Finite Group Databasebeta

← C2×#11741072 #14232546

Subgroups — C2×#11741072 #14232546

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×C7×#554C211yesmaximal, characteristic, complemented
2C2×#90254C211yesmaximal, characteristic
3#11741072C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89850C211yesmaximal, characteristic, complemented
6C2×#89821C212yesmaximal, complemented
7C2×#89817C212yesmaximal, complemented
8C2×#89793C211yesmaximal, characteristic, complemented
9C2×C4×#1143C211yesmaximal, characteristic, complemented
10C2×#89784C211yesmaximal, characteristic, complemented
11C2×#89739C212yesmaximal, complemented
12C2×#89736C212yesmaximal, complemented
13C7×#554—24no—
14C7×#554C2218yescomplemented
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#125—21no—
17C2×C7×C22⋊Q8—22no—
18C2×C7×C22⋊Q8C2212yes—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4C2211yescharacteristic
22C22×C7×C4⋊C4C2212yes—
23C22×#1143C2211yescharacteristic
24C2×#6501—21no—
25C2×#6493C2212yes—
26C2×#6489C2212yes—
27C22×#1136C2212yes—
28#90254—24no—
29#90254C2218yes—
30C2×#6455—21no—
31C2×#6448—22no—
32C2×C4×D28C2211yescharacteristic
33C2×#6432C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2212yes—
36C2×C22⋊(C7⋊C8)C2212yes—
37#89856C2218yescomplemented
38#89850C2218yescomplemented
39#89821C22116yescomplemented
40#89817C22116yescomplemented
41C4×#1143C2218yescomplemented
42#89793C2218yescomplemented
43#89784C2218yescomplemented
44#89739C22116yescomplemented
45C2×#6383C2212yes—
46C2×#6383C2211yescharacteristic
47#89736C22116yescomplemented
48C2×#6382C2212yes—
49C2×#6382C2211yescharacteristic
50C2×#6381C2212yes—
51C2×#6381C2212yes—
52C2×#6381C2212yes—
53C2×C4⋊(C7⋊C8)C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3357—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8C2311yescharacteristic
58C22×C7×D4D411yescharacteristic
59C23×C4×C7—22no—
60C23×C4×C7C2312yes—
61C22×C22⋊D7—22no—
62C22×D28C2311yescharacteristic
63C22×C4×D7—21no—
64C22×Dic14—21no—
65C7×C4⋊Q8—22no—
66C7×C4⋊Q8C2314yes—
67C7×#125—28no—
68C7×C22⋊Q8—24no—
69C7×C22⋊Q8—216no—
70C7×C22⋊Q8C2318yes—
71C4×C7×Q8—22no—
72C4×C7×Q8C2314yes—
73C4×C7×D4—28no—
74C4×C7×D4D414yes—
75C4×C7×D4C2314yes—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4D411yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C4⋊C4C2312yes—
84C2×C7×C4⋊C4C2318yes—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4D412yes—
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C22⋊Dic7—22no—
90C2×#1143—24no—
91C2×#1143C2314yes—
92#6501—28no—
93#6493—24no—
94#6493C2318yes—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—22no—
97#6489—24no—
98#6489C2318yes—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7C2312yes—
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4×Dic7—22no—
103C2×#1136—28no—
104C2×#1136C2318yes—
105C22×C7⋊C8C2311yescharacteristic
106C22×C7⋊C8C2312yes—
107C22×C7⋊C8C2311yescharacteristic
108#6455—28no—
109#6448—216no—
