristic
342C2×C4⋊C4C22×D711yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—72no—
345C2×C22⋊C4—142no—
346C2×C22⋊C4—142no—
347C2×C22⋊C4—142no—
348C2×C42—21no—
349C2×C42—142no—
350C2×C42C22×D711yescharacteristic
351#107—78no—
352#107—78no—
353#107—78no—
354#106—78no—
355#106C22×D714yes—
356C4⋊C8—74no—
357#103—78no—
358#103C22×D714yes—
359#102—78no—
360#102C22×D714yes—
361C22⋊C8—78no—
362C4×C8C22×D714yes—
363C22×C7—42no—
364C22×C7—42no—
365C22×C7—42no—
366C22×C7—84no—
367C22×C7#54712yes—
368C22×C7C2×#13712yes—
369C22×C7#57612yes—
370C22×C7C23×D411yescharacteristic
371C2×D7—24no—
372C2×D7—24no—
373C2×D7—24no—
374C2×D7—48no—
375C4×C7—22no—
376C4×C7—42no—
377C4×C7—42no—
378C4×C7—42no—
379C4×C7#54712yes—
380C4×C7C2×#13714yes—
381C4×C7C22×#4111yescharacteristic
382C4×C7C2×2−1+411yescharacteristic
383Dic7—24no—
384Dic7—44no—
385Dic7—44no—
386C24—21no—
387C24—72no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—144no—
392C2×Q8—144no—
393C2×Q8—562no—
394C2×Q8—562no—
395C2×Q8C23×D712yes—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—74no—
400C2×D4—148no—
401C2×D4—144no—
402C2×D4—564no—
403C2×D4C23×D712yes—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—44no—
409C22×C4—72no—
410C22×C4—74no—
411C22×C4—74no—
412C22×C4—148no—
413C22×C4—144no—
414C22×C4—144no—
415C22×C4—142no—
416C22×C4—142no—
417C22×C4—564no—
418C22×C4D4×D711yescharacteristic
419C22×C4D4×D711yescharacteristic
420C22×C4C23×D711yescharacteristic
421SD16—28no—
422M16—1416no—
423C2×C8—22no—
424C2×C8—74no—
425C2×C8—144no—
426C2×C8#115714yes—
427C2×C8C23×D712yes—
428C2×C8C23×D712yes—
429C4⋊C4—24no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—74no—
433C4⋊C4—74no—
434C4⋊C4—74no—
435C4⋊C4—148no—
436C4⋊C4—148no—
437C4⋊C4—142no—
438C4⋊C4—142no—
439C4⋊C4—144no—
440C4⋊C4—144no—
441C4⋊C4C23×D712yes—
442C4⋊C4C23×D712yes—
443C22⋊C4—24no—
444C22⋊C4—78no—
445C22⋊C4—148no—
446C22⋊C4—148no—
447C22⋊C4—148no—
448C42—24no—
449C42—148no—
450C42D4×D712yes—
451C42C23×D712yes—
452C2×C7—82no—
453C2×C7#335714yescomplemented
454C2×C7C2×#54711yescharacteristic
455C2×C7C22×#13711yescharacteristic
456C2×C7C2×#57611yescharacteristic
457D7—44no—
458C23—22no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—74no—
463C23—144no—
464C23—144no—
465C23—144no—
466C23C2×D4×D711yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—42no—
470Q8—564no—
471Q8—564no—
472D4—22no—
473D4—22no—
474D4—42no—
475D4—148no—
476D4—568no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—48no—
485C2×C4—74no—
486C2×C4—144no—
487C2×C4—148no—
488C2×C4—144no—
489C2×C4—144no—
490C2×C4—144no—
491C2×C4—144no—
492C2×C4—284no—
493C2×C4—284no—
494C2×C4—568no—
495C2×C4#647814yes—
496C2×C4C2×#115712yes—
497C2×C4C2×D4×D712yes—
498C2×C4C2×D4×D712yes—
499C2×C4C2×D4×D711yescharacteristic
500C2×C4#655412yes—
501C2×C4C24×D711yescharacteristic
502C8—22no—
503C8—144no—
504C8C2×#115714yes—
505C7C2×#335711yescharacteristic, complemented, Sylow
506C22—42no—
507C22—42no—
508C22—42no—
509C22—84no—
510C22—144no—
511C22—144no—
512C22—144no—
513C22—288no—
514C22#9024212yes—
515C22C2×#647812yes—
516C22#9046012yes—
517C22C22×D4×D711yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—144no—
523C4—284no—
524C4—284no—
525C4#9024212yes—
526C4C2×#647814yes—
527C4C22×#115711yescharacteristic
528C4C2×#655411yescharacteristic
529C2—82no—
530C2—284no—
531C2#1173713814yesdirect product factor
532C2C2×#9024211yescharacteristic
533C2C22×#647811yescharacteristic
534C2C2×#9046011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC2×#90254C2
hypercenterC2×C4×SD16D7
hypocenterC7C2×#3357
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#90270C2semidirect
3. C2×C4×C7×SD16C2semidirect
4. C2×#89946C2semidirect
5. C2×#89793C2semidirect
6. C2×#89780C2semidirect
7. #11737138C2direct (N × H)
8. C2×#89633C2semidirect
9. C2×#89586C2semidirect
10. C2×#89546C2semidirect
11. C2×#89460C2semidirect
12. C2×#89454C2semidirect
22. #90270C22semidirect
34. C4×C7×SD16C22semidirect
41. #89946C22semidirect
45. #89793C22semidirect
46. #89780C22semidirect
50. #89633C22semidirect
51. #89586C22semidirect
52. #89546C22semidirect
53. #89460C22semidirect
54. #89454C22semidirect
135. C2×C4×SD16D7semidirect
231. C4×SD16C2×D7semidirect
453. C2×C7#3357semidirect
505. C7C2×#3357semidirect
531. C2#11737138direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902702
C2×#902542
C2×C4×C7×SD162
C2×#899462
C2×#897932
C2×#897802
#117371382
C2×#896332
C2×#895862
C2×#895462
C2×#894602
C2×#894542
C2×#33577