110C4×D28—22no—
111C4×D28C2314yes—
112#6432—22no—
113#6432C2314yes—
114#6409C2318yes—
115#6409C2314yes—
116C22⋊(C7⋊C8)C2318yes—
117#6383C2318yes—
118#6383C2314yes—
119#6382C2318yes—
120#6382C2314yes—
121#6381C2318yes—
122#6381C2318yes—
123#6381C2318yes—
124C4⋊(C7⋊C8)C2314yes—
125C4×C7⋊C8C2314yes—
126C2×#555—71no—
127C2×#554D711yescharacteristic, complemented
128#3357—716no—
129C2×#500—71no—
130C2×#485—72no—
131C2×#480—72no—
132C2×#477—71no—
133C2×#476—71no—
134C2×#468—72no—
135C2×C4×SD16—71no—
136C2×#436—71no—
137C2×#428—72no—
138C24×C7C2×D412yes—
139C23×D7—21no—
140C2×C7×Q8—21no—
141C2×C7×Q8—24no—
142C2×C7×Q8—22no—
143C2×C7×Q8—22no—
144C2×C7×Q8—82no—
145C2×C7×Q8C2412yes—
146C2×C7×D4—24no—
147C2×C7×D4C2×D414yes—
148C22×C4×C7—24no—
149C22×C4×C7—24no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—28no—
154C22×C4×C7—84no—
155C22×C4×C7C2×D412yes—
156C22×C4×C7C2×D414yes—
157C22×C4×C7C2×D411yescharacteristic
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2414yes—
160C22×C4×C7C2411yescharacteristic
161C2×C22⋊D7—28no—
162C2×C22⋊D7—84no—
163C22×Dic7—21no—
164C22×Dic7—22no—
165C2×D28—22no—
166C2×D28—22no—
167C2×D28—21no—
168C2×D28C2412yes—
169C2×C4×D7—24no—
170C2×C4×D7—44no—
171C2×Dic14—24no—
172C2×Dic14—82no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4—28no—
175C7×C4⋊C4—22no—
176C7×C4⋊C4—24no—
177C7×C4⋊C4—24no—
178C7×C4⋊C4—28no—
179C7×C4⋊C4C2×D414yes—
180C7×C4⋊C4C2412yes—
181C7×C4⋊C4C2414yes—
182C7×C22⋊C4—28no—
183C7×C22⋊C4C2×D418yes—
184C42×C7—24no—
185C42×C7C2×D412yes—
186C42×C7C2412yes—
187C22⋊Dic7—28no—
188#1143—28no—
189(C2×D7)⋊C4—24no—
190(C2×D7)⋊C4—28no—
191C4⋊Dic7—22no—
192C4⋊Dic7—24no—
193C4⋊Dic7—21no—
194C4⋊Dic7C2414yes—
195C4⋊Dic7C2412yes—
196C4×Dic7—28no—
197#1136—216no—
198C2×C7⋊C8—24no—
199C2×C7⋊C8—22no—
200C2×C7⋊C8#4114yes—
201C2×C7⋊C8C2412yes—
202C2×C7⋊C8C2414yes—
203C2×C7⋊C8C2412yes—
204C22×SD16—71no—
205C22×M16—72no—
206#555—78no—
207#555—144no—
208#554—24no—
209#554C2×D718yescomplemented
210C2×C4⋊Q8—71no—
211C2×C4⋊Q8C2×D711yescharacteristic
212C2×#125—21no—
213C2×#124—142no—
214C2×C22⋊Q8—22no—
215C2×C22⋊Q8C2×D712yes—
216C2×#121—72no—
217C2×#121—141no—
218C2×C4×Q8C2×D711yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—71no—
221C2×C4×D4C2×D711yescharacteristic
222C2×#117—72no—
223C2×#117—141no—
224C22×C4⋊C4C2×D712yes—
225#500—78no—
226#485—716no—
227#480—716no—
228#477—78no—
229#476—78no—
230#468—716no—
231C4×SD16—78no—
232#436—78no—
233#428—716no—
234C2×#107—72no—
235C2×#107—72no—
236C2×#107—72no—
237C2×#106—72no—
238C2×#106—71no—
239C2×C4⋊C8—71no—
240C2×#103—72no—
241C2×#103—71no—
242C2×#102—71no—
243C2×#102—72no—
244C2×C22⋊C8—72no—
245C2×C4×C8—71no—
246C23×C7—24no—
247C23×C7—24no—
248C23×C7—24no—
249C23×C7C22×D414yes—
250C23×C7C22×D411yescharacteristic
251C22×D7—22no—
252C22×D7—42no—
253C22×D7—42no—
254C22×D7—42no—
255C7×Q8—22no—
256C7×Q8—22no—
257C7×Q8—42no—
258C7×Q8—84no—
259C7×D4—28no—
260C2×C4×C7—24no—
261C2×C4×C7—22no—
262C2×C4×C7—28no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—24no—
268C2×C4×C7—42no—
269C2×C4×C7—42no—
270C2×C4×C7—44no—
271C2×C4×C7—88no—
272C2×C4×C7#13714yes—
273C2×C4×C7C22×D414yes—
274C2×C4×C7C22×D412yes—
275C2×C4×C7C22×D411yescharacteristic
276C2×C4×C7C22×D412yes—
277C2×C4×C7C2×#4112yes—
278C2×C4×C72−1+412yes—
279C2×C4×C7C2511yescharacteristic
280C22⋊D7—88no—
281C2×Dic7—22no—
282C2×Dic7—24no—
283C2×Dic7—42no—
284C2×Dic7—44no—
285D28—22no—
286D28—22no—
287D28—42no—
288C4×D7—48no—
289Dic14—84no—
290C7⋊C8—24no—
291C7⋊C8—22no—
292C7⋊C8C2×#4114yes—
293C22×Q8—21no—
294C22×Q8—141no—
295C22×Q8C22×D711yescharacteristic
296C22×D4—71no—
297C22×D4—142no—
298C22×D4C22⋊D711yescharacteristic
299C23×C4—22no—
300C23×C4—141no—
301C23×C4C22×D712yes—
302C2×SD16—74no—
303C2×SD16—144no—
304C2×M16—78no—
305C2×M16—148no—
306C22×C8—71no—
307C22×C8—72no—
308C22×C8—71no—
309C4⋊Q8—22no—
310C4⋊Q8—74no—
311C4⋊Q8—142no—
312C4⋊Q8C22×D714yes—
313#125—28no—
314#124—1416no—
315C22⋊Q8—24no—
316C22⋊Q8—216no—
317C22⋊Q8C22×D718yes—
318#121—78no—
319#121—148no—
320#121—144no—
321C4×Q8—22no—
322C4×Q8C22×D714yes—
323C4×D4—28no—
324C4×D4—74no—
325C4×D4—142no—
326C4×D4C22⋊D714yes—
327C4×D4C22×D714yes—
328#117—78no—
329#117—144no—
330#117—148no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—71no—
337C2×C4⋊C4—72no—
338C2×C4⋊C4—141no—
339C2×C4⋊C4C22⋊D711yescharacteristic
340C2×C4⋊C4C22×D711yescharacteristic
341C2×C4⋊C4C22×D712yes—
342C2×C4⋊C4C22×D718yes—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—142no—
345C2×C22⋊C4—142no—
346C2×C22⋊C4—141no—
347C2×C22⋊C4C22⋊D712yes—
348C2×C42—21no—
349C2×C42—142no—
350C2×C42C22×D711yescharacteristic
351#107—78no—
352#107—78no—
353#107—78no—
354#106—74no—
355#106—78no—
356C4⋊C8—74no—
357#103—74no—
358#103—78no—
359#102—74no—
360#102—78no—
361C22⋊C8—78no—
362C4×C8—74no—
363C22×C7—24no—
364C22×C7—24no—
365C22×C7—24no—
366C22×C7—48no—
367C22×C7#54712yes—
368C22×C7C2×#13712yes—
369C22×C7#57612yes—
370C22×C7C23×D411yescharacteristic
371C2×D7—42no—
372C2×D7—42no—
373C2×D7—42no—
374C2×D7—84no—
375C4×C7—24no—
376C4×C7—22no—
377C4×C7—42no—
378C4×C7—42no—
379C4×C7—44no—
380C4×C7#54712yes—
381C4×C7C2×#13714yes—
382C4×C7C22×#4111yescharacteristic
383C4×C7C2×2−1+411yescharacteristic
384Dic7—42no—
385Dic7—44no—
386C24—141no—
387C24C2×C22⋊D712yes—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—82no—
393C2×Q8—144no—
394C2×Q8—562no—
395C2×Q8C23×D712yes—
396C2×D4—24no—
397C2×D4—72no—
398C2×D4—148no—
399C2×D4—142no—
400C2×D4—142no—
401C2×D4—141no—
402C2×D4—564no—
403C2×D4C2×C22⋊D714yes—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—28no—
410C22×C4—84no—
411C22×C4—141no—
412C22×C4—142no—
413C22×C4—144no—
414C22×C4—284no—
415C22×C4C2×C22⋊D714yes—
416C22×C4C2×C22⋊D712yes—
417C22×C4C2×C22⋊D711yescharacteristic
418C22×C4C2×C22⋊D711yescharacteristic
419C22×C4C23×D714yes—
420C22×C4C23×D711yescharacteristic
421SD16—148no—
422M16—1416no—
423C2×C8—74no—
424C2×C8—72no—
425C2×C8—72no—
426C2×C8—74no—
427C2×C8—144no—
428C2×C8—142no—
429C4⋊C4—21no—
430C4⋊C4—28no—
431C4⋊C4—22no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—28no—
435C4⋊C4—72no—
436C4⋊C4—74no—
437C4⋊C4—141no—
438C4⋊C4—142no—
439C4⋊C4—144no—
440C4⋊C4C2×C22⋊D714yes—
441C4⋊C4C23×D712yes—
442C4⋊C4C23×D714yes—
443C22⋊C4—28no—
444C22⋊C4—148no—
445C22⋊C4—148no—
446C22⋊C4—144no—
447C22⋊C4C2×C22⋊D718yes—
448C42—24no—
449C42—148no—
450C42C2×C22⋊D712yes—
451C42C23×D712yes—
452C2×C7—44no—
453C2×C7#335714yescomplemented
454C2×C7C2×#54711yescharacteristic
455C2×C7C22×#13711yescharacteristic
456C2×C7C2×#57611yescharacteristic
457D7—82no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—142no—
462C23—282no—
463C23—282no—
464C23—282no—
465C23C22×C22⋊D714yes—
466C23C22×C22⋊D711yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—42no—
470Q8—84no—
471Q8—564no—
472D4—28no—
473D4—142no—
474D4—142no—
475D4—282no—
476D4—568no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—28no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—88no—
489C2×C4—142no—
490C2×C4—144no—
491C2×C4—282no—
492C2×C4—284no—
493C2×C4—288no—
494C2×C4#650514yes—
495C2×C4D7×#4112yes—
496C2×C4#655412yes—
497C2×C4C22×C22⋊D714yes—
498C2×C4C22×C22⋊D712yes—
499C2×C4C22×C22⋊D712yes—
500C2×C4C22×C22⋊D711yescharacteristic
501C2×C4C24×D711yescharacteristic
502C8—74no—
503C8—144no—
504C8—142no—
505C7C2×#335711yescharacteristic, complemented, Sylow
506C22—24no—
507C22—24no—
508C22—24no—
509C22—48no—
510C22—282no—
511C22—282no—
512C22—282no—
513C22—564no—
514C22C2×#650512yes—
515C22#9051512yes—
516C22#9052612yes—
517C22C23×C22⋊D711yescharacteristic
518C4—24no—
519C4—22no—
520C4—42no—
521C4—42no—
522C4—44no—
523C4—282no—
524C4—284no—
525C4C2×#650514yes—
526C4#9051512yes—
527C4C2×D7×#4111yescharacteristic
528C4C2×#655411yescharacteristic
529C2—44no—
530C2—562no—
531C2#1174107214yesdirect product factor
532C2C22×#650511yescharacteristic
533C2C2×#9051511yescharacteristic
534C2C2×#9052611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC2×#90254C2
hypercenterC2×#554D7
hypocenterC7C2×#3357
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C7×#554C2semidirect
3. #11741072C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89850C2semidirect
6. C2×#89821C2semidirect
7. C2×#89817C2semidirect
8. C2×#89793C2semidirect
9. C2×C4×#1143C2semidirect
10. C2×#89784C2semidirect
11. C2×#89739C2semidirect
12. C2×#89736C2semidirect
14. C7×#554C22semidirect
37. #89856C22semidirect
38. #89850C22semidirect
39. #89821C22semidirect
40. #89817C22semidirect
41. C4×#1143C22semidirect
42. #89793C22semidirect
43. #89784C22semidirect
44. #89739C22semidirect
47. #89736C22semidirect
127. C2×#554D7semidirect
209. #554C2×D7semidirect
453. C2×C7#3357semidirect
505. C7C2×#3357semidirect
531. C2#11741072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#902542
#117410722
C2×#898562
C2×#898502
C2×#898212
C2×#898172
C2×#897932
C2×C4×#11432
C2×#897842
C2×#897392
C2×#897362
C2×#33577